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International Compressor Engineering Conference School of Mechanical Engineering
1988 Performance Simulations of Twin-Screw Compressors with Economizer Sven Jousson Svenska Rotor Maskiner AB (SRM)
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Jousson, Sven, "Performance Simulations of Twin-Screw Compressors with Economizer" (1988). International Compressor Engineering Conference. Paper 626. https://docs.lib.purdue.edu/icec/626
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/ Herrick/Events/orderlit.html PERFORMANCE SIMULATIONS OF TWIN-SCREW COMPRESSORS WITH ECONOMIZER
Sven Jonsson svenska Rotor Mask~ner AB (SRMl Box 15085 S-104 65 STOCKHOLM, Sweden
ABSTRACT In a compressor refrigeration plant regular expansion with economizer system, the valve is replaced by two med~ate pressure valves and an ~nter vessel. The refr~gerant which the first valve is inJected is vapourized after a via the compressor economizer thread under compression. The inlet to the refrigeration economizer arrangement increases capacity and improves the COP Performance) . In this paper (Coefficient of program a performance simulation computer for twin-screw compressors with presented. economizer arrangement is
Comparisons of economizer performance are often for different arrangements ditficult to carry out if since the performance real tests have not been run, ~s depending on the intermediate and this pressure will not pressure Such be the same for different arrangements. compar~sons can be made with the simulation are presented for program. Examples an economizer arrangement combined liquid subcooling and with external for a two stage economizer arrangement.
1. INTRODUCTION The purpose of performance simulations of scribe the thermodynamic compressors is ~o de- . process inside a compressor. tions then give an overall The s~mula picture of the compress~on give a possibility to put different process and tions to losses in quantitative rela each other. Detailed presentat~ons program and the geometrical of this simulation made data program l~brary have ~n ref (1J, C2J, and (3J. Therefor earl~er been given here. a short overview is only The refrigeration system with economizer scribed in the abstract arrangement, shortly de above and in section 4.1, in different ways which will can be designed this affect performance. With the simulation program, the performance help of mizer alternatives of some different econo are studied in this paper.
2. GENERAL OVERVIEW OF THE SIMULATION PROGRAM One of the fundamental demands possible on simulation is that it must to model the geometrical design be The follow~ng in a mathemat~cal form. geometrical parameters are calculated programs and the results are by computer inputs to the simulation program:
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0> 0> 0> 0> Volume curve, Inlet port area vs. rotation angle, outlet port area vs. rotation angle, Rotor-rotor sealing lLne length vs. rotation Male and female lobe angle, tLp sealLng line length, vs. rotation angle and Blow-hole area. Flgure 1 shows the flow chart o£ the computer programs. For calculation of part load performance one also needs: - Sllde valve by-pass port area vs. rotation angle. It is important to have programs with possible. All the programs as general applLcability input have a set of profile as and they do not deal with coordinates as Thls means analytLcal profile definitions. that they can be used for all types Of profiles. Apart from these geometrlcal inputs, lenqths of leakage average clearances paths, for the leakage and the inputs. The options calculations, are in geometrical input also cases whLch can conceivably are so large that all appear in practice can be dealt with. The simulation program itself considers the effects of: - Internal leakage through all types of clearances blow-hole, and th.rough the - Inlet and outlet port throttling - Gas pulsations losses, in inlet and outlet ports, - Vlscous losses and - Heat transfer between gas and oil. The effects of the solubilitY of refrigerant be considered when simulating in oil also have to compressors with (freonsl as working medium. halocarbons
A condltlon for this type of program is also to use a wide variety that one must be able of operational conditions. parameters are used: The following - Working medium, - Inlet gas temperature and pressure, - Outlet pressure, - Rotor speed and - Oil-injection rate, oil temperature, oil Vlscosity. Together with the instantaneous temperature values of the mass and pressure, the of gas, gas and adiabatic program also calculates efficiencies, specific volumetric ture. torque and discharge tempera As an example, the pressure profile (pressure angle) from both versus rotation a full-load and a part-load in flgure 2. The simulation is shown condensing temperature is ratlo is equal to 3.0. so·c and the pressure on top of figure 2, area curves for the inlet, a diagram showing the presented. the slide valve and This diagram shows the outlet ports is opens "later" that the outlet port at than at full load, Slnce part load towards the discharge the slide valve is pushed end plane at part load.
886 1oo_ r:--....,--1 ------.------r---r--:---,------,.--,--.,...... , ... on) Sl,~Qe 'J'alve by-pa..s.s por"t: a.rea I ' + ra.d1a.l outle-t I ~A1.'ial 80. port I I I I •••• (Full load) A;.;.1al 1nletI port' a.r!!a•I, I 50. I I 1'> h I ' / 1\ I I / I I i 1 40. I ., al + radial OIJtlet I v "' 0rPOr'"t ,!rea ( Pll:r""t. 1cad) 20. I ! \ 1/ \ /' I I 1\ J \ /I N 0 0 oo !Ooo zoo' oo' I 400° 50 oo I 600 700 25. Pressure (bar) I II I I II 1( 20. ~ I v " I 17 15. I Full loi.d'\ 1 I I / 10. I I / "- P.. t load I _/ (50~) 5. I I I I I I Hale rotor rotation angle . 0 ;;o ,u ,,u 0 100 0 200 0 300 400 500 600 700
Figure 2. Pressure and port areas vs. rotation angle. Full load and part load. R22. Cond temp = SO'C. Pressure ratio= 3.0.
3. SIMULATION OF REFRIGERATION TWIN-SCREW COMPRESSORS
Refrigeratlon twin-screw compressors differ in design compared with air compressors in the way that most of them have means for capacity control. Means for adjustable built-1n volume ratio are also becoming more and more used. A survey of these means is made 1n reference [5]. It is important for the geometrical modelling of refrigeration com pressors to have a computer program which both calculates the area variation of the axial outlet port as well as the area variation of the radial outlet port of "slide valve• type.
For part load simulations, information about the slide valve by pass area var1ation is needed, see the example in figure 2 above.
One difference from thermodynamic point of view between oil flooded air compressors and machines compressing refrigerants is the solubility of refrigerant in oil. When the oil is injected into the compression chamber some of the refrigerant dissolved in the oil evaporates. This will affect the compressor performance in a negative way as a larger mass of gas has to be compressed. The modelling of th1s effect has been described in ref. [2].
887 D~fferent comb~nations of o~l type and refrigerant the refr.Lgerant to different w~ll dissolve extent. The number of experimental investigat~ons ~n this field is unfortunately few relationsh~ps are lim~ted why only a available. In ref. C4J the solubility tionsh~ps ~(p,T) are presented rela for the combinat~ons of oils and some of the more commonly m~neral R22 and R114. used refrigerants, e.g. R12,
An ~nteresting quest.Lon is how much the refrigerant the oil affects dissolved ~n the performance when it evaporates. understanding of To get an this, the simulation program was with and without refrigerant executed both dissolved in the oil. By putt.Lng mass flow of gas from the oil-refrigerant the mixture equal to .1t is possible to study a compressor zero, same running w~th an oil of the v~scosity, but free from dissolved refrigerant. The simulations were run on R22 for a compressor cal capac~ty of 175 with a theoreti m3Jh at 3550 rpm (OM= 113.4 mm). The performance increase by the injection of "pure"' oil studied ~n figure 3. The can be optimal Vi performance curve is plotted and compared with the here optimal vi (within Vi 2.5 to 5.0) performance curve from simulations = rant without dissolved refr~ge ~n the oil. The two curves are diverging pressure ratio. with increasing The results show an increase in ciency of around 3 adiabatic effi \ at a pressure ratio of 4.0 and a pressure rat.Lo of 12.0. around 13 \ at
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F~gure 3. Computed performance vs. pressure ratio with without dissolved and refrigerant in the oil. R22. Cond temp = 35"C. n = 3550 rpm. Optimal Vi (Vi= 2.5 - 5.0).
888 A larger amount of gas is evaporat~ng when the mixture ~s injected ~nto a lower cav~ty pressure. ~his is the reason for the larger ~nfluence at h~gh pressure rat~os. A small increase in volumetric eff~c~ency for "pure• oil is also shown in the diagram. This is a resul~ of the "lower" pressure level in the cavit~es under com press~on ~n the case of "pure" oil.
When the oil-refr~gerant mixture ~s leaking back into the ~nlet, an add~tional amount of gas will evaporate due to the pressure de crease. Th~s effect has not been included in these computations.
4. ECONOMIZER
4 1 Theory
To improve the capac~ty as well as the COP in refr~geration plants with twin-screw compressors, economizer arrangements are becoming more and more used. A compressor refrigeration plant with economi zer system ~s accomplished by replacing the regular expansion valve by two valves and an intermediate pressure vessel (flash tank). The refrigerant which is vapourized after the first valve is injected, via the economizer inlet, into a thread under com pression, see figure 4. In the same figure the process ~s describ ed in a Mollier diagram.
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h 1 h' eco Figure 4. Principle of economizer refrigeration system. Economizer arrangements improve the COP, since the gas evaporated in the upper (high pressure) expansion valve is not compressed from the evaporation pressure, but from a higher pressure (~.e. the ~ntermediate economizer pressure) and at the same time the evaporator is fed w~th a larger percentage of refrigerant liquid, which gives an increased cooling capacity. 889 The vapour in]ect~on ~s modelled in the ~ntroduction simulation program by of one more "rate of mass of d~fferential flow" equat~on to equations and by adding the set balance equation one more term ~n the heat (energy equation). The equation ··nozzle flow" has for isentrop~c proved to describe the flow mizer port very well. The through the econo earlier modell~ng of vapour injection been described in ref C2J. has The variation of the exposed hole must also area, A(a) with rotation be modelled. In many cases, angle a housing is chosen. a round hole located in the In a real economizer refrigeration pressure system, the intermediate will automatically be adjusted to the actual economizer to a value corresponding economizer arrangement. In the simulations, pressure ~s not known beforehand, the pressure will depend as the economizer on the ratio of the mass econom~zer hole and the flow through the The mass flow through the compressor mass flow through the economizer inlet. inlet must respectively inlet and the compressor be the same as the the flash tank, see total mass flow from figure 4. This is only possible economizer pressure. The simulation for a certain executed several program has therefore to be times with different economizer determ~ne the correct pressure. pressures to 4.2 Cgmparispn gf Petformsnge With and Withgyt Esongmizer All simulat~on examples in the following pressor type. pertain to the same The compressor has a theoretical com m3fh at 3000 rpm. capacity of 1220 The rotors have outer diameters equal bination is 4+6. to 204 mm. The lobe com The vapour-injection hole ~n these simulations located at a rotation is a round hole angle close to the inlet angle. The hole has the port closing the diameter 25 mm. A hole located ~nlet port closing angle as as close to between the possible, but without connection economizer hole and the inlet, economizer pressure and gives the lowest thereby maximum cooling capacity. In figure 5 simulation results are presented pressure ratio for with COP versus R22 and 40•c condensing temperature and without economizer arrangement. both with different The computations were vi and the curves are presented run with (Vi- 2.5 to 5.0). for optimal Vi 890 5 .o co~ I ! ! I I I ! ! I I I 4. 0 \ I : r I I , I /WITH ECOfOMIIER I I 3 .o \ .I I I 1\: I ~ !--.... 2. 0 ~ 1'::::: ~ r--r-- WTOU~ ErOrEi r-. r-. I 2. 4. 6. e. lO. 12. PRESSURE RATIO F1gure 5. Computed COP vs. pressure ratio Wlth and without economizer. R22. Cond temp~ 40"C. n ~ 3000 rpm._ Optlmal Vi (2.5 to 5.0). The curves show that the COP-improvement at low pressure ratios is very small, in the magnitude of a couple of percent, but becomes signlficant at high pressure ratios. At a pressure ratio of 12.0 the improvement amounts to 16 \. It can also be observed that the optimal vi is lower for the economizer simulations, since the cavity will reach the discharge pressure at a larger cavity volwne due to the "super-filling" with economizer gas. The pressure increase in a compressor with econo mlzer arrangement can be studied in figure 6. The figure shows p-V dlagrams from both a simulation with economizer arrangement and a simulation for the same pressure ratio but without economizer. PRESSURE in bar 1\. / p( 15. \I\ WITH ECONOMUER 1\ '\ 10. r,_'",.___ r-; 1'----- s. I- WrHOr EC0NOM,ZER 1 "' t--::: ~ ~ 20. 40. 60. 60. 100. VOLUME l.n \ 100\ • (MAX. CAVITY VOLUME)/ CwR figure 6. p-V diagram from simulations with and without economizer. R22. Cond temp ~ 40'C. n ~ 3000 rpm. Pressure ratio ~ 6.0. 891 4.3 Performance With Ecgnpmizer and External Suhcqgling By subcooling of liquid refr~gerant, ~.e. removing refrigeration system at heat from the the high pressure side between ser and the expansion valve, the conden valve the percentage of liquid will increase and give larger after the higher COP. cool~ng capacity as well as Somet~me the use of subcooling is regarded as an system w~th economizer arrangement, alternative to a prove the as both types of systems performance by feeding the im l~quid percentage. evaporator with a higher When looking upon to each other, these systems as alternative one is not aware Of the fact subcooling and economizer that the use of both arrangement will improve even more and that they do the performance of not counteract from performance v~ew. The subcool~ng will lead po~nt That means to a lower economizer pressure. higher percentage of liquid be seen in to the evaporator, as the enthalpy-diagram in figure can system with subcooling 7. In this diagram the is shown with dashed lines. LOG p Pc:ond Peoo Pecosub Pevap h~coh·eond Figure 7. Enthalpy diagram for econom~zer refrigerat~on system. External subcooling lines. shown w~th dashed The s~mulat~on program can economizer be used, to get a comparison performance with and between one such without subcooling. The result comparison is presented in of densing temperature figure 8 tor R22 and a con of 4o•c with COP versus make a correct comparison, pressure ratio. To vi· the results are presented The curve tor no subcool~ng for optimal curve in is the same as the economizer figure 5. The results show COP is 0.6 that the relative increase \ per degree Celsius of subcooling. in example, that the COP This means, for w~ll ~ncrease 6 \ for 1o•c of subcooling. In f~gure 9 the relative for ~ncrease in capacity with subcooling an econom~zer system is presented. 892 COP I I 5. 4. \ EXTERNAL SUBCOOLXNG ~ ~ 15°C 3. ~ ~~:~ ~ ~0: 2. ~ 2. 6. s. 10. 12. PRESSUaE RATIO Figure 8. COP VS- pressure ratio. Econom~zer. R22. Cond temp ~ 40'C. 0' to 15'C external subcooling. Optimal Vi (2.5 to 5.0). Since a COP-increase ~s always achieved with economizer arrange ment the conclus~on of this analysis must be that subcooling is a good complement to an economizer arrangement and should not be regarded as an alternative to the economizer arrangement. Oecc+subcool. 0eco RELA.TIVE INCREASE IN cOOLING I I CAPACITY WlTH SUBCOOLING EXTERNAL S.i SUBCOOLING - :....-- 5°C 4 ·' - ooc: 2.l 5°c 1.i 2. 4. 6. 8. 10. 12. PRESSUaE RATIO Figure 9. Relative increase ~n cooling capacity with external subcooling vs. pressure ratio. Economizer refrigeration system. R22- Cond temp ~ 40'C. 893 4 4 Pgrfgrmancg With Twp-Staqe Ecgnomizer Arrangement A on~-stag~ ~conom~zer arrangem~nt ~mproves the COP and cooling capac~ty, as described increases ~n section 4.2. A log~cal lS no~ lf, and in question that case ho~ much, th~ performance ,.,."'""ed by a second ~ill be ln eecmom_t: =• ·- ...... h"...... Figure 10. Principle of two-stage economizer refrigeration system. One problem from a practical point of view, mizer inlet is that the two econo holes must be placed at such ne~ther rotation angles that communication between the holes, inlet nor communication to the or outlet may occur. At the same gas lS time the "superfeeding" of large and this decreases the optimum at lo~ pressure Vi. The optimum vi ratios is therefor lower than w~thout achieving what can be used communication between the high and the outlet port. stage economizer From simulation point of to vie~ the calculations are time consuming carry out. Modelling of the two-stage ltself not more vapour injection is in complicated compared Wlth one-stage modelllng. However, one economlZer has to find a solution for two economizer pressures in this case. unkno~n variables The convergence of two unknown to a correct solution involves cal procedure a complicated mathemati with many individual simulations nomizer pressures. for different eco In figures 11 and 12 the results from two-stage tlons are presented economizer simula with COP and relative increase capacity versus pressure of cooling ratlO for 40"C condensing temperature. For comparison the results from seCtlon 4.2 are also presented. 894 PRESSURE AATIO Figure 11. Computed cOP vs. pressure ratio for one- and two-stage economizer system. COP for a system w~thout economizer is shown for comparison_ R22. Cond temp - 40'C. n = 3000 rpm. optimal vi (2.5 - 5.0). Q::eco: /0 RELATIVE INC> 1 Ot 2. 4. 6. 8. , 0. , 2. PRESSURE AATIO Figure 12. Relative increase ~n cooling capacity with one- and two-stage economizer vs. pressure ratio. R22. Cond temp = 40'C. 895 The results show that a COP improvement pressure is obtained at higher ratio. The increase, compared with ls not as large one stage economi~er, as the COP lncrease that was obtained stage economi~er, with a one compared with a system without economizer. pressure ratio of 12.0 At a the improvement amounts to about pared with a one stage 5 \ com econom~zer system. At low pressure ratios, a COP reduction is obtained due has to the fact that a too hlgh Vi to be used as mentloned above. The ved somewhat performance can be lmpro at low pressure ratios by using lobes than rotors with more the 4+6 comblnation used in these more lobes simulatlons. With there is more "space" for the economizer lower Vi can be used. holes and a The low- and high-stage economizer pressures are plotted 13. The one stage economizer in figure pressure is also plotted for compari son. As can be seen in the diagram the low-stage pressure for the two stage economizer system is lower stage than the pressure for the one economi~er resulting in larger capacity econom~zer. for the two-stage ECONOMIZER PRESSU!lE \ 12. \ 10. ~ TWO STAGE ECONOMIZER 1-- v UPPER !!OLE 8. \ ['.__ \\ ~ ""-..._ ONE STAGE 6. 'EcoNOMIZER t---o r--. "" "-r---.., :--1-- r---. - TWO STAGE ECONOMIZER ::- LO~jl!R ,OLE r--- 2. 1 I - 2. 4. 6. 8. 10. 12. PRESSORE RATIO Figure 13. Economizer pressure vs. pressure ratio. one- and two-stage economizer. R22. cond temp ~ 40"c. 896 REFERENCES 1. S. Jonsson, Computer Calculations for Design and Analys~s of Screw Compressors, Royal Institute of Technology, Department of Thermal Eng~nee~ing, Stockholm, Sweden, Trita. Atk 860907. 2. S. Jonsson, Performance Simulations of Twin-Screw Compres sors for Refrigeration Purpose, "Schraubenmaschinen '87" in Dortmund, West Germany, VDI-Berichte 640, VDI-Verlag, Dusseldorf. 3. B. SAngfors, Computer Simulation of the oil-Injected Twin Screw Compressor, 1984 International Compressor Engineering Conference, Purdue University, West Lafayette, U.S.A. 4. H.P. Jaeger, Kaltetechnik - Klimatisierung, 24, p. 35 - 52, 1973. 5. L. Sjoholm, Variable Volume-Rat~o and Capacity Control in Twin-Screw Compressors, 1986 International Compressor Engi neering Conference proceedings, Purdue University, West La fayette, U.S.A. 897