RESEARCH PAPERS: Radiative Heat Transfer

Metaheuristic Optimization of a Discrete Array of Radiant Heaters

[+] Author and Article Information
Jason M. Porter, J. Wesley Barnes

Mechanical Engineering Department, The University of Texas at Austin, 1 University Station C2200, Austin, TX 78712

Marvin E. Larsen

 Sandia National Laboratories MS 0836, Albuquerque, NM 87185

John R. Howell

Mechanical Engineering Department, The University of Texas at Austin, 1 University Station C2200, Austin, TX 78712jhowell@mail.utexas.edu

J. Heat Transfer 128(10), 1031-1040 (Mar 23, 2006) (10 pages) doi:10.1115/1.2345430 History: Received August 24, 2005; Revised March 23, 2006

The design of radiant enclosures is an active area of research in radiation heat transfer. When design variables are discrete such as for radiant heater arrays with on-off control of individual heaters, current methods of design optimization fail. This paper reports the development of a metaheuristic thermal radiation optimization approach. Two metaheuristic optimization methods are explored: simulated annealing and tabu search. Both approaches are applied to a combinatorial radiant enclosure design problem. Configuration factors are used to develop a dynamic neighborhood for the tabu search algorithm. Results are presented from the combinatorial optimization problem. Tabu search with a problem specific dynamic neighborhood definition is shown to find better solutions than the benchmark simulated annealing approach in less computation time.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

An illustration of a minimization problem with two local minima. (a) The algorithm proceeds following a direction of decreasing f until the local minimum at point 1 is reached. Moving to point 2 requires accepting a solution with a higher value of f. (b) Only after accepting solutions 2 and 3 with increasing f values does the algorithm find solution 4, the global minimum.

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Figure 2

Schematic of the fire simulation experimental setup. (a) The object (cylinder) is located beneath the design surface (thin metal plate). (b) The length of the cylinder, h, is equal to the width of the opening in the water cooled support. (c) Bottom view of the water cooled lamp panel. The lamps are modeled as strip heaters with variable emissivities corresponding to the state of the heater.

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Figure 3

Elements on the plate that exchange energy with the test object: the objective function only considered flux errors for the center elements of the plate (shaded)

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Figure 4

Desired flux distribution used for the SA and TS optimization. The minimum flux is found to be centered over the location of the test object (Fig. 2).

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Figure 5

A 3D plot of the elemental flux error for run 4. The uniformity along the length of the design surface is far better than that along its width.

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Figure 6

A side by side comparison of the best heater positions found using the SA algorithm

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Figure 7

A search neighborhood based on elements with maximum flux error and the heaters that exchange the most energy with them

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Figure 8

Coarse search neighborhood with tabu restrictions. The three heaters chosen from the ordered list cannot be tabu.

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Figure 9

Illustration of heater positions above the plate. The black heater is installed in both (a) and (b). Swapping the position of two adjacent heaters has a fine tuning effect on the optimization.

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Figure 10

Illustration of the general heater positions considered in the fine and coarse neighborhoods. A toggle move switches the state of the heater considered between on (1) and off (0). A swap move turns one heater on and one adjacent heater off.

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Figure 11

Comparison of heater positioning for the best SA solution (469.3W∕m2) and the TSDN solution (440.8W∕m2)

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Figure 12

Comparison 3D plots of the flux error for the best SA solution (469.3W∕m2) and the TSDN solution (440.8W∕m2)

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Figure 13

Results comparison along the centerline of the design surface for the best SA (469W∕m2) and best TSDN (291W∕m2) solutions found

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Figure 14

A comparison of the SA (469W∕m2) and TSDN (291W∕m2) searches. Candidate solutions (TSDN) and rejected solutions (SA) are not shown due to the large number of data points required.



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