Publications

Abstract not provided.

This work applies a projection-based model-reduction approach to make high-order quadrature (HOQ) computationally feasible for the discrete ordinates approximation of the radiative transfer equation (RTE) for purely absorbing applications. In contrast to traditional discrete ordinates variants, the proposed method provides easily evaluated error estimates associated with the angular discretization as well as an efficient approach for reducing this error to an arbitrary level. In particular, the proposed approach constructs a reduced basis from (high-fidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a high-order quadrature using a reduced-order model (ROM) constructed from this reduced basis. This strategy results in a much more accurate solution than might have been achieved using only the ordinate directions used to construct the reduced basis. One- and three-dimensional test problems highlight the efficiency of the proposed method.

Participating media radiation (PMR) in weapon safety calculations for abnormal thermal environments are too costly to do routinely. This cost may be s ubstantially reduced by applying reduced order modeling (ROM) techniques. The application of ROM to PMR is a new and unique approach for this class of problems. This approach was investigated by the authors and shown to provide significant reductions in the computational expense associated with typical PMR simulations. Once this technology is migrated into production heat transfer analysis codes this capability will enable the routine use of PMR heat transfer in higher - fidelity simulations of weapon resp onse in fire environments.

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Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, time, direction, and wavelength. In many heat transfer applications, a quasi-steady assumption is valid. The dependence on wavelength is often treated through a weighted sum of gray gases type approach. The discrete ordinates method is the most common method for approximating the angular dependence. In the discrete ordinates method, the intensity is solved exactly for a finite number of discrete directions, and integrals over the angular space are accomplished through a quadrature rule. In this work, a projection-based model reduction approach is applied to the discrete ordinates method. A small number or ordinate directions are used to construct the reduced basis. The reduced model is then queried at the quadrature points for a high order quadrature in order to inexpensively approximate this highly accurate solution. This results in a much more accurate solution than can be achieved by the low-order quadrature alone. One-, two-, and three-dimensional test problems are presented.

Polymer foam encapsulants provide mechanical, electrical, and thermal isolation in engineered systems. It can be advantageous to surround objects of interest, such as electronics, with foams in a hermetically sealed container in order to protect them from hostile environments or from accidents such as fire. In fire environments, gas pressure from thermal decomposition of foams can cause mechanical failure of sealed systems. In this work, a detailed uncertainty quantification study of polymeric methylene diisocyanate (PMDI)-polyether-polyol based polyurethane foam is presented and compared to experimental results to assess the validity of a 3-D finite element model of the heat transfer and degradation processes. In this series of experiments, 320 kg/m3 PMDI foam in a 0.2 L sealed steel container is heated to 1,073 K at a rate of 150 K/min. The experiment ends when the can breaches due to the buildup of pressure. The temperature at key location is monitored as well as the internal pressure of the can. Both experimental uncertainty and computational uncertainty are examined and compared. The mean value method (MV) and Latin hypercube sampling (LHS) approach are used to propagate the uncertainty through the model. The results of the both the MV method and the LHS approach show that while the model generally can predict the temperature at given locations in the system, it is less successful at predicting the pressure response. Also, these two approaches for propagating uncertainty agree with each other, the importance of each input parameter on the simulation results is also investigated, showing that for the temperature response the conductivity of the steel container and the effective conductivity of the foam, are the most important parameters. For the pressure response, the activation energy, effective conductivity, and specific heat are most important. The comparison to experiments and the identification of the drivers of uncertainty allow for targeted development of the computational model and for definition of the experiments necessary to improve accuracy.

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TDI foams of nominal density from 10 to 45 pound per cubic foot were decomposed within a heated stainless steel container. The pressure in the container and temperatures measured by thermocouples were recorded with each test proceeding to an allowed maximum pressure before venting. Two replicate tests for each of four densities and two orientations in gravity produced very consistent pressure histories. Some thermal responses demonstrate random sudden temperature increases due to decomposition product movement. The pressurization of the container due to the generation of gaseous products is more rapid for denser foams. When heating in the inverted orientation, where gravity is in the opposite direction of the applied heat flux, the liquefied decomposition products move towards the heated plate and the pressure rises more rapidly than in the upright configuration. This effect is present at all the densities tested but becomes more pronounced as density of the foam is decreased. A thermochemical material model implemented in a transient conduction model solved with the finite element method was compared to the test data. The expected uncertainty of the model was estimated using the mean value method and importance factors for the uncertain parameters were estimated. The model that was assessed does not consider the effect of liquefaction or movement of gases. The result of the comparison is that the model uncertainty estimates do not account for the variation in orientation (no gravitational affects are in the model) and therefore the pressure predictions are not distinguishable due to orientation. Temperature predictions were generally in good agreement with the experimental data. Predictions for response locations on the outside of the can benefit from reliable estimates associated with conduction in the metal. For the lighter foams, temperatures measured on the embedded component fall well with the estimated uncertainty intervals indicating the energy transport rate through the decomposed region appears to be accurately estimated. The denser foam tests were terminated at maximum allowed pressure earlier resulting in only small responses at the component. For all densities the following statements are valid: The temperature response of the embedded component in the container depends on the effective conductivity of the foam which attempts to model energy transport through the decomposed foam and on the stainless steel specific heat. The pressure response depends on the activation energy of the reactions and the density of the foam and the foam specific heat and effective conductivity. The temperature responses of other container locations depend heavily on the boundary conditions and the stainless steel conductivity and specific heat.

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.

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Predicting failure of thin-walled structures from explosive loading is a very complex task. The problem can be divided into two parts; the detonation of the explosive to produce the loading on the structure, and secondly the structural response. First, the factors that affect the explosive loading include: size, shape, stand-off, confinement, and chemistry of the explosive. The goal of the first part of the analysis is predicting the pressure on the structure based on these factors. The hydrodynamic code CTH is used to conduct these calculations. Secondly, the response of a structure from the explosive loading is predicted using a detailed finite element model within the explicit analysis code Presto. Material response, to failure, must be established in the analysis to model the failure of this class of structures; validation of this behavior is also required to allow these analyses to be predictive for their intended use. The presentation will detail the validation tests used to support this program. Validation tests using explosively loaded aluminum thin flat plates were used to study all the aspects mentioned above. Experimental measurements of the pressures generated by the explosive and the resulting plate deformations provided data for comparison against analytical predictions. These included pressure-time histories and digital image correlation of the full field plate deflections. The issues studied in the structural analysis were mesh sensitivity, strain based failure metrics, and the coupling methodologies between the blast and structural models. These models have been successfully validated using these tests, thereby increasing confidence of the results obtained in the prediction of failure thresholds of complex structures, including aircraft.

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 to determine optimal configurations for radiant heat experiments was appropriate. SPLASH (Single Panel Lamp and Shroud Helper) is that tool. SPLASH is implemented as a user-friendly, Windows-based program that allows a designer to describe a test setup in terms of parameters such as number of lamps, power, position, and separation distance. This document is a user manual for that software. Any incidental descriptions of theory are only for the purpose of defining the model inputs. The theory for the underlying model is described in SAND2005-2947 (Ref. [1]). SPLASH provides a graphical user interface to define lamp panel and shroud designs parametrically, solves the resulting radiation enclosure problem for up to 2500 surfaces, and provides post-processing to facilitate understanding and documentation of analyzed designs.

A series of tests involving detonation of high explosive blanketed by aqueous foam (conducted from 1982 to 1984) are described in primarily terms of recorded peak pressure, positive phase specific impulse, and time of arrival. The investigation showed that optimal blast mitigation occurs for foams with an expansion ratio of about 60:1. Simple analyses representing the foam as a shocked single phase mixture are presented and shown inadequate. The experimental data demonstrate that foam slows down and broadens the propagated pressure disturbance relative to a shock in air. Shaped charges and flyer plates were evaluated for operation in foam and appreciable degradation was observed for the flyer plates due to drag created by the foam.

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 © 2005 by ASME.

Abstract not provided.

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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