The use of steady-state aerodynamic optimization methods in the computational
fluid dynamic (CFD) community is fairly well
established. In particular, the use of adjoint methods has proven to be very
beneficial because their cost is independent of the number of design variables.
The application of numerical optimization to airframe-generated noise, however, has not received as much attention, but with the significant
quieting of modern engines, airframe noise now competes with engine noise.
Optimal control techniques for unsteady flows are needed in order to be able to reduce airframe-generated noise.
In this thesis, a general framework is formulated to calculate the gradient of a cost function in a nonlinear unsteady flow environment
via the discrete adjoint method. The unsteady optimization algorithm developed in this work
utilizes a Newton-Krylov approach since the gradient-based optimizer uses the quasi-Newton method BFGS, Newton's method is applied to the
nonlinear flow problem, GMRES is used to solve the resulting linear problem inexactly, and last but not least the linear adjoint problem
is solved using Bi-CGSTAB. The flow is governed by the unsteady two-dimensional
compressible Navier-Stokes equations in conjunction with a one-equation turbulence model, which are discretized using
structured grids and a finite difference approach. The effectiveness of the unsteady optimization algorithm is demonstrated
by applying it to several problems of interest including shocktubes,
pulses in converging-diverging nozzles, rotating cylinders, transonic buffeting, and an unsteady trailing-edge flow.
In order to address radiated far-field noise, an acoustic wave propagation program based on
the Ffowcs Williams and Hawkings (FW-H) formulation is implemented and validated. The general framework is then used
to derive the adjoint equations for a novel hybrid URANS/FW-H optimization algorithm
in order to be able to optimize the shape of airfoils based on their calculated far-field pressure fluctuations.
Validation and application results for this novel hybrid URANS/FW-H optimization algorithm show that it is possible
to optimize the shape of an airfoil in an unsteady flow environment to minimize
its radiated far-field noise while maintaining good aerodynamic performance.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/17241 |
| Date | 26 February 2009 |
| Creators | Rumpfkeil, Markus Peer |
| Contributors | Zingg, David W. |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
| Format | 4592209 bytes, application/pdf |
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