Airfoil Optimization for Unsteady Flows with Application to High-lift Noise Reduction

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.Ph

2022: Markus Peer Rumpfkeil, Milestone Book Selection

Promotion to the rank of Professor, Department of Mechanical and Aerospace Engineeringhttps://ecommons.udayton.edu/svc_milestone/1096/thumbnail.jp

Theoretical Analysis of Shrouded Horizontal Axis Wind Turbines

Numerous analytical studies for power augmentation systems can be found in the literature with the goal to improve the performance of wind turbines by increasing the energy density of the air at the rotor. All methods to date are only concerned with the effects of a diffuser as the power augmentation, and this work extends the semi-empirical shrouded wind turbine model introduced first by Foreman to incorporate a converging-diverging nozzle into the system. The analysis is based on assumptions and approximations of the conservation laws to calculate optimal power coefficients and power extraction, as well as augmentation ratios. It is revealed that the power enhancement is proportional to the mass stream rise produced by the nozzle diffuser-augmented wind turbine (NDAWT). Such mass flow rise can only be accomplished through two essential principles: the increase in the area ratios and/or by reducing the negative back pressure at the exit. The thrust coefficient for optimal power production of a conventional bare wind turbine is known to be 8/9, whereas the theoretical analysis of the NDAWT predicts an ideal thrust coefficient either lower or higher than 8/9 depending on the back pressure coefficient at which the shrouded turbine operates. Computed performance expectations demonstrate a good agreement with numerical and experimental results, and it is demonstrated that much larger power coefficients than for traditional wind turbines are achievable. Lastly, the developed model is very well suited for the preliminary design of a shrouded wind turbine where typically many trade-off studies need to be conducted inexpensively