This paper presents an optimization methodology for designing radiant enclosures containing specularly-reflecting surfaces. The optimization process works by making intelligent perturbations to the enclosure geometry at each design iteration using specialized numerical algorithms. This procedure requires far less time than the forward “trial-and-error” design methodology, and the final solution is near optimal. The radiant enclosure is analyzed using a Monte Carlo technique based on exchange factors, and the design is optimized using the Kiefer-Wolfowitz method. The optimization design methodology is demonstrated by solving two industrially-relevant design problems involving two-dimensional enclosures that contain specular surfaces.
Issue Section:
Radiative Heat Transfer
1.
Winston
, R.
, 1991
, “Nonimaging Optics
,” Sci. Am.
, 264
, pp. 76
–81
.2.
Gu¨ven
, H. M.
, 1994
, “Optimization of Parabolic Trough Collector Design for Varying Manufacturing Tolerances Using a Closed-Form Expression for Intercept Factor
,” ASME J. Sol. Energy Eng.
, 116
, pp. 164
–166
.3.
Ryan, J. P., Miller, J. A., and Burns, P. J., 1998, “Development and Use of a Monte Carlo Code to Conduct a Parametric Study of Cylindrical Solar Collector Arrays,” Proceedings of the 1998 International Solar Energy Conference, Albuquerque, NM, June 14th–17th.
4.
Muschaweck
, J.
, Spirkl
, W.
, Timinger
, A.
, Benz
, N.
, Do¨rfler
, M.
, Gut
, M.
, and Kose
, E.
, 2000
, “Optimized Reflectors for Non-Tracking Solar Collectors With Tubular Absorbers
,” Sol. Energy
, 68
, pp. 151
–159
.5.
Ashdown
, I.
, 1994
, “Non-Imaging Optics Design Using Genetic Algorithms
,” J. Illum. Eng. Soc.
, 23
, pp. 12
–21
.6.
Bertsekas, D. P., 1999, Nonlinear Programming 2nd ed., Athena Scientific, Belmont, MA, pp. 32–33.
7.
Modest M. F., 1993, Radiative Heat Transfer, McGraw-Hill Inc., New York, NY, pp. 669–702.
8.
Siegel, R., and Howell, J. R., 1992, Thermal Radiation Heat Transfer, 3rd ed., Hemisphere Publishing Company, Washington D.C., pp. 480–504.
9.
Hammersely, J. M., and Handscomb, D. C., 1992, Monte Carlo Methods, Chapman and Hall, London, pp. 14.
10.
Kiefer
, J.
, and Wolfowitz
, J.
, 1952
, “Stochastic Estimation of the Maximum of a Regression Function
,” Ann. Math. Stat.
, 23
, pp. 462
–466
.11.
Kushner, H. J., and Clark, D. S., 1978, Stochastic Approximation Methods for Constrained and Unconstrained Systems, Springer, New York, NY.
12.
Pflug, G. C., 1996, Optimization of Stochastic Models: The Interface Between Simulation and Optimization, Kluwer Academic Publishers, Boston, MA, pp. 281–288.
13.
Morton, D. P., and Popova, E., 2001, “Monte Carlo Simulations for Stochastic Optimization,” Encyclopedia of Optimization, C. A. Floudas and P. M. Pardalos, eds., Kluwer Academic Publishers, Boston, MA, pp. 439–447.
14.
Maruyama
, S.
, 1993
, “Uniform Isotropic Emission Form an Involute Reflector
,” ASME J. Heat Transfer
, 115
, pp. 492
–495
.15.
Birkebak
, R. C.
, Sparrow
, E. M.
, Eckert
, E. R. G.
, and Ramsey
, J. W.
, 1964
, “Effect of Surface Roughness on the Total Hemispherical and Specular Reflectance on Metallic Surfaces
,” ASME J. Heat Transfer
, C87
, pp. 429
–435
.16.
Ugray, Z., Lasdon, L., Plummer, J., Glover, F., Kelly, J., and Marti, R., 2002, “
A Mulitstart Scatter Search Heuristic for Smooth NLP and MINLP Problems,” INFORMS J. Comput., in press.
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