1d analysis of co2 sub-cooled/supercritical ejector refrigeration cycle

1D ANALYSIS OF CO 2 SUB-COOLED/SUPERCRITICAL EJECTOR 

REFRIGERATION CYCLE: EXPERIMENTAL RESULTS 

E. BOU LAWZ KSAYER , D. CLODIC 

Ecole des mines de Paris, Center for Energy and Processes 

60, Boulevard Saint Michel – F- 75272 Paris Cedex 06, France 

Phone : +33 1 40 51 91 67; Fax : +33 1 46 34 24 91 

elias.boulawz_ksayer@ensmp.fr 

ABSTRACT 

An ejector expansion transcritical CO 2 refrigeration cycle is proposed to improve the performance of 

the basic transcritical CO 2 cycle by reducing the expansion process losses. A 1D analysis is carried 

out in order to investigate the ejector performance of a sub-cooled/supercritical refrigeration cycle 

using supercritical CO 2 as working fluid. More than 18 ejectors composed by a nozzle and a body are 

realized and tested on a test bench. Experimental results are used to adapt the 1D model. A sensitivity 

study is performed to investigate the effect of the evaporating and gas cooler outlet temperatures on 

the ejector energy performances. Also, the effect of the ejector geometry is analyzed. 

The COP of the ejector expansion transcritical CO 2 cycle can be improved by more than 12% 

compared to the conventional transcritical cycle for typical air conditioning operating conditions. 

NOMENCLATURE 

Symbol 

Subscripts 

COP Coef. of performance adim. cal 

d, D diameter m cp 

ettas surface efficiency adim. cr 

L length m cst area 

M,MFR mass flow rate g/s d 

P pressure MPa eff 

Q,q cooling capacity W ej 

s entropy kJ/kg. K ev 

SH superheat K exp 

T temperature °C gc 

V,v velocity m/s max 

w entrainment ratio adim. mix, m 

x quality kg/kg n 

o 

opt 

Greek letter 

p 

s 

efficiency adim. 

sat 

kinetic viscosity Pa.s th 

density kg/m 3 

calculated 

constant pressure 

critical 

constant area 

diffuser 

effective 

ejector 

evaporator, evaporation 

experimental 

gas cooler 

maximum 

mixture 

nozzle 

outlet 

optimal 

primary flow 

secondary flow, threshold 

saturation 

throat 

1. INTRODUCTION 

In a conventional vapor compression refrigeration cycle using an expansion valve, through which the 

refrigerant is expanded from the condenser/ gas cooler pressure to the evaporator pressure, throttling 

8 th IIR Gustav Lorentzen Conference on Natural Working Fluids, Copenhagen, 2008 1

losses are one of the highest thermodynamic losses. When the refrigerant pressure decreases, the 

current isenthalpic process dissipates the refrigerant kinetic energy as friction heat. The isenthalpic 

process generates a larger quantity of refrigerant vapor flash compared to isentropic process. As a 

result, the refrigerating capacity is reduced. In order to recover part of the potential kinetic energy of 

the expansion process, various researchers have attempted to use other expanders rather than the 

expansion engine. An ejector constitutes an attractive alternative to the expansion valve of 

refrigeration systems because of its low cost, its ability to handle two-phase flow without damage, and 

there is no moving parts [2,3,4,5,6]. 

A 1D model of the CO 2 ejector has been developed to characterize the ejector operation. This 

document presents the validation of the 1D model and the description of the CO 2 ejector operation for 

different geometries, and different evaporating and gas cooler outlet temperatures. 

Models are validated generally referred to experimental results or by compared to validated models. 

For the ejector 1D model, a test bench has been designed to test ejectors, which have been sized using 

the 1D model. The main constraint that affects the test bench components is the CO 2 high pressure. 

The main objective of the test bench is the validation of the 1D model of sub-cooled/ supercritical 

ejector cycle. 

To reduce the costs of the test bench and to 

obtain more accurate measured values, the 

heat exchangers are cooled by water. The test 

bench includes a cooled water loop and a CO 2 

refrigeration loop (Figure 1). 

The measured error is lower than 3% 

compared to the different calculated values. 

Taking in account the uncertainty span of the 

measurement instruments, the estimated error 

on the capacities is lower than 5%. 

2. TEST-BENCH COMPONENTS 

Figure 1: CO 2 refrigeration loop with ejector. 

3. EJECTOR TEST RESULTS AND 1D MODEL ADAPTATION 

The objectives of the tests are: 

- Adaptation of the 1D model of the ejector. 

- Characterization of the constant pressure chamber (CPC) length. 

- Characterization of the constant area chamber (CAC) diameter. 

A CFD study of vapor ejector has shown that the diffuser length should be larger than 9 D const area , and 

the CAC length should be larger than 3 D const area . Therefore, the realized ejector bodies have a CAC 

length varying between 6.3 and 8.6 D const area , and the lengths of the diffusers vary between 10.8 and 

40.7 D const area (Figure 2.a). 

4. TESTS 

54 different ejectors can be assembled based on the different parts realized for the tests: 

- 6 body cores (constant area diameter of 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 mm) 

- 3 nozzles (throat diameter of 0.75, 1.0, and 1.25 mm) 

- 3 disc thicknesses (8, 12, and 16 mm). 

18 assembled ejectors have been sufficient to adapt the 1D model and to characterize the non-tested 

ejectors. The test result interpretation is divided in two parts: nozzle characterization and ejector body 

characterization. 


Cst Pressure chamber 

Cst area chamber 

Nozzle 

Body 

core 

Body 

a. Assembled ejector scheme. b. Assembled ejector. 

Figure 2: Ejector design. 

5. NOZZLE CHARACTERIZATION 

Three nozzles with different throat diameters (0.75, 1.0, and 1.25 mm) are tested with variable inlet 

parameters of temperature and pressure: 25 < T o,gc < 50 °C, and 6 

Many authors described the CO 2 expansion flow through nozzles and fixed orifices [1,7], but 

experimental results of the nozzle show that the expansion efficiency in the nozzle convergent is close 

to one and so the expansion can be considered as isentropic. The flow passing through the nozzle 

at the throat is considered as the maximum flow, and phase change can occur in the nozzle 

convergent. At the throat, the flow quality varies from zero (saturated liquid) to one (saturated 

vapor). 

Figure 3.b shows that the relative error between the measured and calculated mass flow rates is lower 

than ±2%. The flow characteristics through a nozzle are as follows: 

- the expansion through our convergent nozzle is isentropic (efficiency = 1) 

- the flow is maximum at the nozzle throat 

- when the downstream pressure is higher than the calculated throat pressure, the throat pressure 

is the downstream pressure. 

T (K) 

340 

330 

320 

310 

300 

290 

280 

T sat liq T sat vap Inlet Throat max 

270 

0,8 1 1,2 1,4 1,6 1,8 2 

s (kj/kg K) 

MFR calculated (g/s) 

50 

45 

40 

35 

30 

25 

20 

15 

15 20 25 30 35 40 45 50 

MFR measured (g/s) 

b. Comparison of measured and calculated mass 

a. Position of test points in CO 2 T-s diagram. 

flow rates. 

Figure 3: Experimental results of the ejector nozzles. 

Figure 4.a presents the nozzle inlet pressure obtained when keeping constant the gas cooler outlet 

temperature while varying the high-side pressure P gc , 4.a, and according to the following assumptions: 

- saturated state at the throat for P sat , 

- maximum mass flow rate for P max , 

- isentropic expansion in the nozzle ( n = 1). 


P (MPa) 

8 

7 

6 

5 

4 

3 

2 

1 

P sat P max T gc = 32°C 

P gc = 8.75 MPa 

0 

5 6 7 8 9 10 11 12 13 14 15 16 

P gc (MPa) 

mnozzle (g/s) 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

6 7 8 9 10 11 12 13 

Pgc (MPa) 

b. Variation of nozzle mass flow rate with P 

a. T gc = 32 °C, P s = 8.75 MPa. 

gc for 

d th =1 mm. 

Figure 4: Variation of the saturated flow and the maximum flow throat pressure with P gc . 

To each T gc , corresponds a threshold gas cooler pressure P gc,s : 

- where the two assumptions are true: P gc P gc,s ; and 

- a P gc range in which only the maximum flow assumption is true: P gc 

Figure 4.b shows that the mass flow rate of the nozzle increases with P gc and decreases with T gc . 

The new adapted nozzle assumptions will be used to characterize the ejector body operation. 

6. BODY CHARACTERIZATION 

According to the ejector 1D model, four parameters should be determined: 

- The nozzle divergent expansion efficiency: n . 

- The secondary flow expansion efficiency: s . 

- The mixture efficiency: m . 

- The diffuser efficiency: d . 

Assuming that n = s and fully developed flow in the CAC, the ejector outlet parameters: pressure 

and quality, are significantly lower than the measured ones. So, the following assumptions are made: 

- The nozzle and secondary flows are considered isentropic: n = s = 1. 

- The diffuser compression is isentropic: d = 1. 

- The two refrigerant flows go through an effective area in the CAC. This effective area is 

characterized by an effective surface efficiency, that will be called ettas and defined as: 

2 

effective area d 

area 

effective 

ettas 

(1) 

d 

constarea 

 

- The CPC (constant pressure chamber) pressure is calculated assuming that the maximum 

entrainment ratio, w, is sucked (Figure 6). 

- The mixture efficiency m is calculated to meet the measured ejector outlet pressure. 

Analyzing ettas and m values lead to the elaboration of empirical equations expressing these values 

as a function of the flow and ejector parameters: 

Re f ( , v , d , , x , , , P ) 

(2) 

ettas 

th 

Re f ( , v , d , 

, 

, w) 

th 

th 

vap, th th sec sec in, 

sec 

m 

 

th th th vapth 

(3) 

ettas f (Re 

ettas 

, dcstarea 

, dth 

) 

(4) 

f (Re m 

) 

m 

(5) 

7. CPC LENGTH 

The effect of the CPC length has been investigated experimentally to define the optimal length. 

28 

30 

35 

40 

45 

50 


m CO2 (g/s) 

35 

30 

25 

20 

15 

10 

5 

m max = 32.22 g/s 

P th,max = 5.97 MPa 

0 

0 2 4 6 8 10 

P th (MPa) 

Figure 5: Variation of CO 2 mass flow rate with the 

throat pressure for P gc = 8.5 MPa and T gc = 35 °C. 

w 

0.25 

0.2 

0.15 

0.1 

0.05 

w max = 0.2226 

P ch,max = 2.87 MPa 

0 

0 1 2 3 4 

P chamber (MPa) 

Figure 6: Variation of CO 2 mass flow rate with the 

CPC pressure for P gc = 8.5 MPa, T gc = 35 °C, 

ettas = 1, T oev = 7 °C and P o,ev = 3.673 MPa. 

Three different lengths L cp of the CPC are analyzed for three different nozzle diameters (0.75 mm, 

1 mm, and 1.25 mm). 

The comparison of ettas and m for different nozzle throat diameters, presented in Figure 7, show that 

these two parameters were not affected by L cp . Therefore, the experimental results prove that the 

tested CPC length L cp does not affect the ejector performance for values ranging from 1.8 to 5 d cst area 

on one side, and from 3.6 to 16.6 d th . 

ettas 

8 mm 12 mm 16 mm 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 0.5 1 1.5 2 2.5 

Re d 

ettas 

th = 1mm 

m 

8 mm 12 mm 16 mm 

0.85 

0.8 

0.75 

0.7 

0.65 

0.6 

0.55 

0.5 

0.6 0.7 0.8 0.9 1 

Re m 

dth = 1 mm 

a. ettas for d th = 1.0 mm b. m for d th = 1.0 mm 

Figure 7: Variation of ettas and m with L cp for different throat diameters. 

8. EXPERIMENTAL RESULT RELIABILITY 

For experimental tests, the gas cooler pressure is varied from 6 to 12.5 MPa and the gas cooler outlet 

temperature from 26 to 45 °C to analyze the subcritical and the supercritical operation modes of the 

ejector. 

The differences between the measured and the calculated values vary from ± 5 to ± 15%. 

For the ejector with nozzle throat diameter d th = 1 mm, the differences between measured and 

calculated values of ettas are lower than 10 % and lower than 5% for m , (Figures 8.b and 8.d). Four 

different constant area diameters are studied: 2, 2.5, 3, and 3.5 mm. 

The increase of d cst area decreases the area efficiency ettas. 

ettas 

ettas ettas cal 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 0.5 1 1.5 2 2.5 

Re ettas 

a. Variation of ettas with Re ettas for different d cst area 

2, 2.5, 3, and 3.5 mm. 

Calculated 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

+ 10% 

0 0.2 0.4 0.6 0.8 1 

Experimental 

- 10% 

b. Differences between the calculated and the 

measured ettas. 


m 

0.9 

0.85 

0.8 

0.75 

0.7 

0.65 

0.6 

h m 

h m cal 

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 

Re m 

Calculated 

0.9 

0.85 

0.8 

0.75 

0.7 

0.65 

+ 5% 

- 5% 

0.6 

0.6 0.65 0.7 0.75 0.8 0.85 0.9 

Experimental 

c. Variation of m with Re m for different d cst area : d. Differences between the calculated and the 

2, 2.5, 3 and 3.5 mm. 

measured m . 

Figure 8: Reliability of ettas and m for d th = 1.0 mm. 

9. EFFECT OF d cst area 

The 1D model is adapted by including ettas and m . These efficiencies are expressed as a function of 

the ejector geometrical parameters: d cst area and d th , and the flow thermodynamic parameters. 

For T ev = 2 °C, and T gc = 35 °C, the variation of the constant area diameter shows the existence of a 

critical diameter d cr (Figure 9): 

- when d cst area < d cr , the surface efficiency ettas is 1, and the ejector does not operate correctly. 

- when d cst area > d cr , the ejector operates with constant performances. 

%COP 

10% 

5% 

0% 

-5% 

-10% 

-15% 

-20% 

-25% 

0 1 2 3 4 

d const area (mm) 

Figure 9: Variation of COP improvement with 

d cst area for T ev = 2 °C, T gc = 35 °C, SH = 5 K. 

d eff (mm) 

2 

1.9 

1.8 

1.7 

1.6 

1.5 

1.4 

1.3 

1.2 

1.1 

1 

25 30 35 40 45 

T gc (°C) 

Figure 10: Variation of d eff with T gc for 

T ev = 2 °C, SH = 5 K. 

For T ev = 2 °C, the effective critical diameter is drawn as a function of T gc , (Figure 10). The effective 

critical diameter decreases with the increase of T gc . 

Consequently, due to the high velocity of the primary flow and the entrained secondary flow, the flow 

is flowing at the center of the CAC, surrounded by a dead zone in which the velocity is equal to the 

wall velocity, Figure 11. In the dead zone, a closed circulation loop can occur without affecting the 

flows. 

Figure 11: Ejector effective flow. 

10. VARIATION Of T gc And T ev 

Considering the ejector composed of a nozzle of 1-mm throat diameter, the ejector performance is 

studied as a function of the evaporating temperature, the gas cooler outlet temperature, and the 

evaporator outlet superheat. 

The effect of the gas cooler outlet temperature on the COP, the evaporating capacity, the effective 

diameter, and the gas cooler outlet pressure of the ejector transcritical CO 2 cycle are shown in Figure 

12. It can be seen that the gas cooler pressure increases with the gas cooler outlet temperature T gc , but 


the evaporating capacity and the effective diameter d eff decrease with T gc . The COP improvement 

presents an optimum value for a defined T gc and T ev . The optimal T gc increases with the increase of 

T ev . For T ev = 2 °C, the COP is improved when T gc varies between 27 and 37 °C. The maximal 

improvement is 10% at T gc = 30 °C. 

The effect of the evaporation temperature on the COP improvement, the evaporator capacity, the 

effective diameter, and the gas cooler outlet pressure of the ejector transcritical CO 2 cycle are shown 

in Figure 12. 

P gc (MPa) 

10 5 2 -1 

12 

11 

10 

9 

8 

7 

6 

25 30 35 40 45 

T gc (°C) 

Q ev (W) 

10000 

9000 

8000 

7000 

6000 

5000 

4000 

3000 

2000 

1000 

0 

10 5 2 -1 

25 30 35 40 45 

T gc (°C) 

a. Gas cooler outlet pressure. b. Evaporator capacity. 

3 

10 5 2 -1 

20% 

10 5 2 -1 

2.5 

10% 

d eff (mm) 

2 

1.5 

1 

%COP 

0% 

-10% 

-20% 

-30% 

0.5 

-40% 

0 

25 30 35 40 45 

T gc (°C) 

-50% 

25 30 35 40 45 

T gc (°C) 

c. Effective diameter. d. COP improvement. 

Figure 12: Variation of ejector parameters with the gas cooler outlet temperature T gc for different 

evaporation temperatures, SH = 5 K. 

It can be seen that the gas cooler pressure increases with the evaporation temperature T ev . Also the 

evaporating capacity and the effective diameter d eff increase with T gc . The COP improvement presents 

an optimum value for defined T ev and T gc . The optimal T ev increases with the increase of T gc . For T gc 

= 35 °C, the COP is improved for T ev varying from 0 to 8 °C, with maximal improvement of 10% 

around T ev = 4 °C. 

The CO 2 ejector refrigeration cycle operates in steady state and so is the mass balance. By varying the 

evaporation temperature T ev between –10 and 10 °C, and the gas cooler outlet temperature T gc between 

26 and 45 °C, and considering a superheat of 5 K, the gas cooler operating pressure is calculated using 

the 1D model and a correlation is elaborated to express P gc as a function of T ev and T gc . 

The error between the model values and the correlation is lower than 3%. The correlation is used as 

reference value to control the high-side pressure of the ejector refrigeration system. 

P gc = a + b T gc + c T ev + d T ev 2 +e T ev 3 (6) 

a b c d e 

3.70416 0.1245456 0.076715 0.01052402 0.000752 

11. CONCLUSION 

For the ejector refrigeration system, 18 ejectors have been tested. The experimental results were used 

to characterize the ejector operation: nozzle and body. 

For the tested nozzle, the expansion through the convergent nozzle has been found to be isentropic. 

Also it has been proven that the maximum flow passes through the orifice separating two chambers at 


different pressures: the upstream pressure is higher than the saturation pressure and, downstream the 

throat, CO 2 is in two-phase flow. 

P gc (MPa) 

d eff (mm) 

12 

11 

10 

9 

8 

7 

28 30 35 40 

6 

-15 -10 -5 0 5 10 15 

3 

2.5 

2 

1.5 

1 

0.5 

T ev (°C) 

Q ev (W) 

28 30 35 40 

10000 

9000 

8000 

7000 

6000 

5000 

4000 

3000 

2000 

1000 

0 

-15 -10 -5 0 5 10 15 

T ev (°C) 

a. Gas cooler outlet pressure. b. Evaporator capacity. 

28 30 35 40 

0 

-15 -10 -5 0 5 10 15 

T ev (°C) 

%COP 

28 30 35 40 

20% 

10% 

0% 

-10% 

-20% 

-30% 

-40% 

-50% 

-60% 

-70% 

-15 -10 -5 0 5 10 15 

c. Effective diameter. d. Cop improvement. 

Figure 13: Variation of ejector parameters with the evaporation temperature T ev for different gas 

cooler outlet temperatures, SH = 5 K. 

For the tested bodies, it has been found that: 

- The CPC length does not affect the ejector performance. 

- The 1D model of the ejector has been adapted by introducing a surface efficiency ettas and a 

mixing efficiency m . These efficiencies are expressed as functions of the flow and the ejector 

parameters. 

- There is a critical constant area diameter above which the ejector performance is constant. For 

constant area diameter lower than the critical diameter, the ejector performance will be 

hampered. 

A parametric study of the ejector refrigeration system has been performed as a function of the 

evaporating temperature, the gas cooler outlet temperature, and the evaporator outlet superheat. The 

COP improvement of the ejector refrigeration system is about 12% for T gc = 30 °C, T ev = 2 °C and 

SH = 5 K. 

REFERENCES 

[1]. J.P. Chen , J.P. Liu, Z.J. Chen, Y.M. Niu: “Trans-critical R744 and two-phase flow through short 

tube orifices”, International Journal of Thermal Sciences 43 (2004) 623–630. 

[2]. Somchai Wongwises, Somjin Disawas: Performance of the two-phase ejector expansion 

refrigeration cycle”, International Journal of Heat and Mass Transfer 48 (2005) 4282–4286. 

[3]. Da-Wen Sun: “Comparative study of the performance of an ejector refrigeration cycle operating 

with various refrigerants”, Energy Conversion & Management 40 (1999) 873 – 884. 

[4]. Daqing Li, Eckhard A. Groll. "Transcritical CO2 refrigeration cycle with ejector-expansion 

device". International Journal of Refrigeration 28 (2005) 766–773. 

[5]. Somjin Disawas, Somchai Wongwises. "Experimental investigation on the performance of the 

refrigeration cycle using a two-phase ejector as an expansion device". International Journal of 

Refrigeration 27 (2004) 587–594. 

[6]. J.M. Chang, B.J. Huang : "Empirical correlation for ejector design”, International Journal of 

Refrigeration 22 (1999) 379–388. 

[7]. K. Martin, R. Rieberer, J. Hager : "Modelling of Short Tube Orifices for CO 2 ”, R111, 

International Refrigeration and Air Conditioning Conference at Purdue, July 17-20, 2006. 

T ev (°C)

1d analysis of co2 sub-cooled/supercritical ejector refrigeration cycle

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