Title page for ETD etd-07262006-113853

Type of Document

Master's Thesis

Author

Amar, Adam Joseph,

URN

etd-07262006-113853

Title

Modeling of One-Dimensional Ablation with Porous Flow Using Finite Control Volume Procedure

Degree

Master of Science

Graduate Program

Aerospace Engineering

Advisory Committee

Advisor Name	Title
Dr. J. R. Edwards	Committee Chair
Dr. A. V. Kuznetsov	Committee Member
Dr. B. F. Blackwell	Committee Member

Keywords

computational heat transfer
ablation
reentry

Date of Defense

2006-07-27

Availability

unrestricted

Abstract

The development and verification of a one-dimensional (planar) material thermal
response code with ablation is presented. The mixture energy, gas phase continuity,
and solid phase continuity equations are solved with Fourier?s law to model heat
conduction, Darcy?s law to model porous flow, and the ideal gas law to model the
state of the pyrolysis gases. Consequently, the temperature, gas density, and solid
density profiles are predicted for a decomposing ablator and the resulting gas flux,
porosity, and pore pressure can be determined.
The control volume finite element spatial discretization method (CVFEM), the
Euler implicit time integrator, and a contracting grid scheme are used for the solution
of the mixture energy and gas phase continuity equations. The solid continuity
equation is solved through direct integration of decomposition kinetics under the
assumption of a constant temperature rise rate within a given time step. The mixture
energy and gas phase continuity equations are solved using segregated Newton
solvers, which allow for nonlinear iteration on the entire system of nodal equations
that are discretized according to a residual formulation. The block Gauss-Seidel segregated
solution procedure has been implemented to globally iterate on the system
of governing equations resulting in a fully coupled solution.
Formal verification studies were performed that show the implemented model
exhibits second order spatial accuracy and first order temporal accuracy. In addition,
the second order nonlinear convergence of the Newton solvers was verified for
temperature dependent material properties, the thermochemical ablation model, the
heat of ablation model, decomposing materials, and several nonlinear boundary conditions.
While not considered a part of the formal verification process, code-to-code
comparisons are also presented.
Timing studies were performed, and when comparable accuracy is considered, the
method developed in this study exhibits significant time savings over the property
lagging approach typically used in legacy codes. In addition, maximizing the Newton
solver?s convergence rate by including sensitivities to the surface recession rate for the
mixture energy equation reduces the overall computational time when compared to
lagging the grid convection terms in the iteration process.

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