1. Supervisor: Prof. Mikhail V. Sorin
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
Hossein Akbari
Supervisor: Prof. Mikhail V. Sorin
Mechanical Engineering Department, Université de Sherbrooke, Sherbrooke, QC, Canada
September 2019

2. Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
Exergy:
Maximum useful work can be obtained between two states in a specified environment
$$ only rational basis for assigning monetary values to interactions $$
Introduction
Case study
Results
Conclusion

3. Exergetic efficiencies:
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
Exergetic efficiencies:
𝑒 𝑥 =𝑓( 𝑇 𝑥 , 𝑠 𝑥 )
𝑒 𝑦 =𝑓( 𝑇 𝑦 , 𝑠 𝑦 )
Introduction
Case study
Results
Conclusion

4. Exergetic efficiencies:
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
Exergetic efficiencies:
𝑒 𝑥 =𝑓( 𝑇 𝑥 , 𝑠 𝑥 )
𝑒 𝑦 =𝑓( 𝑇 𝑦 , 𝑠 𝑦 )
Input-output efficiency
Consumed-produced efficiency
Fuel-product efficiency
Why different exergetic efficiencies ?!
Introduction
Case study
Results
Conclusion

5. Classification of exergy:
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
Classification of exergy:
Exergy
Energy streams
Material streams
Heat
Radiation
Electrical
Chemical
Physical
Thermal 𝜕𝑒 𝜕𝑇 𝑃
Mechanical 𝜕𝑒 𝜕𝑃 𝑇
Introduction
Case study
Results
Conclusion

6. Exergy associated with heat: Thermal exergy:
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
Exergy associated with heat:
Thermal exergy:
𝑒 𝑇 = 𝑐 𝑃 𝑇− 𝑇 0 − 𝑇 0 ln 𝑇 𝑇 0
𝑒 𝑞 = 𝑞 1− 𝑇 0 𝑇
* Marmolejo-Correa D, Gundersen T., 2012, A comparison of exergy efficiency definitions with focus on low temperature processes. Energy , vol. 44, p. 477–489.
Introduction
Case study
Results
Conclusion

7. Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
𝑖𝑓 𝑇 𝑖𝑛 > 𝑇 0 𝑎𝑛𝑑 𝑇 𝑜𝑢𝑡 > 𝑇 0 : 𝑒𝑥 𝑡𝑟 =𝑒𝑥( 𝑇 𝑚𝑖𝑛 , 𝑃 𝑚𝑖𝑛 )
𝑖𝑓 𝑇 𝑖𝑛 < 𝑇 0 𝑎𝑛𝑑 𝑇 𝑜𝑢𝑡 < 𝑇 0 : 𝑒𝑥 𝑡𝑟 =𝑒𝑥( 𝑇 𝑚𝑎𝑥 , 𝑃 𝑚𝑖𝑛 )
𝑖𝑓 𝑇 𝑖𝑛 > 𝑇 0 𝑎𝑛𝑑 𝑇 𝑜𝑢𝑡 < 𝑇 0 ) 𝑂𝑅 ( 𝑇 𝑖𝑛 < 𝑇 0 𝑎𝑛𝑑 𝑇 𝑜𝑢𝑡 > 𝑇 0 : 𝑒𝑥 𝑡𝑟 =𝑒𝑥( 𝑇 0 , 𝑃 𝑚𝑖𝑛 )
Transiting exergy:
Exergy consumed:
𝛻𝐸=𝑒𝑥 1 − 𝑒𝑥 𝑡𝑟
Exergy produced:
∆𝐸=𝑒𝑥 2 − 𝑒𝑥 𝑡𝑟
Introduction
Case study
Results
Conclusion

8. Case study: Base case scenario: Environment temperature
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
Case study:
Base case scenario:
Environment temperature
𝑇 0 = 𝐾
Environment pressure
𝑃 0 = 𝑘𝑃𝑎
Turbine inlet pressure
𝑃 4 = 𝑘𝑃𝑎
Expansion ratio of the turbine
𝛽= 𝑃 4 𝑃 5 =2.5
Extraction ratio
𝑅= 𝑚 𝑚 4 =0.3
Turbine isentropic efficiency
𝜂 𝑇 =0.8
Pump isentropic efficiency
𝜂 𝑃 =0.8
Heat source inlet temperature
𝑇 16 = 𝐾
Heat source mass flow rate
𝑚 16 = 𝑘𝑔 𝑠
Cooling water inlet temperature
𝑇 18 = 𝐾
Evaporation temperature
𝑇 12 = 𝐾
Temperature difference
∆𝑇= 𝐾
Working fluid
Dimethyl ether
Introduction
Case study
Results
Conclusion

9. Ejector: suction chamber diffuser mixed flow primary flow
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
Ejector:
suction chamber
diffuser
mixed flow
primary flow
secondary flow
constant-area section T s
primary flow
secondary flow
mixed flow
Ejector performance curve*
COP
Back pressure
(mbar)
* K. Chunnanond and S. Aphornratana, “An experimental investigation of a steam ejector refrigerator: The analysis of the pressure profile along the ejector,” Appl. Therm. Eng., vol. 24, no. 2–3, pp. 311–322, 2004.
Introduction
Case study
Results
Conclusion

10. 1. Transiting efficiency:
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
𝜼 𝑮𝒓 = ∆𝑬 𝜵𝑬
𝛻𝐸= 𝑚 5 ∙𝛻ex 𝑝 𝑚 13 ∙𝛻ex 𝑠 = 𝑚 5 ∙ 𝑒𝑥 𝑝 − 𝑒𝑥 𝑝 𝑡𝑟 + 𝑚 13 ∙ 𝑒𝑥 𝑠 − 𝑒𝑥 𝑠 𝑡𝑟
∆𝐸= 𝑚 5 ∙∆ex 𝑝 𝑚 13 ∙∆ex 𝑠 = 𝑚 5 ∙ 𝑒𝑥 7 − 𝑒𝑥 𝑝 𝑡𝑟 + 𝑚 13 ∙ 𝑒𝑥 7 − 𝑒𝑥 𝑠 𝑡𝑟
1. Transiting efficiency:
Exergy consumed:
Exergy produced:
Introduction
Case study
Results
Conclusion

11. 2. Input-output (Grassmann) efficiency:
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
2. Input-output (Grassmann) efficiency:
Exergy consumed:
𝛻𝐸=𝐸 5 + 𝐸 13
Exergy produced:
∆𝐸=𝐸 7 T s
primary flow
secondary flow
mixed flow
𝜂 𝐺𝑟 = 𝑚 𝑚 13 ∙ 𝑒𝑥 7 𝑚 5 ∙ 𝑒𝑥 5 + 𝑚 13 ∙ 𝑒𝑥 13 = 𝐸 7 𝐸 5 + 𝐸 13 5 7
mixed flow (7)
primary flow (5)
secondary flow (13) 13
Introduction
Case study
Results
Conclusion

12. Primary flow pressure:
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
𝑃 5
∆ 𝐸 𝑠
𝛻 𝐸 𝑠
𝛻 𝐸 𝑃 𝐷
𝐸 7 𝜔
𝑚 13
𝜂 𝑡ℎ
𝑘𝑃𝑎 𝑘𝑊 −
𝑘𝑔 𝑠 %
900
81.27
5.42
338.99
263.14
859.9
0.2523
2.2304
19.1
1000
104.02
6.95
390.9
293.83
907.9
0.3239
2.8627
20.6
1125
128.52
8.61
448.72
328.81
959.8
0.4012
3.5454
22.2
1285
155.28
10.42
514.02
369.16
1016.7
0.4856
4.2912
23.9
1500
184.89
12.42
589.1
416.63
1080
0.5790
5.1161
25.9 ↑
Primary flow pressure:
𝜂 𝑡ℎ = 𝑊 𝑛𝑒𝑡 + 𝑄 𝑒𝑣 𝑄 𝑔𝑒𝑛
Grassmann
∆𝐸=𝐸 7 = 𝑚 𝑚 13 ∙ 𝑒𝑥 7
Transiting
∆𝐸= 𝑚 13 ∙ 𝑒𝑥 7 − 𝑒𝑥 𝑠 𝑡𝑟
Introduction
Case study
Results
Conclusion

13. Primary flow pressure:
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
𝑃 5
∆ 𝐸 𝑠
𝛻 𝐸 𝑠
𝛻 𝐸 𝑃 𝐷
𝐸 7 𝜔
𝑚 13
𝜂 𝑡ℎ
𝑘𝑃𝑎 𝑘𝑊 −
𝑘𝑔 𝑠 %
900
81.27
5.42
338.99
263.14
859.9
0.2523
2.2304
19.1
1000
104.02
6.95
390.9
293.83
907.9
0.3239
2.8627
20.6
1125
128.52
8.61
448.72
328.81
959.8
0.4012
3.5454
22.2
1285
155.28
10.42
514.02
369.16
1016.7
0.4856
4.2912
23.9
1500
184.89
12.42
589.1
416.63
1080
0.5790
5.1161
25.9 ↑
Primary flow pressure:
𝜂 𝑡ℎ = 𝑊 𝑛𝑒𝑡 + 𝑄 𝑒𝑣 𝑄 𝑔𝑒𝑛
Grassmann
∆𝐸=𝐸 7 = 𝑚 𝑚 13 ∙ 𝑒𝑥 7
Transiting
∆𝐸= 𝑚 13 ∙ 𝑒𝑥 7 − 𝑒𝑥 𝑠 𝑡𝑟
Introduction
Case study
Results
Conclusion

14. Secondary flow pressure:
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
𝑃 13
∆ 𝐸 𝑠
𝛻 𝐸 𝑠
𝛻 𝐸 𝑃 𝐷
𝐸 7 𝜔
𝜂 𝑡ℎ
𝑘𝑃𝑎 𝑘𝑊 − %
164.8
14.28
1.019
321.53
308.27
725.1
0.0299
13.7
192.2
51.61
2.559
331.16
283.11
784.6
0.1297
16.1
223.0
81.27
5.42
338.99
263.14
859.9
0.2524
19.1
257.5
102.34
6.622
345.28
249.56
953.4
0.4086
23.0
295.8
112.69
7.197
350.24
244.75
1091.8
0.6165
28.2 ↑ ↓
Secondary flow pressure:
Introduction
Case study
Results
Conclusion

15. Back pressure: Introduction Case study Results Conclusion
Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
𝑃 7
∆ 𝐸 𝑠
𝛻 𝐸 𝑠
𝛻 𝐸 𝑃 𝐷
𝐸 7 𝜔
𝜂 𝑡ℎ
𝑘𝑃𝑎 𝑘𝑊 − %
410.9
104.8
7.8
372.4
275.3
890.5
0.363
22.1
437.5
81.3
5.4
339.0
263.1
859.9
0.252
19.1
465.3
56.1
3.4
305.2
252.5
834.1
0.158
16.6
494.5
29.6
1.6
271.0
243.1
811.9
0.076
14.3 ↑ ↓
Back pressure:
Introduction
Case study
Results
Conclusion

16. Exergetic efficiency of the ejector operating across ambient temperature in a combined power and ejector-refrigeration cycle
Conclusions:
Transiting exergy provides us with clear and systematic definitions of consumed and produced exergies in a process for different conditions while the other definitions encounter a serious problem in crossing ambient temperature conditions.
The transiting approach establishes a logical link between the produced exergy and the most important ejector’s parameter (entrainment ratio).
Grassmann efficiency cannot reflect the technical purpose of the ejector.
Introduction
Case study
Results
Conclusion