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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Dickey, M. D. , Chiechi, R. C. , Larsen, R. J. , Weiss, E. A. , Weitz, D. A. , and Whitesides, G. M. , 2008, “ Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable Structures in Microchannels at Room Temperature,” Adv. Funct. Mater., 18(7), pp. 1097–1104. [CrossRef]
Cumby, B. L. , Hayes, G. J. , Dickey, M. D. , Justice, R. S. , Tabor, C. E. , and Heikenfeld, J. C. , 2012, “ Reconfigurable Liquid Metal Circuits by Laplace Pressure Shaping,” Appl. Phys. Lett., 101(17), p. 174102. [CrossRef]
Kelley, M. , Koo, C. , Mcquilken, H. , Lawrence, B. , Li, S. , Han, A. , and Huff, G. , 2013, “ Frequency Reconfigurable Patch Antenna Using Liquid Metal as Switching Mechanism,” Electron. Lett. 49(22), pp. 1370–1371. [CrossRef]
Sen, P. , and Kim, C.-J. , 2009, “ Microscale Liquid-Metal Switches—A Review,” IEEE Trans. Ind. Electron., 56(4), pp. 1314–1330. [CrossRef]
Tabatabai, A. , Fassler, A. , Usiak, C. , and Majidi, C. , 2013, “ Liquid-Phase Gallium–Indium Alloy Electronics With Microcontact Printing,” Langmuir, 29(20), pp. 6194–6200. [CrossRef] [PubMed]
Kirillov, I. R. , Reed, C. B. , Barleon, L. , and Miyazaki, K. , 1995, “ Present Understanding of MHD and Heat Transfer Phenomena for Liquid Metal Blankets,” Fusion Eng. Des., 27, pp. 553–569. [CrossRef]
Ghoshal, U. , Grimm, D. , Ibrani, S. , Johnston, C. , and Miner, A. , 2005, “ High-Performance Liquid Metal Cooling Loops,” 2005 IEEE Twenty-First Annual IEEE Semiconductor Thermal Measurement and Management Symposium, Mar. 15–17, San Jose, CA, pp. 16–19.
Wilcoxon, R. , Lower, N. , and Dlouhy, D. , 2010, “ A Compliant Thermal Spreader With Internal Liquid Metal Cooling Channels,” 26th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, 2010, SEMI-THERM 2010, Santa Clara, CA, Feb. 21–25, pp. 210–216.
Hodes, M. , Zhang, R. , Wilcoxon, R. , and Lower, N. , 2012, “ Cooling Potential of Galinstan-Based Minichannel Heat Sinks,” 13th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), San Diego, CA, May 30–June 1, pp. 297–302.
Esser-Kahn, A. P. , Thakre, P. R. , Dong, H. , Patrick, J. F. , Vlasko-Vlasov, V. K. , Sottos, N. R. , Moore, J. S. , and White, S. R. , 2011, “ Three-Dimensional Microvascular Fiber-Reinforced Composites,” Adv. Mater., 23(32), pp. 3654–3658. [CrossRef] [PubMed]
Brown, R. L. , Das, K. , Cizmas, P. G. , and Whitcomb, J. D. , 2014, “ Numerical Investigation of Actively Cooled Structures in Hypersonic Flow,” J. Aircr., 51(5), pp. 1522–1531. [CrossRef]
Lubarsky, B. , and Kaufman, S. J. , 1956, “ Review of Experimental Investigations of Liquid-Metal Heat Transfer,” National Advisory Committee for Aeronautics, Report No. 1270.
Liu, T. , Sen, P. , and Kim, C.-J. , 2012, “ Characterization of Nontoxic Liquid-Metal Alloy Galinstan for Applications in Microdevices,” J. Microelectromech. Syst., 21(2), pp. 443–450. [CrossRef]
Kadid, F. , Abdessemed, R. , and Drid, S. , 2004, “ Study of the Fluid Flow in a MHD Pump Coupling Finite Element-Finite Volume Computations,” J. Electr. Eng., 55(11–12), pp. 301–305.
Kang, H.-J. , and Choi, B. , 2011. “ Development of the MHD Micropump With Mixing Function,” Sens. Actuators A, 165(2), pp. 439–445. [CrossRef]
Hartl, D. , Frank, G. , and Baur, J. , “ Magnetohydrodynamic Liquid Metal Thermal Transport: Validated Analysis and Multi-Fidelity Design Optimization,”. Finite Elem. Anal. Des., (submitted).
Sobieszczanski-Sobieski, J. , and Haftka, R. T. , 1997, “ Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments,” Struct. Optim., 14(1), pp. 1–23. [CrossRef]
Kim, H. M. , Michelena, N. F. , Papalambros, P. Y. , and Jiang, T. , 2003, “ Target Cascading in Optimal System Design,” ASME J. Mech. Des., 125(3), pp. 474–480. [CrossRef]
Michelena, N. , Park, H. , and Papalambros, P. Y. , 2003, “ Convergence Properties of Analytical Target Cascading,”. AIAA J., 41(5), pp. 897–905. [CrossRef]
Kim, H. M. , Kumar, D. K. , Chen, W. , and Papalambros, P. Y. , 2006, “ Target Exploration for Disconnected Feasible Regions in Enterprise-Driven Multilevel Product Design,” AIAA J., 44(1), pp. 67–77. [CrossRef]
Kumar, D. K. , Chen, W. , and Kim, H. M. , 2006, “ Multilevel Optimization for Enterprise-Driven Decision-Based Product Design,” AIAA Paper No. 2006-6923.
Kroo, I. , and Manning, V. , 2000, “ Collaborative Optimization: Status and Directions,” AIAA Paper No. 2000-4721.
Gu, X. , Renaud, J. E. , Ashe, L. M. , Batill, S. M. , Budhiraja, A. S. , and Krajewski, L. J. , 2002, “ Decision-Based Collaborative Optimization,” ASME J. Mech. Des., 124(1), pp. 1–13. [CrossRef]
Cramer, E. J. , Dennis, Jr., J. , Frank, P. D. , Lewis, R. M. , and Shubin, G. R. , 1994, “ Problem Formulation for Multidisciplinary Optimization,” SIAM J. Optim., 4(4), pp. 754–776. [CrossRef]
Milgrom, P. , and Segal, I. , 2002, “ Envelope Theorems for Arbitrary Choice Sets,” Econometrica, 70(2), pp. 583–601. [CrossRef]
Carlsson, C. , and Korhonen, P. , 1986, “ A Parametric Approach to Fuzzy Linear Programming,” Fuzzy Sets Syst., 20(1), pp. 17–30. [CrossRef]
Pistikopoulos, E. N. , Georgiadis, M. C. , and Dua, V. , eds., 2007, Multi-Parametric Model-Based Control: Theory and Applications, Vol. 2, Wiley, New York.
Milgrom, P. , and Shannon, C. , 1994, “ Monotone Comparative Statics,” Econometrica: J. Econometric Soc., 62(1), pp. 157–180. [CrossRef]
Marler, R. T. , and Arora, J. S. , 2004, “ Survey of Multi-Objective Optimization Methods for Engineering,” Struct. Multidiscip. Optim., 26(6), pp. 369–395. [CrossRef]
Malak, R. J. , and Paredis, C. J. , 2010, “ Using Parameterized Pareto Sets to Model Design Concepts,” ASME J. Mech. Des., 132(4), p. 041007. [CrossRef]
Galvan, E. , and Malak, R. J. , 2015, “ P3GA: An Algorithm for Technology Characterization,” ASME J. Mech. Des., 137(1), p. 011401. [CrossRef]
Jones, D. F. , Mirrazavi, S. K. , and Tamiz, M. , 2002, “ Multi-Objective Meta-Heuristics: An Overview of the Current State-of-the-Art,” Eur. J. Oper. Res., 137(1), pp. 1–9. [CrossRef]
Deb, K. , Pratap, A. , Agarwal, S. , and Meyarivan, T. , 2002, “ A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Trans. Evol. Comput., 6(2), pp. 182–197. [CrossRef]
Tax, D. M. , and Duin, R. P. , 1999, “ Support Vector Domain Description,” Pattern Recognit. Lett., 20(11), pp. 1191–1199. [CrossRef]
Ferguson, S. , Gurnani, A. , Donndelinger, J. , and Lewis, K. , 2005, “ A Study of Convergence and Mapping in Preliminary Vehicle Design,” Int. J. Veh. Syst. Modell. Testing, 1(1), pp. 192–215. [CrossRef]
Mattson, C. A. , and Messac, A. , 2003, “ Concept Selection Using S-Pareto Frontiers,” AIAA J., 41(6), pp. 1190–1198. [CrossRef]
Parker, R. R. , Galvan, E. , and Malak, R. J. , 2014, “ Technology Characterization Models and Their Use in Systems Design,” ASME J. Mech. Des., 136(7), p. 071003. [CrossRef]
Beers, W. C. M. v. , and Kleijnen, J. P. C. , 2004, “ Kriging Interpolation in Simulation: A Survey,” 36th Conference on Winter Simulation, Dec. 5–8.
Lophaven, S. N. , Nielsen, H. B. , and Søndergaard, J. , 2002, “ Dace-a MATLAB Kriging Toolbox, Version 2.0,” Technical Report No. IMM-TR-2002-12.
Kohavi, R. , 1995, “ A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection,” 14th International Joint Conference on Artificial Intelligence, Montreal, Quebec, Canada, Vol. 2.
Myers, R. H. , Montgomery, D. C. , and Anderson-Cook, C. M. , 2009, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Vol. 705, Wiley, New York.
Scharf, L. L. , 1991, Statistical Signal Processing, Vol. 98, Addison-Wesley, Reading, MA.
Borghi, C. , Cristofolini, A. , and Fabbri, M. , 1998, “ Study of the Design Model of a Liquid Metal Induction Pump,” IEEE Trans. Magn., 34(5), pp. 2956–2959. [CrossRef]
Homsy, A. , Koster, S. , Eijkel, J. C. , van den Berg, A. , Lucklum, F. , Verpoorte, E. , and de Rooij, N. F. , 2005, “ A High Current Density DC Magnetohydrodynamic (MHD) Micropump,” Lab Chip, 5(4), pp. 466–471. [CrossRef] [PubMed]
Pozrikidis, C. , 2009, Fluid Dynamics: Theory, Computation, and Numerical Simulation, Springer, Berlin.
COMSOL AB, 2014, Microfluid Module User's Guide.
Wu, Y. , McKee, C. , and Armstrong, P. , 1986, “ Galileo EPD Technical Report 86-01,” University of Kansas, Lawrence, KS.
McCaig, M. , 1987, Permanent Magnets in Theory and Practice, Pentacle Press, London.
Qin, M. , and Bau, H. H. , 2011, “ When MHD-Based Microfluidics is Equivalent to Pressure-Driven Flow,” Microfluid. Nanofluid., 10(2), pp. 287–300. [CrossRef]
COMSOL, 2006, Multiphysics C 3.3 User's Manual.
Venturoli, M. , and Boek, E. S. , 2006. “ Two-Dimensional Lattice-Boltzmann Simulations of Single Phase Flow in a Pseudo Two-Dimensional Micromodel,” Physica A, 362(1), pp. 23–29. [CrossRef]
Boek, E. S. , and Venturoli, M. , 2010, “ Lattice-Boltzmann Studies of Fluid Flow in Porous Media With Realistic Rock Geometries,” Comput. Math. Appl., 59(7), pp. 2305–2314. [CrossRef]
Borggaard, J. , Burns, J. , Cliff, E. , and Schreck, S. , 1998, “ Computational Methods for Optimal Design and Control,” Proceedings of the AFOSR Workshop on Optimal Design and Control, Arlington, VA, Sept. 30–Oct. 3, 1997, Birkhauser Boston, Boston, MA.
Yang, Y. , Wang, X. , Zhang, R. , Ding, T. , and Tang, R. , 2006, “ The Optimization of Pole Arc Coefficient to Reduce Cogging Torque in Surface-Mounted Permanent Magnet Motors,” IEEE Trans. Magn., 42(4), pp. 1135–1138. [CrossRef]
Han, J. S. , Rudnyi, E. B. , and Korvink, J. G. , 2005, “ Efficient Optimization of Transient Dynamic Problems in MEMS Devices Using Model Order Reduction,” J. Micromech. Microeng., 15(4), p. 822. [CrossRef]
Krack, M. , Secanell, M. , and Mertiny, P. , 2011, “ Cost Optimization of a Hybrid Composite Flywheel Rotor With a Split-Type Hub Using Combined Analytical/Numerical Models,” Struct. Multidiscip. Optim., 44(1), pp. 57–73. [CrossRef]
Malak, Jr., R. J. , Tucker, L. , and Paredis, C. J. , 2009, “ Compositional Modelling of Fluid Power Systems Using Predictive Tradeoff Models,” Int. J. Fluid Power, 10(2), pp. 45–55. [CrossRef]
Malak, R. , 2008, “ Using Parameterized Efficient Sets to Model Alternatives for Systems Design Decisions,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
Galvan, E. , and Malak, R. , 2013, “ A Predictive Pareto Dominance Based Algorithm for Many-Objective Problems,” 10th World Congress on Structural and Multidisciplinary Optimization (WCSMO), Orlando, FL, May 19–24, International Society for Structural and Multidisciplinary Optimisation (ISSMO).


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. 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)

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.

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)

Grahic Jump Location
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.

Grahic Jump Location
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. 4

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

Grahic Jump Location
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.

Grahic Jump Location
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.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In