Advances in numerical optimization have raised the possibility that efficient and novel aircraft configurations may be ``discovered'' by an algorithm. To begin exploring this possibility, a fast and robust
set of tools for aerodynamic shape optimization is developed.
Parameterization and mesh-movement are integrated to accommodate large changes in the geometry. This integrated approach uses a coarse B-spline control grid to represent the geometry and move the computational mesh; consequently, the mesh-movement algorithm is two to three orders faster than a node-based linear elasticity approach,
without compromising mesh quality. Aerodynamic analysis is performed using a flow solver for the Euler equations. The governing equations are discretized using summation-by-parts finite-difference operators and simultaneous approximation terms, which permit nonsmooth mesh continuity at block interfaces. The discretization results in a set of nonlinear algebraic equations, which are solved using an efficient parallel Newton-Krylov-Schur strategy. A gradient-based optimization
algorithm is adopted. The gradient is evaluated using adjoint variables for the flow and mesh equations in a sequential approach.
The flow adjoint equations are solved using a novel variant of the Krylov solver GCROT. This variant of GCROT is flexible to take
advantage of non-stationary preconditioners and is shown to outperform restarted flexible GMRES. The aerodynamic optimizer is applied to several studies of induced-drag minimization. An elliptical lift
distribution is recovered by varying spanwise twist, thereby validating the algorithm. Planform optimization based on the Euler equations produces a nonelliptical lift distribution, in contrast with the predictions of lifting-line theory. A study of spanwise vertical shape optimization confirms that a winglet-up configuration is more efficient than a winglet-down configuration. A split-tip geometry is
used to explore nonlinear wake-wing interactions: the optimized split-tip demonstrates a significant reduction in induced drag relative to a single-tip wing. Finally, the optimal spanwise loading for a box-wing configuration is investigated.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/17772 |
| Date | 24 September 2009 |
| Creators | Hicken, Jason |
| Contributors | Zingg, David W. |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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