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Maximum ecological function performance for a three-reservoir endoreversible chemical pump

  • Lingen Chen EMAIL logo , Shuangshuang Shi , Huijun Feng and Yanlin Ge
Published/Copyright: December 7, 2022

Abstract

Endoreversible chemical pump (ECP) is a theoretical model of electrochemical, photochemical, solid-state apparatus and mass exchangers. ECP can be classified as two-, three- and four-mass-reservoir devices. The usual performance indicators for ECPs are energy pumping rate (EPR) and coefficient of performance (COP). Energy-based ecological function objective (EFO) is introduced to performance optimization of three-reservoir ECP. Optimization relationships between EFO and COP with linear and diffusive mass transfer laws (MTLs) are deduced. Numerical examples are provided, and influences of cycle parameters and MTLs on optimal EFO performances are analyzed. For linear MTL, compared performances at maximum EFO point and point where dimensionless EPR is 0.016, COP increases 14.4% and entropy generation rate (EGR) drops 52% with only 30% loss of EPR. For diffusive MTL, compared performances at maximum dimensionless EFO point and point where dimensionless EPR is 0.01, COP increases 11.3% and EGR drops 46.9% with only 30% loss of EPR. It demonstrates that EFO is a trade-off between EPR and dissipation of EPR, which is beneficial to utilize energy effectively. With the same chemical potentials of three reservoirs, the maximum dimensionless EFO and the corresponding COP with linear MTL are bigger than those with diffusive MTL.


Corresponding author: Lingen Chen, Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China; Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, P. R. China; and School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China, E-mail:

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: Unassigned

Acknowledgments

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

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This paper is supported by the National Natural Science Foundation of China (Project No. 52171317).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Nomenclature

b

coefficient ratio of mass transfer

E

Ecological function (kJ/s)

h

coefficient of mass transfer

L

Lagrangian function

P

Power output (kW)

R

Cooling load of the refrigerator

T

Temperature (K)

t

Time of mass transfer (s)

W

Work input (kJ)

x

Process variable

Greek symbol

α

Process variable

χ

Coefficient of performance for the chemical pump

ɛ

Coefficient of performance for the refrigerator

ϕ

Coefficient of performance for the heat pump

λ

Lagrangian multiplier

μ

Chemical potential (kJ/kg)

π

Heating load of the heat pump

σ

Entropy generation rate (kW/K)

τ

Cyclic period (s)

ΔN

Amounts of mass exchange per cycle (kg)

ΔS

The entropy generation of the cycle (kJ/K)

Σ

Energy pumping rate (kJ/s)

subscripts

*

Dimensionless

c

Reversible Carnot cycle

E 1 *

Maximum dimensionless ecological function point

H

High mass reservoir

L

Low mass reservoir

max

Maximum

P

Heat pump

R

Refrigerator

r

Reversible cycle

Σ*

Maximum dimensionless rate of energy pumping point

Diffusive mass transfer law

0

Environment

1,2

State points

Abbreviation

COP

coefficient of performance

CPL

chemical potential

EFO

ecological function objective

ECP

endoreversible chemicalpump

EGR

entropy generation rate

EPR

energy pumping rate

MTL

mass transfer law

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Received: 2022-09-16
Revised: 2022-10-25
Accepted: 2022-11-10
Published Online: 2022-12-07
Published in Print: 2023-04-28

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