Publications

Calore is the ASC code developed to model steady and transient thermal diffusion with chemistry and dynamic enclosure radiation. An integral part of the software development process is code verification, which addresses the question 'Are we correctly solving the model equations'? This process aids the developers in that it identifies potential software bugs and gives the thermal analyst confidence that a properly prepared input will produce satisfactory output. Grid refinement studies have been performed on problems for which we have analytical solutions. In this talk, the code verification process is overviewed and recent results are presented. Recent verification studies have focused on transient nonlinear heat conduction and verifying algorithms associated with (tied) contact and adaptive mesh refinement. In addition, an approach to measure the coverage of the verification test suite relative to intended code applications is discussed.

Enhanced software methodology and improved computing hardware have advanced the state of simulation technology to a point where large physics-based codes can be a major contributor in many systems analyses. This shift toward the use of computational methods has brought with it new research challenges in a number of areas including characterization of uncertainty, model validation, and the analysis of computer output. It is these challenges that have motivated the work described in this report. Approaches to and methods for model validation and (model-based) prediction have been developed recently in the engineering, mathematics and statistical literatures. In this report we have provided a fairly detailed account of one approach to model validation and prediction applied to an analysis investigating thermal decomposition of polyurethane foam. A model simulates the evolution of the foam in a high temperature environment as it transforms from a solid to a gas phase. The available modeling and experimental results serve as data for a case study focusing our model validation and prediction developmental efforts on this specific thermal application. We discuss several elements of the ''philosophy'' behind the validation and prediction approach: (1) We view the validation process as an activity applying to the use of a specific computational model for a specific application. We do acknowledge, however, that an important part of the overall development of a computational simulation initiative is the feedback provided to model developers and analysts associated with the application. (2) We utilize information obtained for the calibration of model parameters to estimate the parameters and quantify uncertainty in the estimates. We rely, however, on validation data (or data from similar analyses) to measure the variability that contributes to the uncertainty in predictions for specific systems or units (unit-to-unit variability). (3) We perform statistical analyses and hypothesis tests as a part of the validation step to provide feedback to analysts and modelers. Decisions on how to proceed in making model-based predictions are made based on these analyses together with the application requirements. Updating modifying and understanding the boundaries associated with the model are also assisted through this feedback. (4) We include a ''model supplement term'' when model problems are indicated. This term provides a (bias) correction to the model so that it will better match the experimental results and more accurately account for uncertainty. Presumably, as the models continue to develop and are used for future applications, the causes for these apparent biases will be identified and the need for this supplementary modeling will diminish. (5) We use a response-modeling approach for our predictions that allows for general types of prediction and for assessment of prediction uncertainty. This approach is demonstrated through a case study supporting the assessment of a weapons response when subjected to a hydrocarbon fuel fire. The foam decomposition model provides an important element of the response of a weapon system in this abnormal thermal environment. Rigid foam is used to encapsulate critical components in the weapon system providing the needed mechanical support as well as thermal isolation. Because the foam begins to decompose at temperatures above 250 C, modeling the decomposition is critical to assessing a weapons response. In the validation analysis it is indicated that the model tends to ''exaggerate'' the effect of temperature changes when compared to the experimental results. The data, however, are too few and to restricted in terms of experimental design to make confident statements regarding modeling problems. For illustration, we assume these indications are correct and compensate for this apparent bias by constructing a model supplement term for use in the model-based predictions. Several hypothetical prediction problems are created and addressed. Hypothetical problems are used because no guidance was provided concerning what was needed for this aspect of the analysis. The resulting predictions and corresponding uncertainty assessment demonstrate the flexibility of this approach.

A Chemical-structure-based PolyUrethane Foam (CPUF) decomposition model has been developed to predict the fire-induced response of rigid, closed-cell polyurethane foam-filled systems. The model, developed for the B-61 and W-80 fireset foam, is based on a cascade of bondbreaking reactions that produce CO2. Percolation theory is used to dynamically quantify polymer fragment populations of the thermally degrading foam. The partition between condensed-phase polymer fragments and gas-phase polymer fragments (i.e. vapor-liquid split) was determined using a vapor-liquid equilibrium model. The CPUF decomposition model was implemented into the finite element (FE) heat conduction codes COYOTE and CALORE, which support chemical kinetics and enclosure radiation. Elements were removed from the computational domain when the calculated solid mass fractions within the individual finite element decrease below a set criterion. Element removal, referred to as ?element death,? creates a radiation enclosure (assumed to be non-participating) as well as a decomposition front, which separates the condensed-phase encapsulant from the gas-filled enclosure. All of the chemistry parameters as well as thermophysical properties for the CPUF model were obtained from small-scale laboratory experiments. The CPUF model was evaluated by comparing predictions to measurements. The validation experiments included several thermogravimetric experiments at pressures ranging from ambient pressure to 30 bars. Larger, component-scale experiments were also used to validate the foam response model. The effects of heat flux, bulk density, orientation, embedded components, confinement and pressure were measured and compared to model predictions. Uncertainties in the model results were evaluated using a mean value approach. The measured mass loss in the TGA experiments and the measured location of the decomposition front were within the 95% prediction limit determined using the CPUF model for all of the experiments where the decomposition gases were vented sufficiently. The CPUF model results were not as good for the partially confined radiant heat experiments where the vent area was regulated to maintain pressure. Liquefaction and flow effects, which are not considered in the CPUF model, become important when the decomposition gases are confined.

This report describes the underlying principles and goals of the Sandia ASCI Verification and Validation Program Validation Metrics Project. It also gives a technical description of two case studies, one in structural dynamics and the other in thermomechanics, that serve to focus the technical work of the project in Fiscal Year 2001.

Parameters in the heat conduction equation are frequently modeled as temperature dependent. Thermal conductivity, volumetric heat capacity, convection coefficients, emissivity, and volumetric source terms are parameters that may depend on temperature. Many applications, such as parameter estimation, optimal experimental design, optimization, and uncertainty analysis, require sensitivity to the parameters describing temperature-dependent properties. A general procedure to compute the sensitivity of the temperature field to model parameters for nonlinear heat conduction is studied. Parameters are modeled as arbitrary functions of temperature. Sensitivity equations are implemented in an unstructured grid, element-based numerical solver. The objectives of this study are to describe the methodology to derive sensitivity equations for the temperature-dependent parameters and present demonstration calculations. In addition to a verification problem, the design of an experiment to estimate temperature variable thermal properties is discussed.

Abstract not provided.

The thermal conductivity of 304 stainless steel has been estimated from transient temperature measurements and knowing the volumetric heat capacity. Sensitivity coefficients were used to guide the design of this experiment as well as to estimate the confidence interval in the estimated thermal conductivity. The uncertainty on the temperature measurements was estimated by several means, and its impact on the estimated conductivity is discussed. The estimated thermal conductivity of 304 stainless steel is consistent with results from other sources.

Experimental conditions are studied to optimize transient experiments for estimating temperature dependent thermal conductivity and volumetric heat capacity. Thermal properties are assumed to vary linearly with temperature; a total of four parameters describe linearly varying thermal conductivity and volumetric heat capacity. A numerical model of experimental configurations is studied to determine the optimum conditions to conduct the experiment. The criterion D-optimality is used to study the sensor locations, heating duration and magnitude, and experiment duration for finite and semi-infinite configurations. Results indicate that D-optimality is an order of magnitude larger for the finite configuration and hence will provide estimates with a smaller confidence region.

In parameter estimation considerable insight is provided by examining sensitivity coefficients. This paper focuses on the use of sensitivity coefficients in connection with estimating thermal properties in the heat conduction equation. A general methodology for computing sensitivity coefficients can be an important design tool. The use of such a tool is demonstrated in this paper. A control volume, finite element program is used, and briefly described, to implement numerical sensitivity coefficient calculations. In this approach general problems can be studied. Several example problems are presented to demonstrate the insight gained from sensitivity coefficients. The problems are selected from experimental studies to characterize the thermal properties of carbon-carbon composite. Sensitivity coefficients show that in an experiment that is not well designed, additional materials in the experimental configuration can have a larger impact on the temperature than the material of interest. Two-dimensional configurations demonstrate that there can be isolated areas of insensitivity and the difficulty of estimating multiple parameters.

Understanding the surface heat transfer during quenching can be beneficial. Analysis to estimate the surface heat transfer from internal temperature measurements is referred to as the inverse heat conduction problem (IHCP). Function specification and gradient adjoint methods, which use a gradient search method coupled with an adjoint operator, are widely u led methods to solve the IHCP. In this paper the two methods are presented for the multidimensional case. The focus is not a rigorous comparison of numerical results. Instead after formulating the multidimensional solutions, issues associated with the numerical implementation and practical application of the methods are discussed. In addition, an experiment that measured the surface heat flux and temperatures for a transient experimental case is analyzed. Transient temperatures are used to estimate the surface heat flux, which is compared to the measured values. The estimated surface fluxes are comparable for the two methods.