Direct Analytical Modeling for Optimal, On-Design Performance of Ejector for Simulating Heat-Driven Systems
Abstract
:1. Introduction
- A new analytical model is proposed, which is a direct model and does not need iterative processes to get performance prediction;
- This model uses a systematic approach by employing CFD analysis rather than hit-and-trial approach to calculate the ejector efficiencies;
- The proposed model agrees with data published by various researchers for on-design prediction of ejector performance;
- Ejector performance curves produced with the model are presented;
- System simulation and comparison results for ERS and CCP system have been produced;
- The practical applications of the proposed model involve the designing and optimization of thermal systems involving ejectors, for example, ejector refrigeration systems, ejector enhanced ORC systems and other hybrid systems.
2. The Analytical Modeling of Ejector
- The model is developed to simulate the on-design, optimum ER values for given conditions. Both motive and suction flows acquire chocked conditions for the critical delivery pressure.
- This model is independent of the size of the ejector, that is, it is non-dimensional or 0-D model and is not able to simulate off-design performance.
- It is assumed that the ejector operates at adiabatic and steady-state conditions.
- Both the inlet velocities are assumed to be negligible, that is, stagnation condition is assumed.
- Both the inlets (motive and suction) are assumed to be at a saturated vapor state.
- The speed at the exit of the ejector is assumed to be negligible.
- The diffuser efficiency accounts for the whole compression (pressure gain) process loss due to shock and diffuser section.
- At Section 2, suction fluid is considered to be chocked, and therefore, it is possible to find the pressure of the constant area mixing section by utilizing the thermodynamic relations.
- For the motive fluid’s expansion calculations, its k-value (exponent for compression and expansion) has been taken as constant.
2.1. Governing Equations
2.2. Computational Procedure
2.3. Finding the Ejector Efficiencies
2.4. CFD Modelling of Ejectors
3. Results and Discussion
3.1. Validation of CFD Modelling
3.2. Validation of the Analytical Model
3.3. Ejector Performance Curves
3.4. Thermal Systems Performances
3.4.1. Ejector Refrigeration System (ERS)
3.4.2. Combined Cooling and Power (CCP) System
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
Nomenclature
0 D | Zero-dimensional |
1 D | One-dimensional |
2 D | Two-dimensional |
CCP | Combined Cooling and Power |
CFD | Computational fluid dynamics |
COP | Co-efficient of Performance |
D | Diameter, mm |
EES | Engineering Equation Solver |
ER | Entrainment Ratio |
ERS | Ejector Refrigeration System |
EVCC | Enhanced Vapour Compression Cycle |
HVAC | Heating, ventilation and air conditioning |
h | Enthalpy, kJ/kg |
k | Isentropic exponent |
m | Mass flow rate, kg/s |
NXP | Nozzle exit position, mm |
ORC | Organic Rankine Cycle |
P | Pressure, bar |
T | Temperature, °C |
V | Velocity, m/s |
η | Efficiency |
Subscripts | |
1 | Motive (primary) fluid inlet section |
2 | Entrance of the mixing chamber |
3 | Section where the primary and secondary fluids are fully mixed |
4 | Location of section just before the shock wave |
5 | Location of section just after the shock wave |
6 | Secondary (suction) fluid inlet |
7 | Diffuser outlet |
c | Condenser (or delivery) |
d | Diffuser |
e | Evaporator (suction / secondary) |
g | Generator (motive / primary) |
id | Ideal |
is | Isentropic |
m | Mixing-chamber |
mc | mixing chamber (constant-area) |
n | Nozzle (supersonic, converging-diverging) |
p | Primary or motive fluid |
s | Secondary or suction fluid |
t | Throat, primary nozzle |
Appendix A
Appendix A.1. 1-D Model by Huang et al.
Variable | Value | Units | Variable | Value | Units | Variable | Value | Units |
---|---|---|---|---|---|---|---|---|
A3 | 0.00006642 | m2 | Ap1 | 0.0000159 | m2 | Apy | 0.00002564 | m2 |
Apyi | 0.00002914 | m2 | AR | 10.64 | - | Asy | 0.00004078 | m2 |
At | 0.000006243 | m2 | cpg | 939.3 | J/kg-K | cvg | 807.2 | J/kg-K |
Dp1 | 0.0045 | m | Dt | 0.00282 | m | Effp | 0.95 | - |
Effs | 0.85 | - | ER | 0.4682 | - | Fim | 0.8 | - |
Fip | 0.88 | - | Kg | 1.164 | - | M3 | 0.6595 | - |
Mm | 1.562 | - | Mp1 | 2.23 | - | Mpy | 2.673 | - |
mp | 0.01069 | kg/s | ms | 0.005006 | kg/s | P3 | 58,291 | Pa |
Pc | 74,748 | Pa | Pe | 40,000 | Pa | Pg | 604,000 | Pa |
Pm | 22,866 | Pa | Pp1 | 53,329 | Pa | Ppy | 22,866 | Pa |
Psy | 22,866 | Pa | Rg | 132.1 | J/kg-K | Te | 281.2 | K |
Tg | 368.1 | K | Tm | 283.7 | K | Tpy | 232.3 | K |
Tsy | 259.9 | K | Vm | 326.2 | m/s | Vpy | 505 | m/s |
Vsy | 199.8 | m/s | - | - | - | - | - | - |
Pg (Mpa) | Tc (°C) | A3/At | ω | ||||
---|---|---|---|---|---|---|---|
Theory | Experiment | Difference (%) | Theory | Experiment | Difference (%) | ||
0.604 | 31.3 | 10.87 | 10.64 (EH) | 2.1 | 0.4627 | 0.4377 | 5.7 |
Appendix A.2. 0-D Model by Chen
Pg [bar] | Tg [°C] | Pc [bar] | Pevaporator [bar] | ER (Experiment by Huang et al. [34]) | ER (Chen [40]) | ER (Developed EES Model) |
---|---|---|---|---|---|---|
6.05 | 95 | 0.986 | 0.399 | 0.4377 (Model EH) | 0.4387 | 0.4122 |
Variable | Value | Units | Variable | Value | Units | Variable | Value | Units |
---|---|---|---|---|---|---|---|---|
AR | 10.45 | - | C4 | 148.6 | m/s | cp | 867.6 | J/kg-K |
cv | 763 | J/kg-K | Effd | 0.82 | - | Effm | 0.85 | - |
Effn | 0.95 | - | ERa | 0.4122 | - | ERcal | 0.4122 | - |
h2 | 274,432 | J/kg | h2i | 271,964 | J/kg | h4 | 285,967 | J/kg |
hcideal | 317,315 | J/kg | ho | 271,858 | J/kg | hc | 324,196 | J/kg |
heo | 282,632 | J/kg | hgo | 341,329 | J/kg | k | 1.137 | - |
M4 | 1.861 | - | M4c | 1.884 | - | M4st | 1.747 | - |
M5 | 0.5654 | - | Me2 | 1.012 | - | Me2st | 1.011 | - |
Mg2 | 2.593 | - | Mg2st | 2.218 | - | P2 | 22,750 | Pa |
P4 | 22,750 | Pa | P5 | 82,405 | Pa | Pc | 98,600 | Pa |
Pccal | 98,639 | Pa | Pe | 39,927 | Pa | Pg | 604,929 | Pa |
Pge | 322,428 | Pa | s4 | 1073 | J/kg-K | scideal | 1073 | J/kg-K |
seo | 1021 | J/kg-K | sgo | 1022 | J/kg-K | Te | 281.2 | K |
Tg | 368.2 | K | u2 | 363 | m/s | u4 | 276.5 | m/s |
u4i | 299.9 | m/s | uo | 146.8 | m/s | - | - | - |
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Meshing | Structured |
Turbulence | Model: k-ε realizable |
Solver | Axisymmetric, Pressure based |
Energy | Kept ON |
Compressibility | Considered |
Refrigerant | Constant Cp, Ideal gas |
Boundary Conditions | Pressure outlet and inlet |
Initialization | Hybrid |
Discretization | 2nd order scheme |
Residuals | 10^−6 |
Tmotive | Tsuction | Tdelivery | Compression Ratio | ER Values, Eames et al. | COP Value of ERS Eames et al. | COP of ERS (Proposed Model) | ER Values (Proposed Model) | Difference in ER Values | Difference in COP Values |
---|---|---|---|---|---|---|---|---|---|
[°C] | [°C] | [°C] | Pdelivery/Psuction | - | - | [%] | [%] | ||
110 | 15 | 33.5 | 2 | 0.94 | 0.67 | 0.6522 | 0.896 | 4.7 | 2.7 |
110 | 12 | 33 | 2.213483146 | 0.76 | 0.54 | 0.56 | 0.778 | 2.4 | 3.7 |
110 | 10 | 32.5 | 2.358536585 | 0.69 | 0.48 | 0.51 | 0.719 | 4.2 | 6.2 |
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Riaz, F.; Yam, F.Z.; Qyyum, M.A.; Shahzad, M.W.; Farooq, M.; Lee, P.S.; Lee, M. Direct Analytical Modeling for Optimal, On-Design Performance of Ejector for Simulating Heat-Driven Systems. Energies 2021, 14, 2819. https://doi.org/10.3390/en14102819
Riaz F, Yam FZ, Qyyum MA, Shahzad MW, Farooq M, Lee PS, Lee M. Direct Analytical Modeling for Optimal, On-Design Performance of Ejector for Simulating Heat-Driven Systems. Energies. 2021; 14(10):2819. https://doi.org/10.3390/en14102819
Chicago/Turabian StyleRiaz, Fahid, Fu Zhi Yam, Muhammad Abdul Qyyum, Muhammad Wakil Shahzad, Muhammad Farooq, Poh Seng Lee, and Moonyong Lee. 2021. "Direct Analytical Modeling for Optimal, On-Design Performance of Ejector for Simulating Heat-Driven Systems" Energies 14, no. 10: 2819. https://doi.org/10.3390/en14102819