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Research Papers: Design Automation

Parameterized Design Optimization of a Magnetohydrodynamic Liquid Metal Active Cooling Concept

[+] Author and Article Information
Darren J. Hartl

Materials and Manufacturing Directorate,
Air Force Research Laboratory (UES, Inc.),
Wright Patterson AFB, OH 45433
e-mail: darren.hartl.ctr@us.af.mil

Edgar Galvan

Design Systems Laboratory,
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843

Richard J. Malak

Associate Professor
Design Systems Laboratory,
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: rmalak@tamu.edu

Jeffrey W. Baur

Materials and Manufacturing Directorate,
Air Force Research Laboratory,
Wright Patterson AFB, OH 45433
e-mail: jeffery.baur@us.af.mil

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 9, 2015; final manuscript received November 20, 2015; published online January 18, 2016. Assoc. Editor: Kazuhiro Saitou.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Mech. Des 138(3), 031402 (Jan 18, 2016) (11 pages) Paper No: MD-15-1479; doi: 10.1115/1.4032268 History: Received July 09, 2015; Revised November 20, 2015

The success of model-based multifunctional material design efforts relies on the proper development of multiphysical models and advanced optimization algorithms. This paper addresses both in the context of a structure that includes a liquid metal (LM) circuit for integrated cooling. We demonstrate for the first time on a complex engineering problem the use of a parameterized approach to design optimization that solves a family of optimization problems as a function of parameters exogenous to the subsystem of interest. This results in general knowledge about the capabilities of the subsystem rather than a restrictive point solution. We solve this specialized problem using the predictive parameterized Pareto genetic algorithm (P3GA) and show that it efficiently produces results that are accurate and useful for design exploration and reasoning. A “population seeding” approach allows an efficient multifidelity approach that combines a computationally efficient reduced-fidelity algebraic model with a computationally intensive finite-element model. Using data output from P3GA, we explore different design scenarios for the LM thermal management concept and demonstrate how engineers can make a final design selection once the exogenous parameters are resolved.

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Figures

Grahic Jump Location
Fig. 1

Comparison of (a) classical Pareto (θ fixed) and (b) parameterized Pareto (θ free; feasible domains not shown) optimization. Parameterized Pareto optimization seeks to identify the full family of Pareto frontiers associated with continuously variable design parameters, θ, which in this work represent design or response variables to be strictly defined by engineering collaborators from other disciplines at a later time in the design process. The algorithm P3GA [31] has enabled such an efficient multidisciplinary multi-objective approach for the first time.

Grahic Jump Location
Fig. 2

An illustration of predicted dominance. The population is a set of discrete points used as training data for the SVDD technique. The SVDD is a model of the boundary based on the current population. The nondominated solutions are those for which no point is predicted to be feasible in the space that dominates (the dashed line). Note that a straightforward application of PPD without SVDD prediction would not indicate domination of any member in this example.

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Fig. 3

Simple structurally integrated MHD-driven cooling system: (a) system schematic; inset illustrates detail of the DC MHD pump and (b) illustration of the DC MHD pumping effect (current flux density as streamlines, magnetic field vectors out of plane, and Lorentz force vectors in 1–2 plane)

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Fig. 4

Schematic illustration of the reduced-fidelity MHD-driven fluid dynamic model corresponding to Eqs. (4.5)(4.9).

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Fig. 5

One-way coupled computational modeling approach. The 3D electromagnetic model (LM channel and air box) calculates the in-plane components of the Lorentz force fL. These are imposed onto the symmetric 2D fluid model as volume-specific body forces.

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Fig. 6

Local electromagnetic and fluid responses in the region of the MHD pump for two different channel widths: (a) rchan = 5 (wchan = 2.5 mm) and (b) rchan = 10 (wchan = 5 mm). Electrode lengths are shown to scale; arrow lengths remain proportional and contour colors remain constant across subfigures (EM solution: current flux density streamlines are white, magnetic field vectors out of plane, Lorentz force vectors in 1–2 plane; fluid solution: fluid velocity streamlines and associated vectors in white) (dchan = 0.5 mm, Vapp = 3.0 mV, lchan = 150 mm, Phot = 10 W, and Tcold = 300 K).

Grahic Jump Location
Fig. 7

Comparison of low- and high-fidelity model predictions for hot reservoir temperature and applied current considering changes in dchan and rchan (lchan = 250 mm, Phot = 10 W, Tcold = 300 K, and Vapp = 10 mV): (a) constant channel depth (dchan = 0.6 mm) and (b) constant channel aspect ratio (rchan = 5)

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Fig. 8

Family of Pareto optimal design solutions associated with the parameterized optimization problem of Eq. (6.1) solved using the algebraic system model. Black dots are solutions obtained using conventional multi-objective optimization repeated for each of the 16 combinations of parameter variable values. Solid lines are interpolations of the four-dimensional hypersurface obtained from a single application of P3GA. Note that the P3GA solution includes information for the entire parameter variable domain θlb≤θ≤θub whereas the conventional optimization approach provides only the information shown.

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Fig. 9

Family of Pareto optimal design solutions associated with the constrained optimization problem of Eq. (6.1) solved using FEA. Pareto frontiers are shown for the four limiting design parameter cases. Plot can be easily generated from P3GA data for any design parameter combination and clearly illustrates multidisciplinary tradeoffs.

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