Modeling of two-phase transcritical CO2 ejectors for on-design and off-design conditions

S. TASLIMI TALEGHANI*, M. SORIN & S. PONCETDepartment of Mechanical Engineering, Université de Sherbrooke, Sherbrooke (QC), J1K2R1, Canada

* Correspondance : Sahar.Taslimi@usherbrooke.ca

REFERENCES1. G. Besagni, R. Mereu, and F. Inzoli, “Ejector refrigeration: a comprehensive review,” Renew. Sustain. Energy Rev., vol. 53, pp. 373–407, 20162. S. Taslimitaleghani, M. Sorin, and S. Poncet,“Energy and exergy efficiencies of Different configurations of the ejector-based CO2 refrigeration systems,” Int. J. Energy Prod. Manag. vol. 3, pp. 22–

33,2018.3. K. Ameur, Z. Aidoun, and M. Ouzzane, “Modeling and numerical approach for the design and operation of two-phase ejectors,” Appl. Therm. Eng., vol. 109, Part A, pp. 809–818, 20164. N. Galanis and M. Sorin, “Ejector design and performance prediction,” Int. J. Therm. Sci., vol. 104, pp. 315–329, 2016.5. M. Khennich, N. Galanis, and M. Sorin, “Effects of design conditions and irreversibilities on the dimensions of ejectors in refrigeration systems,” Appl. Energy, vol. 179, pp. 1020–1031, 2016.6. O. Samaké, N. Galanis, and M. Sorin, “On the design and corresponding performance of steam jet ejectors,” Desalination, vol. 381, pp. 15–25, 2016.7. S. Taslimitaleghani, M. Sorin, and S. Poncet, “Modeling of two-phase transcritical CO2 ejectors for on-design and off-design conditions,” In press, Int. J. Refrigration., 20178. J. Smolka, Z. Bulinski, A. Fic, A. J. Nowak, K. Banasiak, and A. Hafner, “A computational model of a transcritical R744 ejector based on a homogeneous real fluid approach,” Appl. Math. Model, vol.

37, no. 3, pp. 1208–1224, 2013.

A two-phase transcritical CO2 cycle

Principal [1]:

Accelerating motive flowEntraining suction flowMixing of two streams Compression

Application of a two-phase ejectorfor an expansion work recoverycycle (EERC) [2] :

Increasing cooling capacity due toisentropic expansion

Reducing the throttling lossesDecreasing the compressor work and COP

improvement due to the increase of thesuction pressure

Mo

de

l Val

idat

ion

& R

esu

lts

[7]

9. Y. Zhu, Z. Wang, Y. Yang, and P.-X. Jiang, “Flow visualization of supersonic two-phase transcritical flow of CO2 in an ejector of a refrigeration system,” Int. J. Refrigeration, vol. 74, pp. 352–359, 2017.10. K. Banasiak and A. Hafner, “1D Computational model of a two-phase R744 ejector for expansion work recovery,” Int. J. Therm. Sci., vol. 50, no. 11, pp. 2235–2247, 2011.

Acknowledgments: This project is part of the CRD research program on Industrial Energy Efficiency established at Université de Sherbrooke in 2014. It has received the support of Hydro-Québec, Natural Resources Canada (Canmet Energy), Rio Tinto Alcan and the Natural Sciences and Engineering Research Council of Canada.

Schematic of an ejector with relevant notations

The

rmo

dyn

amic

Mo

de

ling

[7]

Thermodynamic model

on-design

Given opertaingcondition

Double chocking

off-design

Givengeometry

single chocking

Double chocking

Assumptions

Flow is one dimensional, adiabatic and steady state

Heat transfer between the streams and walls is neglected.

The homogeneous equilibrium model is assumed for the two-phase flow

[3].

The CO2 thermodynamic and transport properties of the primary and

secondary flows are obtained from real fluid properties.

The inlet velocities of the primary and secondary flows are negligible

(stagnation conditions).

Constant polytropic efficiency coefficients are used to account for friction

losses in the nozzles and the diffuser.

The friction losses in the mixing chamber are negligible, however a friction

factor is calculated for constant area duct.

Mass flux maximization criterion is used for both nozzles, as previously

done for single-phase [4–6] and two-phase ejectors [3].

Both primary and secondary fluids are choked at design condition (double

choking).

A normal shock wave takes place at the inlet of constant area duct and the

mixing of two streams is complete before the shock occurrence.

Procedure for CO2 two-phase ejector modeling fora fixed geometry [7]

ሶ𝒎𝒑(g.s-1)

𝑷𝒑

(𝒌𝑷𝒂)

𝑻𝒑(˚C)

Present

workExperiment Error (%)

Experiments ofSmolka et al.

[8]

9915 29.9 54.68 49.73 9.958668 33.4 34.8 31.94 8.959091 26.7 51.3 48.42 5.959850 35.5 45.85 40.73 12.579455 36.3 39.98 35.69 12.028846 36.5 31.93 29.84 7.0048465 35.4 29.51 26.07 13.195

Experiments of Zhu et al. [9]

8002 33.3 33.75 33.95 0.5897980 33.2 33.67 33.45 0.6587690 33.1 27.54 31.23 11.8167300 31.3 24.4 26.74 8.7517240 30.5 24.49 24.9 1.6478440 33.3 39.11 36.76 6.3938390 33.4 38.3 34.97 9.5227940 33.4 32.7 32.19 1.5847610 31.7 31.88 27.54 15.7598910 34.5 43.55 38.46 13.2348640 34.1 40.31 36.96 9.0648550 34.2 38.92 34.88 11.5837910 33.9 30.59 31.02 1.3867500 32.1 26.02 27.12 4.056

Experiments ofBanasiak and Hafner [10]

10112 39.3 39.56 42.25 6.37

𝑷𝒓𝒂𝒕𝒊𝒐

𝑷𝒑

(𝐤𝐏𝐚)

𝑻𝒑(˚C)

𝑷𝒔

(𝐤𝐏𝐚)𝑻𝒔(˚C)

ERPresent

workExperiment

Error(%)

Case 1 9915 29.9 3996 17.4 0.674 1.141 1.096 4.06

Case 2 8668 33.4 3652 6.6 0.57 1.137 1.115 2.01

Case 3 9091 26.7 3595 7.6 0.69 1.132 1.077 5.1

Case 4 9850 35.5 5149 20.7 0.6619 1.103 1.08 2.14

Case 5 9455 36.3 4761 15.1 0.6475 1.107 1.0878 1.78

Case 6 8846 35.6 4255 13.7 0.545 1.113 1.097 1.49

Case 7 8465 35.4 3874 10.3 0.458 1.130 1.106 2.19

Pressure (kPa) Present work

Experiment [9] Error (%)

Pd 4637 4601.46 0.77

Py 3912 3940 0.71

Pmix 4520 4460 1.34

Operating conditions : Pp=10112 kPa, Tp=39.3˚C, Ps=3952 kPa, Ts=5.5°C, ER=0.42

Comparison of calculated pressures at different cross sections of the ejector

Validation of the thermodynamic model with experimental data of Smolka et al. [8]

Comparison of calculated dimensions with values from literature [10]

D,L (mm) Da Dth Dpm D2 Dm Dmix Dd L1

Calculation 6.204 0.992 1.44 4.0485 2.137 2.117 6.215 9.726

Experiment [10] 6 0.96 - - - 3 6 9.4

D,L (mm) L2 L3 L4 L3+L4 L5 L6 Ltot L5/Dmix

Calculation 2.76 2. 58 0.026 2.607 15.54 46.93 77.57 7.344

Experiment [10] 3.72 - - 2.5 24 34.36 74 8

Effect of polytropic efficiencies on ejector dimensions and efficiencies

D, L (mm)

ηpol,p=0.9ηpol,s=0.9ηpol,d=0.8

ηpol,p=0.85ηpol,s=0.9ηpol,d=0.8

ηpol,p=0.9ηpol,s=0.85ηpol,d=0.8

ηpol,p=0.9ηpol,s=0.9ηpol,d=0.75

ηpol,p=1ηpol,s=1ηpol,d=1

D1 6.204 6.295 6.204 6.204 6.04

Dth 0.9921 1.007 0.9921 0.9921 0.9644Dp2 1.088 1.106 1.088 1.088 1.057Dpm 1.44 1.465 1.44 1.44 1.398Dm 2.137 2.153 2.154 2.137 2.075

Dy (Dmix) 2.117 2.139 2.127 2.117 2.057Dd 6.215 6.215 6.215 5.98 6.506L1 9.726 9.867 9.726 9.726 9.471L2 2.76 2.817 2.757 2.761 2.664L3 2.58 2.637 2.565 2.581 2.514L4 0.026 0.0188 0.0348 0.026 0.0241

L3+L4 2.607 2.656 2.5998 2.607 2.538L5 15.54 4.881 9.936 9.778 116.3L6 46.93 46.68 46.81 44.25 50.95Ltot 77.57 66.9 71.83 69.12 181.9

(L5/Dy) 7.344 2.282 4.67 4.62 56.55ηis,p 0.9014 0.852 0.9014 0.9014 1ηis,s 0.903 0.903 0.8543 0.903 1ηis,d 0.7959 0.7962 0.7961 0.7456 1

Distributions of axial pressure and mean velocity along the axis of the ejector for double chocking conditions and different back pressures Pd

Distributions of pressure, velocity and entropy along the axis of the ejector for single choking conditions and different

primary flow inlet conditions

Entrainment ratio versus compression ratio for different primary flow pressures

Comparison of calculated mass flow rates with experimental data for CO2

Critical mode of an ejector

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Entr

ain

men

t R

atio

(ER

)Pressure

Critical point

PLimPcrit

Pd

Double chocking Single chocking

Procedure to evaluate the dimensions of a two-phase ejector [7]

mix