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Title: One-dimensional ablation using a full Newton's method and finite control volume procedure.

Abstract

No abstract prepared.

Authors:
 [1]; ;  [2]
  1. (North Carolina State University, Raleigh, NC)
  2. (Blackwell Consulting, Corrales, NM)
Publication Date:
Research Org.:
Sandia National Laboratories
Sponsoring Org.:
USDOE
OSTI Identifier:
897903
Report Number(s):
SAND2006-3242C
TRN: US200705%%417
DOE Contract Number:
AC04-94AL85000
Resource Type:
Conference
Resource Relation:
Conference: Proposed for presentation at the AIAA/ASME Joint Thermophysics and Heat Transfer Conference held June 5-8, 2006 in San Francisco, CA>
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; ONE-DIMENSIONAL CALCULATIONS; THERMODYNAMICS; ABLATION

Citation Formats

Edwards, Jack R., Amar, A. J., and Blackwell, Bennie Francis. One-dimensional ablation using a full Newton's method and finite control volume procedure.. United States: N. p., 2006. Web.
Edwards, Jack R., Amar, A. J., & Blackwell, Bennie Francis. One-dimensional ablation using a full Newton's method and finite control volume procedure.. United States.
Edwards, Jack R., Amar, A. J., and Blackwell, Bennie Francis. Mon . "One-dimensional ablation using a full Newton's method and finite control volume procedure.". United States. doi:.
@article{osti_897903,
title = {One-dimensional ablation using a full Newton's method and finite control volume procedure.},
author = {Edwards, Jack R. and Amar, A. J. and Blackwell, Bennie Francis},
abstractNote = {No abstract prepared.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon May 01 00:00:00 EDT 2006},
month = {Mon May 01 00:00:00 EDT 2006}
}

Conference:
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  • The exponential differencing scheme of Spalding, which has been used for convection problems, is adapted to solve one-dimensional ablation problems by using a grid attached to the receding surface. Using the finite control volume approach, element conduction, convection, and storage matrices are developed. The method is applied to a steady-state ablation problem for which an analytical solution is known; comparisons are also made with upwind differencing for the convection terms and central differencing for the conduction terms. An example of a realistic ablation problem is presented.
  • The exponential differencing scheme of Spalding, which has been used for convection problems, is adapted to solve one-dimensional ablation problems by using a grid attached to the receding surface. Using the Finite Control Volume approach, element conduction, convection, and storage matrices are developed. The method is applied to a steady state ablation problem for which an analytical solution is known; comparisons are also made with upwind differencing for the convection terms and central differencing for the conduction terms. An example of a realistic ablation problem is presented.
  • 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 uniformmore » free stream environment.« less
  • 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 uniformmore » free stream environment.« less
  • A fully implicit solution algorithm based on Newton's method is used to solve the steady, incompressible Navier-Stokes and energy equations. An efficiently evaluated numerical Jacobian is used to simplify implementation, and mesh sequencing is used to increase the radius of convergence of the algorithm. We employ finite volume discretization using the power law scheme of Patankar to solve the benchmark backward facing step problem defined by the ASME K-12 Aerospace Heat Transfer Committee. LINPACK banded Gaussian elimination and the preconditioned transpose-free quasi-minimal residual (TFQMR) algorithm of Freund are studied as possible linear equation solvers. Implementation of the preconditioned TFQMR algorithmmore » requires use of the switched evolution relaxation algorithm of Mulder and Van Leer to ensure convergence. The preconditioned TFQMR algorithm is more memory efficient than the direct solver, but our implementation is not as CPU efficient. Results show that for the level of grid refinement used, power law differencing was not adequate to yield the desired accuracy for this problem.« less