Licentiate seminar

Adjoint Based Control and Optimization of Aerodynamic Flows

Defendant Main Advisor Extra Advisor Date
Mattias Chevalier Dan Henningson Martin Berggren 2002-06-05

Per Weinerfelt, SAAB Aerospace, Future Products, Linköping

Evaluation committee


Adjoint based optimal controls both for transitional boundary flows and for quasi-1D Euler flow are studied in this thesis. A nonlinear optimization problem governed by the Navier--Stokes equations is solved using the associated adjoint equations to minimize the objective function measuring the energy of the perturbation to a laminar flow. The optimization problem is derived and implemented in the context of direct numerical simulations of incompressible spatially-developing three-dimensional boundary layer flows and the gradient computation is verified with finite-differences. The nonlinear optimal control is shown to be more efficient in reducing the disturbance energy than an optimal control based on the Orr--Sommmerfeld--Squire equations when nonlinear interactions are becoming significant in the boundary layer. For weaker disturbances the two methods are quite similar. Tollmien-Schlichting waves, streamwise streaks, and cross-flow vortices have all been controlled successfully with a nonlinear control. The same adjoint based solution strategy is applied to another optimization problem which is governed by the quasi-1D Euler equations and where we want to find the optimal shape of a nozzle. The impact of the choice of boundary conditions and discretization of the problem on the convergence rate of the optimization algorithm is studied. Numerical experiments at subsonic and transonic speeds, show that the gradient evaluations are accurate enough to obtain satisfactory convergence of the quasi-Newton algorithm.
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