IAEA-TECDOC-1060
XA9949056
LMFR coreheatand exchanger thermohydraulic design: Former USSR and present Russian approaches
INTERNATIONAL ATOMIC ENERGY AGENCY
January 1999 The originating Section of this publication in the IAEA was: Nuclear Power Technology Development Section International Atomic Energy Agency Wagramer Strasse5 0 10 P.Ox Bo . A-1400 Vienna, Austria
LMFR CORE AND HEAT EXCHANGER THERMOHYDRAULIC DESIGN: FORMER USS PRESEND RAN T RUSSIAN APPROACHES IAEA, VIENNA, 1998 IAEA-TECDOC-1060 ISSN 1011-4289 IAEA© , 1998 Printe IAEe th AustriAn y i d b a January 1999 IAEe Th A doe t normallsno y maintain stock f reportso thin si s series. However, copies of these reports on microfiche or in electronic form can be obtained from
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l fasAl t reactor fuel assemblie head san t exchangers hav bundld ero e geometry. Fluid flohead wan t bundld transfero compled a ean n i r x phenomen basid aan c understandinf go these phenomen essentias ai developinr fo l g designs that optimize performance during normal operating conditions and that maintain structural integrity during abnormal operation.
Extensive experimenta analyticad an l l studie liquin so d metal fluid flow distributiod nan heat transfer in fuel pin and heat exchanger rod-bundles have been performed in several countries with fast reactor programmes (notably in France, Germany, India, Japan, the Russian Federation Unitee th , d Kingdo Unitee th d dman State f Americao s ) ove pase th r t decades e validite computeth Th . f o y r code d desigan s n approache s provewa s y b n compariso codf no e results with measured velocity, pressur temperaturd ean e distributionn si rod-bundles cooled/heate liquiy db d metal, usually sodium.
Considerable experimental and theoretical studies on various aspects of LMFR thermohydraulics have been done at the Institute of Physics and Power Engineering (IPPE), Obninsk, Russian Federation e IAEA'Th . s International Working Grou Fasn po t Reactors (IWGFR) recommended that IPPE should generalize its thermohydraulic studies as well as other countries' results that have been published in journals and in proceedings of international meetings.
This report was prepared in response to the recommendation from IWGFR and includes the methodology and philosophy of the analytical and experimental investigations in their applicatio cor e head th ean t o n t exchange r thermohydraulic desig LMFRsf no .
The IAEA officer responsible for this work was A.A. Rinejski of the Division of Nuclear Power. EDITORIAL NOTE
In preparing this publication for press, staff of the IAEA have made up the pages from the original manuscnpt(s) The views expressed do not necessarily reflect those of the IAEA, the governments nominatingthe of Member nominatingStatesthe or organizations. Throughout the text names of Member States are retained as they were when the text was compiled ofThe use particular designations countriesof territoriesor does imply judgementnot any by the publisher, the IAEA, as to the legal status of such countries or territories, of their authorities and institutions delimitation ofthe or of their boundaries The mention namesof specificof companies productsor (whetherindicatednot or as registered) does imply intentionnot any infringeto proprietary rights, should construednor be it as an endorsement or recommendation on the part of the IAEA CONTENTS
INTRODUCTION...... 1
CHAPTER 1. THERMAL HYDRAULIC ANALYSIS OF FAST REACTOR COR HEAD EAN T EXCHANGERS. EXPERIMENT PREDICTIONS...... D SAN 3 1.1. Some features of fast reactor thermal hydraulics...... 3 1.2. Classificatio bried nan f overview...... ,...... 9 1.3. Technical modeling of fast reactor subassemblies and heat exchangers ...... 20 1.4. Electromagnetic technique as a basis of data securing in thermal hydraulic analysis of fast reactor core and heat exchangers...... 28 1.5. Liquid metal facility 6B...... 38 Conclusions...... 53 References ...... 54
CHAPTER 2. THERMAL HYDRAULIC SUBCHANNEL ANALYSIS ...... 57 2.1. Developmen subchannef o t l approach...... 57 2.2. Macro-transport equations...... 61 2.3. Various factors in thermal hydraulic analysis of reactor core...... 62 Conclusions...... 75 References...... 76
CHAPTER 3. NOMINAL SUB ASSEMBLY THERMAL HYDRAULICS...... 81 3.1. Friction factors...... 81 3.2. Classificatio inter-channef no l exchange processed san experimental technique ...... 89 3.3. Inter-channel exchang internae th edgn ed i lan e areaf so wire wrapped pin bundle ...... 94 3.4. Molecula turbulencd ran e exchang smootn ei h bundle exchange due to heat conduction of the pins...... 112 3.5 Two-phase inter-channel exchange ...... 120 3.6. Temperature behaviour and heat transfer in nominal geometry...... 122 3.7. Entrance thermal section. Variable power production ...... 138 3.8. An influence of some factors...... 152 Conclusions...... 7 .15 References ...... 160
CHAPTER 4. EXPERIMENTAL AND NUMERICAL THERMAL HYDRAULICS OF FAST REACTOR CORE...... 167 4.1. Velocity fields ...... 167 4.2. Temperature behaviour in fast reactor fuel subassembly (nominal and deformed geometry)...... 185 4.3. Fue temperaturn lpi e distributio somn i e variant deformatiof so n ...... 203 4.4. Pin bending...... 209 4.5. Deformation of bundle and subassembly wrapper tube...... 215 4.6 Subassembly thermal interaction...... 216 Conclusions...... 230 References ...... 231
CHAPTERS. INTERMEDIATE HEAT EXCHANGER THERMAL HYDRAULICS...... 235 5.1. Feature LMFBRIHf so X thermal hydraulics...... 235 5.2. Hydraulic results...... 235 5.3. Thermal results...... 240 Conclusions...... 277
CHAPTER 6. THERMAL HYDRAULIC ANALYSIS OF TRANSIEN ACCIDEND TAN T PROCESSES. LIQUID METAL BOILIN LMFBGN I R CORE...... 281 6.1. Transient thermal hydraulics modelling...... 281 6.2. Experimental study of critical heat flux in liquid metal natural circulation contour...... 283 Conclusions...... 297 References ...... 297
OVERALL CONCLUSIONS...... 299
CONTRIBUTORS TO DRAFTING AND REVIEW...... 305 INTRODUCTION
The information given in this report is concerned with liquid metal fast breeder reactors, some of whicoperation i e har n (France, Japan, Russian Federation), others under construction. Comprehensive thermal hydraulic research applied to such reactors has been carried out in the SSC IPPE.
It should be noted that liquid metal reactors can now be considered as the most safe and promising type of reactor in nuclear power engineering. However, in order for fast reactors to be widely used in industry it is necessary to improve their economic indicators, as well as to make their performance more reliable. This requires analysi probleme th reactoe f so th f so r performance under deviation subassemble th f so y geometry from nominal (deformation)s a , wel undes la transiene rth t condition resolvede b o st wels , a variou s la s accident situations.
e problemTh s note de resolveb abov n y ca boteb d h experiment d predictionsan s e Th . information accumulated mus processede b t , firstl steadr yfo y state operating conditions with the ensuing extension to the transient behavior.
The authors believe that the material given below will be useful for the further advanced thermal hydraulic analysis of fast reactors in the situations closely approximating the in-pile conditions.
The codes developed up to now are rated in order of governing equations, calculation procedures, syste closinf mo g relation theid san r accuracy. However model al , me codeth e sus momentum and energy transport factors, heat transfer coefficients, pressure drop and others to close relation between velocity and temperature fields. These factors should be evaluated relationshipf o e witus e hth s presented here theo s , y have been derive processinn do date gth a gaine speciae th n di l experiments.
Detailed analysis and rating of the thermal hydraulic codes which have been developed in the IPPE s appliea , reactoo dt r subassembl head yan t exchanger givee ar , thin ni s publication. Also, results of experimental investigations and numerical modelling of velocity and temperature distributio e illustratedar n . Experienc f faso e t reactor performance (Russian Federation, France, Kazakhstan) suggests that subassemblie subjece sar greao t t t deformation in campaigns associated with swellin creepingd gan authore Th . s have obtained considerable experimental data on temperature behaviour in deformed bundles, that have allowed this data to be generalized and used in the complex code TEMP-MIF. Considerable attention has been e problemgive th e equalizatio o th t n f o s f temperaturo n e behaviou e fasth t n reactoi r r subassembly whicr fo , h purpos influencn ea variouf eo s paramete analyseds ri .
On the whole, the authors demonstrate advanced approaches, new experimental techniques and numerical procedures, hydrauli thermad can l constants require thermae th r dfo l physical validatio liquif no d metal reactor cor head ean t exchanger.
NEXT PAGE(S) Uft BLANK Chapter 1
THERMAL HYDRAULIC ANALYSI FASF SO T REACTOR COR HEAD EAN T EXCHANGERS. EXPERIMENTS AND PREDICTIONS
1.1. SOME FEATURE FASF SO T REACTOR THERMAL HYDRAULICS
The need to improve fast reactor performance (in particular of reactor core and intermediate heat exchangers vitaa s )i l problem, resolutio whicf no h depends largele th n yo quality thermal physic validation. Feature f faso s t reactor performance (high neutron flux, great pressure of gas fission products inside of fuel pins, high levels of fuel and pin clad temperatures), uncertaintie somn i s e parameters have resulte a specia n di l attentioe b o nt give in-deptno t h analysi thermaf so l physic processe investigationd san phenomenw ne a f so a that are adequate for the modern knowledge. Inter-channel hydrodynamic and thermal exchange, variable power production, entrance thermal region, deformatio bundlen pi f o n , non-standard geometry, thermal loads far from symmetric and availability of spacer structures, regular and stochastic temperature non-uniformity and ensuing hot spots is far not whola probleme eth lisf o t s posed recentl practicy yb bein d greaa ean f go t importancn ei thermal physic validation of fast reactor core. Conceivable boiling of sodium within reactor cor inherend ean t emergency problems have assume dgreaa t significance.
The necessit knowledgf yo locae th f l eo hydrodynami thermad can l parametere th n si combined axial-transverse flows in the IHXs with the object of their efficiency validation is not lesser currently central. To take into account the factors mentioned above makes its a very complex problem in the thermal hydraulic analysis. Among the requirements to thermal hydraulic analysis there are a large volume of information, a reliability of the results including, above all, the local hydrodynamic and thermal characteristics: on the one hand - high temperature t allowablno e sar e (the powe efficiencd ran facilite th f limited)e yo yar n o , the other han d- loca l temperature shoulovee b t r dacceptablno e limits, tharesuln ca t n i t failure.
The necessary conditions for ensuing reactor safety are restrictions on maximum temperatures of pin wall and nuclear fuel. Respectively, the heavy demands are imposed on e thermath l physic validatio f fasno t reactors o satisfT . e limitationth y e th t onl r no s yfo average parameters thosr fo t e representinbu , g deviations fro nominae mth l values, invitee sth study of their influence on the temperature behaviour in subassembly, their contributions in reactor core thermal physics and normal fast reactor subassembly performance.
Reliable operation of modem fast breeder reactors has called for the combined study of thermal hydraulics (experiments & predictions), development of a new analytical methods on the local characteristics in subassemblies and heat exchangers, that has allowed the data (constants derivee b o )nominat r dfo accidend an l t operating conditions effecte th , variouf o s s factors on temperature behaviour to be analysed. mechanisme Th inter-channer sfo l exchang combinee th d ean d axial-transverse flown i reactor units, hydrodynamics and heat transfer features in the system of parallel channels, as well as in non-standard channels (near to the wrapper tube), temperature fields in regular and deformed bundles under unifor variabld man e power production (including heterogeneous variant) steady-statn ,i transiend ean t flow have forme basie dcalculationr th sfo . e pointTh s mentioned above concer nwida e e problemrangth f o edefind an s n i e essence the further evolution of reactor thermal physics, in general. For example, analysis of pin bundle under deformation includin pin'e gth s displacements, local temperature rises, blockages, pin bending is of a great importance in reactor core design.
Such characteristics as the pin clad temperature and temperature non-uniformity around the pins arising under the local distortion of the pin arrangement (shifting and bending pins)o tw r , o elevate e ofon d power productio separate th n ni e pins, rise clan si d temperature behin wire dth behinr eo blockage d th f differeno e ear t value. Sensible overheatinge th d an , temperature non-uniformity, respectively mored ,tak an n (-20 t )ca e evenplacA e %f th o n tei fuee ofth l pin displacee sar one-halda inter-pie fth n clearanc evene th f moren o td i ed an an , the blockage of subassembly cross section.
The hot spots can be of local character and involve a small number of pins (2, 3, 7), and of global character covering the sizeable part of the pin bundle. Pin temperature can exceed the average level due to specific construction of subassembly; with the exceed flow edge ratth en e i channel s leadin coolane th o gt t becomes subcoole edge th en d i channel d san the wall temperature elevated in the internal area of subassembly. At the linear power production acros subassemble sth y positione periphere th t da reactof yo r core (q 12)= max q ,/ additionae th l elevatio clae th d f ntemperaturo 10-^15~ observey s e i ib f A aree %f o th f ao n d i maximum power production.
In the compact pin bundle when pins are in contact with each other the clad temperature is much more than in statistic arrangement. The rise in coolant temperature behind the blockage in the internal area of subassembly can be of 50% of Af, and in the edge area -100%. Als significanoa t change observee b wrappee n th sca n di r tube temperatureo T . reduce clad temperature irregularitie non-uniformitied san coolann si t temperature calleo s , d counter-directed wir usede erandob e pinwrape n Th .th sca n mso arrangemenn i f fuen o t pi l subassembly setproblee sth choice th f mjustifief o eo d geometrical modelr statistifo s A .c model t estimatei , subassemble sth y geometr improved yt an spo ho te factorsth ideaw ssho woul predictede db . Temperature t spo deviatioho tdefineways e o o factot b e tw n n.y du ca rd b First (analytical) calculates the known temperature function depending on many random parameters (factors), provided their distributions are given. Second is the method of statistical iterations (Monte-Carlo approach). Analytical method is faster and more mobile than Monte- Carlo procedure t restricti t bu e functiona, th s l dependenc f temperaturo e a variou n o e s parameters. Monte-Carlo procedure woul appropriate db user efo , when temperature effecn o t governing parameters is multidimensional and non-linear and provided a random deviations are grea follod an tarbitrare wth y distribution laws t allowI . more sth e approximate analytical method to be corrected. Also, it is advantageous to use the superposition of these methods, when temperature deviations causelocae th ly db factor definee ar sf Monte o e d us wit -e hth Carlo procedure generae th d ,an l deviation predictee sar analyticay db l method.
As a fast reactor core is a large and combined system of subassemblies representing bundle of fuel pins, which, in its turn, being of a complex structure, the thermal hydraulic analysis can be performed in some steps. In the first step - at the design stage - the coolant flow rates through subassemblies and average coolant temperatures are defined. Then, thermal hydraulic characteristics of individual subassembly and fuel pin are predicted. This step, in its turn, assumes determining the subassembly geometry, the coolant flow distribution throughou e subassemblieth t s taking into account inter-channel momentum exchangee th , coolant temperature in the channels taking into account inter-channel thermal exchange, the wall-liquid temperature difference and maximal temperature irregularities around the pin, the contribution of various factors into temperature behaviour, and maximum clad temperatures. Inasmuc s coolanha t overheatin fasn gi t reactor subassembl e quityar e large (~200 °C)n a , accuracy in definition of the maximum pin clad temperature is appreciably specified by the correct calculation of coolant temperature distribution over the subassembly channels.
Velocit d temperaturan y e field n i subassembls y representin a gsyste f o m interconnected channels, between which the mass, momentum and heat exchanges take place, are formed unlikely thos insulaten ei d channels. Liter-channel mass exchange being more strong tha insulaten i d channels influencn ,a casuaf eo l deformations (bending, displacements and others) on flow distribution, impact of helical wire wrap on mixing and degree of turbulence, non-uniform flow distribution thoug channele hth differena f so t form (internal, edge ones thesl al )- e factors define hydrodynamic interconnectee th n si df channelso e us e Th . the methods and relationships for insulated channels in hydrodynamic and thermal predictions cause greae sth t error appearo st , that resultspeciae th n si l approaches having regare th o dt feature interconnectef so d channel developede b o st .
Interchannel heat and mass transfer is a very important factor in generation of temperatur flod ewan behaviou fasn ri t reactor core. Cause helicay db l wire wrap t reducei , s temperatur doinservo n s ca n enhanc t spoti o et g t i d ho sn an ei e subassembly power usiny .B g none of the modem approach of thermophysic prediction of reactor, you can not do away with the inclusion of this factor, an importance of which is reflected when the processes are considered, as inside of the pin bundle and in reactor core, as in whole (inter-subassembly interaction). Accoun f heamasd o t an t s transfe framewore th n i calleo rs f o kd subchannel approaches can be considered as a significant contribution into development of thermohydraulic prediction of fast reactor core.
Accordin e approacth o t g h mentione n bundlpu s e dividei eth d d int a paralleo l channels, for which the system of mass, momentum and energy conservation equations is solved wit resultine hth g derivatio f velocitno temperaturd yan e distributions. Systemf o s governing equations written by other authors are distinguished by a degree of completeness. Respectively codee th , s realising solutio f balancno e equation ratee classea e sar n dth i f so problem under consideration and hi the validity of hydrodynamic description. Analysis performed have allowe correce dth t statemen f subchanneo t l approac developee b o ht d dan resulted in the development of the codes TEMP, TEMP-M and MIF.
Much attention in thermohydraulic analysis has to be given to the edge area of subassembly bein gserioua s hazar termn di temperaturf so e irregularity edge Th .e pine sar surrounded by the channels of a different geometry, that is why conditions of their performanc fror fa m e symmetricear differeno t e Du . t amount coolanf so t passing througe hth channels surrounding the edge phis, coolant temperature varies significantly around the edge pins.
Liquid metals have a larger heat conductivity, smaller volumetric heat capacity. Great temperature differences and great heat transfer coefficients result in that the temperature of pin surface cooled by liquid metal is defined in general by the local temperature of coolant, but not local heat transfer coefficients. This is largely concerned with the edge pins, where the great differences in coolant temperature take place. Tolerance e size th f fasr o s fo ts reactor subassembly that involves smala pin f o s l diameter arranged with a relative small pitch are comparable with the size of the channel surrounding pins, with a consequent sensible effect of bending and shifting of the pins appearing even in the wire wrapped bundles. Of prime importance is such a problems for the edge pins wrapped by the half as many wire as those at the internal pins. Due to this the edge pins have a chance of shifting along the subassembly cover.
Heat transfe edge th en i rchanne rulea transiena s f a o , , is l t natur dependd e ean th n so equivalent thermal conductivity, relative pitch of the bundle, displacers' diameter, gap between pins and wrapper tube and others. Features of liquid metal heat transfer in the wrapped pin bundle are determined by the facts that, on the one hand, wire wrap is favourable for mixing, that improve heat transfer othee th n r o ,hand ,cause n wirfi locar e eo walsn th lpi l temperatur enhanceo et .
Thus, features of hydrodynamics and heat transfer in fast reactor subassembly are connected, in general, with the near wall area and the use of sodium as a coolant. New problems causefeaturee th y db s mentione comparison di n wit infinitn ha bundln e b epi n eca summarise followss da : • greater temperature nonuniformities around the edge pins as compared with internal pins; • greater flow non-uniformities around the edge pins; • noticeable effect of inter-channel mixing on the temperature and velocity behaviour; • influenc bundln pi f eo e deformatio temperature th n no velocitd ean y behaviour; • transient heat removal in the edge channels.
Thermal hydraulics of fast reactor intermediate heat exchangers has been investigated by as experimental and numerical modeling of velocity and temperature fields with the use of the modem measurement technique computed san r codes, suc : electromagnetihas c technique to measure local liquid metal velocity in transverse and axial directions, local measurements of thermal characteristics in tube bundle, advanced numerical procedures based on the quasi homogeneou subchanned san l approaches datw aNe . gaineyearlase w variour th fe t sfo n d i s geometry of tube bundle (triangular, square, combined) at low velocities and under conditions of mixed convection testifies that a possibility of reversal circulation occurs. Criteria were derived that describe the processes under consideration, time and space limits of transients were defined, recommendations for designing heat exchanger equipment were proposed.
Correlation made between the local data and the results of common integral experiment allowes sha drevealina g distinctioreasone orden th a f d o r san f heano t transfer coefficients, determining their variation ove heae rth t exchanger zone advisind san g meanr sfo the heat transfer surface optimisation. Variation in the height of the inlet and outlet windows of heat exchange significancf o s ri equalisinn ei g coolant flows acros bundle sth e sectiod nan possible decreasing heat transfer surface, that says the inlet and outlet structures are of a great importance.
Material discussed belo resula ws i f long-ter o t m investigations into reactor cord ean intermediate heat exchanger thermal hydraulics and is a foundation for the modern approaches to thermal hydraulic analysis of fast breeder reactor.
Brief information on the subjects under discussion. Fig. 1.1 presents the view of the integral fast breeder reactor indicat.7 Positiond an e4 reacto, s3 r core breede head an rt exchanger, respectively, bein objece gth presenf o t t thermal hydraulic analysis. Fig 1 1 Integral fast reactor block 1 -pumps, 2- high pressure header, 3core,- blanket- 4 zone, spent- 5 assemblies storage, 6- in-vessel neu- tron shield, heat7- exchanger, dumps,- 8 reactor9- vessel Fig. 1.2. BN-600core:
O subassembly View reactof so r corbreeded ean wels a radia s r, a l l distributio powef no r production are shown in Fig. 1.2 and 1.3, respectively. Subassembly geometry is presented in Fig. 1.4 and 1.5. Specific features of the structures under discussion are the smaller pin diameter (d = 6.9 largee arrangemenn th mm)t pi r e bu pitc, th f ho t (s/d 1.17= reacto)n i r cor compares ea d with those in breeder (d = 14.1 mm, s/d = 1.04) with the considerably greater amounts of fuel pins in the core subassembly. sho7 1. w d schematican 6 Fig 1. axiae . th f l so vie crosd wan s section intermediatf so e heat exchanger providing the foundations of experimental and analytical modeling of heat exchanger thermal hydraulics. r Fig. 1.3. Heat production with reactor core radius: - without - —- - levelling, ———— - —two-zone levelling. 1.2. CLASSIFICATIO BRIED NAN F OVERVIEW Let us take a look at the thermal hydraulic approaches applied to fuel subassemblies. This will allo probleme wth subchannef so l analysi potentialities it d san inspectee b o st r dfo more th e general point viewf so placs wels it a , s ea l amon thermae gth l hydraulic approaches having regard to an interchannel exchange to be defined. Thermal hydraulic analysis of reactor subassembly implies that mass, momentum and energy conservation equations are solved in association with initial and boundary conditions. Mathematical modeling concerning hydrodynamic head an st transfe fasn i r t breeder reactor have been analyzed in [1-4]. Fuel pins in combination with the subassembly wrapper and displacers form the channel of complex shape with essentially variable thermal and hydraulic characteristics across of the channel, resulting in 3-D coolant flow. That is why, researcher fails to find thermal hydraulic characteristics with a required accuracy by the methods based on an idea of "equivalent channel" determining average parameters of subassembly. Three lines in thermal hydraulic analysis of pin bundle (Fig. 1.8) can be currently recognised, with eac thef ho m advantagehavinn ow s g it disadvantages d san : • prediction of local velocities and temperatures; • predictio averagf no e characteristic framewore th n si poroua f ko s body model; • predictio f lumpeno d parameters (coolant velocit temperaturd yan e averaged acrose th s subassembly), that is subchannel analysis. A-A 3500 + 1.4.Fig Fast reactor core fuel subassembly. 10 A -A JA Dfl I Fig.5. Blanket 1. assembly. 11 Unit - A Jslal Fig. 1.6. BN-600 intermediate heat exchanger: 1 -pipe, 2 - secondary coolant outlet header, biological- 3 protection, pipe- 4 panels, secondary5- coolant inlet header, 6heat- exchanger vessel. 12 Fzg. 7.7. Fast reactor heat exchanger pipe bundle. e maiTh n difficultie n applicatioi s f mathematicano l model thermao t s l hydraulic analysi complee sar x geometr largd yan e lengtbundlen pi f ho . Local methods based on the system of differential equations allow the local flow characteristics to be predicted and starting from them an integral parameters (factors of friction, heat transfer, maximum non-uniformity of temperature at the pin cladding) to be evaluated. Moreover e complexitth , bundle th f o ye geometry (especiall e eventh f o n tyi deformation), a tedious procedure of solution of the heat and mass transfer equations give no wa f takino y g into accoun influencn a t f variouo e s factor n temperaturo s e behavioun i r subassembly problee Th . mconsideres i generan di steads a l y state coolan tbundle floth wn i e of smooth pins. The procedure, provided uses a similar mesh, requires a time of calculation being several orders greater than those in subchannel approaches. 13 Local differential equations: Governing diffusion- (concentratio component)f no , equations - momentum (velocity, pressure), energy- (enthalpy, temperature) Over time Over channels Over space Averaging (local characteristics) (subchannel model) (porous body model) Mathematical Differential equations Macro transport model (Reynolds approximation) equations Molecular and Inter-phase Inter-channel Hydraulic Constants turbulence diffusion exchange exchange resistance Transient Steady state Approximations Axial diffusion Boundary layer Stable Finite Finite Analytical Numerical differences elements methods procedures Semi-explicit scheme Fig. 1.8. Classification approachesof thermalto hydraulic analysis 14 fino T d average flow parameter e basith f averageo sn o s d momentu energd man y equations (a porous body model and subchannel analysis) extends calculation domain, allows an influence of various factors to be taken into account. But, such a methods involve an additional procedure, from which a temperature of subassembly structure to be defined. A porous body model, which implies that an averaging is carried out with the greater scale, and in some cases, the vastly greater, than the size of the channel in bundle, which uses the mesh being not coincident with the bundle channels allow us to gain solution being less detail. This method reflect effectn a s s being much more extended tha channee nth bundlen i l , whereas subchannel analysis covers phenomena with inherent scale being e equath o t l distance betwee axisesn pi e n.th Thus poroua , s body model describes macro parametersd an , subchannel approac consideree b n hca s macro-micrda o approximatio sense th n eni that i t describes macro effects in reference to the phenomena occurring in the channel, and yet describes micro effects in reference to the bundle size. In spite of a commonness for setting up a problem, similarity of equations, and respective calculation procedure, there is distinction between them associated with the evaluatio constante th f no s (transport factor others)d an s . These method followee sar e b o dt mutuall locae th f ly o method relativee us e sTh . allow constante sth definee b o st inpus a d t parameters for solving transport equations with averaged flow approximation. Single phase steady state flow methode Th . locaf so l characteristics calculation have been developed as applied to solving the momentum and energy equations in a differential form. They includes analytical methods, finite differential, finite elements, variable differential procedures. Some works are concerned with the analytical solution of the problem of stable heat transfe bundln pi n i re [5,6] drawbacke Th . complexite sar f calculationyo d san approximations required taking account the structure of velocity field and turbulence characteristics. mose Th t widely used amon locae gth l method finita e esar difference finitd an e] [7 s elements [8] limitatioA . thesf no e approache calculatee th o t thats si e ddu , are confineds ai , the need for its division into multipointed pattern, and, besides, these methods, as a rule, take into accoun n approximata t e local flow structure, turbulence characteristict no o d d an s account transverse convective exchange produced by helical wire wrap on fuel pins. Variable differences allopredico t s wu t velocit temperaturd yan arean ei s with arbitrary boundary [9]. Approximating heat transfe bundln pi n i re having regartransverse th o dt e convective flow have been base poroua n do s body model. Metho pointef do d source being under development for an appreciable length time invites definition of so called «functions of influence», which are not universal and by virtue of this the method approximates temperature behaviour under condition combinef so d heat transfer [10]. Subchannel analysis consists on solution of mass, momentum and energy conservation equations written for elementary channels, which a subassembly is divided on [11] (Fig. 1.9). It allow determino t s su thermohydraulie eth c characteristic f coolanso t everywhere ovee th r subassembly taking into consideration all mechanisms of interaction between channels, as well as taking into account heat exchange between subassemblies. There are a lot of codes in whic subchannee hth l approac realises hi applies da steado dt y stat non-stabld ean e hydraulics in subassembly. Their analysis is given in [11]. Drawback of these codes is connected with the difficulty of inclusion of inter-channel exchange in subassemblies, the approximations 15 n—i—r S/d = i,08 M M 3 1 = d At L=1170MM 10 1.0 0.8 1,2 ————-TEMR-M ——.—— COBRA-IV 0,8 —— —— -5UPERENERQY ————— -COTEC ®-experiment MAPKlev R.A? 0,6 I i i i i Fig. 1.9. Comparison coolant temperature over modelthe section: experiment- ® Markley R.A. ————— - prediction TEMP-M — - — - COBRA-IV — — -COTEC SUPERENERGY- - —- 16 required to take into account the subassembly deformation and the difficulty connected with longitudinae th l momentu masd man s exchange. Accordingly, prediction y varioub s s codes appreciably differ eve r suce fo nth h commonly used versions, suc COBRA-Is ha V [12], COTEC [13], SUPERENERGY [14d ]an TEMP-M [15] (Fig. 1.9). A complete and precise system of interchannel exchange coefficients have been written as a result of systematic experiments performed in the State Scientific Centr f Russiao e n Federation «Institut f Physico e d Powean s r Engineering)) (Obninsk realises codee wa th d n dsi )an TEMP-allowe s [16]F ha improvo t t MI I . s d dMu an e predictions as compared with the foreign codes mentioned above (Fig. 1.9). Also calculation approach of statistic thermal characteristics of fast reactor subassembly [15] was developed. Code MIF is the only code making possible predictions of local temperature in subassembly in evene th f deformatioo t f botno h fuel pinsubassembld san ycode coverth es i TEMP- t I . M around which the procedure of probability analysis of "hot spots" factors was improved. A porous body model describes the fields of elementary unit-averaged coolant velocity temperaturd an e valuebases i solutiod n do san f momentuno energd man y equations with volumetric friction and heat production [5]. It only approximately takes into account the local flow structure, peculiaritie subassemblf so y geometry (periphery, deformation effectivs i d an ) e at temperature behaviour calculation in highly disturbed flows, for example, of a partial solid flow blockade. mathematicaBasee th n do l model transporf so anisotropin i t c porous bode yth codes PROTVA and UGRA were developed [5]. In single phase flow a porous body model s realisedwa particularn i , sucn i , h code s SABRsa , UZUE-1 , COMMIX-1, COMMIa Xl which can be used to predict transients associated with the loss of coolant, enhancement of subassembly power, blockades. Dynamic approache phaso tw en si liquid metal coolant analysie Th . f transienso t coolant flows in pin bundle has become especially urgent in connection with investigating transient operating condition analysie reactof so th d variouf ran so s emergency situations sa well firse Th .t model calculatinr sfo g sodium boilin reactoe th n gi r channel were basen do consideration of a single bubble expansion [17]. It was due to sodium tendency to superheating, which was initially estimated as very high, and also due to very fast transition to slug and annular flow pattern. Further development of calculation models were carried out towards increasin numbee gth bubblef o r s generate channele th n di thin I . s case modern i , n mode sodiue th l m superheating abov saturatioe eth n temperatur rulea s o a ,n , takee is b o nt more than 20°C. It should be noted that these models are in good agreement with experimental data. Up-to date code calculatinr fo s ULOe gth UTOd Fan , P3D typS eSA accidents, 4A S SA - EAC-1, FRAX. CAPR-1, CARMEN mos- t often represent boilin versiof o e g f witus n o e hth well known multi-bubble models as SAS-2A (USA) and BLOW-3 (Germany). Later the models were made more complicated due to improvement hi an account of friction, liquid film motion and its separation, and due to an added criterion of pin dryout. In the framework of such a models the initial thickness of liquid film is taken, on the base of the liquid fraction over the channel cross section, as equal to, and crisis occurs when 1/3 of its initial thickness remains firse Th .t code develope Russin di fasr afo t reactor channel dynamic calculations, taking into account sodium boiling alss o,wa base single-bubbla n do e model. maie Th n conten up-to-datf to e model conservatios si n equation massr sfo , energd yan momentum for the two-phase non-equilibrium flow, the closing relations and inherent 17 boundary conditions developmene delaA .th n yi f suco t h model r sodiufo s ms concernei d with large great non-linearit discontinuitiea d yan derivativf so liquid-steae th t ea m interface, as for sodium the ratio between liquid density to steam density is larger than for water. Of fundamental importanc als s erelationshii e oth p betwee absolute nth e pressur mediue th f eo m and pressure drop ove channele rth . A 3D two-liquid model has been obtained by using temporal or statistical averaging.. The model is expressed in terms of two sets of conservation equation governing the mass, energ momentud yan m balanc eacn ei h phases. However, sinc e averageeth de fieldon f o s phase are not independent on the other phase, the interaction term appear in the field equations as source term. For the most general dynamic problems such models were developed previously [18]. A similar system of governing equations can be used also in subchannel analysis of nuclear reactor core i thih , s case a surface ,contro th f o e l volum s determinei e e th y db presently accepted subdivisio reactof no r core into elementary channelsa s r doina Fo , . gso rule n additionaa , l equatio f momentuo n m balanc n transversi e e direction s wela ,s a l respective modeling notion substancn o s e transport betwee e channelsnth . Ignoring these effects and also analysing the process going on in simply connected domain a system assume terme th s mentione lefe b t o doutt . Interphase exchange terms are derived from the balance conditions at the interface. It require locae sth l phase parameter eacn o s hinterface th sid averagede f b eo o t e , wite hth mixture satisfyin e mutuath g l exchange conditions. Initia d boundaran l y conditions, relationship r turbulencfo s e transpor f head momentuo t an t m shoul e amplifieb d y b d governing relationships for each of interaction terms in two-fluid model. At present, technical difficulties restrict obtaining experimental information e establisheth s a , d relations under development are defined by the significant uncertainties. It should be marked that the system of equations is neither the only possible nor the totally validated locae Th . l transient equation beine sar g derive studyind dan numbea n gi f ro R&D centres. Two-liquid mode vera s i ly powerful procedur bess i d t ecapablan describinf eo e gth two-phase phenomena, where the flow areas are available with the «loosely» held phases. Flow stratificatio particularn (i n horizontan i , l channels), including those under counter- current motio phasese th f nwelo s a ,sudde s a l n mixing (one phase injects into another)o tw , phase flow under acceleration are an examples. Let us notify that phenomena mentioned is far of the whole list of events attendant on loss of coolant accidents. That is why the two-fluid model is a basis of the majority of developments in this direction. In practice, due to a high leve generalitf o l equatione th f larga yo d esan amoun closinf o t g relations simplificationa , s are needed to define numerical results, in particular. The first way to simplify equations is connected wit e reductioth h f dimensiono n s (numbe f spaco r e coordinates) e seconth , d assumes the abandonment of the two-liquid description (reduction of phase number). Two-phase non-equilibrium flows orden I . havo rt e analysed transien accidend an t t approximatioD floI wn i nlarga e amount codef so s were developed, basically concerned with steam generators design [19-21]. 18 Thos t numeroueno s works involving analysi qualita f efficienco sd yan f codeo y s developed are of prime interest for practice. Reference [22] can be presented as an example, althoug traditionale s basei th t hn i d o , simple «homogeneous» slip model t containinbu , g detailed analysi numericaf so l efficienc modelse th f algorithe yo Th . m TRANS [23] usesa "hybrid" approach introduce combininy db gfinita e difference implicit process (for masd san momentum balances methoe th d characteristicf d)o an s (for energy balance). The use of the formal averaging of conservation equations is a reasonable expedient to descriptionD e I transitio th e th o t n , this e resultappearancth n i s f averageo e d factors (C=0,l,...) referre distributios a o dt n parameters. Representatio equationD I f no s containing distribution parameters whic s appropriat i equae 1 har o assumptioe t l th o plane t th en no profiles of phase parameters to be accepted. Forms and number of distribution parameters depends on the kind of two-fluid model. Analytical relationships for averaged factors were gained in [24]. Subchannel two-phase codes greaA . t variet subchannef yo l code conditiones si , dby on the one hand requirements on researches for the specific reactor cores, and on the other hand by an attempts to develop specific codes capable of processing as various structures, and different performances. Accepted description of two-phase flows can be classified by types of modele th , namely: homogeneous separatf o , e flo drifd wan t flow. A very important feature of two-phase models is the description of the following exchange mechanisms between the adjacent channels: 1. Microtransport referred to as turbulent mixing, which arises from the random turbulence in the inter-channel gaps. Energy transport direction in this event is set so that the enthalpy gradient between channels reduces. Analysis of the data available is presented in [11], for example. 2. Macrotransport referred to as transverse (or convective) flow is governed by the difference in axial pressure gradient e channelth n i s s under consideration, which arise froe mth change in the channels geometry, dissimilar heat fluxes and other irregularities. Physical prerequisites accepted in deriving mathematical models, empirical relationships as well as native and abroad codes are discussed in [11]. 3. Drif r diffusio(o t f steao ) nm phase whic s takehi proportionas na gradieno t l f maso t s velocit adjacenn yi mechanisf o t e channelsus e th m y indicate.B becoms ha t di e possiblo et explain the observed during experiments tendency to the steam runs into the high-velocity channel subassemblyf so . Two-phase codes taking into accoun axian a t l diffusion. Recently numbea , f o r code bees sha n develope basie th solutio n so n macrotranspor do D 3 f no t equation termn si f so an axial diffusion (momentum and energy) partially in the framework subchannel analysis and, basicall frame poroua th f n yeo i s body model [25-27] maie Th .n codegroue s th f pswa o developed to analyse two-phase thermal hydraulics, but some of them have a single-phase versions, including those applie reactoo dt r fuel subassemblies coole liquiy db d metal. Two- phase flo simulatedws i rulea homogeneous y a ,,b s model solvo T . e liquid dynamic equations the methods ICE [28], SEMPL [29] and their modifications are used, basically. The codes applied to fast breeder reactors have been developed, for the most part, to analyse loss of flow accidents, blockades of subassembly cross section, subassembly warming up. Three-liquid models (heat transfer crisis) o analysT . e heat transfer crisin i s disperse-annular flow the three-liquid models are currently used [26], in which three 19 interacting phases are under consideration, namely: liquid film, vapour core and disperse (drop) flow. In this case, as a rule, the following assumptions are allowed: the phase temperatures is equal to saturation temperature, velocities of vapour and drops are equal. A considerable gain in physics and mathematics of three-liquid models turns into a serious problems associated wit richa h variet comparison y(i n with two-liquid modelsf o ) closing relation difficultied san thein si r numerical realisation. 1.3. TECHNICAL MODELIN FASF GO T REACTOR SUB ASSEMBLIE HEAD SAN T EXCHANGERS The need to have the reliable data on fast reactor core and heat exchangers thermal hydraulics has required that the principles of thermal modeling to be adhered to. basie technicar Th sfo l simulatio f fasno t reactor subassembl head yan t exchanges i r the developed and introduced in practice methods applied to design the fuel pin simulators anmodele dth f subassemblso head yan t exchanger develoo t , heatee plargeth a f o r r power with the uniform or variable power production, to choose amount of pins and tubes, to measure temperature and so on [30]. The principles, among theoretical grounds of thermal modeling of fuel pins developed previously [31,5], are usefully employed now. They are presented below. Fuel pin simulators. Let us consider a general construction of cylindrical fuel pin being compose cladding» «n f o d s wit e contacth h t thermal resistance between d fuean l claddin betweer g(o nhavs u cladding t e le changed 0-a)1 an Figs- 1. , relativd.a e e pitcth f ho pin arrangement thin I . s case, criterion equatio dimensionlesr nfo s d temperaturean n pi e th n si coolant can be written as: (1.1) T f =f7,z,V,x,$l£2,...t>n,h0,bl,...hH,<5l,v2,... Here T, =t,'kf/(qRn+l), Tf = tfKj-/(qRn+l) - dimensionless pin and coolant temperatures, respectively - dimensionlesp r/Rc = , £ z ;n+l , s coordinate radialn si , axiad an l azimuthal directions / 2Rs = n+l pitch-to-diametex - ; distance rth ratis i 5 oe( betwee pine nth s axises), n - amount of claddings on the pin, £, = R, /Rn+i (i-1 *n) - dimensionless thickness of the cladding; A, = A,,/Xy (i=0-m) - dimensionless thermal conductivity of fuel (Ao) and claddings (Aj4-A =<|>,X, ncr ); )_l//?n_ , 1(i=I-Hj) - dimensionles s contact resistance between d claddinfuean l g (a d betwee(^an n claddings (d2.CJ3---CJ,J $ -therma. l resistance, 2 q = qv /fj /2 /?n+1 - mean heat flux at the pin surface (£= 1 ); Re = wdh /v - Reynolds number, Pe = wdi,/a - Peclet number, w - mean coolant velocity, dh - hydraulic diameter of the channel. The otherwise is specified in the Fig. l.lO,a. Equations (1.1 and 1.2) follow from the analysis of the heat conduction equations in a pin and the thermal transport in liquid written in dimensionless form. They assume that heat transfer is stable, coolant and pin have the invariant properties, volumetric heat production in 20 e) Fig. 1.10. Cross section of fuel pin (a, c, d, e) and pin simulator (b). pin is isotropic, the pin is of symmetric structure in its properties and geometry, the second temperatures derivation with respect to axes z is negligible, turbulence characteristics of coolant flo define e channewe ar th y db l geometry, propertie cooland san t velocity only. In modeling fuel pin parametere sth , -sA - , reproducede Aeasx e sb n ar ,Re,o y t e P . Difficulties aris esimulaton whepi e nth mads ri e with volumetric power production (modeling A0) and contact thermal resistance ( The essence of the thermal modeling of fuel pins [31,5] consists in the integration of the parameters responsibl azimuthar efo l thermal conductivit pine th ,f ynamelo y AO, Ai-r-An, ^i-r-^n ,singla cri-KJ o t e nparamete f equivaleno r t thermal conductivite th n i d yan (e^J m 5 fulfillment of equality of parameters E, for the natural structure and for the model. This *O parameter is calculated on the basis of the main temperature harmonics in Fourier - series expansion. The possibility of such an integration was approved by the analytical solution of equatioe th fuef hean o pi lt conduction. N.I solve.o firse Buleeth wh t s d vthiwa s problei mh application with cylindrical pin containing the fuel and one cladding. The general solution of the problem on cylindrical pin embedded in ««» claddings and having the contact interlayers was performe A. .P Ushakovy db , thaallowes tha relationshiderivede e db th o t t .s f po 21 3n ?i simulato r JM 0 i: t=400(U0=Z9wt/ c i_____i_i_i_i_i_ 0123456 K Fig. 1.11. Fast reactor assembly model. 0 200 400 600 Fig. 1.12. Pin simulator. The use of 8t allows us to obtain criterion equations: (1.3) (1.4) Having regar o thest d e equations e technicath , l concept f thermao s l modeling presented below were developed. Thsimulaton epi r (Fig. 1.11, 1.12 groovea s )i d pipe, insid whicf eo helicae hth l wire heater manufactured from a high-temperature material (chromel) or nichrom strip (wire). 23 Electric heater is insulated from the wall by the casting wrapper with a subsequent annealing. Finishin wrappee gth reamey rb r ensure intee sth r diamete helie pipe th th x o e t f sizro e witha high accuracy. The heater helix is filled with the silicon organics, and a free volume of the pipe with aluminium dioxide. The heater is designed so to provide a rather great heat flux at w/m5 surfacn 10 pi t temperatur8 2e a ) eth (~ 850°Ce~ produco T . e non-uniformn pi ove e rth length power production the helixes of formed strip are used. Fig. 1.12 shows the heater with resulting cosine power production inheren fasr fo tt reactor core. heatere Th s discussed abov simple ear manufactureo et , reliabln i maintai o et w lo d nan cost. They ensur unifore eth m power production aroun periphere witn dth pi h higa a f hyo accuracy, being primarily responsible for that we can gain reliable data using approximate thermal modelin f fuego l pins. Allowin variour gfo s (warranted) shap f length-variatioeo n ni the power production and giving great heat fluxes at the pin surface at the reasonable great pipe diameter (12^-25mm), the heaters represent a very feasible structures. e majoTh r practica evaluato t lw issuaccuracn ho a e s i e f approximatyo e thermal modeling of fuel pin. Examples of well simulated fuel pins are found in fast reactors (BN-350, BOR-60, BN-600, BM-800) being of a small thermal conductivity of fuel (X0~l.8-^2.9 W/m K). At the inner surface of the pin the condition q=const should be met. Dependence of 2 parameter Sk on thermal resistance or on number of harmonics for such a pins and their simulators are similar in kind. Values of Sk are little different (not more by 5%) from each other (Fig. 1.11). To calculate £k for fast reactor pins the following relations can be used: + x. ^•(l-*,)-* .(!-. ' » " I -X__V _ , *i -X, (1.5) \ / n ji Jtr - i X, +Xf a + ^——2. .(i + x)_ ' * ^ / !V - _ _ v -x. •0- where $0=R0/R2; a = The remainder are explained in Fig. 1.1 0-c. Number of the main harmonics in Fourier serie acceptes si equae b o dt l k=k regulae th 0r =6fo r par bundlf o t k=kd edge ean th 0er =lfo pins. The contace valuth f eo t thermal resistance originated betwee stainlese nth s steed an l dioxid uraniuf edefineo e b y accordancmn di ma e with [32] thosd ,an e betwee helie nd th xan insulatio defines nwa experimentn di s [30] Rf=l.3 10~2(m2K)/W. mosvalue e effeco internan th th n f r £A tn es o ko fo partt ha s ln a ,structur pi e th f eo show [30]n i . Therefore predictee b , £n kca d wit single hth e pipe formula: 2k (1.6) See nomenclature in Fig 1.10.b. 24 AMAMETP TEPMMtxmiA 0.05 0,10 0.15 0,20 (MM) PmnH» 2 3 4 RA3A 0.06 0.12 0,18 0,25 (MM) UlHPHH* nu* 0,12 0,25 0.35 0.55 (MM) Measurement13. Fig. 1. technique of wall coolantand temperature: local- tj temperature, inlet- n tj temperature, central- c t channel temperature. 25 i\_^«^_^-^_^«^_^=^^)-0:0:o:0:0:o-(« ^/. —'j. i Fig. 1.14. Experimental model: measurement- 1 pipe, mobile- 2 thermocouple, -pipe3 bundle wrapper tube, 4, 5 - diagrids, 6, 15 - inlet of outlet of coolant, spring- 7 tensionto capillars, inlet- outlet 9 and 8, hot headers, 9, 11 - hot coolant supply leadaway, 12, 13 -pipe bundle mindo\vs, 14-case, seal,- 17 (coolant flows from bottom top).to 26 •JS -\i£/i X - oooooooo o a) OOOOOOO ooooooo ooooooo ooooooo d) Fig. 1. 15. Models of triangular (a, c) and square (b, d) pipe bundles. 27 The model (Fig. 1.11) measures the mean mixed outlet temperatures in every channel. The thermocouples are fixed hi the special grids attached to the flange of the header, which allows the thermocouples to be inserted into the channels during the flange mounting. Fig. 1.13 presents also an additional information on the micro thermocouples construction, their sizes and the measurement technique. On thermal hydraulic modelin fasf go t reactor intermediate heat exchangers. Into the housing-piping heat exchanger (Fig. 1.6 uniformn )a , over perimeter coolane th , t supply has been designed, that is a non-symmetric flow distribution is realised in the inter-pin space. In cylindrical bundl pin e positionee eth ar s circla n do e wit hgivea regulane th pitc d rhan triangula squarr ro e channel formee sar d (Fig. 1.7). Replacin isolatee gth d secto cylindricaf ro l bundle by a rectangular area, we can study (to a certain approximation) the coolant flow in a sector using «planar» model flos a , w through suc hmodea l doe t diffesno r noticeably from those throug cylindricae hth l bundle r thiFo s. purpos thermae eth l hydraulic experimentr sfo intermediate heat exchanger have been carried out on liquid metal planar models (Fig. 1.14, 1.15, a-d) involving one or three rows of tubes and displacers attached to the wrapper (structur [30]detain n ei i e . lse The local modeling of thermal hydraulics have received detailed attention, defining finally a competence to use the data found in the full-scale systems (heat exchangers involving large number of tubes, long tubes and so on). The main questions of thermal hydraulic modelin multi-tube th f go e heat exchange concernee rar d wit numbee hth tubef ro s e modelith n , lengt f experimentao h l bundle, velocit d temperaturan y e measurement techniques. It has been established that the single-row hydraulic model (7 pipes, together with displacers attached to the planar walls) simulates hydrodynamics in general terms, whereas in orde simulato rt thermaea l processe modee sth needes li d involving three tubes e rowth f t sa o , least (modeling governe internae th y db l centrae tubeth f o sl row) lengte modee th ;th f ho l bundle is sufficient to simulate a full-scale heat exchangers, as an experiments have shown the stable velocit temperaturd yan e differenc cold e betweean d t coolantsho e nth . The fact that results convertee gaineb n reliable e full-scaldca ar th d o dt ean e heat exchange suggestes ri d thalocale t averagedth ,no , velocit temperatured yan measuree sar n di the models mentioned above. Hydrodynamics is studied with the use of electromagnetic technique, which allows a longitudinal and lateral components of liquid metal velocity to be measure eacn i d h e volum pointh f o te under consideration n studyinI . g characteristica s specially developed techniqu uses ei measuro dt e temperaturcold an d t coolantho f eo y b s mobile thermocouples (metho locaf do l thermal modeling). 1.4 ELECTROMAGNETIC TECHNIQUE AS A BASIS OF DATA SECURING IN THERMAL HYDRAULIC ANALYSI F FASO S T REACTOR CORD HEAAN ET EXCHANGERS General insights inttechniquee oth . Traditional measurement techniques basen do e Pitoth t tube d thermaan s l anemomete s difficul i re use b n liquii do t t d metal flows. Experiments with coolant moderata f so e Prandtl numbers (water, air) generate ofte neea n d modele foth r larg a f so e siz compares e(a d with in-pile bundles) , greaf thao s i tt expensd ean it does not give an appropriate consistency between the experimental and standard reactor technology. 28 Thermal hydraulic mode f faso l t reactor fuel subassembly s showA . Charten ni r 1.1, the reactor core consists of hexagonal subassemblies, in every of which the cylindrical fuel pin arrangee sar triangulaa y db r manner wit givee hth n pitch-to-diameter ratio (Fig. 1.4, 1.5). Fuel is uranium dioxide or plutonium dioxide, the pin cladding is stainless steel. Spacer structure is performed by wire wrap. Edge pins are offset by the inter-pin gap (or half of gap) fro covermthe equaliz.To e coolant temperature acros bundlesthe , displacer incorporatesare d in the structure. Power production along the core follows a cosine. thermae Th l hydraulic model (Fig. 1.11) simulate powee sth r par subassemblf to e th t ya scale 2.5:1 t involveI . fuesimulators7 n s3 pi l , that certain i , n cases numbee equas i , th o t lf ro pins in in-pile subassembly (BOR-60), and less for other types (BN-350, BN-600, BN-800). 37 pin bese sar t suite numbern di , becaus onlt eno y internal are subassemblyf ao close th t e bu , to wrapper area are strictly specified (in terms of thermal hydraulics). When assembled togethe triangulas a r r bundle wit givee hth n pith-to-diamete rsimulatorn ratiopi e th , s (wire wrapped arrangee ar ) d hexagonainside th f eo l cover. Cylindrical displacers mountee th t da d bottoan peripher p mto e aligninsecuree ar yth n i dg grids. Phis equipped wite th h thermocouple positionee sar specifie th n di c modee areath f so l (internal, edge, corner). They are made as turning ones and allow the temperature behavior in specific areas of subassembly studiede tob relative Th . e lengt f simulatoho r little tendb eo t s less than those in-pilet I . permits extrapolatin date gth a gainewhole th o det lengt f in-pilho e pin, whic f greao s hi t importanc neae th r n ewrappei r areas, where hydraulithero n s ei c stabilization usuals a , e Th . internal area of subassembly comes into steady state rather steeply and the question does not raised abou choice tth relativf eo e lengt simulatorf ho . The fact that the edge pins are positioned in the immediate vicinity of the wrapper complete with displacers results in an additional parameters, in comparison with the internal pins, influenc temperature eth e behavio pinse th f , o ramon g them: geometr f wrappeyo d an r displacers, clearances between the wrapper and the pins, boundary conditions and so on. Of particular importanc reproductioe th s ei edge th ef no area' s characteristic choice th d f eo s an the main harmonic n Fouriei s r series thermaA . l interaction between subassemblies i s simulated by heat removal using a controlled coolant flow hi the clearance between the wrapper and the model body (inter-subassembly flows). Temperature measurement technique. Micro thermocouples (covered by the capillar f stainleso y s steel 00.8x0. , 0.5x0. , 0.3x0.mm 6 ; thermoelectrodsmm 3 mm 2 : chromel-alumel, cooper-constantan 0 0.1, 0 0.05 mm) are embedded in longitudinal grooves (Fig. 1.13), which displaced an angle of 30° (12 points) from each other. Micro thermocouples are applie a dmeta l coating. Als e mobiloth e micro thermocouple e use ar so measur dt e temperature distributio lengthn witpi e h.th hi studying the pin overheating caused by the helical wire the technique for rotating the smoot insidi immobile hth ph f eo e structur developeds ewa accordancn I . e wit spacee hth r type (either a fin touches an adjacent pin cladding or a fin touches a fin of adjacent phi) the structure mentioned above is made either from wire helix or from the pipe having been put through a milling. The last is slipped over the pin with a slide fit and its wall thickness is heightn fi structure e equaTh th . o t l welde s ei spacee th n do r grids. Inspected tensioe th f no structure over the phi yields that the fin is tight against the pin surface. In addition, without minimising the importance of hydrodynamic modeling, it should be noted that a precise knowledge of local in-pile hydrodynamic characteristics is of 29 paramount importance in thermal hydraulic validation of liquid metal reactor, that defines temperature behaviou n reactoi r r coree nee r studyinTh fo .d e locath g l hydrodynamic characteristics in three main types of flows achieved in reactor units - axial flow (local flow distribution over fuel pin perimeter), transverse flow (mass exchange in the inter-pin space), combined axial-transverse flo heawn i t exchanger requires ha s- universan da l technique b o et develope applies dmentionea y an o dt d typ flowf eo . Hydrodynamics is conveniently studied using the model bundles, those geometry is in-pile closth o et e subassembly, provide same dth e liqui uses coolanda i s da t (liquid metal). advisabilite Th f pursuinyo g suc researcheha s evidentsi s experimenta , s provide neae th r natural hydrodynamic conditions, and the conduction of the experiments is found to be economical. Once hydrodynamic measurements have been amplified by thermal ones, a full informatio thermar nfo l hydraulic validatio nucleaf no r reacto deriveds ri . Electromagnetic technique developed in the Institute of Physics and Power Engineering allows a local hydrodynamic characteristics to be measured in the immediate mock-up liquid metal bundles [33-34]. This enables usin e mock-uth g p assemblies manufactured in accordance with the standard practice and conforming reactor design specifications, except that fuel materia lackings li . Analytical and experimental researches in the framework of the technique were carried out, the local magnetic sensors were constructed (sensors are used with the magnets in size 5x3x2mm, which are mounted in the pin cladding of 6mm in diameter), concepts of calibration transformatiod san sensorse th f no ' findings int locae oth l flow rate (velocity) were developed, as applied to liquid metal flows. As of now , the technique is used to measure both longitudinal [34,41] and transverse [11,35-38] liquid metal bundle flowth n smooti sf e o wird han e wrappe lasde pinth t n cass(i e technique th validates typeewa o tw helicaf so o d t l wrap: fin-to-cladding [11,37,38 find -]an to-fin [11,39] s usei t I d. als n studyini o e combineth g d axial-transverse th flo n i w intermediate heat exchanges [40,41]. Technique is found to be suited in measuring the local flow distribution over the pin perimeter arranged in distorted manner (shifting, bending), in non-regular channels, beyond a subassembly (stream flow in the headers), along the channels . on o s d [42an ] Performance and construction of the local electromagnetic sensors. If the permanent magne locates i t d tubeinside th distributef a ,e o d e.m.f. magnetarisee th n si s a , wel differencs a l i potentialh e turnes channei e surface t tubth e i th th n s t d i ea sa f eo l [33]. Problem is associated with the development of such a construction that assures the findings converte reliablo dt e local flow (velocity) withi e specifienth d par f floo t w cross section, which hereinafte shale w r l designat s «thea e fundamental contribution part» reasoe Th . f no discrepancy between the measured signal and the desired flow rate (velocity) can lies in the magnetic field which follows distinct paths at the magnet ends, that is responsible for the stray (being beyond the fundamental contribution part) areas of coolant flow can contribute into the fundamental signal. From this viewpoint a construction of sensor has to assure the local magnet fiel specifien di d par f floo t w section being adjacen electrodeso t t resolutioe Th . f no the issue was derived during combined analytical & experimental investigations resulting in the constructions presented in Fig. 1.16. 30 a) a) Fig. 1.16. Local action electromagnetic sensors and channels used to develop sensors, construction. Permanent magne enteres i t d int tube ostainlesf th eo s steel surrounde by-pasy db s ring of armco steel (Fig. 1.16, a). The magnet axis is coincident with the tube diameter being at righ dealine t ar angle floe e th gw (w o witst axiae hth l direction) externae th t A . l surface th f eo tub nece e th mad s ki e wher coopee eth r shield ring enclosin magnee g th rine fittes gTh i t . dto has the cut filled with insulator, in which two electrodes being in contact with the coolant and reading longitudinal component of velocity are fixed. Central angle between electrodes (2A Based on the experimental [11, 34-42] and analytical [5, 11, 34, 43] validations of electromagnetic technique, it has been shown that difference in potentials resulting from the electrode liquin i s d metal passing throug bundle hth e (longitudina associatee l b flow n ca ) d wit meae hth n coolant velocity withi e elementarnth y area forme radiay b d l rays drawing throug electrodee hth e lin f maximuth o e d an s m velocity greaa n I .t numbe f caseo r e th s length of the elementary area is chosen equal to the distance between the tube surface and the channel wall. Signal distribution around the tube measured in the rotating tube should be in conformity wit hydrodynamice hth channee th f so l under consideration. To convert a signal into velocity is performed in dimensionless form on the assumption tha proportioe tth n facto relationshin i rk p W = k-e (1.7) same isth e withi areae nth s under consideratio counsellee b n ca d processinn dni an g dat: aas W e ______,______/l O\ — — \, ^ I 1. • o I wher - channe eQ l cross section area, C D- surfac e element that defines velocity- w , mean velocity withi channele nth . To define velocity distribution along the model the electromagnetic sensor is moved along the tube axis (commonly either together with the tube or inside of the tube). A tube rotation allows the azimuthal distribution of velocity to be measured. In order to measure variatio e integrath n ni l flow rate around pip e sensorth e e usedar s , where electrodes i s positioned along the tube diameter (Fig. 1.16, b). Electrodes are in contact with the internal surface of the tube and are moved integrally with the magnet in axial and azimuthal sucf directionso e hsensora us e vers si Th . y attractiv bundle th n ethin-wallef i e o d tubea f so small diameter (~5-r6 mm), whe doee t succeenw sno positioninn di electrodee gth e th n si immediate vicinity of a magnet end [39,43]. To replace the sensor from one tube to another open waye sdetectinr th sfo g subchannel flow rate sAttempt. arrango st e sensor in-pile th n si e subassembl (BOR-60f appropriatye o th o t d )le e data were gained. Electromagnetic sensor designe measuro dt transversea e flo subassemblwn i y wite hth «fin-to-cladding» spacer consists in the two magnets placed in to adjacent tubes, with the permanent magnetic field produced betwee tubee nth s (Fig. [11) c , 1.16, 35-38]. Magnete sar concurrently moved inside the tubes. Using the sliding contacts an e.m.f. due to transverse flow of liquid metal throughout the clearance between the contacts is measured. For the transverse flow in the bundle of the pins wrapped by «fin-to-fin» type of wire spacer to be 32 measured [36, 37, 40, 47), when an opposite in directions flows occur between the pins, the sensor with one magnet is used (Fig.l.l6,d) which operates in the area covering not more than half a gap between the pins (appropriate magnet to be chosen). To investigat combineea d axial-transverse flow sensore th , s equippe pairo f tw so y db electrode usede ar s , wit electrodee hth s located nea magneo t r (azimuthad en t axiad an l l directions) (Fig. 1.16 . Sucd) , hsensora s allo e concurrenwth t measuremen f axiao d t an l transverse component velocitf so y [35, 36,40,41]. Theoretical notion electromagnetin so c technique fino bese T .d th t constructioo nt be followed, some variously of the sensors constructed were investigated, which differ in shape and in size of the magnet, in material and number of electrodes, in technique of the electrodes embedded into the tube surface, in an angle between the electrodes, in extent to which a magnetic field to be located at the magnet end (the availability or the absence of shield rings) and so on. Experiments were carried out in the channels of various sharp, (Fig. 1.16 , includine) , g regular triangular bundle (1.0 <1.2 d non-standard Hypothesise possibilite constance th th n n factoe o s o (1.7 n th d i f confinyk ro yo an )t e fundamentae th l contribution elemen linee th sy passinb t g throug electrodee hth true sar n ei the sensors mentioned. As empirical data have been derived from the hypothesis, they are approve solvinn di g some problem f magnetio s c hydrodynamics followe quantitativy b d e estimations consides u t .Le r some examples. Sensors containin shielo gn d rings analytican A . l solutio mose th r t nfo simpl e model of the uniform flow in annuli, with the internal cylinder containing permanent magnet (Fig. 1.17, a) [35, 43, 45], shows that difference in potentials originated at the surface of internal cylinder between two points AU(r,) varies in proportion to the coolant velocity (W), electrical conductanc wale th magnetif lf o liquie (ao d wm an ) su d d c(a fluxefan ) s over separate harmonics m involved through the weight function, f as m (1.9) — wher= m ef v l-\r/R] 1 V O' / ' 2m l/ = ! + ——-——1, _ / _ •' T = I + iY >; Jf m =———4i fin \2m — \"••'•"/(1.10' ) 33 a) 3 2 111-2*0060 1 0 1 R/r Z =X +LY ^. 7.7 7. Theoretical foundation of electromagnetic technique measureto liquid metal local velocity. 34 - externawher 0 r , internad eR an l l radi f annulio i , respectively. Values fm appearo st approximate asymptoticall unitn ya y wit widte hth annulaf ho r clearance, makin seriea p gu s of functions fm(r/ra), which converge to the ^function, as m—#x>: R/rat I 0-l>Q; Q(R/r0-l)= (1.11) t R/ra 0 0 -1<0. function/Ae sth „ increases with R/r0, signal also rises with R/r0. Magnets possessing concentratee th d field (top harmonic ) giv e fastem eth f o s r signal saturation, then onef o s lesser concentrated field (low harmonic. m) f so The preceding is illustrated in Fig. 1.17-a as a dependence of AU/rJBw (that is inversely relate factodo t (1.17)n i rk R/rn )o 0 (here inductio- B , liquid-wale th t na l boundary). Rectangular magnets having a field concentration angles 2Aa equal to 3, 7, 5, 60° and cylindrical magnets with 2Aa=l8Q° are considered. picture Ath s e suggests e conditioth , n k=idem s compliei d wit hgreatea r ordef o r accuracy for the concentrated magnets but an influence of 'side' areas of the flow on the signal generatio s reflecteni a lessee o th t d r5 7. degree d r anglean Fo a equa.3 2A so t l hypothesis that k=idem is rigorously fulfilled in a wide range of 1.1 < R/r0< Sensor with shielding rings. To detect operating features of the electromagnetic sensors equippe e shieldinth y db g ring more th s e common proble t restrictemno e th y db channel shape has been resolved Fig. 1.17 b. Cylindrical pin contains an infinite (in axial direction) magne arbitrarf o t y profile, that produces magneti surfacen e pi th c e t fielth A . t da magne therinsulation d a en ts e i n area remaindee th , r perimete coopee s th i s ri n r pi ringe Th . flowed by the electrical conductive liquid, with the conductance of the liquid being equal to conductanc channee th f eo l wall. An assumption, that velocit arbitrarf o s yi y profil problee th n ei m under consideration, is of principle importance, because it is the assumption which allows analysing the sensor locatio t shouln(i notee db d tha analysinn i t g combined channebundln fore pi th f e m o en th i l velocity value must be considered as equal zero in the places of the pins location. Definition of fundamental contribution area. Field of the values for weight function (Fig. 1.17 c) is exemplified by a positive and negative contributions (central and side areas relative to the electrodes, respectively). The full signal is determined by the signals' sum. Ratio betwee areae n th f positiv o s negativd ean e contributions into signal depende th n o s character of magnetic field. Magnetic field narrowing in angle direction results in reduction of negative th e areas' proportion. In dependence of the weight function the area of fundamental contribution can be detected. In the sensor with cooper ring the area mentioned is less than fundamental contribution area in the free of ring sensor by a factor of 2. Thus, the availability of cooper cylindee rinth t ga r surface result more th i esh concentrated distributio weighf no t function ni an area clos electrodeo et compares sa d with variant where rin lackinggs i . 35 m7] m m > -; I I I I I i i 22 18 14 m R m — 3 10 0 X I I I I i i i i i i i I 1 3 ' 5 7 9 8, mm 1,0 1,08 1,16 S/d Wy W S/dH,15 1,02 0,98 0,94 5/d=1,17 0,90 A-Re=42^-103 0,86 0,2- 0,82 5 2 0 2 5 1 0 1 5 0 9 5 2 0 2 5 1 0 1 5 0 Fig. 1.18. Experimental validation of electromagnetic technique. 36 A knowledge of weight function allows an approximation due to limitation on the fundamental contribution estimated e areb o at particularn .I bees ha nt i , shown tha magnee tth t of definite properties and under conditions of uniform velocity if angle between the electrodes is 2A e extenTh f fundamentao t l contributio radian ni l directio s mucni h superioe th o t r thickness of near wall layer, within the which the main velocity varies. Then, variation in fundamental contribution area in radial direction does not change the mean velocity. For convenienc fundamentae eth l contributio assumee nb distance areequae n th b aca o o dt t l e betwee maximue th wale d nth lan m velocit yspecifin i lin , eor c cases, betwee e walle th nth f so channel. Oinfluencn na opposite th f eo sensoe walth n ro l signal greatese Th . t influencf eo adjacent wal signan lo l appear evente th n si , whe wale nth l surrounds sensor (annuli)e th d an , mino whe e curvature a wal e ron s nth l caseha l al influencn signae n sa I . th wale n th l o lf eo generation sharply decreases with the distance between the sensor and the wall, as well as the magnet becomes smaller (the «wall effect» disappears practically when magnet f definito s e size is used). The wall effect sharply decreases as cooper ring is used (magnetic field in the area close to electrodes becomes more local): in bundle with s/d =1.02 this effect does not exceed some percents, whereas the sensor without cooper ring gives ~ 15%. The availability of additional armco ring results in the effect is completely eliminated. Experimental validatio hypothesie th f no s that proportional factor between e.m.f. and coolant velocity is constant. Sensors with the magnet of length 10,8 and 6mm (Fig. 1.18 wer) a e teste axian di l flow. Proportional factobees ha nk r realise independene b o dt e th n o t width of annular. On checking hypothesis k=idem axian i l flow throug varioue hth s bundl showe ear n i Fig. 1.1 8 b. As the figure indicates, value of k does not depend on pith-to-diameter ratio. The hypothesis of the combined axial-transverse flow has been checked in the model of heat exchanger BN type [40,41] (see Fig. 1.14). The local coolant velocity distribution along the tubs measureewa electromagnetiy db c sensors which were move axian di azimuthad an l l directions. Flow balanc evern ei y cross sectio betwee) i n( inle e outled nth tan t windows: const= V = W 7& ke^).S = Q( V= t (1.12) converged to better than 0.5%, and proportional factor k in (1.12) written for simplicit 7-pipr yfo e mode defines swa constans da t value. Heraverage- n e d over perimeter signal of the n-pipe, /2 - coolant flow section around the n - pipe, w - averaged over the model cross-section coolant velocity . 37 Inherent velocity measure testdn i . Axial flow. Fig.l.l8-c shows velocity fields in the channels of regular triangular bundles produce y cylindricab d l smooth pins positioned wite pitch-to-diameteth h r ratio s/d=1. s/d=1.15d 0an . Electromagnetic measurement agreemenn i e sar t wit othee hth r authors' data, which have been obtaine traditionay db l techniques base Pilon do t tubes wels a , wits la h predictione th well-knowy sb n procedures. Fig. 1.19 presents the axial velocity distribution over perimeter of near wall pins in fast reactor subassembly model (smooth pins). Data gained in the various combined channels (shape channel th n Figi f o e.e s analyse1.1se i s ) 6e d belo Chapten we i result Th . s4 r mentioned have been generalise usew therman di no d dan l hydraulic analysi reactorsf so . Transverse flow pattern s betweep withiga e e wirnth nth e wrapped pins (fin-to- cladding) follow approximatel ya sin e function (Fig. 1.20), that reflect a mechaniss f mo convective interchannel mass exchange. Electromagnetic technique has allowed the processes of interchannel exchang reacton ei r studie e corb o e t detai n d i appropriat d lan e constante b o st derived (see Chapte. r3) Combined axial-transverse flow in the model of intermediate heat exchanger is demonstrated in Fig. 1.21 and 1.22. From the data presented it follows an important practical conclusions descriptive the heat exchanger performance in terms of hydrodynamics (see Chapter 5). 1.5. LIQUID METAL FACILITB Y6 The main functions. Experimental facility 6B (Fig. 1.23) is designed for studying hydrodynamic head an st transfe modele th n i f reactor o s r corhead ean t exchangers metal- metal (coolants: Na, NaK). Detail description of the loop is given in [45]. The general fundamental problems of liquid metal heat transfer and hydrodynamics, and in particular, fields of velocity and temperature are studied by local measurements of coolant and wall temperatures using micro thermocouples, and local velocities (flow rates) by electromagnetic sensors. Based on the results gained in experiments the in-pile fuel pin temperature behaviou s establishedi r wels a ,s operatin a l g efficienc heae th tf o yexchange r equipment. The main parameters are as follows: coolant flow rate (Na or NaK) up to 150 m3/h, temperature 20-:-4500C MPa,0 pressur1. ,o t referencp u e , liquieMW d powe 2 meta1. ~ rl volume -1m3. Facility engineering. The rig 6B includes three circuits: first - NaK, second -Na, third -NaK, with the first and second circuits being the main. They are intended for performing experiments on the models simulating reactor core and liquid metal heat exchangers. The third circui designes ti coolinr dfo cole gth d catcher firssecone d th an t n si d circuits. Electromagnetic pumps (Fig. 1.24) are intended to produce liquid metal circulation. The operation of the pump is based on interaction of rotary alternating magnetic field in stator with the induced magnetic field in liquid metal. The pump involves stator and core (rotor). The space between stator and core representing annular clearance is packed in liquid metal. 38 wJ1 w SAMIO 14 12 - A-S-d Fig. 1.19. Dimensionless velocity along the smooth corner pin perimeter. 39 d-19-lO~m I ' I • I I ' I ' I ' I ' _ • 30600. = e R , . 03 *iu\^in/WWWWrWWYW l^lUgaii ftIj/Jilr- 4=5.05 -Re=18000 -———————————__ clearanc. jf I e . Re=24ioxxikrx.my^xo \ /\ '-xr"', --i /"N -v ,*" sM I *H"?' 0,1 0 -0,1 01 1 Pe ' — 0 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 Fig. 1.20. Sensor signal with channelthe lengthat various wire wrap pitchesnumbers.Re and The stator slots receiv three-pasea s winding that induce alternatinn sa g magnetic field shorted to the core. In response to the interaction of magnetic field with induced hi liquid metal currents a magnet rotates within the clearance. Three-pass fins welded to the wall impose directional motion. Heat given out by the stator windings is removed by the water flowing in a jacket windine .Th g temperatur measures ei thermocouplesy db . The pumps mounted in the first and second circuits have the following characteristics coolant flow rate (NaK and Na) -150 m3/h, pressure head 6 kg/cm2, power consumed ~ 170kW, maximum coolant temperature ~500°C, allowable temperatur f windineo g180°C~ , maximum allowable current ~ 250 A. Electromagnetic pump in the third circuit is of the following parameters: coolant flow 0 m1 ~ /h, pressure 0 kg/cmhea1 ~ d , electrica , maximul kW powe 4 ~1 mr coolant 3 2 temperature ~300°C, temperatur windinf eo g180°C~ , allowable . currenA 0 4 t~ 40 mm Fig. 1.21. Axial coolant flows (Vn) in sections around pipes «n» (n = 1+7) with the pipe length. Inlet window height: 150mm350mmand (a) (b). 0,2 - L o=80mro Fig. 1.22. Transverse velocity component with tube pipe length. Carbon heaters (Fig. 1.25) serves to produce appropriate temperature of sodium coolant. From the pump 2 a part of metal is sampled for the carbon heaters, with the heating up to needed temperature, and is directed to the chamber where it is mixed with the main flow of sodium. The heater consists of the carbon tube enclosed by cylindrical wrapper where vacuum r filleo inern i d t gas e tubs longitudina.Th ha e l slits allowinf needeo e e tubeb dgth o t resistance d losseo reducen e T carbo. th e s th e botto nth tubs mha e thermal shields. Cylindrical wrapper is enclosed the heater body. In the space between body and wrapper a sodium flow downp s to fro e m. th Guid e fins create rotation, that produce uniforn a s m heat removal fro wrappee mth r surface. Powe applies ri d throug watee hth r coole dcoopea r current feeds. The feeds are in a contact with the carbon tube by the natural fall. Design characteristic carboe th f so n heate followse rar : power -18voltag, , currenV 0 kW 4 e -9 200- t 0 A, mean temperature ~ 800°C, maximum coolant flow ~ 10 m /h, surplus pressure of inert gas 3 -0.3-5-0.5 kg/cm2. 42 Fig. 1.23. Schematic diagram of three-lop contour: 1. 2 - cold catcher, 3. 11, 18-cooler 4, 5, 10, 20-tank, -sampler,6 electromagnetic- 7 cooler,pump,air - test- 8 9 section, recuperator,- 12 electromagnetic- 13 pump, 14 - cold catcher, 15 - mixer, 16 - carbon heater, 17 - water heating tank, 19 -filter maine th - loop, — -{X3:— valve,-- magnetic flow-meter, manometer,- 0 - -flown - - relay,—— " s line. -water— ga — . line,— . — u> Coolers (Fig. 1.26 seconfirsd n i )an t d circuit designee sar removo dt heaea t released in the models. The third circuit cooler is meant for heat removal in the catchers of first and second circuits. Coolers 1 and 2 have the same structures. They involve 30 triangularly arranged cylindrical elements, with every element representing three pipes (internal, intermediate, external) mounted one inside the other. Water comes into the internal pipe, flow dowp s pocke e leaved to fro th e n an r m th s fo t between interna intermediatd an l e pipes. Another pocket between the intermediate and external pipes is vacuumed or filled in inert gas. The element flowee sar liquiy db d outside e metath n o l , thus coolee th , r design excludee sth possibility that water be in contact with liquid metal in the event of loss of pressure. Contact ca causee nb d just concurrent wate metad an r l leaks. However suce th even,n ha almoss i t t incredible intermediatn A . e pocke s controllabli t e with vacuu r inermo s pressur ga t y b e electromagnetic vacuum-meters. Pipes are welded overhead together with the plats of the cooler or the upper flange, wherea lowee th n sri part spacethee grie freb e th ydo ar Interna. et y db l pipe withdrawe sar n together wit cooler'e hth s flange allowt I . pipee cleanee sb th o st regulat da r intervals. Vertical arrangemen coolere th f o t s mad mountine eth g much easier coolee secone th Th . n i rd circuit (sodium coolant) has six internal elements separated from the other elements by the curly cover, which equipped with the sodium valve. Thus, in this cooler , apart from the control of heat remova chango t e watedu ln e i r flow throug regulatcoolern e hth ca e w ,e heat removay lb redistribution of sodium flow between the internal and edge areas of the cooler. Characteristics of the coolers in circuits I and n are as follows: water flow -Ck-6-10~3 m3/h, water pressure - 6 kg/cm2, water inlet temperature -20°C, water outlet temperature - 30°C, water velocity -0.36 mVs, sodium flow -0-^27.8-~ m /s, pressure -10 kg/cm , velocity - 3 3 2 O-fl.15 m /s, inlet temperature ~300°C, outlet temperature ~ 290°C, allowable sodium 3 temperature in the cooler II ~600°C. To remove heat flow the first circuit at low temperatures the cooler are designed here, with the sodium alloy running through the internal pipes arranged in regular triangular manner, and external pipes being flowed by water. The spaces between the internal and the external pipes are united into the header and filled with the Wood alloy having melting temperature in 60°C. Oxide catchers (Fig. 1.27, 1.28) are designed for purification of liquid metal from oxygen operatioe Th .catche e th f n o bases ri oxidn do e precipitatio catchera n i s space filled wit stainlese hth s steel chicooled watepa an y db r (low temperature catche Figr- . y b 1.27 r o ) NaK alloy (high-temperature catcher- Fig. 1.28). Water cooled catchers are designed in the circuits I and HI of the 6B facility. They have either internal or external cooling. In one case or another, a heat from liquid metal is conveyed to water through the cooper wall. Operating conditions of low-temperature catcher ars followsa e : circulation velocit 4mm/so t p -u y , inlet temperature o 250°Ct p u - , water pressure - up to 3 kg/cm2. NaK catchers are designed in the circuits I and n . Any one of these catcher consists of internal pipe which receives coolant to be chained (flow from top to bottom) maie th , n space filled with stainless steel chip (flow fro externamd an botto p to l mo t cooling space (flowitK hwNa from botto mtop)o t . Operating condition maie th nf so coolant Text cont. on p. 53. 44 Fig. 1. 24. Electromagnetic pump: 1 - inlet connection, 2 - base, 3 - body, 4 - cooling shell, 5 - wrap, 6 - stator compensator,- 7 supply- 8 box. 45 water Fig. 1.25. Carbon heater: 1 -bottom, 2- body, 3 -plug, 4 - wedge, 5- current supply, 6- cover, 7- wire, 8 - current supply, 9- ring, 10- shield, 11 - heater. 46 the gas water Fig. 1.26. Sodium-water heat exchanger: inlet- 1 connection, 2 -flange, 3, 4, 5 -pipe grids, 6 - valve disc, 7 - valve, 8-shell, 9-displacer, 10-body, 11-pipe 50x3, 12-pipe 42x2, 13-pipe 27x2. 47 water water -*-^m Na-K ouitet Operating condition Parameter Na-K water Flow rate ms/h 0.83 3.0 Inlet tem- °C 100 20 perature Outlet tem- °C 80 23 perature Pressure MPa 1 0.3 water Velocity m/s 0.04 0.028 Fig. 1.27. Cold catcher: 1 - bottom, 2 - grid, 3 - wrapper tube, 4 -packing of stainless steel chip, displacer,- 5 cover,- 6 ther-- 7 mocouple, 8 - shell, 9 - -wrapper tube. 48 Na-K Fig. 1.28. Cold catcher: 1 - shell, 2 -body, 3 -compensator, 4 -wrapper tube 5 - cover, 6,7- thermocouple, 8 - canopy, 9 - bottom, 10 - stainless steel chip. Operating condition Parameter Na Na-K Inlet tempera- 400 40 ture, °C Outlet tempera- 280 90 ture, °C Pressure, MPa 10 3 Flow rate, m /h 0.77 3.5 49 Fig. 1.29. Sampler - distiller: 1central- valve, -furnace,2 barrel,- 3 drain,- 4 5 - reflector, 6 - bottom flange, 7 - gasket, 8 - top flange. 50 Fig. 1.30. Sylphon valve: 1 - valve, 2 -body, 3 - sylphon, 4 - rod, 5 -flange, 6-seal, 7 - screw, 8-nut, 9 - sensor. 51 Fig. 1.31. Valve of cooling seal: guide- 1 rod, bottom,- 2 connection,- 3 ring,- valve,- 4 5 12 split- sleeve, cap,- barrel.14- 13 52 (NaK in the circuit I, Na in the circuit II): flow ~0.8 m3/h, pressure -up to 6 kg/cm2, inlet temperatur 400°Co t col e same p th u d f eTh . - e o coolant : flow -3.5 m /h0 , pressur1 o t p e-u s kg/cm , inlet temperature - 40°C, outlet temperature -90°C. 2 Sampler-distillators (Fig. 1.29) are designed for sampling sodium and NaK alloy (weight lOOg), and ensuing distillation in vacuum and determination of the oxygen in oxides. Sampler consists of the vacuum chamber and three valves. The space chopped off by the valves is that from which the sampling is performed. In order that metal should not be splashed around during period the sample is drained into the barrel designed within the vacuum chamber, a special pipe is provided. To improve washing the pipe is made as removed one. Given temperature of distillation is supported with use of the furnace of variable power. Temperatur measures ei thermocouplesy db condenseK Na e d .th Vapouan t sa a N f ro surface of the bottom flange and the breaker that keeps the liquid metal vapour from entering e vacuuth m line o extracT . t barrel with remaining aftee distillatioth r e sampleth n s i r disassembled. 6B facility is completed with the sylphon sealing (Fig. 1.30) and seal of frozen sodium (Fig. 1.31) wels a , devices a l measuro st e temperature, flopressurd wan coolantf eo . Among the ancillary structure are tanks, mixers, catchers, filters and so on. Water service is from the main water header, where the pressure valves connected wit associatee hth d unit mountee sar . Gas-vacuudin m servic designes ei evacuato dt e loop and to feed inert gas into the units. Electric design provide currene sth t supply throug followine hth g voltage controller: • electromagnetic pumps - through the automatic transformators ATMKT-250/0.5, • electrical heaters - through the automatic transformators AOMKT-250/0.5 or inductive controller MA-195.750 kVA, • carbon heaters -throug e inductivth h e voltage controller MA-19 d stean p5 down transformator OCY-80. 6B loop incorporates the working place for operator equipped by sensor reading panel and distributing frame to control thermal and electric equipment. CONCLUSIONS 1. Analytical analysi fasf so t reactor thermal hydraulic maio bases si tw nn dapproacheso : subchannel analysi a porou d an ss body model e firs s basei Th t. n solutiodo f no governing momentum, mass and energy conservation equations written for channels formed by the adjacent pins. In the framework of the second the pin bundle is represente anisotropis da c porous body with distributed volumetric power production. possibilite Th predictior yfo non-nominaf no l performanc diabatio t e edu c conditiont sa the subassembly wrapper, accidental deviations of parameters, deformation of subassembly in campaign, transient conditions and others receive primary attention in developmen moderf o t n codes. 2. The following experimental techniques serve as a basis for gaining thermohydraulic constants: • approximate thermal modeling of fuel pins including development of the heaters which produce unifor variablr mo e power distribution; • technical modeling of reactor core and heat exchangers; 53 » local measurement technique using special miniature sensors (electromagnetic flow meters, micro thermocouples); > high powered liquid metal facilities allowing for a great coolant flow and wide range of temperature variation whicn o , h large-scale experiment carriee b t witn dsca ou s h a "natural" coolant (sodium simulatind )an g (sodium-potassium alloy) one. Electromagnetic technique intended for measurement of local velocity of liquid metal in combined channels allow mock-ue sth p subassembly manufactured wit standarha d technology, except that fuel is absent, to be used. The method was validated by prediction experimentsd san , wit desige hth miniaturf no e local sensor calibratiod san n principles developed. This method is used to measure as longitudinal (axial) and transverse component liquif so d metal local velocity (flow rate bundlen )i smootf so r ho wire wrapped pins. It was been shown that the method is very effective as applied to combined flow. The method is convenient to use for studying distributions of local flows around and along the pins arranged in deformed bundles (stream flow, pin bending, blockage non-standar n on)i o s , d san d channels bundle th t a , e outlet (headers and chambers) and so on. REFERENCES [I] Zhukov A.V., Kirillov P.L., Matjukhin N.M., et al. Thermal Hydraulic Calculation of LMFBR. M., Energoatomizdat, 1985 (in Russian). [2] Recommendation Therman o s l Hydraulic Calculatio f Faso n t Reactor CoreM PT . 1604. 008-88. State Committee on Nuclear Energy. M., ONTI IPPE, 1989 (in Russian). ] [3 Zhukov A.V., Sorokin A.P., Matjukhin N.M. Interchannel Exchang Fasn ei t Reactor Subassemblies. M., Energoatomizdat, 1991 (in Russian). Overvien W.Ta BundlA d Sh . Ro n we o ] Thermal-Hydrauli[4 c Analysis. Nucl.d Engan . Des.. 3-21p , ,. 62 1980. v , ] [5 Subbotin V.I., Ibragimov M.H., Ushakov P.A.. Hydrodynamic Head san t Transfen i r Nuclear Power Plants. M., Atomizdat, 1975 (in Russian). [6] Yeung M.R., Wold L. Multi-Cell Slug Flow Heat Transfer Analysis for Finite LMFBR Bundles. Nucl. Eng. and Des., 1980, v. 62, p. 101-121. ] [7 Zhukov A.V., Kirillova G.P. Temperature Behavio t Entrancra e Sectio Bundln Pi f no e in Turbulent Liquid Metal Flow. Preprint IPPE-715, Obninsk, 1976 (in Russian). [8] Milbauer P. Application of Finite Elements Method for Calculating Turbulent Flow through the Non-round Tube. Hydrodynamics and Heat Transfer in Core and Steam Generato Fasf ro t Breeder Reactors, v.l, Prague, 1984, p.104-105. [9] Trevgoda V.M. Numerical Calculation of Laminar Velocity and Temperature Behavior in Combine Geometry. Problem f Nucleao s r Scienc Engineeringd ean . Physicd an s Eng., 1980, 4, p. 89-95 (in Russian). [10] Sholochov A.A., Zasorin I.P., Minashin V.E.. Calculatio Temperaturf no e Behavion ri Nuclear Reactor Fuel Elements Atomizdat, .M. , Russian)n 197(i 8 . [II] Zhukov A.V., Sorokin A.P., Matjukhin N.M. Interchannel Exchange in Fast Reactors. M., Energoatomizdat, 1989 (in Russian). [12] Stewart C.W., Rowe D.S. Advanced Continuous Fluid Eulerian Computation Scheme for Flows with Large Density Gradients. TANS, 1976, v. 24, p. 178. [13] Novendstem E.H. Mixing Mode Widr fo l e Fuel Assembly. TANS . 866p , - ,15 1972. v , 867. 54 [14] Chen B.C., Todreas N.E. Predictio f Coolanno t Temperatur ee Breede Fielth n i d r Reactor Including Interassembly Heat Transfer. Nucl. EngDes.d . an .p , , 197535 . v , 423-440. [15] Bogoslovskaya G.P., Zhukov A.V., Sorokin A.P. et al. Code TEMP-M for Thermal Hydraulic Analysi f Faso s t Reactor Subassemblies. Preprint IPPE-1401, Obninsk, 1983. [16] Kazachkovski O.D., Sorokin A.P., Zhukov A.V. et al. Lumped Parameters in Problems on Temperature Behavior in Deformed Subassemblies of Fast Reactors under Diabatic Boundary Conditions. Preprint IPPE-1672, Obninsk, 1985. [17] Cronenberg A.W. et. al. A Single-Bubble Model for Sodium Expulsion from Heat Channel. Nucl. Eng. and Des., 1971, v. 16. [18] Ishi Two-Flui. iM d Model Hydrodynamic Constitutive Relations. Nucl. Eng Des.d an . , 1984. v. 82, p. 107-126. [19] Spasskov V.P. et al. Complex of Programs to Predict Transient Thermal and Hydraulic Processes in Designing WWER. Problems of Nuclear Science and Engineering. Physics and Eng., 1981, 7 (20), p.72 (in Russian). [20] Kolev N.I. Comparision of the RALIZA-2/02 Two-Phase Flow Model with Experimental Data. Nucl. Eng. and Des., 1985, v. 5, p. 217-237. [21] Bogoslovskaya G.P., Bogatyrev I.L., Zhukov A.V. et al. Two-Liquid Model of Two- Phase Flow Prediction. Preprint IPPE-1991, Obninsk, 199 Russian)n 1(i . [22] Gerliga V.A., Kirillov V.V. Conservative Difference Schem r Steaefo m Generating Channel Dynamic Equations. Problems of Nuclear Science and Engineering. Physics and Eng., 1982, 6(19), p.43 (in Russian). [23] Mironov Yu.V., Razina N.S., Fomicheva T.I. et al. Analysis of Transients in Nuclear Reactor Contours. Atomic energy, 1986, v.60, p.255-260. [24] Komienko Y.N., Kuzevanov V.S., Sorokin A.P. The Technique of Calculation of Non- equilibrium Two-Phas e n BundleFlowPi n i s s Using Quasi-Two-Dimensional Approaches and Subchannel Approximation. Advanced in Gas-Liquid Flows, Winter Annular Meeting of ASME, Dassal, Texas. 1990, FED-vol 99, p. 321-330. [25] Macdougall J.D., Lillington e J.NSABRTh . E Cod r d FueClustefo eRo l r Thermohydraulics. Nucl. EngDes.d an . . 1984 . 171-190, p Vol , 82 . . [26] Ninokat , OkanaH. . SABENAoT : Subassemby Boiling Evolution Numerical Analysis. Nucl. Eng. and Des.. 1990, Vol. 120, p. 349-367. [27] Kumaev V.Y., Leonchuk M.P., Dvortsova L.I. Numerical Procedure for Calculating 3- D Coolant Flow in Pin Bundles. Preprint IPPE-1733, Obninsk, 1985 (in Russian). [28] Karlow F.H., Amsden F.F. A Numerical Fluid Dynamics Method for All Flow Speeds. Compf J.o . Physics ,. 197-213 p 1974 , 8 . ,v . [29] Patanka . NumericaS r l Solutio f Liquino d Heat Transfe Hydrodynamicsd an r , M. . Energoatomizdat, 1984. [30] Zhukov A.V., Sorokin A.P., Sviridenk o. Experimenta al E.Y t e . d Numericaan l l MODELING of Heat Exchanger Thermohydraulics. Models, Sensors, Techniques. Textbook, ONPEI, Obninsk, 1992 (in Russian). [31] Ushakov P.A. Approximate Thermal MODELING of Cylindrical Fuel Elements. Liquid metals, M., Atomizdat, 1967 (in Russian). [32] Lastman B. Radiation in Uranium Dioxide. M., Atomizdat, 1964, p. 196-208. [33] Subbotin V.I., Ibragimov M.H., Loginov N.I. Measurement f Velocito s d an y Temperature in Liquid Metal. Atomic energy, 1968, v.25. 55 [34] Subbotin V.I., Zhukov A.V., Sviridenko EJ. et al. Experimental and Theoretical Validation of Electromagnetic Technique. Heat Transfer and Hydrodynamics in Reactor Core and Steam Generators, Nove Mesto, Czech Republic, 1973. [35] Zhukov A.V., Sviridenko EJ., Sorokin A.P. Electromagnetic technique to measure velocity and temperature fields in combined geometry. Proc. of Int. Conf. "Thermal Physics-96", Obninsk, IPPE, 1996, p.48-56 (in Russian). [36] Zhukov A.V., Sviridenko EJ., Sorokin A.P. Sensor Measuro st e Liquid Metal Local Velocit Flod yan w Bundlesn RatPi n ei . Proc IPPf o . E "Thermal Physic Measurement Techniques", ONTI IPPE, 1996,p.l50-166. [37] Zhukov A.V., Sviridenko EJ., Matjukhin N.M. et al. Measurement of Local Hydraulic Inter-channel Characteristics. Preprint EPPE-665, Obninsk, 197Russian)n (i 6 . [38] Zhukov A.V., Sviridenko EJ., Matjukhin N.M . Studal t f Combine.e y o d Flon wi Bundl Wirf eo e Wrapped Pins. Preprint IPPE-867, Obninsk, 197Russian)n (i 8 . [39] Zhukov A.V., Sviridenko EJ., Matjukhin N.M . Studal f t .Locao e y l Mixing Characteristic Bundlen Pi n si s (Spacer Fin-to-Fin). Preprint EPPE-908, Obninsk, 1979 (in Russian). [40] Ushakov P.A., Zhukov A.V., Yuriev Yu.S. et al. Local Hydraulic Characteristics in Fast Reacryor Heat Exchangers. Thermal Physical Investigations , VIMI,M. , 1977. [41] Zhukov A.V., Sorokin A.P., Sviridenko EJ. et al. Experimental and Numerical MODELING of Heat Exchangers. Hydrodynamics. Overview IPPE-0270-M., CNnAtominform, 1995. [42] Zhukov A.V., Sorokin A.P., Ushakov P.A. et al. Thermal Physic Validation of Temperature Behavior in Fast Reactor Subassembly Having Regard to Hot Spot Factors. Preprint IPPE-1816, Obninsk, 198 Russian)n (i 6 . [43] Zhukov A.V. et al. Theoretical Validation of Magnetic Measurement Technique. Preprint IPPE-406, Obninsk, 197Russian)n (i 3 . [44] Catalogu Facilitiesf eo , Mock-up Reactor Experimentad san l Models. CEMR, KNTS- 2, 1978, p.20-22 (in Russian). 56 Chapter2 THERMAL HYDRAULIC SUBCHANNEL ANALYSIS 2.1. DEVELOPMENT OF SUBCHANNEL APPROACH firse Th t subchannel codes, which take into accoun heaa mastd an t s inter-channel exchange, were developed for single-phase flows as applied to the detection of the hottest channel in the reactor subassembly (THINC-1,USA[1]; JOYO, Japan [2]; MISTRAL, Germany [3], TEMP, USSR [4] and others), and for two-phase flows (light water reactors) in order to evaluate a critical margins and to calculate temperature behavior under critical conditions (HAMBO, Great Britain [5,6], COBRA, USA [7], FLICA, France [8], POUCHOK, USSR [9] and others). Boundary conditions were written at the bundle inlet, with the macro-transport equations solved ste stey pb p alon channele gth codese Th . ' ratins gi presented in the Tables 2.1-2.3. The need to study a blockades generated in the liquid metal fast reactor core has called e developmenfoth r e codeth f so t simulatin e combinegth d coolant circulatio strond nan g transverse flow. Since the main challenge of the code is to provide means for prediction of non-standard structures, the code had to involve consideration of all types of subassembly flow deformation occurring in campaign (bending, blockades, coolant boiling, natural convection and so on). It should be noted that a large transverse coolant flows, as well as an availability of recirculation areas are possible in such an events. Widenin probleme e clasth gth f o s s under consideratio s resulte more nha th en di combined statement subchannef so requires l codeha d san d recent advance computation si o nt be used for solution of source equations. Development of the completely governing codes (supercodes) are conditioned by the up-date methods intended to solve problems of continuous medium hydrodynamics suc MACs ha , ICE, SIMPL othersd Ean . Some generation f subchanneo s l codes have been currently develope differenn di t countries (Russia, USA, Germany, UK, France, Japan and others), which vary in a completenes governinf so g equations, numerical procedur theif eo r solution and, respectively, are intended for the different problems. Although the main group of the codes have been develope orden di predico rt t velocit temperaturd yan e field separata n i s e subassembly with the smooth or wire wrapped pins, there are thermal hydraulic codes which allow the reactor core temperature behavior to be analyzed taking into account heat transfer and coolant interflow between subassemblies considerablA . e numbe codee th f so r permits analysinga transient behavior in parallel with the study of steady state processes. A lot of codes have been developed to calculate two-phase characteristics, as well as an efforts have been made to develop liquid metal boiling codes l instanceal n I . more sth e important inclusiofactoe th s i r n of inter-channel exchange. e difficultieTh s associated with programming caus numbea ee th e f codeo rus o t s square mesh in the area under consideration, that is a porous body model is applied. mose Th t expande successivd dan e studie developmenn so subchannef o t l codes were carrieversionn i t dou f COBRAso , COMMIX, THI-3D (USA), SABRE (UK), POUCHOK, TEMP (Russia). So, among the versions of SABRE: the SABRE-1 and SABRE-2 were developed to predict single-phase steady or transient flows in subassemblies; SABRE-3 and SABRE-3 usee D ar predic o dt t two-phase bundlesflown pi n si . 57 00 Table 2.1 Rating of the codes predicting stabilised coolant flow Heat exchange Momentum exchange Code , Convective Convective Local Integral Periphery Molecular- Heat Inter- Molecular Local Integral Periphery turbulent conduction of subassembly turbulent the pin BMP + 4- + + + + + + + + CODE [10]; _ + — _ _ _ HECTIC [11] JOTO[2] + - - _ _ _ MISTPAL[3]; _ + _ + __ - _ _ _ ENERGY [121 -1 ] - FULMIX[13] + ; - _ _ _ PACT [14] COTEC[15]; + __ + __ - — — - SWEEP [16] _ _ + _ + _ HEPA [17] - 4+ - - + + + CORA [18] - -+ - CHANG; + + — _ _ _ MORENO [19] SUPERENERGY + + _ _ + — _ _ — [20] + - + MONICAN[21 - ] - - - - Table 2.2. Ratin codee th predicf o sgt o t transient flows Heat exchange Momentum exchange N° Codes Convective Molecular Fuel pin Molecular Convective Flow divergence Local Integral Periphery Flow turbulent heat con- turbulent Local Integral Periphery Axial Transvers Pressure Friction divergenc duction drop e 1 TEMP-MIF [22, 23] + + + + •f + + + + + + •f + + 2 THINC-II [24] - - - + + - + - - - - + - - 3 ENERGY-1 [25] - + - + + - + - + - - + - - 4 ORRIBLE [26] + . - + + - - + - . - + - - 5 SAMOVAR [27] THING [1] - - - + - - •f - - - - - + •f HAMBO [5,6] MATTEO [28] 6 COBRA-KFKI [29] COBRA-II [7] TURMIX [30] - - - + + - + - - - - - + + DIANA [31] RETSAC [32] 7 POUCHOK-] 2[9 - - - + + - + - - - - + - . 8 THI-3 [33] - + - + + - + - + - + - + + 9 HOTRAN [34] - - - + + - + - - - - + - - 10 COBRA-NIC [35] - •f - + + - - - + - + - + + COBRA-IY [36] 11 COBRA-IIIM [37] - + - •*• + - - . - + - + - + + a\ o Table 2.3. Rating of the reactor thermal hydraulics codes Reference Code Approach Single-phase Two-phase Transient Procedure Country Homogeneous Heterogeneous [38] SABRE-1 PBM + + ICE UK SABRE-2 PBM + + SABRE-3 PBM + - + IMPL based SABRE-3B PBM/SUB + + on SIMPLE [39] BACCHUS 2DPBM + + Implicit, France Newton iteration [40,41] TOPFRES SUB + - + + ICE Japan [42] UZU PBM + - - + ICE Japan [36] COBRA-IY SUB - + - + ICE USA [43] 44 , COMMIX-1 PBM + + ICE USA COMMIX-1a PBM + + COMMIX-2 PBM + + + IMF [45] PORTER PBM + - - + Semi-implicit, Russia iterative [46] BACCHUS- 2DPBM - - + + ICE Germany 3D/TP [47] COMMIX- SUB - - + + iterative, Germany 2/KFK overrelaxation [48] SABENA SUB + + Semi-implicit, Japan Newton iteration [49] TEMP-MIF SUB + - + + Semi-implicit, Russia iterative PBM - porou s body subchanne- modelB SU ; l analysis e Modecodth ef o sTEM P include prediction f single-phaso s e flo n nominawi l subassembly under adiabatic (TEMP) and diabatic (TEMP-T) boundary conditions taking into account stochastic deviations of parameters from the nominal values (TEMP-M), in the event of counter directed helical wire wrapped on the fuel pins (TEMP-R), in the event of subassembly deformation (TEMP-MIF), under conditions of liquid metal boiling (TEMP- MF). The use of the codes based on the simplified statements of subchannel approach is often justified, because allowin e widgth e clas f thermophysicao s l problem e solveb o t sd withou lose accuracth tn reasonabla s i n i d yan e time inter-subassembld an , y heat transfeo t r be taken into account, that requires the calculation domain be extended considerably. References [50-54] illustrate the possibility for using subchannel codes in the combined prediction of neutron, thermohydraulic and thermomechanical processes in reactor core, as reactoweln i s la r design optimization [55]. 2.2. MACRO-TRANSPORT EQUATIONS What followe completioe dth firse th tf nsteo p includin statemene gth f calculatioo t n procedure (differential equation boundard san y conditions developmena s wa ) f numericao t l procedur r macro-transporefo t equations which mee wantee th t d stability, convergencd ean accuracy. In [49] an analogy between a subchannel approach (as well as between a porous body model) and continues medium equations was stated. Thus, in solving a macro-transport momentum, mas d energan s y equation e procedurth s f solutioo e f continuouno s medium equation appeares si applicablee b o dt finite Th . e difference procedur mose th s tei effective. The spectrum of block designs developed by different researchers is very wide - from completely explici completelo t y implicit. Basic distinctions between approachee s th lie i sh degree of momentum equation implicity with respect to time. The completely explicit block schem t everea y time widt realizes hi d more simply limitatioa t bu , f stabilitno y requiresa very small time width that results in a great calculation time. In the completely implicit design, which is perfectly stable, the time width limitation is determined by a wanted accuracy. hi predicting fast reactor subassembly the time width has to be -10"6 s for explicit schem ~10~d r semi-implicifo an e s 3 t one lase applies .i tTh faso dt t transient processest bu , require n abundanca s f timo e e step r slofo sw processes wherei e implicinth t schems i e preferable to be used. In subchannel approach the completely implicit schemes result in a very complex syste mnon-lineaf o r equation higa f sho order, with more tedious solution than in using an explicit procedure. An optimum scheme is to suppose a reasonable time step and has not-too-complex algorithm. It is of value to describe correctly effects being properly accounte equatione th n di relativd varioue san th o et s time scales: • propagation of sound, at high liquid velocity the pressure impulse time scale is about lO^-HlO'5 s; • local transport effects (inter-phase, at channel wall); • convective mixing with the greater time scale that is connected with lower velocity; • diffusive mixing sambeine th ef g o scal convectivs ea e one. It shoul e notedb d , that many researchers appl e conservativth y e difference approximation that give e morth s e precise results n expliciA . t procedure r solvinfo s g 61 momentum equation wit e direchth t time differences, central difference e diffusivth r fo s e terms and opposite differences for the convective terms have gained a wide-spread acceptance [56]. In doing so, disturbance imposed on functions is transferred only in flow direction. The semi-implicit design is used in MAC approach (implicit a pressure and momentum designs), where the pressure field is first defined, then velocity profiles [57]. Subsequent modes of the approach mentioned received the names SMAC, ICE [58], SOLA, SOLA-ICE. For example, approach ICE is involved in SABRE code [38,59]. The pressure solution must be more accurate. Code SABRE uses the variable relaxation directions in axial planes, as well as the block correction betwee axiae nth l planes that hasten iterativn sa e convergence. The semi-implicit approach restrict time sth e ste Courany pb t conditions orden I . o t r desige th n woul more db e stabl time eth lesee b widt s o t tha e s htimi n th f liquieo d passing over the mesh with the velocity of the main flow. The limitation on the time step can be removed when using implicit design for energy and momentum equations. Such approach as SIMPLE [60,61] enjoys a wide application. Every iterate in this case includes the sequential solution of momentum equation with the further correction of pressure, the mass balance to be satisfied desigo T . completele nth y implicit procedure algorithme th , f semi-impliciso t ones are often used. The completely implicit procedure IMPL based on the idea of SIMPLE is presented in [38]. 2.3. VARIOUS FACTOR THERMAN I S L HYDRAULIC ANALYSI F REACTOO S R CORE General insights. Thermal hydraulic analysis of reactor core is performed in three steps (Fig. 2.1) [62], we find: • coolant flow distribution over the core; • flow rate and coolant temperature over subassembly cross section and with the length; • temperature distribution in separate pins. The input data are geometry, variation in power production with the core length and acros coree sth , flow rate throug coree hth , coolan structurd an t e properties maie Th .n factors controlling temperature behavior (deformation of pins and subassembly cover, power production in reactor core), in their turn, depend on temperature behavior in the reactor core. Thus e probleth , reacton mo r core temperature behavio s conjugati r e probleth o t ef m o deformation of the core units and power distribution (neutron-physical calculation). Predicting reactor core deformation is a very combined problem that, as a rule, also is divided inte stageoth s determining deformatio e cover th bundl n f pi o n, d separat an e e pinse Th . ensuing iterative procedur possibls ei predico et t temperature behavio fasn ri t reactor elements taking into account their deformation (Fig. 2.2). firse Th t approximatio inpue th take e f b tn o tha dats y na f nomina o tama l geometry. The main block involves neutron-physical part, prediction of coolant flow distribution over coree th , thermal hydraulic analysi f separatso e subassembly, wrapped estimatioan n pi r f no deformation. Using the data found, the thermal stress in the wrapper and pins are determined. e procedurTh s repeatei e d unti e convergencth l e condition e metb o r examplet s, fo r fo , criterion of normal performance. Predictions based on the pattern outlined allow the changes subassembln i y geometry temperaturn i , e behavio performancn i d ran cor e th ef eunito e b o st followe campaignn di . 62 Selection of Total power throttling zones productioA S n i Total subassembly Flow rate through Coolant temperature Wrapper tube pressure drop separate th A eS in subassembly temperature Headers Subassembly path Coolant temperature pressure drop pressure drop distribution Subassembly over the channels geometry Pin bundle Velocity distribution Subassembly pressure drop ove channele rth s Thermal mixing performance T factors Hydraulic Spacing grids mixing factors pressure drop Inlet velocity Internad lan distribution Local temperatures of edge channels pin cladding and fuel pressure drop Velocity Local heat distribution transfer over the channel Local temperature irregularities o\ u» Fig. 2.1. Thermal hydraulic analysis of reactor core assemblyofan type. Total power Total coolant flow Properties of structure of reactor core throug core hth e and coolant Nominal geometry Neutron-physical Flow rate through Thermal hydraulic Wrapper tube Deformation of subassembly analysis the subassembly analysis of subassembly, deformation bundln pi f o e wrapper tube, pins and individual pins Stresse wrappen si r tube, fuel pinsubassembld san y performance Fig. 2.2. Scheme of combined analysis of reactor core taking into account fuel pins deformation in campaign Flow distribution over reactor core based on the statistic estimation of temperature behavior taking into account mixin d deformationan g e maiTh .n input parameter n predictini s g flow distribution over reactor core powe ar ed geometrica an r l characteristics of subassembly and their variations in campaign. In fast reactor design, as a rule, the problem on maximum coolant temperature is solved with the nominal performance of reactor core in mind. The most simple approach is the flow distribution based on the uniform temperature distribution through the subassembly. The drawback to the approach is an incomplete using a thermal possibilities of subassembly of a lesser power. Another procedure starts fro same mth e margin til allowablo t l e valu determininf eo g parameter examplr fo , e till to maximum pin wall temperature [62-66]. If the power production varies in campaign, so called distribution with envelope is used [63]. This procedure assumes that coolant flow throug e subassemblth h y doe t changno s n campaigni e e commoTh . n limitatioe th f o n procedures indicated is an incomplete consideration of engineering and operating parameters' variation. Prediction of flow distribution based on the estimation of maximum pin temperature, with regard to so called hot spot factors, ignores inter-channel and inter-subassembly exchange wels ,a mutuas la l correlatio parametersf no , wit randoe hth m deviations being small s comparea d wit nominae hth l ones [67-69] doinn I . , temperaturgso s estimateei e on n di point, where the maximum temperature occurs. But, to provide a reliable design of reactor core areal ,al s with high temperature considerehave b o et leastt da thin .I s event, inter-channel and inter-subassembly heat transfe reacton i r takee b ro nt cor s inteha o account. Subassembly performance is limited by that the maximum pin temperature (having regart spoho t o dfactorst ) shoul t exceedno d value prescribe variour dfo s steels wels i t o I .t l bear in mind, that this criterion do not completely reflect conditions of nominal performance of the pins. It is evident, that such a factors as maximum azimuthal non-uniformity of pin temperature s pressura , f fissioo e n gas n wal, pi leve lf o swellingl , deformatioe th f o n subassembly shoul n wrappeo o takee s db pin d d nan rs an into account generan I . l casee th , criterion has to be combined. Thus, an allowable temperature of the pin is expressed as a function of other limiting parameters: tnmit=f(steel properties, At^,p...) (2.1) where At? - maximum azimuthal non-uniformity of pin temperature, p - fission gas pressure. Thermal reliability is governed by the number of allowable failures (pin's destructions) occurring in a separate subassembly. If the possibility of pin failure does not exceed p0, that the possibility the pin temperature in separate subassembly does not exceed P0: W" > tlimit) Statistic evaluatio f temperaturno e z'-tth hn ei subassembly allow t valuee no sth , / s exceeding allowable valucalculatede founde b b o efactot e o t th :o d f r an , (2.3) 65 where /,„/,, -core inlet temperature, Atl - mean coolant overheating in the /-th subassembly, F- geometry, Pe - Peclet number based on the mean velocity, t - mean coolant temperature, (q""1* /q) - non-uniformity in power production over the subassembly cross section. It shoul notee db d that statistic analysis allow inter-channen sa l heamasd an t s transfer being responsibl temperature th r efo e behavio subassemblye th n ri takee b o nt , into accountt I . also allows for various deviation of parameter from nominal distribution [70]. Coolant flow rate through the subassembly at the given inlet temperature is limited by the following relationship: 3 max rj ~Q,N, (2.4) wher -numbeL eN subassemblief ro zon -maximuh , t Q - i e; e th n smi power production ua in the /- th zone; KQi = (Q^ / Q°) - factor describing the rise in power production in campaign (inde » mean «o e xbeginnin th s f operation)o g (G™'"= G / K G°)- ; factor describin reductioe gth coolanf no t flow throug subassemble hth /-te hth zonen yi ; a,=(t t,- n iet) / ((' -1miet) - factor which accounts the change in allowable pin temperature as compared to the temperature under ideal conditions; J5,=K,° -factoK, / r whic , hvarie K show n w i s ho s campaign. Maximum overtemperatur coolane foune b th f followsn s eo da ca t : 1 "Ar"' core** =• limit' (2.5) K wher e-subassembly zoneh y -t numbe/ .e th n ri Relationships (2.4 (2.5d )an ) indicate that change powen si r productio cooland nan t flow though subassemble tth y caus increasn e a temperatur e th n ei e non-uniformity, that results lessee inth r possible coolant temperatur zone th en e i unde r consideration. allowabln Ia f e temperaturn valupi f eo e talhw gives i less na s than limit temperature tlunif> the optimal reactor flow distribution is calculated as follows on the basic of the maximum thermal reliability of the most loaded subassembly: K/- K, G,r = (2.6) K. P, 66 .^••^ *s // //s"' /i f \N\ / V _ _ - - / N R a) start end of campaign max COV max 0 t °C 680 COV Fig. 2.3. Power production and radial temperature behaviour (a) and distribution ofpinsover subassembly overand core (b) having (c) no regard "hot spot" factors; 1 -mixing is absent, 2 - mixing available, 3 - optimal throttling having regard "hot spot" factors, 4+6 - similar to 1+3. 67 where max ip.-ir^atf, (2.7) ' allow here Atallo tw]imi= t- tinlet . Average coolant heatin varioun gi s zone calculates si : das K°KQ, IP, K , r (2.8) K G, At the given total flow rate the optimization of flow distribution (2.6) allows the thermal reliability of the reactor zone to be enhanced. In this event, the pin temperature m< compatible wit conditioe hth foune b : n t( wdnas P ca t limit"> P < ) K, max „ KG, 'limit inlet~~ (2.9) As statistic estimations of pin temperature behavior in reactor, taking into account inter-channe inter-subassembld an l y heamasd an t s transfer s showha , optimizatioe nth f no flow distribution over reactor carried out in the procedure mentioned above could result in the more flat temperature profile than those conditioe baseth n do n when maximum temperatures mose ofth t loade same dth pinvariou n ei e sar s zone reactof so r (Fig.2.3). Statistic estimatio temperaturf no e field implies tha temperaturseriee ta th f so e field elements is defined using stochastic distribution of input parameters followed by statistic processing (to find mathematical expectation, variance and distribution function). The stochastic distribution of parameters in the specific case can be found from the distribution functions deduced from experiments or analytical studies (for example, [68, 71]). In calculating the global parameters, such as flow rate throughout the subassembly, total power production, sizes and local parameters, such as pitch-to-diameter ratio, pin diameter, pin wall thickness, powe distributee r ar productio n pi e randon dth i f no m manner t shoulI . e db noted, that in the event of subassembly deformation in campaign the distributions of input geometrical parameters hav significantle eth y greater variance than thos nominan ei l bundle [72]. Thermal hydraulic analysis involves the subchannel procedure. The end of calculation means the convergence of mathematical expectations of coolant temperature, maximum pin temperature and non-uniformity of pin temperature. As a result of analysis, distributions of temperature characteristics are determined, too. 68 Code TEMP-M (regular flow throughou e reactoth t r core) [73] allows securing stochastic and averaged temperature characteristics to be defined in fast reactor subassembly. Since the reactor core follows the sizable shield and gas space, the coolant flow in reactor core is regular under nominal operating conditions. Distributions of coolant velocity and temperature over the channels result from the solving the system of momentum and enthalpy equations which (onc pressurea bees eha n exclude, tha possibls i t regulan ei r flow) appeas ra (see [74, 75]): in internal channels (2-10) .5/4 LIT. - (2.11) in edge channels w™ -Q.-; (2.12) 2 W. + W. dZ^ ' ' k=\ (2.13) inter-subassemblye cetth on i p ga (2.14) dZ 69 where A, =< = 0.3167 £e025; - typica17 , q l, scalew , hydraulir wo dho,sfo c diameter, channel area, coolant velocity, heat flux, heat removal perimeter, respectively betweep ; As- ga - tJL channel e ; nth j d an si subassembly length; ^ - heat mixing factor; ^ - mixing factor due to fuel pin thermal conductivity. Mixing factor u^, jac, u.x , u(^ are defined as presented in [49]. The fuel pin wall temperature is calculated using procedure indicated below. Temperature of subassembly wrapper as viewed from the edge channels is predicted as follows: --i Niip 6' (2.15) A. Uhf> JY«£ Uhp where t, - coolant temperature in the edge channel, t% - coolant temperature between subassemblies; Nup , Nu% - Nusselt numbers in the edge channels and between subassemblies, respectively; Af , /I - thermal conductivity of coolant and wrapper tube, dhp - hydraulic diameter of the edge channel; 8 - inter-subassembly gap, S' - thickness of the subassembly wrapper. Temperature differenc wrappee writtee th b n n eo : nrca as • 1 - X8 X rf,•' t ______*^ ______I ______1 1 _ _.______'kj- 8 Nup "kj- 5 Nu^ System of the macro-transport equations for momentum (2.10), (2.12) is solved by introducin tim e cFo,I g, th e tercW wherFourie- m ( o F e r parameter explicin )i t procedure. Also, explicit procedure is applied for solving energy macro-transport equations (2.11), (2.13) and (2.14). The code is built up on the block principle. The subroutine RNDM (generator of random numbers uniformly distributed between 0 and 1) is used, distribution of power over the pins is governed by normal law [76]. Prediction TEMP-n so M were compared wit date hth a gaine fase th t n reactodi r out-of- pile experiments with a good agreements between velocity and temperature distribution over subassemble th y radius (Fig. 2.4). Velocitie temperatured san edge th en si channel agree sar e wit accuracn (Figha % .10 f 2.5)yo . Here n influenca , f inter-channeo e l exchang s verei y noticeable. When predictions on TEMP-M are compared with experimental data [79] for the pin bundle with non-uniform power distribution in subassembly cross section, it is apparent that varianc s aboui e t 0,8%s gooA s thi.a d s resul s connectei t d wite morth h e full 70 At o-o-o- 0,8 0,6 I___I 01234 01234 try-rt)/r0 a) b) Fig 2,4. Radial distribution of coolant velocity (a) and temperature (b): A -, O - experiments, —— - mixing is available, mixing- — —absent.— is •H -H .0.5 o.5 1.0 erp 0.5 1.0 (We/Wi> a) b) Fig.Comparison2.5 of predictions experimentsand for velocity (a) coolant temperature (b) in edge and internal channels of the model. 71 b) C) Fig. 2.6. Schematic diagram of lateral (a) and axial section of deformed subassembly distributionand c) (b, of maximal temperature claddingofpin middlethe in cross sectionof PHENIX reactor (d). 72 mathematical statement in comparison with other codes (see Table 2.2), as well as with the careful analysi inpuf so t constants. Predictions of temperature behavior in BN-600 core subassembly in the event of non- uniform power distribution over the cross section have shown that variance estimated having regar inter-channeo dt l exchang orden i founs e ei b r leso dt s than those evaluated without regarding for inter-channel exchange (variance procedure). Code TEMP-MI predico Ft t thermal hydraulic deformen i s d subassembliesn I . the special case that subassembly is subjected to deformation in campaign a coolant flow is of irregular character, wite bundlth h e flow being practically longitudinal (quasi-stable). Predictions have shown that even in case of large deformation (when pins bending is so great that compact channels are formed) the transverse component of velocity does not exceed about 30% of axial component and pressure out-of-balances for a length not more than (0.1 -^ . Thusdh 0.2) , macro-transport equatio f momentuo n n transversmi e directioe b n ca n approximately written as p, - PJ = cy *wtj or substituted by the relationship p=idem (hypothesis of isobaric flow), with the value \vy being determined from the mass equation. The feature of thermal hydraulic analysis in deformed subassemblies is also that the transverse mass transfer due to centrifugal effect is taken into account in the channel when bending assuminy B . g that transverse centrifuga o flowt e sdu l balancn effeci e ar tcentra n ei l channels, it is easy to verify that specific momentum and energy fluxes (Fig. 2.6) are in proportion wit transverse hth e flow: (2.17) wher donor-channeindee - th * e* f x o . l t, if H£ > 0 0 > £ H f i A, > Having performed the needed transformations for the purpose to exclude pressure and assuming p=const subassembln i y cross section [22] fine macro-transpore w ,dth t equationn si isobaric approximation: —————•= 2w, -M< u w s—— ————— / ; I~~ [+ l~— '— . £ dI w Iz— w s/ 8 11( ,=, y 2 v ; *; co i/CO. ——— (w** - w. fe - -7———— "Z^ (2.18) D ( l j / ( v 2 •*» x^ / ;=I ' ife - w , zV 73 (2.19) W., •_ly Ay w j w - hI / \ ] W< ~2^"'y / W (2.20) l f 3 * i\( 1 f = f '-oKH X *' 2^'*• y=lL y=i In (2.18 (2.19d )an hydraulie )th thermad can l mixing factorcentrifugao t e sdu l effects ca expressee nb : das _ w CD (2.21) h w Local mixing convectivfactoro t e du s e exchang moleculad ean - turbulenr t diffusion formse th n i , e respectivelar y (2.22) wher - coefficien a e t considering mutual relation between convective exchangd ean M T molecula - turbulenr t diffusion. Three parameters //,_ e definebasi, e /Jar ,th V f a co ,n o d [76,74,81]. From momentum balance written for the gap between channels we can write the following relationship for the mixing factor due to centrifugal effect, 1/m: 1143 / \0$7 0143 s/d-l 1.5= ' 8Re l 1 S 1 (2.23) 2V3, o UJ d L n Wd' \ wher curvatur- v eR e radius. Coefficient of non-equivalence between heat transfer and momentum transport /? may be though beins a f to g deformeaboun i 7 t0. d geometry. basiThene th (2.21f cn o ,o have )w e u=0.7T= uM (2.24) 74 evaluateds wa t i s thermae A ,th hydraulid an l c mixing factorcentrifugao t e sdu l effect can achieve some unites. hi the event of pin out-of-roundness, that may be responsible for the significant decrease in the width of inter-pin clearance, the transverse convective flows is more intensive than those evaluated with the averaged parameters of pin bundle. For example, the limiting degreout-of-roundnese th f eo s attended wit pine hth s touch each other result value th f n eo si thaf o t % define40 d using averaged parameters: lsy. (2.25) Onc havu eyo e decided upo averagee nth d parameter subassemblf so reference th s ya e one shoult i , introduce db e correctio e out-of-roundnessth n no : (2.26) where correction factor^' is determined as follows: (2.26a) Macro-transport equations are also supplemented by the equations for the cells chosen in the gap between subassemblies. Velocity and temperature boundary conditions are given at bundle th e inlet. System (2.18 d (2.19an ) e explicis resolvei )th f o te dfinit us wit e ehth difference approach. Code TEMP-MIF was verified on experimental data on temperature behavior in the model bundle being exposed to deformation in the edge area under conditions of uniform power distribution over the cross section, as well as under conditions of strong coolant flow throug e clearancth h e between subassemblies. Thera goo s i ed agreemen f coolano t t temperature distribution ove outlee rth t cross section. Let us demonstrate the possibilities of the code on the example of PHENIX subassembly deformation (Fig. 2.6), when the pin bundle and subassembly wrapper are bended (Fig. 2.6 - 2.6a). First of all, the rearrangements of collant flow and temperature are observed. Coolant passing close to the sides with the lesser distance from the edge pins becomes more heated and significantly subheated near the opposite sides. Predictions show the large temperature waln enhanced pi an lf so d azimutha temperaturn lpi e non-uniformitn yi the event of the channels are formed close to compact ones (Fig. 2.6-a,d). Comparison of mathematical description of the TEMP-MIF and those for other well known codes indicates the more complete account of mechanisms of momentum and energy exchange (see Table 2.2) and the more plausible predictions on this code. CONCLUSIONS 1. Subchannel analysis being the most effective procedure for predicting thermohydraulic n fasi s t reactor subassembl s receiveyha d much attentioe th f o n authors. Recently analysis of the codes available was performed; spectrum for use was 75 determined; the most promising codes that answer modern needs were selected, with the rating. It has been shown that subchannel codes have gained a wide-spread acceptanc practicn ei t onl eno predictinn yi g single-phase flows t undebu , r boiling conditions. Some generations of subchannel codes developed in such countries as Russia, USA, Germany , FranceUK , , Japan diffe governinn i r g equations, methodf so their solution, and, respectivel intendee yar differeno dt t problem tacklede b o st . 2. At the SSC RF IPPE some versions of subchannel codes GID and TEMP were develope predico dt t thermal hydraulic fasn si t reactor subassembly. Complex TEMP includes predictio f singlno e phase flo nominan wi l bundle geometry under adiabatic (TEMP) and diabatic (TEMP-T) conditions at the wrapper, having regard to accidental deviation of parameters from nominal values (TEMP-M), in the event of the pins are space counter-directey db d wire wrap (TEMP-R) deformen i , d subassembly (TEMP- MIF), under transient conditions accompanied by liquid metal boiling (TEMP-MF). 3. The validity of the versions of TEMP has been demonstrated in predicting flow distribution ove reactoe rth r core base statistican do l determinatio temperaturf no e field having regard to interchannel exchange and subassembly deformation. Statistical analysis causes the temperature field to be more smooth, than those predicted from the criterion on equality of maximum wall temperature at maximum loaded pins (taking into account hot spot factors) in various zones of reactor core. The potentialities of code TEMP- e illustrateMar n predictini d g distribute d averagean d d temperature characteristics of several adjacent subassemblies. The more complete mathematical descriptio f TEMP-no mord Man e careful analysi f closino s g correlations leado t s more accurate prediction compares sa d with experimental data advantagee Th . e th f so code TEMP-MI s Fshowexample i th y n b f temperatur eo e distributio deformen ni d subassembl PHENIXf yo . REFERENCES [1] Zernic , Elyat, CurriB. , W. 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Nuclear Reactor Designing, M., Energoizdat, 1982. [65] Usynin G.B., Kusmartsev E.V. Fast Breeder Reactors , Energoatonizdat,M. , 1985. [66] Waters A., Reynolds A. Fast Breeder Reactors, M., Energoatomizdat, 1986. [67] Kleomin A.N., Polianin L.N., Strigulin M.M. Thermal Hydraulic Calculation and Technological Realibilit Nucleaf yo r Reactors , Atomizdat,M. , 1980. [68] Kurbatov I.M., Tikhomirov B.B.. Estimation of Random Temperature Deviations in Reactor Core. Preprint IPPE-1090, Obninsk, 1980 (in Russian). [69] Carelli M.D. Hot Channel Factor for Rod Temperature Calculations in LMFBR Assemblies. Nucl. Eng Des.d an . . 1980. 62 . ,v [70] Zhukov A.V., Sorokin A.P., Ushakov P.A., et al. Statistic Estimation of Fast Reactor Core Having Regar Deformatioo dt Campaignn ni . Preprint IPPE-1845, Obninsk, 1987 (in Russian). [71] Bogoslovskaya G.P., Zhukov A.V., Sorokin . CalculatioA.Pal t e . f Statistio n c Temperature Characteristics in BN-600 Subassembly Using Monte-Carlo Procedure. Preprint IPPE-1376, Obninsk, 198 Russian)n 5(i . [72] Tikhomirov B.B., Savitskaya L.V., et al. Models of Statistic Estimetion of Radiative Deformations. Paper on French-Soviet Seminar "Problems of Reactor Core Thermal Hydraulics", Cadarache, 1986. [73] Bogoslovskaya G.P., Sorokin A.P., Tikhomirov B.B. et al. Code TEMP-M for Thermal Hydraulic Analysis of Fast Reactor Subassemblies. Preprint IPPE-1401, Obninsk, 198 Russian)n 3(i . 79 [74] Recommendation n Thermao s l Hydraulic Calculatio f Fasno t Reactor CoreM PT . 1604. 008-88. State Committe n Nucleao e r Energy , ONTM. . I IPPE, 198n (i 8 Russian). [75] Zhukov A.V., Kirillov P.L., Matjukhin . N.MThermaal t e . l Hydraulic Analysif o s Liquid Metal Fast Breeder Reactors, M., Energoatomizdat, 1985. [76] Knut D. Art of Programming, M., MIR, 1977, v.2. [77] Zhukov A.V., Sorokin A.P., Ushakov P.A. et al. Influence Interchannel Exchange on Velocit Temperaturd yan e BundlesFieldn Pi n si . Preprint IPPE-1062, Obninsk, 1980 (in Russian). [78] Sorokin A.P., Ushakov P.A., Yuriev Yu.S. Influenc f Interchanneo e l Exchangn o e Velocit Temperaturd yan e BundlesFieldn Pi n i s . Problem f Nucleao s r Sciencd ean Engineering. Physic Eng.d san (41),4 , 198 Russian)n 4(i . [79] Markley R. A., Engel F. C. LMFBR Blanket Assembly Heat Transfer and Hydraulic Test Data Evaluation. Thermodynamics of FBR Fuel Subassemblies under Nominal and Non-nominal Operating Condition. Summary Report, Vienna, 1979. [80] Kirillov P.L., Zhukov A.V. Modern Methods of Thermal Hydraulic Analysis of Reactor Subassemblies. Text-Book, Obninsk, OINPE, 198 Russian)n 8(i . 80 Chapter 3 NOMINAL SUBASSEMBLY THERMAL HYDRAULICS 3.1. FRICTION FACTORS Bundles of smooth pins. Laminar flow. Friction factor is defined as: 64 K — = ^ (3.1) Re wher valuee fore eth th m f s o factoindicate e ar Tablaccordance n i rK th 1 n dei 3. e with the data [l];Re = (\v*dh)/v is the Reynolds number based on the mean velocity and hydraulic diameter of "infinite" pin bundle. Table 3.1. Values of factor Klam in laminar flow through the smooth bundle Type Relative pitcd s/ h, bundlf o e l.O 1.02 1.05 1.10 1.20 1.30 1.40 1.5 2.0 Triangular 0.407 0.663 0.966 1.274 1.56 1.715 1.834 1.940 2.46 Square 0.406 0.518 0.679 0.913 1.264 1.510 1.699 1.858 2.51 1.0 Fig. 3.1. Relative hydraulic resistance in the bundle of smooth pins with the pitch-to-diameter ratio: —— - relationship by the authors, 0 , o, 0 , 0 , 0 , a -experimental predictions- ••— — , oj'other •— — authors , data, (A—— - hydraulic resistancec in compact bundle (S/d = 1.0) 81 Turbulent flow. Considerable recent attention has been focused on the analysis of a rich variety of the data accumulated on the friction factors in "infinite" bundles of smooth pins that results in the following simple relationship [2]: - ' 0.21'°0 32 (3.2) Re 025 1.0 Transition from lamina o turbulent r t flowe followinTh . g e relatiob n ca n recommended: _ - 2.3+ 5 2 =5. (3.3) The same formula describes friction factor over a wide range of parameters (10 < Re < .5)1 , < wit d accuracn hs/ a < 0 . y1 ; bein5 0 20%1 ± g* 2 . When arrange squarn di e bundl pine eth s produce resistanc accordancn ei e wite hth well known relationship: = 0.5 0.9+ 1 9((s/d) 10.52J- ) + 1exp[- - lo((j/rf )1)]- } (3 .4) 0.3 1 6 Re~025 1.0 Wall channel subassembld san wholea s ya . Friction factor n laminai s d turbulenan r e expresseb t flon ca w d througe th h geometrical parameters XL and %T, respectively [3] : -0.8 (3.6) Experiments have shown that parameters relateXe d XTLar an eaco dt h othe: ras lr = 1-^ (3-7) 0.25 < xt < 1-25; 0.45 < xr < 1.2 Fig. sho3 3.2 value3. e w, th f parameterso s concerning fast reactor subassemblye Th . wall channels are considered here and an influence of the pin number on these parameters is demonstrated. 82 Fig.Coefficient3.2 schematicand elements ofBN-600 subassembly (S/d =1.166, =0.1045):m/d %L = 1.030; XT = 1-023 (a) XL = 0.603; XT = 0.703 (b) 4,71+ 7,504(3- 2 3 9 0+ 9,42 2 5H6,425(~H)+23,36I 5 3 n 3£L aeT \ 7 0,774- 0,830 2 9 0,982 0,987 3 37 4,059 1,044 4- 6i 1,098 1,073 5 91 1,120 1,090 3-1 -X 6 127 1,135 1,10-1 7 • 169 1,145 1, 109 8 217 1,152 1,114 9 271 1,8 15 1,119 10 331 1,163 1,122 m H 397 1,166 1,125 Fig. 3.3. Coefficients*'L and*T for pin bundle of BN-600 type: - number J of rows, number- n of 0.1045.1.166; = = pins, S/d m/d 83 Bundle wirf so e wrapped pins. When in laminar flow in the bundle of wire wrapped pins, friction factor can be evaluate: das 64 = —0.407 1 + (3.8) Re\ (h/d) 7.725 2 3 In turbulent flow analysi date friction th ao f so n facto triangulan i r r bundl pine th sf eo spacehelicae th y d b ltype wirth ef eo "fi n touchewalln s pi cause e "ha followine sth dth g formula for the infinite pin bundle [2]: 0.210 124 (3.9) 1.0 The formula is simple in structure, with passing on to (3.2), if s/d = 1.0. It is in agreement wit experimentae hth l data [4,5] wit accuracn ha 15%± f yo . To predict friction factor exactly, but in the lesser range of parameter h/d, the following formula is recommended [2]: ^p = l + f(h/d)-( /d-l)Re°'m (3.10) X, S where f(h/d) = 30.3956 - 4.591 l(h/d) + 0.24308(/2/W)2 - 0.0042955(/z/W)3 <1.5; 8.0 A is defined by the (3. 2). Relationship (3.10) agrees with the experiments [4.5] with an accuracy ± 10%, but improves formulas recommended in [5,6] (Fig. 3.4). It, as relation (3.9), makes possible going to the compact bundle of smooth pins. It is interesting to notice that experimental data generalized by the well-known Novendstern's formula [6]: 5 -lO88 _ 0.3164 1.034 "•- Re 025 1.06 lie in the range ± 30% (at least at great Re), that is worse than ± 15% indicated by the autho publicatiof ro n [6]. 84 ~ P»CMSTHOE AD '10 , T 4 1, 2 1, 0 1, 2 0, 3 0 0.1 +6 0. Fig. 3.4. Comparison of predicted hydraulic resistance' with experimental data by different authors. Markley R.A. presented the following relations: laminar flow 110 A* p —- (3.12) Re (2 transition flow 110 0.48 (3.13) Re' Re0'25 (2 where \\i = 0.22 • 10~3 (Re- 400) 85 0 Fig. 3. 5. Relative hydraulic resistance in the bundle of wire wrapped pins. turbulent flow 048 0.25 (3.14) (Re 5000;> 1.067 For the BN-600 fuel subasserably the following formula was derived by the authors fro in-pile mth e measurements: 0.25 (3.15) roughnese surfacen th wher pi s i e - th .e f A Rati so o show s i A pA / Fig.3.5n i . Also in the transition flow it is recommended that the following relationship be used: + X»(l-c) (3.16) where Ap/ am- frictio n bundlfactoe th n i f rwrappe eo d pin laminan si r flow defininy gb (3.8), Ap - friction factor in accordance with (3.9). 86 Parameter e can be determined as: e = 0.5 1 - th 0.801 — -r-lj (3-17) [ I ^1.45- 103 JJJ V An accurac relationshie th f yo p (3.16 abous )i t 20%. In the event the pin spacer is performed by the "fm-to-fm" type of wire wrap, the friction factor adheres to the relations [1 J: laminar flow (h/d)] (3.18) (s/d varies from 5);1.131.1 to turbulent flow d-i) <20-10 where n is the number of entries of the fin. Inclined flow throughou bundlee tth . In triangular bundl frictioe eth n factor depend slopee th n :so = sin*2 where Apd -2 ——=Y h ~ is the friction factor in longitudinal flow, r =2~ is the friction factor in transverse flow, /Pw velocit- c v/ = y averagew d ove bundlee rth fre- v , e flow velocity porosity- e , . 87 oo 00 15 456 8 ' 110 0 8 6 5 A 3 3^56 Fig. 3. 6. Comparison of experimental data with predicted on universal Prandtl velocity in deformed bundle. Transverse flo triangulan wi r bundle. Friction facto determines i r d wit accuracn ha y ± 20% as: -0125., (3 14 to"022-042) (3.21) where parameter Kp account influenc n / -entriea r e sth fo f wirf eo so e wrap wite hth pitch h;x = s/d - relative pitch of the bundle. -2 (3.22) Distribution of local velocity over the bundle (smooth pins). The basis for the calculation of velocity in turbulent flow is distribution of shear stress around the pin which is used when universal velocity profile is defined ( for the bundle of smooth pins at least). The use of universal velocity profile for the bundles of as nominal and deformed geometry was warranted by experiments [8,9]. practicn i Foe e mosus r eth t simpl rathed an e r precise relatio Prandte y nb b n ca l recommended: U+=y+ forO Figcompare6 3. . s relation (3.23) with experimental data [10] gaineinternae th n di l channel of the fast reactor subassembly model under deformation. 2 CLASSIFICATIO3. F INTER-CHANNEO N L EXCHANGE PROCESSED AN S EXPERIMENTAL TECHNIQUE Inter channel exchange (mixing) is the process when the coolant flowing in the parallel channels exchanges by liquid portions, that causes the temperature difference between the channel reduceo st . Clearances betwee pine nth s joinin channele gth s int unifieoa d system assure generally an exchange by mass, momentum and energy. Among the main mechanisms are convective transport, turbulence diffusion and molecular transfer (electronic one in liquid metal). Classification of inter-channel exchange processes. Natural and forced mixing are recognised. In its turn process of natural mixing can be subdivided into turbulent exchange and lateral diversion flow, induce pressure th y db e gradient when flowing unde t steadrno y 89 conditions (entrance section departury b r )o geometrf eo y fro nominale mth . Forced mixins gi associated with the coolant flow due to special mechanical means (wire wrap, spacer grid and so on). It can be subdivided into dissipation flow and spin one. The first mechanism is governe e meanth t responsibly no b sd a directiona r fo e e enhancemenl th flow t bu , f o t turbulence (spacer grid, end pieces and so on). Spin flow is due to means setting up directional flow (helical wire wrap). Non-uniform temperature distribution over the pin brings into existence the heat flux be redistribute perimeten d pi ove e rth r definin more gon e mechanis f inter-channemo l energy exchange due to heat conduction within the pin. In the event of the coolant passing the clearance between subassemblies, the heat exchange due to wrapper heat conduction occurs. Mixing factor can be identified in a accordance with the transported substance. Having considere e masdth s transfer s defina t le e, mass mixing factorse , th m" s a 1, ratio between transverse mass flow, accounteunie th t y lengtsloe b r th t d f fo channelh o d an , the full axial flow. M V. =G9/G,. (3.24) where GtJ is the transverse coolant flow from the channel i to the channel/ per the unit length e axiath 3 /m*sm s l,i coolan, G ; t flow throughou e channeth t , m/ ln suc 3I /s. ha definitio mixine nth g facto hydrodynamicas ha r l meaning. Having written a quantity of the heat transferred from one channel to another in the from Q = G Azih — h I , we obtain the thermal mixing factor: (3-25t-, ic\) that shows what fraction of the enthalpy difference between the adjacent channels the transverse heat flux wil. lbe When solving momentum equation, it is important to know the value of momentum mixing factor determinin followss ga : (3.26) momentue th s i n d m / transferreW )d T V gradienwhery + db v p( e t mechaniso t e mdu molecular frictio small-scald nan e eddies momentue th ;s i pW'Vm transfe largeo t e -du r scale eddies ( W- velocity pulsation in axial direction, V- large eddies velocity pulsation around the channel perimeter); a>y - area of the clearance between the channels i and j; CD, - 90 the channel cross section area; W = \Wl+WJ\/2 - mean velocity in the channels / and j. It should be noted that (3.26) is written for the bundle of smooth pins. The mixing factor, obtained by this means, shows what a fraction of momentum difference between the adjacent channels represent transverse sth e momentum flow. n speaca e k w abou , e massSo th t , momentu energd man y (heat) mixing factorsn I . general, these factors vary in value. It is essential that mass and heat mixing factor can be measured in experiments, but techniques for momentum mixing factor are unavailable. From assume herw n eo e tha mase th t s mixing facto momentue equas i rth o t l m mixing factor (jj.= m ///,) and use hydrodynamic and thermal mixing factors. The specific mixing factor representing ratio between the transverse and axial mass velocity is: G co co. ~ — (3.27) \vz s — aG s — As for the local and average mixing factor [11,12], it should be noted that periodical (for example sinusoidal) variation in local mixing factor (wire wrap on the pin) [12] the averag lengtn e pi ove e hrth facto defines ri »h):z ( s da 1 A/z ,2n 12 »'-»'=2 amplitude whereth s locai e th :A f le o mixin g factor variation wire th es i wra ,h p pitch. Resul divides i t becaus2 o dt suggestioe eth mads nwa e abou unifore th t m exchange alone gth clearance between pins (discrete rectangles resulting from the averaging sinusoid half-periods are replace equivaleny db t continuous rectangle). Generally dimensionless mixing factor depend relative th n so e pitch (s/d), pitcf ho helical wrap (h/d), Reynolds and Prandtl criteria, number of fins (7) and their geometry: \nL = f(s/d,h/d, Re, Pr, Tp, j), (3.28a) where Lisa some linear dimension criterioe th s i p nF , involving geometrical features finsmose e ofth Th . t essential parameters effecte mixine dth g chose e factoth t (a rn e typth f eo wrap) are : bundlee pitcth f ho ,wra e pitcReynoldd th pf an h o s number influencn A . thesf eo e parameters are discussed in detail below. Mixing factors are required to close system of mass, momentum and energy conservation equations accuracn .A predictione th f yo s performe appreciabls di y definen a y db accurac numericae th f yo l relation mixine th n so g factors. Being correc evaluatinn i t g mixing e necessarth f o e y on condition t factorme r fase fo w sst reactor subassembly thermal hydraulics. 91 Effective (combined) mixing facto f rcomponentso representm su e th s . When momentum exchange considered, these are convective and turbulence transport M M (3.29a) when heat exchange considered including convective, molecular, turbulence exchange and heat transfer due to pin heat conduction: (3.29b) factoe th s i r 1 allowin wher< a influencr e gfo convective th f eo e componene th n o t turbulence one. This influenc estimatee b n eca followss da : , if uc/u°<4; (3.29c) where JU Tmixin- g factobundle th n i r e involving smooth pins. e effectivth f o ee us mixin e Th g facto s convenieni r e concretth r fo t e reactors a , allowing the temperature behaviour to be calculated (if the value of this factor is given). Also e knowledgth e componentth f e o effective th f o s e heat mixing f factopracticao s i r l importance applies A . faso dt t reactors, measurement effective sth e (total) mixing factod an r its separate components were carried out. Facto non-equivalenf ro t heamasd tan s transfer "flate Th . " mode mixinf o l g holds tha uniforn a t m temperature distribution takes place e paralleinsidth f o e l channelst bu , temperature ste s obtainepi clearance th n di e betwee channelse nth thin I . s case, transverse mass flow transfers the greatest possible quantity of heat due to convection and thermal M mixing factor is equal to hydrodynamical one (juj — JUC ) Any disagreement with the flat model (account for the molecular and turbulent diffusion, heat conduction) results in the non-uniform temperature distribution across the channe responsibls i d face an l th t r thaefo t convective heat transfe lesses i r r than those under the uniform temperature conditions. This allows entering the non-equivalence factor between energ masd yan s transfer: H^/u^p= . (3.29d) liquid n dependI d . whican Pr 1 s n < withso t f varierange h th < Pr&l n e0 si (water, gas) P«1.0 firsa s t A . approximation non-equivalence th , e througe th b facto s y a f hma o r same for the pins with the various types of wire wrapping. The effective mixing factor /4/r measure therman di l experimen responsibls i t t no r efo only convection heat bu , t transfe turbulenco t e du r e diffusio head nan t conductio f coolanno t 92 and pins, that is why the difference (/^/ T - fl*ju M) corresponds to conduction and turbulence diffusion. Theoretical analysie non-equivalencth f o s e facto s i performer n [14]i d , with experimental validatio valus it f neo presente authore th ] y db [1216 n si , ,15 Experimental techniques. An overview of methods available to detect the mixing factors with referenc accuracn a o et y performe authore th y d b presentes si ] [9 n di Tracer technique starts from recording transverse mass flo f somwo e transmitted substance (saltcategore falld th ,n an si paint ) indirecf yo on ,o s freo d t methodsnan tracef .I s ri entered into the channel / bordering three channels/, the mixing factor can be recognised from the variation in tracer concentration over the channel length ( (3.30) mixine Th g factor define thiy db s means include componente sth s being responsible for convection, turbulenc d moleculaan e r diffusion t i shoul t e noteBu b d. d that tracer techniqu t sufficientlno s ei y sensitive (expec freoe tth n technique), becaus elarga e quantitf yo tracer needs to be injected into the flow under study, that may cause the coolant flow to be distorted. This technique furnishes information on the mean mixing factors and is in common for controlling the small Prandtl number coolant. Thermal trace technique. As a peculiar kind of tracer in studying process of inter- channel exchange the heat is supplied to the coolant. Modifications of the method vary in way of energy supplying. So, in injecting coolant at higher temperature into the main flow, a knowledge of the heat released and liquid temperature behaviour along the channels allows the mixing factor to be estimated in integral form. Dissipation of hot spot from the flow injected is a transient process going on from the "entrance thermal section" law, with the strong heat dissipation into the adjacent channels. This version is applied in studying mixing under condition greaf so t temperature differences accuracn A .date th af yobtaineo d depende th n so inlet structure (hydraulic instability), on the edge region influence and others. To improve accurac favoures yi enhancemeneffective e th Th numbern y . db pi 37 e th o t leas t a ,f o p t u t mixing facto measureds i r studins a , locae gth l characteristics becomes more complicateds A . usual, liquids with the moderate Prandtl number are used as coolants. studo T integran ya l mixing characteristic technique sth usee b dn involvineca e gth power productio ninternae onlth n yi l pin, wit radiae hth l temperature distribution being measured ove bundlee rth mixine .Th g facto determines ri d fro heae mth t balance equation: qini (3.31) where U, is the heat removal perimeter. 93 This metho uses di viewinn di sectione gth remover sfa d fro subassemble mth y inlet, where considerable temperature difference between channels take place. The measurements are performed, as usual, under the stabilised hydraulic conditions. An influence of the edge regions and inlet structure on the readings shows itself as the more slight effect than in injecting. e modifieTh d thermal trace technique involvin e measurementth g f o locas l temperature distributions ove lengte rth radius d han , when onl internae heateds yon i n s pi l wa , develope e authorth y db s applie liquio dt d metal reactors [17] e maiTh . n objective th f o e modificatio provido t s i nr measurin fo e e locagth l characteristic f inter-channeo s l mixing. Mobile thermocouples to measure pin wall temperatures are embedded into the surface of turnin simulatorn gpi havinn O . g solved thermal proble coolane mth t temperature distribution along the channel is defined. The local mixing factors are put in calculation, and when varying value f mixino s g n gaifactorca n e goow s d agreement between predictio experimentd nan . Coolant temperatures measure outlee th t da t allow integran sa l (effective) mixing factore b o st determined. This techniqu developes ewa d als applies o a bundle th o dpinf t e o s with spacing "fin- to-fin" thin I . s case, temperature measuree sar mobile th y db e thermoprobes moved insidf eo the pin simulator as in axial and in azimuthal directions. Electromagnetic technique. The problem of evaluation of a "pure" convective component of mass exchange providing the local measurements is of great importance. Separatin convective th t gou e components fro totae mth l mixing factor allow procese sth f so interchannel exchange to be expanded, an influence of this component on the main parameters to be defined in experiments. The local character of the measurements permits a nature of the process to be studied, departure of integral characteristics from the local readings to be defined. Electromagnetic techniqu capabls ei meetinf eo requiremente gth s mentioned above modee th in-pil d n i lan s a e experiments [16,18]. As noted above e techniquth , f s electromagnetibuili eo e t us upo e nth c sensors involving one or two magnets inside of the pin simulator. Voltage between electrodes varies in proportion to the local mass flux. Electromagnetic technique gives the measurements being in not more 2-3% error, that is more precise than techniques mentioned above. This technique is very simple, low in cost, economic and effective, that places it among the most advanced experimental technique in studying inter-channel exchange. 1.3. INTER-CHANNEL EXCHANGE IN THE INTERNAL AND EDGE AREAS OF WIRE WRAPPED PIN BUNDLE Mass exchange. In practice, to guard against any possible bendings the pins are space helicae th y db l wire. The main component of inter-channel exchange when in bundle of wrapped pin is a convective mixing objece Th . f systematio t c researches using electromagnetic techniquo t s ei get reliable data on mass mixing factor, to study influence of the component on defining parameters, recommend relationshi hydraulin po c mixing factor. 94 b) Fig. 3.7. In-pile subassembly ofBN-350 (a) and positions of sensors (b): a) 1 - bottom flange, 2 - bottom header, 3 - body, 4 -fins, 5 -pipes, 6 - barrel, 7 - top header, flange,top seal,- wrapper- - 9 8 10 tube: VO b) 1+36 -pin number, -H-^Qr? radii- pins ofthe axises. Fig. 3.8. Subassembly model studyto inter channelex- change: I -flange, header,- 2 barrel,- 3 body,- - 4 5 fins, 6 - gland, 7 - gasket, 8 - pipes 19 0.5mm, 9 - wrapper tube, 10 - tail, 11 - supporting grid. Fig. 3.9. Model cross section: 1turning- withpin electromagnetic sensor inside, 2 -fuel pin simulator, 3 - -wrapper tube, 1+111 - specific channels. 96 e,1CTz MB 28 21 20 16 b) 12 8 Fig. 3. 10. Calibration model (a) and sensor (b): 1model- body, wrapper- 2 tube, pipes- 3 -wire4 , wrap, gland,- 5 guide- 6 barrel, displacers.8- 7 mobile- contacts, guide- 9 rod, Fig 3.11. Signal of sensor with the length of the calibration 10 sleeve- holder, -permanent11 magnet, model (a) and measurement scheme for lateral flows in the plugs,12 end -pipe 13 spaces. clearance - directions + (b), •, of lateral flows. do J2 28 20 18 12 calibration before 8 o- experimentf after experiment 0 20 60 80 100 Z JAM a) b) Fz'g. 3.72. Sensor signal with the length of calibration section (a) and signal value with the flow through modelthe (b) 500 600 700 2, MM Fig. 3.13. Lateral mass flow with length of clearance internalthe in channel of fast reactor subassembly model. 99 e, point EP-09 7 Re=2180 o SO 60 70 80 Z,sm Fig. 3.14. Signals of sensor with lengththe of clearancein Fig. 3.15. Average lateral mass flow (in dimensionless form) internal channel ofBN-350 subassembly. through clearance one through and (a) three clearancesof (b) internal channel (S/d =1.062, Pe =8400, number of averaging procedures - 24), x=z/h. Experiments wer modele eth carrie n f o LMFBso t dou R subassembly with pitch-to- diameter ratio changin e rang1.06= th d n es/ 21.1gi + 7 (Fig. 3.7, 3.8). Electromagnetic sensors were positioned insidtypicae th f eo l simulators (internal, edge, corne - Fig.3.9r r o ) inside of any other simulator that allowed measuring local velocity distribution around the pin simulator. In order to measure an axial and transverse components of velocity simultaneously the sensor involving two normally arranged pairs of electrodes were used. Sensors were calibrated on the two-pin models (Fig.3.10). Area under the curve representing dependence of the sensor's reading on the length e = f(z) shows the full coolant flow throughou modee calibratioe th tth t a l n aren sectioa ad undean n curv ) e (Figla rth 1 e.3. othee atth r section proportion i s si coolane th o nt t flowing throug inter-pie hth n clearance edu to wire wrap (Fig. 3.lib) s obvioui t I . s from Fig. 3.12, thasensor'e th t s reading lineae sar r wit coolane hth t flow. Feature inter-channef so l exchang wirn ei e wrapped bundl followss a e ear : Transverse coolant flows thoug e inter-pihth n clearances vary wit lengte hsina th s eha function (Fig. 3.13), with the period being equal to the wire wrap pitch; Maximum transverse velocit ysectione fallth o t s s arranged halfway betwee pointe nth e sth wire touches the adjacent pin; velocity component is equal to zero in the points of contact; exchange intensity increases with the wire pitch reduction, with Reynolds number and relative bundle e pitcth f ho . When a small bundles are considered (small pin diameters, small pitches), an influence locae th f ls o pulsation' flof so w aris curveholt d eno an d o theisd r smooth character (Fig. 3.14). Procesing of statistic data becomes more important [13]. bees Iha t n revealed (Fig. 3.15a) thamaie th t n very intensive flow (first harmonicss )i complemented by the local flow in the regions of wire (harmonics of a higher order). Thus, the mass mixing facto basicalls i r y determine firse th t y harmonicsdb expansioe Th . e th f no inter-channel exchange curve into trigonometric series [13] shows that: i J&! sin2iiX\dX l 1/2 A = ——————— = - J&! \sin2nX\fK = = J6, sin2nXdX =0,967 «1. (3.32) { \\v(X)\dX Here, X = z/h is the dimensionless axial distance. Inter-channel exchange curve e somar s e non-symmetri s relativa c o zerot e , that indicates that the flow balance through the selected clearance is distributed. Full flow balance agreemenin si t wit hhiga h degre f accuracyeo , when considered through three clearances. The local balances agree onl separatn yi e sections generan i , l ther transverse ear e flows (Fig. 3.15b), that cause axiae sth l coolant flo varwo t y alon channele gth axian .A l flow amplitude 101 h ft 1 j]8£}|a!z = — JVlSl^' (3-33) o o 6 o where SQ - total transverse flow. definitiony B : 1 h J v(z)dz — = . i (3.33a) 2/» o Thus, it can be written as: AP^_0 ^28 (3.33b) V ~ 6 where h 1 0 0 bundle Inth .06 1 value ; experimentae ; 2th = wit1 8< 2 ed « 2 | h/ s/ 1 v l h valuju f eo 0.3, thus, zlPm/Fw 0.05, tha maximus i t m variatio axian ni l flo wrange . lieth n esi 5% In every cross section ther coolans ei t flow directed wrappee frosidth e f mon eo o t r anothe accordancn i r e wit type hth f oriente eo d wire wrap (Fig. 3.16) t alsBu o. thera s ei turning movement of the coolant, because the wire changes its location in accordance with helical line. Along the wrapper tube the coolant flows in one direction (Fig. 3.17). Mass exchang governes ei periodiy db c (sine (Figw la ) . 3.13), that define locae th s l mixing factor varies periodically with the length. The local mass mixing factor representing ratie th o between mass flux y-t e fro /-tth e h mth o hchannet l throug unie hth t clearancd ean axial flow can be described by only one harmonics: \iy=v/V -tf=Asiav= e 9, (3.34) 3 where Vc - axial flow through the central channel, m /h; where *"(,/ 102 (l.Q\ are the experimentally found functions. The mixing factor averaged over the length and derived from (3.28) using (3.34) (3.34cs )i UM = « 3 Tth (3.35) , wit bein50 e range us < hth 1.4< gf d e2*10o d 1.0< h/ ; s/ 2*10e < 1 R 5< 2 ; < 3 M . Functioaccurac % 10 ns yi (]f(s/d) 3{i= representh c * averagee sth d mixing factor (with respec threo t e clearances) multiplie wrae th py d b pitc h (Fig. 3.18). Function y/(Re) obtained fro analysie mth experimentaf so l data presente (Fign di . 3.19) mose Th . t strong dependence on Reynolds number is observed to be at Re < (20 * 25) * 103. It should be noted an importance of determining correctly the coolant flow through the channel where the mixing factor is predicted using an uniform velocity distribution and those obtained from experimental data. The difference is evident to be significant. In spite of the mixing factor increases with Reynolds number (Fig. 3.19), in liquid metal there exist independenc thermaf eo l mixing facto Reynoldn o r s number [17,20]s i t I . connected wit componene hth t being responsibl liquie th r de fo metal heat conduction, that varies in inverse proportion to Reynolds number. If added to the convective component, it can caus mixine eth g facto depent [21]e no r R n .do Relationships presented allow reliable predicting the mixing factors for the bundles of the wire wrapped pins. Universal relations (3.34), (3.35) can be used in wide ranges of relative pitch, wrap pitch and Reynolds number. Inter-channel thermal exchange. Many experiments were performe thermae th y db l technique [20-34]. Analysis of these studies presented in [35] shows, that the bundles under investigations differ greatly in length (1 103 just effective (integral) mixing factors were measured. Only several works [20, e 24-26]b n ca used in the data generalisation. e locath t l mixinge o T g factor e thermath s l experiments were eth carrien o t dou sodium models, wit wrae hth p pitch varying [17]. Experimental model (Fig.3.21-a,be th s i ) triangular bundle of the wire wrapped pins. Four pins are made as rotating ones (the shaded in Fig. 3.21-b). Internal pin is heated, with the heat flux at the outer surface being about 1.2*106 W/m2. Walcooland an l t temperature e measurear s thermocoupley db s (enumeration i e nse Fig.3.21-b). Experimental result locan so l temperature distribution over subassembly length [17] permit revealing information supplementing our view of the process of inter-channel exchang bundle th n ewrappef i eo d pins: • Due to helical wire wrap the hot and cold streams of liquid are forced out from the channel comd san e into adjacent channels, where coolant temperature either increaser so decreases; • Temperature distribution ove channee th r l lengt maximus hha minimumd man , wite hth perio temperaturf do e non-uniformity being wraequae th po lt pitch ; wale lTh temperatur • e averaged over perimete same th es characterha r (Fig. 3.22) Authors have shown [11] that when the pins are spaced by helical wire wrap the convective mass exchange is followed to (3.34) and convective heat exchange between channel presentee b n sca : das W + W L Qyte= J Jp^co=^p- — ^h'-aAz, (3.36) where (3.37) locae th s li thermal mixing factor, 4 h = Here Aa - the phase shift between the mass flow harmonics effected in the section z actuad an l mas non-equivalence s th flow s i t f ; e factor between mas energd san y transport; Local thermal mixing factor (convective component), m"1, for one-directional wrap is determined by: (3.38) where /?« 0.7. 104 gaps -0,1 -0,2 mliiiiliiiilmilnii! until nl inilmili i H liitiliiiilimlmi 0 60 z,m 0 m50 O fO 0 30 0 20 100 Fig. 3.16. Lateral mass flow with length of different channels (arrows show directions of lateral flow in cross sections 1-1, 2-2). 105 0 Fig. 3.17. Averaged lateral mass flow dimensionless(in form) with axialthe clearancesaxisthe in between wrapper tubepinsand (number of averaging procedures 16), x = z/h. 1 i t - con 5 Re = 16500 4 3 2 \ 0 S/d 4A 15 Fig. 3.18. Experimental (symbols) ands averaging (solid line) of0 parameter on relative pitch of bundle. 106 — g— «- 5,0 V —H. = 1V 17 2,5 •J c 1,0 •«— £.= 3 10 20 30 Re,10 0,6 0,t 0,2 Fig. 3.19. Mass transfer factors with Reynolds number. Fig. 3.20. Mixing coefficient with the model radius (S/d = 1.17): - m as- sumption of uniform velocity distribution across model,the taking -O -, -A-, -D- - taking into account cross section velocity profile. outlet Fig. 3.21. General view of fast reactor sub- assembly model (a) and the model cross sec- tion (b): edge,5 1,2, internal cornerand turning simulators, current- 3 supply heater,to spacing- 4 grid, 6 - thermocouples faxing arm, 7,8- gland, 9,24 - thermocouple seals, 10 - thermocou- 8o3ki ples, 11, 13 - to header, 12 - gasket, 14 - •*—Bxod Bodu grid holding thermocouples, mixing- 15 chamber, 16, 26 - thermocouple covers, 17 - a) pin simulator, 18, 28 - bottom and top align- ing grids, 19 - bottom header, 20 - distribu- tive barrel, drainage,- 21 gland, - - 22 23 insulation, 25 - cooler, 27 - hexagonal wrapper tube. I-IV - turning pin simulators, 1+72-thermocouples. Arrows indicate directions of lateral flow of coolant, heated pin is in centre of the model. 108 Having averaged inter-channel heat flux over the wire wrap phase, we can obtain the following integral relation: 1 \ W.+W.r r, -ir r - da. = n J ——^-(h, - hj JtnAz, (3.39) OIJ where /TT. (3.40) zx Pulsating characte forcee th f do r convective exchang subassembln ei y with wrapped pins cause the coolant temperature to pulsate, that appears in a distance two-three pitches of wire wrap from the beginning of power production [36]. Heat balance equatio /-te th h r channenfo l [14,18]: dtt nqd ^ , ^ T v, * 3 ^ J I K T y v J ' i J= ' 'Vd z > ' 2cA py= G M T wher locae ft,th l}s i hydrauli c mixing factor define (3.3y db 4 - 3.34c) , jUrn* ; - mixing factors due to heat conduction and turbulent diffusion, respectively; y/y (q),j) - periodic function taking the values: Here Numerical solutio (3.41f no shows )ha n that prediction gooa n i d e agreemensar t with experimental data (Fig .0.7 3.22= ? / .t )a Thus value th ,non-equivalencf eo e heamasd an ts transport factor was found and the values of local mixing factors determined in experiments electromagnetie witus e hth c technique were validated edge th er channelFo . s (3.42) /=! ' x ' " *=1 Tp wher econvective th ^ cs i e mixing factor between interna edgd an le channels- , ;g relative flow rate through the edge channel. Equations (3.42) are equal to the edge channels in number. 109 Mixing factors are determined with the highest accuracy in the channels surrounding the heated pin (Fig. 3.23) [35]. Data of hydrodynamic measurements multiplied by the non- a gooequivalenc n i d e agreemenar 7 e0. facto= t t wit f e datr th h a obtaine therman i d l experiments. The final relationship for the averaged thermal mixing factor is of the form: 1.01 Thus, it was found from the correlation made between experimental data obtained by thermal and electromagnetic technique that the non-equivalence factor in liquid metal ft is equal to 0.7. Convective inter-channel exchang edge th en ei area . Mass exchange. Relationshi e convectivth r fo p e mass exchang e clearancth n i e e between wrapper and edge channels was found from processing of hydraulic data [13, 37-42] (Fig. 3.24): 2 3 - 373.4( / G/ A)[l7.34( l y centd} G =( / 144(A = / + where W'(Re) - 0.69 1 4= exp(- 0.132-10" Re),3 (3.45) A is the clearance between subassembly wrapper and the edge pins Result f experimentso convectivn so e thermal mixing betwee edge nth e channel [39, 41, 42, 45-50, 51] is described as (Fig. 3.25): (3-46) 4 W<(d A)/d MP Mass mixing factor /JC is calculated by (3.42). It is well to bear in mind that an enthalpy in donor-channel appears in denominator of t enthalp(3.46no t )bu y differenc centrae th n i l s areea subassemblyf ao , considering that here we are dealing with directed heat transfer. Mass and heat mixing factors reduce with the wire wrap pitch (approximately hi inverse proportion) and increase with Reynolds number and clearance between the wrapper and edge pins. 110 4 J 2 7 0 300 200 SOO 600 2, mm Fz'g. 3.22. Coolant temperature along channel:e th O - measurements by mobile thermocouple, —— - prediction on the basis of local mixing coefficients. vr -0-°-^?-;—c>- Vhells " un\M1-6t , , i a «aa 00 |0 0 o-o 9 OOP 05 o 2,0 ^v 0 1 Z 3 Fig. 3.23. Experimental effective mixing coefficients, numberof channels fig. 21b.3. see Ill 0 1,0 s/OL Fig. 3.24. Thermal mixing coefficients with relativethe pitch of bundle: C,6 - S/d = 1.062 (h/d = 5.1, 7.6); 0 -S/d= 1.115 (h/d =7.6); -S/dV 1.15 = -S/d A 1.17, (h/d = 16.4);A = , & (h/d = 5.1, 7.6, 10.1); + , ®-S/d = 1.185 (h/d =12, 22.7); experimental data of other authors: D , D , D , - S/d = 1.14 (h/d 14.3,= 21.4, 27.4); S/d=L06- • « (h/d-S/d=, 19.5);3 = , 0 1.32 (h/d = 16.7, 33.3, 50); • - SD/d = 1.17 (h/d = 16.7); 4 -S/d = 1.25 (h/d =51.4); 0 -S/d =1.10 (h/d =14.8); V -S/d =1.22 (h/ 3.4. MOLECULA D TURBULENCAN R E EXCHANG N SMOOTI E H BUNDLE EXCHANG HEAO T E T ECONDUCTIODU PINE STH F NO estimatTo e mixing factor component turbulencto sdue moleculaeand r diffusioin n liquid metal the experiments were carried out on smooth bundles with sodium and NaK alloy, as a coolants [52]. Having expresse heaa d turbulenco t flue xdu e diffusios na (3.47) "T A, turbulence th e mixing written e factob n rca : 112 Having expressed a quantity of heat transferred from one channel to another due to molecular heat conduction: the molecular mixing factos i r > s-d 8 1 s/d-l (3-49) where Ary is the inherent path of interaction. Suggestin analogn ga y occurs between heamomentud an t md transfeVan = T j T (a r 7* T Sinc. x n ecalculat n therr othed usino ca an e s e e i rg ArT w d on expressio e\I l}, an T V r nfo greae th t diversit relationsf yo , estimations availabl literaturn ei e [53-62] differ widely from one another. The great distinction has been demonstrated also in water and air experiments. The same picture can be seen in respect of mixing factor due to heat conduction [53, 63, 64]. The all mentioned above and even that the liquid metal data are entirely lacking is mainly responsible for the performing experiments on liquid metals. Experimental models (Table 3.2.) were the bundles of smooth pins arranged by triangular manner with relative pitch s/1.13d= , 1.15, 1214, 1.32. Local coolant flows were measure electromagnetiy db c sensors. Experimental dat effectivn ao e thermal mixin formule givee th g ar y , factornb a~ m , (Fig.3.26-a) Pe07 s/d d (3-50) <1.35; 70 contributioe Ifth f moleculano r component evaluate formule th y db a [64]: -, (3.51) re s is eliminated from the effective mixing factor, that turbulence component will be consistent with the relationship: _ 2 l50-Js/d-lRe° d . (3.52) 0 Fig.3.26-b presents experimental data on turbulence component of mixing factor compared with those predicted by some relations [35, 62]. 113 Table 3.2. Geometry smooththe of models Value Parameter Model 1 2 3 Pin number 19 Outer diamete pinf ro m ,m 14 24.7 15.8 Relative pitch, s/d 1.15 1.214 1.32 Bundle lengthm ,m 1720 1300 Heated sectionm m , 0 ,1 1620 1200 Relative clearance, A/(s-d) 0.75 0.43 0.52 Displacer diameterm m , d d , 4 5 Cross section area of internal channels co, mm2 35.3 150.1 89.3 Hydraulic duameter, dh , mm 4 6. 15.5 14.4 Coolant Na NaK T" D-[39] •-[470 ] -[51] •-[48] $-[49] A -[45] A-[50] ~O-[46] z 1 0 1,00 1,05 1,10 1,15 1,20 1,25(oL+A)/cL Fig. 3.25. Comparison of experimental data on convective mixing heat between subassembly wrapper tube and edge pins obtained by different authors. 114 o £7,2 -^^ 0,2 0 0 0,2 .4—4— 0 T—— Qfi 0,2 -.4—f——- f 1500e P 20 to.. 40 b) Fig. 3.26. Molecular-turbulence turbulenceand mixing with Peclet Reynoldsand number bundlethe in of smooth pins: O- experiment, ——', — •— - empirical formulae's, — —, — + — - relationships (0.01-Vs/d-1)/ [0.068(8/d-1?d an d 7 /(S/d-1+ 1 )°-2 j/S• Re0-2 Cl],C62]. Thus, experiments have resulte gettinn di g relation evaluatior sfo effectivf no e mixing factor and its components. It has been shown that component due to molecular heat conduction shoul calculatee db e formulth y db a (3.51). Analysis performe e authorth y db s notioe baseth n dno that molecula turbulencd ran ef «gradient o exchang m su a s e»i transport, induced by molecular diffusion and small-scale turbulent eddies, and convective transport induce large-scale th y db e eddie calleo s(s d secondary flows) allows deriving formule th r afo thermal molecula turbulenr- t mixin liquin gi d metal [65]: [350 s/d-l 0.318 T* _ J ____ ._____.______^______-^t s/d Pe(s/d)Js/d-\ , ^ ± (3.53) (2j3/n)(s/d)2-l <1.32; 70 and also relation for the hydraulic molecular - turbulent mixing in coolants of 1 [66]. 0.0293-0.051(5/ (lO4 Really, beliebasee th n dfo tha maie tth n axisesmall-scale th f so e turbulence diffusion tenso e arrangear r d alon channee gth l symmetri cs writ u line t ele , «gradient»e th flu f o x substance *¥, trough the area A®l } between the channels i andy as follows (3.55) where )*,y\ - specific molecula turbulencd an r esubstance th fluf o x, T e / respectively; E, eT - molecular and turbulence diffusivity; T, and 4 y- mean values of the substancchannele th n i * andy/ se4 , respectively, ArJ* effectiv- ' e pat f interactionho . As the secondary flows carry substance from the internal areas of channel to the area between channels / andy, we can write: \ _ / , ,¥,+¥ ^ — I _ , f Aco,y substanc- W Hered velocit , ean 4" , y pulsation' clearancee th n si , respectively} l W ; -mean velocit large-scalf yo e eddies; Aco*- flow cross section. 116 0,1 Stprs1 Re- 0,04 0,02 0 1,0 1,2 1,t 1,6 S/cL a) S~d>\\ +20%/ S-b calcul^J / r 1,5 X / />/ /-%)%/ I I 0 0,5 1,0 1,5 2,0 experim b) Fig. 3.27. Comparison liquid and of water, metal(a) mixing(b) air parameter: Liquid metal: authors- • data. 117 T 8 2 S/d-1,1 o 10 Re=80103 5 Pe=400 2 -1 10 S/d=1,0- 1,0 4 51, i i i —2 5-10 5 10 0 4 10 20 40 100 200 Fig. 3.28. Heat mixing coefficient heatto conductivitydue withofpin the equivalent thermal conductivity andPeclet number. 118 Having regar (3.56)o dt , molecular turbulence mixing facto dimensionlesn i r s form writtee b n : nca as = 1+ (3.57) Ar y where firse th , t term describes gradient exchang secone th d larg- dan e escal- e one, ASy - clearance between the channels / and j, to- averaged area of internal channel cross section. Analysi f experimentao s l dat inter-channen ao l exchang bundlee th n ei s involving spacer grids has shown that, in first approximation, relationship for bundle being free from usee b grid dn (Figsca . 3.27) thit causn sca Bu e .transvers eth e turbulence diffusion behind the grids to reduce. Inter-channel exchange due to pin heat conduction. In the event of the coolant in the channels surrounding the pin is heated non-uniformity, the heat flux distribution around alss i on non-uniformitypi e th , that cause heae sth t exchange between hea n channelpi t o t e sdu conduction to occur. By assuming that temperature distributio describee b n nca Fouriearouny n db pi e drth series with harmonics bein obtaie w gmultipl a followin e , nth 6 - f eo g expressio power nfo r production in the /-th channel: 3 y /s where qk - heat flux averaged over the k -th pin perimeter, qkl - mean heat flux e i-tth ho producechannelt n e i &-th th n mea- y pi , e/ b ,d n coolant temperature coolan- " / , t temperature averaged ovechannele th r s surroundin e &-tth g h pin, "k - coolanf t thermal conductivity, &: - equivalent thermal conductivity evaluated through the first harmonics, Nu - Nusselt number; dh - hydraulic diameter. Having performed the needed transformations, we obtain [71]: T ^ 8. 11 The relationship shows, thae thermath t l mixin hean pi g t o t conductiofacto e du r n reduces with Peclet number and pin diameter and depends only weakly on the relative pitch bundle ofth e (Fig.3.28). 119 3.5 TWO-PHASE INTER-CHANEL EXCHANGE Homogeneous model e distinguishinTh . g e two-phasfeaturth f o e e inter-channel exchang thas ei locae th t l behaviou mixine maximuma th f s o rg ha transition i n region from nucleat annuao et l boiling (quality 5-10%), wit value hth e depending heavil pressuren yo , mass velocit relativd yan e bundle e pitcth f ho . An appreciable pressure pulsations under flow conditions compatible with those on maximum transpor liquif to d phase were pointe maximue th o dt m amplitud 0.0s ei 50.0- r 7ba at frequency 0.2Hz. Suc amplitudn ha e appear sufficiene b o st educo t t intensivn ea e mixing in the slug flow. In other flow patters maximum pressure amplitude is lesser, but frequency increases. At great quality, corresponding to annular and disperse flow (x>0.14-0.2) an intensity of transverse exchange decreases, with the great effect of inter-pin clearance. Information on systematic researches of two-phase inter-channel exchange processed framewore inth homogeneoue th f ko s model indicates thafloe th tw parameters influencn eo the mixing intensit single-phasn i s ya e flow t reduceI . s wit coolane hth t mass velocity (Fig. 3.29). lowee floe Th th rw velocity greatee molecular-turbulene th , th s i r t mixing beine gth ratio between transverse molecular-turbulent transpor axiad an t l one. With increase th n ei clearance between the pins, the greater parts of stream-liquid mixture are forced through the clearance into adjacent channels. Reductio pressurn ni e result decreasa n streae si th n mei density and, respectively earliee th n i ,r transitio annulae th no t r flow. Si,i 1-3 16 12 6 0 0,05 0,10 0,15 0,20X Fig. 3.29. Intensity of inter channel mixing (in the frame of homogeneous flow) with quality two-phasein flow with (solid line) and without (dash lime) spacing grids. 120 In the square or mixed bundle the value St is somewhat above than those in triangular v bundlee datth as [73A . ] have show e availabilitnth f spacero y s effect e inter-channeth s l exchange, this relatio approximatee b n nca : das in nucleat plud eXan < gM )x flow < 0 s( t*=St? +f(s/d) f(pW)(p,/pg)"x; (3.60) dispersn i annulad ean r flow) 1 s< (Xx M< (3.61) wher pattere eth n boundar defines yi : das -| 1/2 1/2 P/ g-Pi + 0.6 + 0.6 , (3.62) P/ e worInth k [74 followine th ] g relation coefficiente th r sfo (3.60n i s (3.61d an )e ar ) suggested: 0.0157 p-1 l-0.17Jge°-417 (3.63) The drawback to the formula (3.63) is that the limiting transition to St^ at x -» 1 does not assert. The check has shown that relationships (3.60 - 3.63) describe experimental data [74, 75] poorly. More exactl date y th correspon] a [7475 , followine th do t g relations 0.745 (3.64) 0.0575 (3.65) (3.65a) 1/2 + 1 1/2 (3.66) Data [76] show that mixing in subcooled boiling is close to the mixing in liquid flow. When quality approaches zero (x > -0.1) the intensity of inter-channel exchange is observed to factoa ris y ethreeb f ro : 121 h .673 ( ) . ) 0 < x < 1 0. 6.66x- U ( [ , r 0 fo = 3J / 3S = S t In the corner channel of the square 9-pin bundle the enthalpy appears to be lesser than those in the internal channel, against the predictions on COBRA. Distinction is likely due to availabilite th e thicth k f liquio y dunheatee th fil t ma d surfac t considereno e s thawa t n di predicting heterogeneouo t alsd e an ,odu s transfe combinen i r d channels e overwhelminTh . g stream entertainment occurs from the most loaded channel. To describe exactly this effect in the fram homogeneouf eo s mode t witl havme h t successeno . Two-liquid model. Experiments carried out in [75, 77, 78] to study inter-channel exchange for either of the two phases have shown that intensity of inter-channel exchanges in dissimilare ar s liquiga d .dan n qualitf o compleo Dependencieg s St i y d x an charactei St s r associated with rearrangemen f two-phaso t e flow (Fig. 3.3a . Pea b) ,exchangf ko e intensity, well definer dfo liquid phase, have been suggested to fall on the transition area from plug to moist flow [77]. Data [75] show that at low mass velocity (60 ^120 kg/m s) each phase mixing is 2 observed to depend on pw, whereas at great velocity this dependence may be degenerate. In [75] the following relations were proposed: (3.68) , x (l.035 definee d St^ar an wherg J d St efro single-phase mth e flow relations, functions Having regard to the non-equilibrium flow, we obtain: -(»:" S, ) l-JC,, (3.70) .c)2 ; 0 3.6. TEMPERATURE BEHAVIOU D HEAAN RT TRANSFE N I NOMINAR L GEOMETRY Information on heat transfer coefficient and pin temperature in the bundle cooled by liquid meta extractes lwa d fro mmeasurementa LMFBn si R core (1.0 s/d<< 4 1.17) alsd o,an from the common physical notions in a wide ranges of defining parameters (1 .0 < s/d < 1 .18; Text cont onp 136. 122 a) X 0,8 0,6 0,4 0,2 b) X 8 0, 6 0, l Qf 2 0, Fig. 3.30. interchannel exchange by liquid (a) and vapour (b) in two-phase flow (model of separated flows) with quality,as pressure changes. 123 4 0 . DiagramsJ7 zg. 5 . find Nusselt number laminarn i flow of coolant through bundle.e th 0 1,00 105 1.-IO0 2, 8 1, 6 1 , i/ 1,2 Fig. 3.32. Diagram to define «f» and «q>» in relation (3.) Table 3.3. Calculation relations r Nu, (3.71)cfo ,f n p i lam si d = 1.0 1< sf d < 12 0 2. < d i .1s 2< 6 3 ^ c / o } 1"5(l s Q 9 75 5* ^ 42 -)- 25s J ycc 63 / A^vJ d £-V-r\d| ^ Nula ' —___/y — /S^C0,81 Q \ f / S 1r m f d \ ( 5^ C rI 36{s/ d) (s/ d)20 25s(+ l 2 OB63 )+ 0.041 0.041 0041 1 ^ ^/124s + 1.1 5 J (s/ d)2 ' -^ - 1 (s/ d30 - 1) ^ . dC.nri I 'v " o i V1 °4c i 1 51 6 065 125 3500< e allowin) 0.03P ;< 0.00 < 16 r ;4 P < mai 0.0e 7s < g th 2< n feature heaf so t transfer in liquid metal bundle to be revealed. Relationships are universal, as applied to any pins. Central are f subassemblyao . Heat transfe "infiniten i r bundlpredictee n b pi " n eca s da [5-8]: Nu = (3-71) l - wherNussel i Nu e t numbe n laminai r r - flowtherma 6 s , l modeling parameter calculated by the main harmonics (k = 6) [79] ;/ and Values ofNui, y and 6.3 3.6s 155(s/d)- w I — (3.72a) 0.041 f= (3.72b) . U (p= 80 (3.72c) or taken from nomograms (Fig. 3.31, 3.32). The formula view is conserved just in the range 1.0< s/d < 1.2. In reference points the formula becomes simpler: ,0,65 Nu =NUlam+ 0.041 1- (3.73) where N =l.25\l- 3'6 ;for I20 (3.74) (s/d)' where 126 13 Nulam = 7.55(5 / d) - 2Q(s / d)~ (3.74a) . accuracn A 5% 1 ± s yi Table 3.3 presents relationships to predict M//, /and #> in different bundles. In Fig. 3.33 predictions are compared with experimental data. In order to approximate Nusselt number the nomogram presented in Fig. 3.34 is conveniently used. Maximum temperature non-uniformitie predictee b n sca arounfollowss n da pi e dth : ^ minmax. _ * y AT= (3-75) qR wher thos- i laminaen eAT i r flow defined fro nomograe mth m (Fig. 3.35), 3 0.038+ l =( 6)-8-lCT; (3.76) (3.77) The deviation of the temperature distribution from a cosine law can be evaluated using nomogram (Fig formulae . th 3.36 y b r ):o + 0.2exp\- 0.6+ 6 I1gs - . (3.78) Fig. 3.37 compares prediction (3.75y s b experiment d )an . Edge e closareasth en I .bundle s (s/d 1.04= , 1.062) free from displacere th s temperature non-uniformit edge th et y a pin conditiones si subcoolee th y db d coolant neae rth wrapper tube (Fig. 3.38) [82]. Periodical non-uniformity caused by the channel geometry is superimposed on the general non-uniformity, with the periodic behaviour being the most expresse t largda e Peclet number smald san l distances fro sectioe mth f poweno r production oneself, where azimutha t largel flowno e . ar sEve n thougtherman pi e hth l conductivity yma be increased (pin with cooper cladding) t doe i ,t caus stotano e eth l non-uniformit reduco yt e significantly, although a periodic component disappears virtually. Displacers considerably decreas temperature eth e non-uniformity. In the bundle with s/d =1.1 and relative pitch between wrapper and edge pins A/(s-d) 1.0= , temperature field becomes more smooth (Fig. 3.39) [83] greatese .Th t temperature non- uniformity's are observed to be in the bundle of smooth pins free of displacers. Wire wrap, as well as displacers, produce the more filled temperature profile and non-uniformity reduces markedly. 127 flu T I I I I I I I I I 1 I 1 I I I I I I 6 I I I I 4 1,0 6=14,8 2,0 I I I to tI I I I I •"-•" 1,6 1,2 0,8j I I to 1=1,0 £=0,27 07 0,5 5 10 50 100 0 10050 0 30QoPe -a 33. Fig. 3. 128 40 20 -•—•-•-•- 10 I I I I I Mil I I I I Mill I I I I Mil I Ml 40 20 S/d=lA2 10 flu, i i i i i i l m i i i i i i i i mil i I I i ii.. 40 20 S/dH32 ^ 10 8=0,38 6 J_L 20 S/d = 1,214 10 6 0-6- 0.581 4 10 6 4 1 1 i i i i il 0.4L 4 2 3 1Q 2 461Q 6 0 4 1 6 2 2 4 2 \ ' 4Pe b) Fig,. 3.33. Comparison of experimental data (9,O, •with predicting relations on Nusselt numbers. 129 -0,6 8 3, 4 13, 0 0 1f3, t 6 1.2, 8 2 2, Fig. 3.34. Diagram evaluateto Nusselt numbers bundle.pin in 130 4. maximal Iw ~ -2 Fig. 3.35. Diagram defineo t maximal irregularities temperaturen ofpi laminarn i flow -2 Fig. 3.3<5. T/ze i'ame ro define parameter Z (see fig. 3.35). 131 n ml , x «* , / T> A 1 = Uw -t 10 20 40 100 200 400 1000 2000 a) b) Fig. 3.37. comparison of experimental data IPPE with relationship maximalfor irregularity of temperature pin in the compact bundle (a) and for pins arranged with various relative pitch S/d (b): 1.0;l'+7= i+7S/d laminar- - f flow; experiments- € , A , 3 IPPE. y , b D •,O, A , 132 0,20 = - cTh 'S9 0,16 ~ Pe=993 /stainless V OO ~ o j...-u_ - OQ\-S x_X 0,121- 0,08 0,04- 60 120 180 240 300 360 Fig. 3.38. Temperature behaviour of edge pin in the bundle with S/d - 1.062 without displacers: 1 - simulator of stainless steel, - 2copper simulator, experiments- • , O 133 0 36 0 24 Fig. 3.39. Temperature behaviour in edge pins ofBOR-60 reactor: smooth- • pins without displacers, • - smooth pins with displacers, O - wire wrapped pins without displacers, © - wire wrapped pins with displacers. .nxrx w t T- V i I I I I I I I I i i i i i Pe=700 n--i. i i i i i i i i S-d 1,0 0,8 0,6 0,4 0,2 b) Fig. 3.40. Maximal irregularities of the edge pin temperature: a) smooth pins, b) wire wrapped pins. 134 Table 3.4. Factors A,B,C,D in (3.79) Peclet A B C D P number Bundle of smooth pins without displacers ( 1.06 < S/ d < 1.15;0 < ¥ < 1.05) 700 0.10 0.40 0.63 15 5.4 Ig Pe - 7.52 400 0.21 0.41 0.89 12.5 (e=s-d) 200 0.47 0.82 1.3 10 Bundle of wire wrapped pins without displacers (1.06 < S/ d < 1.1 5; 03 < T < 1.05) 700 0.02 0.48 0 0 Pe+0.39g I 0.28 6 400 0.27 0.31 0 0 [e=0,5 (s-d)J 200 0.52 0.62 0 0 Bundle of smooth pins with displacers (1.06 < S/ d < 125; 025 < *F < 1.05) 700 0.214 0.083 1.03 4.15 6.86-1.951gPe 400 0.33 0.12 1.17 5.05 0.5(s-d)= e [ j 200 0.40 0.5 3.66 5.07 Bundle of wire wrapped pins with displacers (1.06 < S/ d < 125; 025 < T < 1.05 ) 700 0.0525 0.16 1.33 7.25 0.34 Ig Pe + 0.783 400 0.132 0.17 2.25 6.72 [e=0.5(s-dj] 200 0.45 0.19 4.08 5.9 /•mo* A-"in \>w —'•w >i S/d ^3 *tii C-nl I«] o 0.162 1,062 0^9 24.7 (200 e - - V Q£i T 317 e 1,10 1,00 (7A 900 - • 31?" • 02SJ vs 050 (7 280 690 o — 7 tt 4 .0 5 0. A O 3 0. . Of 1 0. D V* OA3 01202 24,7 A 052 038 U2 B 0515 ~* - 1200 15,8 B »,42 1W> 4O3 6 ^52 0577OJM Fig. 3.41. Correlation between predictions and experimental data on temperature irregularities around the edge pins. 135 Temperature behavio edge th ef ro pins rulea s unstables a ,i , connectes i t I . d wite hth fact that the points of maximum and minimum temperature are diametrically opposite and this makes heat exchange difficult. Unstable characte f temperaturro e distributio moss ni t conspicuou bundlee th n si s with e smalth l relative pitch. Enterin e displacerth g s into suc a hbundle s doet changno s e temperature distribution along the bundle, provided that displacer diameter is not as great to generate high leve temperaturf o l edge th en e i channels . Maximum temperature non-uniformity around the edge pin is generalized by the A A parameter vy = ——- - -—,———-r , combining the bundle pitch (s/d) and the clearance —a \) / d(s —s d between wrapper and pins (A) (Fig. 3.40). recognizes Valui T eA positives da maximuf i , m temperatur observes ei viewes da d from the internal channels (periphery is subcooled), and negative, if maximum temperature is observed fro wrappee mth r (peripher superheateds yi conventionals i T ) A sin f go t helpbu , s the subcooled and superheated regions to be ascertained. Maximum temperature non-uniformity aroun edge dth evaluatee b pin n sca s [84da ] recommends: Jt ftUM.max tA mmI Cexp(-- y B + A £ty = . ) i » ~ _ * (3.79) = T A qR 200 presentee ar Coefficient Table D , th C n de i , 3.4B , .A s Also, approximately the maximum temperature non-uniformity around the edge pin can be estimated reasoning from the superposition of coolant temperature non-uniformity (Fig. 3.41 locad )an l temperature non-uniformit "infiniter yfo " bundl inherene th t ea t partf so pin perimeter [85]: Substituting expressions for the local non-uniformity in the "infinite" triangular and square bundle gives that: * " Imfin ° gefj TM , -(AT"™*} > I (3.81) wher overtemperatur- o At e internae th n ei l channels, 136 , max _ . mm ' u ' t. -Kf, Z--2- I H -' are calculated by (3.75 - 3.78) for triangular bundle [80, 81] and by the nomogram for square bundl t laminaea r flow [86], wit correctioe hth flowe th r .nfo e correctioTh s insertei n d fro e relativmth e parameter r triangulafo s d squaran r e bundle equae sar l each other: AT' AT' trian oo Statistic processing shows that experimental data [84, 87] are agree with the relationship (3.81) (Fig. 3.41). Edge pin heat transfer. Considerable temperature non-uniformity around the edge pin reduces heat transfer intensity as compared with internal pins, and special relationship needs to be used in prediction [84, 87]: ad. (3.82) 3000 d< displacer< e 0 P ; 0.32d- 0.52< )< < 5 ( 0 / 3 ; 1.3 < A ; d = 0.3 / ¥ 5 9 1.0< < 4 0.04 < e, <0.14. Table 3.5. Calculation relations for factors a, b, n (3.82) Typf eo a b n pins without displacers Edge 4.69 s/d- 4.131 0.577 s/d -0.566 ( s\2 s 353- -8.71 - + 537 \dJ d Corner 7.13s/d-6.972 0.33 -0.34d 1s/ 2 J s\2 s 527^ 13.12- - 8B-+ 3 vo/ d Displacers Edge 4.81 s/d -3.348 1.381 s/d -1.376 \2 - s -335 - +s 274 137 Here dh - hydraulic diameter of internal zone of subassembly, Pe = \vdz / a ; q/\ta= w-tfj- mean heat transfer coefficient under stable heat removal conditione th n s(i event when there is no stable temperature difference "wall - liquid", that is often observed at edge th e pins, heat transfer coefficien evaluates i t crosp to sn di sectio powef no r production length); q,tw-- averaged heat flux and pin temperature, t,- mean coolant temperature defined as arithmetic mean between temperatures in adjacent channels, £; - equivalent thermal conductivity firse baseth t n harmonicdo Fourien si r series, d ddisplace- r diameter. Factor, sa b, n are calculated in accordance with the Table 3.5. Value f Nusselo s t number (Fig. 3.42 e segregate)ar d with relative pitch with decreasing and tend to limiting value internal in laminar flow Peclet number [88], 3.7. ENTRANCE THERMAL SECTION. VARIABLE POWER PRODUCTION Hydraulically stable flow turbulenn I . t flow [89.90 problee ]th mresolves i d undee rth assumptions that power production is constant with length and across the pin, and physical properties do not depend on temperature. Mathematical description for the inherent channel in triangula rfore bundlth m f o (Fig s ei . 3.43a) ,b £>' " 4 (df df ( d 1 df ( d I f 2 6 1 d 1 d d 1 2 d 1 0 3 84 - = Pe' T 2 T 4-^• dXT 7 •£ - + + 7 ( - ) 2 / * f 2 d 1 ] df d 1 f 2 d 1 a = + (3+ '85) + Boundary conditions: df =0; The following designation usee s(3.8ar dn i 3 3.85)- : 1 d Pe = —— = — — Pe , where Pe = wdh / a; a 2 ah ~ 4 - —-X; ——yT = T= T - dimensionlesstemperature 138 j= "0 ; Vrf r^_ a_i to P- o /5z a« 3'J ^ tfu n s a asu ooa • .P"* 40 O (06 -x'O J S/d Fig. 5. 43. Specific element of pin bundle (a) and mesh (b): • - nodes, O - boundary conditions. 139 a a a turbulence thermal diffusivity in different directions (z, r, 1 D thicknes claddingn pi f so temperature,- t powe,- - j r — productio= v q . unir npe t volumey f , Ri , AO -thermal conductivit f coolanyo fueld an t , respectively molecula- a , r thermal diffusivity, rb rb rb ,az'" , ar'" , a^" component- turbulencf so e diffusivit directionn yi , (pr ., sz Enterin , whicT g differenca s hi e between real temperatur poiny an tn i (wit T e h consideratio axiar nfo l heat transport mead )an n coolant temperature without considering axial s convenieni j transpor X 1 mako — t TjtI = -t4 e (~calculation s more accuraten s a wela , s a l influence of axial transport of heat to be estimated. The problem is resolved by finite differences [90]. Sequential Yang-Frankel overrelaxatio uses ni iterativs da e scheme [96, 97]. lengte Th entrancf ho e sectio calculates ni assumptioe th n do n thaparametee th t r under consideration (heat transfer coefficient, maximum temperature non-uniformity aroun pine dth ) differs from "stabilized" value (z—>ao)t morno ey b tha. t2% To determine heat transfer coefficient and temperature behaviour at the entrance region in turbulent, laminar and plane flow the following formula is recommended F(X) en,s. = 1- (3.86) 1.02<5/J<2.0; 0.01 wher e th valuf eo functions ei d F(X)an - s u N F/ l 1 (X = ) F (X) = AT = = w -—^~"k-f at the entrance section, F 6 - is the value of functions Fj(X) 2 qR SW d F2(X)an unde e stablth r e heat removal conditions - dimensionles e *P # enX , .M/ s. I N Us= lengt f Nucleatho e number entrance section *Pe' R - / dimensionles, t XI en.s.= s lengtf ho temperature non-uniformity entrance section hea- ,q t flux averaged perimeterarounn pi e dth . Values ofXeH.s..Nu and Xeri_s, are taken from Fig. 3.44 and 3.45, respectively. Functions presentee ar Fign di . 3.46, 3.47. In the plane and laminar flows [90, 91] the temperature behaviour and heat transfer coefficient governee ar s (3.86)y db , with substituting inherent lengt coefficients/d han ? (Fig. 3.48 - for plane flow, Fig. 3.49 - for laminar flow), with the ranges of application: 7.01 140 XHT*U 0,12 i±: Pe=1dOp / 0,<0 / \ £ 0.08 y 0,0' YA 0,06 0,1 •4$^^ '•?* 0.04 IT ^sS^i? 0.02 s?l^"" 4%' / 0 l,0 1,1 1.2 1.3 1,4 1,5 1,6 1,7 1,0 1,1 1,2 f,3 1,4 1,5 1,6 1,7 S/d Fig. 3.44 Diagram to define the length of initial section when Nusselt number is set (turbulent flow). N) ^ T H X 0,30 0,35 Pe=lOO 0,20 OXV 0,15 mX^ 10\\ 0.10 0.05 1,0 f,05 1,1 f,13 1,2 1,25 1,0 1,03 f,1 1.15 1,2 1,25 •t Pe= 1000 0,08 0,06 t 001 0,04 1 [7 0,02 1,0 1,05 1.1 1,15 1,2 1,25s /d. 1,0 1,05 1.1 1,15 1,2 1,25 Fig. 3.45. The same when maximal irregularity of temperature is set. 7 1 1, 1. 1.0 6 1, 5 1. 4 1, 1,3 7 1 6 1, 5 1, 4 1, 3 1, 2 1, 1 1, 1.0 1.0 1.1 1.2 1,3 1.4 1.5 1.6 1,7 /g. 3.46. Diagram defineo t coefficients relationn i u p^ (3.86) when Nusselt number t (turbulentse s i flow). t 1,4 1,2 1,0 Pe=ioo 0,8 0, 0,6 10' 0,4 \ OA 0,2 0 1,0 1,05 U 1,15 1,2 1,25 '05 1.1 f.1 52 1, 1,2d 5S/ Pe=2500 0,01 ,0 1,05 1,10 1.1 52 1, 1,25d / s F/g. 147. TTzrelationn i e t samep r (3.86)fo when temperature irregularity set.s i H.T.fAl :>/ 0 I.ml I 7 1. 6 1 5 1, 4 1, 3 1, 2 1, 1 1, 1,0 1 7 1, 1, 0 1, 6 1, U 5 ' 1, 4 1, 3 1, 2 1, 1,5 ~ 10 0,5 S/d S/d 1.0 1,05 1,10 1,20 1,05 , 1,10 1,20 c) d) Fig. 3.48. Diagram to define the length of initial thermal sections (a, c) and coefficients PNu " ft) an^ Pt @) in the flow with uniform radial distribution of velocity (rod flow). I I I I I I I LI I i_|- I. I fO 0\ • MITI I I I II 1I =I I I I I I I X IlllllllllIlllll Csj X 146 0,20 trX HIj\fu 0,15 0,10 0,05 0 JJJ S. 12 13 d Fig. 3.50. lengthThe of initial thermal section with relative pith of bundlein rod (——) and laminar (— —) flows. Comparison betwee lengte nth f entrancho e section turbulentn i s , lamina pland an r e flows (Fig. 3.50, 3.51) shows tha plann i tlamina d ean r flow lengte sth h varies proportionally to Peclet number. In turbulent flow the length of entrance section has a peak. Such a behavioudiffereno t e du s t i r transport processe liquin si d Peclemetalw lo t ta : numbee th r molecular heat conductio s dominatei n n heai d t transfer t highea , r Peclet numbere th s turbulence transport prevails longese Th . t entrance sectio t givena n Peclet numbe observes ri d plann i te oeb flow throug close hth e bundle (s/d- 1.02) . Hydraulically instable flow lengte Th . heaf ho t transfer coefficient entrance section (Fig. 3.52) can be evaluated by empirical formula [93 -94] B A _ n (3.86a) ,dj.. 255 + Pe ' where A = 156.2-1 02.4(5 /d) ; for \ = 95(s/d)-5*, for l.2 147 00 ,(*U) HT 2 4 6 Sfl)1 2 46 8J03 246 8« f6 4 8|Q4 1 6 8^Q2 0 34 2 6 &102 4 Fig. 3.51. Relative length of initial thermal sections in pin bundle with Peclet number in turbulent (——), laminar (— • —) and rod (— —) flows. (LAO, 50 40 30 20 0 6 6 4 8^Q 4 6 BIO 4 2 32 2 2 \Q Pe 30 £=600 Pr=3 20 2 4 68^^ 2 4 681Q5 2 Re F/g. 3.52. Relative length of initial thermal sections in pin bundle with Peclet and Reynolds numbers for coolant of small (a) and large (b)Prandtl number, round—) (— pipes. , (——) • The area applicatiof so n are: 0.4 0.4<86<1.6 for l.2 for Peclet number: 15 , 30 50 In close bundle pinf so s having high thermal conductivit) 15 * 0 y1 1.10(s/d= ~ 6 £ ; the length of thermal entrance section defined by (3.86a) has to be reduced by 30 •*- 40%. 149 The length of temperature non-uniformity entrance section can be evaluated by: (l/dh)Nu(lS,l-4,5lgPe)(j-l]+l (3.87) W Variable power production. If power production varies with the channel length, stabilizatio s lackingi n . Heat removal enhances, when heat flux gradien s positivi t d an e reduces, whe negatives i t ni . Give e hydraulinth c stabilization easn a estimato yt s i t i , influencn ea f variablo e e power productio hean no t removal usin calleo gs d Duhamel integral [98] (3.88) dz ,(*-*>' wher e standardizeth e s TJ(Z)i unio dt t dimensionless heat flux; - initiarj(0) l jumf po heat flux, /„ (z) - temperature distribution at uniform heat flux being equal to unit (transition function defined by (3.86)). In advanced approach the generalized Duhamel integral was proposed [92]. Instead of one transition function the system of such a function is established, with each function corresponding to specific part of length (Fig. 3.53): ,(Z-z}dz' (3.89) transitioe th s i wher- J —z n.( z efunctiot n correspondin sectioo gt n from inle croso t s sectio. nz' 1 I Fig. generalised To 3.53. definition of Duhamel integral. 150 100 200 300 400 500 600 700 800 max .mirt q-R2 •"•* 0,07 . S/dH.10 . ? PeH9.^ 4 0,06 ^ - o~-t> 0,05 **" 0,04 0,03 ' v^ cQo 0,02 - 9 # ^. o o ^-^ 0.01 ~f/ i i I ! r I I I I ZMM Fig. 3.54. Heat temperaturetransferand (a) irregularity along *b) central the pin in the BOR-60 model: ax experiments- q%- = O w - w ^const. q , cos[2.19(zq - t d a • an / H 0.5)];- calculation- —— Duhamelon integral In many actual cases an influence of variable power production in second half of bundlestimatee b common e eca th y db n Duhamel integral supportes i t I .experimente th y db s carrieBOR-6n o t dou 0 subassembly [100] (Fig. 3.54). Furthermore evaluato t , e temperature difference "wall-liquid possibl s veri a t "e i y us simpl o et e formula [101] (3.90) a where a - heat transfer coefficient under conditions of uniform power production predicte relationy db s from Chapter 3.6; len entranc.- s e section length. 151 3.8. AN INFLUENCE OF SOME FACTORS Calculation procedure in liquid metal reactor assumes that an influence of following factors on heat removal and temperature behaviour to be taken into account: wire wrap, diabatic conditions at the wrapper tube, power production of the pins. Wire wrap notes A . d above pine , wirth s n cooleeo liquiy db d metal cause locae sth l enhancemen n temperaturpi f o t o appeart e . Thi s particularli s y trur pin f fo esmalo s l equivalent thermal conductivity (fuel-uranium dioxide, cladding - stainless steel, coolant - sodium), define parametey db fasn I t. rs reactor s ovaries from 0.0 0.3o 5t . In dependenc f relativeo ee bundl pitcth f influencn ho a e f wiro e e wrap showp u s variously. In close bundles (s/d < 1.04) temperature distribution around the pin depends, in general, on the channel shape: for wire wrapped pins , max _ , mm qd/2 J for smooth pins (3-91) T f 0.61 •/./-—• qd/2 f ~ 1 + 8.1 Q-3Pe1046 300< e ) P 0.271.04(s/d< = = 6 0 e ; 2 ; In relatively free wire bundleth e) 5 wra 1 s. s somp(s/d1 i ~ e large temperaturd an r e distribution features the local wall temperature rises under the wire (Fig. 3.55). Such a rises under one-entry of a wrap and three-entries are approximately the same and can be evaluated as: _, = 1.86Pe-a44 (3.92) 2 / qd 40 here Af"" - temperature rise under the wire. In the more close bundles (1.08 < s/d< 1.1) spaced by the wrap of "fin-to-fin" type: , = 0.066 - 5 • 1 0-5 Pe, (3 .93) qd/2 40 Wir epracticallo wran s pha y influenc Nusseln eo t numbe bundlee th n i r s when (s/d 1.15) [82] Nusself i , Pecled tan t number definee sar : das ~qdrr \vdr Nu=, '"- . — ; Pe = — ^ (3.94) 152 X -Pe-358 O - o -Pe=24fl A - Pe= 200 -Pe=15S I I I ! I I 0 10 20 30 40 50 60 70 80 90100110 Fig. 3.55. Temperature behaviour around the pin in the area of wire location. To calculate Nusselt number the relationship presented in Chapter 3.6 should be used. In close bundles (s/d - 1.04 more )th e strong dependenc Peclen o e t numbes i r observed [82]: Pe...... 22 33 66 106 175 Nu (wire wrapped pins)...... 1,26 1,62 2,90 4,60 5,90 Nu (smoothpins)...... 1,53 1,64 1,95 2,27 2,79 Diabatic boundary conditions at the wrapper. In common case an influence of diabatic condition s definei s y subassemblb d y geometry y intensitb , f heao y t transfer insidf o e 153 a) 2CKL Fig. 3.56. Power production coolantand (1) temperature crossthe in section interactingoftwo subassembly: intersubassembly- 1 exchange 0.02;0; is 2 -flow in the intersubassembly clearance is 0; 0.02; ofco coolant 0.4and flow through subassembly.the 154 TI*I .xnun u iff -Tw ^ i^•L~bV *JU* l^-R Jl* 4 a ) c \ : > \ <" O ""• / 2 % / O ^ 0 —» J \/dQ / » tOfc / _ o a& : x 2 a<* l - o» ^ 0,2 ; , , , "T^WPe 0 20 40 6080100 200 400 8 90 0 wax i •"!« t:* ~~ H_f Q2 f ;< V ^,-R f ^ v~*6 1 \o d) *H *V \ 1 / < 06 - V 5 \ aL9° ' , H.I....X.I . 1 , .97. 1 I •ft-i^ilM n 1 i i M i \tfT 4 \ -€K>e 6 B 3 _6 0 0 30 0 12024 0 <8 0 t «• ~ tw 1 \ 9 3 ~~ q-R X* * 0 0.8 2 ^— ^~-«-_ _ \0-^^ 0,6 oe o00crooooooo b) 1 " Pe=160; ' ^^-« —--•^~-~o _ _ Pe z \ — •^"l»1 " 1 - 1 1 01 1 t C 0.4 /d 232 20 40 6080100 200 400 800 I "^ / n mi •na i x r*\\ t 0.2 2* _ \v_0 , q,-R * 0 : _ /— — I Pe=450 e) " / ±k!l \ Q! y° o' Uwt 04 .x^^X. /° i \^J1 -€K>XV^O/ ^«»^ »»^,! © / : e 0 \, 0.6 0.2 ~J- o/ \ \ ^^"" rt_ °f 1 1 1 ^™i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 *TI 1 i t | i i 1 t i i i i f i i » i i >tf fy 0 0 36 0 30 0 24 0 18 0 12 0 6 0 r 0 24 0 20 0 16 0 12 80 Fig. 3.57. Temperature behaviour in corner (a), edge (b) simulators under adiabatic diabaticand conditions(1) (2) wrapperthe at tubemaximaland temperature irregularities with Peclet length numberand d) of(c, power production (e). 155 thermo- (tw-tln),(point E-2/1) couple 180 2W 300 fl Fig. 3.58. Temperature behaviour around simulatormodelthe in subassembly(10 when power of simulators 1, 3, 4 is twice as large as for power of other simulators. ± max / nun v w ~" ^ w - 2,0 ?const 0 200300 500 600 Pe /g. J. 5P. Dimensionless temperature irregularity of edge pin with Peclet number uniformfor (——) variableand power across(——) subassembly. 156 subassembly and inter-subassembly heat transfer, by inter-subassembly flow, by character of power production field. Solution of the system of energy equations written for the group of interacting subassemblies shows that in the event of low inter-subassembly flow (g ,., < 2%) in parallel with some decreas maximun ei m temperatur mose th n tei powerfu l subassembly there alsa s oi rise in coolant temperature in adjacent subassembly (Fig. 3.56). Heat removal through the wrapper effect temperature th s e behaviour near only three-four row f pinso s adjacene th o t t e importanb e subassembln wrappeth ca n i d t an r y involving small numbe f pinso r s a , demonstrated by out-of-pile experimental data obtained on BOR-60 [21] and BN-350 models (Fig. 3.57). Different power production of the pins. If power of one or three adjacent pins is doubled (trebled) that temperature at the pin surface facing the "not" channel increases by 10 - 15% [102] (Fig. 3.58). Approximatel vera n yi similar manne maximue th r m temperature non-uniformity increases. In alternating power and empty wire wrapped pins in bundles simulating fast reactor subassembl ysignificano thern e ear t temperature variation froe mon channel to another, but dimensionless temperature non-uniformity can be doubled. The experiments now under way [103] have shows that temperature non-uniformity around the pins in the bundle with non-uniform power production is more by 50-60% than those under uniform power production conditions (Fig. 3.59). This raises the need for the further researcher on temperature variation around the pins under non-uniform power conditions in subassembly cross section. CONCLUSIONS 1. Analysis of available experimental data on pressure drop in various channels allowed the hydraulic resistance factors to be determined in the bundles of smooth and wire wrapped pins (regular and near-wall areas) in laminar, transition and turbulent flows and recommendations to be granted reflecting influence of inherent parameters on hydraulic resistanc providind ean g associated limiting transitions formulae Th . s recommendee dar true withi wide nth e range pitch-to-diametef so r ratio, wire wrap pitch, Reynolds number and take into consideration diversity of the channels within fast reactor subassembly. 2. Correlation r interchannefo s l therma hydraulid an l c characteristics were gained wite hth use of electromagnetic and thermal techniques. To conclude a problem of interchannel exchang reacton ei r subassembl followine yth g remark madee b n s:ca a) Physics of interchannel mass exchange in the bundle of wire wrapped pins is as follows: • convective component varie sins sa e wit lengthe hth pinf ,i wrappe e sar y db wires which touc adjacene hth walln pi t ; • exchange intensity depends on pitch-to-diameter ratio, type and pitch of wire wrap, Reynolds number; • the directed flow occurs through the clearance between wrapper and pins alon hexagonae gth l wrapper. b) Modified thermal track technique allow e locad th integrasan l l thermal characteristic interchannef so l exchang definede b o et this A .s technique showsa 157 temperature behavio n fasi r t reactor subassembly correspond o resultt s f o s electromagnetic measurements actioe th col d wirf y n:o b an d t eportion wraho e pth s f liquio d leav r adjacenfo e t channels, where temperature either increaser o s decrease dependencn si f inhereneo t enthalpy; coolant temperature distribution over the channel length has maximums and minimums. c) A joint use of electromagnetic and thermal track techniques allows dividing total interchannel exchange facto componentsn o r , correlating heamasd an t s exchange, defining non-equivalence factor between heamasd tan s exchange. e maidTh ) n componen f interchanneo t l exchang fasn ei t reactor cor s convectivei e one wiro (dut ee wrap) e generalizeTh . d relationshi s recommendepi predico dt t convective componen widn ti e rang defininf eo g parameters (s/d, h/d, Re). e) Non-equivalence factor between heat and mass transfer was found in experiments on liquid metal bundle 0.7e b . o st Thi s value need correlatioo st hydraulif no d can thermal characteristics in computer code development. f) In order to calculate mixing factors due to turbulence diffusion and molecular heat conductivity the empirical and analytical formulas are recommended for the most important in designing reactor core and heat exchanger range of relative pitches 1.0 < s / d < 1.5. The relationships for mixing factor due to pin heat conduction are presente wels a s mixind, a l g factor homogeneoun i s s two-phase th en i flod wan framewor two-liquif ko d model. g) Experimental dat interchannen ao l exchang methode usebasie a th er ar s da fo s s developed to predict velocity and temperature behavior in reactor core and heat exchangers. Knowledg f thermaeo l mixing factors allows revealing some factors' effects, such as the pin bundle deformation, variable power production, blockages, thermal interaction of adjacent subassemblies and so on. Notions of interchannel exchange inferred from theoretical analysis allows the calculation approaches for reactor core and heat exchanger thermal hydraulics to be developed. 3. Generalized correlations on Nusselt numbers and dimensionless temperature non- uniformities aroun e pinth d s whic e arrangear h regulan i d r bundle represen a basit c constant performinr sfo g thermal hydraulic calculation liquif so d metal reactor core within the following ranges of defining parameters: Peclet number \ . Therma4 l hydraulic constant instablr sfo e heat removal (variable power production, entrance thermal sections) were derive combinatioa y db analyticaf no experimentad an l l methods. The length of entrance section was estimated for two cases - hydraulically stable flow and transient flow. In the first case, the heat transfer problem was resolved for the channel of "infinite" pin bundl laminarn ei , turbulen pland an t e flow taking into accoun secone th t d derivativf eo temperature with respec axiao t l coordinat influencd ean relativf eo e pitc equivalend han t 158 thermal conductivity on temperature behavior have been analyzed, that is such a parameters, influences of which are of great importance in fast reactors. In the second case, experimental data on temperature fields at the entrance sections were generalized. Thus, needed data were gained for predicting thermal hydraulics under variable power production as well as for deriving recommendations for the stable heat removal. face tTh deduced from experiments, that DuhameFs integra usee b predictinn dn i ca l g flow under instable conditions, allow experimentae th s l dat instabln ao e flow recalculaten do variable power productio evene usede th b stablf n o tI o n t . e flo analyticae wth l data have to be used for recalculating. Among the main physical features of entrance section there are as follows: • Length of entrance section representing in scale of hydraulic diameter decreases with relative pitch and equivalent thermal conductivity of pin, but increases in proportion with Peclet numbe laminan ri pland ran e flow (hea transferren i t o t e ddu molecular heat conduction) turbulenn i , peaka ts floha . wt i • Temperature non-uniformity around the pin is stabilized over the length being more than thos stabilizatior efo averagf no e heat transfer coefficients. • Heat transfer coefficient in turbulent, laminar, plane flows varies with exponential law, that defines the relationships for temperature field and Nusselt number are universal in mentioned types of coolant flows. The greatest temperature non-uniformities take place around the edge (wall) pins of subassembly mucy , thawh hs i tattentio n mus givee b t thermophysicao nt l validatiof no such type of pins. Relationships recommended for wall pins and relationships for "infinite" bundle comprise information thaneedee ar t validatior dfo temperaturf no e behavior liquid meta bundlesn lpi . The followings can be noticed as the main thermoophysical features of edge phis in fast reactor subassembly: • Temperature non-uniformities aroun edge dth e pin greatee sar r than those aroune dth internal pins and can be generalized by the parameter y = (A/d)/(s/d -1), including relativ p betweega e n pind subassemblan s y wrappe pitch-to-diameted an r r ratio. Relationship e presentear s r foudfo r type f subassemblieso s : with smoot r wirho e wrapped pins, with/without displacers in edge channels. • Heat transfer coefficients in edge areas of fast reactor subassembly are less than those in the internal area by factor of 1.5 - 2.0. • Maximum temperature non-uniformitie wale th lt a pins s occurrin t smalga l Peclet number (transition from turbulen laminao t t serioua re b flow n s ca hazar) reactoo dt r performance provide powee dth r releas keps ei higt a t h level. Maximum valuee b n sca estimate graphicay db l representation experimentaf so l data. • Heat transfe edgn i r e channel f fasso t reactor subassembl rulea f instabls o a , , yis e character. Instability is defined by equivalent thermal conductivity and relative pitch bundlee ofth shapy b ,siz d displacersf ean o clearancwidte y b ,th f ho e between pins and subassembly wrapper. • Coolant passing throug e clearancth h e between adjacent subassemblies reduces coolant temperature in the edge channels and causes the temperature non-uniformity to 159 enhance. Close to the wrapper area is acted upon by deformation, that also increases temperature non-uniformit decreased yan heae sth t transfer intencity. REFERENCES ] [I Subbotin V.L, Ibragimov M.H., Ushakov P.A. Hydrodynamic Head san t Transfen i r Nuclear Power Plants. M., Atomizdat, 1975 (in Russian). [2] Zhukov A.V., Sorokin A.P., Titov P.A. Analysi f Hydraulio s c Resistanc f Faso e t Reacto Bundlesn rPi . Atomic Energy, 1986, v.60, p.317-321. [3] Malak J., Heina J., Schmid J. Pressure Losses and Heat Transfer in Non-circular Channels with Hydraulically Smooth Walls.. Ing. J. Heat Mass Transfer, 1975, v.18, p.139-149. 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Difference Methods in Solution of Partial Derivative Differential Equations, M., 1963. [97] Fadeev D.K., Fadeeva V.N. Numerical Methods of Linear Algebra, Fizmatgiz, 1963. [98] Minashin V.E. ,. Calculatio Sholochoal t e , A. . Temperaturf vnA o e Behavio Reacton ri r Core Under Arbitrary Power Production. Atomic Energy, 1967, v.22, p.362-366. [99] Ushakov P.A., Sorokin A.P. Analysis of Generalized Duhamel Integral as Applied to Calculation of Temperature Behavior in Reactor Fuel Pins. Thermal Physics of High Temperatures, 1978, v.!6,p.787-790. [100] Dobrovolski V.F., Zhukov A.V., et al. Investigation into Temperature Behavior of Fast Reactor Fuel Pins under Non-Uniform Power Production. Atomic Energy, 1970, v.28, p.490. 164 [101] Gubarev V.A., Trofimov A.S. Determination of Temperature Difference Wall-Liquid in Reactor Design. Atomic Energy, 1974, v.3, p.251-252. [102] Zhukov A.V., Matjukhin N.M., Sviridenko EJ. Temperature behavior in Deformed Pin Bundles under Unifor and Non-uniform Loads. Preprint IPPE-909, Obninsk, 1979 (in Russian). [103] Kazachkovski O.D., Zhukov A.V., Matjukhin N.M. Intensification of Heat Tranfer in Fast Reactor Subassembly with Counter-Directed Wire Wraps and Non-uniform Power Production. Preprint EPPE-1306, Obninsk, 198Russian)n (i 3 . NEXT PAGE(S) I left BLANI K •••«•••••••••••«•••5 16 * Chapter 4 EXPERIMENTA NUMERICAD LAN L THERMAL HYDRAULIC FASF SO T ACTOE R R CORE 4.1. VELOCITY FIELDS Nuclear reactor subassembly represents the system of interacting channels. Mass exchange, more stron ge insulate th tha n i n d channels, influenc f randoo e m geometrical deviations, effect of spacer structures, non-uniform distribution of the coolant over the channels of a different shape and other factors determine hydrodynamic features of the system under f methoddiscussiono e correlationd us an se Th . r insulatefo s d channel hydraulin i s c predictin interactine gth g channel causy greae sma eth t erro appearo rt . Velocity fields in the bundles of smooth pins. Experiments were performed on the model pins1 6 d , s witan involvine electromagneti7 hth 3 , 7 , g3 c sensors inserted inte oth measuring (rotating (Fign pi ) . 4.la . Rotation b) ,measurine th f o aboun g pi s axi it t s made possible recording velocity distribution aroun pinmodee e dth Th . l design allowen pi e dth arrangement within triangular bundle to be varied (1.01 < s/d < 1.31). Tables 4.1 and 4.2 contain geometry of 3- and 7-pin models. r correlatiofo s A n betwee e valuenth s measure electromagnetiy db c techniqud an e those measure Pilo y e notedb b t n dtube ca tha t i , t velocity distributions ove channee th r l perimeter are in agreement with the experimental data by authors [1, 2], as well as with the results of numerical analysis [3-5] (Fig. 4.2). When results were compared, the data are averaged throug e are , enclosehth W ae wall th y , db lin f maximuo e m velocit radiad yan l axises, with the angle between them being dq>: R R R \wrdr Jdcp \w(y2 Jwrr0+ )dy dr IdY 21 = Y + (s / d + COS where r - current radius, r0 - pin radius, R - distance from the pin axis to the line of maximum curren- ) r, velocity - tr ( distanc= ;y e fro walle mth ; ymax - (R-r^ distanc- e fro wale mth o t l the line of maximum velocity; Y — y/ym(a. Results of electromagnetic measurements and those in [6] are generally in agreement (Fig. 4.4), except for a small difference (~ 5%) in velocity amplitudes being due to variety of relative pitches in the bundles under investigation, as well as distinction between Reynolds numbers. It should be noted that velocity non-uniformity in a wide bundles (Fig. 4.5, 4.6 soms )i e lesser than tha channen i t "Palmerf o l " type (simulating two adjacent channe fouy b l r smooth pins wit axiae hth l space , 2]) [1 rt seem .I s likely thaa t number of hydrodynamical factors, such as secondary flows, inter-channel mixing and so on, appear in different manner in pin bundle and Palmer channel. 167 Table 4.1. Geometry of the 3-pin models Parameter Value Numbe pins,«f ro , 3 Outer pin diameter, d, mm 24.7 Inne diametern rpi m m , j d , 20 Pin lenghm m , ,L 792 L/d,. 32.1 Inner diamete m covere m th , f o ,rD 58.9 Distancem fro bottom e m, / th m gri o dt 686 electromagnetic sensor l/d 27.8 55.7(withour displacers) 95.8(displacers) Relative bundlee pitcth f ho d ,s/ 1.01; 1.02; 1.05; 1.10; 1.15; 1.20 Displacer diameter, dd, mm 12 Hydraulic diameter of the model, dh , mm 12.3(without displacers) 7.16(displacers) Cross sectio2 nmm , are Q a 1290(without displacers) 948 (displacers) Table 4.2. Geometry 7-pinofthe models Parameter Value Number of pins, «, 7 Outer pin diameter, d , mm 24,7 Inne diametern rpi m m , j d , 20 Pin lengtm h m betwee L n 740 d L/ gridd en se th 30 Distancm em fro, botto/ e mth m 560 to electromagnetic l/d 21.9 sensor l/dh 154; 10549.6; 68 ; ; 38.6 Relative pitch of the bundle, s/d 1.02, 1.05, 1.10, 1.15, 1.20 Hydraulic diamete m r, d m h , 3.65, 5.34, 8.27, 1 1.3, 14.5 Cross section area Q , mm2 221,310,482,658, 845 168 Table 4.3. Geometry experimentaland techniques studyto inter-channel exchanger in the edge area Author Pin d, s/d h/d L, Re, Coolan Technique numbe mm mm 104 t r LorenzJ. e.a. 91 — 1,24 48 - - Water Salt injection Chen Y.e.a. 61 6,125 1,25 48 ~ 0,064 Water LDA 24 0,45 Chiu C.e.a. 61 12,73 1,063 4 1524 0,2 Water Salt injection 8 1,7 Pedersen D. 91 — 1,20 48 — — Water Hot water e.a. injection Fontana 19 5,75 1,24 52 — 0,1- Water Pin heating M.e.a. 7,0 Skok J. 7 21 1,14 14 800 4,2 Water Hot water 28 injection Collingham 217 5,84 1,24 51,3 1445 1,0- Water Salt injection R. 3,0 — Hanson A.S. 61 — 1,25 24 — Water Salt injection e.a. Khan E.e.a 19 — 1,09 21 heatinn Pi g 61 1,2 43 " " " Table 4.4. Geometry model ofthe simulating fast reactorsubassembly Parameter Value Outer pin diameter, 2.96 (all pins) Helical wire diametem m , rd* 2.96 (inner pins) 1 .48(edge pins) Wire wrap pitch, h ,mm 192 Clearance between cover and pins, A, mm 2.96; 1.48 Relative clearance *P=A/(s-d) 1.0; 0.5 Pin number, n 37 Displacer diameter, dj , mm 4.27 Hydraulic diameter of the inner channel 6.94 Cross section area, a>, mm2 48.67; 40.93 169 a) Fig. 4.1. Cross-sections of7-pin 3-pinmodelsand (b) (a) equipped by electromagnetic sensors. I——I——1——I——I S/cHOO 3 Re Re-40 o -53000 A-42,6 A - 17QQO 3-26,2 D - 10 000 - 28,— 0 0 3 5 2 0 2 5 4 0 4 5 0 0 3 5 2 0 2 5 1 10 Fig. 4.3. Velocity distribution over the pin ^ - electromagnetic- D perimeter, 7.02A = , a O .V . t a ^ - Fig. 6 4.2. Velocity distribution over the compact „„„;„,„+„„ „+ c/j 7 n-> /-\ A n 7 *~ *• arranged perimeter:pin 9 -electromagnetic sensors, — — , — • — - Pitot tubes. measurement, measurement- A Pitotby tube, 2-4 -predictions [4.3 - 4.5]. 170 Wy/W 107 106 105 104 103 102 101 100 0,99 0.97 Oj96 055 0.94 0.93 Fig.4 Dimensionless4. velocity: 3-electromagnetic Fig. 4.5. Dimensionless velocity in the integral sensors (7-pin bundle, S/d = 1.15), +, x - Pitot channel of triangular bundle (S/d = 1.2): tubes (19-pin Pitot- bundle, 1.17),— = • d — S/ electromagnetic- D , A , O , x sensors,O , tubes (Palmer channel, 1.15).= S/d Pitot- ••— — tubes. , — — > i i ' T I i __?,• f=U2 103 £= a a _ IN - &' '*•' 0,99 & c Rencf3 — / o-50 5- 9a / q, ~4 A 7 & n 0,97 '§XA »-83 — S^ 0-95 * •-m o-iU 0,95 - 0,93 i i i i i J 5 10 15 20 25 Fig.Dimensionless4.6 velocity internalthe in channel of triangular bundle 1.32;= S/d O,D,A,3,C,*,DI - electromagnetic measurements, —— - averaging relationship m T F Wx ma -W Fig. 4.7. Maximum velocity irregularity «isolated»the in channel (—pin i—and ) bundle (—o—) with the pitch-to-diameter ratio S/d 111 25 30 Fig. 4.8. Velocity distribution internalthe in channel ofpin bundle1.062:= S/d A , D , O , • - electromagnetic measurements, * - data derived by interpolation [63 As relative pitch of the bundle is reduced, a difference between the velocity non- uniformities decrease accordancn si e with (wmax 2 " /ds ( )o i -l= 8.4(s /d)+9.4 (4.2) and dies away in the compact bundle (Fig. 4.7). Velocity profile in the individual channel is formed under influence of adjacent channels . channele Eve th sam e n ni th f eso geometr differene yth t velocity profile takn ca se place depending on the features of flows in adjacent channels. So, velocity at the interface betwee standare nth edgd dan e channel cornee th n si r are subassemblf ao lesses yi r than those side inth e area (Fig. 4.8) [7]. This effec moss i t t conspicuou 3-pin si n bundle with /without displacers (Fig. 4.9, 4.10). Detail measurement velocitf so y performe BN-60e th n di 0 model bundle wit smoote hth h pins have allowed studyin nominas ga deformed lan d geometr. 8] , y[6 173 60 90 120 (50 180 b) Fig. 4.9. Velocity 3-pinthe in model involving displacers beingand free(a) of displacers (b). 1.0 1,O4 fOB 1.12 1.16 Fig. 4. 10. Maximum velocity irregularity -within elementary channel: electromagneticO- measurements, Pilot- D , data A C1,2J, 3 , + -pin model with and free of displacers, respectively. 174 oooo ooo c) Wm/s 57 55 cNZO, e=20Amm ReK= 40 4Z5 45 335 30 275 36.5 f) Fig. 4.11. Schematic diagram of the model bundle (a), various arrangements (b-e)shearand stresses coolantand T velocity deformedin (w) bundle (f). 175 -J 0\ wm/a \\;\ & Wm/s z^y/- f •»: <\ -ft \ f«-' ^\ — -~l ------.--\-ir-slfi l I T Wm/^ s . VelocityF/g72 . ^ . distribution edgee th n i area bundlen opi f calculated using procedure] 3 C ULJ UJ ** m, t m : 0,06 0,05 0,03 0,02 0,01 c I I O 1,6 S/d Fig. 4. 13. Comparison experimental data and analytical relation ship of molecular-turbulence exchange momentumby with otherthe authors data : 0,®,€>,d, <&,•, ©- experiments, 500 ) parts of the channel. In last case, some pins were shifted from their nominal positions. Fig. 4.11 show modee sth l bundle, examples of pin shifting and velocity distributions in the internal and side areas of deformed bundle e morTh . e detail informatio . Fig9] , s .availabl8 i n4.1 , [6 2 alsn i e o illustrates velocity distribution in the nominal side area of hexagonal bundle predicted on the basi procedurf so e mentione [3]n di . Turbulent inter-channel momentum exchange. Fro e momentumth m macro- transport equation written in axial direction for the stable coolant flow, the momentum mixing factor e expressebetweeb n ca e channel nth j d d througan / s e differenchth e between wall shear stresses and momentum flow throughout the other clearances [10]: (4.3) where co,, C0j - areas of the channels; Ik. FIk. - perimeter of the &-th pin facing the channels/ and /, respectively, Tk. ,Tk. -shear stresses. —/ w + i w 1————co co. Zu -co (4.3a) CO ,' J y Relationship (4.3) indicates that momentum mixing factor can be found at the non- uniform velocity distribution (Fig. 4.12) or in the event of disturbed velocity, when one or several pin shiftee sar d from their nominal positio. c) n, (Figla 1 4. . Processin date gth a mentioned abov allowes eha d derivin followine gth g formulr afo the bundl smootf eo h pins [10]: M 8. IP'2 [1.0744^ / d - I) + 0.1864] (4.4) MT ltd ;/dY- Re 01 at 1.035< s/d<1.25; 6.5 104 Values predicted by (4.4) are in agreement with an accuracy 15% with those predicted followine byth g formula derive authorse th y db : .1 15] (4.5) Re 01 at\.Q 178 CMC 180 1BO Fig. 4.15. The senses of lateral flows in narrow (a) and wide (b) parts of channel wlateral . 4.16. Sketches of lateral velocity around the pin in narro\v (a) wideand parts channel ofthe (b). 179 oo o t, mm O SO 100 150 200 250 t, mm e'mv ~0,O2 - 180 120 60 Fig. 4.17. Lateral flows clearancesin between channels: everyin Fig. 4.18. Axial flows differenta at around pin levels:the clearance (a) and averaged over six clearances (b). , 144mm ... 48, narrow- 24, 0, part,1= ...,1=12,60, 132mm36, -wide part. Q flj I I I-UJJ I I I I L/J I I I I I I .1 I I I I •b) mm 1, 250 200 150 100 50 F/g. 4.19. Sketches of axial flows in narrow (a) and wide (b) parts of Fig. 4.20. Axial flows with the length of clearances (a) and the channel, schematic views of arrangement(c) pin wirethe ofthe on averaged over six clearances (b). oo velocityand distribution ahead behind ofand wirethe (d). Q-660OO 9U500O- 0-26000 0 210 240 270 300 Fig. 4.21. Velocity distribution around the wire wrapped corner pin in the model bundle in shifting pin along the cover. X1 1,0 0,8 0,6 0* 0,2 0 1 1,05 1,10 1,151,251£0 S/d f,30 1J5 Fig. 4.22. Experimental data on convective interchannel mass exchange in the integral region of bundle: »,«,€, A, A, A , O , ® , 182 Velocity distribution in the bundle of wire wrapped pins. Physical picture of coolant flow through the bundle is as follows [15]: In the points where the wire wraps are bridges the inter-pin clearance, transverse coolant flow is unavailable (Fig. 4.14). At the region between these points, the maximum transverse flows coolanoccure th n sideo .pi t Nea samf tw e flow so e th reth n si directions , that crose th sn i sectios i n under consideratio nliquia d flows frobundle mon e sid anotheo et n ri accordance with the wire orientation. (Fig. 4.15a, b). In going from the narrow part of the maximue th , channe wide of t th m eou o t l valupar d f transversan t eo e velocit displaces yi d from (p120= °o t ( p240°= l tim wide al th t r fall,ei channethae fo n o sth pars i tf o t l (Fig. 4.16a, b). Distribution of transverse velocity over the height of inter-channel clearance is of periodic character (Fig. 4.17a,b). Axial componen velocitf to y vanishe perimete n parte pi th f t so s a r engage wire th ey db (Fig. 4.18), coolant velocit greates yi r over that hal perimetef o f whico t r wire h th tiltes ei d (180 360(p< < ° , Fig°) . 4.19a-d wire Th .e represent "barriersa axiae th lo " t flow that defines velocite th y behaviour befor behind ean wire e dth , Fig. 4.19d. Axial velocity distributios nha minimum with the zeroth value in the points, where the wire is tight against the pin (Fig. 4.20a, b). Zeroth axial velocity under the wire, is naturally observed at the edge pins (Fig. 4.21). Thus, velocity distribution over the pin height is non-uniform (has maximum and minimum), tha define s i combinete th y db d hydrodynamics. Variatio axian ni l componenf o t velocit cause s yinter-channei e th y db l mixing. Analysis of inter-channel exchange. Intensity of transverse convective mass inter- channel exchang describee b ratie y th eoma y db betwee averagee nth d value f transversso e and axial velocities, tha Stantos ti n criterion: (4.6) where wy - mean velocity of a directional transverse coolant flow through the clearance between the channels / andy; w,, Wj - mean axial velocities in the channels / and j; CD statistica- channele areth f ao l cross section. To perform the subsequent analysis the parameter is to be introduced [18]: X' = (4.7) describing the extent to which a liquid follows the wire wrap and the degree of the completeness of transverse velocity, here 183 Experimenta ] shol dat20 w, a 1.1= tha19 [15 d 0.8' , o 7riset x ts/ (Fig16 ,t p 3sa u . 4.23), that correlates wit 1.3= hx' cosint 8a e variatio transversf no e velocity. Thus, maximum value of transverse component of velocity is found to be more by 38% than those predicted unde assumptione rth s that liquid follow wire sth e wrap. Transverse velocity through the clearance between the pins can be close to axial component of velocity [15] (Fig. 4.16, 4.19), that indicates the velocity vector departs from wire wrap toward an increase in (p. Datagreemenn i e a ar [19 ] ,20 t wit electromagnetie hth c measurementd an ] 17 - 5 s[1 reinforce the formula 0.478 212 1.84-22..5 exp -119I--1 + 0.7 (4.8) h ['"d ~ * """"*' "*' ' *"'\W s-dV a where y(Re] = 1.085 - 0.754exp(- 0.132 • 10~3 to); 1.0 < s/d < 1.4; 7.6 < h/d < 52;2.103 < Re < 2.105. Inter-channel exchang bundle th n ei e wall areknoo T a. w temperature behavioun ri the bundle wall area of fast reactor being, as a rule , non-uniform is very important. Reliable values of transfer coefficients define authentic predictions with the use of thermal hydraulic codee th handlinr f fo so e codesus turngs it e dat i th inter-channe,n h ,ao l exchange th t ea bundle periphery is the most effective techniques for predicting transfer coefficient in that areas of bundle. Authors have performed experiment sodiue th n mso model involvin wir7 g3 e wrapped pins arranged with relative 1.18pitc= d hs/ 5 (Fig. 4.24).One wal generaten pi l d heat, wite hth length of heated section (10 / dh * 248) simulating the whole length of BN-600 core. The outlet coolant temperature measured in experiments were compared with those determined from the energy equation system: internafoe rth l channels (Fig. 4.25a) w As, (4.9) wale foth r l channels (Fig. 4.25b) dz^1 \ / / / (4.10) 184 whermea- w n, et coolant temperatur velocitd ean y respectively channe- a ; l cross- section area hea- ;q t flux axia- 2 ; l coordinate - hea;77 t removal perimeter clearance th - s A ; e between pins; Ap m exchange due to heat conduction of the pin; a>, Aso - mean cross-section aremead aan n clearance, respectively. The system of energy equations is resolved by finite difference realized in the code TEMP-M. Thermal molecular-turbulent mixing factor (juj) and that due to heat conduction (jipm) were calculated and assumed to be the same in all channels, convective mixing factor in the internal channels (/^') was also calculated and desired value of convective mixing factor betwee edge nth e channels varied. Analysis experimental data performed invoking calculation results allows the value of thermal convective mixing factoevaluatee b edge o t r th ebundlee n d i areth f ao . Fig. 4.26 presents calculated curves being distinct in value of ftcp , that coinciding with experimental data gives required value. Thus, feature heaf so t transfe edge th ebundl e n followsri s are th a f e ao e ar : • by the action of coolant flow directed along the bundle wrapper the maximum temperature displaces i (Figd° fro40 heateA The data obtaine gooa n i d e agreemendar t wit relationshipe hth : / A\ f \\^ f \\^~ , 17.34 -+14 - 4 -373.4- V?'(Re) (4.11) \dJ \dJ \dJ h at 1.0<(A + d)/d< 1.25/7.6 and non-equivalence heamasd tan s transpor 0.7= t/? . 4.2. TEMPERATURE BEHAVIOU FASN I R T REACTOR FUEL SUBASSEMBLY (NOMINA DEFORMED LAN D GEOMETRY) Some general insights. In fast reactor subassembly there is a gap between wire wrap and adjacent pins, due to which pins can be shifted that causes the temperature behaviour to change. Also nominaa , l geometr swellingvarieo e t b e n ddu yca , bendin othed gan r reasons. Some subassemblies come under an influence of great power, gradients, some fuel pins (or group f pins o sproducn ca ) e energy more than predicted fro neutroe mth n field. Various blockages can prevent the coolant flowing through the subassembly. 185 As a result of the action of factors mentioned above, the temperature distribution over the subassembly becomes non-uniform. Equalizing the temperature behaviour is aided by the inter-channel exchange that is illustrated below by the examples of predictions performed for BN-350, BN-600, BN-800 and others. The pin power, displacers' diameter, clearance between the edge pins and subassembly wrapper were varied in calculating. The effect of the three adjacent pins approach each other within toleranc s estimatedwa ) e (aboumm . 1 Unde0. t r condition f variablso e power across subassembly (Fig. 4.30) temperature behaviou internae th n ri l are subassemblf ao y followe sth power variation t shoulI . notede db , that inter-channel exchange doe t overcomsno generaea l non-uniformity in the coolant temperature but has only a local effect on thermal processes. As pin power increases by 10 and 50%, the coolant temperature in adjacent channels rises by as low as 1 and 4%, respectively, whereas a neglect of inter-channel exchange is responsible for temperature th e 50%d elevatioan 0 , respectively1 y nb . When three internal pins approach each other till bein contacn gi t with their wire wrap, it causes the temperature to increase by 1.5%, although the coolant flow rate reduces by 15%. Shifting the edge pin to the half inter-pin clearance is found to act vigorously (about 13%) on temperature field, constitutthay tma threaea fueperformanceo n t pi l . Evaluatio evene th f nto without consideratio f inter-channeno l exchange give temperature th s e ris mory eb e than 100% (Fig. 4.31). As the clearance between the wrapper and edge pins varies, the correlation between the coolant temperature in the internal channels and those in the edge ones changes. Wite clearancth h e bein ge inter-channelth smalle , 0) r = (tilS l exchange reduces overtemperatur (Fig% 8 o .et 4.32)fro sensor% y m40 An . devicer so s inserted int channee oth l deforms the regular arrangement of the pins, that results in deformation of temperature fields (Fig. 4.33). Thus, mass and energy inter-channel exchange is responsible for the more smooth temperature distribution and it follows, that maximal temperatures of pins and wrapper reduce this A .s takes place, inter-channel exchange equalizes a larg o t ,e measure a loca, l temperature peak temperaturd an s e non-uniformities (loca t spotsho l ) associated wite hth excess powepinse th f , o rcoolan t superheating withi ngroua f channelspo t shouli t e Bu .db noted, that inter-channel exchange equalizes a global non-uniformities not so intensively (Fig. 4.33,4.30b, 4.32). The extent to which the temperature reduces is a function of the following parameter (Fig. 4.34): r*=^T- (4-12) o where pz - total value of thermal mixing factor; z - length of heated section; g - variation in relative flow rate through the deformed channel. Experience on fast reactor performance has shown that significant deformations take plac campaign i e n associated wite creepinth h d swellinan g g [22, 23], Fig. 4.35e .Th subassembly wrapper changes its from, also geometry of pin bundle is varied too. Text cont. on p. 198. 186 Fig. 4.23. Axial velocity elementarythe in cell formed wirethe wrappedby pins (a)smooth pins (b). 112 113 12S 125 11** 0000; 0*0*0*0\^Stt\-/72\-SS7 ^~/SJ* 116 117 127 130 126 118 119 129 Fig. 4.24. Model bundle cross section outletand coolant temperature diagram: 1heat- pin, 13+132 thermocouples,- Q^j^J e darkerH^ " highere th tempera- ture. 187 7=3 Fig. 4.25. Schematic diagram of internal (a) and edge (b) channels. At,°C 5 4- J 2 20 15 1 0 100 130 49 109 110 112 125 98 35 117 105 106\107 \120\ 131 \101 \ 12* 1113\ 104\ 31 \ 116\ \ ill_I i I ,_I i__ i I i I i I i I i I 127 1118 ' 129 ' 54 ' 132 ' /721 W I 103' //* ' 56 \ 99 « J 5 11 6 12 2 10 3 12 1 12 0 5 8 10 9 1211 8 HOMep mepfionapbi Fig. 4.26. Predicted coolant temperature along the cover for various mixing fac- tors (ip (lines) and comparison with the experiments (symbols). 188 Fig. 4.27. Comparison of coolant temperature in the clearance between the pin modele th d an cover. 1 t S= a K =0.5¥ d an 126 125 103 113 102 112 111 12* 123 ° - 11094 f22 95 79 87 80 96 97 11410* 1O112186 * 78 - 67 68 58 69 70 81 8B 11598 36 31 32 62 71 53 16 15 14- 57 66 77 93 1Off 132 - «> ° - 13i SO 51 52 65 56 13 18 17 60 72 83 33 34 35 * - 49 54 53 76 64 63 5S 62 61 73 84 11699 H7 105 89 90 74 85 75 91 92 106 12O - ® 127 119118128100 106 1O7 129• - 130 HOMep mepMonapbt Fig. 4.28. Outlet coolant temperature along the pin rows. 189 I I I 1 II I_1 Fig. 4.29. Relative factor of inter channel convective exchange in the edge area of bundle (^max - maximum value of the factor being independent ofPe greatat Peclet numbers. b) Fig. 4.30. Radial distribution of coolant temperature 1,0 eventthe in of 'excess power production edgethe pin in under conditions non-uniformuniformof and (a) \ 1.35(q= maxg )/ (b)power distribution overe th subassembly cross section: 1 - power distribution, 2,3 - nominal regime disregarding and regarding interchannel 0,5 exchange, respectively; excess- 5 4, power production10 7 6 5 4 3 2 1 1' 2' 3' k' 5' 6' 7' and 50%. ——— HOM6P PflAA KAHAAOB lit/At V l.< ^ '/J • ••• -<= ^ I < 1f 'i<"N 1.0 - S -j A 2 -3 4' m\ k f 0.9 v 'H ""J-1 i 0,8 -ft -t — .— , 0.7 i [ 1 I op c-' - — - ™ - 0,5 0,5 0,4 ' 8 ' 7 8 ' 76 ' 654325 ' 4 ' 3 ' 2 T 1 channenumbew ro f o rl 5123 4 765432' ? ' 3'4' 2 6 ' 1 1 1'5 number channel channenumbew ro f o rl Fig. 4.31. Variation of coolant tem- Fig. 4.32. Radial distribution of coolant tem- Fig. 4.33. Coolant temperaturethe at perature around the edge pin: 1,2- perature at a various clearances between edge uniform power distribution in BN-350 sub- assembly: 1,2- subassembly withoutde- nominal geometry disregardingre- and pins and the cover 1.3 q= max 5: q / tector; 3, 4 - with detector. garding interchannel exchange; 3,4 - 1 - power distribution; 2.7 - disregarding inter- distorted geometry, the same. channel exchange; 3+6, regarding- 8 interchan- exchange.nel e P f AtA 4 HI II f II number channel f) Fig. 4.34. Variation of the dimensionless relative coolant temperature -with the mixing with factorsubassemblyand the (a) producespin radiusone ofthe (b) channel- I heat:II - I numbers. 192 Subassembly bending Loaded flanges due to flanges Fig. 4.35. Subassembly cover deformation (a), bending cover bundleand (b), twisting pins (c), swelling (d). 7 ^OOO 0° !.-.. - U) AlWPe 0 90 180 27no0 MOJ60 T goo) e=o,s(s-d) J ^ W Wi Al?60,9-Pe -1028 0 90 ISO 270 360 J ? 200 400 =0.iTv,=a(8*l67e)(pHO«II Pe) 4.36-a. 194 m m T ^/j_Iw" "I4.w t"M\ j QW•5 D -2,8+ 6,45 e-°'008Pe ovo 0 30 O M 0 18 0 1: d E 0 0 SO 120 180 «0 JOO 3oo OlO o T> 0 60 120 190 2m JOO 2oo OOo 1 OO O.Q.O f W 3 O H O 'B 0 12 > U 0 02Pe 50 100 200 400 800 Pe 4TW=0,18^72e°' Fig. 4. 36-b. 195 0-v CD 2,5 2 e-S-d o f w o n a te 0 12 o s a -0,83 2 .00; aoo' f < 0 30 0 24 0 18 0 12 D E 0 oo mm ooo www oo 0——60——i20 f < 180— 0 H30 O 1 •••••••••«...... „ 0 80 0 40 0 20 0 10 00 5 d) Fig. 4.36-d. Maximal azimuthal non-uniformity of pin temperature during various types of bundle deformation in the edge (a, b), corner (c) and internal (d) areas of subassembly. 197 In the last few years, a great interest has been expressed in studying temperature behaviou deformen ri d bundles. Experimenta analyticad an l l investigations have been carried Russin i a (IPPE 26]- 4 , )Czec[2 h Republic othe[27d an ]r countrie -30]8 s[2 , Systematic investigations performed in the IPPE have allowed having analyzed specific features of the formation of temperature fields under the effect of subassembly deformatio derivind nan generalizee gth d relationship [31- 34]. Belo wgives i resulte nth f so experimenta numericad an l l investigation dat spresentew e presente aar ne - 38] 4 A . [3 dn di also in the form of generalized approaches to temperature estimation taking into account an inter-channel exchange as a decisive factor of subassembly thermal hydraulics. Temperature field differenn i s t variant shiftingn pi f so . Throug variane e hth th f o t bundle deformation, when one pin or group of pins is shifted parallel with the pin axis is idealized, but it yields a very important information on the limiting temperature non- uniformities. Temperature field of the pin shifted along the subassembly wrapper is non-symmetric: maximum temperatur reducee th fall n o sd cross section area. Value f temperaturso e non- uniformit significantle yar y greater than thos nominan ei l geometry. Temperature behavios i r qualitatively the same in the bundles of wrapped and smooth pins, with and without displacers in the edge channels (Fig. 4.36 a-d). From these figure followt si s that: • in reactors of BN-600 type (subassembly contains displacers, pins wrapped with helical wire e maximuth ) m temperature non-uniformities aroun e th edgd e pin, whes i t i n displace haln da f inter-pin clearance s morei , , than expecte nominan di l geometrya y b , facto f 1.3-1.7o r ; • fuel pin f BN-60so 0 type, providing they hav wiro en e wrap, induce significantly greater non-uniformities, that is responsible for the lesser inter-channel exchange. Prediction f temperaturo s e non-uniformitie e singl th displacementn pi n eo s . Temperature non-uniformities systematized in Fig. 4.36, a-d are generated in response to the inter-channel heat and mass exchange being inherent in every specific case and can be evaluated by the relationships presented in the same figures. Naturally, inter-channel exchange shoul consideree db totaa s da l (effective) process. subjece Whilth n f predictionseo o t t shouli , notee db d that temperature distribution s determinei arounn pi e dth generan di l case, fro conjugate mth e proble f heamo t removal: heat conduction (witn equationpi he volumetrith r sfo c heat productio fuel e massd th r an ) nfo , momentum and energy conservation equations for the coolant, with the problem in irregular geometry a under conditions of non-uniform distribution of power over the subassembly cross-section being solved in sufficiently large (minimum two-there rows of interacting channels) combined domain taking account turbulence anisotrop transversd yan e convection wiro t e e wrapdu solutioe problee .Th th f no mfraughs i t wit larga h e bod calculationf yo e sdu locao t l structur transversf eo e coolant circulation particularn i , currentls i d an , y difficulo t t fulfill. The use of the local heat transfer coefficients [39] makes the calculation procedure the more difficult to be realized, because of the need for local-coolant temperature averaged 198 throug locae hth l volume d becaussan relationshipf eo s availabl locae th ln eo heat transfer coefficients holding within the wide ranged of input parameters. In view of the mentioned above, of particular interest is the development of approximate, but reliable, procedures for calculating temperature distribution around the pin (followe definitioy db f maximuo n waln mpi l temperature ) e featurebaseth n df o liqui o s d metal heat removal. Among these feature a grea e ar ts coolant temperatur ~ 200°( e C difference between inlet and outlet), high coolant thermal conductivity, strong inter-channel mixin helicao t e g du pinsle wirth .n eo In irregular areas of pin bundles a wide geometrical variations can be observed: some channels come into the compact shape, other ones are more separated. Calculations have shown, that the coolant flow rate through the compact channel falls by the order and more as compared with thos nominan i e l channel. Respectively e coolanth , t temperature becomes higher (above 50-^10 averagef o 0% d coolant temperature) mose th . f tThuso importane on , t proble o determint s mi e coolanth e t temperature distribution having regar r massfo d , momentu energd man y macro-transport. Suc hpredictiona subchanne e basee th b n n do sca l approach indicates A . d above, domain (subassembly divides )i celle th sn dwithio n whice hth coolant temperatur defines ei d fro masse mth , momentu energd man y conservation equations. Thus, we can specify that premises to approximate calculation of pin temperature distributio followss a e nar : • the coolant temperature distribution over the channels surrounding the fuel pin is crucial in determinin temperaturen gpi ; • an inter-channel exchange exerts a primary control over equalization of the coolant temperature around the pin; • heat removal in the clearance between pins is of a local nature; • temperature in the inherent points of the pin cladding (narrow, wide parts of the channel) ca determinee nb superpositios da f locano l coolant temperature, temperature difference «wall-liquid» and wall temperature non-uniformity. Numerical scheme (Fig.4.37) assume followine sth g operations: • prediction of coolant temperature distribution over the channel surrounding the pin; • the first harmonics is isolated from the coolant temperature distribution + bsiny (4.13) where y iz « z 1 —= J t,cos® ?.aqa J ; > — = / ? 271 e0 n 0 1 2lt 6 = — J t, sinq pin surface temperatur narroe th channen e ei wf th o par f m s calculateo i tl su a s da arithmetic mean coolant temperature between the channels i and j and temperature difference «wall-liquid» 199 (4.14) MA, where Nu = Nu s,,/d,Pe\ w,,, su/d\,s (\v2; * Wj / y + lj \v ; firse th t harmonic temperatur• n pi e th n si e distribution (dotted lin Fig.4.37n ei isolateds )i : -(0 w =tw+c cos i IT. 2n temperature in the inherent points of the pin perimeter is defined as superposition of the first harmonies and local temperature difference (4.16) clearancee th whern i s i t ei s betwee channele nth sandji that: (4.17) Here, in the wide part of the channels: A,efe z+ where -,£ ; • rtPer ww - p 2d ' j- ' 200 • continuou n walpi sl temperature distributio s i founn y numericab d l interpolation (Lagrange s formula, for example): (4.19) J=0 wher functionae eth fora s mha l £»= (9- e splinth f eo Thapproximatione us e r examplfo , a cubie c spline-functionss i , preferential thin I . s case, findin interpolatine gth g spline-functions reduce solutioe th o st f no systee th mf lineao r equations n eacI . h interval ( A . 5 *w where A interval of partition. Thus, we obtain the system of equations: 2 6 i W.j.1 If, W, M>,_1 ^ —— ~ —— ^T-^-1 • 7 = U.., »-l (4.21) derived with referenc (n+1o t e ) unknown variables Sg,S?,....,S% defino T . e these variables identically, we add the equations resulting from the periodic temperature distribution: o = £ , $ = &i • (4-22) doingo Is n firse ,th t equatio substitutens i followine th r dfo g 2 = s n+l . (4.23) and new equation is added ^.^L-faL.fa^fcL (4.24) 201 A curvatur interpolatiof eo n curv appears ei minimume b o st . Valued san ofNu, T A Z in the correlations mentioned above are calculated in [34-36, 41] for regular pin bundles. Authors have derive followine dth g generalized formula (regular bundle): 1.0 (4.25) where 6.93(5 /d}ln(s/d) A(s / d) = exp 1.411- (4.26) •Js/d-1 X = B(s / d}zc(s/d) (4.27) (4.28) C(s / d) = 0.7l[exp(js/d-l)] / [(s (4.29) P,(e) = 0.98158 + 1.0923s2 - 0.0892e3 ; (4-30) , 0.1- - 2« - 1)]; y , (e) = ex/?[- e / (l + 1.68e)]; (4.31) y 2 (* / rf) = 0.74(l + {(s / d - 1) / [l - 1.5(5 / J - Correlation (4.25) describe xperimentan ca s l wida dat n i ae range f parametero s s (Fig.4.38). The following expression on maximum pin temperature non-unifonnity in the event of the pin is shifted in accordance with the Fig. 4.37 was obtained from the subchannel approach: max _tmm r. T ( \t A/ i al L 5 w l w 1 A,/— - qd/2 f Pe A/ Z, -H (4.32) Nut Nup Zp+l where Pe and A/0 - Peclet number and coolant overtemperature in the internal standard channel - subscrip / maximue , th f o t m temperature channel - subscrip P ;e th f o t minimum temperature channel. 202 Relative coolant temperature difference is found as: \ / I (4.33) where g, = W,a>, I (W0a>0}; gp = Wta>, I (W0a>0}; f(TM) = (4.33a) •*= T ——— = —— T ; M g, MP S g,,gp-relative coolan te i-th d p-thfloth an n wi channels axia- Z ; l coordinate; //J, //J, /£,n*p mixin- g g factorclearancee th n i s , / d s betweean / , channele / nth d an / s p and q respectively, calculated by relatioships from [34, 35]: (4.34) Fig.4.37 compare predictee th s experimentad dan l temperature distributions around e shiftef reliablo th e s evidentdi us et i pins e datmixins n th o A ,.a g factors offer good relation. 4.3. FUEN TEMPERATURPI L E DISTRIBUTIO N SOMI N E VARIANTF O S DEFORMATION Belo wpresentes i d some variant f deformatioso n when thre four eo r smooth pine sar displaced until touching one another (Fig.4.39, a-e). It seems likely that variant, when four smooth pins touch each other, involves the high temperature non-uniformities, as the area being clos infinito et e compac arete bundlth a witd ean h subcooled liquid nea plane th r e wrapper side are formed. Temperature field inherent at the shifting four pins is presented in Fig. 4.40. e maiTh n effect relationshipsd an s . Temperature distributio generaln i , a nis f o , smooth character (the first harmonic Fourien si r series dominates); local temperature splashes pointe inth contacf so reflectes i t dbeginnine justh t heatee a t th f go d section, when coolant temperatur higho s t .no s ei The maximum temperature non-uniformities in deformed bundle produced by three shifted pins are followed the empirical correlations: edge pins * ma m. mx _ _ . mm w w = 107Pe-°52, lld = 185; 50 < Pe < 800; (4.35) qR h 203 corner pins 0 74 AT 204Pe~W= - , l/dh= 185; 50 1M ATW = 1072Pe- , 11 dh = 185; 70 edge pin (Fig.4.41): N 0.23u= 10~+ 4Pe128,20 corner pin: N 0.19u= +1.2.10~4Pe'28JO Fig.4.41 illustrate shiftingeffecte n sth pi f o s . Maximum temperature non-uniformitie foue evene th th r f n smootso ti h pins comn ei contaco t t ove bundle rth e length (without displacers evaluatee )ar : das edge pins (Fig.4.39,d) j. max _ y. nun AT = " -~ w l =16- 2.58(\g Pe)2 + 4.36 Ig Pe, (4.40) W qR f Ildh=l85\ 30 ^ max _ . min 1135-4.8(\gPe)= A w — 1178\gPew AT + 2 = , (4.41) f W qR l/dh=185, 30 517 where TM=———; gc = gc > . 204 — mixing factor due to pin heat conduction, z - distance from the beginning of heatee th d section, subscrip mean» «c t s compact arrangemen pins.e th f .to Temperature non-uniformity of the pins producing the compact channel can be evaluated as: 43"4 C ) a e * , Aj c ma c ^ x . _A m .ma,m x J • \ ' I j r r o _, _7 c t \ \ ° w w VAr^ L,+tc 8L J with the maximum pin temperature being: d\ Pe (4.44) where Nitcomp, ATconv> are calculated in accordance with Chapter 3. Relationships (4.42-4.44) show that high coolant temperature e compacth o t e t du , channel is formed, can result in the intolerable pin temperature at the inherent for fast reactor range (Pe= 100+400). Statistic evaluations. Universal relationship. Variation in the in-pile channel geometry is of statistic character. Under these conditions, relatioships mentioned above can yield only some limit values. At the same time, geometry of real subassembly are so widely diverse, hardls thai t i t y probable their modelin investigatiod gan n under specific conditions. temperature Th e non-uniformitie requires i s estimatee b o dt variour dfo s bundle kinth f do e deformation (taking into account statistic nature of variation of the channel cross sections, for which the more universal, than the correlations discussed above, relationships should be derived. These relationship generalizee b n sca functioa s da f geometricano l parametee th n i r form: * ma m. mx_ w w ATW = - Af=K+Mexp(-mPe) . (4.45) qR 3 where the generalized geometrical parameter represents the relative area of deformed channel being of a maximum cross section. wl(o*= f , (4.46) h averagee th are- f n ao / d , 0 channe £ wher= w l e(Fig.4.42) ; coe * th are- f ao /=; largest channel Factofunctione th , ManK e r ar sdm of/(Fig.4.42) f factoro m K ssu e Th / representM d laminan i an value W sth AT er flow thoroug channee hth l under consideration. Three domains can be separated: 1. 0.5 205 t,°c Fig. 4.37. Fragment of deformed algorithmbundleand (a) of .calculationof temperature distribution over the shifted pin (b): tj - coolant temperature, tj - wall temperature averaged over the separate parts of surface, O -experimental data, —— - final distribution tw(y). 206 _v Fig. 4.38. Predictions of maximum temperature non-uniformity regularthe in triangular pin bundle compared with experiments':(&T™3* )^° -laminar flow. 207 to o oo (tw-tin)'C 60 h 0 60 120 180 240 300 Fig. 4.39. Schematics of combined shift of non-wrapped Fig. 4.40. Temperature around the smooth corner pin, when internalpinsthe in corner (a),areas.and e) edged) (c, (b, four pins are shifted until they touch one another. J/14 10 6 4 2 ^ 04 -o-co - I I I I I I I I 50 100 200 400 600 800 Fig. 4.41. Variation of edge heatpin transfer with Peclet number: - -four-O pins shifted,e ar -limiting1 shift of one nominal- pin, 2 geometry. Prediction (4.45agreemeny n i sb e ar ) t with experimental dat variour afo s variantf so shiftinn pi g withi nwida e rang Peclef eo t number (Fig.4.43,a-c). BENDINN 4.4PI . G Experimental investigations. Experiments have bee authore nth carriey n b so t dou measurements of the local pin wall temperature when the pin under investigation touches the six adjacent bended ones (one amplitud bending)f eo shows i t i Figs n i a , , 4.4e a,b- th 4 s .A thermocouple embeddee sar t variouda s levels t allowi , s temperature distributio foune b o ndt aroun internae dth l non-deformed (Fig.4.44,b)n )pi . Geometry of the model is as follows: Oute diametern rpi ...... m m , c/ , 6 1 . Inte diametern ...... rpi m m , ,J/ 3 1 . Relative pitch, s/d, ...... 1,185 Length of heated section, 10, mm ...... 1700 Distance ...... betwee gridsm d m en , ,L e nth . 1820 Clearance between the wrapper and edge pins, A, mm ...... 1,5 Relative clearance A / (s - d)...... 0,5 Thickness of the wrapper 3, mm ...... 2,5 Wrapper size, b, mm ...... 117,5 Heater ...... stainless steel 0 2 Numbe pinsf ro ...... ,n 7 .3 Model cross section, w, cm2 ...... 43,1 Hydraulic diameter n mm...... ,d 9 .6, 209 K) t——» O M m 10 -a, 2 V. 1 S-d D h V 0 fc»-—-CH a o II \l -1 ,„ ,0) i i 0 Ad) -10 ii ACO AU) 0,5 Q6 0,7 0,8 0,9 1,0 0.5 0,6 0,7 08 0,9 1,0 0,5 0,6 0,7 0,8 0,9 1,0 a) b) Fig. 4.42. Schematic view on the edge pins shift (a) and coefficients k, Mandm ; symbols experimental- data variouson types of shifting. & © p © O-t CO 9 Q g o -s Si" U3< OJ< QC <*-« £s •C I I I i i i i a" I O CM o .OJ ..o S rtS- CD g 1 1 1 1 1 i i i i i 211 "_ • Iw = -3 t™™—1°"" qf* N --o. 00" uMumamocod "o'-oo. e-os(s-d) cnemeHue uwumamopa 2- Se3 BumecHumeneu 00' COvO _J______1____1 ~~q—o ^ Kacanu unumamopo* 2 e s " Pe 20 40 0 60 0 40 200 c) Fig. 4.43. Maximal non-uniformity of pin temperature as internal (a) and edge (b, c)pins shifted in triangular bundle: O - experiments data, —— -prediction. 212 60 in PC =280 50 >r Ic, A - A in o HanpaS/ieHue J-J o, 10 20 10 2 • • i " i —T" 7 ~ i ' i~T'~ r i " i i i i i i i i i i i 0 60 120 180 2W 0123if5678910 1112131^1516 KaHa/ta HanpaS/ieHuu6 n /max~ *CWt " 0,9 25O 0,8 0,7 1,01 200 0,6 0,5 50 100 150 L/dr 100 200 300 WOPe d) Fig. 4.44. Cross section (a) and axial view (bO of the model Fig. 4.45. Perimeter (a) and length (b) distributions of central pin temperature to with the pins banded in the middle zone (c). in such modela (see 4.44), coolant temperature relativeand (c) temperature non-uniformities central- (d)(O pip) compared with bundles. thosepin for Against a background of the appreciate enhancement of temperature the periodic non- uniformit observes yi contace th n di t point (Fig. 4.45a); temperature distributionn alonpi e gth peas ha k displaced alon coolane gth t flow (Fig. 4.45b); coolant becomes highly heatee th n di compact channel becomed an s s subcoole enlargen thosn a i d f o e d section channels (Fig. 4.45c). Dimensionless periodic temperature non-uniformities at great Pe (Fig. 4.45d) is lesser than in compact bundles of the same equivalent thermal conductivity (f = 0.2), but is practically coincident with those in the bundle with s/d = 1.01. Analytical solutions. Equation boundard san y conditions. Typical failure situation when pins bend compace tilth l t channe s formei e internall th n i d , edg r corneeo r aref ao subassembl dscribee b n yca d wit followine hth g equations: Governing energy conservation equation: r. t,, Zi q,n, + : and using mass balance equation written for the channel d , , , (4.47) we obtain a.. where i = . = J T ' 4 qL ' ' L qU *' & f ' w 1 Pe = pcp \vL I kj -- Peclet number based on the heated length, w - - mean coolant velocity, w- internal channel cross section, q - mean heat flux, IT- perimeter of the internal channel - perimete , U , z'-te th h f channel o rmolecula- t A , f turbulenA d , an r t coolant thermal 3 w conductivity, wZj = 2] ,y^,y --total transverse flows, wy - transverse velocity between the j=i channel sandy/ - clearanc y As , e betwee channele nth sandy/ . Boundary conditions: Tt(0) = 0; } (4 49 lT(1)lV> = ±T 214 Assuming, that change in temperature in the deformed channel does not influence on the temperature in adjacent nominal channels, we obtain: ] Q= TtdZj . (4.50) o constanevene e Inth th f to lengtn ti h power productio fine nw d that: r = (4.51) Main features of temperature behaviour in deformed channels. An influence of the following factors on coolant overheating has been analyzed: • axial thermal diffusion (ter Tm2 /d dz2) • kin deformatiof do n (exten shaped tan ) • power production distribution over the bundle length. Variation in near wrapper clearance is given by the correlations: 1 + k sin 2 (4.52) (4.53) positiv- whern , m , ek integers nomina- 0 ,A l clearance. The feature temperature th f so e behaviou follows a e rar s (Fig. 4.46): • the coolant temperature increases with the length of deformed section (curves 3 and 4 in Fig. 4.46) and as the minimum flow decreases; • maximum temperature in deformed region does not exceed those under maximum allowable deformation (curv Fign i e2 . 4.46); • the maximum coolant temperature is displaced up from the section of minimum flow, extenbendino n s t pi evene de no th gs (abouth i f n to i • t 10-20mm moderat)a e ris coolann ei t temperatur maximuee (lesth f o s tha% m n10 allowabl etake) s place (curv , Fige4 . 4.46)f I . s i bende n thpi ed ovee lengt00mm1 th r0- 5 h , coolant temperature approachee th s maximum value (curv Fig, e3 . 4.46). 4.5. DEFORMATION OF BUNDLE AND SUB ASSEMBLY WRAPPER TUBE The great deformatio f campaigbundle o th d f o ns observeen ei e n th [23] r t da Fo . example middle th n i , e cross section together wit bundle hth shiftes ei d till touchin sideo gtw s wrappee odisplacemenn fth pi e rth observes ti d (Fig. 4.35) doingo s compacn e .I ,th t channels can be formed in the internal and edge areas of subassembly. 215 Experimental results variane wrappee th On . f o t r deformatio s presenteni Fign di . 4.47a wrappee Th . r deflect sucn i s hmannea pine rth s touc sidee hon , wit cavite hth y being formed near the opposite side in the middle cross section. As to the performance of the experiment, it should be noted that the cavity can be approximately reproduced by the plate with the window inserted between the wrapper side and pins (Fig. 4.47b). The plate is made so, that displacers are regularly arranged (Fig. 4.47b, c). Wall clearance is bridged in the top and bottom parts. Other side undee sar r nominal conditions (Fig. 4.47c). Geometry of the deformed region of the model defines the process of heat and mass transpor than i t t region. Three inherent section separatede b n sca inlee ; th the te (l/dyar h< 70), intermediate (70>l/dh>200) and outlet (l/dh>200). At the inlet section the maximum temperatur e corneth n (Fig.4.48 pi f r o e ) falls e wrappeclosth o t e r 30°}(#?+ d 0 «an minimum temperatur observes ei opposite th t da e side (< p180°).« Withi centrae nth l section temperature behavior becomes more smooth, but the region of regular channels ( Respective chang maximue th n ei m temperature non-uniformity alon comee gth n rpi is presente Fign i d . 4.50 evidents i t .I , thacornee th t produce n rpi greatese sth t temperature non-uniformity alon cornee gth r pin valuee ,th f temperaturso e non-uniformities aroune dth specific pins (internal, intermediate, corner) at the same length are presented in Fig. 4.51. Under deformatio temperature nth e behavior becomes non-symmetric (Fig. 4.51-4.53). Prediction of temperature behavior in fast reactor subassembly. Calculations have shown [33 tha] temperature 42 ,th t e behavio subassemblyn ri , defined having regaro dt stohastic deflection geometryn i s , differs essentially from thos regulan ei r geometre th f yo bundle. The compact channel formed in the edge or the corner area causes the intensity of inter-channel exchange to reduce, that is associated with the coolant temperature increases. Thtemperaturn epi e pointpeake th t f contactsa so , wit temperature hth e distribution around the pin increasing significantly. These effects predicte r BN-80fo d e illustratear 0 n Figi d . 4.54 together wite hth general temperature non-uniformity induced by the wrapper bending, there are hot spots, where temperature is comparable with the mean outlet temperature. But there is no a high pin wall temperature observe reactoe th t da r core outlet. A great neutron flux in the middle of reactor core can cause the pins and wire to be twisted together (Fig. 4.35, 4.55). Joint twisting and bending effect results in the pins touching the subassembly wrapper. When swelling of the wrapper is more than swelling of the bundle, with the cavity being generated, the coolant flow is redistributed over the subassembly cross section, wit temperature hth e non-uniformity increasing (Fig.4.56). 4.6 SUBASSEMBLY THERMAL INTERACTION The periphery of reactor core incorporates a non-uniform power production, that cause radiatioe th n deformatio proceeo nt d unevenl finalld yresponsibls an i t yi wrappee th r d efo ran bundle deformation, which can change in campaign. Text cont.230.p. on 216 0,3 0,2 0.1 4 3 2 J———L i___i___I___i___i_____I 0,5 1,0 F/g. 4.4(5. Deformation bundlep ofpi when cornere th d bendsn an pi ) (a variations in relative temperature T, coolant flow g in the corner channel mixingand factor with bundle length (b): nominal- 1 bundle, -bundle2 re- tained against the cover, 3 - bending bundle, ——— - uniform equipped power production, — — — - cosine power production. 217 to I—I oo tifl Fig. 4.47. Deformed modelthe coverd). and axial c, (a) (b, 7,52 7,50 7,W 7, 0 60 120 180 ZW 300 Fig. 4.48. Corner pin temperature in the model of deformed cover. / mi/ _ 7 x ma w 1 - 0 50 100 150 200 250 l/dr Fig. 4.49. Maximum temperature non-uniformity alongthe cornerin the pin subassembly of deformed cover. 5OO 200 100 0 Fig. 4.50. Maximum temperature non-uniformity inherentofthe pins l/dat h =256 1 - corner, 2 - intermediate, 3 - internal pin; — — - corner pin in nominal experimental- geometry,O , € , O data. 219 Pe = 196 19*+ 192 190 ______Number 98 88 59 16 13 56 86 101. of cell 101 Fig. 4.51. Sodium temperature distribution outletthe in model cross sectionof deformed cover: 13+101 - channel numbers, O -measurements, —— - averaging line. in -tin 1,0 0,8 X-0- 0,6 0,* 0,2. 0 J___1 III III Fig. 4.52. Outlet coolant temperature modelthe in of deformed cover: displacer- • abundant,is displacer- abundant,O not is tjn - inlet coolant temperature. 220 t,°c 198 '00 197 196 195 y>'300 2W 180 120 0 60 Fig. 4.53. Cover temperature measured experiments.in to to to q=const i mAX 1/OBOA oooooo ,100 ooooooo oooooooo oooapooo ooooooooooOOOOOOGOOo oooo®©oooc»ooooooo y A3 ooooooooooooo 13579 >JSTB3AA Fig. 4.54. Schematics of deformed bundle sections (a), maximum pin temperature and maximum temperature non-uniformity around underpin the conditions of variableuniformand (b) (c) power production. q=const LIEHTP AKTMBHOI* 30Hbl BblXOA U3 AKTHBHOM 3OHbl 12.c = var LIEMTP AKTMBHOft 30MN max 8'C Altp BblXOA M3 AKTMBHOPl 30Hbl Fig. 4.55. Twisting wire wrapped pins (a), maximum pin temperature and maxi- temperaturemum non-uniformity under conditions of variable uniformand (b) power production (c). 223 to HA BblXOAE M3 AKTMBHOM 3OHbl max ___593'c \\ HA BblXOAE M3 RA3VXM .70-C inlet d) a) Fig. 4.56. Cover expansion (a), coolant temperature axialin cross section bundle ofthe (b), temperaturepin and temperature non-uniformity at the core outlet (c) and in the top expanded section (d). 3 z=> Centre i core Fig. 4.57-a. 1,2 1,0 I-P 1 < 0,8 a>X 0,6 < 5V o ° ID 0,4 0,2 A E C D Fig. 4.57-b. 225 0,20 - 0,16 _ 0 0,12 -P <3 0,08 0,04 A B C D c) Fig. 4.57. Schematic of the peripheral area of reactor core (a), predictions of maximum pin temperatures (b), of maximum temperature non-uniformity (c) in deformed geometry: 1 - nominal geometry, 2 - bundle bending when the edge pin wires touch to one side of the cover, bundle- 3 bending when edge claddingsthe pin cover,touchthe to combined- 4 cover bending until touchit adjacent-specificE) D, C, coverB, (A, pointscoverthe at sides). 226 240 300 360 Fig. 4.58. Temperature distribution over coverthe variousin type bundle ofthe coverand deformation (symbols Fig.in 4.57).see A B C D Fig. 4. 59-a. 221 0,20 0,16 - Q Q 0.12 00 -(-> 0,08 <] 6 0,04 A B C D Fzg. 4.5P. Maximum pin temperature (a), maximum temperature non-uniformity (b) in the events of deformation. -P 1,0 - x CO -P - 8 0, 1 X Q) 3* 0,6 0,4 - 0 36 0 30 0 24 O IS 0 12 0 6 0 .Fig. 4.60. Temperature around coverthe (symbols fig.in 4.47).see 228 UCHTP AKTMBHOM 30Hbl max ,628 'C - 4 /627- BblXO 3 AKTMBWOAM M 30Hbl ,54'c Fig. 4.61. View fastof reactor subassembly coverin crushing (a), maximumpin temperature maximumand temperature non-uniformity middlethe in cross section (b) and the core outlet (c). bundle evene Ith nth f o te bende directioe th cor e n di th ef ncenteo r (Fig.d 4.5an ) 7a the edge pins touchin covere gth , maximu temperaturn mpi e (Fig. 4.5 , wel7 b) maximus a l m azimuthal temperature non-uniformity (Fig. 4.57 c) increases. The pin bundle deformation results in the distorted temperature behavior at the wrapper (Fig. 4.58). If the pin bundle is bended away from the core center, the lesser temperature non-uniformitie observee sar d (Fig. 4.59,4.60). crumplee th r Asfo d cover t shouli , notee db d tha forca t e applie wrappee th o dt n rca amoun somo t p eu t kiloNewtons. Unde effece rth sucf o t hdistributea d loa deformatioe dth n may be significant [43,44] (Fig. 4.61): the bundle and wrapper are deformed, the bundle pitch change n i ssevera l directions, that result n i svariatio n coolani n t flow througe th h subassembly. But, becaus deformee eth d are s usuaaa l cover t morsno ee thathire th f on ndo subassembly length, variation in pressure drop seems to be not more that 10-15%. CONCLUSIONS 1. A joint analytical and experimental studies of fast reactor thermal hydraulics result in the data obtained on influence of various factors on distribution of local velocities (flow rates) of liquid metal coolant aroun alon d inherene pinde an th gth n si t subassemble areath f so y (internal, edge and others), as well as across the subassembly. The relationships and graphical representatio needee nar predico dt t hydrodynamic reacton si r core. The following amone sar mose gth t important result hydraulif so c studies: • Channel-to-channel interaction of the coolant flows is the basic factor defining variation in hydraulic characteristics of the pin bundle, as whole and separate channels, as particular, that generates a need for performing analytical and experimental studies of multi-pin bundles simulating a fast reactor subassembly. hydraulice Th • fasf so t reactor subassembl larga o t e s yi exten t define greaa y db t non-uniformitie f velocito s y aroun edge dth e pincombined san d exchange within the subassembly due to wire wrap on the pins. • Contrary to the previous notion on the possibility for predicting subassembly hydrodynamics based on the coolant velocity averaged over the subassembly cross section or based on the hypothesis of isobaric cross section, it has been show that such an approaches, as a rule, do not ensure the wanted accuracy of results. • Hydrodynamic calculations taking into account channel-to-channel interaction of coolane th t flows reflect realistically specific hydraulic feature f interconnecteo s d channels and allows the prediction of velocity distribution over the subassembly to be defined reliably. • Flow parameter geometrd san edg e th ef y o area subassemblyf so wels a ,dat s a ln ao the local hydraulic characteristics of the edge channels allow the optimal variants of the subassembly geometry to be chosen, as an important conditions for the uniform distributio coolanf no t temperature ove subassemble rth y cross section. • An irregular field of velocity in the edge area of subassembly or deformed field due to shifting of one or several phis from nominal positions can serve as input data for gaining momentum mixing factor (smooth pins), velocity distribution in the bundle of wire wrapped pin s usei s o derivt d e convective componen f interchanneo t l exchange, including those in the channels between pins and the subassembly wrapper. The parameters mentioned were gained and used in the code developed to validate thermal hydraulics of fast reactor core. 230 2. The study of deformed subassemblies (shifting, bending, swelling, creeping and so on) occupies a highly important place in the thermal hydraulic validation of reactor core. The following problems have been solved: • Temperature behavior of pins hi the various events of single or coupled shifting s studiewa d during experiments s limitina , g variants e maiTh .n effect were understood and the basic relationships were derived. Numerical procedures were developed that gave results bein agreemengn i t with experimental data. • Universal relationship was derived which allows estimations of temperature non- uniformity under the real operating conditions taking into consideration statistical character of variation in the channel cross section during deformation. • Experiments were carried out on the mock-up subassemblies to study temperature behavio n i rbendin n bundlpi wrapped f go an e r tube. Analytical solutior fo n different cases of pin and wrapper bending was obtained, with the following comparison predictions and experimental data. • Subchannel code TEMP-MTF intended to predict thermal hydraulics of reactor core having regar o subassemblt d y deformation allows validatio f temperaturo n e behavio fasf ro t reactor core performance wit higha h accuracy. This codhigf o s hei wide e usee th b n dn ri speerangeca d dparameteran f so s than other known codes. 3. The temperature distribution in several adjacent subassemblies were analyzed having regard to variable power production over the core radius, that is responsible for non- uniform radioactive deformation in campaign. subassemblevene e Inth th f to y wrapper bends towar core th e o dcentert maximue th , n mpi temperature increases, as well as azimuthal temperature non-uniformity. At the same time the pin temperature decreases in the area close to opposite sides of the wrapper, that is connected with the enhancement of the width of clearance between the edge pins and wrapper tube. The force exertee wrappe o thermath t n e do du r l interactio f subassemblieno e b n ca s significant (some kiloNewtons), and as a result the wrapper deformation occurs: there observed variation meae th nn si pitch-to-diameter ratio, bundle cross section area, coolant flow throug subassemblye hth . Effectestimatee b differene n ar sca d d an usint codee gth s developed. REFERENCES [1] Subbotin V.I., Ushakov P.A., Levchenko Y.D.. Velocity Fiel Turbulenn di t Flow Passing through the Pin Bundle. Preprint IPPE-198, Obninsk, 1970 (in Russian). [2] Eifler W., Nijsing R. Experimental Investigation of Velocity Distribution and Flow Resistance in a Triangular Array of Parallel Rods. Nucl. Eng. and Des., 1967, v.5. [3] Ibragimov M.H., Yusoupov LA., Kobzar . CalculatioL.Lal t e . Walf no l Shear Stresses and Turbulant Velocity Distribution. Atomic Energy, 1964, v.21. ] [4 Buleev N.I. Calculatio f Velocitno y Fiel Turbulencd dan e Thermal Conductivitn yi Combined Channels. Thermal Physics of High Temperature, 1971. [5] Subbotin V.I., Ushako . CalculatioA . vP Bundln Pi f no e Hydrodynamics. Simulatinf go Thermodynamic Fasn si t Reactor Core, Prague, 1971, p.44-57. ] [6 Ushakov P.A., Zhukov A.V. . (USSR)al t ,e , Mantli . (CSFRal , Heint ke F. , .aJ. Investigatio f no Thermadynamic Regulan i s Deformed an r d Bundle f Pins, o s M. . CEMR, 1978. 231 ] [7 Subbotin V.I., Zhukov A.V., Ushakov P.A. Liquid Metal Velocity Distributio Fasn i t Reactor Subassembly Models. State and Trends of LMFBR, Obninsk, 1975, v.2, p.100-127. ] [8 Hein , ChervenkJ. a , MantliJ. a . ResultkF f Locao s l Measurement f Hydraulio s c Chracteristics in Deformed Pin Bundle. UJV - 4156-T, parti. Rzez, Czech Republic, 1977. [9] Zhukov A.V., Sorokin A.P., et al. Thermal Physic Validation of Temperature Behavior in Fast Reactor Subassembly Having Regard to Hot Spot Factors. Preprint IPPE-1816, Obninsk, 198 Russian)n 6(i . [10] Zhukov A.V., Sorokin A.P., Titov P.A. Turbulent Momentum Exchangn Pi n i e Bundle. Preprint EPPE-2015, Obninsk, 198 Russian)n 9(i . [11] Rowe D.S., Jonson B.M., Knudsen L.G. Implication Concerning Rod Bundle Mixing Base Measurementn do f Turbuleno s t Flow Structure. Int . HeaJ . t Mass. Transfer, 1974, v.l 7. [12] Rowe D.S. A Mechanism for Turbulent Mixing between Rod Bundle Subchannels. TANS, 1969. 12 . v , [13] Roidt, Pecherski, Markin et al. Determination of Turbulent Mixing Factor in Pin Bundles. Heat Transfer, 1972, v.96. [14] Rudzinski K.F. et.al. Turbulent Mixing for Air-Water Flow in Simulated Rod Bundle Geometries. Canadian J. Chemical Eng., 1972, v.50. [15] Zhukov A.V., Sviridenko E.J., Matjukhin N.M., et al. Investigation of Combined Flow Hydrodynamics in Wire Wrapped Pin Bundles. Preprint IPPE-867, Obninsk, 1979 (in Russian). [16] Zhukov A.V., Sviridenko E.J., Matjukhin . LocaN.M.al t e l, Hydrodynamic Characteristics of Interchannel Exchange hi Fast Reactor Subassembly. Preprint IPPE- 665, Obninsk, 197 Russian)n 6(i . [17] Zhukov A.V., Sviridenko E.J., Matjukhin N.M. . Studal t Interchannef ,e y o l Exchange in pin Bundles of Small Relative Pitch. Preprint IPPE-799, Obninsk, 1977 (in Russian). [18] Zhukov A.V., Sorokin A.P., Titov P.A. Analysis of Data on Interchannel Exchange in Wire Wrapped Bundles. Par . Interna1 t l Area. Preprint EPPE-1574, Obninsk, 198i 4(h Russian). [19] Bolle L. et. al. Experimental Determination of the Local Transverse Mixing in a Rod Bundle with Helical Wire Spacer / Rep. Int. Meeting on Reactor Heat Transfer. 1973. Karlsruhe, Germany. [20] Patch L. Experimental Studies of Flow Distribution hi a Wire Wrapped LMFBR Blanket Assembly. Ibid. 1979. Karlsruhe, Germany. [21] Markley R.A. Status of Core Thermohydraulic Development in the USA. Thermodinamic FueR FB l f Subassemblieo s s under Nomina d Non-Nominaan l l Operating Conditions, EWGFER / 29, 1979. [22] Proshkin A. A., Likhachev Yu.L, Touzov A.N. Analysis of Experimental Data on Fast Reactor Subassembly Deformation. Atomic Energy, 1981, v.50. [23] Marbac . J Comportemenh t d'un Faisceau d'ajgulles Phenix Sour Irradiatio1 1 n Irradiation Behavio f Metallio r c Material Fasr fo s t Reactor Core Components.CEA- DMECH-B. P.N.2-91190, YJF-Sur-Yuette, France, 1979. [24] Zhukov A.V., Sviridenko E.J., Matjukhin N.M.. Temperatural t e , e Field Head an s t Transfe Edge th en i rArea f Hexahonao s l Bundles. Problem f Nuclo s . Sciencd ean Eng. Reactor Des., 1977,4(18 Russian)n )(i . 232 [25] Zhukov A.V., Matjukhin N.M., Nomophilov E.V. Temperature Field Non-standarn si d and Deformed Bundles. Thermal Physics and Hydrodynamics of Fast Reactor Core and Steam Generators, Prague, 1978. [26] Zhukov A.V., Sviridenko E.J., Matjukhin N.M., et al. Temperature Behavior in Deforme n Bundlepi d s under Unifor Non-uniford man m Thermal Loads. Preprint IPPE-909, Obninsk, 1979, Russian)n Par(i 1 t . [27] Shul . ExperimentacV l Investigatio Temperaturf no e Field Deformen si Bundlesn dPi . Hydrodynamics and Heat Transfer in Fast Reactor Core and Steam Generators, Prague, 1984, v.l. [28] Hishida H. Detailed Consideration on Wire-Spaced LMFBR Fuel Subassemblies Unde Effece rth Unsertaintie f o t Non-nominad san l Operating Conditions. IWGFR/29. Vienna: IAEA, 1979. [29] Mik . DeformatioK i n Analysi Fuef so l Pins Withi Wire-Wrae nth p Assembln a f yo LMFBR. Nucl. Eng. and Des., 1979, v. 52. [30] Molle , TchokR. r . Steady-StateH e Local Temperature Fields with Turbulent Liquid Sodium Flo Nominawn i l Disturbed Bundle Geometries with Soacer Grids. Nucl. Eng. and Des., 1980,v. 62. [31] Zhukov A.V., Sviridenko E.J., Matjukhin N.M. Heat Remova Fasn i l t Reactor Core. Atomic Energy, 1985, v.58. [32] Zhukov A.V., Sorokin A.P., Ushakov P.A., et al. Thermal Physic Validation of Temperature Behavio Fasn i r t Reactor Subassembly Having t RegarSpoHo to t d Factors. Preprint IPPE-1778, Obninsk, 1986 (in Russian). [33] Kazachkovski O.D., Zhukov A.V., Sorokin A.P., et al. Temperature Behavior uiDeformed Fast Reactor Subassemblies. Atomic Energy, 1988, v.65. [34] Recommendations on Thermal Hydraulic Calculation of Fast Reactor Core. PTM 1604. 008-88. State Committee on Nuclear Energy. M., ONTIIPPE, 1989. [35] Zhukov A.V., Kirillov P.L., Matjukhin N.M., et al. Thermal Hydraulic Analysis of LMFBR Subassembly, M., Energoatomizdat, 1985. [36] Zhukov A.V., Sorokin A.P., Khudasko V.V. Problems of Thermal Hydraulics in Non- Nominal LMFRB Operations, Textbook, ONPEI, Obninsk, 1990 (in Russian). [37] Zhukov A.V., Sorokin A.P., Matjukhin N.M.. Interchannel Exchange in Fast Reactor Subassembly: Code Applicationsd san , Energoatomizdat,M. , 1991. [38] Zhukov A.V., Matjukhin N.M., Sviridenko E.J. Experimental Stud f Influencyo f o e Deformation on Temperature Behavior of Edge Pins. Thermal Physical Investigations, IPPE, 1980, Parti, p.27-3 Russian)n 7(i . [39] Bobkov V.P., Savanin N.K. Local Heat Transfen i e r Us Coefficien s It d an t Temperature Calculations. Atomic Energy, 1981, v.51. [40] Zhukov A.V., Sviridenko E.J., Matjukhin . InfluencN.M.al t e , f Deformatioo e n o n Tempeature Behavio d Heaan r t Transfe n Specifii r c Area f Faso s t Reactor Subassembly. Preprint EPPE-979, Obninsk, 198 Russian)n (i 0 . [41] Zhukov A.V., Sviridenko E.J., Matjukhin . ExperimentaN.M.al t e , l Investigatiof no Liquid Metal Temperature Behavior and Heat Transfer in Triangular bundles. Preprint EPPE-800, Obninsk, 1978 (in Russian). [42] Kazachkovski O.D., Sorokin A.P., Zhukov A.V., et al. Stochastic Temperature Non- Uniformitie Deformen i s d Subassemblies. Preprint IPPE-1678, Obninsk, 198n 5(i Russian). [43] Zabudko L.M., Likhachev Yu.I., Proshkin A.A. Operation of Fast Reactor Subassemblies, M., Energoatomizdat, 1988. [44] Lieb . SubassembleR y Experiment Computea d san r Cod Analyzo et Dynamie eth c Code Deformation During Local Failure Propagation. Nucl. Eng. and Des., 1977, v.43. 233 NEXT PAGE(S) <«ft BLANK Chapter 5 INTERMEDIATE HEAT EXCHANGER THERMAL HYDRAULICS 5.1. FEATURES OF LMFBR fflX THERMAL HYDRAULICS Thermohydraulic processe e inter-tubth n si e spac f faseo t reactor intermediate heat exchangers (combined transversal-axial flow) were studied in the wide ranges of the main parameters' variation, including low-velocity and natural convection heat removal [1-3]. The studies were concerned with the validation of thermal hydraulic performance of heat exchangers undes a , r nomina non-nominad an l l operating conditions particulaf O . r value ear experimental and calculation data on the local velocity and temperature behavior inside of the tubes and in the inter-tube space, allowing calculation of full-scale heat exchanger or developing numerical procedures and codes of IHX thermal hydraulic analysis. Thus, the case in point will be the combined approach to fast reactor IHX thermal hydraulics. The main feature of such an investigations is detailed velocity and temperature measurements in the "hot" and "cold" coolants compromising a local (in each tube and in each channel) and an integral (in headers) techniques. Some of ideas on the modeling of fast reactor IHX thermal hydraulics have been considered in the chapter 1.3. The others are presented below t wil I .recallee b l d that transversa axiad an l l component f liquio s d metal velocity are measured with the use of electromagnetic method, whereas the temperature behavio s controllei r e mobilth y b de thermocouples t shoulI . e noteb d d that only local modeling provide gaininr sfo gplausibla e thei r resultfo rd convertinsan g intfull-scale oth e IHX performance, wherea "globale sth " measurements (when temperature "hote th d n si "an "cold" flows are determined in the headers) produce particular results which are considered inappropriat actuae th o et l desig multi-tube th f no e IHX. Doing it away to reproduce and study hydrodynamics and heat transfer in full scale, it shoul notee db d that local thermal modeling mentioned above allow experimente sth e b o st carried out on a simple tube bundles considering the main hydrodynamic and thermal effects of transversal-axial flow not associated with that the particular structure are reproduced in general terms, the data gained to be converted into "infinite" (regular) zones of full-scale heat exchangers and the most important effects involving one or another of heat exchanger's design reproduce e modelth n i d. However n developini , g suc a hsimpl e modele th s fundamental condition f multi-tubo s e heat exchangers shoul e accountedb d e , th suc s a h number and length of the tubes, their arrangement, coolant flow and so on. Under this performance the data gained in the experiments, as pointed above, are a great convenience to be applied as a reference data in the development of calculation procedure. 5.2. HYDRAULIC RESULTS Triangular arrangement Experiments were carried out on the "plane" models (Fig. 1.14 and 1.15 from the Chapter 1.3) involving one or three rows of the tubes, displacers attache wrappee th o dt r (the model justifiee sChaptear e th n di r 1.3). Experimental one-row model with triangular arrangemene th e tube s th ha f so t following geometrical parameters: 235 Outer diamete tube th ef r(displacerso mm...... , )d 9 1 . Inner diamete mm...... , rdi 8 .1 Number of tubes n...... 7 Numbe displacerf ro s N...... 6 1 Pitch-to-diameter ratio s/d...... 1.315 Tube length enclosed by the spacing grids L, mm ...... 1000 Heigh inlee th tf o twindo , mm...... 0 w1 . 350(150) Height of the outlet window LO, mm...... 80 Deptwrappee th f hmm...... , o rho 5 17 . Thicknes wrappee th f so mm...... , rb . 43,5 Coolant (eutectic alloy NaK) comes from the "large volume" (bottom header) throughou windoe tth w int tube oth e bundle, wit headerhp flowinto e th , thao gt t simulatee sth inlet conditions (see Fig. 1.14). Electromagnetic techniqu s useei d (se detain ei l Chapter 1.4 measuro )t e locaeth l velocit liquif yo d metal locae Th . l electromagnetic sensor (Fig. 1.16 mountes )i d inside th f eo measurement tube, whic introducehs i varioue turn th d i n i s modezonee th f so l cross section. At the tube surface, near the magnet, there are two normally posioned pairs of electrodes, which control the transversal and axial components of liquid metal velocity. Rotating and moving tube wit e sensohth r inside allo locae wth l velocit measuree b o yt differena t da t level sensor'e Th s geometr followss a s yi : width magne(a),e th heighf d lengto an t) ) (c th (b are 5:15: respectively, 5mm coopee ,th r wir distanc, e mm diamete 2 e0. betwee - \ rd ende nth s of electrodes 5i= 1.7 mm. electromagnetie th f o e us e Th c techniqu measurinr efo g local velocit modee th f n yi o l LMFBRIHX has permitted a study of the structure of transversal-axial flow, establishment of the laws that govern the variation in transversal and axial components of velocity with the length and depth of the tube bundle. Experimental results. Transversal component of velocity azimuthae Th l direction (Fig.5.2, 5.3). Maximum velocite observes th ywa n i t dno narrow clearance betwee e tube nth displacersd an s t rotatebu , . Thi•*5 Acy 1 d20 b • s pi s= revealed as during the sensor calibration (Fig. 5.2), and in experiments itself (Fig. 5.3). The maximum amplitude of velocity is observed to be at the first tube. The axial direction (see Fig. 1.22). Distribution of transversal velocity in the clearance betwee tube displaced nth ean r ove inlee rth t windo wexponentiae th heigh f o s i t l form. windowe Beyonedgp th to f eo e dth , velocity reduce zeroo st , wit increasine hth s ga approache outlee th o dt window. Relationship othee th r rsamee stubefo th velocitt e bu , sar y varies more smoothly. Maximum values reduce wit bundledepte e hth th f ho . Axial component f velocity o se inle th t A (Fig. outled . an 5.4 ) ta , (Fig. 5.4) b , sections of the model the distribution of axial velocity incorporate the great non-uniformity (especiall firsr second yfo an t d tube), wit maximue hth m velocity (flow rate) being observed aftee th rn i zon f tub eo e outle th e r ( 236 Maximu ensuine th r mfo g (alon coolane gth t pass )minimu e tubth precedine s ei th r mfo g tube that is evident from the velocity distribution over the outlet window of the model bundle. There are reverse flows (of a weak intensity) at the comer of the rectangular wrapper as demonstrated by negative values of the signal at the last tube 170° < Hydrodynamic f variouso s tube row hean i s t exchanger. Distribution f coolanso t flows averaged around the tube perimeter (Fig. 5.5, a-d) are of considerable importance in reaching conclusio performance th n no variouf eo s tube rows coolane Th . t irregulaf floo ws i r character: at the inlet section it rises gradually with the length and the depth of the model, at the outlet section it decreases with the model depth (c). In the top edge cross section flows e inleth tn i levewindow f of l t stratifbu , y with increasing length floe , thath w s i tenhance s aroun lase dth t tube (lag effect reduced an ) s aroun firse dth t tube. Maximums appearine th n gi flow distribution around every tube are shifted along the length in dependence of the depth of the tube location. Thus, finally we have practically linear function (d). A total flow rate through the area of «closed» cross section is constant (see relationship floe th w d balancan 5 5. confirmes e i Fig n i . measurement) e th (b y db s wit accuracn ha y ±1%. (Ivn) /; / v= (5.1) Profile coolane th f o s t velocity (Fig. 5.5 ) allo,a w gainin impression ga n aboue th t coolant flow variation wit tube hth e rows propee .Th r flow lines show Fig.5.n i 5 e diffeth n i r percentage proportio fulf no l flow that permits analyzin tube gth e performance. It is evident, that an uniform distribution of the flow rate takes place in the cross section / = 350 and 800 mm. Between these sections the flow lines are shifted to the back wall e cover th e followin f o Th . g flow distribution observee ar s e inle e outled th th an t f da o t model: Inlet window (lo - height) Length 0.4 10 - 25% of full axial flow % 50 - 0 1 7 0. 0.9 10 - 75% Outlet window (Z,o - height) Length 0.5 L0 - 25% 0.7 Lo - 60% % 75 - o L 8 0. If the transversal and axial components of velocity are plotted along the horizontal and vertical axis, we can draw the vector diagram of resulting flows in the inlet and outlet sections of the model (Fig. 5.6). If the inlet window is involved, the slopes of the flow path reduce as e moveth d away fro bottoe mth m inlee edgth tf eo windo w (Fig slopee .th 5.7)a t t sa Bu . distance / = 380 and 400 mm from the edge of the inlet window are abnormal. It should be noted that the flow around first tube is practically axial (^?s 5 4- 10°), but those around second and third tubes have the slopes in the range 237 It should be noted, that the rate of transversal flow drop with the depth of the inlet windo wapproximatels i axiae y th rate equa f lth eo flo o t l w rise wit heighinlee e hth th tf o t window (Fig. 5.8). Equalization of the coolant flow over the tube rows can be achieved by the reduction of the inlet window size. So, if the inlet window is overlapped by 60%, flow non- uniformity reduce factoa , resultin 2 y morf e sb o rth en gi graduate flow variation wite hth bundle length (see Fig. 1.21, a, b). Practical value of the effect indicated is that the possibility appear reduco st e heat transfer are hean ai t exchanger. The model with the reduced inlet window (10 =150 mm instead of 10 = 350 mm) gives the more completed transversal velocity of a parabolic character with the blurred maximum falling on the 1/3 of the inlet window (Fig.5.9). Velocity distribution at the inlet section is also more 1 0- 350mm . In the event of the reduced inlet window in parallel with the improved hydrodynamics there alsbees oha n som risea hydraulin ei c resistance (Fig. 5.10mose th r t) thafo par s i tt connected with the pressure drop over the inlet window. However, the rise in hydraulic resistance may be thought of as a small in comparison with the rather great and benefit effect of flow equalization. The effect mentioned above was also observed in hydraulic experiments on the three- row models wit triangulae hth squard ran e arrangemen tubee th shows f sa o t Fign i . 5.11, ,c d. Measurements performed in the three-row model with the triangular bundle have revealed, a wholesa same th , e relationshop one-rothose s sa th n ei w model, thaallowes ha t d drawinga conclusion that the one-row model with displacers readily simulates the multi-row bundle hydrodynamics. Square bundle (low velocities). Experiments have bee three-roe nth carrien o t wdou mode f heao l t exchanger (Fig. 1.15 ) unde,b r condition coolanw lo f so t velocitiesn ca e W . follow the coolant flow direction, along which the lesser resistance takes place most likely. clearance Thith s si e betwee wrappee nth firsd ran t tube, wher maximue eth m axial velocits yi generate demonstrates da resulte th y dsb presente Fign di . 5.1 5.13d 2an ; whenc t followei s that maximum axial velocity falls within the first tube perimeter ( A(p « 120°) adjacent to the plan inlee eth modee t wal th a (Fig f s outlee o la l th . t 5.12a t (Figd )an . 5.13)of coolanta s A . e enhancemenresulth f o t f velocit o te spac th n eyi between first tubcoverd an e , velocity reduce othen si r modele partth f sparticulao n i , distanc a frot m bottora e mm th 0 e9 m edgf eo the window (Fig. 5.14). Transversal velocity distributions around the tube in the area of inlet (Fig. 5.15 outled )an t (Fig. 5.16) windows have maximum clearancee th n si s between tubes and minimums (zeroth value velocityf so frontae th afte d n )i an lr tubee areath f .so Behavio axiaf ro l velocity averaged ove tube rth e perimeter wit modee hth l heighs a s ti follow (Fig. 5.17): • At the inlet section (0< h < 130 mm) velocity rises gradually as with the length and with the modeldepte th f ho ; • At a level h = 130 mm velocities coincide, near the top edge ( h = 10 = 150 mm they are little different from each other, excep tube th twhicjuma 1 e s f velocitpo hha y that represent coolane sth t arriving unde windoe rth w edge (Fig.5.12); modee Th l • outlet velocity increase directef si d fro sevente mth firso ht t tube, where thers ei the clearly defined velocity maximum. The maximum is due to flow "summing" over the channel in the outlet window (the whole coolant flows the tube 1). 238 maie Th n hydrodynamic bundl e effecth f o te under consideratio bundlee th n i s a , nis previously investigate a reduce f o d d inlet window a relativel, y uniform distributiof o n subchannel flows ove depte heighth d r han f tubo t e bundle. Thus, this effect revealee th n di model with triangular bundl s validatei e n experimenti d s wite squarth h e bundles A . mentione greada f aboveo t s importanci t i , possibln ei e decreasin heaf go t transfer surfacn ei fast reactor heat exchanger. Distribution f axiao s l flows ove perimetee th r varioun i r s models (triangular, square bundles, one-, three-row models, with reduced or enhanced inlet window) are summed in Fig. 5.11, where it is evident an influence of the inlet window height, as well as the fact that data obtained on one-row and three-row model are identical. Prediction hydrodynamicf so triangulaf so r heat exchangers. Macro-distributiof no the coolant velocit inter-tube th n yi e spac heaf eo t exchange calculates ri e basie th th f cn o d o porous body model (code RAPORT-1). Theoretical approach presented in [4-8] and prediction procedur includes ei d int Governine oth g Technical Materials [9]. Later the procedure was essentially improved, since the mathematical model, numerical procedure, constants were verified and tested using experimental data on velocity distribution ove inter-tube rth e space. Electromagnetic techniqu velocitf eo y measurements a , wel informatios a l ntechnique gaineth f greaa o s e d etus ha wit advantagee hth s ove othen ra r measurements. The velocity fields were predicted for the one-row and three-row models with the triangular and square arrangement of the tubes hi a wide range of Reynolds numbers (104 10< e ) R unde < r various boundary conditions. Basically, three type boundarf so y conditions 6 givee onth n velocit inle e modeloutlee d th th t an y f a to : A) uniform distribution (considerable resistance of the inlet grid), B) non-uniform distribution (answering experimental velocity around first tube in the model), C) non-uniform distribution definite giveth y nb e laws (relationships) Pressure event e droth axian pf i slatera o d lan l flows were taken fro [10e mth ] aftee th r processin datd gan a generalization. When analyzin one-roe gth w model, consideration must be given to the following features of the problem under discussion. The model has one row of seven tubes t meanI . s that withi pitce transverse non hth axiad ean l velocitie noticeabln sca y vary. A porous body model assumes that the averaged velocity is of "smooth" profile and varies only slightly pitche withion e . nThusth , calculatio f low-tubno e bundl usiny eb e gth porous body model furnish insights int nature procese oth th f helpd eo san answerin n si e gth questions: how the model can be applicable to the low-tube bundles and what discordance can be appeared in the process. In calculatin one-roe th f go w bundl witex displacerse enclosebo hth e th e n di th , porous body model uses friction factors in transverse and axial flows deduced from experiment multi-ron so w ("infinite") bundles. Comparison analysi calculatiof so n allowe sth following conclusio reachede b no t : 239 • wide variatio Reynoldf no s numbe cause) 0 velocit1 e rs< th (10e y4 Fig. 5.18 presents experimental and calculated curves for axial velocity distribution along the first and seventh tube of the model. Calculations have allowed improvement of the inlet section hydrodynamic modee th n si l wit square hth e tube arrangement hydrodynamiy .B c improvemen s meani t t that coolant axial velocity become f uniforso m characte inlee th t a r section, more exactly in the edge of the inlet window. Hydraulic non-uniformity varies in a wide ranges in dependence of the inlet window height and relative pitch of the bundle. In the compact bundle wit smale hth l windows maximum velocit firse th observes y ti t tubea e b .o dt In the free bundles with the large windows maximum velocity takes place on the internal tubes. Three model f heaso t exchanger were calculated. Here relativ 1.06= d e; s/ pitc s hwa 1.2 relativd ; an 1.3 4 e;1. heighinlee th tf o twindo w H/ B0.55= ; 1.0; 2.0; 3.0, e wherth - eB width of the tube bundle. It is evident from Fig. 5.19, that if windows are small a free bundle s optimumi compaca d an , tlarge bundlth r e fo windows e- modee Th . l teste s neadi e th r optimum. 5.3 THERMAL RESULTS On techniqu e locath f le o thermal modeling. Experiments were eth carrien o t dou three-row mode triangulaa f lo squard ran e tube arrangement (Fig. 1.14, 1.15) usin alloK gyNa as a hot (inter-tube space) and a cold (inside of tubes) coolant. Every tube and every channel is equippe capillariee th y db s insid whicf eo mobile hth e thermocouple movee sar d (Fig. 5.20). Essentially locae ,th l techniqu thermaf eo l measurement followss a s si : Temperature variation of every tested tube with the height (Fig. 5.21) is determined for the purpose of analyzing temperature difference "maximum temperature of the hot coolant" - "minimum temperatur cole th d f ecoolant"o . Text cont.265.p. on 240 6 mV A-A V///7///7777\7 7///////A ! T B I B B-B Al J_A 0 60 j 120 180 240 J300 360 84 276 F/g. 5.7. Single-row assem- Fig. 5.2. Calibration transversee modelth d an velocity behaviour bly cross section. 1 - header, 2 - support plate, 3 - pipe - 4wrapper, - displacer. 5 30 60 90 120 150 ISO 210 240 270 300 330 360 0 30 60 90 120 150 180 210 240 270 300 350 Fig. 5.3. Transverse component of velocity around pipe in inlet (a) outlet and -windows(b) model ofthe assembly. 242 e mv e mv (3AT4HK AOKOAbHOrO 8»HCT»H«) •-.-i.^*"i • • 1^1 COCTABAflHJlUAfl CKOPOCTM (dATMMK AOKAAbHOrO 8cHCTtMR) 60 I20 180 240 300 360' /g. 5.4. Axial component of velocity around pipe in inlet (a) and outlet (b) windows. mm Fig.5 Axial5. velocity (a); axial flow rate with modele th length (b); withe th height deepnessand (c); maximum axial velocity differenta for pipes (d). Mlltfff mm 0 40 0 30 0 0 20 100 Fig. 5. 6 Inherent vector diagram for inlet window of the model. 244 f 90 80 70 \ 60 \ Zk ,j^- .-.^—^ 50 a V \ v?, \ 2 40 N*. «\ 1 Px \ \\ N pipe 30 h io ^A 3800—0^A ?o=350 mm O ^^^N. x\\; 20 A V .A^^ ~-A^A -\\>B ' 10 r 0 J I i i pipe 1234567 ig. 5.7. Change in the slope of the flow with the deepness of the inlet window. v ' 0 8 Q 6 0. 4 0. 2 B 0 Fig. 5.8. Transverse and axial flow in the inlet window. 245 ,mm 800 900 1000 Fig. 5.9. Transverse velocity with the model height in the event of the reduced size inlet ofthe window. JVu] 16 / 1,4 12 1,0 ' 0,8 0,6 0.4 0,2 0 20 40 60 80 EX/* Fig. 5.10. Hydraulic losses with the flow through the model assemblies in the inlet windows. 246 •=kioo% v 30 20 a) 10 m ^h.100% c) 't. m 0 1, 9 0, 8 0, 7 0, 6 0, 5 0, 4 0 3 0, 2 0, 1 mkV 20 d) 10 0,2 0,4 0,6 Fz'g. 5.77. Coolant flow with the model sizes at various height of inlet window - triangular c (a,b, arrangement of pipes, - square d arrangement). 247 Fig. 5.12. Axial velocity around pipe in the outlet window at a level 150mm. * -V"~"'-^ • ^^— - r V 0 30 0 24 0 18 0 12 0 6 0 360 f Fig. 5.13. Axial velocity around outlete pipeth n i window levela t a 980mm. 248 0 60 120 180 240 300 360 Fig. 5.14. Axial velocity around inlet pipethe in window levelat 90mm. -pipe/v1, •4-- —'—»— Fig. 5.15. Transverse velocity around square arranged pipes at h =30 and 100mm. 249 IP' 0 36 0 30 0 24 0 18 0 12 60 Fig. 5.16. Transverse velocity around pipes (square arrangement) outletthe in window model: ofthe • , + , - pipe 1 and O , x - pipe 2 for h = 950 and 970mm, respectively. 250 0 80 0 70 0 60 0 50 0 ^0 0 30 0 20 100' 1000 . Axial7 Fzg7 5. . flows with pipelengthe +7th 1 r . fo 251 — - —° __— — — . 0 L 1000 Fig. 5.18. Dimensionless velocity around the pipes Ms 7: - prediction inclined1,2 the at inlet; 3, 4 - prediction at the direct inlet; 0,3 - experiments, respectively. Hin 0,5 1,0 1,5 3,0 B Fig. 5.19. Optimal pipe bundle pith with outletthe window height; -model.B 252 Hot coolant Inter-tube space mln Cold coolant Fig. 5.20. To heat transfer calculation. to 0 4, 0,2 8 0, 0,4 6 -0, Fig. 5.21. Internet coolant temperature fields inside (T) and outside (M). 50 0 1, 8 0, oe o. o.a 4 0, . Pe =15,7 ,Re=7<4 l f " \Q 2 H 6 Fig. 5.22. Nusselt-Peclet numbers relation: Fig. 5.23. Measurement scheme coolantfor temperature: local- modelling of internal area model, ofthe U- mean logarithmic temperature difference, processing- with averaged temperature headers,in A ©- temperature header.the in other subscripts - near wall pipes. Fig. 5.24. outletThe chamber design downwardin flow of«cold» coolant. Fig. 5.25. The outlet chamber design in forward flow of the «cold» coolant: 1 - insulation, 2- pipe plate, - operating 3 pipes instrumented thermocouplesby 4 - fabric body., to (J\ L/l 345 Fig5.26. Cross-sectional diagram - model 1 layer,air case, - 2 3 - empty displaces, 4- insulation, 5 - wrapper tube, 6- clamping band, 7 - coolant-filled cavity, 8 - pipe. £ mV L Fig. 5.27. Temperature field downwardin flaw of coolant (moderate velocities)low 256 V m E 4,0 - 3,5 £ 0 1, 9 0, 8 0, 7 0, 6 0, 5 0, 4 0, 3 0, 2 0, 0,1 Fig. 5.28. Temperature field in downward flow of coolant (very low velocities). Nu Test N° 2 16 PeM=307 A 12 8 DPI 4 — 10 2 1 5 11 13 7 K pipe 9 1 8 1 7 1 6 1 5 1 14 .F/g. 5.29. Nusselt number for various pipes. 257 10 5 10 0,5 0,1 0,05 Pe 10 0 10 0 5 500 Fig. 5.30. Nusselt number as a function Peclet number: - internal B area (local modelling) - data * , processing 3 based averageon header temperature. 258 J\fu 40 1 0,1 Ill 1 I I I 1 I III I I I I HI Pe 40 40 2 Fig. 5.31 Comparison differentthe authors =f(Re)for dataNu on heat exchangers: - 1[15], - [16], - [17],2 - 3 [19],5 4 - [18]. "3 Vt/m2K 9,0 8,0 70 6,0 5,0 3,0 2,0 1,0 0,2 0,3 0,4 0,5 0,6 0,8 1,0 1,5 2,0 Fig. 5.32. Heat transfer coefficient K with the heating coolant velocity: - using 9 average temperature headersin 9 - local modelling ...... gi universal. profile of temperature n - data + [22]'.us 259 J\fu 10 1,0 Fig. 5.33. Inherent temperature distribution in square arrangement. 0,1 0,01 I i i iIPe 8 10 20 30 40 50 60 70 Fig. 5.34. Nusselt-Peclet numbers relation squarein arrangement of pipes: 9 - internal area (local modelling), © - processing with average temperatures. r y**"*./ ^ ^ ______„______^ V>^sVC (-__ "-E-E^-^^f^ O a) 2 0, 0 0,3______0,1, .1.2 4 1. 4 0, 6 to F/g. 5J5. Schemes of reverse circulation. ON to (t - (t-tin).°c T——I——I——f Pipe «r*5i '«?,* 9T '85,3 Fig. 5.36. Temperature fields with reflooding flows; a, b - forward row; c, d - middle row; f,e- deep row of pipes. (t -tin),°c 2/L ftZ/L a) (•t-tj.-e i i i i i. i i r I 3 2/L 2/L F/g. 5.36-ad , c , 6 , 150 e CD 100 50 u, 1 234C M/ 5 6 0, 4 0, 2 0, Fig. 5.3 7. Part of model section enclosed F/g. J.3& Boundaries of non-stable flow by a natural eddy with the main criterion heatin exchanger BNfullin modeland (1) (evaluated by Yuriev Yu. S.) O , CD, 6 , ® , ® size heat exchanger (2) (evaluated by ,»,e,e,»,e,€>,0,*,>l - experi- ,9,9,9,9 , CD , ® ,0 ) YurievS. <, . T , e Yu mental data, ---- -formula(5.3.35) - experimental , M , • , © C , data. 309C 350° 350° 400C 400C 450' 450C 500 500 547C r Fig. 5.39. Prediction of velocitytemperature and heat BN (a) in exchanger (b) taking into account natural convection (data Oefanovby A.D. al.)et. 264 Heat transfer is defined on the section Az = 500 mm between z = 300 mm and z = 800 mm measured fro bottoe m(thith x mbo s e sectioedgth f eo selectes ni middle th n di ee parth f o t model for the end effects connected with the inlet and outlet windows to be excluded). followine Th g simple transformation usede sar : Balanc f heaeo writtelengts e i t th r , usinhnd fo g temperature difference (F0 /"""*- ) founn di experiments (Fig.5.20): (t™-tr) (5-2) where k(z) - local heat transfer coefficient relative to the temperature difference (/wax - /"""); w? - coolant velocity inside of the tube; temperature f^ is taken as the arithmetic mean thermocouple ofth e reading enclosine th n si g channels. • Thermal resistance between the channels' centers determined in experiments is presented as: (5-3) Here we deal with the thermal resistance related to the liquid thermal conductivity A/- choseaveragee th scala s s i n a e k d ove lengte rth heaz hA t transfer coefficient relatee th o dt external temperature difference: teT&= 1 \&(z)dz (5.4) ZeAZ wTd,pc and AtT - coolant heating on the length Az ; PeT = ——-—— - cold coolant Peclet number. Thermal resistance (fy/k) incorporates thermal resistanc inter-tube th f eo e spach e(d / Nuu'}, thermal resistance inside of the tube (di / NuT') and thermal resistance of the tube wall ——In—, thas i t 2/0, d, d d d n l (V)+ - h , i , W_\ (t ^ , » , + , , A , exp, r , - (.•>••>) df Aw2 T Nu M Nu k) \ Here Nusselt numbers in the inter-tube space (NitM ') and inside of the tube (Nwr ') are Wflx based on the external temperature difference (/ - tw ) and (tw - /"""), respectively. Since the Nusselt numbers, thus defined, form only a part (fl) of the Nusselt number relative to the averaged temperature, that is Nu '=jBNu, relationship (5.5) can be written as (5-6) 265 Required criteria is a v exp /t' - pNuT Factor /?is taken to be equal 0.65 -^ 0.7 [11-13]. Nusselt numbe rouna r rfo d tub calculates ei d accordin [4]go t : 8 NuT=5 0.025Pe°'+ (5.8) We are reminded that an essence of the universally accepted " integral" measurement technique for the heat transfer coefficient in the inter-tube space is as follow: 1. General (integral) over the model heat transfer coefficient is determined with the logarithmic temperature difference: Q M (5.9) F-9l Qo)/2+ i arithmeti- wher(Q = eQ c mean betwee heae n th inter-tub e t losth o t e space "hote byth " coolan heae t (Qith t d perceive)an "colde th y d"b coolant insidtubee o th f s(Q eo ),F- heat transfe, m lengte 1 th r= d hareL an a 2 mea e base/ th j nd n d o diamete + , (d = rd = ln(Afmax-Afmin) is the logarithmic mean difference of temperatures, Atmax and Atmin - maximum and minimum temperature difference between "hot" and "cold" coolant in the model headers. 2. Fro integrae mth l heat transfer coefficien Nussele th t t numbe inter-tube th n i r e spacs ei determined as: (5.11) 3. Nusselt numbers in the inter-tube space found by the local thermal modeling are compared with those found by the "integral" method. 266 Result triangulae th n si r bundl f tubeseo . Ther some ear e point e typeth f Fign so i . 5.22: tubee th r s ApositioneFo ) experimenta ) 21 centrae , th (tube w 16 n d i , ro l 11 s l date aar given by the equation: N 9.36u= 0.023 + Peosl (5.12) <1200(20 which can be derived, when substituting relative pitch of the tube arrangement in heat exchange 1.31= generalizee th d s/ rn 5 i d relationshibundlen pi e th s r (sepfo e Chapter 3.3). Thus, heat transfer processes going on near the tubes 11, 16, 21 simulate those in the internal zones of multi-tube fast reactor heat exchanger, and the local technique allows studding full scale heat transfer in the models with relatively small number of tubes. Relationship (5.12) is propose predico dt t Nusselt number internae th n si l are fasf ao t reactor heat exchangea f ro triangular arrangement of the tubes. modee wholth a r s a lB Fo logarithmie)a c mean temperature differenc useds i e . Fig. 5.23 presents variation in the integral flows inside of tubes and through the inter-tube space maximue foth r minimud man m Peclet (Reynolds) numbers achievable during experiments. Inlet and outlet temperatures here are the mean temperatures (for every flow) in the model headers. Experimental data available on Nusselt number fall on the most low-lying curve in Fig.5.22e th , that demonstrate Nussele sth t number underestimatee sar compares da d wite hth relationship (5.12): they are 3.5 times lover at Pe=200 and -140 times at Pe = 15. Thus, the commonly used approac studo t h y heat transfee basi th f measurement o cn o r f meao s n temperatures in the model headers gives a particular results (being time only for the model under consideration) which can not be extended to the multi-tube heat exchangers. C )tube e Datth r sa fo adjacen wrappee th o t t r ruleliea s ,a , below than those gainen di local measurements for the internal tubes, but higher than those in integral measurements in modee th l headers thin I . s event, result observee sar stratifo dt i dependencyh tube th ef eo number, that is connected with the different hydraulic and thermal conditions. Thus, some limiting (boundary) values of Nusselt number can be separated, which are inherent for the different thermal hydraulic conditions: maximum values for the internal region of heat exchanger (local measurements) and minimum value for the whole of model, including influenc headerse th f eo . Nusselt number edge th er tubesfo s fall withi range nth e betwee limitine nth g values. In the average, they are described as: IgNu -0.734= 0.632IgPe+ (5.13) 20 This relationship can be advised to carry out the estimated calculations of the edge tubes of fast reactor heat exchanger, assuming that the edge tubes compose noticeable part of the tube bundle and individual approach is required in calculating. 267 Various flow directions in the inter-tube space (modeling, experiments, results). Results mentioned above were obtained when hot coolant flows from bottom upwards (due to construction), wherea n fasi s t reactor heat exchangers coolant flow so bottom t frop mto . Special experiments have shown that flow direction does not have a pronounced effect on thermal hydraulic performance, as at relative great and low coolant velocity. Let us enlarge on the experiments mentioned here. e modeTh l bundle presente Fign di . 1.1 s modified4wa s applieproblea w , ne o dt m (flow bottom)o t fro p mto additionn I . modee th ,s improve wa lpurpose th r dfo f equalizin eo g temperature fields. Fig.5.24 present unie sth t through whic e coolanhth t intere leaveth r -sfo tube space when flowing from bottom upwards. When reversing flow the inlet chamber (Fig.5.25) was formed from the unit. To distribute coolant flow ove tubee rth s more uniformit extrn ya a poomads reducinwa ly eb g bottoe th siz f emo tube plate. Originally tubes were sealetube th en di plate p , ga wit e hth between tube and hole in the plate being 0.02 mm. Big thickness of the tube plate reduced the flow through the gap to zero. Possibility of such a flow increases as the tube plate thickness is reduced. To eliminate flow a layer of special rubber was introduced in the plate which had no direct contact with the coolant and by this means it was safe against mechanical destruction's. Also this layer reduces heat flux throug tube hth e plate fro coolant mho colo t d one. An extra pool, formed because a thickness of the tube plate was decreased, as well as working tubes were lifted, is covered by the oval frame. In order to prevent the possible pollution penetrates intinlee oth t chamber fro coolante mth ovae th , l for surroundes mi y db stainlese th s steel net. The model wrapper (Fig.5.26 rectangulaa s )i positionex rbo d insidtese th t f sectioneo , which contains working tubes arranged in three rows across the width and 6-7 rows across the depth by a triangular manner with the relative pitch s/d = 1.315. Tubes are spaced and sealed by the plates and their upper ends are supported by the special plate made fast to the cover. Thus, tube fixee sar d relativ wrappee th o et r while themovn yca e abou tube th t e plates, that keeps they away from possible deformations during experiments. Modeling hydrodynamics of a full-scale heat exchanger using the model with the lesser numbe tubef ro validates si followine th y db g ideas [1]: • To choose one or three rows of tubes and two rows of displacers at the wrapper provides the measurements of transverse and axial components of liquid metal velocity are the same one-ron i s a three-rowd wan s model; chooso T • e seven rows acros modee depte th sth f justifies ho i l flo e th w y db stabilizatio n beyond fro third-fourte mth h row; • To choose length of the test section LO = 1000 mm and the size of the inlet window - 150 outlee th mreasonabls d i t m windoan m m 0 8 w e- relyin face th t n thago t transverse supply an dt coolan removaho e th t f havo l effecn e a temperatur n o t e behavior ove distancra e that is not more than twice window size, and as a result more than half height of the model (section between windows) operates under self-similar conditions. As to a compatibility between an in-pile and out-of-pile thermal processes, the lesser heat losses in the model wrapper the more strict is modeling. 268 In orde eliminato rt e suc losseha s three rectangulae sideth coveree f so ar x y dbo rb thermal insulation - quartz textile (Fig. 5.26), which has no contact with liquid metal. All described above serves to provide adiabatic conditions at the test section. Quality data (temperature fields) were obtained practicall modele l tubeth al f r so y fo . Fig. 5.27 and 5.28 illustrate, as an example, data for internal tube at the relative great (Pe = smals 20.9d e an ) (P l) 1coolan87 t velocities, respectively. Nusselt numbers were predicteo dt a good accuracy. They are shown in Fig. 5.29 for one of the flow along the internal row (tubes 1-5-7) and the edge row (tubes 8-^-19). See Numbers of tubes in Fig. 5.30. Although Nusselt number t separata s e tube e diffear s r noticeably (du differeno t e t geometr hydrodynamics)d yan , experimenta e othel th dat n r ao row approximatele ar s e yth same, that arises from the uniform temperature distribution over the front and depth of hot flow Fig. 5.30 presents experimental data as a function Nu =f(Pe). Mean value falls withi nsmala l range (not more than ±10% relationshipe th n )o : Nu~72 0.0235+ Pe0-81 (5.14) 10 Calculation results by this relationship lie some below than (5.12) gained provided the coolant flows in the internal space from bottom upwards. But discrepancy is not so great to notice effect of flow direction within the range under discussion. It should be noted that (5.12) and (5.14) wrapper a wide range of Peclet number (10 < Pe < 1200), with the range of small Peclet number enclose (5.14y db )f grea o tha s i tt practical importance (regio f possiblno e natural convection). Combinatio (5.12f no (5.14d )an ) gives very simple average relationship: 0.0235+ 4 8. Pe= 0'81 (5.15) 10 e applieb whic n calculatinn ca i hd g heat transfee inter-tubth n i r e spac f heao e t exchanger whe t coolannho t flow sbotto o t fro p m to mfror o m bottom upward indicaten a n si d lase tTh formul. rangPe f eo a differs from (5.12 (5.14mord o n )an y e)b than 10%. As to experimental data on integral heat transfer (predictions based on the average temperature headers)e th n si , heat transfer coefficient rathee ar s expectere highar t e b bu , o dt much less than thos infinite" r efo tubf "o e bundle determine locay db l measurements. It is evident that at low coolant velocity "integral" Nusselt number does not depend on Peclet numbe laminan i s (a r r flow) being approximately equa o 2.5t l , that indicates that temperature field is uniform at small Pe. Value Nu ~ 2.5 is about three times as less than those for "infinite" bundle (Pe < 120). Of course, in this event, also heat transfer coefficient is some lesser due to the average temperatures in the headers differ from the tube bundle temperature in spit absencf eo wrappee th f eo rtemperatur e effecth n o t e behavio tubn ri e bundle. A correlation betwee e datth na availabl d (5.14an e ) testifies that n resulti e ar s agreement in the range 70 < Pe < 200 and differ widely at small Peclet number (Pe < 70), with 269 the discrepancy increasing with the Pe reduction. All this suggests that heat transfer coefficient based on the mean temperatures measured in the headers are of partial character. Notice that the data obtained in other well known studies on heat transfer in the intertube space using mean temperature headere th n t onlsi belowe sno yli t reducbu , e shortly wite hth Pe reduction (5.31). Predictions in a triangular tube bundle . Here we consider numerical procedure on defining heat transfer coefficients universae baseth n do l profil f liquieo d temperature. shows Iwa t [20n i ] that under stable heat removal condition relative sth e temperature is approximated by the universal relationship: T+= 1.87 0.065y+\n(y+ ++-1) +0.36- (5.16) 2.5\ny++-l where a tw - local wall temperature, / - coolant temperature at a distance y from the wall, a = /Ij- \pcp \ - thermal diffusivity, TM and qu - shear stress and heat flux at the wall (local values). Muc whaf ho t follow connectes i s d with Fig. 5.20 whic makine useth s h i r dfo g that clear. We conside internan ra l channe heaf lo t exchange witd ran h obtain n (5.16ca e ):w (5.17) =PMf(y» (5.18) where a a A-f-JtwrlP TWd an M Tshea- r stresoutee inned th t sran a rtubee walth f ,lo respectively. Fro heae mth t conduction equation writte tube th er walnfo l follows that: ————— or 270 t ~ wr) (5.19) Syste f equationmo s (5.16 - (5.18) ) allow e connectioth s n between temperature difference wall-coolant and heat flux to be found at the outer surface of the tube: f max , mm (5.20) Blasiue Ifth s relationshi hydraulir pfo c resistanc useds ei : = 0.3164 Re"025, (5.21) So will: = 5.14 (5.22) u. = y" (5.23) where ys = tw/Tw - relative shear stress at the wall. Let>>7-++ andjy^/ maximue *b m value dimensionlesf so s coordinates insidtube th ef eo and in the inter-tube channel, respectively. Relation (5.20) may be written as: (5.24) where heat transfer coefficient is defined by the following expressions: (5.25) (5.26) A = 5.14 (5.27) r U.S75 A u = 5.14 ,0.875 (5.28) 271 meaM thicknese A , nth thermae AT Her, th f sAw o e l resistance walle th n ,si insidf eo the tube and in the inter-tube space, respectively. It follows fro (5.24e mth ) tha M referq t heao st t flux appearin outee poine th th t n ra gti wall of the tube answering the maximum temperature difference (/A/""" - IT"""), while in processing experimental data heat transfer between coolan inter-tube th n i t e spac thosd ean e insidtube th defines ei f eo (5.24y db ) implying average- tha M q t d over perimeter heat flut a x outee th tubere walth f , o ltha : is t f c / < \f\\ x ,mmma f / / \ tube Inth e bundles with sheas/d>2 1. r stress doe t varsno y aroun tube dth e d [21an ] becaus considen ca thisf eo e (5.27)n w ,i r 1 assumin y /= B . g also that heat flu invarians xi t wit tubee hth perimeter obtaie w , e procedurenth calculatinr fo s g heat transfer coefficients wit formulae hth s (5.24 same e (5.29d th )an e .)ar When evaluatin heae gth t transfer coefficients averagee baseth n do d temperaturee w , resort to the fact that relative temperature (as relative velocity) depend only slightly on Peclet number. Fro universae mth l temperature profil followt ei s that: (5.30) ' M 1WM (5.31) Having indicate thicknese dth thermae th d f an so l' resistanceA d an ' s AT',sa AM taking into account in (5.30) and (5.31) we obtain A'T,M = 0.65 AT,M AM+ T 0.6+ ) (A 5w A A = ' Fig. 5.32 presents compariso experimentaf no l data with those predicted with (5.25)- (5.28). Thermal studie f squarso e tube bundle (low coolant velocity). Experiments were carried out in the range of low liquid metal velocity (NaK), including natural convection(90 < modee 70)Th < .l e R3650bundlP e < < 2 ; e schemati presentes ci . Belo5b 1 Figwn s di i 1. . given specific feature thermaf o s l hydraulic datd hean san ao t transfer coefficient squarn i s e bundle with. relativ5 1 3 . e1 pitc= d hs/ Heat transfer coefficients. Inherent temperature behavior is presented in Fig. 5.33 (as mentioned above, measurements have been conducted by the use of the local thermal modeling technique). Experimental data on Nusselt numbers (Fig. 5.34) are clustered close to value Nu = 5.9 and remained practically constant as Peclet number varies, only at Pe > 50 heat transfer is observed to rise somewhat with Peclet number, but it is beyond reason to say about 272 calculatee dependencar e P d d an wit=f(Pe)u u ehydrauliN e h(N th c equivalent diametef ro "infinite" square bundle as a reference size and mean coolant velocity in the inter-tube space is used as reference velocity). The value Nu = 5.9 is distinctly smaller than those in triangular bundle (Nu = 9.36 -see Fig. 5.22 or (5.12)). As hydraulic diameter in square bundle is more than in triangular bundle, heat transfer coefficients in the inter-tube space of the square bundle under discussion fall far shor thosf to triangulan ei r bundle othel ,al r factors bein samee gth . Nusselt numbe fore th f m o n i r Nu=5.9 (5.32) (2 recommendee b n ca calculatinr dfo g heat transfe internae th n i r lsquare zonth f eo e rube bundle within indicated rang parallen ei l with relations (5.12 r (5.15)o r triangulafo ) r bundle. As intermediate channels located between the regular rectangular and triangular channel calculatede sar heae ,th t transfer coefficients fall withi range nth valuef eo s predicted with (5.12), (5.15) and (5.32). Nusselt numbers predicted with (5.32) being the limiting one (low coolant velocity) have of course to be supplemented by experimental data at Pe > 70. For the model as a whole experimental data (as in triangular bundle) lie along a lowest curv Fign ei . 5.34 presentin gconservativa e result compares sa d with (5.32) factoa 6 s a f :o r at Pe = 70, and of 120 at Pe = 2. Thus nexe th , t evidenc bees eha n provide supporn di thaf traditionao e t tth l technique of studing heat transfer based on the measurements of mean temperatures in the headers evene th f triangulacausen o ti s (a s r bundle particulae th ) r result gainede b o st , whice har inheren tmodee onlth n yi l bundle under consideratio convertee b t whicd no nan n dh ca int o multi-tube heat exchangers. Specific feature thermaf so l hydraulic coolant velocitho w e lo t th ts a f (reversayo l circulation) mose th i t h ,design heaf so t exchange t coolanho e rth t run sbottomo t fro p mto , with density increasing, that ensures stabilit s circulationit f yo . Otherwiset , wheho e nth coolant moves from bottom upwards increasn ,a f densiteo y caus floe eth becomwo t e non- stable and the possibility for reversal circulation in the inter-tube space appears. This is most e squarth n i e e likelbundleb o t y , becaus e greateth f o er coolant porosity than thosn i e triangular bundle. Heat transfer coefficien heae th t n i exchanget whola s a r e reduceo t t onle sno ydu hydraulic and temperature non-uniformities, but due to actual blockage of the part of heat exchange naturay rb l circulation eddy, which form lessenesa d temperature area ("cold" eddy) inter-tube inth e space. typicae th Fig showf e o ., lf e performanc, 5.36-ad son , c , ,b modee th f eo l bundle with the formation of recirculation loop deep inside bundle (Fig. 5.36-c, d, f, e) and with the common coolant recirculation nea firse rth t row tubef so s (Fig. 5.36-a . Yurie . S Prof . ,b) Yu v. performed analysi flowe th f sso indicated above that allow e conditionsth f sucso hflowa s occurrenc revealee b eo t som d dan e criteri estimatinr afo derivede b go t . 273 Le indicats u t floe eth w fraction blocke edde th yy d b asfxcmar d an k that velocitn yi the rising part of recirculation loop increases: Uz If a balance of forces acting on the liquid within the recirculation loop is states as the hydraulic resistance between the weights of «hot» and «cold» half-loops», we can derive relationship to define the blockage fraction: f»c= ———— ' (5-33) rz UZ.L Here C/ and Q - empirical factors, Reef = ——— - effective Reynolds number Vef including the length of the tube bundle L and nominal velocity in the inter-tube space (U^)', v- effectivef e viscosity - hea p ; t transfer parameter (see (5.39)); other parameters wile b l further explained. Puttin obtaie w g, fon0 eboundar- y equation non-stablfoe rth e flows: <± /~i Tt 2 sr\ A \ \ * / Condition kp -> a? gives the limiting blockage fraction (see 5.33) "C max =77 Taking into consideratio na smal l contributio f viscouno sderiv n forcesca e a e w , simple formula: (536) JNC max KNC where 0.5p+ Kl P ( } is the main combined similarity criterion for the velocity and temperature with the availabilit naturaf yo l circulatio inter-tube th n i e minimumindicats s spacea u t ° Le . e^0 , critical value of the criterion setting the boundary of the natural circulation existence. 274 KNc - natural circulation exists, if KNC ^KNc°, so will be no. Value of KNc° was determined in experiments described above. The main combined similarity criterion can be written in the expanded form: ____ Mi ______M_ (5.38) e R ?2* ^ V ~ / -aj C i N K J4 iv c^ if remembering that 2 2i/Z , ~ w 4kL p = 4- or 4- P = (5-39) PeAf P^; Nu M d NudTr . , ,,//i/jt, -, amsotropif c factor (x-I) k s definu t Le e parameters: ' T 9 ^* — n PeM havn resula an ca es de a w t Pe.,+107'M GrL PeM+215 R.QJ 1 — (5.40) PeM+J07 GrM PeM+215 ReM 275 Blockage factor was defined in experiments through analysis of the tube temperature behavior: firs allf o t, number "coldf so " tube c clos sN whico et coolane hth t runso t fro p mto calculates tota1 , wherwa =2 /N l c x s value es N followsbottoN df a th f - ed o mc an :fu number of the tubes in the model. Experimental data are evident from Fig. 5.37 to be in satisfactory agreement with the analytical main similarity criterion s founwhic wa experiment n ds i h a , thaKNe s b 26 ha tC o s= t allowed to set the boundary of recirculation flow, as well an order of power reduction. An absolut - U MT A ploe t yields (wher - inle T etA temperature difference betweecold an d t nho streams, UM- mean velocity) the boundary of stability as: • + - 8.32-102vk Nu d T h (5.41) a - + NuTdh s shoIi t Figwn i e mode. th 5.3 r 8lfo bundl in-pild an e e heat exchanger wite hth following parameters: 3.1= v 4 *10'7 m 1.49 2= /s3.1/ = ;* 0 ; 4 "KT4 1/k1.5= 6;h *10"; m 2 5 2 ,-3 *10"5 6. = m0 a *1 /s9 ;1 Nu <; f5 = M= =6;T Nu m An area being ove e curvth r e represent non-stabla s e flows resultin powee th n gi r reduction. 2-D calculation of IHX taking into account natural convection. The basis for the procedure is an anisotropic porous body model with the momentum and energy conservation equation numericae sth [8]r .Fo l solutio equatioe th f no n system writtefase th t r reactonfo r heat exchange code th r e TAK bees Tha n developed. Predictions were compared wite hth experimental data indicated above on the liquid metal model, as well as on the air model [23]. Thermal hydraulic analysis of Super PHENIX IHX conducted with the code was in a good agreement wit predictee hth d outlet temperatures. The next ste improvinn pi g code developmen e TAK blocth D s 2- Tkwa e witth f ho t natural convection [24] reveao .T l natural convection effect followine th s g assumptions were accepted: • transien consideredtt flono ws i ; • coolant in the inter-tube space is accepted to have no contact with reactor body, that is boundary condition velocitn so temperaturd yan givene ear ; • only turbulent flow throug inter-tube hth e spac considereds ei . The first assumption facilitates significantly numerical procedure and the two last permit analyzing pure th en ,i state , natural convection effects. 276 Mathematical formulatio e problemth f o n . Momentum, masd energan s y conservation equations written for the coolant in the inter-tube space are analyzed and discussed in [8]. Boundary conditions are given in the following forms: • for velocity: conditions of impermeability and sliding are given at the solid borders; uniform distribution is given at the inlet and outlet; r temperature:fo • condition insulatiof o s solie givee th nar dt na surface t coolanho ; t inlet- unifor r lineamo r distribution t coolanho , t outlesame th - et heat flux; cold coolant inle- t fixed temperature, cold coolant outlet - the same heat flux [8]. Numerical procedur presentes ei detain di [25]n i lproblee Th . ms e solvei th y db sequential approximations, : velocittha s i t s determinei y d without considering natural convection, the temperature nth e distributio calculates ni f whicdw o througne e ha us e hth velocity distributio s founi n d even taking into account natural. convectioon o s d an n Sequential approximations are performed till the attainment of velocity will be determined witneedee th h d accurac debugginn I . y convergence th g e problem investigatede ar s , test checking is performed and coefficients are found [24]. LMFBRIHX performance was predicted provided the following parameters: • Tube bundl, em length3 7. = ,L • Outer wrapper radius - 1.14 ,R , 7m • Inner wrapper radius 0.46= 0 , 7R ,m • Heigh inleoutlee d th an tf t, o t windowsm 0 1. = ,H • Relative pitch of the bundle, s/d - 1.34, • Outer diameter of the tube, d = 0.016 m, • Mean velocity in the inter-tube space, U = 0.74 m/s, • Mea ncoolant velocitho e tth (insidf yo tubes)f eo 0.72 = ,w 8 m/s, • Inlet temperatur, °C 7 coolantt 54 ho f = eo n i T , • Inlet temperature of cold coolant, 0in = 309 °C. Predicted distributio axiae th f ln o velocit shows yha n thaside th te inleoutled an tf o t the coolant cause the hydraulic irregularities to occur (Fig.5.39-a). They initiate the temperature non-uniformities with the maximum value attained at the cold coolant outlet. It may be as much as ~ 60 ° C (Fig. 5.39-b) and realized in the hot area of heat exchanger, that is the possibility of thermal stresses occurring can be greatly enhanced. In changing ratio betwee fule nth l specific heat capacitie maximue sth m temperature gradien replacn e ca t th o et cold par heaf o t t exchanger. CONCLUSIONS 1. The study of intermediate heat exchanger thermal hydraulics was performed on the mock- up tube bundles wit limitee hth d numbe f tubo r e rows (one-, three-row bundle with displacer e wrapper)th t a s . Hydrauli thermad an c l modelin s allowegha d obtaininn a g experimental dat multi-tubn ao e system. Thermohydraulic investigations were carriet dou in triangular and square tube bundles as applied to nominal performance and during low- velocity transients, including natural convection and reversal circulation. Experimental data can be used both to predict temperature behavior in the full scale heat exchangers and to verify computer codes. 277 2. Investigations of hydrodynamic parameters are based on the electromagnetic measurements whic founs verhe i b yo dt effectiv studyinn i e g combined (axial-transverse) flow; whereas thermal investigation locae th e l modelinsus g technique, that allow date sth a obtainee b o dt extended to the full-scale fast reactor heat exchanger. In addition, it is shown that traditional integral measurement meae th f nso temperatur modee th n ei l headers causee sth particular result obtainede b o st , whic unsuitable har usinr efo multi-rubn gi e system such heaN B t s exchangersa . 3. Among the constants needed to validate BN heat exchanger thermal hydraulics there are: • heat transfer coefficient triangulan i s squard ran e tube bundle (regular are heaf ao t exchanger nominan i ) l coolant flows s wel a ,s unde a lvelocit w lo r y conditions, including natural convection; • heat transfer coefficients for the edge areas of heat exchangers which differ noticeably from thos regulan ei r tube bundle; • value lawd variatiof san so axia n transversi d lan e component velocitf so y wite hth height and depth of the tube bundle, as an input information for verification of computer codes; • formatio f temperaturo n einter-tube th fiel n i d e spac varioun i e s coolant flows, including low velocities; • criteri flof ao w stabilit theid yan r value applies smock-ua e th o dt p bundle- in d san pile heat exchangers. 4. The most important effect observed during experiments on mock-up bundles is an equalization of coolant flow over the depth of tube bundle when the inlet window reduces in height. This effect appears in different arrangement of the tubes in bundle (triangular, square), in different number of tubes and so on, varies in its value and allow the heat transfer surface to be optimized. It also shows a significant reserve of the heat transfer surface in the BN heat exchanger under operation. The data gained on velocity and temperature behavior in mock-up tube bundles when the inlet window varie siz n swideli e ear y use improvo dt e computer code fasn so t reactor heat exchanger thermal hydraulics. Codes PROTVA, UGRA, TAKT, RAPOR otherd Tan s built on a porous body model are successfully employed in practice. REFERENCES [1] Zhukov A.V., Sorokin A.P., Sviridenko . E.J.Experimentaal t ,e Numericad an l l Modellin f Heago t Exchanger Thermal Hydraulics. Models, Sensors, Measurement Techniques, Liquid Metal Facility. Textbook, Obninsk, ONPEI, 1992 (in Russian). [2] Zhukov A.V., Sorokin A.P., Sviridenko E.J., et al. Experimental and Numerical Modelling of Nuclear Power Plants Thermal Hydraulics. Overview IPPE-0270M, CNIIAtominform, 1995. [3] Zhukov A.V., Sorokin A.P., Sviridenko E.J., et. al. Experimental and Numerical Modellin f o Heag t Exchanger Thermal Hydraulics. Overview IPPE-0269M, CNIIAtominforai, 1995. [4] Subbotin V.I., Ibragimov M.H., et al. Hydrodynamics and Heat Transfer in Nuclear Power Plants, M., Atomizdat, 1975. [5] Kolmakov A.P., Yuriev Yu.S. Application of a Porous Body Model to Calculate Velocit Temperaturd yan e Field Reacton si r Core. Preprint IPPE-249, Obninsk, 1971 (in Russian). ] [6 Gorchakov M.K., Kolmakov A.P., Yuriev Yu.S. Friction Factor Anizotrop Poroun yi s Body Representing Pin Bundle. Preprint IPPE-446, Obninsk, 1973 (in Russian). 278 [7] Gorchakov M.K., et al. Application of a Porous Body Model to Reactor and Heat Exchanger Thermal Hydraulics. Thermal Physics of High Temperature, 1976, v.14, p.866-870. [8] Subbotin . ComputationV.I.al t e , f Problemo s f Reactoo s r Thermal Physics, M. . Atomizdat, 1979. [9] Trojanov M.F.et al. Recommendation on Computation and Design of Intermediate Liquid Metal Heat Exchangers CKTIO , 47,198.NP ,L. Russian)n 2(i . [10] Zhukauskas A.A. Convective Heat Transpor Hean ti t Exchangers. Nauka, ,M. , 1982. [11] Kirillov P.L., Subbotin V.I., et al. Round Tube Heat Transfer to Na-K Alloy and to Mercury. Atomic Energy, 1959, v.6, p.382-390. [12] Kaliaskin V.I., Kudriavtseva L.K., Ushakov P.A. Forced Convection Heat Transfer to NaK Allo Compacn yi t Bundle. Thermal Physic f Higo s h Temperature, 1973, v.ll, p.781. [13] Ushakov P.A., Zhukov A.V., Matjukhin N.M. Liquid Metal Turbulent Azimuthal Temperature Non-Uniformitie n Regulai s r Bundles. Thermal Physic f Higo s h Temperature, 1977, v.15, p.76-83. [14] Subbotin V.I., Ushakov P.A., Gabrianovich B.N., et al. Round Tube Liquid Metal Heat Transfer. Engineering & Physics J., 1969, v.4, p. 16-21. [15] Graber H., Rieger M. Experimentelle Untersuchunge der Warmeubergangs an Flussigmetalle (Na-K n parallei ) l durchstromten Rohrbundel i exponentiellebe n r Warmeflus - sVerteilun erzwungenen i g r laminarer oder Turbulenter Stromung. Internationa Hea. lJ Mas d tan s Transfer, 1970 . 1645-1703,p . [16] Zhukov A.V., Sviridenko E.J., Matjukhin N.M. Experimental Investigation Liquif so d Metal Heat Transfer in Triangular Pin Bundles. Preprint IPPE-800, Obninsk, 1978 (in Russian). [17] Kondratiev V., Krupkin L.K., et al. Heat Transfer in the Inter-Tube Space of BOR-60 Heat Exchanger. Atomic Energy, 1974, v.36, p.305-306. [18] Broks R.D., Rosenblatt A.L. Mech. World and Engng. Rec., 1953, vol. 75, p. 363. [19] Kirillov P.L., Suvorov M.J. Liquid Metal Heat Transfer in the Inter-Tube Space of Heat Exchanger. Liquid Metals Atomizdat, ,M. , 1967 194-203. ,p . [20] Kirillov P.L. Generalisation of Experimental Data on Liquid Metal Heat Transfer. Atomic Energy, 1962, v.13, p.481-483. [21] Subbotin V.I., Ushakov P.A., Levchenko Yu.D. et al. Turbulent Velocity Field in Longitudinal Flow in Pin Bundle. Preprint IPPE-198, Obninsk, 1970 (in Russian). [22] Boudov V.M., Golovko V.F. Intermediate Heat Exchanger n Fasi s t Reactors (Analytical Overview). OKBM, Nizni Novgorod, 1976. [23] Boudov V.M.. Predictional t e , Experiments& Combinen so d Axial-Transverse Flow in Fast Reactor Heat Exchangers. Heat Transfe Hydrodynamicd an r Single-Phasf so e BundleFlon Pi w n Nauka, i ,L. , 1979, p.56-68. [24] Yefanov A.D., Vlasova . ForceV.N.al t e ,d Convectio n Liquii n d Metal Heat Exhcanger. Preprint IPPE-1257, Obninsk, 1982 (in Russian). [25] Gosman A.D.. Numericaal t e , l Method Viscoun si s Liquid Flow , 1972,M. . NEXT PAGE(S) left BLANK 279 Chapter 6 THERMAL HYDRAULIC ANALYSIS OF TRANSIENT AND ACCIDENT PROCESSES. LIQUID METAL BOILING IN LMFBR CORE In recent years the necessity of analysing flow and temperature behaviour in pin bundles arises fro stude s transiena mth f yo t operatio f reactono analysid an r f accidento s s associated with circulation contour failures. Thermo hydraulic analysi problese callth r sfo m of combined heat removal in the «liquid-pins» system to be resolved, it should be noted that it is the more complex problem than a steady-state calculations. Specific problems arise in studying the coolant boiling. Vapour generation in any part of subassembly, taking into account the great difference between specific volumes of vapour and liquid a stron s i , g disturbing factor responsibl realignmena r fo e f hydrodynamicso t , causin floe gbecomth o w t e instable. Stud possiblf yo e failures cover eventn sa f fuen so pi l cooling under condition flow wlo f ratso naturar eo l circulation. 6.1 TRANSIENT THERMAL HYDRAULICS MODELLING Subchannel approach to transient thermohydraulics was realized in the code MID . Numerous verification tests have been performed with the experimental data IPPE and others [1,2] temperaturn . shoFig.6.2 pi e 6. wth d 1Duhamean f o e e predicteus e lth integraly db . Temperature relaxation parameters. Numerical solutio heaf no t transport equations and inherent transient distributio f temperaturno cooland fuen ei an l s presentei t [3]n di . Predictions were carried out in turbulent flow at various Reynolds numbers, with the convective heat transport, molecula d turbulenran t diffusio n radiai n d axiaan l l directions taken into account. Different fuel d coolant, UO an , (U H s) 2 2Na )Ob wer( sP , e studied. Results of numerical analysis were supported by experimental data gained in momentary switching-off the heater of the model. Data analysi s showha s n tha powen i t r ste ptemperaturn pi inpu e th t r coolan(o e t overtemperature) is pproximately described by exponential correlation: (6.1) where r - time, rr - parameter of temperature relaxation. In orde derivo t r e explici bundle t th correlatio n o e parameter r l f no analytican a s l solution of transient heat conduction problem was considered under isothermal boundary surfacen conditiopi e .th t Thina s solution hold temperatursn thapi time e th tt take ei th r sfo e to be established is defined by the following parameter: A/ i\ \ A* 0.1729 + 0.94521 -p- + -~t Hr (6.2) n d I L / , A \ diametern wherpi - d fue- e 0 d l, diameter thicknes- , A , f claddingso - thicknesc A , e th f so contact sublayer between claddingd fuean l , - therma/i /^ c ;,/i l conductivit f yo fuel , claddin contacd gan t sublayer therma- 0 ,a l diffusivity. 281 Analysis of data at Re < 104 has shown that dynamics of fuel temperature change essentially depends on the coolant flow. It is primarily due to coolant overtemperature AT, which is comparable to radial non-uniformity of the fuel temperature at relatively small Reynolds number. parameteThene th o t , n muspi r raddee &T/q • b t\pctim = e \ dpq th t ve neede increaso dt e fuel temperatur Fro. energe AT m y th e b y balanc obtaine w e : 3 wher- density p e , kg/m - specifi p c ; c heat capacity, J/kg'K - volumetri v q ; c heat 3 production lengt- , W/mq h f poweho ; r production measection- W n ; coolan,m t velocity, m/s; CO flo- w cross section . Subscript2 ,m d <an > mea» «o s n fuefluidd an l , respectively. Transient heat conductio i n fuee cooleplani n th ph l y eb d coolant flow (uniform velocity distribution) suggests that the time it takes for the coolant passes through the power production sectio /vtrnusq h n e takeb t n into accoun , influenct f whico e temperaturn ho e relaxation is essential. As a result, we have Tr = (2/7r) •( rpin + rq+hq /W\. Having presente temperaturn pi e dth coolanr eo t overtemperatur functioa s ea f timno e fore i nunifieth f m o d dependence (6.1) shows that parametegeneralisee th s i r u r d dynamic characteristic. Fig.6.3 presents correlation (6.1 n (616^-i ) coordinates) r r I T . Geometrf yo subassembly and annular channel for which these data were calculated is presented hi the Table 6.1. Fig. 6.4. presents the same data in the (01 O^-T I TO) coordinates, where T0is the pin constant. Correlation is presented in the form: 0 = 9a.\l — exp(- r / r0)l It is evident that the pin constant can not be considered as generalised dynamic characteristic. The following nomenclature is used: R0 (d-2A=djd,= R 2h= q}/d, H )/d, f, ,A,=a}/af, Re - Reynolds number, Pr - Prandtl number, x - relative pitch of the bundle, Ra - the outer radiu inne o t e ratios on r , - coolan /lyf a . t thermal conductivit d thermayan l diffusivity, a0 - pin thermal diffusivity. Parameter TO contains an empirical variable being the heat transfer coefficient which takes into account thermal resistance, as the temperature establishes inside of the pin [4]. Other paramete r r doe rt contai no s na simila r variable e concludeb . n Thusca t i d, that relaxation temperature in subassembly of fast and water reactors is scarcely affected by the 282 thermal resistance explainee b n face ca th t t y I .thad b t coolant overtemperatur excesn i s ei f so temperature th e difference «wall-liquid» In modeling steady state heat removal the tubes heated from the inside by electrical heli used e layee xar f silicoTh . o r n organic insulate electricae sth l helix fro tube mth e wall. The condition for approximate modeling is that the equivalent thermal conductivity of experimental tub s equaei thao t lfue n n i t[5] pi l . Experiment predictiond san s have shown that under conditions of power step the tube wall temperature is also governed by the relationship (6.1. Thus, parameter Tr is a generalised dynamic characteristic of the subassembly or the model . It allows the conditions for approximate modeling as an equality of dimensionless values of relaxation parameters in nature and in the model to be established. If the time it takes for coolant to transported through the heated section is chosen as the time scale, that conditio r approximatnfo e modelin : \T..W/hgis a} =\r\ n rWh I rr ° V r t)model \ r qlnature 6.2. EXPERIMENTAL STUD CRITICAF YO L HEAT FLUXN I LIQUID METAL NATURAL CIRCULATION CONTOUR Having regard to physical and thermal dynamic properties of liquid metal coolants, to choose sodiu coolana s ma fasn i t t breede idean a re l b reactor decisiono t s swa nominan I . l performanc outlee eth t sodium temperatur mucs ei h less than sodium boiling temperature. However, boiling is possible in improbable severe accident. Among the consequences of such n superheatingpi e th e a procesb y , losma s f pressureo s . Furthermore n causca e th t ei , reactivity to enhance due to positive void reactivity factor of sodium. That is why, liquid metal boiling was given much attention over the last three decades. Heat transfer, flow patterns, hydraulic resistance, heat transfer crisis, mechanisf mo boiling, problems of stability were being discussed. Results of studies presented for example in [6-15] have shown that boiling in liquid metal has some specific features in comparison with water boiling, among these are: • the growth of liquid metal vapour bubble is of explosion character, with the rate of the bubble growth bein m/sorde0 n gi 1 f ;ro • two-phase pattern liquin si dsame meta th thos s ee a ar commoln e i n liquids, wite hth disperse-annular flow dominating at the pressure close to atmospheric; • two-phase friction wit energe hth y supplie lesses di r than thos adiabatin ei c flows, that is connected wit vapoue hth r pushe mai e interface th sth nf o flowt eou ; • phase transition in disperse-annular liquid metal flow is, as a rule, performed by evaporation of near-wall film provided bubbles are not generated at the wall (boiling is lacking), heat transfer coefficien greas a hundreds s i ta f kW/mso n influenc2a , f eo mass velocity and quality appears to be moderate. Attention hi studying the pin bundle liquid metal boiling focuses on the analysis of transient and emergency performance caused by the drastic changes in power, by the various kinde blockagesf so pume th y p,b shut-down. Experimental facility. Fig.6.5 presents test section containing 7-pin bundl studo et y boilin f eutectigo c alloy NaK. Pin-displacer usee sar reproduco dt e «infinite bundlen »pi , 283 pins are spaced with the spacer grids positioned in four cross sections, two in each section, wit crose hth s sections bein grido evergtw aparn s i m placed m yan t0 sectiod13 n beinm m 5 g apart. Two grids together form a peculiar kind of chamber-header, from where thermocouple readings com pressurd ean extracteds ei . The length of heated section is 420 mm, with the section of hydrodynamic stabilisation 165 mm long being upstream from the heated section. Mobile 7-pin bundle 200 mm in length is mounted next, which can be moved to a distance up to 300 mm directly during boiling. In firse th t experimenta tubee th t s se lwit roughnese hth s 0.15werm e mk elementsn usea s da n ,i the second set the tube of roughness 7.25 -r- 0.63 mkm were used. Circulation contour AR-1 and test section. Fig.6.6 shows the contour with the test section to study liquid metal boiling. As it is clear from Fig.6.6, the electromagnetic pump, coolant heater, equipment to calibrate magnetic flow meters, as well as cold catcher are inserted in the contour. Before testing, liquid metal coolant was purified during three days steadily. In that tim cole eth d catcher maintaine temperature th t da e 80°C (thermocoupl , wit7) he N oxide concentration being 5^-10% weight. Experimental results. Reading f flow-meteso foud an r potentiometer measuro st e coolant qualit e presenteyar Fig.6.n i d t pressur7A e e boilinp=0.06th a g MP onse s i t observe heae th t da flu x q=117 kW/m2. Local boiling (senso ) extend l 5 heate al rN r fo sd section, as the power supplied to the test section increases. In doing so, the inlet flow rate was kept practically constant at a level established before boiling. Such a behaviour was conserved unti boiline th l g cover heatel al s d section conventioy B . mode nth boilinf eo g with invariant flow rate and heat flux to the value q= 133 kW/m2 way named the mode 1. On further heating, transitio pulsatinno t g mod observeds ewa , name mode dth . e2 mode boilinf o Th e2 g appear periodis sa c process beginnine th t :A heatee gth d section is steamed, then the developed vapour plug floats up, but the area being freed from the plug s fillewa d with «cold» visibl s liquidi t i s e A .fro m Fig.6.7, durin vapoue gth r plug generation the coolant flow rate failed to zero and at the instant the plug floats up it rises steeply. Thus, experiment have shown that at heat flux q being from 100 and 133 kW/m2 and flow rate G-0.75 ms/h the stable heat removal due to coolant boiling was observed. As the heat flux increases up to 150 w/m , the boiling becomes pulsating, flow rate reduces 2 periodically to zero and then drastically grows. Temperature characteristics are shown in Fig. visibls i t i 6.8 s eA . fro figuree mth , under conditio mode outlee th th f e1 no t wall temperature remained constant and was equal to 740°C. In the mode 2 (pulsating) a drastic increases in wall temperature with amplitude ~90°C were observed. It should be noted that the outlet coolant temperature behavior presente s som ha Fign di e8 .specifi6. c features e firsth n tI . (stable) mode of boiling the coolant temperature did not vary and was 730°C, that was practically equa saturatioo lt n temperatur pressure th t ea e 0.06 MPa. The sensor signals were recorded and processed by computer in order to define the correlation relationships between the individual parameters, the wall temperature, and quality being correlated wit inlee hth t flow rate. Text cont.296.p. on 284 (tclad tin/ ?°C 80 oxo 60 0 100 Z/d. Fig. 6.1. Temperature variation with the form lines A and B in the event of the edge pin bending: - experiment, , © prediction- O , — — taking into account bending,n pi e th — — — -prediction -without regard bending. 285 to t ole ut inlet I I.. 1 I I I I I i L 654321 1254 channel number 6) d) Schematic6.2 Fig. diagram model ofthe subassembly (a), flow rate variation with an time (b) coolant temperature variation with the length © and across subassembly (d): experimental- • , O , V , dataA , [4], - SABRE, — ——— • — - MID, — — - - - - BACCHUS t/t ig'. 5.3. Dimensionless temperature at the pin surface as a function of parameter t/tp. 00 fl5 4 » •0 Fig. (5.4. Dimensionless temperature at the pin surface as a function of parameter t/t0. 287 SIMULATORS T405\ T413 (i I?A 3; Current suooliedo t the gauges •Resistance Box + Current supplied 032x35 to the gauges Fig. 6 5 Schematic of the contour 288 gas vacuum fir EM pamp Test section Calibration S region c heater - flow 3 1,meters2, 4, 5,6,1 - thermocouples - thermocouples 8,9 for flow-meters calibration to oo Fig. 6.6. Scheme of circulation. to Plow rate at test section inlet 3 3 68X= 0,75m /h G6)( =1,9 ra /h 10 L T ,rain UV/cm. void fraction potentiometer 4 10 JhJu... in.. I. .k Ja,. f ( mifrr*- L* I stag f boilino e g stagI I boilinf o e g (21 min ) 3 rain11 ) 4UV/cm potentiometei'3 mm from beginning of heating) , min U.V/cm potentiometer 2 from (19m 4m of heating) potentiomete1 r mm from beginning of heating) Fig. 6.7 Characteristics of the first (I) and second (II) stages of boiling in model subassembly. fL/V V °^c 900 800 700 600 C 10 15 20 25 30 35 "800 700 600 500 0 10 15 20 25 30 35 f.min 80 U 60 40 10 15 20 25 30 35 I,nun Fig. 6.8. Temperatures of simulator wall (a), coolant temperature at heating re- gion outlet (gross-section IV) (b) and temperature difference «\vall-fluid» cross- section III (c). 291 oC, W/rrv^K 8 6 D4 8 6 4 10- I ( q, 105 4 8 10' Fzg Pd .. /fga/ transfer variation with surfacee th heat flux density- A : ex- perimental set, O - second experimental set. 292 Fzg. 5.70. Comparison of external data liquidn o metal boiling heat transfer- po tassium [15]: 1 - large volume (3q°'7) - 2 tube,10mm = d (electrical heating) - tube,JOmm = 3 d (heat electrical) 4 - tube, d = 8.3mm - tube,22mm = 5 d electrical 6 - tube, d - 4mm heating 7 - tube, d = 6mm eutectic sodium - potassium alloy [IPPE] © - 7-pin bundle de-3.52mm (electrical heating) 293 10' IOJ z } Kg/(m s) Fig. 6.11. CHF value with coolant mass velocity on tube: sodium , potassium) • , ( annuli: O) ( sodium ) [2],(x experiments IPPE on 7-pin bundle, eutectic sodium-potassium alloy (*). 294 ^-105 W3<= First pressure splash -± Rewetting Wall temperature surge _"fcw "T"/ ~ (second pressure splash) V/cm V/cm 1 2800 2900 3000 Fig. 6.12. Time - variation of boiling characteristics. 295 Boiling heat transfer coefficient. The main factor influencing heat trasfer coefficient value is the heat flux value (Fig.6.9) Due to small variation in circulation velocity a direct relationship between heat transfer coefficient and velocity failed to be revealed. Fig.6.10 shows a good correlation between experimental data and data on potassium boiling in tubes 4 -10 mm in diameter in the rages 0.2-4 bar, x= 0.04 -0.8, pW=22-1490 kg/ (m2.s), q=ltf-1.4, 106W/m2. Thus boiline th , g heat transfer coefficien eutectir fo bundltn e allo K b pi n cn yNa i e ca followed to relationship for tube potassium boiling: 3-q°= a 7p0-15 (6.4) wher W/m= ] e[q 2 , {[p] bar.= Analysis performe Kottowsky db i [15 othed ]an r authors (Borishanski [9], Subbotin [8], Shah [11] shows )ha n tharoune th t d tubd ean boilins C , liquin gHg i m dK metal, Na s- other describes i s- unifiey db d function tha relationshi e closs i tth o et liquir pfo d metal pool boiling. To predict boiling heat transfer in sodium bundle with pitch-to-diameter ratio s/d = 1.18 the following relationships are recommended: for = 4-10-5+10~3 5 (6.5) 3 3 for p/Pcr=10- + 2-10~ (6.6) Here, q in MW/m2; r - specific evaporation heat, J/kg; a- surface tension, N/m2; A, in 3 kg/mn i p , \ W/(msaturatiok) . n welcriterion s temperaturi A s . la K nn i fors T em [16] 4 07 7 N 8.7-10u= -Pe -K°p (6.7) where Nu = cd/A; Pe = (q/rp") cp'ff(l/x) Critical heat flux. During experiment heat sa t flux -151 kW/m amplituden a 2 walf so l temperature pulsations and coolant temperature rises sharply, that is a forerunner of heat transfer crisis. Thus onle th , y approximate dat critican ao l heat flux wer t undeege r conditionf o s natural circulation. The value obtained is in a good agreement with relationship presented in (6.8) 296 uniquBasee th n do recommendinef o poin y twa thero n s ei reliable gth e relationshio pt predict qcr in pin bundle, additional experiments must be called on to analyze results in-depth. Some results on liquid metal boiling presented here were get when pressure was release 0.06-0.05y db aftea rMP 2800 experimentas l performance t firstA . , during more than 10 0this s pressure bringint releasno s ewa g abou obviouy an t s change boilingn s i tim s a t e bu , passe firse sth t pressure jump occurred whic attendes hwa d wit wale hth l temperature rise, fast change in all sensors signals and ejection of some amount of the coolant from the test section (Fig.6.12) thin .I s cas inlee eth t flow rate droppe zero amplituddd t oan magnetie th f eo c flow meter signal was coming under reduction at the test section outlet flow meter dropped to zero that indicated that the test section is filled with vapour and liquid is absent. Liquid evaporation finished after 3000 s. In that moment the process was coming to be hard controlled and to be of explosion character. Second, more strong pressure jump was observed. Wall temperature exceeded 1100°C (registratio nwaln limitpi ld sectioan )0 5 f no mm in length was melted Heaters itself were not destroyed. Thus, experimental results indicate that pressure release bring threae sth faso t t reactor core performance. CONCLUSIONS The following features of liquid metal boiling in the pin bundle under natural circulation condition emerges sha d fro experimentse mth : stable th e• boiling takes place only withi limitee nth d rang f heaeo t flux variation, boundaries it conditiond san transitiof so unstable th o nt e boilin definee gar a y db number of factors; • development of unstable boiling being attended with the great temperature and flow pulsation heae lean th ts o dca transfet r crises, wit safete hth y margi lackins ni g in essence; • wall-liquid temperature difference stabln i s e boilin 15-20°Cs gi , thos n unstablei e boiling - 25-50°C; • in the event of dryout the pin wall temperature achieves the melting temperature very rapidly; • dat hean ao gooa t transfen i d agreemene ar r t with experimental dat liquin ao d metal tube and pool boiling; unifiee th • d relationshi r criticapfo l heat flu liquin i x d meta a bundln n pi li s ei satisfactory agreement with boiling in tube and annuli. Technical base generate perforo dt m boiling experiments permit carryin futura t gou e researches wit followine hth g purposes: • to define the borders of the stable boiling in dependence of different parameters and factors; • to develop criterion analysis of liquid metal boiling heat removal; • to study conditions of pin wall integrity. REFERENCES [1] Zhukov A.V., Sorokin A.P., Matjukhin N.M. Interchannel Exchange in Fast Reactor Subassemblies. Codes and Applications, M., Energoatomizdat, 1991 (in Russian). [2] Huber F., Mattes K., Peppier W., et. al. Loss of Flow Experiments in Sodium in an Electrically Heated 37-Pin Bundle with Sinusoidal Axial Heat Flux Distribution.. Proc. LMFBe ofth R Safety Topical Meeting, Lion, Franc p.341-349, e V 1982 l v. , . 297 [3] Mikhin V.I., Fetisova L.N. Numerical Analysis of Transient Temperature Behavior in Central Area Subassemblyf so . Preprint IPPE-2240,199 Russian)n 2(i . [4] Kuznetso . AccidenLA vd Transitioan t n Processe n i Fass t Reactors, M. , Energoatomizdat, 198 Russian)n 7(i . [5] Subbotin V.I., et al. Hydrodynamics and Heat Transfer in Nuclear Power Plants, M., Atomizdat, 1975. [6] Zeigarnick Yu., Litvinov V.D. Heat Transfer and Pressure Drop in Sodium Boiling in Tubes. Nucl. Science and Des., v.72. [7] . EvaporatioC u Dwye MicrolayeHs e , th rf O. n o n Hemisphericari l Bubble Growtn hi Nucleate Boiling of Liquid Metals. Intern. J. of Heat and mass Transfer, 1976, v. 19, p. 185. [8] Subbotin V.I., Sorokin D.N., et al. Heat Transfer in Liquid Metal Natural Convection Boiling, M., Nauka, 1969. [9] Borishanski V.M., Kutateladze S.S.. Liquial t ,e d Metal Coolants , AtomizdatM. , , 1976. [10] Kirillov P.L. Heat Transfer in Liquid Metal Flows in Round Tube (Single- and Two- Phase Flows. Docto Sciencf ro e Thesisis, IVTAN, Moscow, 1968. [11] Shah M.M. A Survey of Experimental Heat Transfer Data for Nucleate and Poll Boiling of Liquid Metals and New Correlations. International J. of Heat and Fluid Flow, 1992, v. 13, p. 370-379. [12] Chan Criticaw g S.H.Y.BNe e A lLe , . Hea t Flux Mode Liquir fo l d Metals undew rLo Heat Flux-Low Flow Conditions. Nucl. Eng. and Des., 1994, v. 148, p. 487-498. [13] Kaizer A., Huber F. Sodium Boiling Experimental A Low Power under Natural Convection. Nucl. Eng. an Des. 1987, v.100, p. 367-376. [14] Yamaguch . FloiK w Patter Dryoud nan t under Sodium Boiling Conditions. Nucl. Eng. and Des., 1987, v. 9, p. 247-263. [15] Kottowski H.M., Savateri C. Evaluation of Sodium Incident Overheat Measurements with Regard to the Importance of Experimental and Physical Parameters. International J. of Heat and Mass Transfer, 1977, v. 20, p. 1281-1300. [16] Kirillov P.L., Yuriev Y.S., Bobkov V.P.. Hand-Boo Therman ko l Hydraulics (Nuclear Reactorts, Heat Exchangers, Steam Generators), M., Energoatomizdat, 1988 (in Russian). 298 OVERALL CONCLUSIONS e validit1Th . f yo thermohydraulic n fasi s t reactor corhead an et exchange s largeli r y influence accurace th systee y sth b f ycorrelationmf o o s writte frictioe th r nfo n factors, heat transfer coefficients, mixing factors and so on. The development of the complete and accurate system is critical in nuclear power engineering. Method of thermohydraulic analysis, features of thermohydraulic phenomena, computer codes developed with the use of closing relation experimentae basee th sar n do l result d numericasan l modeline th f go processes in nuclear reactor units. o computatio2Tw . n procedures for e basi mr th predictio fo s f reactoo n r cord heaan et exchanger thermal hydraulics: subchannel approach (subassembly poroua d an )s body model (intermediate heat exchanger) workin n I codee . th t s gou muc h attentio bees nha n non-nominaIPPgivee e th th Eo n t i l reactor operation being cause diabatiy db c conditions at the wrapper, by the random departure of parameters from nominal values in campaign, transiente th y b s associated with liquid metal boiling l instanceal n I . inter-channee th s l exchange is of primary importance in the computations. 3. Analysis of the process and performance of experiments with the ensuing development of computer code followinbasee e th sar n do g principles: • thermal modelin f fuego l pins (hea2 MW/m1. to t flu p xu ) wit distributee hth d 2 power production; • modelin reactof go r corhead ean t exchanger thermal hydraulics; • local measurement technique, including electromagnetic flow meters, miniature thermocouples, wit ensuine hth g correlation between hydrauli thermad can l data, that gives sufficient information on fast reactor subassembly performance; • high-power liquid metal facilities operating in a wide range of working temperatures with sodium or sodium-potassium alloy used as a coolant, which allow the large-scale out-of-pile experiments to be carried out. . Electromagneti4 c technique allow locae sth l hydraulic characteristic f axialo s , transverse and combined (axial-transverse) flows through the models simulating subassembly and heat exchange measurede b o rt advantagee Th . possibilitied an s technique th s f a so e ear follows: • experiment performee b y sma d wit same hth e coolant thoss sa reactorn ei ; • small-sized sensors meet reactor technological standards; • local flow rate can be defined around and along the pins; • local hydrodynamic feature deformen i s d systems (bendin shiftind gan pinsf o g , blockages, manufactoring tolerances and others) can be revealed; • Measurements remain precise due to sensors' sensitivity as well as due to the lack of any elements inserted into the flow which can distort the hydrodynamics. • The technique is easy to realize, low in cost, advantageous for reading information. It can be convenient means for studying physics of combined transverse-axial flow. 5. Features of thermohydraulics in reactor core and heat exchangers are as follows: • Among the main factors defining hydraulic behavior in fast reactor core subassembly are large velocity non-uniformities around the edge pins and intensive inter-channel exchange due to wire wrap; • Inter-channel exchange is one of the most important reasons for the hydraulic characteristics in pin bundle to differ from those in insulated channels; • Combined predictionand experiment researches have yielded informatioe th n o n influence of various factors on liquid metal flow behavior; 299 s distincA • t froe previouth m s hypothesi e possibilitth n o so t predicy t hydrodynamics using the averaged, across the subassembly, coolant velocity or hypothesi f isobariso c section s beeha nt i , shown that suc hpredictioa n doct no s provide the wanted accuracy. Feasibility of the hypothesis of isobaric section should be limited by the bundles of smooth pins being free from displacers; • Hydraulic features in mutually relative channels are properly reflected by the subchannel analysis accompaning for inter-channel exchange, which allows predicting reliable velocity distributions over the pin bundles; • Subassembly hydrodynamics wholea s a , , depends a larg o t ,e measuree th n o , feature bundleedge n th pi ef e so area th . f Predictiono s experimentad san l datn ao local hydrodynamic characteristic e edgth en i schannel s allo e optimawth l geometrical variant chosene b o st ; • Local hydrodynamic measurements s appliea , o fast d t reactor heat exchangers, permit gainin e experimentath g l data neede r predictinfo d g combined flow. Appropriate codes have been developed and verified on the experimental data available. 6. On the subject of inter-channel exchange in fast reactor subassembly the following remarks are in order: • Study of inter-channel exchange was performed by the use of the electromagnetic technique which permits probing deeper int finee oth r detail procese th f so s wite hth ensuing correlations derived for the local and integral mixing factors within a wide ranges of defining parameters; • Physical picture of the inter-channel exchange in the bundle of wire wrapped pins is followss a ; • convective component of inter-channel exchange intensity distribution along bundle th e follows sine law; exchange th • e intensity depend relative th n so e bundlee e pitcth th f hn o o , kind and pitch of wire wrap, on Reynolds number; • directed coolant flow is observed around the subassembly wrapper. • Modified thermal track technique allows investigatio locae integrated th an f l no d mixing factors. Using this techniqu totae th date ln eth a o therma l mixing factor have been obtained; • Joint applicatio f electromagnetino thermad can l track technique allo totae wth l mixing factodividee b o t r d into separate components non-equivalence th , e factor between heat and mass transfer to be determined; • The main component of inter-channel exchange in fast reactor core subassembly is convective component due to the wire wrapped on the pins, whereas in reactors with high conductive pins an exchange due to pin heat conduction dominates; • The equivalence factor is found in liquid metal experiments to be equal to about 0.7; • To evaluate mixing factors due to turbulent, molecular diffusion and convective transpor empiricae th t analyticad an l l correlations have been derived withie nth pitch-to-diameter ratio range 0.1 300 subchannel approach and the porous body model are straightforward and reliable procedures; • Theoretical analysis of liquid metal heat removal supplements experimental investigations e notionTh . f inter-channeo s l exchange (mass, momentum, energy mixing factors, non-equivalence factor between heat and mass transport, "effective" mixinallo) numericae n wo th g o s facto d an lr procedur developee b e o et th d dan syste thermamf o l hydraulic governing equation reducee b o st singlo dt e equatiof no convective heat transfer (using the concept of equivalent thermal conductivity of pin bundle). 7. Generalized relations derived from the experiments form the basis for most calculations of steady state heat removal in any axi-symmetric system cooled by liquid metal; 8. Analytical procedures and experimental techniques have been successfully combined in considering an irregular processes (variable power production, entrance section). The main physical feature followss a e sar : • Relative lengt f entrancho e section reduces wit pitch-to-diametee hth r ratid oan equivalent thermal conductivit pinsf yo laminan I . r flo entrance wth e section length is in direct proportion to Peclet number (heat transfer due to molecular heat conduction), in turbulent flow it has a peak; • Universal formula describing variation temperaturn i s head an et transfee th t a r entrance section has been proposed; • It is Duhamel's integral that allows the experimental data gained under hydraulically unstable conditions being converted into those under variable power production (at least in fast reactors). e attentioDu . 9 n shoul thermophysicagivee e db th o nt l validatio edge th ef n o (wall) pins sa mose th t dangerous are subassemblf ao termyn i temperaturf so e non-uniformity maie Th .n features of the edge pins performance are as follows; • Temperature non-uniformity at the edge pins far exceed those at the inner pins; • Heat transfer coefficients in the edge area of fast reactor subassembly are lesser than expecte internae th n di l factoarea y af 1.5-2.0b o r relatione .Th s presented take into account the availability of displacers within the edge channels; • Maximum temperature non-uniformit Peclew lo t ta y number s (transition region) can presen severa t e hazar emergenco dt y coolin f reactogo r core provided that powe keps ri sufficientlt ta y high level; • Heat remova edge th en i l channel rulea s unstablf a o , , sis e character, that depends on equivalent thermal conductivity, relative pitch, shap sizd f displacerean o d san other factors; bundln Pi e• deformation cause temperature sth e non-uniformit increaso e yt th d ean heat transfer coefficient to reduce at the edge pins; • As coolant passes through the gap between subassemblies, it reduces coolant temperatur edge th en e i channels temperaturo ,s e non-uniformity increase -50y sb % in the event of the ratio between flow through the inter-subassembly space and those throug subassemble hth -5-6%ys i ; 10. Transient reactor core and heat exchanger behavior is the key problem of fast reactor thermal hydraulics: • During operation subassembl subjec s ycombinei e th o t t d actio variouf no s factors, with the temperature non-uniformity being among the most important one. e combineTh • d subchannel codes TEMP involving solutio f macro-transporo n t equations, having regard to inter-channel exchange, has been verified on the extensive experimental data that allows predicting to a high accuracy nominal and 301 non-nominal temperature behavior in fast reactor core. The code TEMP is of high- performanc gaines ha d d ean widesprea d acceptance. • Thermal mechanical analysis performed having regar subassemblo dt y deformation indicates the enhancement of maximum temperature of the pins, as well as maximum temperature non-uniformity. 11. Combined experimental & analytical investigations of intermediate heat exchanger thermal hydraulics have presente a dbasi c informatio n velocito n d temperaturan y e behavior maie .Th n result followss a e sar : in the field of hydrodynamics: • The use of electromagnetic technique has allowed the physics of axial-transverse flow to be studied, as well as characteristics of triangular and square arrangement of the tube wida n si e rang Reynoldf eo s number; • Fro locae mth l measurement f transverso s axiad ean l component velocitf o s e yw can conclude whethe givee rth n desig heaf no t exchange optimums ri ; • Equalizatio coolanf no t flow ove tube rth e bundle reduces heat transfer surface area and economidoins n i ,it , gso c feasibilit enhanceds yi ; • Experimental data have been useclosina s da g constant code th en si development . fieldinthe of thermal behavior: • Dat hean ao t transfer coefficient temperaturd an s e e behavio usee th b n i dn ca r validation of heat exchanger equipment and in the development of optimization methods; • The local thermal modeling allows the processes going on in the multi-tube heat exchange studie e small-scale b th o rt n do e model tubes)9 s(1 ; • Computer codes verifiee experimentath n o d l datprofitable ar a y employen i d thermal hydraulic validatio fasf no t reactor heat exchangers. 12. For the purpose of developing procedure of transient data generalization and to derive approximate criteria transiene ,th t temperature behavio bees rha n investigatee th n di bundle with various kinds of fuel. It has been shown that pin wall temperature dynamics can be expressed in the form of universal time-dependence; objectivee Th . 13 f experimentao s analyticad an l l validatio f reactono r core performance under accident condition pursuee b o st extensivy db e researches into sodium boiling. Experiments have been concerned with the investigations: • onset and development of the coolant boiling under various flow and power productions; • critical heat flux; possible destruction of pins and inherent phenomena. Predictions have been concerned wit analysie hfollowinth e th f so g processes: • molten fuel/coolant interaction; • drastic increase in the fragment surfaces within the system under consideration; • vapor explosion; • aerodynamical effects; • the process propagation. followine th w no U gpo t researche s have been performed: • Experimental bass beeeha n buil (higp u t h temperature facility, equipmend an t measurement technique); « Experiments have been carrie studo t t ydou liquid metal boiling dynamics; • The model two-phase flow has been stated; 302 e systeTh f macro-transpor mo • t governing equation s beeha sn analyzee th n i d framework of subchannel approach; • Inter-channel characteristics have been analyzed, as applied to two-phase flow. 14. The foregoing shows that the complete system of closing relations and constants require therman di l hydraulic analysi fasf so t reactor cor d ean heat exchangers have beenderived for the following : • prediction of coolant flow distribution over the channel having regard to inter- channel exchange; • predictio coolanf no t temperature distribution ove channele rth ; • definitio temperaturf no e difference "wall-liquid maximud "an m temperature non- uniformity; • consideratio variablf no e power production; • inclusion of various factor defining temperature behaviour; • definition of maximum pin temperatures. The most advanced thermohydraulic codes are the codes GID, TEMP, MIF, MID develope e LMFBth r dfo R core thosd r intermediatan , efo e heat exchange PROTVAe ar r , UGRA, TAKT and others. Authors consider that the material presented fulfill the modern thermal hydraulic requirements. NEXT PAGE(S) left BLANK 303 CONTRIBUTORS TO DRAFTING AND REVIEW Bogoslovskaya, G.P. Institut Physicf eo Powed san r Engineering, Russian Federation Cevolani . S , Institut Nucleaf eo Alternativd ran e Energy, Italy Ninokata, H. Tokyo Institute of Technology, Japan Rinejski . A . A , International Atomic Energy Agency Sorokin, A.P. Institut Physicf eo Powed san r Engineering, Russian Federation Zhukov . V . A , Institut Physicf eo Powed san r Engineering, Russian Federation 305e<4000,0.2;