Investigation of Thermal Hydraulics of a Nuclear Reactor Moderator

Araz Sarchami

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Mechanical and Industrial Engineering Department University of Toronto

Araz Sarchami

Doctor of Philosophy

Mechanical and Industrial Engineering Department University of Toronto

2011 Abstract

A three-dimensional numerical modeling of the thermo hydraulics of Canadian Deuterium

It is important to keep the water temperature in the moderator at sub-cooled conditions, to prevent potential failure due to overheating of the tubes. Because of difficulties in measuring flow characteristics and temperature conditions inside a real reactor moderator, tests are conducted using a scaled moderator in moderator test facility (MTF) by Chalk River

Laboratories of Atomic Energy of Canada Limited (CRL, AECL).

MTF tests are conducted using heating elements to heat tube surfaces. This is different than the real reactor where nuclear radiation is the source of heating which results in a volumetric heating of the heavy water. The data recorded inside the MTF tank have shown levels of

ii fluctuations in the moderator temperatures and requires in depth investigation of causes and effects.

The purpose of the current investigation is to determine the causes for, and the nature of the moderator temperature fluctuations using three-dimensional simulation of MTF with both

(surface heating and volumetric heating) modes. In addition, three-dimensional simulation of full scale actual moderator tank with volumetric heating is conducted to investigate the effects of scaling on the temperature distribution. The numerical simulations are performed on a 24-processor cluster using parallel version of the FLUENT 12. During the transient simulation, 55 points of interest inside the tank are monitored for their temperature and velocity fluctuations with time.

iii

To my dear mom and dad, Aziz and Giti

Acknowledgments

In the first place I would like to pay attribute to my supervisor, Dr. Nasser Ashgriz for his supervision, advice, and guidance from the very beginning of this research as well as giving me extraordinary experiences throughout this research. He is truly more than a scientific supervisor who helped me through all my ups and downs during 5 years of my work in

MUSSL lab. He will always be my mentor and I will never forget his role in shaping my future.

I also offer my regards and blessings to all my lab mates for their companionship and greatly appreciate their patience and good attitude toward me.

My special thanks goes to all my family specially my dear parents, Aziz and Giti, whose affection and support are immeasurable and unforgettable forever. They were beside me whenever I needed and they never gave up in encouraging me to keep going. It would have not been possible to pursue my PhD without them.

Table of Contents

Acknowledgments ...... v

List of Tables ...... ix

List of Figures ...... x

1 Introduction ...... 1

1.1 Nuclear Reactor ...... 1

1.2 Pressurized Heavy Water Reactor (PHWR) ...... 2

1.3 Moderator ...... 3

1.4 Heavy Water ...... 5

1.5 CANDU Reactor ...... 6

1.6 Studies on moderator tank ...... 9

1.7 Heat Exchangers ...... 14

1.8 Moderator Test Issues ...... 17

1.9 Objectives ...... 19

2 Numerical Setup ...... 21

2.1 MTF and Actual Tanks Geometry ...... 21

2.2 Operating Conditions ...... 24

2.3 Heating Methods ...... 25

2.4 Mesh Construction ...... 28

2.5 Computational Code ...... 32

2.6 Solution Strategy ...... 32

2.7 Planes - Points ...... 35

2.8 Parallel Processing – Physical Run Time ...... 41

3 Moderator Test Facility Simulation ...... 44

3.1 Temperature and Velocity Distributions ...... 44

3.2 Temperature and Velocity Fluctuations ...... 50

3.3 Asymmetry ...... 54

3.3.1 Main Flow Regimes ...... 54

3.3.2 Inlet Jets and Secondary Jet ...... 60

3.3.3 Momentum versus Buoyancy ...... 65

3.3.4 Asymmetry Effects ...... 67

4 Methods of Heating: Surface Heating and Volumetric Heating ...... 75

5 Scaling Effects ...... 82

vii

6 Comparison of Two and Three Dimensional Simulations ...... 90

7 Summary and Conclusion ...... 96

8 Future Work ...... 102

9 Reference ...... 104

viii

List of Tables

Table 2-1 MTF and actual tank Shell and Core Dimensions ...... 21

Table 2-2 MTF and actual tank Tubes Array Dimensions ...... 21

Table 2-3 MTF and the actual tank operating conditions used here ...... 24

Table 2-4 Planes Coordinates ...... 35

Table 2-5 Monitored points coordinates ...... 41

Table 2-6 Parallel processing time ...... 41

Table 5-1 MTF and actual tank operating conditions ...... 88

List of Figures

Figure 1-1 Heavy water moderator [51] ...... 5

Figure 1-2 CANDU reactor design [1] ...... 8

Figure 1-3 various moderator designs [10] ...... 8

Figure 1-4 The experimental data taken at the CANDU MTF ...... 18

Figure 2-1 The CAD data views of MTF tank and its Inlet Nozzles ...... 22

Figure 2-2 The CAD data views of Inlet Nozzle ...... 23

Figure 2-3 The schematic drawing of the MTF tank (all dimensions are in mm) ...... 23

Figure 2-4 MTF heat generation map - surface heating ...... 26

Figure 2-5 Mesh Generation - XY plane ...... 29

Figure 2-6 XY plane - mesh around tubes ...... 30

Figure 2-7 XY plane - mesh near the wall ...... 30

Figure 2-8 Inlet pipes ...... 31

Figure 2-9 Water outlet ...... 31

Figure 2-10 XY-Planes ...... 36

Figure 2-11 XZ-Planes ...... 36

Figure 2-12 YZ-Planes ...... 37

Figure 2-13 Nozzle planes ...... 37

Figure 2-14 Outlet pipe plane ...... 38

Figure 2-15 Temperature fluctuation - long range run for point 4 ...... 42

Figure 2-16 Velocity fluctuation - long range run for point 4 ...... 43

Figure 3-1 Temperature contours at two different times for plane S ...... 44

Figure 3-2 Velocity contours at two different times for plane S ...... 46

Figure 3-3 Temperature contours at two different times for plane B2 ...... 47

Figure 3-4 Velocity contours at two different times for plane B2 ...... 48

Figure 3-5 Temperature contours at two different times for plane D1 ...... 49

Figure 3-6 Temperature contours at two different times for plane SX ...... 49

Figure 3-7 Point 3 temperature and velocity fluctuations with time ...... 50

Figure 3-8 Point 12 temperature and velocity fluctuations with time ...... 51

Figure 3-9 Point 20 temperature and velocity fluctuations with time ...... 52

Figure 3-10 Point 50 temperature and velocity fluctuations with time ...... 53

Figure 3-11 Comparison between simulation and experiment ...... 54

Figure 3-12 Temperature distribution on 4 planes on Z and Y directions ...... 55

Figure 3-13 Velocity vectors (colour by velocity magnitude) in two nozzle planes and symmetry plane ...... 58

Figure 3-14 Impingement point...... 59

Figure 3-15 Effect of buoyancy force ...... 59

Figure 3-16 Inlet jets path. The marked points are used to record data on temperature and velocity...... 60

Figure 3-17 Secondary jet path. The marked points are used to record velocity and temperature data ...... 60

Figure 3-18 Temperature along the inlet jets penetration path. The x coordinate is angular position with respect to positive X direction ...... 62

Figure 3-19 Velocity along the inlet jets penetration path. The x coordinate is angular position with respect to positive X direction ...... 62

Figure 3-20 Temperature along the secondary jet penetration path. The x coordinate is position along the penetration path with respect to impingement point ...... 64

Figure 3-21 Velocity along the secondary jet penetration path. The x coordinate is position along the penetration path with respect to impingement point ...... 64

Figure 3-22 Moderate buoyancy ...... 65

Figure 3-23 Strong buoyancy ...... 66

Figure 3-24 Asymmetrical flow...... 67

xii

Figure 3-25 Left and right nozzle planes. These planes are used to study the effect of jet on jet impingement ...... 68

Figure 3-26 Left nozzle plane. Y axis velocity represents x-velocity and Z axis velocity represents z-velocity ...... 70

Figure 3-27 Left nozzle plane. Y axis velocity represents x-velocity and Z axis velocity represents z-velocity ...... 70

Figure 3-28 Right nozzle plane. Y axis velocity represents x-velocity and Z axis velocity represents z-velocity ...... 71

Figure 3-29Right nozzle plane. Y axis velocity represents x-velocity and Z axis velocity represents z-velocity ...... 72

Figure 3-30 Center plane in Z direction. this shows the transfer of symmetry plane effects to the other planes along the Z-direction ...... 74

Figure 4-1 Location of compared points ...... 76

Figure 4-2 Temperature fluctuations ...... 78

Figure 4-3 Temperature and velocity contours for t=150 s (three different simulations) ..... 81

Figure 5-1 Temperature contours for MTF and actual reactor ...... 84

Figure 5-2 Velocity contours for MTF and actual reactor ...... 85

Figure 5-3 Temperature and velocity fluctuations plot for actual moderator and MTF ...... 86

xiii

Figure 6-1 Comparison between 2D and 3D temperature and velocity distributions ...... 92

Figure 6-2 Node 15 (located at top of the tank in XY plane) comparison between 2D and 3D

...... 94

Figure 6-3 Node 4 (located at the centre of the tank in XY plane) comparison between 2D and 3D ...... 95

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1 Introduction

1.1 Nuclear Reactor

A nuclear reactor is a device to initiate, and control, a sustained nuclear chain reaction.

Nuclear reactors are commonly used in electrical power generation plants. It is usually accomplished by methods that involve using heat from the nuclear reaction to power steam turbines. When a large fissile atomic nucleus such as uranium-235 or plutonium-239 absorbs a neutron, it may undergo nuclear fission. The heavy nucleus splits into two or more lighter nuclei, releasing kinetic energy, gamma radiation and free neutrons; collectively known as fission products [1]. A portion of these neutrons may later be absorbed by other fissile atoms and trigger further fission events, which release more neutrons, and so on. This is known as a nuclear chain reaction.

Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts often producing free neutrons and photons (in the form of gamma rays), as well. Fission of heavy elements is an exothermic reaction which can release large amounts of energy both as electromagnetic radiation and as kinetic energy of the fragments (heating the bulk material where fission takes place) [2]. The key to maintaining a nuclear reaction within a nuclear reactor is to use the neutrons being released during fission to stimulate fission in other nuclei. With careful control over the geometry and reaction rates, this can lead to a self- sustaining reaction, a state known as "chain reaction".

Natural uranium consists of a mixture of various isotopes, primarily 238U and a much smaller amount (about 0.72% by weight) of 235U. 238U can only be fissioned by neutrons that are

1 fairly energetic, about 1 MeV or above. No amount of 238U can be made "critical" to sustain a chain reaction, since it will tend to parasitically absorb more neutrons than it releases by the fission process. 235U, on the other hand, can support a self-sustained chain reaction, but due to the low natural abundance of 235U, natural uranium cannot achieve criticality by itself

[3].

The "trick" to making a working reactor is to slow some of the neutrons to the point where their probability of causing nuclear fission in 235U increases to a level that permits a sustained chain reaction in the uranium as a whole. This requires the use of a neutron moderator, which absorbs some of the neutrons' kinetic energy, slowing them down to energy comparable to the thermal energy of the moderator nuclei themselves [3].

1.2 Pressurized Heavy Water Reactor (PHWR)

A pressurised heavy water reactor (PHWR) is a nuclear reactor, commonly using un- enriched natural uranium as its fuel, which uses heavy water (deuterium oxide D2O) as its coolant and moderator. The heavy water coolant is kept under pressure in order to raise its boiling point, allowing it to be heated to higher temperatures without boiling. While heavy water is significantly more expensive than ordinary light water, it yields greatly enhanced neutron economy, allowing the reactor to operate without fuel enrichment facilities [3].

A great advantage of PHWR is that we are not required to use enriched Uranium. Enriched

Uranium has many complications. One would the requirement to build a uranium enrichment facility, which is generally expensive to build and operate. They also present a nuclear proliferation concern; the same systems used to enrich the 235U can also be used to produce much more "pure" weapons-grade material (90% or more 235U), suitable for

2 producing a nuclear bomb. This is not a trivial exercise, by any means, but feasible enough that enrichment facilities present a significant nuclear proliferation risk [3].

Pressurised heavy water reactors do have some drawbacks. Heavy water generally costs hundreds of dollars per kilogram, though this is a trade-off against reduced fuel costs. It is also notable that the reduced energy content of natural uranium as compared to enriched uranium necessitates more frequent replacement of fuel; this is normally accomplished by use of an on-power refuelling system. The increased rate of fuel movement through the reactor also results in higher volumes of spent fuel than in reactors employing enriched uranium; however, as the un-enriched fuel was less reactive, the heat generated is less, allowing the spent fuel to be stored much more compactly [3].

1.3 Moderator

In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium-235. Commonly used moderators include regular (light) water, solid graphite and heavy water [1]. Beryllium has also been used in some experimental types, and hydrocarbons have been suggested as another possibility [48].

Neutrons are normally bound into an atomic nucleus, and do not exist free for long in nature.

The unbound neutron has a half-life of just less than 15 minutes. The release of neutrons from the nucleus requires exceeding the binding energy of the neutron, which is typically 7-

9 MeV. Whatever the source of neutrons, they are released with energies of several MeV

[48].

Water makes an excellent moderator. The hydrogen atoms in the water molecules are very close in mass to a single neutron and thus have a potential for high energy transfer, similar conceptually to the collision of two billiard balls. However, in addition to being a good moderator, water is also fairly effective at absorbing neutrons. Using water as a moderator will absorb enough neutrons that there will be too few left over to react with the small amount of 235U in natural uranium. So, light water reactors require fuel with an enhanced amount of 235U in the uranium, that is, enriched uranium which generally contains between

3% and 5% 235U by weight. In this enriched form there is enough 235U to react with the water- moderated neutrons to maintain criticality [6, 7].

Use of enriched Uranium has several issues which are explained partially. An alternative solution to the problem is to use a moderator that does not absorb neutrons as readily as water. In this case potentially all of the neutrons being released can be moderated and used in reactions with the 235U, in which case there is enough 235U in natural uranium to sustain a chain reaction. One such moderator is heavy water, or deuterium-oxide. Although it reacts dynamically with the neutrons in a similar fashion to light water, it already has the extra neutron that light water would normally tend to absorb [6, 7]. The use of heavy water moderator is the key to the PHWR system, enabling the use of natural uranium as fuel which means that it can be operated without expensive uranium enrichment facilities. A schematic of a heavy water reactor is shown in

Figure 1-1.

Figure 1-1 Heavy water moderator [51]

1.4 Heavy Water

Heavy water is water containing a higher-than-normal proportion of the hydrogen isotope

deuterium, either as deuterium oxide, D2O or H2O, or as deuterium protium oxide, HDO or

HHO [8]. Physically and chemically, it resembles water, H2O; in water, the deuterium-to- hydrogen ratio is about 156ppm. Heavy water is water that was highly enriched in deuterium, up to as much as 100% D2O. The isotopic substitutiion with deuterium alters the bond energy of the water's hydrogen-oxygen bonnd, altering the physical, chemical, and, especially, the biological properties of the pure, or highly-enrriched, substance to a degree greater than is found in most isotope-substituted chemical compounds. Pure heavy water is not radioactive. It is about 11% denser than water, but otherwise, is physically very siimilar to water.

1.5 CANDU Reactor

Canadian Deuterium Uranium (CANDU) nuclear reactor is a Pressurized Heavy Water

Reactor (PHWR) which uses a moderator tank to moderate the water temperature. The moderator system in a CANDU reactor is a low-pressure system that is separate from the primary heat transport system. The moderator-circulation system ensures that heat deposited in the moderator is removed so that a certain amount of sub-cooling is maintained during normal operation. Heavy water is used both as the moderator and as the primary heat transport fluid. CANDU power reactor is comprised of several hundred horizontal fuel channels in a large cylindrical Calandria (the reactor core of the CANDU reactor) vessel.

Each fuel channel consists of an internal pressure tube (containing the fuel and the hot pressurized heavy water primary coolant), and an external Calandria tube separated from the pressure tube by an insulating gas filled annulus. The Calandria vessel contains cool low- pressure heavy-water moderator that surrounds each fuel channel. CANDU utilize natural

Uranium UO2 fuel. The fuel is in the form of half-metre-long cylindrical bundles, typically containing 37 clustered elements. Twelve bundles sit end-to-end within the pressure tube, roughly six metres long, through which pressurized heavy-water coolant is circulated [7].

CANDU is the most efficient of all reactors in using uranium: it uses about 15% less uranium than a pressurized water reactor for each megawatt of electricity produced. Use of natural uranium widens the source of supply and makes fuel fabrication easier. Most countries can manufacture the relatively inexpensive fuel. There is no need for uranium enrichment facility. Fuel reprocessing is not needed, so costs, facilities and waste disposal associated with reprocessing are avoided. CANDU reactors can be fuelled with a number of

6 other low-fissile content fuels, including spent fuel from light water reactors. This reduces dependency on uranium in the event of future supply shortages and price increases.

The CANDU reactor is conceptually similar to most light water reactors, although it differs in the details. Like other water moderated reactors, fission reactions in the reactor core heat pressurized water in a primary cooling loop. A heat exchanger transfers the heat to a secondary cooling loop, which powers a steam turbine with an electrical generator attached to it. Any excess heat energy in the steam after flowing through the turbine is rejected into the environment in a variety of ways, most typically into a large body of cool water, such as a lake, river or ocean. The schematic of the plant is shown in Figure 1-2. The main difference between CANDUs and other water moderated reactors is that CANDUs use heavy water for neutron moderation.

The large thermal mass of the moderator provides a significant heat sink that acts as an additional safety feature. If a fuel assembly were to overheat and deform within its fuel channel, the resulting change of geometry permits high heat transfer to the cool moderator, thus preventing the breach of the fuel channel, and the possibility of a meltdown.

Furthermore, because of the use of natural uranium as fuel, this reactor cannot sustain a chain reaction if its original fuel channel geometry is altered in any significant manner.

The CANDU product line, developed in Canada, includes the Generation III+ 1,200 MWe class ACR (Advanced CANDU Reactor), known as the ACR-1000, and the 700 MWe class

CANDU 6 power reactor [9]. Each of these models varies in their geometry specifications

(as seen in Figure 1-3) as well as some other operating parameters and energy output.

Figure 1-2 CANDU reactor design [1]

Figure 1-3 various moderator designs [10]

CANDU 6 is the smaller output reactor and it was designed specifically for electricity production, unlike other major reactor types that evolved from other uses. This focused development is one of the reasons that CANDU has such high fuel efficiency.

ACR is the latest model of CANDU series and it is offered with higher power output. The other major differences in ACR as compared with CANDU are

 The use of slightly enriched uranium fuel (2.1 % wt. U-235 in 42 pins of the fuel

bundle)

 Light water (as opposed to heavy water D2O) as the coolant, which circulates in the fuel

channels

This result in a more compact reactor design (Calandria inside diameter 31.6 % less than that for CANDU 6) and a reduction of heavy water inventory (72% less D2O mass inventory when compared with CANDU 6)[57].

1.6 Studies on moderator tank

The specific studies on thermal hydraulics in CANDU reactors or in general term, pressurized heavy water reactors are very limited in the open literature. This is due to the fact that CANDU reactors are relatively new (since 1970s) and also due to limitation on accessibility to existing studies due to sensitivity of the issue. Broader range of studies which are physically similar to moderator tank can be considered as well. Studies on flow over tubes and flow inside shell and tube heat exchangers are two examples of similar devices.

Many of the references used here do not exist in open literature and are published only as internal reports and presentations inside the nuclear industry. The studies are in two categories of experimental and numerical.

Koroyannaski et al [12] experimentally examined the flow phenomena formed by inlet flows and internal heating of a fluid in a Calandria cylindrical vessel of SPEL (Sheridan Park

Engineering Laboratory) experimental facility. They observed three flow patterns inside test vessel and their occurrence was dependent on the flow rate and heat load. Carlucci and

Cheung [13] investigated the two-dimensional flow of internally heated fluid in a circular vessel with two inlet nozzles at the sides and outlets at the bottom, and found that the flow pattern was determined by the combination of buoyancy and inertia forces. Austman et al.

[14] measured the moderator temperature by inserting thermocouples through a shut-off rod

(SOR) guide tube in operating CANDU reactors at Bruce A and Pickering. Huget et al. [15] and [16] conducted 2-dimensional moderator circulation tests at a 1/4-scaled facility in the

Stern Laboratories Inc. (SLI) in Canada. From these researches, three clearly distinct flow patterns were observed according to certain operating ranges. Sion [17] measured the temperature profile of the D2O moderator inside a CANDU reactor, within the calandria vessel, by means of a specially instrumented probe introduced within the core.

Measurements were made under steady and transient reactor conditions using two different sensors, resistance temperature detectors (RTD) and thermocouples. The results established the feasibility of in-core moderator temperature measurement and indicated that the thermocouples used were relatively not affected by the intense radiation.

Hohne et. al. [18] studied the influence of density differences on the mixing of a pressurized water reactor. They presented a matrix experiments in which water with the same or higher

10 density was injected into a cold tank leg of the reactor with already established natural circulation conditions at different low mass flow rates. Sensors measuring the concentration of a tracer in the injected water were installed in the tank. A transition matrix from momentum to buoyancy-driven flow experiments was selected for validation of the computational fluid dynamics software ANSYS CFX. The results of the experiments and of the numerical calculations show that mixing strongly depends on buoyancy effects: At higher mass flow rates the injected slug propagates in the circumferential direction around the core barrel. Buoyancy effects reduce this circumferential propagation with lower mass flow rates and/or higher density differences.

Khartabil et al. [19] conducted three-dimensional moderator circulation tests in the moderator test facility (MTF) in the Chalk River Laboratories of Atomic Energy of Canada

Limited (AECL). Along with separate phenomena tests related to the CANDU moderator circulation, such as a hydraulic resistance through tube bundles, velocity profiles at an inlet diffuser, flow development along a curved wall, and the turbulence generation by temperature differences were measured. Based on these experimental works, a computer code for a CANDU moderator analysis has been developed by Ontario Hydro and selected as Canadian industry standard toolset (IST). This computer tool has been used for the design of ACR and CANDU as well as a CANDU safety analysis. He also [20, 21] experimentally studied the moderator tank and recorded its temperature in many points during the operation using fixed thermocouples. He was able to create temperature maps on moderator cross section plane. In order to perform the experiment, a scaled Calandria vessel was designed and tested. The CANDU Moderator Test Facility (MTF) is a ¼ scale CANDU Calandria, with 480 heaters that simulate 480 fuel channels. It is specifically designed to study

11 moderator circulation at scaled conditions that are representative of CANDU reactors. The

MTF was operated at various operating conditions that simulate moderator circulation in

CANDU reactors and temperatures were recorded. This study is initiated by these tests in order to numerically simulate the same tank to have more in depth analysis and extract data which are impossible to obtain using experimental devices. The comprehensive goals of this study are mentioned in objective section of the thesis.

Quaraishi [22] simulated the fluid flow and predicted temperature distributions of SPEL experiments computational codes. Collins [23, 24] carried out the thermal hydraulic analyses for SPEL experiments and Wolsong units (Korea Republic nuclear power plant) 2, 3, 4, respectively, using PHOENICS code using porous media assumption for fuel channels.

Yoon et. al [25] used a computational fluid dynamics model for predicting moderator circulation inside the CANDU reactor vessel. It was to estimate the local sub-cooling of the moderator in the vicinity of the calandria tubes. The buoyancy effect induced by the internal heating is accounted for by the Boussinesq approximation. The standard k-e turbulence model with logarithmic wall treatment is applied to predict the turbulent jet flows from the inlet nozzles. The matrix of the calandria tubes in the core region is simplified to a porous media. The governing equations are solved by CFX 4. They did a parametric analysis and since their simulation was steady state, it was a base for future transient simulations. In their next paper, Yoon et. al. [26] developed another computational fluid dynamics model by using a coupled solver. They did the simulation for Wolsong Units 2/3/4. A steady-state moderator circulation under operating conditions and the local moderator sub-cooling were evaluated using the CFD tool. When compared to the former study in the Final Safety

Analysis Reports, the current analysis provided well-matched trends and reasonable results.

This new CFD model based on a coupled solver shows a dramatic increase in the computing speed, when compared to that based on a segregated solver.

In addition, there have been several CFD models for predicting the thermal hydraulics of the

CANDU moderator. Yoon et al. [27] used the CFX-4 code (ANSYS Inc.) to develop a CFD model with a porous media approach for the core region in order to predict the CANDU moderator sub-cooling under normal operating conditions, while Yu et al. [28] used the

FLUENT code to model all the Calandria tubes as heating pipes without any approximation for the core region. The analytic model based on CFX-4 has strength in the modeling of hydraulic resistances in the core region and in the treatment of a heat source term in the energy equations, but it faces convergence issues and a slow computing speed. It occurs because CFX-4 code uses a segregated solver to resolve the moderator circulation.

There are some studies also on the future designs of the CANDU. These studies focus on high temperature reactors with application in other areas such as hydrogen production.

Duffey et. al. [29] introduced the CANDU–Super Critical Water-cooled Reactor (SCWR) concept. In this design the coolant outlet temperatures are about 625ºC. IT achieves operating plant thermal efficiencies in excess of 40%, using a direct turbine cycle. In addition, the plant has the potential to produce large quantities of low cost heat. It has flexibility of range of plant sizes suitable for both small (400 MWe) and large (1200 MWe) electric grids and the ability for co-generation of electric power, process heat, and hydrogen.

In the interests of sustainability, hydrogen production by a CANDU-SCWR is discussed as part of the system requirements.

As mentioned in the beginning of this section, similarities of the moderator tank with heat exchangers can be utilized to use more extensive available studies. The main function of the moderator tank is cooling the pressure tubes which contain nuclear fuel. In other word, heat is transferred from hot pressurized heavy water to cool, low pressure water. It is essentially the same as heat exchanger’s function.

1.7 Heat Exchangers

A heat exchanger is a device built for efficient heat transfer from one medium to another.

The media may be separated by a solid wall, so that they never mix, or they may be in direct contact [30]. There are two primary classifications of heat exchangers according to their flow arrangement. In parallel-flow heat exchangers, the two fluids enter the exchanger at the same end, and travel in parallel to one another to the other side. In counter-flow heat exchangers the fluids enter the exchanger from opposite ends [31]. The counter current design is most efficient, in that it can transfer the most heat from the heat (transfer) medium.

There are many types of heat exchangers for different applications. These types include: shell and tube, plate heat, plate fin, and etc. the most relevant type to our moderator tank is the shell and tube type. It is the most common type of heat exchanger in oil refineries and other large chemical processes, and is suited for higher-pressure applications. As its name implies, this type of heat exchanger consists of a shell (a large pressure vessel) with a bundle of tubes inside it. One fluid runs through the tubes, and another fluid flows over the tubes (through the shell) to transfer heat between the two fluids. The set of tubes is called a tube bundle, and may be composed by several types of tubes: plain, longitudinally finned, etc. [30] and [32].

There can be many designs for shell and tube heat exchangers based on their application.

The tubes may be straight or bent in the shape of a U, called U-tubes. Large heat exchangers called steam generators are two-phase, shell-and-tube heat exchangers. They are used to boil water recycled from a surface condenser into steam to drive a turbine to produce power [31].

Most shell-and-tube heat exchangers are 1, 2, or 4 pass designs on the tube side. This refers to the number of times the fluid in the tubes passes through the fluid in the shell. In a single pass heat exchanger, the fluid goes in one end of each tube and out the other.

Due to the similarities between design and application of this type of heat exchangers with

CANDU reactor moderator core, studies on these heat exchangers can be related to moderator. In the following a brief overview of such studies are included.

Pekdemir et. al. [34] measured Shell side cross-flow velocity distributions and pressure drops within the tube bundle of a cylindrical shell and tube heat exchanger using a particle- tracking technique. In the context of modeling of the shell side flow, the experiments were designed to study variation in the cross-flow component of the shell side flow within the tube bundle. In addition, the results were used to test an empirical method of predicting overall cross-flow in tube bundles. They [35] later on measured pressure distributions within the tube bundle a shell-and-tube heat exchanger. Strategically placed tubes forming part of the bundle were fitted with pressure tapings and were used to measure axial distributions of cross-flow pressure drop. Comparison of the results with those obtained in the previous study revealed the effect of various tubes configuration on the shell-side flow distribution.

Wang et. al. [36] performed an experiment of the heat transfer of a shell and tube heat exchanger. For the purpose of heat transfer enhancement, the configuration of a shell-and-

15 tube heat exchanger was improved through the installation of sealers in the shell-side. The gaps between the baffle plates and shell was blocked by the sealers, which effectively decreased the short-circuit flow in the shell-side. The results of heat transfer experiments showed that the shell-side heat transfer coefficient of the improved heat exchanger increased by 18.2–25.5%, the overall coefficient of heat transfer increased by 15.6–19.7%. They concluded that the heat transfer performance of the improved heat exchanger is intensified, which is an obvious benefit to the optimizing of heat exchanger design for energy conservation.

Kapale and Chand [37] developed a theoretical model for shell-side pressure drop. Their study aimed to determine the overall pressure loss in the shell from the point of entry of the fluid to the outlet point of fluid. It incorporated the effect of pressure drop in inlet and outlet nozzles along with the losses in the segments created by baffles. The results of the model matched more closely with the experimental results available in the literature compared to analytical models developed by other researchers for different configurations of heat exchangers. Vera-Garcia et. al. [38] presented a simplified model for the study of shell-and- tubes heat exchangers. The model aimed to agree with the HXs when they are working as condensers or evaporators. Despite its simplicity, the model proved to be useful to the correct selection of shell-and-tubes HXs working at full and complex refrigeration systems.

The model was implemented and tested in the modeling of a general refrigeration cycle and the results were compared with data obtained from a specific test bench for the analysis of shell-and-tubes HXs. Ozden and Tari [39] numerically modeled a small heat exchanger. The shell side design of a shell-and-tube heat exchanger; in particular the baffle spacing, baffle cut and shell diameter dependencies of the heat transfer coefficient and the pressure drop

16 were investigated. The flow and temperature fields inside the shell were resolved using a commercial CFD package. A set of CFD simulations was performed for a single shell and single tube pass heat exchanger with a variable number of baffles and turbulent flow. For two baffle cut values, the effect of the baffle spacing to shell diameter ratio on the heat exchanger performance is investigated by varying flow rate.

1.8 Moderator Test Issues

The real time data recording at various locations inside the MTF tank have shown some level of fluctuations in the moderator experimental temperatures (see Figure 1-4). The observed frequency of the temperature fluctuations appear to be real and higher than the sampling rate of the fixed thermocouples. Fluctuations in moderator temperatures are believed to be due to the flow turbulence resulting from the interplay of local momentum and buoyancy forces, inlet nozzle jet impingements, and the flow passing through the tube bundle. The magnitude of the temperature fluctuations measured in the three-dimensional moderator test facility (3D-MTF) depends on the test conditions and on the location in the core.

Due to data sampling limitations in the experiments, the full spectrum of the fluctuations could not be identified. Also, analysis of the experimental data could not identify any dominant frequencies.

The purpose of the present study is to determine the causes for and the nature of the moderator temperature fluctuations using three-dimensional simulation of MTF and actual moderator tank. The results for two simulations will be compared to experimental data as well as previously performed two-dimensional simulation. The results will be used to

17 identify the limitations of two-dimensional simulation and the issues with scaling of the tank

(MTF versus actual tank). Suggestions also will be made to control and enhance the temperature fluctuations.

Figure 1-4 The experimental data taken at the CAANDU MTF

Two-dimensional simulations revealed that the main cause of the temperature fluctuations is the interaction of momentum and buoyancy driven flows inside the MTF tank. Buoyancy driven flows in enclosures have special featurees which include coherent structures, intermittent fluctuations, and anomalous scaling. There are two coherent structures, which are found to coexist in the convection cell. One is the large-scale circulation that spans the height of the domain, and the other is intermittent bursts of thermal plumes from various thermal boundary layers. An intriguing feature of turbulent convection is the emergence of a well-defined low-frequency oscillation in the temperature power spectrum.

The 2-dimensional isothermal modelling of the MTF tank revealed that the largest flow fluctuations occurred outside the tube bank where the inlet jets flow, and around the top of the tank where the two inlet jets impinge on each other. The high velocity gradients between the inlet jets and the initially stagnant surroundings generate small vortices with low fluctuation amplitude but high frequencies. As the vortices travels with the jets, their fluctuation amplitudes amplify but their frequency recede. The impingement of the two inlet jet results in a downward moving secondary jet which penetrated inside the tube bank. The simulation concluded that the the source of flow fluctuations in the isothermal case is outside of the tube bank, and the tubes dampen the fluctuations.

The thermal solution of the MTF model indicated that the buoyancy forces dominate at the inner core of the tank, whereas, the inlet jet induced inertial forces dominate the outer edges of the tank. The interaction between these two flows forms a complex and unstable flow structure within the tank.

The most important issue in two-dimensional simulation which should be addressed is that whether the 2-D model misses any major effects that may occur in the actual Calandria tank.

Therefore, the objective of the 3-D modelling is not only determining the thermo-fluid behaviour inside the actual MTF, but also to check the applicability of 2-D model results.

1.9 Objectives

The main objectives of the present investigation is to study the temperature and velocity fields inside the moderator tank, characterize the effects of inertia and buoyancy forces on the flow and temperature distribution inside the tank, determine the nature and causes of the temperature gradients in different zones inside the tank, determine the nature of the

19 temperature fluctuations in the moderator, and possibly give suggestions on how to modify the geometry and/or operating conditions to improve mixing and make the temperature distribution inside the calandria tank more uniform.

A three-dimensional simulation of the moderator tank is computationally expensive and time consuming. In order to enhance the size of the simulation, parallel processing is employed.

The simulations are performed on a 24-processor cluster using parallel version of FLUENT

12.

Simultaneous calculation of the local flow velocity and temperature are carried out using

Reynolds Average Navier-Stokes (RANS). The simultaneous velocity and temperature calculations fully characterize the spatial structure of the velocity and temperature oscillations and allow us to answer some important open questions that are related directly to the physical understanding of the convective turbulent flows. Detailed numerical methods employed in the simulations are not mentioned here and can be found at Fluent help [41].

The simulations are conducted for both scaled down version of the calandria tank (MTF) for which experimental data are available, and for a real full size actual mderator.

2 Numerical Setup

2.1 MTF and Actual Tanks Geometry

The MTF tank is a ¼ scale of actual Calandria tank. As their main dimensions are shown in

Table 2-1 and Table 2-2, the MTF tank comprises a 2115 mm diameter cylindrical tank with

1486 mm length, eight inlet nozzles (four at each side tank), two 152 mm diameter pipes as outlets at the bottom of tank, and 48033 mm diameter tubes.

The MTF and the aactual tanks and their inlet nozzles (with flow splitters) are shown from various views in Figure 2-1 and Figure 2-2. The dimensions and arrangements of the elements are shows in Figure 2-3.

Scale SHELL AND CORE DIMENSIONS MTF Bruce B Bruce/MTF

Inside diameter of the Calandria main shell: DC 2.115 m 8.458 m 4

Length of Calandria main shell: L 1.486 m 5.94 m 4 C

Table 2-1 MTF and actual tank Shelll and Core Dimensions

Table 2-2 MTF and actual tank Tubes Array Dimensions

Front-View Side-View

Top-View Isometric-View

Figure 2-1 The CAD data views of MTF tank and its Inlet Nozzles

Top-View Isometric-View Figure 2-2 The CAD data views of Inlet Nozzle

Figure 2-3 The schematic drawingn of the MTF tank (all dimensions are in mm)

2.2 Operating Conditions

During the normal operation of CANDU reactor, the cold moderator water enters the tank through eight nozzles, four nozzles at each side, as shown in Figure 2-1, and heated fluid exits from two outlet pipes at the bottom of the tank. Throughout the operation, two major flow characteristics are identified inside the tank: Buoyancy driven fluid flows formed by the internal heating, and momentum driven fluid flows by the jet flows through the inlet nozzles, respectively. The flow behaviour depends on the operating conditions, such as, moderator mass flow rate and its temperature, and the rate of heat influx to the moderator. In addition, the method of adding heat to the moderator, i.e., volumetric (in the actual moderator) or using heated channels (in MTF), can also have an effect on the flow and temperature patterns inside the tank.

The operating conditions for the MTF and the actual moderator used in the simulations are listed in Table 2-3.

Bruce B, NOMINAL CONDITIONS MTF 50% FP Power (kW) 1,090 64,500

Average heat source 14.74 kW/m2 277 kW/m3

Moderator mass flow rate (kg/s) 22.9 948.0

Number of nozzles 8 8

Number of outlets 2 2

Inlet Temperature (ºC) 40.1 44.8

Outlet Temperature (ºC) 51.5 61.0

Temperature difference (ºC): T 11.4 16.2

Table 2-3 MTF and the actual tank operating conditions used here

2.3 Heating Methods

In the actual Calandria vessel of a CANDU reactor, the cold fluid is heated by direct heating of neutrons, decay heat from fission products, and/or gamma rays in the vessel. However, in many of the test models, electrically heated rods are used to replace the nuclear heating process, as a result, two different methods of heat transfer inside the tank can be considered.

 Surface heat transfer: In this method, similar to the experiments, heat source is at the

surface of the tubes (this method is used to simulate MTF).

 Volumetric heat transfer: In this method, heat source is throughout the whole fluid

inside the tank (this method is used to simulate both MTF and the actual moderator

tank).

In numerical simulation, the first method is modeled through heat influx at the boundaries of the tubes inside the calandria. Since the heat flux inside the actual tank is dependent on the coordinate along the length of the tank, the heat influx in numerical model is divided into 24 zones along the tank length (each of 12 zones along the tank length is divided to inner and outer sub zones) and every zone has a different influx of heat at its boundary. Figure 2-4 shows the heat influx for each zone along the tank length for MTF simulation.

The second method is represented through heat sources inside the tank. Similar to the previous case, the tank volume is divided into 6 zones and each zone has its own volumetric heat source. In this case although the total heat generation inside the tank is the same as surface heating, but the method of heat generation distribution is different. Here we explain the calculation method for MTF volumetric heating case.

Figure 2-4 MTF heat generation map - surface heating

Volumetric heat flux for volumetric case is calculated based on heat generation in surface

heating method. Surface heating generates 14,740 of heat in average throughout its tubes surface. The total tube surface is:

. . . m2 (Eq 2-1)

where AT is the total tubes surface inside the tank.

Total heat generation inside the tank is:

, . . (Eq 2-2)

where QT is the total heat generation for surface heating case. As mentioned previously it will be used for volumetric heating calculation. We need to calculate tank volume and net fluid volume inside the tank:

. . . (Eq 2-3)

. . . (Eq 2-4)

. . . (Eq 2-5)

Where VTA is total tank volume, VT is total tubes volume and VNT is the net fluid volume inside the tank. for the purpose of numerical simulation and to have various heat generation along the tank length, the tank domain is divided to 6 zones and each zone has its own volumetric heat generation. Zone 1 is explained in the followings and the rest of the zones will be calculated similarly.

Zone 1:

≡ 22164

≡ 19571

. . (Eq 2-6)

≡ . . (Eq 2-7)

≡ . . (Eq 2-8)

. . (Eq 2-9)

. . (Eq 2-10)

.. ≡ . . (Eq 2-11)

This is the quantity which will be used in numerical simulation.

2.4 Mesh Construction

An unstructured non-uniform tetrahedral mesh was used to construct meshes in the MTF and the actual tanks. A total of 3,200,000 meshes were generated using the commercial software

Gambit. The mesh size was limited by the capacity of the parallel computing memory although accurate measures (i.e. mesh adaption and gradient) have been employed to make sure that the accuracy of the simulations are not compromised by the mesh resolution. The generated meshes are shown in Figure 2-5 to Figure 2-9.

Figure 2-5 Mesh Generation - XY plane

Figure 2-6 XY plane - mesh around tubes

Figure 2-7 XY plane - mesh near the wall

Figuure 2-8 Inlet pipes

Figure 2-9 Water ooutlet

The solution domain is divided into 20 partitions for parallel processing. Minimum number of cells in each partition is 150,000 and the maximum is 160,000 with Cartesian partitioning method. Maximum and minimum number of cells in partitioning is crucial since less variation in number of cells will increase computation efficiency.

2.5 Computational Code

The fluid is assumed to be incompressible and single-phase. The flow is considered to be time dependent and turbulent. The RNG k-ε turbulence model with non-equilibrium wall treatment is chosen for turbulence modeling. Since the flow is strongly anisotropic, especially in the near wall zones, the RNG k-ε turbulence modeling for this typical geometry covers both, anisotropic turbulence and secondary flows. The surface heat flux is applied to the tube walls and the inner wall surface of the tank is considered as an adiabatic boundary condition. The buoyancy effects are accounted for the density changes using the Boussinesq approximation.

Fluent solves the governing integral equations for the conservation of mass, momentum, energy, and turbulence. The Pressure Implicit with Splitting of Operators (PISO) pressure- velocity coupling scheme is used to approximate the relation between the corrections of pressure and velocity. The second-order upwind scheme is employed for the momentum, turbulence, and energy equations. This approach produced a higher order of accuracy.

In each time step, the inner iteration is progressed until the normalized residuals in the numerical solution of governing equations reach less than 10-4. The physical properties of water are used in MTF simulations. The time step in all transient simulations is equal to 0.01 sec.

2.6 Solution Strategy

Any transient solution of numerical modelling needs an approaching strategy. This strategy can be set up based on the limitations of the numerical models or the physics of the real

32 operating conditions (e.g. the time dependent operating and boundary conditions). All these approaches may affect the calculation convergences, simulation results, and the numerical computational times. Two different methods can be employed in this case:

 The Steady-Transient Solution Strategy: In this approach, three steps are taken. First,

we start with the steady state solution of the flow equations to form an initial flow

structure. Then, the steady state solution of the flow and the energy equations are

solved to form an initial flow and temperature structure. Finally, we switch to the

transient solution of the energy and flow equation solvers. This approach is

considerably faster in comparison with the next approach.

 The Transient Solution Strategy: In this approach, the transient energy and flow

equations are solved right from the start. This approach is time consuming and takes

significantly longer time to finish.

Based on our initial assessment and considering the fact that due to the turbulent nature of the problem and existence of the fluctuations, it will be faster and more stable to employ the first method as our preferred method of solution.

The following Steps are taken for each of the MTF and actual tank simulations:

 MTF

o Parallel, three-dimensional simulation of isothermal-steady state conditions,

o Parallel, three-dimensional simulation of steady state conditions with heat

transfer,

o Parallel, three-dimensional simulation of transient conditions with heat

transfer. (two different methods of heat transfer is considered; The methods

are explained in the following section).

 Actual tank

o Parallel, three-dimensional simulation of isothermal-steady state conditions,

o Parallel, three-dimensional simulation of steady state conditions with heat

transfer,

o Parallel, three-dimensional simulation of transient conditions with heat

transfer (only one method of heat transfer which is volumetric heating is

considered).

 Actual tank – long range run

o This includes near 1000 physical seconds of run to see if any significant

effect is missed in the short range simulations. This also will help to optimize

the minimum time chosen for short range simulations.

During the transient simulation, 55 points of interest inside the tank are monitored closely for their temperature and velocity fluctuations with time. The data extracted from these points are used along with other results to explain the flow processes that occur inside the tank. In the coming sections, results for different simulations, their comparisons, and in depth analysis will be presented. The main difference between simulations is their method of heat generation inside the tank. The following section comprehensively explains different methods and their difference.

2.7 Planes - Points

Total of 16 planes and 55 points with different orientations and coordinates are considered for monitoring and result analysis. Figures 6-8 shows the corresponding planes. There are seven planes in the X-Y, three in the X-Z and three in Y-Z planes. The exact location of each plane and their names are shown in Table 2-4, Figure 2-10, Figure 2-11 and Figure

2-12 (the following coordinates corresponds to MTF geometry and for the actual tank, the numbers are multiplied by 4 to get the equivalent coordinates).

Plane Name Location Plane Name Location

A1 Z = 0.6875 C2 Z = -0.1875

B1 Z = 0.375 B2 Z = -0.375

C1 Z = 0.1875 A2 Z = -0.6875

S Z = 0.0 D1 Y = 0.503246

Sy Y = 0.0 Sx X = -0.177461

D2 Y = -0.503246 E2 X = -0.638858

E1 X = 0.505763

Table 2-4 Planes Coordinates

Figuure 2-10 XY-Planes

Figuure 2-11 XZ-PPlanes

Figuure 2-12 YZ-PPlanes

There are 3 more planes which are shown in Figure 2-13 and Figure 2-14. The first two are called nozzle planes and they pass through the nozzles at the injection plane. The last one is called outlet pipe plane and it passes vertically through outlet pipes.

Figure 2-13 Nozzle planes

Figure 2-14 Outlet pipe plane

Chosen points are monitored throughout the domain for their temperatuure and velocity fluctuations with time. The point coordinates are chosen (based on preliminary steady simulations) in the regions with high temperature, cold and hot interaction zones, and jet penetration path as well as deep inside the tank. The temperatuure and velocity fluctuations for these points will be presented in results section. The exact coordinates of the points are shown in Table 2-5 (the following coordinates corresponds to MTF geometry and for the actual tank the numbers are multiplied by 4 to get the equivalennt locations).

Points X Y Z

1 0 0 -0.75

2 0 0 -0.60

3 0 0 -0.45

4 0 0 -0.30

5 0 0 -0.15

6 0 0 0.00

7 0 0 +0.15

8 0 0 +0.30

9 0 0 +0.45

10 0 0 +0.60

11 0 0 +0.75

12 0 +0.5712 -0.75

13 0 +0.5712 -0.60

14 0 +0.5712 -0.45

15 0 +0.5712 -0.30

16 0 +0.5712 -0.15

17 0 +0.5712 0.00

18 0 +0.5712 +0.15

19 0 +0.5712 +0.30

20 0 +0.5712 +0.45

21 0 +0.5712 +0.60

22 0 +0.5712 +0.75

23 0 +0.713993 -0.75

24 0 +0.713993 -0.60

25 0 +0.713993 -0.45

26 0 +0.713993 -0.30

27 0 +0.713993 -0.15

28 0 +0.713993 0.00

29 0 +0.713993 +0.15

30 0 +0.713993 +0.30

31 0 +0.713993 +0.45

32 0 +0.713993 +0.60

33 0 +0.713993 +0.75

34 -0.357876 +0.713993 -0.75

35 -0.357876 +0.713993 -0.60

36 -0.357876 +0.713993 -0.45

37 -0.357876 +0.713993 -0.30

38 -0.357876 +0.713993 -0.15

39 -0.357876 +0.713993 0.00

40 -0.357876 +0.713993 +0.15

41 -0.357876 +0.713993 +0.30

42 -0.357876 +0.713993 +0.45

43 -0.357876 +0.713993 +0.60

44 -0.357876 +0.713993 +0.75

45 -0.624268 +0.682956 -0.75

46 -0.624268 +0.682956 -0.60

47 -0.624268 +0.682956 -0.45

48 -0.624268 +0.682956 -0.30

49 -0.624268 +0.682956 -0.15

50 -0.624268 +0.682956 0.00

51 -0.624268 +0.682956 +0.15

52 -0.624268 +0.682956 +0.30

53 -0.624268 +0.682956 +0.45

54 -0.624268 +0.682956 +0.60

55 -0.624268 +0.682956 +0.75

Table 2-5 Monitored points coordinates

2.8 Parallel Processing – Physical Run Time

Transient, three-dimensional simulations of MTF and the actual tank are performed for 150 physical seconds. As mentioned before, the simulation is run on a 24-processor cluster and related information for MTF with surface heating is shown in Table 2-6. These are typical numbers and similar quantities can be considered for other simulations as well.

AVERAGE WALL-CLOCK TIME PER 7.827 Sec

TOTAL WALL-CLOCK 346 hrs. 24 min 18 sec

TOTAL CPU TIME 6922 hrs. 56 min 15 sec

Table 2-6 Parallel processing time

The experiments have been performed for much longer times (several order of magnitude larger), but using the same period of simulation is impossible since it will require very long simulation time as well as considerable amount of processing power and data storage facility. As a result a more practical approach is chosen here. OOne simulation is performed for about 1000 physical seconds to find the proper time period which can be used as our time frame for all simulations. The results for long run revealed that 150 physical seconds is the minimum time period which is proper for investigation. Typical results for long run are shown in Figure 2-15 and Figure 2-16 and the rest oof the results are in the appendix section for reference purposes. The figures show that although some very low frequency fluctuation cannot be captured in 150 seconds, but their frequencies none the less are detected and accounted for in FFT analysis. The long range run also shows that these low frequency fluctuations are not a concern since their amplitude relative to high frequency fluctuations is small and they cannot cause sudden and unpredicted changes in tank temperature.

Figure 2-15 Temperature fluctuation - long range run for point 4

Figure 2-16 Velocity fluctuation - lonng range run for point 4

3 Moderator Test Facility Simulation

Moderator used in moderator test facility is simulated using surface heating method as explained in previous chapters. In this section the result for the simulation is presented and analyzed using temperature and velocity distributions throughout the tank.

3.1 Temperature and Velocity Distributions

Experimental results on MTF have revealed existence of temperature fluctuations inside the tank. This may occur in the regions where hot and cold flows interact. Fluctuations may also occur on regions with high fluid velocities where the flow is more prone to turbulence effects, causing velocity fluctuations, and consequently, temperaature fluctuations. Figure 3-1 shows temperature contours for plane S, which is in the middle of the tank in the XY plane at two different times:

t= 20 s t= 150 s

Figure 3-1 Temperature contours at two different times for plane S

The lowest temperature in this plane is 40 oC, which is the inlet water temperature and the highest temperature is 63 oC. The highest temperatures are at the top inner zone of the tank and remain in the same zone as time proceeds. As we move from the inner to the outer zones of the tank, temperature decreases due to the cold inlet jets flow near the outer wall. The most intense fluctuations in temperature can be expected in the regions where the low velocity hot fluid in the inner parts of the tank, referred to as the inner flow, mixes with the cold high velocity flow on the outer regions, referred to as outer jet flow.

The hot region is shifted toward the left inlet resulting in asymmetric flow in the tank in this plane. This asymmetry arises due to the competition between momentum and buoyancy forces inside the tank. The detailed interaction of these forces and their effects on the temperature distribution will be discussed later on this chapter. Figure 3-1 not only shows that asymmetric flow in this plane but also an unsteady flow. In fact an unsteady flow is observed throughout the whole tank and it is a particular nature of this moderator.

Figure 3-2 shows the velocity contours for the same plane and the same times as in Figure

3-1. The high velocity inlet fluid takes the path of least resistance and flows close to the walls of the tank and outside the tube bundles. Inlet nozzles are designed to guide the fluid toward the top of the tank. Therefore, the right and the left cold inlet fluids meet each other somewhere close to the top of the tank. The flow generated by the impingement of these fluids turns downward the core of the tube bundle opposing the upward moving buoyancy flows. The bulk fluid velocity is almost 0.1 m/s, whereas the velocities close to the inlet nozzle are around 1 m/s.

Figure 3-2 shows that similar to temperature distribution, the velocity distribution is also unsteady. This is evident when comparing flow contours at two different times close to the inlet nozzles.

t= 20 s t= 150 s

Figure 3-2 Velocity contours at two diifferent times for plane S

Several other planes are presented in Figure 3-3 to Figure 3-6. These include plane along the height, SX and the length, D1 of the tank. Asymmetric nature of the temperature and velocity distribution is observed in all planes. In adddition, segregation between hot and cold regions where temperature and velocity gradients are large is visible.

Figure 3-3 shows temperature contours in plane B2 which passes through inlet nozzles. As expected the coldest regions shown in the figure are near injectiion nozzles. The temperature is close to 40 oC (same as the inlet temperature). The temperature increases to more than 50

46 oC as we proceed to the inner core. Although the general location of the hot zone is the same as plane S (top section of the tank), but it is moved toward one side of the tank.

t= 20 s t= 150 s

Figure 3-3 Temperature contours at two different times for plane B2

Figure 3-4 shows the velocity contours for the same plane as Figure 3-3. The velocity in the bulk of the tank is under 0.4 m/s. the flow velocity is the highest close to the inlet nozzles.

The flow velocities are relatively large close to thee outlet pipe as well as in the path of the impinging jets which penetrates into the core. In these regions the velocities can be as high as 1 m/s. The impingement zone for the inlet jets is clearly visible on the top right-hand side of the tank and this side remains cooler than the left side of the tank.

t= 20 s t= 150 s

Figure 3-4 Velocity contours at two diffferent times for plane B2

Figure 3-5 shows the temperature contours in a plane along the length of the tank, plane D1.

It clearly shows that the hot zone is not extended throughout the whole length of the tank and it is more toward the left side. The high velocities for plane D1 are in the range of 1 m/s or less similar to the previous planes. The result shoows almost uniform velocities in the main portion of the tank, specifically in the middle far from the walls. Large velocity gradients are observed at the front (left) and back (right) sides of the tank near the walls. The large velocities in these zones keep the fluid cooler than the other zones. The large velocity gradients near the walls result in a relatively large mixing between the hot and cold fluids.

Figure 3-6 shows the temperature contours for a plane along the height of the tank, plane

SX. This particular plane passes through the tubes and shows the temperature variation around them. Based on the input conditions, the tubes in the middle have higher heat fluxes compared to the lower or upper tubes. Temperaturees are as high as 63 oC in some regions

48 near the tubes. The velocities close to the tube walls are low and below 1 m/s except for those close to the water outlet. Low velocities result in lower mixing and higher temperatures as shown in Figure 3-6.

t= 20 s t= 150 s Figure 3-5 Temperature contours at two different times for plane D1

t= 20 s t= 150 s

Figure 3-6 Temperature contours at two different times for plane SX

3.2 Temperature and Velocity Fluctuationns

This section presents results for several points inside the tank which are monitored for their temperature and velocity variation with time. Figure 3-7 shows the temperature and velocity fluctuations for point 3, which is located on the tank centerlinee close to the end of the tank.

Since this point is not in the high temperature zone, the highest temperature observed is 59.9 oC at t=78 s. The temperature variation is as high as 6 oC. The frequency of the fluctuations can be categorized as low frequency with high amplitude. The velocity fluctuations are within 0.03 m/s to 0.06 m/s.

Figure 3-7 Point 3 temperature and velocity fluctuations with time

Figure 3-8 shows the fluctuations for point 12. Although this point is located at thhe top portion of the tank near the end wall, but it is not affected by high temperature zone characteristics since it is at the end of the tank, far from high temperature zone. The fluctuations start with high amplitude, but it quickly damps too a low amplitude fluctuation

50 around 53 oC. This point is far from the jet penetration path, where the large temperature fluctuations are located. It starts with high temperaatture but as time proceeds, mixing forces the temperature to decrease significantly and stay at that level. The velocities show a sudden decrease at early times which can be associated with the initial flow development phase.

After t=20 s, the velocity seems relatively stable buut having higher mean temperature than the previous point. This is due to its location being at generally high velocity zone.

Figure 3-8 Point 12 temperature and velocity fluctuations with time

Figure 3-9 shows the temperature and velocity fluctuations for point 20, located in the hot region. Temperatures fluctuate close to 60 oC. Velocity plots show sudden increases and decreases every 20 to 30 seconds. Although this point is located in the inner zone of the tank, but these sudden changes indicate that the outer high velocity flow penetrates into the low velocity bulk flow and periodically reaches to point 20 causing sudden changes.

Figure 3-10 shows the fluctuations for point 50, located at the top left-hand side of the tank and exactly at the center of it. Two different patterns of fluctuations are observed. The first one is the high frequency which exists throughout the whole simulation time. The second one is a much lower frequency which completes every 120 seconds or so. The high frequency fluctuations are due to the location of the point being close to the jet penetration zone, as well as being at the interface of the cold and the hot water. The temperature at this point does not go higher than 56 oC since it is in contact with low temperature inlet water.

The low frequency is the result of larger flow patterns inside the tank. These flow patterns are partially caused by the mixing of hot and cold water and partially by the fluid flow between inlet nozzles and outlet pipe.

Figure 3-9 Point 20 temperature and velocity fluctuations with time

Figure 3-10 Point 50 temperature and velocity fluctuattions with time

The simulations are performed based on the experiments conducted in the laboratories of

Atomic energy of Canada Limited. Here the simulation results are compared to those of experiments. Figure 3-11 shows a qualitative comparison between simulation result and experimental measurements in symmetry plane. Three distinctive zones are determined in the experimental results: Hot, Medium, and cold zones. Similar zones can be identified in simulation result at almost the same coordinates. The temperature in different point has less than 10% variation with respect to the experimental results. This is considered accurate if we account for the errors from experimental results as well as numerical simulation errors and also the chaotic and unpredictable nature of the flow inside the tank.

Figure 3-11 Comparison between simulation and experiment

3.3 Asymmetry

3.3.1 Main Flow Regimes

Simulations show an asymmetry in temperature distribution in aall three directions inside the tank. Figure 3-12 shows three planes in Z direction and one plane in Y direction. These planes essentially cover the entire tank and it clearly shows the asymmetry in every direction.

Generally, high temperature areas are concentrated close to the symmetry plane (z=0) and the upper parts of the tank. It also should be noted that, current distribution is not desirable since it will reduce the cooling efficiency. The ideal condition is than when the cold water is injected at the top of the tank; the flow passes through a large number of tubes and exits the tank with high temperature. But what occurs in reality is that the hot zone lies at the top and flow which passes through the tubes does not pass through maximum number of them.

These two factors greatly reduce the cooling effects inside the tank. If we can find the reason

54 behind the asymmetry, we can suggest a solution which will make the distribution close to symmetry at all directions.

Figi ure 3-12 Temperature distribution on 4 planes on Z and Y directions

In order to reveal the causes behind the asymmetry, it is necessary to analyze the flow regimes inside the tank. Figure 3-13 shows velocity vectors (which are shown with constant length and coloured by their velocity magnitude) for three different planes parallel to the XY plane. These planes include the symmetry plane in the middle and two inlet planes. The first inlet plane contains two nozzles and the second inlet plane contains two nozzles and an outlet pipe.

The flow pattern in the inlet planes show that the injected fluid from the left and the right nozzles goes through the outer edges of the tank at a high velocity. These two flows impinge on each other at some point close to the top of the tank. This impingement forms a secondary downward moving flow which passes through the tube bundle (mostly on the right hand side of the tank) and exits through the outlet pipe. This pattern is the strongest in the plane with inlet and outlet and weakens in the plane with only-inlet nozzle and in the symmetry plane (z=0). On the plane having only-inlet nozzle, although there is strong trace of the above pattern, but upward flow is also strong and it dominates the left hand side of the tank. A substantially clock-wise flow circulating the outer edges of the tank is noticeable in this plane. This substantially clock-wise flow is the strongest on the symmetry plane. This flow has certain effects which will be explained in the remainder of this chapter.

Three different flow regimes can be identified inside the tank. These flows are:

 Inlet jet impingement flows: these are the flows generated due to the inlet nozzle

flows which go through the upper edge of the tank, impinge on each other, and form

downward moving flows, which goes through the tube bundle (Figure 3-14).

 Buoyancyc -driven flows: there is a strong flow at the left hand side which passes

through the tubes but toward the top of the taank. This is against the bulk flow regime

(from inlet to the outlet) and as will be explained later is mainly due to the strong

buoyancy forces inside the tank (Figure 3-15).

 Clock-wise flow: this flow regime is the strongest in symmetry plane and it occupies

almost ¾ of the outer edge periphery. It consists of two sub-flows. The firsst one

comes from the right nozzle which goes through the bottom of tthe tank and the

second sub-flow runs from the left nozzle to the top of the tank.

As explained in the previous chapters, the impingement poinnt is yielded toward the right nozzle and the hot zone is pushed to the left. It results in a highly asymmeetrical flow inside the tank. The reason behind the asymmetry and how it occurs and what the consequences are, will be explained in the coming lines.

Injection plane -1

Injection plane -2

Figure 3-13 Velocity vectors (colour by velocity magnitude) in two nozzle planes and symmetry plane

Figure 3-14 Impingement point.

Figure 3-15 Effect of buooyancy force

3.3.2 Inlet Jets and Secondary Jet

Close investigation of inlet jets and the secondary jet reveals valuable information which can help us in explaining the phenomenon in the tank. Figure 3-16 and Figure 3-17 show the path used for monitoring the inlet jets and the secondary jet. The results for inlet jets are presented with respect to the angular position of the presented points. The angular position is measured against the positive X direction and it increases counter clock-wise as shown in

Figure 3-16. The results for the secondary jet aree presented from the impingement point along the secondary jet path as shown in Figure 3-17.

Figure 3-16 Inlet jeets path. The marked points are used to record data on temperature and velocity.

Figure 3-17 Secondary jet path. The marked points are used to record velocity and temperature data

Figure 3-18 and Figure 3-19 show temperature and velocity along the inlet jets. The impingement point is indicated with a red line in the middle and the points on the right side attribute to the right nozzle and vice versa. The temperature plot shows that temperature increases from the inlet toward the impingement point. This is expected since as flow passes through the tubes and interacts with hot water inside the tank, its temperature increases more than 15 oC for the left jet and less than 10 oC for the right jet. The average temperature is also higher for the left jet compared with the right jet. This is due to two main factors:

 The impingement point is on the right side of the tank and the left jet travels a large

distance to the impingement point. Therefore, it heats up more.

 The hot zone is pushed to the left and therefore, the left jet passes through a hot

boundary, which will cause an increase in its temperature comparing to the right jet.

The velocity plot shows that the inlet jets lose their momentum as much as 90% once they reach to the impingement point. The velocity decreases from more than 1 m/s at the nozzle inlet to less than 0.5 m/s at the impingement point. It is not desirable since very low impingement velocity will produce low-momentum secondary jet that cannot penetrate the tank efficiently and will affect cooling efficiency of the tubes inside the tank.

) C o ( erature erature p Tem

Tetha (Deegree)

Figuure 3-18 Temperature along the inlet jets penetration path. The x coordinate is anngular position with respect to positive X direction Velocity (m/s)

Tetha (Degree)

Figi ure 3-19 Velocity along the inlet jets penetration path. The x coordinate is angular position with respect to positive X direction

Figure 3-20 and Figure 3-21 shows the temperature and velocity for the secondary jet.

Temperature variation shows an oscillatory nature. The penetration path for the secondary jet lies at the boundary of cold and hot zones and as a result their mixing will affect the temperature on the penetration path, forcing it to show an oscillatory behaviour. As the flow passes through more tubes inside the tank, we expect the temperature to increase as shown in the plot. The variation between the highest and the lowest temperature on the secondary jet penetration path is close to 12 oC. This large variation in a short distance is a driving force behind buoyancy force inside the tank. Its presence changes the temperature distribution inside the tank while competing with the momentum force.

The velocity of the secondary jet also decreases by distance from the impingement point. It is expected since the secondary jet has to penetrate into the bulk flow inside the tank which has very low velocity. The secondary jet only carries 10% of the initial momentum injected by the inlet nozzles. This amount reduces further significantly. Half way through its path, the secondary jet has lost 80% of its already small initial momentum. It is a problem since it greatly reduces the mixing inside the tank and by the time the flow is near the exit, the inertia is not the driving force anymore and flow becomes buoyancy driven.

Initial increase C) o

Clock-wise cooling effect Temperature ( Temperature

Close to Hot boundary inlet jet warming effect

Distance from Impingement (m)

Figure 3-20 Temperature alongn the secondary jet penetration path. The x coordinate is position along the penetration path with respect tto impingement point Velocity (m/s)

Distance from Impingement (m) Figure 3-21 Velocity along the secondary jeet penetrationn path. The x coordinate is position along the penetration path with respect too impingement point

This effect is also shown in detail in Figure 3-15. Temperature increases and velocity decreases as the secondary jet goes toward the outlet pipes. Near the outlet the flow stream

64 has very low velocity and high temperature. Most of The hot flow which has lost most of its momentum turns around (creating circulation zone at the bottom)) and moves toward the top of the tank at the left hand side instead of going to the outlet pipes.

3.3.3 Momentum versus Buoyancy

In order to analyze the main reason behind the asymmetrical distribution inside the tank, first a symmetrical distribution is considered in Figgure 3-22. In these conditions moderate buoyancy is competing with momentum forces due to inlet jets penetration. Two inlet jets impinge on each other exactly at the center line. A secondary jet forms and penetrates into the tank. The buoyancy force creates two hot tempeerature circulating zone at the bottom of the tank. These circulations prevent the secondary jet to go directly toward the outlet pipe.

This is called moderate buoyancy since it has not enough strength to dominate the flow inside the tank.

Figure 3-22 Moderate buoyancy

The second scenario is to have stronger buoyancy force inside the tank. It can occur due to higher heat flux or higher temperature gradient inside the tank. In these conditions, the circulations due to buoyancy force expand to the top of the tank. They occupy most of the inner core and prevent the secondary jet from penetrating into the tank. The secondary jet finds its way to the exit pipe by going around the circulation zone through the outer surface of the tank as shown in Figure 3-23.

Figure 3-23 Strong buoyancy

In the third situation, strong buoyancy exists inside the tank but due to turbulence and external disturbances which affects the flow inside the tank, the flow distribution transforms from symmetrical to asymmetrical. The buoyancy circulation occupies one side of the tank and the momentum driven secondary jet occupies thhe other side. This is what occurs inside the moderator reactor. It is a mix of strong buoyancy and momentum force which have been distributed asymmetrically due to various disturbances in the flow.

Figure 3-24 Asymmetrical flow.

3.3.4 Asymmetry Effects

When the asymmetrical distribution develops inside the tank, it generates other flows which their existence contributes to more asymmetry inside the tank. One of the most important flows is called “3D effect” flow. To fully understand it, we have to look into to new planes inside the tank. These are called nozzle planes and there is one at the right and one at the left, which we are looking at them from top position.

Figure 3-25 Left and right nozzle planes. These planes are used to sstudy the effect of jet on jet impingement

Figure 3-26 and Figure 3-27 shows velocity vectors and stream lines for nozzle plane at the left hand side. The vectors and streamlines at these figures as well as Figure 3-28 and Figure

3-29 are specially sketched. The planes are in YZ plane, but the velocity components are borrowed from another plane. The Y-component present X-velocity and Z-component presents Z-velocity. In this way the vectors which are toward positive Y, are rotating clock- wise in left plane and counter clock-wise on the right plane.

There are four nozzles on each plane (left plane and right plane) which are symmetrical with respect to symmetry plane (z=0). The inlet flows from nozzles 2 and 3 impinges on each other on symmetry plane. They form a secondary jet which rotates clock-wise on the symmetry plane. The same phenomenon occurs between nozzles 1 and 2 and nozzles 3 and

4. This is visible on both vector and stream line presentations. In the case of right nozzle plane, vectors in negative Y direction are rotating clock-wise in symmetry plane. Here flows from nozzles 2 and 3 impinge on the symmetry and again form a secondary jet which rotate clock-wise on the symmetry plane. Similar to the left plane, the same phenomena happen between nozzles 1 and 2 and nozzles 2 and 3. The reason for being clock-wise flow is the downward push from the secondary jet which is formed at the right hand side of the tank.

Symmetry Plane

1 2 3 4 Zoom Area

Zoom Area

Figi ure 3-26 Left nozzle plane. Y axis velocity represents x-velocity and Z axis velocity represents z- velocity

Symmmetry Plane

Figi ure 3-27 Left nozzle plane. Y axis velocity represents x-velocity and Z axis velocity represents z- velocity

Symmettry Plane

Zoom Area 1 2 3 4

Zoom Area

Figure 3-28 Righht nozzle plane. Y axis velocity representts x-velocity and Z axis velocity represents z- velocity

Symmeetry Plane

Figure 3-29Righht nozzle plane. Y axis velocity represents x-velocity and Z axis velocity represents z- velocity

The sum of these clock-wise flows on the left and right creates an overall strong clock-wise flow inside the tank on three planes: symmetry plane, symmetry plane between 1 and 2, and symmetry plane between 3 and 4. These clock-wise rotations are transferred to the other parallel plane by means of flows in YZ direction. Flows in YZ direction are shown in Figure

3-30. As observed, there are two large scale rotations with respect to symmetry plane which will transfer anything on the symmetry plane to the other parallel planes.

The large scale clock-wise flow results in weaker innlet jet on the right hand side and stronger inlet jet on the left hand side. This in turn, will intensify movement of the impingement point to right side and contributes to the asymmetry inside the tank. This effect is called “3D effect” because it cannot be captured in two dimensional simulations. Although this

72 phenomenon does not initiate the asymmetry but since it contributes to it, should be accounted for in our analysis.

Figure 3-30 Center plane in Z direction. this shows the transfer of symmetry plane effects to the other planes along the Z-direction

4 Methods of Heating: Surface Heating and Volumetric Heating

Moderator test facility simulation is carried out using two methods of heating which are explained in previous sections: MTF with surface heating, and MTF with volumetric heating. The volumetric heating occurs in actual reactor whereas surface heating is the method employed in test facility due to practical reasons. It is beneficial to compare the results of these simulations to fully understand the effect of different heating method on temperature and velocity distributions as well as fluctuations inside the tank.

From 55 points which are monitored in each of the simulations, three points have been chosen (17, 39, and 50), along with the temperature and velocity contours in the several planes, to show difference between heating methods and the effects they will have on final results. Locations of These three points are shown in Figure 4-1. They are located inside the hot zone, near the interaction between hot and cold, low velocity and high velocity flows.

First, temperature fluctuations with time for three points are compared with each other

(Figure 4-2). The first plot corresponds to point 17 which is located deeper inside the tank comparing to other points. The general trend shows that the volumetric actual tank simulation has the highest temperature. This is expected since the actual tank has higher influx of heat comparing to MTF simulations (surface heating and volumetric heating).

MTF surface heating has a lower temperature than MTF volumetric heating. Volumetric heating results in a better heat distribution throughout the tank. This results in a better mixing of hot and cold flows which in turn results in lower overall temperature. The other advantage of the volumetric heating over surface heating is lower fluctuation amplitudes.

Point 50 Point 39 Point 17

Figure 4-1 Location of compared points

Point 39 is closer to the outer wall and lies just besside the jet penetration path. Comparing surface heating model with volumetric model reveals that the temperature shows chaotic behaviour at this point due to its approximate distance to the mixing zone. This effect shows itself fully in the surface heating simulation while it is dampened in the case of volumetric heating due to better mixing and less temperature gradient inside the tank. Point 50 is the closest to the outer wall and it is at the heart of jet penetration path. As observed in the figure, the fluctuations are more intense and with higher frequuency. MTF surface heating and MTF volumetric heating are very close to each other and they almost follow the same pattern. The main driving force for the mixing in this zone is the flow momentum rather than

76 buoyancy effects inside the flow. As a result different methods of heating have minimum effect on the temperature fluctuation. The flow has high velocity in this region and all the mixing occurring here is due to the incoming fluid from injection nozzles. The other interesting point is the comparison between average temperatures in each point. The average temperature in the case of MTF surface heating is visibly higher than MTF volumetric heating (although in some occasions it drops below surface volumetric heating). It shows that in critical zones where interaction between hot and cold zones occurs, heat is better distributed in the case of volumetric heating which results in lower average temperature.

Figure 4-2 Temperature fluctuations

Comparison between temperature and velocity distribution in symmetry plane of S is presented in Figure 4-3. Temperature in the MTF-volumetric is distributed more uniform and mixing is stronger. Therefore, MTF-volumetric compared with MTF-surface heating has less temperature gradient. The hot zone is almost in the middle in the case of MTF surface heating. But it has moved toward the left hand side in MTF-volumetric, although the temperature variation inside the tank is less in the latter case. The jet penetration into the tank is stronger in MTF-volumetric. This is due to the fact that temperature is more uniform in volumetric which results in weaker buoyancy force. The weaker the buoyancy, the stronger the effect of momentum and more is the jet penetration into the tank. It will cause better cooling inside the tank since the cold jet will pass through more tubes on its way to the exit pipe.

The volumetric simulation for the actual reactor shows that the hot zone has moved further to the left and temperatures are generally higher due to higher heat influx. Temperature gradient is more intense in this case. Although the heat generation method here is volumetric, but due to higher heat generation, buoyancy forces play more important role in shaping flow regimes inside the tank. As a result the final temperature distribution more looks like MTF-surface heating rather than MTF-volumetric.

The velocity contour comparison reveals that in the case of MTF-volumetric, jet penetrates into the tank with higher velocity in comparison with MTF-surface heating. The jet impingement point is closer to the center line in the case of MTF-volumetric. This confirms why the hot zone is leaning more toward the left hand side in MTF-volumetric. The velocities in actual tank-volumetric are 30-40% higher due to higher mass flux injected from the nozzles. The high velocity zone is wider in this case and many regions on the jet

79 penetration path have velocities higher than 1 m/s. The jet impingement point is also closer to the center line compared with both MTF simulatioons. This will force the hot zone to move further to the left hand side of the tank.

Temperature –MTF – Surface Heating Velocity –MTF – Surface Heating

Temperature –MTF – Volumetric Heating Velocity –MTF – Volumetric Heating

Temperature –Actual tank – Volumetric Heating Velocity –Actual tank – Volumetric Heating

Figure 4-3 Temperature and velocity contours for t=150 s (three different simulations)

Generally, volumetric heating results in better temperature distribution and less temperature gradient inside the tank. This can be observed from the fluctuation plots as well as temperature distributions in different planes. The fluctuations are less intense and the average temperature is generally lower. This shows that although the surface heating method is practical due to experimental limitations, but one should be cautious using the surface heating result since the result in this chapter shows that the actual method of heating results in visibly less gradient in temperature and lower average temperature throughout the tank.

5 Scaling Effects

The Experimental and numerical results for MTF are used to analyze the flow regimes in

MTF tank and draw conclusions to be used to analyze the actual reactor moderator. Due to practical limitations it is impossible to do experiment in actual reactor environment but the advantage of the numerical simulation is that there is no limit in the simulation conditions and we are able to simulate actual reactor moderator. This is crucial case to simulate since it will determine two issues:

 Actual case simulation: it will help us to assess the situation based on the real

operating geometry and condition. It will enable us to analyze flow regimes inside

the tank more accurately.

 Comparison between MTF and actual tanks: If MTF and actual tank are simulated

with the same operating conditions, their results can be compared and the effect of

scaling can be investigated.

The results for temperature and velocity distributions along with fluctuations are presented here and compared for both cases. Figure 5-1 shows the temperature distribution inside the moderator tank for both MTF and the actual reactor tank. It presents a plane which passes through two inlet nozzles and one outlet. This is one of the most important planes inside the tank since it shows the interaction between inlet jets, bulk fluid inside the tank, and the exit flow.

Temperature contours are shown for two different times. The first one is the initial phase simulation at t = 20 s and the second one is for t = 150 s which is considered the end of the

82 simulation. The upper row corresponds to MTF simulation and the lower row is the resuult of actual moderator simulation. Two inlet nozzles are visible at two sides of the outer wall with inlet temperature of 40 oC. The highest temperature observed for MTF is around 55 oC at the opposite side of the impingement location while the high temperature is close to 73 oC (at almost the same location as MTF) for the actual reactor. It is close to 35% variation in maximum temperature between to cases. The average temperature in bulk flow in the case of

MTF is close to 55 oC while in the case of actual reactor it incrreases by 18% to 65 oC. The location of the hot zone is almost the same in both cases as the impingement point for inlet jets are located on the top right hand side of the tank.

The temperature distribution is more uniform in the case of MTF and less segregation can be observed between high and low temperature zones. This can be the result of better mixing of hot and cold flows in the case of MTF comparing too the actual reactor. The competing forces here are the momentum of the inlet jets and the buoyancy force due to temperature difference inside the tank. Since the method of heat generation is the same for both MTF and the actual reactor, this significant variation in temperature distribution can be attributed to the scaling method employed in modeling the actual reactor.

t= 20 s t= 1500 s MTFM MTFF

t= 20 s t= 1500 s Actual reactor Actual reactor

Figure 5-1 Temperature contours forr MTF and actual reactor

Figure 5-2 shows the velocity contours for the same plane as Figure 5-1 at the same instances. The impingement point is located at the top right hand side of tthe tank for both cases. The velocities are nearly 45% higher in the case of the actual reactor with the maximum velocity as high as 1.3 m/s comparing to only 0.9 m/s for the MTF. After two inlet jets impinge on each other a secondary jet is formed which passes through the tube bundles and goes toward the exit pipe. The velocity distributions show that the secondary jet penetrates more in the case of actual reactor comparing to the MTF simulation.

t= 20 s t= 1500 s MTFM MTFF

t= 20 s t= 1500 s Actual reactor Actual reactor

Figure 5-2 Velocity contours for MTF and actual reactor

As explained before, several points inside the tank havee been monitored for their temperature and velocity. Considering all monitored points, no general trend can be identified for the frequency and amplitude of temperature and velocity fluctuations. But in most points as shown in Figure 5-3, the frequency is higher and amplitude is lower for the actual reactor comparing to the MTF simulation. The higher frequency can be attributed to more temperature gradient visible in the case of the real reactor. Since the real reactor experiences more segregation between high and loow temperatures, the interaction between these two flows are more intense and results in higheer frequency fluctuations in temperature.

MTF Actual reactor

MTFM Actual reactor

Figure 5-3 Temperature and velocityt fluctuations plot for actual moderator and MTF

Based on the results presented, it can be concluded that the flow inside the tank is dominated by two forces: momentum and buoyancy. The first is due to the inlet jets and the latter one comes from density variation (due to temperature gradient) inside the tank. Momentum causes the bulk flow motion from the inlets to the outlets and buoyancy causes the formation of hot zone on the top left corner of the tank.

In order to be able to quantify the phenomena, two non-dimensional numbers are considered in the open literature for similar cases. These numbers are Archimedes and Rayleigh numbers. The definitions for these numbers are as follow:

Δ (Eq 5-1)

Δ (Eq 5-2)

Where g is the acceleration of gravity, V is the inlet average velocity, β is the thermal expansion coefficient, is thermal diffusivity, ΔT=Tout – Tin , is kinematic viscosity, and

D is the tank diameter. Archimedes number shows the ratio between buoyancy and momentum forces which are the main competing forces here and the Rayleigh number adds to this ratio the effect of heating method inside the tank. Khartabil et. al. [20] (the experiments which this research is based on) used Archimedes number as the basis of their experiments. They wanted to scale down their experiment tank 4 times smaller in each direction comparing to the actual reactor (64 times smaller in volume). They assumed constant Archimedes number for both cases and then scaled down both the volume and the heat input by a factor of 64.

Comparing the simulation results for the actual reactor and the scaled down MTF model shows that the differences between the two are noticeable and can be attributed to the method of scaling. The temperature distributions, maximum and minimum temperatures, velocity distributions, and the fluctuations frequency and amplitude vary in the two cases in

87 a way that cannot be ignored or being associated with numerical errors. Table 5-1 shows the comparison between Archimedes, Rayleigh, and Grashof numbers for MTF and the actual reactor. It is clear that although the Archimedes numbers match, but the Rayleigh numbers vary by 2 orders of magnitude. This can be the main reason behind the differences observed between two cases which are supposed to present each other with an acceptable accuracy.

Ar Ra Gr

MTF 0.1027 3.6×1012 1186.7×108

Actual Tank 0.1131 4.6×1014 9060.65×108

Table 5-1 MTF and actual tank operating conditions

The main issue which triggered the experimental and numerical investigation of the moderator tank was the fluctuation observed in temperature and velocity inside the tank. The result presented here, clearly shows that the fluctuation for the same points inside the MTF and the actual tank are noticeably different. Although one may expect to see different fluctuations at the same point (since the nature of the fluctuations is random and unpredictable), but their frequency and amplitude and also the average quantity should be similar which is not the case in comparing several points between the two cases.

There are several papers [63, 64, 65] which suggest that the fluctuations inside the tank have direct relation with Rayleigh number. In fact, they suggest that Rayleigh number is the determining factor for the fluctuations and higher than a critical Rayleigh number the fluctuations are initiated. For example cheng et. al. [63] suggests that for air convective flow inside a bottom heated cylinder, flow is chaotic for Rayleigh number higher than 105. All

88 other papers also suggest similar ranges for the initiation of fluctuation and chaotic flow.

The Rayleigh number for our specific case is much higher than critical Rayleigh number and we are well inside the chaotic zone which will cause unsteady fluctuations in temperature and velocity. As a result, Rayleigh number becomes an important part of our conditions and should be considered in scaling procedure from the actual reactor moderator to the MTF tank.

6 Comparison of Two and Three Dimensional Simulations

Two dimensional simulations are essential for the initial assessment of the problem. Its computational time is significantly less than three dimensional simulations and as a result it can be used to obtain an initial analysis of the issues involved. A brief section here is presented for two dimensional simulation results and their comparison with three dimensional simulation results.

Two-dimensional simulations revealed that the main cause of the temperature fluctuation is the interaction of momentum and buoyancy driven flows inside the tank. Buoyancy driven flows in enclosures have special features which include coherent structures, intermittent fluctuations, and anomalous scaling. There are two coherent structures, which are found to coexist in the convection cell. One is the large-scale circulation that spans the height of the domain, and the other is intermittent bursts of thermal plumes from various thermal boundary layers. An intriguing feature of turbulent convection is the emergence of a well- defined low-frequency oscillation in the temperature power spectrum.

The 2-dimensional isothermal modelling of the MTF tank revealed that the largest flow fluctuations occurred outside the tube bundle where the inlet jets flow, and around the top of the tank where the two inlet jets impinge on each other. The high velocity gradients between the inlet jets and the low velocity surroundings generate small vortices with low fluctuation amplitude but high frequencies. As the vortices travels with the jets, their fluctuation amplitudes amplify but their frequency recede. The impingement of the two inlet jet results in a downward moving secondary jet which penetrated inside the tube bank. The

90 simulation concluded that the the source of flow fluctuations in the isothermal case is outside of the tube bank, and the tubes dampen the fluctuations.

The most important issue in two-dimensional simulation which should be addressed is that whether the 2-D model misses any major effects that may occur in the actual Calandria tank.

This question was answered in the previous sections. As observed, many three dimensional effects were missing especially along the tank length. For example in 2D, we only have one

XY plane whereas in 3D there are several XY planes. Each of these planes, as explained

(depending on their location), has distinctive flow regimes and they interplay with each other through flows running along the tank length. None of these effects can me captured in two-dimensional simulation. These are game changing phenomenon and should be considered in full detail.

Figure 6-1 compares temperature and velocity distributions in two and three dimensional simulations. Since 2D simulation has only one plane to present, it is compared to one arbitrary plane in 3D which has similar geometry. The temperatures are in the same range spanning from 40 oC (inlet temperature) to above 60 oC. The hot zone in 2D is more concentrated and toward the top middle while it is more scattered in 3D and toward middle centre. Although the high temperatures in both cases are close to each other, but they vary in low temperatures. While 2D has a large zone close to inlet temperature, the 3D has confined

91 the inlet temperature to their vicinity and lowest viisible temperatures are around 50 oC and mostly near outlet pipe. Velocity distributions are compared in the second part of the figure.

The velocities are almost in the same range. Two simulations mainly differ in their flow regimes. 2D has a strong flow going from the leftt nozzle counter clock-wise to the outlet pipe, while 3D has less strong flow going from the right nozzle clock-wise to the outlet pipe.

Generally, flows are better distributed in three dimensional simulation compared to two dimensional simulation.

Hot Zone Hot Zone

3D 2D

Figure 6-1 Comparison between 2D and 3D temperature andd velocity distributions 92

Temperature and velocity fluctuations are the next items to be compared. One-on-one comparison is difficult here since one should make sure that the same point in 2D and 3D are compared together. Two points are chosen for comparison. Point 15 which is located at top of the tank (Figure 6-2) and point 4 which is located at the center of the tank (Figure

6-3). Simulation in 2D can be run for much longer period of time comparing to 3D, as a result, the plots for 2D are over 700 physical seconds while the plots for 3D are over 150 physical seconds. Top node (node 15) is located near the hot zone. Although the plots shows the same trend up to 150 seconds, but the temperature for 3D is higher in the order of 2-3 oC.

The amplitude of fluctuations in 2D is noticeably higher than 3D. It can be the effect of less mixing and more segregation (between hot and cold zones) which will make the flow unstable and prone to fluctuations.

The same phenomenon is occurring for node 4 which is a center node. The temperatures in

2D and 3D are close with higher temperatures in 3D. The fluctuations in 2D have higher amplitude comparing to 3D. a general conclusion one might draw from these figures is that while 2D and 3D compare almost the same temperature range at each node, but they are quite different in the fluctuation behaviour and its amplitude and consequently the fluctuation frequencies.

50 Temperature (C) Temperature 2D – Node 15

40 0100 200 300 400 500 600 700 Arbitrary Time (sec)

3D – Node 15

Figure 6-2 Node 15 (located at top of the tank in XY plane) comparison between 2D and 3D

60 (C) 55

50 Temperature (C)

45 2D – Node 4

40 0100 200 300 400 500 600 700 Arbitrary Time (sec)

3D – Node 4

Figure 6-3 Node 4 (located at the centre of the tank in XY plane) comparison between 2D and 3D

7 Summary and Conclusion

A three-dimensional numerical modeling of thermal hydraulics of Canadian Deuterium

Uranium (CANDU) nuclear reactor is conducted. The moderator tank is a Pressurized heavy water reactor which uses heavy water as moderator in a cylindrical tank. The main use of the tank is to bring the fast neutrons to the thermal neutron energy levels. It consists of several hundred horizontal fuel channels. Each fuel channel consists of an internal pressure tube and an external tube separated from the pressure tube by an insulating annulus. The tank contains cool low-pressure heavy water that surrounds fuel channels.

There have been several studies on the operation of CANDU reactors. Three-dimensional moderator circulation tests have been conducted in the moderator test facility (MTF) in

Chalk River Laboratories (CRL) of Atomic Energy of Canada Limited (AECL). The

CANDU Moderator Test Facility (MTF) is a ¼ scale of CANDU Calandria, with 480 heaters that simulate 480 fuel channels.

The data recorded inside the MTF tank have shown levels of fluctuations in the moderator temperatures. The frequency of the fluctuations is higher than the sampling rate of the fixed thermocouples. Fluctuations in temperature are believed to be due to the interaction between local momentum and buoyancy forces, inlet jet impingement, and the flow passing through the tube bundle. Because of the limitation in data sampling, full range of the fluctuations could not be identified. Also, analysis could not identify any dominant frequencies.

The purpose of the current investigation is to determine the causes for, and nature of the temperature fluctuations using three-dimensional simulation of MTF with two different

96 heating methods (surface heating and volumetric heating) and three-dimensional simulation of actual tank with volumetric heating.

The simulations are carried out for two geometries (different in size), two heating methods, and two solution strategies. These simulations include: MTF with surface heating, MTF with volumetric heating, actual tank with volumetric heating. The numerical modeling is performed on a 24-processor cluster of computers using parallel version of the FLUENT 12.

During the transient simulation, 55 points of interest inside the tank are monitored for their temperature and velocity fluctuations with time. These data along with temperature and velocity distributions in different planes inside the tank are used to analyze the phenomena occurring inside the tank. The result for MTF simulation is presented in extended length and the main flow regimes inside the tank are identified. Asymmetry in temperature and velocity distribution is presented in different spatial planes and the causes behind the issue are explained and discussed. The after effects for asymmetry is identified and explained. Two different heating methods are compared and their differences are identified. The effect of scaling on the temperature and velocity distributions is studied and at the end a quick comparison between two and three dimensional simulations is presented. Based on all the assessment in various phases of the study, the following conclusions are made:

 Temperature contours in various planes show the hot region at the top and left-hand

side (close to the center line) of the tank for the case of MTF-surface heating.

 Hot region moves further to the center in MTF-volumetric and temperature

distribution is more uniform and less temperature gradient is observed.

 Actual moderator has the highest temperature recorded due to higher heat influx. The

hot region is also at the left side of the tank. 97

 The general trend is that the inner zones of the tank are higher in temperature

specifically at the middle of the tank (close to z=0). It means that the flow is colder

near the walls at both ends of the tank.

 Temperature increases to 65 oC in hot zone for MTF-surface heating while it is

below 60 oC and near 55 oC in most parts of the tank. Temperature drops from the

inner zones to the outer wall of the tank due to the close distance to the jet

penetration path.

 In the case of MTF-volumetric, maximum temperature is near 58 oC and the

minimum is 46 oC.

 Temperatures are lower in MTF-volumetric comparing to MTF-surface heating. This

is mainly due to the different method of heating. Volumetric heating encourages

mixing of cold and hot flows and results in more uniform temperature inside the

tank. In the volumetric method, the heat is distributed as a heat source throughout the

domain while in the surface heating, local heating occurs, which makes the heat

transfer concentrated to specific sections.

 The buoyancy effects in the tank are more visible in the case of MTF-surface heating

and the actual moderator. In the case of MTF-surface heating, the method of heat

generation through the surface of the tubes discourages better flow mixing and

creates segregated hot and cold zones, which in turn boosts the buoyancy effects

inside the tank. In the actual moderator, although the heat generation method is

volumetric, but since the heat influx is higher in comparison with other cases,

powerful temperature gradients exist inside the tank, causing strong buoyancy forces

as opposed to inertia forces.

 Depending on the location of the monitored point, the behaviour of the fluctuations

is different. Points which are located near the hot and cold boundaries have higher

frequencies and, depending on the conditions (e.g. level of mixing) high or low

amplitudes.

 The impingement point of inlet jets lies at the left hand side of the tank. A secondary

jet is formed after jet impingement which goes to the outlet pipes passing through the

heated tubes, cooling them down along the way.

 The inlet jets lose 90% of their momentum upon reaching to the impingement point.

 The velocity of the secondary jet further reduces once it reaches bottom of the tank.

It only carries 20% of its initial momentum.

 The impingement point is important in temperature distribution inside the tank. It

affects flow mixing and its location can strongly influence the location of hot region.

 The best case scenario is to have the impingement point on the center line. In that

case, the secondary jet will pass through a maximum number of tubes along its way

resulting in maximum cooling. This also will result in a uniform temperature

distribution.

 The asymmetry inside the tank is severe and has many after effects. It is the result of

competition between strong buoyancy and momentum flows. The buoyancy has

occupied most of the core region while the momentum driven flow goes through the

edges. A small disturbance from turbulence or any other involved parameter forces

out the temperature and velocity distributions from symmetry, resulting in current

distributions inside the tank.

 Investigation of the nozzle planes revealed the existence of a jet impingement effect

on the symmetry plane (in XY). It creates a clock-wise rotating flow in the symmetry

plane (which is transferred to the other planes through flows in the YZ plane). The

rotating flow is strongest in the symmetry plane, then the nozzle plane without exit

pipe and it is the weakest in the nozzle plane with the exit pipe, which is mainly

dominated but by the bulk flow from the inlet nozzles to the outlet pipe.

 The rotating flows weaken the right inlet flow, contributing to the movement of the

impingement point to the right hand side of the tank.

 The asymmetry in the jet impingement point causes many issues such as:

o The hot zone lies asymmetrically at the left, which forces the left inlet jet to

the outer walls, decreasing its X-section and increasing its velocity

furthermore. This eventually results in a stronger left inlet jet, which in turn,

intensifies the asymmetry and causes less efficiency in the cooling process.

o Since the hot zone is at the left hand side, it heats up the left hand side jet.

The temperature in the right hand side jet is on the average, about 18%

higher. This will cause a higher temperature at the impingement point, which

reduces the cooling effect of the secondary jet.

 Velocity contours show relatively small velocities throughout the tank. The bulk

flow moves with a steady and slow pace and most of the momentum action is

observed near the inlet nozzles, penetration path of the inlet jets, and the boundaries

between the low and the high velocity currents.

 Comparison between two heating method shows that the surface heating results in

more temperature gradient as the heat is distributed on the surface of the tubes

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through conduction while in the volumetric method; the heat is distributed as a

source term throughout the domain.

 The comparison between MTF and actual moderator result revealed the effect of

scaling on the temperature and velocity distributions. The method of scaling

becomes important and it is concluded that Rayleigh number should be used along

with Archimedes number for scaling purposes. The Rayleigh number is a crucial

parameter in fluctuation analysis as it is suggested in the literature that beyond a

critical Rayleigh number, the fluctuations are initiated inside the tank and

temperature and velocity show a chaotic, unsteady and un-periodic behaviour.

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8 Future Work

Flow inside actual calandria tank is very complicated and it is dependent on many factors including operating conditions and heat generation inside the fuel bundles. Simulations so far have indicated that buoyancy and inertia forces are the determining factors in the flow regime inside the tank. The fluctuations in the temperature and the velocity are strongly location dependant and vary significantly in hot and cold zones.

The phenomenon and its causes and consequences have been comprehensively explained in this research, but what remains is the cure for the problem and how actually, the fluctuations and segregation in hot and cold zones can be utilized to achieve more stable and distributed flow inside the tank. Based on this assessment the followings are suggested for the future works:

 Long range run: The experimental results are performed in the range of 3000 to

4000 physical seconds. Moreover, there are some practical evidences that the hot and

cold zones will change sides in time. But this is in the range of 2000 to 5000 physical

seconds. It is suggested to carry out a very long run in the range of 3000 to 4000

physical seconds to see the effects in long range and also detect any possible changes

in the flow temperature distribution inside the tank.

 Mass flux modifications: flow distribution inside the tank is explained here

comprehensively and it is observed that most of the occurrences inside the tank are

due to asymmetrical injected jet penetration. Practically it is possible to change the

mass influx through the inlet nozzles as explained in the followings. Several

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simulations should be carried out to be able to draw conclusive results and to

quantify the improvement in the flow versus the changes in the mass flux:

o It is possible to vary the mass flux in one side nozzles with respect to the

other side as much as 5% (for practical reasons).

o The total mass influx to the nozzles can be increased as much as 10% (for

practical reasons) to achieve stronger injection which will encourage the

mixing inside the tank.

 Geometry modifications: although it is practically very difficult due to the

limitation with nuclear safety and restrict regulations, but it is a proper theoretical

pilot project to observe the effects of geometry change on the flow and temperature

distributions inside the tank. It can include changes in the nozzle locations, nozzle

angle and changes in the outlet pipe location.

 Start-up phase modeling: at the moment, all solution strategies start from a filled

tank with an initial velocity and temperature distribution. One more realistic scenario

will be to start the simulation right from the start-up phase. In this method, the

simulation will start from quiescent flow with zero velocity and temperature all over

the domain. In this way we will be able to capture the physics involved in its entire

entirety showing the initial phases which lead to asymmetry in the tank.

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