Power Density Analysis and Multi-Objective Optimization for an Irreversible Dual Cycle

Yanlin Ge; Shuangshuang Shi; Lingen Chen; Difeng Zhang; Huijun Feng

doi:10.1515/jnet-2021-0083

Published by De Gruyter April 29, 2022

Power Density Analysis and Multi-Objective Optimization for an Irreversible Dual Cycle

Yanlin Ge , Shuangshuang Shi , Lingen Chen , Difeng Zhang and Huijun Feng

From the journal Journal of Non-Equilibrium Thermodynamics

https://doi.org/10.1515/jnet-2021-0083

Showing a limited preview of this publication:

Abstract

Considering the various irreversibility conditions caused by heat transfer and working processes in a dual cycle, the power density performance is optimized by applying finite-time thermodynamics theory, and multi-objective optimization is performed by using NSGA-II. The effects of cut-off ratio, maximum cycle temperature ratio, and various losses by heat transfer and working processes on the relationships between the power density and the compression ratio and between the power density and the thermal efficiency are analyzed. The thermal efficiency and engine size obtained under the conditions of maximum power output and power density are discussed. The results show that for a dual cycle, the heat engine has a smaller size and higher thermal efficiency under the condition of maximum power density. The cycle compression ratio and cut-off ratio are selected as decision variables, and the dimensionless power output, thermal efficiency, dimensionless ecological function, and dimensionless power density are selected as objective functions. Multi-objective optimization is performed with different objective combinations. The deviation indexes under the LINMAP, TOPSIS, and Shannon entropy approaches are discussed, and the number of generations when the genetic algorithm reaches convergence are obtained. The results show that the genetic algorithm converges at the 341st generation for the quadru-objective optimization, at the 488th generation for the tri-objective optimization, and at the 399th generation for the bi-objective optimization. When the bi-objective optimization is performed with dimensionless power output and dimensionless ecological function as the objective functions, the deviation index obtained based on the LINMAP approach is 0.1400, which is better than those obtained for other single- and multi-objective optimizations.

Keywords: dual cycle; power density; finite time thermodynamics; NSGA-II; multi-objective optimization

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 52171317

Award Identifier / Grant number: 51779262

Funding statement: This work is supported by the National Natural Science Foundation of China (Project Nos. 52171317, 51779262).

Acknowledgment

The authors wish to thank the reviewers for their careful, unbiased, and constructive suggestions, which led to this revised manuscript.

Nomenclature

B: Heat transfer loss coefficient (W/K)
C p: Specific heat at constant pressure (J/(mol·K))
C v: Specific heat at constant volume (J/(mol·K))
D: Deviation index (–)
E: Ecological function (W)
k: Specific heat ratio (–)
m ˙: Molar flow rate (mol/s)
n: Piston speed (s⁻¹)
P: Power output (W)
P d: Power density (W/m³)
Q ˙ out: Heat release rate (W)
Q ˙ in: Heat absorption rate (W)
T: Temperature (K)
v: Volume (m³)

Greek symbols

γ: Compression ratio (–)
η: Thermal efficiency (–)
η c: Irreversible compression efficiency (–)
η e: Irreversible expansion efficiency (–)
μ: Friction loss coefficient (kg/s)
ρ: Cut-off ratio (–)
σ: Entropy generation rate (W/K)
τ: Maximum cycle temperature ratio (–)

Subscripts

di: Diesel cycle
leak: Heat leak
max: Maximum
ot: Otto cycle
P ‾ d: Maximum power density
0: Environment
1–5, 2 s, 5 s: State points

Superscripts

–: Dimensionless

Abbreviations

DC: Dual cycle
FL: Friction loss
FTT: Finite time thermodynamics
HTL: Heat transfer loss
IIL: Internal irreversibility loss
MPD: Maximum power density
MPO: Maximum power output
MOO: Multi-objective optimization
SH: Specific heat
WF: Working fluid

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Received: 2021-11-07

Revised: 2022-02-18

Accepted: 2022-03-25

Published Online: 2022-04-29

Published in Print: 2022-07-31

Power Density Analysis and Multi-Objective Optimization for an Irreversible Dual Cycle

Abstract

Acknowledgment

Nomenclature

Greek symbols

Subscripts

Superscripts

Abbreviations

References

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