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Research Papers: Porous Media

Genetic Algorithm Optimization of a Finned-Tube Heat Exchanger Modeled With Volume-Averaging Theory

[+] Author and Article Information
David Geb

e-mail: dvdgb15@ucla.edu

Ivan Catton

Morrin-Gier-Martinelli Heat
Transfer Memorial Laboratory,
Department of Mechanical
and Aerospace Engineering,
School of Engineering and Applied Science,
University of California,
Los Angeles, 48-121 Engineering IV,
420 Westwood Plaza,
Los Angeles, CA 90095-1597

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received July 22, 2012; final manuscript received March 18, 2013; published online July 18, 2013. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 135(8), 082602 (Jul 18, 2013) (10 pages) Paper No: HT-12-1394; doi: 10.1115/1.4024091 History: Received July 22, 2012; Revised March 18, 2013

This paper proposes and implements a new methodology for optimizing finned-tube heat exchangers (FTHEs) using a volume-averaging theory (VAT) hierarchical physical model and a genetic algorithm (GA) numerical optimizer. This method allows for multiple-parameter constrained optimization of FTHEs by design of their basic morphological structures. A consistent model is used to describe transport phenomena in a FTHE based on VAT, which allows for the volume-averaged conservation of mass, momentum, and energy equations to be solved point by point, with the morphology of the structure directly incorporated into the field equations and full conjugate effects included. The equations differ from those often presented in porous media modeling and are developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in every pore space. These averaged equations have additional integral and differential terms that must be dealt with in order for the equation set to be closed, and recent work has provided this closure for FTHEs. The resulting governing equation set is relatively simple and is discretized and quickly solved numerically. Such a computational solution algorithm is fast running, but still able to present a detailed picture of the temperature fields in both of the fluid flows as well as in the solid structure of the heat exchanger. A GA is integrated with the VAT-based solver to carry out the FTHE numerical optimization, which is a ten parameter problem, and the FTHE is optimized subject to imposed constraints. This method of using the VAT-based solver fully integrated with a GA optimizer results in a new all-in-one tool for performing multiple-parameter constrained optimization on FTHEs.

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Figures

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Fig. 1

VAT-based porous media model of a FTHE

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Fig. 2

Schematic of computational grid and coil circuitry

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Fig. 3

Representative elementary volume (REV) for a finned-tube heat exchanger [25]

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Fig. 4

Geometrical constraints in (a) x − y and (b) y − z planes

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Fig. 5

Visual outline of the basic GA optimizer

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Fig. 6

Schematic of the genetic operators acting during the breeding process. (a) Two parent individuals are selected and paired for mating. (b) A location on their chromosomes is randomly selected for splitting. (c) The crossover mechanism then occurs. (d) Subsequently, genetic mutations are allowed to take place.

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Fig. 7

Fitness evolution of the best individual in each generation for five trials

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Fig. 8

Optimum heat exchanger body dimensions, Lx, Ly, and Lz, drawn to scale with tube pass and row numbers, Nx and Ny, indicated (tube diameters not drawn to scale) for the five trials

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Fig. 9

Evolution of x¯ for the best individual in each generation for (a) Trial 1 and (b) Trial 3

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