Kevin Dowding | Sandia National Laboratories (original) (raw)

Papers by Kevin Dowding

Computational thermal sciences, 2024

Journal of verification, validation, and uncertainty quantification, Dec 1, 2022

This paper discusses the application of the area metric to the quantification of modeling errors.... more This paper discusses the application of the area metric to the quantification of modeling errors. The focus of the discussion is the effect of the shape of the two distributions on the result produced by the Area Metric. Two different examples that assume negligible experimental and numerical errors are presented: the first case has experimental and simulated quantities of interest defined by normal distributions that require the definition of a mean value and a standard deviation; the second example is taken from the V&V10.1 ASME standard that applies the Area Metric to quantify the modeling error of the tip deflection of a loaded hollow tapered cantilever beam simulated with the static Bernoulli–Euler beam theory. The first example shows that relatively small differences between the mean values are sufficient for the area metric to be insensitive to the standard deviation. Furthermore, the example of the V&V10.1 ASME standard produces an Area Metric equal to the difference between the mean values of experiments and simulations. Therefore, the error quantification is reduced to a single number that is obtained from a simple difference of two mean values. This means that the area metric fails to reflect a dependence on the difference in the shape of the distributions representing variability. The paper also presents an alternative version of the Area Metric that avoids this filtering effect of the shape of the distributions by utilizing a reference simulation that has the same mean value as the experiments. This means that the quantification of the modeling error will have contributions from the difference in mean values and the shape of the distributions.

OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information), Sep 1, 2007

CRC Press eBooks, Jul 27, 2021

Coupled fire-environment/thermal-response models were validated using data for an object engulfed... more Coupled fire-environment/thermal-response models were validated using data for an object engulfed in a JP8 hydrocarbon fuel fire. Fire model predictions of heat flux were used as boundary conditions in the thermal response calculations of the object. Predictions of transient external shell temperatures as well as the surface temperatures of the embedded mass were averaged spatially and compared to data. The solution sensitivity to mesh size, time step, nonlinear iterations, and radiation rays were assessed and the uncertainties in the predictions were quantified using a Latin Hypercube Sampling (LHS) technique. The comparisons showed that the response variable was more sensitive to fire model parameters than to thermal model parameters. The observed relative difference in measurements and model predictions was also compared to the model uncertainty. The comparisons showed that the model plus uncertainty bounded the experimental data. I. Introduction Sandia National Laboratories has been engaged in testing weapon system safety in fire environments since the 1950s. Due to the high consequences involved, system safety has traditionally been demonstrated through full scale system tests, albeit with a limited number of tests. Historically developed standardized tests include the placement of a system in a fully engulfing fire for 1 hour. Systems are declared qualified and ready for production based on passage of these standardized tests and with reference to the testing and analysis during development. Beginning in the early to mid 1990’s, the DOE began a program of Science Based Stockpile Stewardship. A significant part of this program is the Advanced Simulation and Computing (ASC) program, in which modeling and simulation, through high performance computing has been applied to system development and qualification. As part of the ASC program, Sandia engaged in developing the capability to model fire environments coupled to system response in those environments. An important thrust area within the ASC program includes the advancement of the verification and validation (V&V) methodologies and uncertainty quantification techniques. Sandia National Laboratories has made strides in developing new capabilities in this area and applying them to current applications. A best estimate plus uncertainty approach has been fully adopted and incorporated into safety themes for system qualification. Providing uncertainty estimates along with deterministic results has provided value to Sandia programs and gives more insight into predictive capability. The direct contribution of this study to current and future systems is an understanding of the uncertainties in predicting internal system temperatures when an object is engulfed in a JP8 fire environment. The uncertainty in input parameters can be used with other scenarios and configurations to evaluate situations that challenge safety themes. Confidence gained in validation processes such as discussed in the current work is crucial when evaluating system qualification activities that include modeling and simulation. II. Numerical Modeling

John Wiley & Sons, Inc. eBooks, Jan 18, 2008

ABSTRACT Methods are discussed for computing the sensitivity of field variables to changes in mat... more ABSTRACT Methods are discussed for computing the sensitivity of field variables to changes in material properties and initial/boundary condition parameters for heat transfer problems. The method we focus on is termed the ''Sensitivity Equation Method'' (SEM). It involves deriving field equations for sensitivity coefficients by differentiating the original field equations with respect to the parameters of interest and numerically solving the resulting sensitivity field equations. Uncertainty in the model parameters are then propagated through the computational model using results derived from first-order perturbation theory; this technique is identical to the methodology typically used to propagate experimental uncertainty. Numerical results are presented for the design of an experiment to estimate the thermal conductivity of stainless steel using transient temperature measurements made on prototypical hardware of a companion contact conductance experiment. Comments are made relative to extending the SEM to conjugate heat transfer problems.

Journal of verification, validation, and uncertainty quantification, Feb 16, 2022

The goal of this paper is to summarize and clarify the scope and interpretation of the validation... more The goal of this paper is to summarize and clarify the scope and interpretation of the validation procedure presented in the V&V20-2009 ASME Standard. In V&V20-2009, validation is an assessment of the model error, without regard to the assessment satisfying validation requirements. Therefore, validation is not considered as a pass/fail exercise. The purpose of the validation procedure is the estimation of the accuracy of a mathematical model for specified validation variables (also known as quantities of interest, system responses or figures of merit) at a specified validation point for cases in which the conditions of the actual experiment are simulated. The procedure proposed in V&V20-2009 can be applied to variables defined by a scalar. For the sake of clarity, the paper reiterates the development and assumptions behind the V&V20-2009 procedure that requires the knowledge of the experimental D and simulation S values at the set point and an estimate of the experimental, numerical and parameter uncertainties. The difference E between S and D is the centre of the interval that should contain the model error (with a certain degree of confidence) and the width of the interval is obtained from the validation uncertainty that is a consequence of the combination of the experimental, numerical and parameter uncertainties. The paper presents the alternatives to address parameter uncertainty and expands upon the interpretation of the final result. The paper also includes two examples demonstrating the application of the V&V20-2009 validation procedure.

International Journal of Heat and Mass Transfer, 2020

Inverse theory is an emerging field of study with application to a diverse range of problems. Inv... more Inverse theory is an emerging field of study with application to a diverse range of problems. Inverse thermal problems are the focus of this dissertation; specifically, the parameter estimation problem and inverse heat conduction problem (IHCP) are investigated. Although one-dimensional inverse thermal problems have been widely investigated, multi-dimensional problems are beginning to receive an increasing amount of attention. One-and two-dimensional cases are addressed for both the noted inverse problems, including an experimental application. Parameter estimation techniques are applied to estimate the thermal properties of a carbon-carbon composite from transient experiments. Properties are determined as a function of temperature and direction relative to the fiber orientation. The thermal conductivity is assumed to be orthotropic, varying in the direction normal and parallel to the fibers; the volumetric heat capacity is assumed isotropic. Thermal properties from room temperature up to 500C are obtained. The thermal conductivity normal to the fiber is found to be less than one-tenth of the thermal conductivity parallel to the fiber. Agreement within 7% is demonstrate between independent one-and two-dimensional results. A sequential-in-time implementation is proposed for a conjugate gradient method, utilizing an adjoint equation approach, to solve the IHCP. Because the IHCP is generally ill-posed, Tikhonov regularization is included to stabilize the solution. The proposed sequential method benefits from the efficiency and on-line capabilities of a sequential implementation, without requiring a priori information about the (unknown) surface heat flux. Aspects of the sequential gradient method are discussed and examined. Several promising features of the sequential gradient method are noted. Simulated one-and twodimensional test cases are presented to study the sequential implementation. Numerical solutions are obtained using a finite difference procedure. Results indicate the sequential implementation has accuracy comparable to a standard whole domain solution, but in certain cases requires significantly more computational time. Methods to improve the computational requirements, which make the method competitive, are presented. iv to my wife v ACKNOWLEDGMENTS The input and help of my Ph.D. guidance committee, James Beck, Patricia Lamm, Alejandro Diaz, and Craig Somerton, is acknowledged. Special thanks are due Patricia Lamm for her patience working with an engineer, help with understanding the gradient/ adjoint methods, and availability to discuss the research. To my advisor James Beck, I thank for his encouragement and introduction to the field of inverse problems. His enthusiasm and dedication were inspiring, not only in helping realize this work, but in helping me develop as a teacher and researcher. I have benefited from interaction with several fellow students and researchers. Input and help from Arafa Osman, Bob McMasters, Heidi Relyea, and Matt White is appreciated. Support from Sandia National Laboratories under US Air Force contract number FY1456-91-N0058 and the Research Excellence Fund of the State of Michigan through the Composite Materials and Structures Center at Michigan State University is acknowledged. Completing this work would not have been possible if it were not for the endless support of my parents and family. To my wife I'm indebted for her understanding, support, and patience. vi TABLE OF CONTENTS LIST OF TABLES .

Journal of Verification, Validation and Uncertainty Quantification, 2022

The determination of the transverse tip deflection of an elastic, hollow, tapered, cantilever, bo... more The determination of the transverse tip deflection of an elastic, hollow, tapered, cantilever, box beam under a uniform loading applied over half the length of the beam presented in the V&V10.1 standard is used to compare the application of the validation procedures presented in the V&V10.1 and V&V20 standards. Both procedures aim to estimate the modeling error of the mathematical/computational model used in the simulations taking into account the variability of the modulus of elasticity of the material used in the beam and the rotational flexibility at the clamped end of the beam. The paper discusses the four steps of the two error quantification procedures: (1) characterization of the problem including all the assumptions and approximations made to obtain the experimental and simulation data; (2) selection of the validation variable; (3) determination of the different quantities required by the validation metrics in the two error quantification procedures; (4) outcome of the two v...

ASME 2020 Verification and Validation Symposium, 2020