Discrete Optimization of Radiant Heaters With Simulated Annealing

Abstract

The simulated annealing algorithm is used to seek optimal radiant heater configurations that provide a desired distribution of incident radiant energy onto a surface. The problem is motivated by a need to create well-understood boundary conditions that simulate fire environments. A bank of halogen lamps irradiates the back of a thin black plate (called a shroud), which simulates the fire environment. For such fire simulations, shroud temperatures routinely exceed 1000 °C and thermal radiation is the dominant mode of heat transfer. The test specimen is then heated by placing it in front of the shroud. The panel, accommodating the radiant heaters (lamps), provides equally spaced slots all of which are powered at the same voltage. Lamp positioning is crucial to obtaining a uniform temperature on the shroud, but determining the best positioning of the lamps experimentally through trial and error has proven difficult. The discrete optimization problem searches possible lamp configurations by simulating adding or removing lamps from the panel. Inverse heat transfer methods have been successfully applied to similar problems. Applying inverse heat transfer methods to this problem, the desired boundary conditions on the shroud are used to solve for the required heater settings. Two boundary conditions are needed: the temperature profile and the heat flux profile on the shroud. The heat flux profile is determined by calculating the radiation heat transfer between the shroud and the test object. However, because the heaters used in the design can only assume discrete positions and are all maintained at the same power level, traditional inverse methods fail. A discrete inverse radiation heat transfer solution method is needed. In this study, a simulated annealing optimization routine is used to determine optimal heater positions given desired boundary conditions on the shroud. Computational characteristics of simulated annealing are presented as well as results of the optimization.