Marvin E. Larsen

Comparison of Methods for Inverse Design of Radiant Enclosures

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.

Metaheuristic Optimization of a Discrete Array of Radiant Heaters

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.

Use of Contact Resistance Algorithm to Implement Jump Boundary Conditions for the Radiation Diffusion Approximation

Thermal conduction codes can be used as solvers for the diffusion approximation for radiation heat transfer. Energy fluxes and temperature distributions that result from thermal radiation in an optically-thick participating medium can be estimated. Allowing dependence on temperatures from either side of the interface, a contact resistance algorithm can be used to implement “jump” (or slip) boundary conditions appropriate for the diffusion approximation in solving the radiation transfer equation. For steady, pure radiation (no conduction) systems analytical expressions exist to specify the temperature in the radiating medium at the wall as a function of the wall temperature, wall emissivity, and extinction coefficient. Radiation and conduction solutions for gray, absorbing/emitting and conducting media bound by diffuse surfaces for the simple case of the steady planar layer are considered. Reference solutions are developed by detailed zone-methods solving the coupled differential forms of both the radiation and conduction heat transfer equations. From the reference solutions, empirical relations are developed for surface resistance as functions of the local wall and adjacent media temperatures, the wall emissivity, the absorptivity, and the thermal conductivity of the medium. Performance of the approximate solution is compared to the reference solutions.Copyright

Discrete Optimization of Radiant Heaters With Simulated Annealing

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.Copyright

Validation of Heat Transfer Thermal Decomposition and Container Pressurization of Polyurethane Foam.

Polymer foam encapsulants provide mechanical, electrical, and thermal isolation in engineered systems. In fire environments, gas pressure from thermal decomposition of polymers can cause mechanical failure of sealed systems. In this work, a detailed uncertainty quantification study of PMDI-based polyurethane foam is presented to assess the validity of the computational model. Both experimental measurement uncertainty and model prediction uncertainty are examined and compared. Both the mean value method and Latin hypercube sampling approach are used to propagate the uncertainty through the model. In addition to comparing computational and experimental results, the importance of each input parameter on the simulation result is also investigated. These results show that further development in the physics model of the foam and appropriate associated material testing are necessary to improve model accuracy.

Theory and experimental validation of SPLASH (Single Panel Lamp and Shroud Helper).

The radiant heat test facility develops test sets providing well-characterized thermal environments, often representing fires. Many of the components and procedures have become standardized to such an extent that the development of a specialized design tool was appropriate. SPLASH (Single Panel Lamp and Shroud Helper) is that tool. SPLASH is implemented as a user-friendly program that allows a designer to describe a test setup in terms of parameters such as lamp number, power, position, and separation distance. Thermal radiation is the dominant mechanism of heat transfer and the SPLASH model solves a radiation enclosure problem to estimate temperature distributions in a shroud providing the boundary condition of interest. Irradiance distribution on a specified viewing plane is also estimated. This document provides the theoretical development for the underlying model. A series of tests were conducted to characterize SPLASHs ability to analyze lamp and shroud systems. The comparison suggests that SPLASH succeeds as a design tool. Simplifications made to keep the model tractable are demonstrated to result in estimates that are only approximately as uncertain as many of the properties and characteristics of the operating environment.