Publications

Abstract not provided.

A multi-dimensional finite element solver for decomposing and non-decomposing ablating materials has recently been developed and is discussed in this paper. The underlying mathematical and material models are presented along with its discretization via the finite element method. The governing equations and solution algorithm is based on the one-dimensional control-volume finite element method (CVFEM) Chaleur code, a successful ablation code in use at Sandia National Labs, and this paper represents a multi-dimensional extension of Chaleur. The Equilibrium Surface Thermochemistry (EST) code, an equilibrium gas/surface thermochemistry code for decomposing and non-decomposing materials that was previously developed by the authors is used in conjunction with this new multi-dimensional ablation code to provide ablation thermochemistry information (i.e. B0c and enthalpy tables). This new multi-dimensional ablation response code is first applied to solve two established code-to-code comparison problems with tabular aeroheating data. Another aspect of this work has been to develop the ability to couple CFD-based aeroheating data to the ablation code as a spatial and time variant boundary condition. Towards this end, we have established a one-way passing of aeroheating data from a hypersonic CFD code to the ablation code. We then examine the problem of simulating the ablation response of non-decomposing and decomposing materials in two arc-jet facilities.

A multi-dimensional finite element solver for decomposing and non-decomposing ablating materials has recently been developed and is discussed in this paper. The underlying mathematical and material models are presented along with its discretization via the finite element method. The governing equations and solution algorithm is based on the one-dimensional control-volume finite element method (CVFEM) Chaleur code, a successful ablation code in use at Sandia National Labs, and this paper represents a multi-dimensional extension of Chaleur. The Equilibrium Surface Thermochemistry (EST) code, an equilibrium gas/surface thermochemistry code for decomposing and non-decomposing materials that was previously developed by the authors is used in conjunction with this new multi-dimensional ablation code to provide ablation thermochemistry information (i.e. B0c and enthalpy tables). This new multi-dimensional ablation response code is first applied to solve two established code-to-code comparison problems with tabular aeroheating data. Another aspect of this work has been to develop the ability to couple CFD-based aeroheating data to the ablation code as a spatial and time variant boundary condition. Towards this end, we have established a one-way passing of aeroheating data from a hypersonic CFD code to the ablation code. We then examine the problem of simulating the ablation response of non-decomposing and decomposing materials in two arc-jet facilities.

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.

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.

Equations are presented to describe the sensitivity of the temperature field in a heat conducting body to changes in the volumetric heat source and volumetric heat capacity. These sensitivity equations, along with others not presented, are applied to a thermal battery problem to compute the sensitivity of the temperature field to 19 model input parameters. Sensitivity coefficients, along with assumed standard deviation in these parameters, are used to estimate the uncertainty in the temperature prediction. From the 19 parameters investigated, the battery cell heat source and volumetric heat capacity were clearly identified as being the major contributors to the overall uncertainty in the temperature predictions. The predicted operational life of the thermal battery was shown to be very sensitive to uncertainty in these parameters.

Three different methods are discussed for computing the sensitivity of the temperature field to changes in material properties and initial-boundary condition parameters for heat conduction problems. The most general method is to derive sensitivity equations by differentiating the energy equation with respect to the parameter of interest and numerically solving the resulting sensitivity equations. An example problem in which there are twelve parameters of interest is presented and the resulting sensitivity equations are derived. Numerical results are presented for thermal conductivity and volumetric heat capacity sensitivity coefficients for heat conduction in a 2-D orthotropic body. The numerical results are compared with the analytical solution to demonstrate that the numerical method is second order accurate as the mesh is refined spatially.

This report represents a summary of a Laboratory Directed Research and Development (LDRD) project to develop general purpose unstructured grid techniques for solving free and moving boundary problems in computational fluid dynamics and heat transfer. Both control volume finite element and Galerkin finite element techniques were utilized. A very robust technique for keeping the deforming mesh from tangling was implemented; the mesh was treated as a fictitious elastic body. Sample results for an ablating nose tip and buoyancy driven flow in a box are presented. References to additional publications resulting from this work are included.

An element based finite control volume procedure is applied to the solution of ablation problems for 2-D axisymmetric geometries. A mesh consisting of four node quadrilateral elements was used. The nodes are allowed to move in response to the surface recession rate. The computational domain is divided into a region with a structured mesh with moving nodes and a region with an unstructured mesh with stationary nodes. The mesh is costrained to move along spines associated with the original mesh. Example problems are presented for the ablation of a realistic nose tip geometry exposed to aerodynamic heating from a uniform free stream environment.