Title page for ETD etd-04262002-101328
|Type of Document
|Author's Email Address
||Gradient-Based Optimum Aerodynamic Design Using Adjoint Methods
||Aerospace and Ocean Engineering
|Cliff, Eugene M.
|Borggaard, Jeffrey T.
|Devenport, William J.
|Grossman, Bernard M.
|Mason, William H.
- Optimum aerodynamic design
- Boundary conditions
- Adjoint method
- Transonic airfoil design
|Date of Defense
Continuous adjoint methods and optimal control theory are applied
to a pressure-matching inverse design problem of quasi 1-D nozzle flows.
Pontryagin's Minimum Principle is used to derive the adjoint
system and the reduced gradient of the cost functional. The
properties of adjoint variables at the sonic throat and the shock
location are studied, revealing a logarithmic singularity at the
sonic throat and continuity at the shock location. A numerical
method, based on the Steger-Warming flux-vector-splitting scheme,
is proposed to solve the adjoint equations. This scheme can finely
resolve the singularity at the sonic throat. A non-uniform grid,
with points clustered near the throat region, can resolve it even
better. The analytical solutions to the adjoint equations are also
constructed via Green's function approach for the purpose of
comparing the numerical results. The pressure-matching inverse
design is then conducted for a nozzle parameterized by a single
In the second part, the adjoint methods are applied to the problem
of minimizing drag coefficient, at fixed lift coefficient, for 2-D
transonic airfoil flows. Reduced gradients of several functionals
are derived through application of a Lagrange Multiplier Theorem.
The adjoint system is carefully studied including the adjoint
characteristic boundary conditions at the far-field boundary. A
super-reduced design formulation is also explored by treating the
angle of attack as an additional state; super-reduced gradients
can be constructed either by solving adjoint equations with
non-local boundary conditions or by a direct Lagrange multiplier
method. In this way, the constrained optimization reduces to an
unconstrained design problem. Numerical methods based on Jameson's
finite volume scheme are employed to solve the adjoint equations.
The same grid system generated from an efficient hyperbolic grid
generator are adopted in both the Euler flow solver and the
adjoint solver. Several computational tests on transonic airfoil
design are presented to show the reliability and efficiency of
adjoint methods in calculating the reduced (super-reduced)
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