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A new model of screw compressor for refrigeration system simulation
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journal homepage: www.elsevier.com/locate/ijrefrig
A new model of screw compressor for refrigeration system simulation Jinghui Liu*, Qinggang Li, Fazhong Wang, Lei Zhou R&D Department of DUNHAM-BUSH Co., No.1 DUNHAM-BUSH Road, Yantai 264005, China
article info
abstract
Article history:
A performance predicting model of screw compressors, for refrigeration system simula-
Received 14 March 2011
tion, is developed. The model correlates the running condition and some of the design
Received in revised form
parameters of a screw compressor. Compared with the experimental data, the errors of the
29 September 2011
model predictions are about 2% for the volumetric displacement, less than 3% for the
Accepted 16 January 2012
input power at full load condition, about 4% for the input power at part-load displacement
Available online 24 January 2012
condition, and about 2% and less than 4% for vapor injection mass flowrate. This model can also be used to optimize the built-in volumetric ratio of a screw compressor. ª 2012 Elsevier Ltd and IIR. All rights reserved.
Keywords: Refrigeration Screw compressor Vapor injection Part-load performance System simulation
Nouveau mode`le de compresseur a` vis pour la simulation des syste`mes frigorifiques Mots cle´s : Froid ; Compresseur a` vis ; Injection de vapeur ; Performance sous des conditions de charge partielle ; Simulation du syste`me
1.
Introduction
Refrigeration system is becoming more important for people’s daily lives. For the conventional design method of refrigeration system, a prototype unit must be developed and be tested to verify the design. For getting the satisfactory result, the prototype building process may be repeated several times, which will increase the cost and prolong the design period. In order to make the system design process more efficient and economic, system simulation is widely used to predict
the performance and optimize the system design before the equipments are manufactured. Screw compressor is a kind of positive displacement rotary machine. Due to the advantage of high efficiency, wide operating scope and high reliability, it is widely employed in the refrigeration equipments in both commerce and industry, which have gradually substituted for the reciprocating compressor employed in the small cooling capacity unit and part of centrifugal compressor employed in the large cooling capacity unit.
* Corresponding author. Tel.: þ86 05356725250; fax: þ86 05356589999 5816. E-mail address: [email protected] (J. Liu). 0140-7007/$ e see front matter ª 2012 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2012.01.016
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Nomenclature A C k P p R T V Vi h r f h w
2
area, m coefficient polytropic index power, kW pressure radius lead of rotor volume, m3 built-in volumetric ratio efficiency density, kg m3 helical angle of teeth enthalpy, kJ kg1 specific power, kW
Compressor is the heart of refrigeration systems. A good compressor model is the key for system simulation. According to the study objectives, the compressor model can be cataloged into steady model and dynamic model. A complicated dynamic compressor model (Wu et al., 2007; Lee et al., 2001; Seshaiah et al., 2006), as well as CFD model (Kovacevic et al., , 2006), which is usually used to study 2000; Vimmr and Fryc the working process and/or to optimize the structure of the compressor, may make the system simulation run too slowly. It is not suitable for refrigeration system simulation. For the compressor model to predict the refrigeration system performance, three parameters including the refrigerant mass flowrate, the input power and the refrigerant temperature at the compressor exit should be calculated accurately and other unimportant parameters can be ignored (Ding, 2007, 2006). Long Fu et al. (2002) employed a very simple model of the screw compressor in his system simulation. The model only correlates the running condition parameters, including the suction pressure and the discharging pressure, not considered any design parameters of the compressor. Some key design parameters have definitely influence on the performance of a screw compressor. For example, the built-in volume ratio has distinctively contribution to the input power for various running conditions. According to the different ratio of discharging and suction pressure, under-compression or overcompression may occur in its working process, which results more power consumption. The built-in volumetric ratio efficiency can theoretically be deduced as (Xing, 2000). 1 0 k @ k1 ε k 1A k1 hVi ¼ k ε Vi0 k k1 1 þ V Vi0 k 1 i0
(1)
Where, k is polytropic exponent. Vi0 is the built-in volumetric ratio of the compressor for full load condition. ε is the ratio of the discharging pressure and the suction pressure. For a given built-in volumetric ratio, there is a pressure ratio who has the built-in volumetric ratio efficiency equal to
ε y T m a Z
pressure ratio specific volume, m3 kg1 temperature, K mass flowrate, kg s1 load percent, % teeth number
Subscript 0 1 2,3 v m s b
Design parameter, theoretical Male rotor, refrigerant state point refrigerant state point volume motor isentropic vapor injection
1.0. Either lower or higher than the pressure ratio makes the efficiency drop, which means more input power to be needed. Therefore, a too simple compressor model, which does not include the compressor design parameters, is not enough to depict the real performance of a screw compressor in a wide running condition scope. It may make the system simulation result not accurate. Compared with other types of compressor (piston, centrifugal, scroll, etc.), VI (Vapor Injection) is the unique advantage of a screw compressor, which can improve the capacity, as well as COP, of a refrigeration system with economizer cycle. Economizer cycle can easily work with a singlestage screw compressor to realized two-stage compression while two compressors or a two-stage compressor must be used for other types. Few compressor models for system simulation can present the performance of a screw compressor with VI in the referenced articles. Since cooling capacity requirement varies with climate and work schedule, for most of the time, refrigeration systems run under part-load condition. A slide valve is the most frequently used device to regulate the displacement for screw compressors. With the slide valve moving, the displacement can be changed from 100% to 25%, which results the system capacity change. Among the articles the authors have read, few models for system simulation can calculate the part-load displacement performance of a screw compressor, which is important for estimating the running cost of the refrigeration equipments. In order to simulate the performance of the screw compressor in a wide running condition scope, with VI and under part-load displacement conditions, some key design parameters of the compressor must be considered. In this article, a new steady model is developed, which correlates both the running parameters and some key design parameters of the compressor. The coefficients used in the model were regressed on the base of experimental data. The model can predict the performance of the screw compressor with and without VI in a comparatively wide running condition scope and under part-load displacement condition with a fast running speed.
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2.
Test stand
The standard compressor performance test stand in DUNHAM-BUSH Co. (DBYT), which was certified by AHRI and CQC, was used to test the performance of the screw compressors. The systematic diagram of the test stand is shown in Fig. 1. It consists of a compressor which will be tested, an oil separator, a water-cooled condenser which is used to control the discharging pressure of the compressor, a receiver, two mixing tanks which are used to regulate the refrigerant state (saturated temperature and superheat) in suction port and VI (Vapor Injection) port respectively, and some regulating valves which are controlled by PID controller. The displacement of the tested compressor is tested in two ways. One is using the volumetric flow meter in suction line. The other is using the mass flow meter in liquid line from the condenser. The displacement is calculated through thermal balance. The test result is regarded effective only when the relative error of the two methods is less than 1%. In order to guarantee test accuracy, all the temperature sensors, the pressure sensors, and the instruments are calibrated each year by the qualified institute.
3.
Model establishment
3.1. Working process analysis of a twin screw compressor Fig. 2 (Xing, 2000) shows the working process of a twin screw compressor. When the working volume between the male and the female rotors is closed off the suction port, the compression process begins (Fig. 2(a)). When the working volume is opened to the discharging port, compression process ends (Fig. 2(c)). There are several working spaces under different pressure in which compression is occurring, between the suction port and discharging port (Fig. 2(b)). Owing to the clearance between the rotors, between rotor and case, and between rotors and seats, leakage is unavoidable from high pressure zone to low pressure zone. If the compressed vapor
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leaks into the suction port, it will result the volumetric efficiency drop, which will influence on the real displacement. If the compressed vapor leaks into a lower pressure working space, it has no influence on the volumetric efficiency, but results the input power increase. According to the analysis above, the factor which influences the displacement can use volumetric efficiency, whose calculation will be discussed in the next paragraph, to depict. The factors which influence on the input power can be expressed with several efficiencies, the motor efficiency which represents the relationship of the output and the input of the motor, the built-in volume ratio efficiency stated above which correlates the design parameters and running condition, and the internal leakage efficiency which expresses the integrated leakage effectiveness in compression process. It may be easily regarded that the internal leakage efficiency may be a function of volumetric efficiency. It will be discussed in the following paragraph. Therefore, the following equation is defined. P¼
rs Vws hm hVi hn
(2)
Where, V is the real displacement, V ¼ hvV0. hv is volume efficiency and V0 is the theoretical displacement. hVi is the built-in volumetric ratio efficiency, which is calculated with equation (1). hn is a new defined efficiency in this article, called internal leakage efficiency, which will be discussed in the following. ws is the specific work in an isentropic compression process. The isentropic efficiency can be calculated with the following equation. hs ¼ hVi hn
3.2.
(3)
Volumetric efficiency calculation
Volumetric efficiency equation has different forms for different application objectives. Long Fu et al. (2002) employed a very simple equation form as the following. hv ¼ 0:95 0:0125
p2 p1
Fig. 1 e Schematic diagram of the test stand.
(4)
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Fig. 2 e Working process of a twin screw compressor. Where, p1 and p2 are the suction pressure and the discharging pressure respectively. It is just a pure empirical formula, whose application range is limited. The main advantage of the form is that it has none of the business with any design parameters of the compressor. It can be easily employed under the circumstance that the design parameters of the compressor are not known. Since screw compressor has no suction and discharging check valves, and no clearance volume, Huang Zhong et al. (2002) thought that the volumetric efficiency of a screw compressor was affected only by two factors, leakage in compression process and suction mass decreasing owing to suction vapor being preheated, and gave the following equation form for volumetric efficiency. hv ¼ a
k1 p1 y1 p2 k p2 p1 þb y1 T2 p1 V0
(5)
Where, y1 is the suction specific volume. T2 is the discharging temperature. a and b are coefficients who are regressed with experimental data. On the base of the work of Huang Zhong et al. (2002), the authors further deduced the equation. The suction vapor is preheated by the rotors and the case, whose temperature is higher than suction vapor for absorbing heat from the discharging vapor. According to ideal gas state equation, the ratio between the real suction mass flowrate and the theoretical suction mass flowrate can be expressed as the following. k1 mT T1 p1 k ¼a ¼a m0 T2 p2
(6)
Where, mT and m0 are the real suction mass flowrate and the theoretical suction mass flowrate respectively. a is the correcting factor. According to the theory of compressible fluid, leaking vapor mass flowrate can be calculated by the following equation. ml ¼ CYAl
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2r2 p2 p1
(7)
Where, C is flow coefficient. Al is the sectional area of leaking clearance. r2 is the density under p2. Y is the expansion exponent. Y ¼ 1 Kð1 p1 =p2 Þ. K is a constant. Then, the volumetric efficiency can be calculated by the following equation. hv ¼ a
k1 p1 k ml 1 p2 mT
(8)
Further deduce, the following equation can be gotten qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p 1k1 2k1 CAl 1 K 1 1 2y1 p2 p1 p2 p2 p2 hv ¼ a p1 p1 V0
(9)
Let ε ¼ p2/p1, then 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 hv ¼ aεk ε1 þ b þ cε1 ε2k 2y1 p2 p1
(10)
Where, b ¼ CAl(1 K )/(V0), c ¼ (CAlK )/(V0) a, b and c can be obtained through experimental data regression.
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3.3.
Motor efficiency
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Motor efficiency has no influence on the compression process, but it influences on the input power. The relationship between motor efficiency and the output load percent can be gotten from the motor producer or be gotten from the free load test and holding-up test of the motor. In this article, the author used a fitted polynomial according to the data that the motor producer offered. The equation is expressed as
of compressor, one of the advantages of a screw compressor is that economizer cycle can be easily done with one singlestage compressor. The schematic view and the diagram of Vapor Injection (VI) of a screw compressor are shown in Fig. 4. pb and pbw are the pressures in the working volume and at the VI port respectively. Since there is loss when vapor flows through the VI port, pb must be lower than pbw. According to fluid dynamic theory, the VI mass flowrate can be calculated as the following.
hm ¼ 0:000000000085257a6 þ 0:000000039531015a5
mb ¼ mAb
0:000007425550328a4 þ 0:000710878578191a3 0:036781638486758a2 þ 1:022249912331848a þ 80:49017380645648
(11)
Where, hm is the motor efficiency. a is the output load percent.
3.4.
Internal leakage efficiency
Internal leakage efficiency in this article is used to express the integrated effectiveness of the internal leakage in the compression process. It may be proportional to the internal leakage mass flowrate from the high pressure zone to the low pressure zone, which means that it may be the function of volumetric efficiency. It can be calculated on the base of experimental data once the built-in volumetric ratio efficiency, the volume efficiency, and the motor efficiency are known. Fig. 3 shows the calculated internal leakage efficiency of a screw compressor varying with volume efficiency, according to the experimental data. From the figure, it can be seen that the nearly linear relationship exists between the two parameters. Therefore, it can be fitted with linear regression. hn ¼ dhv þ e
(12)
Where, d and e are the regression coefficients.
3.5.
Vapor injection
Economizer cycle can improve the capacity as well as COP for a one-stage refrigeration system. Compared with other types
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2rb pbw pb
(13)
Where, mb is the VI mass flowrate. m is flow coefficient of VI port. Ab is the section area of VI port. rb is the vapor density at VI port. Usually, pbw can be easily tested with a pressure sensor, while pb can be calculated in the following way. According to thermal dynamic theory, point 20 pressure can be calculated by k p1 p20 ¼ Vib
(14)
Where, Vib is the design built-in volumetric ratio at VI port location. Assume no heat exchanging occurring, the enthalpy of point 9 can be regarded equal to point 8, and the enthalpy of point 2 equal to that of point 20 . According to the mass and energy balance, there are the following equations. m1= þ mb ¼ rb V0 =Vib hv h3 ¼
m1 mb h9 þ h2 m1 þ mb m1 þ mb
(15)
(16)
Where, h is the specific enthalpy. m1 is the mass flowrate entering from the suction port. Solving equations (13), (15) and (16), together with the refrigerant property equations can obtain the pressure pb as well as the VI mass flowrate mb. Owing to the vapor injection, the pressure in the working volume linked to the VI port must be lifted, which makes more vapor leak into the suction port. Therefore, the volume efficiency should slightly drop when VI is available. According to the experimental data of a screw compressor, the scale of the drop is shown in Fig. 5. In the Figure, pVI and pVI0 are the pressures at VI port with and without vapor injection respectively. The dropping scale can be expressed with a linear relationship through experimental data regression. pVI hv ¼ hv0 c1 c2 pVI0
(17)
Where, hv0 is the volume efficiency without vapor injection. c1 and c2 are the coefficient which can be obtained from experimental data regression.
3.6.
Fig. 3 e Relationship between the internal leakage efficiency and volumetric efficiency, according to experimental data.
Slide valve and capacity regulation
Slide valve is the most frequently used device to regulate the capacity for a screw compressor. Compared with VFD (Variable Frequency Drive), the slide valve not only is an economical way to regulate the capacity, but also can let the screw
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Fig. 4 e Diagram of vapor injection of a screw compressor and mixing process in lgp-h diagram.
compressor have good part-load performance. A slide valve and the relationship of the built-in volumetric ratio and the displacement varying with its position are shown in Fig. 6. The discharging port in the slide valve is usually designed in V or U shape. Changing the dimension of N can change the starting discharging angle which determines the design built-in volumetric ratio of the compressor. Commonly, an oil piston is employed to drive the slide valve to make it move along the axial direction of the rotor. The moving of the slide valve can change the effective length of the rotors to lets some sucked vapor bypass into the suction port directly to change the displacement. Commonly, there are two types of discharging port for a screw compressor, the axial discharging port, which is in the discharging seat, and the radial discharging port, which is in the slide valve. Corresponding to the starting discharging angles of the two discharging ports, there are two design builtin volumetric ratios. The built-in volumetric ratio of a compressor varying with the slide valve position can be expressed in the following way.
Fig. 5 e Relationship between the volumetric efficiency and VI pressure.
8 L > > for : x ¼ 0 > > T1 R1 tanðf1 Þ > > N Lþ > > > Z1 > > > T1 R1 tanðf1 Þ > > < Lþ Nx L x x0 Z1 Vi ¼ < Via for : > T1 R1 tanðf1 Þ L > > Lþ Nx > > Z1 > > > > T1 R1 tanðf1 Þ > > Lþ Nx > > L x x0 > Z1 : > Via Via for : L L (18) Where, L is the length of the rotors. T1, R1, f1, Z1 are the lead of the male rotor, the radius of teeth top circle of the male rotor, the helical angle of the teeth of the male rotor, and the number of teeth of the male rotor, respectively. Via is the design built-in volumetric ratio for the axial discharging port. N, x0, x are the geometry dimensions shown in Fig. 6(a). For a given compressor model with the Vi ¼ 2.2 for the radial discharging port and Vi ¼ 4.0 for axial discharging port, the relationship between the built-in volumetric ratio and the slide valve position is shown in Fig. 6(b) and the relationship between the displacement and the slide valve position is shown in Fig. 6(c). Owing to the starting position of a slide valve is not at the terminal face of the rotor, the suction working volume has a jump decrease at the beginning of the slide valve moving, which theoretically results the built-in volumetric ratio a jump drop. With the moving of the slide valve, the built-in volumetric ratio increases first, then decreases when the radial discharging port does not work (Fig. 6(b)). The built-in volumetric ratio varying with the displacement does not follow the rule, because not all sucked vapor before the bypassing port can flow into the suction port for flow resistance (Fig. 6(c)). According to the built-in volumetric ratio and the displacement varying with the slide valve position, the relationship between the built-in volumetric ratio and the displacement can be gotten, just shown as Fig. 6(d). Then for part-load displacement conditions, the built-in volumetric ratio efficiency can be calculated with equation (1). With the decreasing of the effective length of the rotors, the internal leakage efficiency must drop for higher pressure
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Fig. 6 e Slide valve and the relationship of built-in volumetric ratio and displacement varying with its position.
drop per meter along the rotor length. It should be corrected with the displacement percent. hn ¼ hn 100% f ðaÞ
(19)
Where, hn100% is the internal leakage efficiency with full load displacement. f(a) is the correcting factor varying with displacement percent, which can be regressed with experimental data.
4.
Model validation and discussion
4.1.
Tested compressors
Eight compressors who are made with the same teeth profile and manufacturing level were tested with the test stand stated above. The tested condition scope is selected from 12 C to 10 C for saturated suction temperature and from 30 C to 55 C for saturated discharging temperature. The VI pressure scope is set to achieve 0%e25% increase of the input power without VI. The tested displacement scope is from 100% to the minimum (not less than 25%). Some of the experimental data are selected to get the coefficients with regression method. Some key design parameters of the tested compressors are listed in Table 1.
4.2.
Model validation
4.2.1.
Displacement validation
For the compressors tested by the authors, through regressing from the experimental data, the, and in equation (10) are 0.787773, 0.000052881, 0.0024345 respectively. c1 and c2 in equation (17) are gotten by 1.02 and 0.02. Fig. 7 shows the displacement comparison between the tested and model calculated for without and with VI respectively. From the figures, it can be seen that most of the errors between the calculated and the tested are within 2%.
Table 1 e Some key design parameters for the tested compressors. Compressor no.
#1 #2 #3 #4 #5 #6 #7 #8
Theoretical displacement m3 h1
Rating motor power kW
Slide valve Vi
664 790 790 900 1200 1200 1200 1200
89 112 150 130 250 250 250 250
2.2 2.2 3.5 2.2 2.6 2.9 3.1 3.3
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Fig. 7 e The error of displacement between the model prediction and the tested with and without VI.
4.2.2.
Input power validation
For the tested compressor, the coefficients of d and e in internal leakage efficiency equation (12) are 0.75683362, 0.104654476 respectively, regressing from the experimental data. For part-load conditions, the relationship of f(a) in equation (19) is nearly linear relation(Fig. 8). Regressing the experimental data with the linear equation, f(a) can be expressed as. f ðaÞ ¼ 0:00294a þ 0:706
Fig. 8 e The correction coefficient of internal leakage efficiency varying with displacement percent.
(20)
Fig. 9 shows the input power comparison between the model calculated and the tested for with and without VI respectively. Fig. 10 shows the input power comparison for part-load displacement conditions. From the figures, it can be seen that all the predicted data agree well with the tested data. The maximal error for with and without VI is 2%w3%. Most of the errors for part-load displacement condition are within 4%. For low displacement percentage conditions, the errors are slightly higher, the maximal error is about 9%.
Fig. 9 e Comparison of input power between the model prediction and the tested with and without VI.
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4.2.3.
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Vapor injection
The VI mass flowrate comparison between the model calculated and the tested is shown in Fig. 11. The test covers the possible VI port pressure. Shown as the figure, most of the errors are within 2%, but for the low VI flowrate zone, the errors are comparatively higher.
4.3.
Fig. 10 e Comparison of input power for part-load displacement between the model prediction and tested.
Fig. 11 e Comparison of VI mass flowrate between the model predicting and the tested.
Model discussion
Looking back to the model establishment process, some of the key design parameters, including the design built-in volumetric ratio, the slide valve dimensions, the internal leakage effectiveness, the VI and the motor efficiency are considered. It may be deduced that for a specific rotor profile, the model can predict the performance of the compressor with different design built-in volumetric ratios and different displacements, which can also be used to optimize the built-in volumetric ratio for the given running condition. Using this model, the authors calculated the performance of compressor #5 with the built-in volumetric ratios of 2.0e3.6 under the conditions of 2 C for saturated suction temperature and varying saturated discharging temperature from 26 C to 62 C. The results with and without VI are shown in Fig. 12. From the figures, it can be seen that with the running pressure ratio increase, the less power is consumed for the compressor with bigger built-in volumetric ratio. It means the higher the pressure ratio is, the bigger the optimal built-in volumetric ratio should be. The result can be explained by that with the increase of running pressure ratio, the built-in volumetric ratio corresponding to the highest built-in volumetric ratio efficiency gets bigger. Comparing the two figures, it can be found that the optimal design built-in volumetric ratio with VI is definitely smaller than that without VI under the same running condition, which means that the built-in volumetric ratio for compressors running with VI should be smaller than that running without VI if they run under the same condition. The cause for this is that since refrigerant vapor is injected into the working space under compression, the pressure in it, as well as the vapor pressure before discharging, is lifted, which has the same effectiveness of lifting the running
Fig. 12 e Performance comparison for a compressor with different built-in volumetric ratios without and with VI.
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compressor. It can accurately predict the performance of a screw compressor with and without VI in a wide running condition scope and under part-load displacement conditions with a fast speed. Compared with the experimental data, the errors of the model predictions are about 2% for the volumetric displacement, less than 3% for the input power at full load condition, about 4% for the input power at part-load displacement condition, and about 2% and less than 4% for vapor injection mass flowrate. This model has enough precision for refrigeration system simulation.
references
Fig. 13 e Screw compressor performance with and without VI.
pressure ratio. The more the VI mass flowrate is, the lower the optimal built-in volumetric ratio should be. According to the calculation result, under the typical aircooled chiller running condition of 2 C for the saturated evaporating temperature and 50 C for the saturated discharging temperature, the optimal built-in volumetric ratios without and with VI are about 3.5 and 2.9 respectively. In order to verify the conclusion, the compressor with design displacement of 1200 m3 h1 and built-in volume ratios of 2.6, 2.9, 3.1, 3.3 was tested. The result is shown in Fig. 13. From the figure, it can be seen that the compressor with the slide valve of 3.3 built-in volumetric ratio gets the best performance for the conditions without VI, while the compressor with the slide valve of 2.9 built-in volumetric ratio gets the best performance for the condition with VI. It agrees well with the prediction.
5.
Conclusion
On the base of experimental data regression, a screw compressor model is developed, which correlates the running condition and some of the design parameters of a screw
Ding, Guoliang, 2006. Simulation technology for refrigeration and air conditioning appliances. Chinese Sci. Bull. 16, 1913e1928. Ding, Guoliang, 2007. Recent developments in simulation techniques for vapour-compression refrigeration systems. Int. J. Refrigeration 30, 1119e1133. Fu, Long, Ding, Guoliang, Su, Zujian, Zhao, Guoquan, 2002. Steady-state simulation of screw liquid chillers. Appl. Therm. Eng. 22, 1731e1748. Kovacevic, A., Stosic, N., Smith, I.K., 25e28 July 2000. The CFD Analysis of a Screw Compressor Suction Flow. Purdue University, West Lafayette, Indiana. 2000 International Compressor Engineering Conference at Purdue. Lee, W.S., Ma, R.H., Chen, S.L., Wu, W.F., 2001. Numerical simulation and performance analysis of twin screw air compressors. Int. J. Rotating Machine 1, 65e78. Seshaiah, N., Ghosh, Subrata Kr., Sahoo, Ranjit Kr., Sarangi, Sunil Kr., January 2006. Performance Analysis of Oil Injected Twin Screw Compressor. IIT, Guwahati, India. 18th National & 7th ISHMT ASME Heat and Mass Transfer Conference. , Ondrej, 2006. Numerical simulation of leakage Vimmr, Jan, Fryc flow between moving rotor and housing of screw compressor. _ Modelowanie Inzynierskie 32, 461e468. Gliwice. Wu, Huagen, Li, Jianfeng, Xing, Ziwen, 2007. Theoretical and experimental research on the working process of screw refrigeration compressor under superfeed condition. Int. J. Refrigeration 30, 1329e1335. Xing, Ziwen, 2000. Screw Compressor: Theoretical Design and Application. Mechanical Industry Publishing Company of China. Zhong, Huang, Yong, Ding, Chunwu, Sun, 2002. A method of calculating the volumetric flow rate for screw refrigerating compressor. J. Chongqing University (Natural science edition) 25, 118e119.
Available online at www.sciencedirect.com
w w w . i i fi i r . o r g
journal homepage: www.elsevier.com/locate/ijrefrig
A new model of screw compressor for refrigeration system simulation Jinghui Liu*, Qinggang Li, Fazhong Wang, Lei Zhou R&D Department of DUNHAM-BUSH Co., No.1 DUNHAM-BUSH Road, Yantai 264005, China
article info
abstract
Article history:
A performance predicting model of screw compressors, for refrigeration system simula-
Received 14 March 2011
tion, is developed. The model correlates the running condition and some of the design
Received in revised form
parameters of a screw compressor. Compared with the experimental data, the errors of the
29 September 2011
model predictions are about 2% for the volumetric displacement, less than 3% for the
Accepted 16 January 2012
input power at full load condition, about 4% for the input power at part-load displacement
Available online 24 January 2012
condition, and about 2% and less than 4% for vapor injection mass flowrate. This model can also be used to optimize the built-in volumetric ratio of a screw compressor. ª 2012 Elsevier Ltd and IIR. All rights reserved.
Keywords: Refrigeration Screw compressor Vapor injection Part-load performance System simulation
Nouveau mode`le de compresseur a` vis pour la simulation des syste`mes frigorifiques Mots cle´s : Froid ; Compresseur a` vis ; Injection de vapeur ; Performance sous des conditions de charge partielle ; Simulation du syste`me
1.
Introduction
Refrigeration system is becoming more important for people’s daily lives. For the conventional design method of refrigeration system, a prototype unit must be developed and be tested to verify the design. For getting the satisfactory result, the prototype building process may be repeated several times, which will increase the cost and prolong the design period. In order to make the system design process more efficient and economic, system simulation is widely used to predict
the performance and optimize the system design before the equipments are manufactured. Screw compressor is a kind of positive displacement rotary machine. Due to the advantage of high efficiency, wide operating scope and high reliability, it is widely employed in the refrigeration equipments in both commerce and industry, which have gradually substituted for the reciprocating compressor employed in the small cooling capacity unit and part of centrifugal compressor employed in the large cooling capacity unit.
* Corresponding author. Tel.: þ86 05356725250; fax: þ86 05356589999 5816. E-mail address: [email protected] (J. Liu). 0140-7007/$ e see front matter ª 2012 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2012.01.016
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Nomenclature A C k P p R T V Vi h r f h w
2
area, m coefficient polytropic index power, kW pressure radius lead of rotor volume, m3 built-in volumetric ratio efficiency density, kg m3 helical angle of teeth enthalpy, kJ kg1 specific power, kW
Compressor is the heart of refrigeration systems. A good compressor model is the key for system simulation. According to the study objectives, the compressor model can be cataloged into steady model and dynamic model. A complicated dynamic compressor model (Wu et al., 2007; Lee et al., 2001; Seshaiah et al., 2006), as well as CFD model (Kovacevic et al., , 2006), which is usually used to study 2000; Vimmr and Fryc the working process and/or to optimize the structure of the compressor, may make the system simulation run too slowly. It is not suitable for refrigeration system simulation. For the compressor model to predict the refrigeration system performance, three parameters including the refrigerant mass flowrate, the input power and the refrigerant temperature at the compressor exit should be calculated accurately and other unimportant parameters can be ignored (Ding, 2007, 2006). Long Fu et al. (2002) employed a very simple model of the screw compressor in his system simulation. The model only correlates the running condition parameters, including the suction pressure and the discharging pressure, not considered any design parameters of the compressor. Some key design parameters have definitely influence on the performance of a screw compressor. For example, the built-in volume ratio has distinctively contribution to the input power for various running conditions. According to the different ratio of discharging and suction pressure, under-compression or overcompression may occur in its working process, which results more power consumption. The built-in volumetric ratio efficiency can theoretically be deduced as (Xing, 2000). 1 0 k @ k1 ε k 1A k1 hVi ¼ k ε Vi0 k k1 1 þ V Vi0 k 1 i0
(1)
Where, k is polytropic exponent. Vi0 is the built-in volumetric ratio of the compressor for full load condition. ε is the ratio of the discharging pressure and the suction pressure. For a given built-in volumetric ratio, there is a pressure ratio who has the built-in volumetric ratio efficiency equal to
ε y T m a Z
pressure ratio specific volume, m3 kg1 temperature, K mass flowrate, kg s1 load percent, % teeth number
Subscript 0 1 2,3 v m s b
Design parameter, theoretical Male rotor, refrigerant state point refrigerant state point volume motor isentropic vapor injection
1.0. Either lower or higher than the pressure ratio makes the efficiency drop, which means more input power to be needed. Therefore, a too simple compressor model, which does not include the compressor design parameters, is not enough to depict the real performance of a screw compressor in a wide running condition scope. It may make the system simulation result not accurate. Compared with other types of compressor (piston, centrifugal, scroll, etc.), VI (Vapor Injection) is the unique advantage of a screw compressor, which can improve the capacity, as well as COP, of a refrigeration system with economizer cycle. Economizer cycle can easily work with a singlestage screw compressor to realized two-stage compression while two compressors or a two-stage compressor must be used for other types. Few compressor models for system simulation can present the performance of a screw compressor with VI in the referenced articles. Since cooling capacity requirement varies with climate and work schedule, for most of the time, refrigeration systems run under part-load condition. A slide valve is the most frequently used device to regulate the displacement for screw compressors. With the slide valve moving, the displacement can be changed from 100% to 25%, which results the system capacity change. Among the articles the authors have read, few models for system simulation can calculate the part-load displacement performance of a screw compressor, which is important for estimating the running cost of the refrigeration equipments. In order to simulate the performance of the screw compressor in a wide running condition scope, with VI and under part-load displacement conditions, some key design parameters of the compressor must be considered. In this article, a new steady model is developed, which correlates both the running parameters and some key design parameters of the compressor. The coefficients used in the model were regressed on the base of experimental data. The model can predict the performance of the screw compressor with and without VI in a comparatively wide running condition scope and under part-load displacement condition with a fast running speed.
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2.
Test stand
The standard compressor performance test stand in DUNHAM-BUSH Co. (DBYT), which was certified by AHRI and CQC, was used to test the performance of the screw compressors. The systematic diagram of the test stand is shown in Fig. 1. It consists of a compressor which will be tested, an oil separator, a water-cooled condenser which is used to control the discharging pressure of the compressor, a receiver, two mixing tanks which are used to regulate the refrigerant state (saturated temperature and superheat) in suction port and VI (Vapor Injection) port respectively, and some regulating valves which are controlled by PID controller. The displacement of the tested compressor is tested in two ways. One is using the volumetric flow meter in suction line. The other is using the mass flow meter in liquid line from the condenser. The displacement is calculated through thermal balance. The test result is regarded effective only when the relative error of the two methods is less than 1%. In order to guarantee test accuracy, all the temperature sensors, the pressure sensors, and the instruments are calibrated each year by the qualified institute.
3.
Model establishment
3.1. Working process analysis of a twin screw compressor Fig. 2 (Xing, 2000) shows the working process of a twin screw compressor. When the working volume between the male and the female rotors is closed off the suction port, the compression process begins (Fig. 2(a)). When the working volume is opened to the discharging port, compression process ends (Fig. 2(c)). There are several working spaces under different pressure in which compression is occurring, between the suction port and discharging port (Fig. 2(b)). Owing to the clearance between the rotors, between rotor and case, and between rotors and seats, leakage is unavoidable from high pressure zone to low pressure zone. If the compressed vapor
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leaks into the suction port, it will result the volumetric efficiency drop, which will influence on the real displacement. If the compressed vapor leaks into a lower pressure working space, it has no influence on the volumetric efficiency, but results the input power increase. According to the analysis above, the factor which influences the displacement can use volumetric efficiency, whose calculation will be discussed in the next paragraph, to depict. The factors which influence on the input power can be expressed with several efficiencies, the motor efficiency which represents the relationship of the output and the input of the motor, the built-in volume ratio efficiency stated above which correlates the design parameters and running condition, and the internal leakage efficiency which expresses the integrated leakage effectiveness in compression process. It may be easily regarded that the internal leakage efficiency may be a function of volumetric efficiency. It will be discussed in the following paragraph. Therefore, the following equation is defined. P¼
rs Vws hm hVi hn
(2)
Where, V is the real displacement, V ¼ hvV0. hv is volume efficiency and V0 is the theoretical displacement. hVi is the built-in volumetric ratio efficiency, which is calculated with equation (1). hn is a new defined efficiency in this article, called internal leakage efficiency, which will be discussed in the following. ws is the specific work in an isentropic compression process. The isentropic efficiency can be calculated with the following equation. hs ¼ hVi hn
3.2.
(3)
Volumetric efficiency calculation
Volumetric efficiency equation has different forms for different application objectives. Long Fu et al. (2002) employed a very simple equation form as the following. hv ¼ 0:95 0:0125
p2 p1
Fig. 1 e Schematic diagram of the test stand.
(4)
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Fig. 2 e Working process of a twin screw compressor. Where, p1 and p2 are the suction pressure and the discharging pressure respectively. It is just a pure empirical formula, whose application range is limited. The main advantage of the form is that it has none of the business with any design parameters of the compressor. It can be easily employed under the circumstance that the design parameters of the compressor are not known. Since screw compressor has no suction and discharging check valves, and no clearance volume, Huang Zhong et al. (2002) thought that the volumetric efficiency of a screw compressor was affected only by two factors, leakage in compression process and suction mass decreasing owing to suction vapor being preheated, and gave the following equation form for volumetric efficiency. hv ¼ a
k1 p1 y1 p2 k p2 p1 þb y1 T2 p1 V0
(5)
Where, y1 is the suction specific volume. T2 is the discharging temperature. a and b are coefficients who are regressed with experimental data. On the base of the work of Huang Zhong et al. (2002), the authors further deduced the equation. The suction vapor is preheated by the rotors and the case, whose temperature is higher than suction vapor for absorbing heat from the discharging vapor. According to ideal gas state equation, the ratio between the real suction mass flowrate and the theoretical suction mass flowrate can be expressed as the following. k1 mT T1 p1 k ¼a ¼a m0 T2 p2
(6)
Where, mT and m0 are the real suction mass flowrate and the theoretical suction mass flowrate respectively. a is the correcting factor. According to the theory of compressible fluid, leaking vapor mass flowrate can be calculated by the following equation. ml ¼ CYAl
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2r2 p2 p1
(7)
Where, C is flow coefficient. Al is the sectional area of leaking clearance. r2 is the density under p2. Y is the expansion exponent. Y ¼ 1 Kð1 p1 =p2 Þ. K is a constant. Then, the volumetric efficiency can be calculated by the following equation. hv ¼ a
k1 p1 k ml 1 p2 mT
(8)
Further deduce, the following equation can be gotten qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p 1k1 2k1 CAl 1 K 1 1 2y1 p2 p1 p2 p2 p2 hv ¼ a p1 p1 V0
(9)
Let ε ¼ p2/p1, then 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 hv ¼ aεk ε1 þ b þ cε1 ε2k 2y1 p2 p1
(10)
Where, b ¼ CAl(1 K )/(V0), c ¼ (CAlK )/(V0) a, b and c can be obtained through experimental data regression.
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3.3.
Motor efficiency
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Motor efficiency has no influence on the compression process, but it influences on the input power. The relationship between motor efficiency and the output load percent can be gotten from the motor producer or be gotten from the free load test and holding-up test of the motor. In this article, the author used a fitted polynomial according to the data that the motor producer offered. The equation is expressed as
of compressor, one of the advantages of a screw compressor is that economizer cycle can be easily done with one singlestage compressor. The schematic view and the diagram of Vapor Injection (VI) of a screw compressor are shown in Fig. 4. pb and pbw are the pressures in the working volume and at the VI port respectively. Since there is loss when vapor flows through the VI port, pb must be lower than pbw. According to fluid dynamic theory, the VI mass flowrate can be calculated as the following.
hm ¼ 0:000000000085257a6 þ 0:000000039531015a5
mb ¼ mAb
0:000007425550328a4 þ 0:000710878578191a3 0:036781638486758a2 þ 1:022249912331848a þ 80:49017380645648
(11)
Where, hm is the motor efficiency. a is the output load percent.
3.4.
Internal leakage efficiency
Internal leakage efficiency in this article is used to express the integrated effectiveness of the internal leakage in the compression process. It may be proportional to the internal leakage mass flowrate from the high pressure zone to the low pressure zone, which means that it may be the function of volumetric efficiency. It can be calculated on the base of experimental data once the built-in volumetric ratio efficiency, the volume efficiency, and the motor efficiency are known. Fig. 3 shows the calculated internal leakage efficiency of a screw compressor varying with volume efficiency, according to the experimental data. From the figure, it can be seen that the nearly linear relationship exists between the two parameters. Therefore, it can be fitted with linear regression. hn ¼ dhv þ e
(12)
Where, d and e are the regression coefficients.
3.5.
Vapor injection
Economizer cycle can improve the capacity as well as COP for a one-stage refrigeration system. Compared with other types
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2rb pbw pb
(13)
Where, mb is the VI mass flowrate. m is flow coefficient of VI port. Ab is the section area of VI port. rb is the vapor density at VI port. Usually, pbw can be easily tested with a pressure sensor, while pb can be calculated in the following way. According to thermal dynamic theory, point 20 pressure can be calculated by k p1 p20 ¼ Vib
(14)
Where, Vib is the design built-in volumetric ratio at VI port location. Assume no heat exchanging occurring, the enthalpy of point 9 can be regarded equal to point 8, and the enthalpy of point 2 equal to that of point 20 . According to the mass and energy balance, there are the following equations. m1= þ mb ¼ rb V0 =Vib hv h3 ¼
m1 mb h9 þ h2 m1 þ mb m1 þ mb
(15)
(16)
Where, h is the specific enthalpy. m1 is the mass flowrate entering from the suction port. Solving equations (13), (15) and (16), together with the refrigerant property equations can obtain the pressure pb as well as the VI mass flowrate mb. Owing to the vapor injection, the pressure in the working volume linked to the VI port must be lifted, which makes more vapor leak into the suction port. Therefore, the volume efficiency should slightly drop when VI is available. According to the experimental data of a screw compressor, the scale of the drop is shown in Fig. 5. In the Figure, pVI and pVI0 are the pressures at VI port with and without vapor injection respectively. The dropping scale can be expressed with a linear relationship through experimental data regression. pVI hv ¼ hv0 c1 c2 pVI0
(17)
Where, hv0 is the volume efficiency without vapor injection. c1 and c2 are the coefficient which can be obtained from experimental data regression.
3.6.
Fig. 3 e Relationship between the internal leakage efficiency and volumetric efficiency, according to experimental data.
Slide valve and capacity regulation
Slide valve is the most frequently used device to regulate the capacity for a screw compressor. Compared with VFD (Variable Frequency Drive), the slide valve not only is an economical way to regulate the capacity, but also can let the screw
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Fig. 4 e Diagram of vapor injection of a screw compressor and mixing process in lgp-h diagram.
compressor have good part-load performance. A slide valve and the relationship of the built-in volumetric ratio and the displacement varying with its position are shown in Fig. 6. The discharging port in the slide valve is usually designed in V or U shape. Changing the dimension of N can change the starting discharging angle which determines the design built-in volumetric ratio of the compressor. Commonly, an oil piston is employed to drive the slide valve to make it move along the axial direction of the rotor. The moving of the slide valve can change the effective length of the rotors to lets some sucked vapor bypass into the suction port directly to change the displacement. Commonly, there are two types of discharging port for a screw compressor, the axial discharging port, which is in the discharging seat, and the radial discharging port, which is in the slide valve. Corresponding to the starting discharging angles of the two discharging ports, there are two design builtin volumetric ratios. The built-in volumetric ratio of a compressor varying with the slide valve position can be expressed in the following way.
Fig. 5 e Relationship between the volumetric efficiency and VI pressure.
8 L > > for : x ¼ 0 > > T1 R1 tanðf1 Þ > > N Lþ > > > Z1 > > > T1 R1 tanðf1 Þ > > < Lþ Nx L x x0 Z1 Vi ¼ < Via for : > T1 R1 tanðf1 Þ L > > Lþ Nx > > Z1 > > > > T1 R1 tanðf1 Þ > > Lþ Nx > > L x x0 > Z1 : > Via Via for : L L (18) Where, L is the length of the rotors. T1, R1, f1, Z1 are the lead of the male rotor, the radius of teeth top circle of the male rotor, the helical angle of the teeth of the male rotor, and the number of teeth of the male rotor, respectively. Via is the design built-in volumetric ratio for the axial discharging port. N, x0, x are the geometry dimensions shown in Fig. 6(a). For a given compressor model with the Vi ¼ 2.2 for the radial discharging port and Vi ¼ 4.0 for axial discharging port, the relationship between the built-in volumetric ratio and the slide valve position is shown in Fig. 6(b) and the relationship between the displacement and the slide valve position is shown in Fig. 6(c). Owing to the starting position of a slide valve is not at the terminal face of the rotor, the suction working volume has a jump decrease at the beginning of the slide valve moving, which theoretically results the built-in volumetric ratio a jump drop. With the moving of the slide valve, the built-in volumetric ratio increases first, then decreases when the radial discharging port does not work (Fig. 6(b)). The built-in volumetric ratio varying with the displacement does not follow the rule, because not all sucked vapor before the bypassing port can flow into the suction port for flow resistance (Fig. 6(c)). According to the built-in volumetric ratio and the displacement varying with the slide valve position, the relationship between the built-in volumetric ratio and the displacement can be gotten, just shown as Fig. 6(d). Then for part-load displacement conditions, the built-in volumetric ratio efficiency can be calculated with equation (1). With the decreasing of the effective length of the rotors, the internal leakage efficiency must drop for higher pressure
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Fig. 6 e Slide valve and the relationship of built-in volumetric ratio and displacement varying with its position.
drop per meter along the rotor length. It should be corrected with the displacement percent. hn ¼ hn 100% f ðaÞ
(19)
Where, hn100% is the internal leakage efficiency with full load displacement. f(a) is the correcting factor varying with displacement percent, which can be regressed with experimental data.
4.
Model validation and discussion
4.1.
Tested compressors
Eight compressors who are made with the same teeth profile and manufacturing level were tested with the test stand stated above. The tested condition scope is selected from 12 C to 10 C for saturated suction temperature and from 30 C to 55 C for saturated discharging temperature. The VI pressure scope is set to achieve 0%e25% increase of the input power without VI. The tested displacement scope is from 100% to the minimum (not less than 25%). Some of the experimental data are selected to get the coefficients with regression method. Some key design parameters of the tested compressors are listed in Table 1.
4.2.
Model validation
4.2.1.
Displacement validation
For the compressors tested by the authors, through regressing from the experimental data, the, and in equation (10) are 0.787773, 0.000052881, 0.0024345 respectively. c1 and c2 in equation (17) are gotten by 1.02 and 0.02. Fig. 7 shows the displacement comparison between the tested and model calculated for without and with VI respectively. From the figures, it can be seen that most of the errors between the calculated and the tested are within 2%.
Table 1 e Some key design parameters for the tested compressors. Compressor no.
#1 #2 #3 #4 #5 #6 #7 #8
Theoretical displacement m3 h1
Rating motor power kW
Slide valve Vi
664 790 790 900 1200 1200 1200 1200
89 112 150 130 250 250 250 250
2.2 2.2 3.5 2.2 2.6 2.9 3.1 3.3
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Fig. 7 e The error of displacement between the model prediction and the tested with and without VI.
4.2.2.
Input power validation
For the tested compressor, the coefficients of d and e in internal leakage efficiency equation (12) are 0.75683362, 0.104654476 respectively, regressing from the experimental data. For part-load conditions, the relationship of f(a) in equation (19) is nearly linear relation(Fig. 8). Regressing the experimental data with the linear equation, f(a) can be expressed as. f ðaÞ ¼ 0:00294a þ 0:706
Fig. 8 e The correction coefficient of internal leakage efficiency varying with displacement percent.
(20)
Fig. 9 shows the input power comparison between the model calculated and the tested for with and without VI respectively. Fig. 10 shows the input power comparison for part-load displacement conditions. From the figures, it can be seen that all the predicted data agree well with the tested data. The maximal error for with and without VI is 2%w3%. Most of the errors for part-load displacement condition are within 4%. For low displacement percentage conditions, the errors are slightly higher, the maximal error is about 9%.
Fig. 9 e Comparison of input power between the model prediction and the tested with and without VI.
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4.2.3.
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Vapor injection
The VI mass flowrate comparison between the model calculated and the tested is shown in Fig. 11. The test covers the possible VI port pressure. Shown as the figure, most of the errors are within 2%, but for the low VI flowrate zone, the errors are comparatively higher.
4.3.
Fig. 10 e Comparison of input power for part-load displacement between the model prediction and tested.
Fig. 11 e Comparison of VI mass flowrate between the model predicting and the tested.
Model discussion
Looking back to the model establishment process, some of the key design parameters, including the design built-in volumetric ratio, the slide valve dimensions, the internal leakage effectiveness, the VI and the motor efficiency are considered. It may be deduced that for a specific rotor profile, the model can predict the performance of the compressor with different design built-in volumetric ratios and different displacements, which can also be used to optimize the built-in volumetric ratio for the given running condition. Using this model, the authors calculated the performance of compressor #5 with the built-in volumetric ratios of 2.0e3.6 under the conditions of 2 C for saturated suction temperature and varying saturated discharging temperature from 26 C to 62 C. The results with and without VI are shown in Fig. 12. From the figures, it can be seen that with the running pressure ratio increase, the less power is consumed for the compressor with bigger built-in volumetric ratio. It means the higher the pressure ratio is, the bigger the optimal built-in volumetric ratio should be. The result can be explained by that with the increase of running pressure ratio, the built-in volumetric ratio corresponding to the highest built-in volumetric ratio efficiency gets bigger. Comparing the two figures, it can be found that the optimal design built-in volumetric ratio with VI is definitely smaller than that without VI under the same running condition, which means that the built-in volumetric ratio for compressors running with VI should be smaller than that running without VI if they run under the same condition. The cause for this is that since refrigerant vapor is injected into the working space under compression, the pressure in it, as well as the vapor pressure before discharging, is lifted, which has the same effectiveness of lifting the running
Fig. 12 e Performance comparison for a compressor with different built-in volumetric ratios without and with VI.
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compressor. It can accurately predict the performance of a screw compressor with and without VI in a wide running condition scope and under part-load displacement conditions with a fast speed. Compared with the experimental data, the errors of the model predictions are about 2% for the volumetric displacement, less than 3% for the input power at full load condition, about 4% for the input power at part-load displacement condition, and about 2% and less than 4% for vapor injection mass flowrate. This model has enough precision for refrigeration system simulation.
references
Fig. 13 e Screw compressor performance with and without VI.
pressure ratio. The more the VI mass flowrate is, the lower the optimal built-in volumetric ratio should be. According to the calculation result, under the typical aircooled chiller running condition of 2 C for the saturated evaporating temperature and 50 C for the saturated discharging temperature, the optimal built-in volumetric ratios without and with VI are about 3.5 and 2.9 respectively. In order to verify the conclusion, the compressor with design displacement of 1200 m3 h1 and built-in volume ratios of 2.6, 2.9, 3.1, 3.3 was tested. The result is shown in Fig. 13. From the figure, it can be seen that the compressor with the slide valve of 3.3 built-in volumetric ratio gets the best performance for the conditions without VI, while the compressor with the slide valve of 2.9 built-in volumetric ratio gets the best performance for the condition with VI. It agrees well with the prediction.
5.
Conclusion
On the base of experimental data regression, a screw compressor model is developed, which correlates the running condition and some of the design parameters of a screw
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