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RESEARCH PAPERS: Radiative Heat Transfer

Comparison of Methods for Inverse Design of Radiant Enclosures

[+] Author and Article Information
Kyle Daun

 National Research Council of Canada, Ottawa, Canada

Francis França

 Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil

Marvin Larsen

 Sandia National Laboratories, Albuquerque, NM

Guillaume Leduc

Laboratoire d’Energétique,  Université Paul Sabatier, Toulouse, France

John R. Howell

 University of Texas at Austin, Austin, TX

J. Heat Transfer 128(3), 269-282 (Aug 03, 2005) (14 pages) doi:10.1115/1.2151198 History: Received March 09, 2005; Revised August 03, 2005

A particular inverse design problem is proposed as a benchmark for comparison of five solution techniques used in design of enclosures with radiating sources. The enclosure is three-dimensional and includes some surfaces that are diffuse and others that are specular diffuse. Two aspect ratios are treated. The problem is completely described, and solutions are presented as obtained by the Tikhonov method, truncated singular value decomposition, conjugate gradient regularization, quasi-Newton minimization, and simulated annealing. All of the solutions use a common set of exchange factors computed by Monte Carlo, and smoothed by a constrained maximum likelihood estimation technique that imposes conservation, reciprocity, and non-negativity. Solutions obtained by the various methods are presented and compared, and the relative advantages and disadvantages of these methods are summarized.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Basic dimensions of three-dimensional enclosure: (a) enclosure geometry and (b) computational domain

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Figure 2

Discretization of the computational domain for calculation of exchange factors

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Figure 3

Required transient spatially uniform temperature profile imposed on the design problem

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Figure 4

Singular values of matrix A for H∕W=0.25 and 0.50

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Figure 5

Partitioning of the heater surface into six regions for simulated annealing

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Figure 6

Predicted power to heater zones using simulated annealing: H∕W=0.5; Tref=1000K

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Figure 7

Predicted power to heater zones using simulated annealing: H∕W=0.25; Tref=1000K

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Figure 8

Heater power distribution at t=4hr, TSVD method: truncation parameter p=3; Tref=1000K; average design surface dimensionless temperature: (a) θ¯=0.460 and (b) θ¯=0.4598±0.0005

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Figure 9

Heater power distribution at t=4hr, Tikhonov order 1: regularization parameters λ=0.2; L=L1; Tref=1000K; average design surface dimensionless temperature: (a) θ¯=0.460 and (b) θ¯=0.4599±0.0006

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Figure 12

Heater power distribution at t=4hr, simulated annealing method: Tref=1000K; average design surface dimensionless temperature: (a) θ¯=0.4601±0.0001 and (b) θ¯=0.4602±0.0001

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Figure 13

Element numbering on enclosure surfaces

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Figure 10

Heater power distribution at t=4hr, CG Method: iterative step: I=2; Tref=1000K; average design surface dimensionless temperature: (a) θ¯=0.460 and (b) θ¯=0.4599±0.0007

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Figure 11

Heater power distribution at t=4hr, quasi-Newton minimization: Tref=1000K; average design surface dimensionless temperature: (a) θ¯=0.4603±0.0022 and (b) θ¯=0.4600±0.0018

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