Date of Award

Spring 1992

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Mechanical Engineering

Committee Director

Oktay Baysal

Committee Member

Osama Kandil

Committee Member

Albert S. Roberts

Committee Member

David S. Miller


A new and efficient procedure for aerodynamic shape optimization is presented. The salient lineaments of this procedure are: (1) using a discrete sensitivity analysis approach to determine analytically the aerodynamic sensitivity coefficients; (2) obtaining the flowfield solution either by a computational fluid dynamics (CFD) analysis or, alternatively, by a flowfield extrapolation method which is based on a truncated Taylor's series; (3) defining the aerodynamic shape in such a way that it is not restricted to any class of surfaces and the optimizer automatically shapes the aerodynamic configuration to any arbitrary geometry; and (4) requiring no expertise other than that needed for formulating the optimization problem in question. This procedure is successfully demonstrated on different aerodynamic optimization problems.

In one of the optimization problems, the ramp shape of a scramjet nozzle-afterbody configuration is optimized to yield a maximum thrust force coefficient. However, prior to its design optimization, a CFD capability for the mixing of two-dimensional, viscous, multispecies flows has been developed in order to gain a detailed understanding of the complex flowfield features of the scramjet nozzle-afterbody configuration. It is shown that heavier exhaust mixture (simulated by a Freon-Argon mixture) undergoes gasdynamic expansion at a smaller rate than does lighter "air" exhaust flow.

In the sensitivity analysis approach, both Euler and thin-layer Navier-Stokes equations are used. Their discretized equations are solved using an implicit, upwind-biased, finite-volume scheme. The van Leer flux-vector splitting is used in the discretization of the pressure and convective terms.

The direct and iterative solution methods, which are deemed most applicable to the large linear systems of algebraic equations arising in the sensitivity approach, are investigated with regards to their accuracies, computational time, and computer memory requirements. These methods are shown to be feasible only for small two-dimensional problems. Due to the prohibitively high memory requirements, they become impractical for large two-dimensional problems and inapplicable for any of the three-dimensional problems. To alleviate this limitation, a new scheme based on domain decomposition principles has been developed and is called the Sensitivity Analysis Domain-Decomposition (SADD) scheme.