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Multi-objective optimization design of a planar membrane humidifier based on NSGA-II and entropy weight TOPSIS

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Abstract

The external humidifier plays an important role in regulating the internal water content and improving the output efficiency of the fuel cells. In the current study, parameter influence research and multi-objective optimization were carried out on the planar membrane humidifier. The length, width, and height of the flow channel and the thickness, porosity, and acid equivalent concentration of the membrane were specified as design variables; the humidification capacity, pressure loss, and volume were set as the optimization objectives. Based on the detailed numerical simulation results, the radial basis function (RBF) meta-model combined with the non-dominated sorting genetic algorithm II (NSGA-II) was employed to approximate the performance of the humidifier and search for the Pareto fronts. Then, the optimal point was selected by the technique of order preference similarity to the ideal solution (TOPSIS) with entropy weight. The validated results showed that the RBF meta-model can achieve high-precision fitting of the performance of humidifiers. It was also found that the channel geometry factors were the most significant design variables for humidifier performance, far exceeding the impacts of membrane-related parameters. In this paper, the influence of geometric parameters and material parameters on the planar membrane humidifier was comprehensively studied, and a complete process of multi-objective optimization was proposed, guiding for determining the design parameters.

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Abbreviations

a :

Water activity (−)

C :

Species concentration (kg m−3)

\(C_{{{\text{acid}}}}\) :

Acid equivalent concentration (mol m−3)

Cp :

Specific heat (J kg−1 K−1)

D :

Species diffusivity (m2 s−1)

E W :

Equivalent weight (kg mol−1)

H :

Channel height (m)

k :

Thermal conductivity (W m−2 K−1)

K :

Membrane permeability of (m2)

L :

Channel length (m)

\(\mathop m\limits^{ \bullet }\) :

Mass flow rate (kg s−1)

p :

Pressure (Pa)

R :

Universal gas constant (J mol−1 K−1)

\(R_{{{\text{adj}}}}^{2}\) :

Adjusted coefficient of determination

\(r_{xy}\) :

Correlation coefficient

\({\text{S}}\) :

Source term (kg m−2 s−2)

S x , S y , S z :

Momentum equation source terms (kg m−2 s−2)

T :

Temperature (K)

t :

Membrane thickness (m)

u, v, w :

Flow velocity components (m s−1)

\({\mathbf{V}}\) :

Flow velocity (m s−1)

W :

Channel width (m)

ANOVA:

Analysis of Variance

GDL:

Gas Diffusion Layer

MOPSO:

Multi-Objective Particle Swarm Optimization

NSGA:

Non-dominated Sorting Genetic Algorithm

PSO:

Particle Swarm Optimization

RBF:

Radial Basis Function

RSM:

Response surface methodology

SIMPLE:

Semi-Implicit Method for Pressure Linked Equations

SQP:

Sequential Quadratic Programming

TOPSIS:

Technique of Order Preference Similarity to the Ideal Solution

\(\lambda\) :

Water content in membrane (−)

\(\varepsilon\) :

Membrane porosity (−)

\(\mu\) :

Dynamic viscosity (N s m−2)

\(\rho\) :

Density (kg m−3)

\(\varphi\) :

Relative humidity (−)

\(\omega\) :

Weight factor (−)

0:

Standard condition

c h :

Channel

dry :

Dry channel

eff :

Effective value

i :

Index of species or samples

in :

Inlet

m :

Membrane

o pe :

Operational

out:

Outlet

sat :

Saturation

w :

Water

wet :

Wet channel

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Acknowledgements

This study was supported by the Foshan **anhu Laboratory of the Advanced Energy Science and Technology Guangdong Laboratory (Grant No. XHD2020-003) and the National Natural Science Foundation of China (Grant No. 52175111).

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Authors and Affiliations

  1. Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan, 430070, China

    Yongchao Li, Hao Chen, Chihua Lu, Hui Zhou, Zhien Liu & Ben Chen

  2. Foshan **anhu Laboratory of the Advanced Energy Science and Technology Guangdong Laboratory, Foshan, 528200, China

    Yongchao Li & Chihua Lu

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  1. Yongchao Li
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Li, Y., Chen, H., Lu, C. et al. Multi-objective optimization design of a planar membrane humidifier based on NSGA-II and entropy weight TOPSIS. J Therm Anal Calorim 148, 7147–7161 (2023). https://doi.org/10.1007/s10973-023-12202-4

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