Comparison of Methods for Inverse Design of Radiant Enclosures

Abstract

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.

Optimal Boundary Design of Radiant Enclosures Using Micro-Genetic Algorithm (Effects of Refractory Properties and Aspect Ratio of Enclosure on Heaters Setting)

“…1 where L=2m, W=1m, and H=0.5m. This is similar to the imaging enclosure described by Daun et al (6) . As the enclosure has two perpendicular planes of symmetric, we have considered a one-quarter model.…”

“…Some examples for design and control of radiation sources can be found in the papers by Erturk et al (1) , Kudo et al (2), (3) , Howell et al (4) , Franca et al (5) and Daun et al (6) . They compared various regularization techniques and applied them to inverse design problems for radiation-dominant environment.…”

Inverse design of thermal systems with spectrally dependent emissivities

“…Notwithstanding these difficulties, there have been considerable advances in the inverse design in the past 10 years, including solutions that involve combined-mode heat transfer and transient processes. Some of the advances in the inverse design in radiative systems can be found in França et al [2,3], Ertürk et al [4,5], Daun and Howell [6], França and Howell [7], Daun et al [8], Mossi et al [9] and Kim and Baek [10]. Those works obtained satisfactory solutions using different solution techniques, such as regularization of the system of equations, quasi-Newton minimization, LevenbergMarquardt method and stochastic optimization.…”

“…Finally, a new proposition can be made for the distribution of the partial radiative heat fluxes on the design surface as an improvement of the uniform distribution of Eq. (8), based now on the definition of a band factor C Dk i ;jd , which is computed by:…”

Design of radiative enclosures by using topology optimization

“…By using optimization, the determination of heater temperatures of an industrial radiative oven such that the surface of a continuously moving load achieves a prescribed temperature profile is addressed in [8]. In [9], the steepest descent, Newton and quasi-Newton methods are applied to optimize the geometry of a 2-D radiative enclosure with diffuse walls, and in [10] optimization approaches are compared with results obtained by using regularization methods in the determination of heater settings.…”