Mathematical model of bypass behaviors used in scroll compressor

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Mathematical model of bypass behaviors used in scroll compressor

Yangguang Liu

a

, Chinghua Hung

a,*

, Yuchoung Chang

b

a

Department of Mechanical Engineering, National Chiao Tung University, EE452, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan b

Energy and Environment Research Laboratories, Industrial Technology Research Institute, Taiwan

a r t i c l e

i n f o

Article history:

Received 11 February 2008 Accepted 19 May 2008 Available online 5 June 2008 Keywords: Bypass Valves Scroll compressor Efﬁciency

a b s t r a c t

This paper has constructed a bypass mechanism mathematical model in scroll-type compressor (STC) and has been integrated into a simulation package to predict the STC performance. The bypass mechanism, when added to a fixed scroll, is used to prevent over-compression and liquid slugging. Under five specified oper-ating conditions, it was found that the STC with the bypass action increased the isentropic efficiency 2.5–10% more than the STC without the bypass action. Meanwhile, the calculated results of the developed model have been validated by a STC testing apparatus. In addition, it was found that the design of the bypass mechanism in the paper, can completely avoid over-compression and pressure discrepancy while the STC is in operation. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction

The scroll-type compressor (STC) of variable pressure ratio was developed in recent years due to higher efﬁciency and power sav-ing considerations. The pressure ratio is deﬁned as the ratio of the saturated condenser pressure to the saturated evaporator pressure ðpdis

psÞ, and is decided by operating conditions.

In general, volume ratio is fixed after the geometrical parame-ters of the STC have been decided. When the pressure ratio does not match with the volume ratio of the STC, two cases, over-com-pression and under-comover-com-pression, will happen[1]. For under-com-pression, the repetitive compression in the final chamber or back flow from discharge chamber will occur in different designs of STC. For over-compression, the STC will compress the gas to its de-sign point regardless of the high pressure in chambers and extra work is consumed. Under-compression could not be avoided ex-cept by designing a STC with low volume ratio while narrowing the range of operating conditions. Nevertheless, over-compression could be reduced by using bypass valves added to the fixed scroll. Discussions of bypass valves of STC are seldom seen in papers but have been presented in several patents. Murayama et al.[2] de-signed two groups of bypass holes for each compression chamber with valves operated by pressure to prevent over-compression. Fuji et al.[3]use a plurality of symmetrical bypass holes to avoid over-compression caused by the open delay of the bypass valves. A STC with a back pressure mechanism for axial seal and bypass valves for over-compression is also exposed[4]. In addition, a study using bypass mechanism and optimization of the volume ratio in STC was presented to improve efficiency by 10–20% under the conditions of

both low speed and low pressure ratio[5]. Even so, the examples above merely illustrated the design of bypass valves with abbrevi-ated drawings and brief statements. They do not disclose the de-tailed mathematical models of the bypass mechanism, such as the selection of the position of bypass holes, valve models, and the by-pass behavior during the compression and discharge process.

This paper constructs a general bypass valves model and inte-grates it into an already developed STC package[6]. Through the simulation results, the effects of bypass mechanism in the STC are investigated. The reliability and accuracy of this model were veriﬁed by the experimental test platform for an actual STC prod-uct using CO2as refrigerant.

2. Mathematical models

The whole mathematical models of STC include the geometry of the scroll, thermodynamics with refrigerant in compression and discharge processes, leakage through clearances, back pressure mechanism, superheat of suction pipe, and dynamic balance of mechanical components. For simplicity, some assumptions must be employed in the models:

(1) Refrigerant in working chambers is homogeneous. (2) Gravitational, kinetic energy variations are neglected. (3) Oil effects are neglected.

(4) Chambers of the scroll pairs are symmetrical. (5) The bypass holes are located at ﬁxed scroll. 2.1. Geometrical model of scrolls

The proﬁles of a pair of scrolls in the study are created by an involute with base circle. Equations of a ﬁxed scroll can be written as follows:

*Corresponding author. Tel.: +886 3 5712121 55160; fax: +886 3 5720634. E-mail addresses:[email protected](Y. Liu),[email protected] (C. Hung).

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Applied Thermal Engineering

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xfi o¼ rb½cos / þ ð/

a

Þ sin /

yfi o¼ rb½sin / ð/

a

Þ cos / ð1Þ

xfi i¼ rb½cos / þ ð/ þ

a

Þ sin /

yfi i¼ rb½sin / ð/ þ

a

Þ cos / ð2Þ Some fundamental calculations were derived from the papers[7,8]. 2.2. Geometry of bypass holes

The scroll pairs were divided into several symmetrical cham-bers initially as shown inFig. 1a. The relation of bypass holes be-tween ﬁxed scroll and orbiting scroll during the orbiting operation can be derived by using coordinates transformation. 2.2.1. Corresponding angle of the orbiting scroll

First, the range of one bypass hole’s position (Fig. 1a) with outer proﬁle(1)on the ﬁxed scroll is considered as follows:

/o uP /o aP /o l When /o u>2

p

; /o u¼ /r

p

ðN iÞ2

p

:i ¼ 1; 2; . . . ; N /o l¼ /o u 2

p

ð3Þ When /o u62

p

; /o u¼ /r

p

ðN iÞ2

p

:i ¼ 1; 2; . . . ; N /o l¼ 0

After the involute angle /o_ais deﬁned, the other two parameters, r

and d, shown inFig. 1b, as constraints must be satisﬁed as follows:

0 6 r 6 t=2 r 6 d 6 pt t r

ð4Þ

It is important to provide reasonable values to assure the simulated results are physically meaningful.

Secondly, by observingFig. 1b, the center of the bypass hole can be derived accordingly. Letting the slope m as:

xt¼ rbcos /o a yt¼ rbsin /o a ð5Þ m ¼ðyo a ytÞ ðxo a xtÞ

The center of the bypass hole at the ﬁxed scroll is:

xo By¼ xo aþ d cosðtan1mÞ

yo By¼ yo aþ d sinðtan1mÞ

(

ð6Þ

Then the line equation from the tangential of basic circle of the ﬁxed scroll to the center of bypass hole was derived as:

y ¼ mðx xo ByÞ þ yo By ð7Þ

The equations of the inner proﬁle of the orbiting scroll and(7)are considered simultaneously as:

y ¼ mðx xo ByÞ þ yo By

x ¼ rb½cos / þ ð/

a

Þ sin / þ robcos h

y ¼ rb½sin / ð/

a

Þ cos / robsin h

ð8Þ

Nomenclature

A area (m2₎

ABy uncovered cross-section area (m2)

C coefﬁcient ()

Cvalve spring constant of valve (N m1)

CC1 convergence criterion ()

d distance between wrap proﬁle and center of bypass hole (m)

dtu tube diameter (m)

f ﬂow friction factor (m)

G refrigerant mass ﬂow rate (kg min1₎

h height (m)

htu coefﬁcient of heat convection (W m2K1)

Li length of the inner involute (m)

Lo length of the outer involute (m)

li distance between inner involute and bypass hole center (m)

lo distance between outer involute and bypass hole center (m)

_

m mass ﬂow rate (kg s1₎

m slope ()

N, n turn number of scrolls; polytropic index () p, P pressure (MPa); power (W)

Pr Prandtl number ()

pt pitch of scroll (m)

Re Reynolds number ()

r radius of bypass hole (m) rb basic radius (m) req equal radius (m) rob orbiting radius (m) t thickness (m) V volume (m3) x, y coordinate () Greek symbols

a

initial angle of involute (°)

d clearance (m)

/ involute angle of scroll (°)

h orbiting angle of scroll (°)

k coefﬁcient of heat conductivity (W m1_K1₎

q

density (kg m3₎

x

rpm (rev min1₎ Subscripts b base circle back back-side C, c isentropic; current dis discharge dw downstream e end-side eq equivalent f ﬂank

fi_i inner involute of fixed scroll fi_o outer involute of fixed scroll

i index number

in inlet

l leakage

l,c current leakage

l,e end side leakage

l,p previous leakage

motor motor

out outlet

o_a corresponding involute angle for bypass hole o_By Bypass hole coordinate to outer involute

o_l lower limit of the outer involute angle for bypass hole o_u upper limit of the outer involute angle for bypass hole ob_i inner involute of orbiting scroll

ob_o outer involute of orbiting scroll r roll angle of scroll

s suction

s,h superheat

t tangent coordinate

up upstream

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Newton–Raphson method is used to solve these numerically and the corresponding involute angle / on orbiting scroll can be ob-tained eventually.

2.2.2. Uncovered area of the bypass holes

While / is determined, the relations between the center of the bypass hole and orbiting scroll proﬁle can be deﬁned asFig. 1c. Therefore, two parameters lo and li are derived as:

lo ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxo By xob oÞ2þ ðyo By yob oÞ 2 q li ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðxo By xob iÞ 2 þ ðyo By yob iÞ 2 q ð9Þ

These two parameters can be used to deﬁne the uncovered area of the bypass hole.

If lo < li holds, four possible calculations exist:

(A): As Condition (A) in Fig. 2, if li P t + r, then the uncovered area is

ABy¼

p

r2 ð10Þ

(B): As Condition (B) inFig. 2, if li P t and li < t + r, then

ABy¼

p

tan1 ðr 2_lo2 Þ0:5 lo " # ( ) r2_{þ loðr}2_lo2 Þ0:5 ð11Þ

(C) As Condition (C) inFig. 2, if li P t r and li < t, then

ABy¼ r2tan1 ðr2_lo2 Þ0:5 lo " # loðr2_lo2 Þ0:5 ð12Þ

(D) As Condition (D) inFig. 2, if li 6 t r, then ABy= 0.

If lo > li, those calculations still hold if the definition of the two parameters are interchanged. Aside from the uncovered area of the bypass holes to the outer profile of the orbiting scroll, the calculation to the inner profile proceeds similarly. 2.2.3. Corresponding chambers to bypass holes

Due to the motion of the orbiting scroll, the bypass holes may span to different chambers during a cycle. Determination of

Fig. 2. Uncovered areas of the orbiting scroll and the bypass hole. Fig. 1. Scheme of bypass holes (a) range of positions (b) relations from ﬁxed scroll

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corresponding chambers to bypass holes must be performed. Observing the variations of the uncovered area of the bypass holes at current and previous steps during a cycle is a way to settle it. 2.3. Bypass valve model

A one-dimensional valve was used for simplicity [8]and the dynamics of the bypass valve was neglected. If the pressure in the compression chamber surpasses pdis, the valve opens and the

distance raised is determined with static forces balance relation:

y ¼

p

r2

eqðp pdisÞ

1

Cvalve

ð13Þ

where reqis the equivalent radius for the uncovered area as follows:

req¼

ABy

p

0:5

ð14Þ

Then the equivalent ﬂow area is calculated by

Aeq¼ 2

p

reqy ð15Þ

2.4. Compression process

The mass conservation of refrigerant in chambers during the compression process is

_

m ¼ _min _mout ð16Þ

The refrigerant state in the control volume can be described by a polytropic process[9]as follows:

pc¼ ps

q

c

q

s

n

ð17Þ

where n can be measured by laboratory experiment[10]. 2.5. Refrigerant property

The Refprop 7[11]published by NIST is a powerful tool that is used to obtain lots of data in thermodynamics for most refriger-ants. This study integrates it by linking the dynamic link libraries to acquire the related properties.

2.6. Suction heating of the inlet refrigerant

The inlet refrigerant is heated by the suction pipe in the STC and the pipe is filled with refrigerant which flows out from the dis-charge chamber. The heat transfer coefficient for the pipe can be expressed by the Gnielinski relationship[12]:

htu¼

k dp

ðf =8ÞðRe 1000ÞPr

1 þ 12:7pffiffiffiffiffiffiffiffif =8ðPr2=3 1Þ ð18Þ

Then the suction superheat can be evaluated. 2.7. Back-pressure mechanism

The back-pressure may be decided to be either proportional to psor pdis[8]. Because psor pdischanges with operating conditions,

so the back-pressure would change, which would cause difﬁculties in designing a balanced mechanism to maintain suitable seal. Tsubono et al.[4]has shown that it is appropriate to treat back-pressure as proportional to ps only, and the simpliﬁcation was

adopted in this study. 2.8. Leakage and bypass

Generally, end-side and ﬂank leakage occur in the STC and can be shown as follow:

_

ml¼ _ml;eþ _ml;f ð19Þ

where _ml;eand _ml;f are the end-side and ﬂank leakage mass ﬂow

rates. Gap sizes of the two kinds of leakage are both dynamically re-lated to pressure ratio[8]and back-pressure. The end-side gap de, in

meters, can be derived as shown below:

de¼ 1:02 pd pback ps 0:45 106 ð20Þ

The end-side ﬂow areas can be calculated[8]as

Ain¼ de Z /kþ1 /k Lod/ Aout¼ de Z /kþ1 /k Lid/ ð21Þ

where /k+1 and /kare the involute angles of the conjugate end

points for the scroll pair.

For end-side leakage, one-dimensional isentropic compressible ﬂow[8]is used as _ ml;e¼ C A pup

q

up 2n n 1 pdw pup !2 n pdw pup !nþ1 n 2 4 3 5 8 < : 9 = ; 0:5 when pdw pup ! P 2 n þ 1 n n1 ; _ ml;e¼ C A pup

q

up n 2 n þ 1 nþ1 n1 " #0:5 ð22Þ when pdw pup ! < 2 n þ 1 n n1

where A is Ainor Aoutfor inﬂowing or outﬂowing conditions.

Simi-larly, the ﬂank gap is expressed in meters as follows:

df¼ 6 pdis pback ps þ 20 106 ð23Þ

The ﬂank ﬂow area[13]is

Af¼ hdf ð24Þ

For _ml;f, Eq.(22)is also used with A = Af. Then the total leakage mass

ﬂow rate can be calculated. In additions, the bypass ﬂow rate can also be obtained by using Eq.(22)but substituting A with Aeq.

3. Computer model and simulation process

The simulation process with the computer package was devel-oped by using C++ Builder, EXCEL and REFPROP 7. The inputs and outputs of the models and simulation process are described below. 3.1. Inputs

The inputs of the STC package include scroll geometry, related mechanisms, bypass valves, operating conditions and motor inputs that came from a dynamometer test.

3.2. Simulation process

The ﬂowchart of the package is shown inFig. 3a. The leakage and bypass model is included in the process and solved with numerical iterations. The ﬂowchart of the leakage and bypass mod-el is shown inFig. 3b. When the pressure in the chamber is greater

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than the pressure of the discharge chamber (pdis), the bypass action

occurs. Then the bypass ﬂow can be calculated as leakage ﬂow in the model. The 4th R–K method was the solution with convergent criterion as follows: j _ml;p _ml;cj _ ml;c <CC1 ð25Þ 3.3. Outputs

Three outputs used in the follow-up sections are stated as follows: (1) Volumetric efﬁciency:

g

V¼ _ ms;h _ml _ ms ð26Þ (2) Isentropic efﬁciency:

g

C¼ Padiabatic Pmotor ð27Þ

(3) Refrigerant mass ﬂow rate:

G ¼

g

V ðVs

q

s

x

motorÞ ð28Þ

4. Results and discussion

A CO2STC product is used for the simulation. The scheme of the

STC and design of the bypass holes are shown inFig. 4. The geo-metric parameters of the scroll pairs and bypass holes are dis-played inTable 1. It can be seen that bypass hole 1 and bypass hole 2 are related to the outer involute and bypass hole 10

and by-pass hole 20to the inner involute. Five operating conditions for the simulation are used and the details are shown inTable 2.

The behavior of bypass holes can determine how long the holes would be exposed to the orbiting scroll during one orbiting cycle,

however, the actual bypass action only occurs when the pressure in the chambers is greater than the pressure in the discharge chamber. Furthermore, thermodynamic calculation can estimate the amount of bypass ﬂow rate.

4.1. Effect of bypass valves behavior 4.1.1. Bypass holes 1 and 2

Fig. 5shows the change of uncovered area of the four bypass holes. It can be seen that the bypass hole 1 initially opened in chamber 2 and is covered by the orbiting scroll from 180° to 256°. Afterward, it opens in chamber 3 up to the end of the orbiting cycle. The bypass hole 2 is uncovered in chamber 2 from 0° to 20°, and is covered up to 66°. Then it appeared again in chamber 3 and remains there toward the end of the cycle.Fig. 6a illuminated that the two bypass holes may take effect in chamber 2 only from 720° to 797° (discharge angle) during the whole orbiting cycle, and after that, chamber 2 reaches the discharge stage. Similarly, chamber 3 also has a stage from 360° to 426° where the bypass holes were closed.

For chamber 2, the discharge angle of the scroll pairs must be considered. Since after the discharge angle, chamber 2 will com-municate with chamber 1 and proceed to the discharge process. Therefore, if the discharge angle is appropriate, chamber 2 can avoid over-compression completely during the orbiting cycle. The discharge angle, 797°, is inside the useful acting interval of the by-pass hole 1 (0°–180°), so the design is good for chamber 2.

For chamber 3, discharge angle does not interfere with bypass action, hence it merely needs to design bypass holes that can ap-pear during the orbiting cycle. However,Fig. 6a shows that there are no bypass holes that open in chamber 3 from 360° to 426°. Though the interval is not very long, it is possible to cause over-compression in chamber 3. Besides, chamber 3 inhales refrigerant from the suction chamber. If too much liquid refrigerant ﬂows into chamber 3, it could arise liquid slugging because of no bypass dur-ing the interval. It implies that the design of bypass holes in cham-ber 3 must be improved further.

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4.1.2. Bypass hole 10and 20

Returning to Fig. 5 again, bypass hole 10 is initially open in chamber 20

and closed after 194°. At 260°, it is opened again in

chamber 30. A similar trend occurs to bypass hole 20, which is opened initially in chamber 30and closed at 180°. After 260°, the hole is uncovered again in the next chamber (suction chamber).

As shown inFig. 6b, chamber 20

also can retain no over-com-pression during the cycle. For chamber 30, it can be seen that from 540° to 620°, bypass holes are covered, and if the refrigerant in chamber 30

is over-compressed, there is no passage to bypass it. The design of bypass holes in chamber 30may cause serious effects because generally speaking, over-compression occurs at the mid-dle or later interval in outer chambers and at the early interval in inner chambers during a cycle. Hence, the possibility of over-compression in chamber 30may occur during 540°–620° because of the lack of bypass effect.

Therefore, different geometrical designs could produce different design requirements for the bypass holes. Geometrically, the major consideration is to design bypass holes which have longer uncov-ered intervals during an orbiting cycle.

4.2. Effect of bypass valves in thermodynamics 4.2.1. Effects with and without bypass action

Five conditions originated from JRAIA (Japan Refrigeration and Air Conditioning Industry Association) JRA4050:2005 were simu-lated with and without bypass action.Fig. 7shows the compared simulation results in G,

g

Vand

g

Cof the STC with and without

by-pass action. It can be seen that G and

g

Vhave hardly been

inﬂu-enced by bypass action but

g

C, which is related to the power

consumption of the compression process, changes ﬁercely and de-pends on various operating conditions. Improvement for bypass action in

g

Cat conditions 2 and 5 are almost 10% and 6% at

condi-tion 1, which implies the importance of the bypass accondi-tion, even though at conditions 3 and 4, a lesser improvement of 2.5% was found. The observations above explain the necessity of designing Table 1

Parameters of the STC

Parameters Value

Basic circle radius (rb) (mm) 1.91

Thickness of the scroll (t) (mm) 3

Roll angle of the scroll (/r) (degree) 990

Height of the scroll (h) (mm) 4.27

Involute angle of bypass hole 1 (/o_a) (degree) 234

Radius of bypass hole 1 (r) (mm) 0.73

Distance of bypass hole 1 (d) (mm) 1.21

Involute angle of bypass hole 10

(/o_a) (degree) 402

Radius of bypass hole 10

(r) (mm) 0.73

Distance of bypass hole 10

(d) (mm) 1.34

Involute angle of bypass hole 2 (/o_a) (degree) 407

Radius of bypass hole 2 (r) (mm) 0.73

Distance of bypass hole 2 (d) (mm) 0.92

Involute angle of bypass hole 20(/o_a) (degree) 770

Radius of bypass hole 20

(r) (mm) 0.73

Distance of bypass hole 20

(d) (mm) 1.57 Table 2 STC operating conditions Refrigerant CO2 Suction pressure (MPa) Discharge pressure (MPa) Motor revolution (RPM) Condition 1 3.67 10.44 2400 Condition 2 4.37 10.59 2892 Condition 3 3.25 11.19 3180 Condition 4 2.82 10.79 4200 Condition 5 4.5 11.06 2892

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bypass valves in varied pressure ratio STC for more efﬁcient and power-saving purposes.

4.2.2. Variation of pressure inside the compression chambers Take notice ofFigs. 5 and 6again. Chambers 3 and 30are sym-metrical with the same volume and the same change rate of

vol-ume during an orbiting cycle. The same conditions hold for chambers 2 and 20. If bypass holes are designed inappropriately, they could produce pressure differences between the symmetrical chambers if bypass action occurs. Though the amount is small, the difference could affect the dynamic balance of scroll pairs and other mechanical components in STC [14]. For this reason, the

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design of bypass holes should make bypass action occurs at the same interval as far as possible in symmetrical chambers during a cycle and uncovered areas should close to equal.

Fig. 8presents the simulation results of the pressure variations inside the compression chambers with and without bypass action. ThroughFigs. 6 and 8, it can be seen that the design of the four by-pass holes can completely prevent over-compression during the orbiting cycle under these ﬁve conditions. The pressure discrepan-cies between chambers 2, 3 (Fig. 8a) and chambers 20

, 30

(Fig. 8b)

Fig. 8. Prediction of pressure variation with and without bypass valves (a) chambers 2, 3 (b) chambers 20

, 30

. Fig. 6. Uncovered area of bypass holes in (a) chambers 2 and 3 (b) chambers 20

and 30

.

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during the cycle are small, so the inﬂuence to dynamic balance can be neglected. However, the explanation cannot guarantee other operating conditions, because for chamber 3, bypass holes do not open during 360°–426° (Section4.1.1) and for chamber 30do not open during 540°–620° (Section 4.1.2) of the orbiting cycle. Be-sides, the liquid slugging may occur in chamber 3. Hence, the de-sign of current STC in the study can be further improved by using optimum method to determine better bypass holes for varied operating conditions.

4.2.3. Veriﬁcation of bypass action

The simulation results were validated through the experimental apparatus which was developed by ITRI in cooperation with SINTEF [15,16]. A CO2STC product for heat pump system was installed in

the testing apparatus, as a sample. The compared results are shown inTable 3. It was found that the models conform to the experimen-tal results very well and the relative errors for these three results (G,

g

Vand

g

C) are 3.2% to 0.8%, 2.7% to +1.2%, 0.7% to +2%,

respectively. The models provided in the study can predict the per-formance with bypass action accurately.

5. Conclusions

The study has constructed a bypass mechanism mathematical model for preventing over-compression and liquid slugging inside the chambers of STC. Five aspects of the research are summarized below:

(1) The change of uncovered areas of bypass holes can be derived through the whole orbiting cycle of the developing STC by using coordinate transformation and some numerical schemes. Then the open and closed interval and correspond-ing chambers are also determined.

(2) The model is integrated into the compression and discharge processes of a comprehensive STC simulation package that can predict general efﬁciencies and performance.

(3) The model has been simulated under ﬁve speciﬁed operating conditions with and without bypass action and its accuracy has been validated by the experimental testing apparatus for a developing CO2STC product. It was found that the STC in

this study with bypass valves increases 2.5% to 10% in isen-tropic efﬁciency and volumetric efﬁciency is scarcely affected.

(4) Pressure variations inside the chambers can also be viewed from the simulation results. It was found that the design of the bypass holes in the study can avoid over-compression completely inside the compression chambers under the ﬁve operating conditions. However for other different conditions, over-compression may occur because an interval (540°–620°) with covered bypass hole in chamber 30exists during the orbiting cycle. In addition,

liquid slugging probably occurs at the initial stage (360° to 426°) in chamber 3.

(5) When exploiting a STC product for varied pressure ratio, the bypass valves model presented in the research is a useful tool that can determine whether the design is suitable or not for speciﬁc operating conditions. In addition, it can be further combined to an optimization tool to obtain new designs for particular conditions.

Acknowledgement

The authors would like to express gratitude for ﬁnancial sup-port from the Energy and Environment Research Laboratories, Industrial Technology Research Institute in Taiwan.

References

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[16] H. Rekstad, Technical speciﬁcations of CO2-compressor test rig, Technical Report No. 03082192212, SINTEF Energy Research, 2007.

Table 3

Comparison between simulation and experimental results of G,gVandgC Refrigerant CO2

G (kg/min) gV gC

Simulation Experimental Error (%) Simulation Experimental Error (%) Simulation Experimental Error (%)

Condition 1 0.7 0.721 2.9 0.782 0.8 2.3 0.59 0.59 0.0

Condition 2 1.134 1.125 0.8 0.85 0.84 1.2 0.651 0.64 1.7

Condition 3 0.818 0.845 3.2 0.759 0.78 2.7 0.566 0.57 0.7

Condition 4 0.956 0.973 1.7 0.773 0.78 0.9 0.571 0.56 2.0