Summary: The use of steady-state aerodynamic shape optimization methods in the field of computational fluid dynamics (CFD) is fairly well established. In particular, the use of adjoint methods has proven to be very beneficial because their computational cost is independent of the number of shape design variables. However, the application of optimization methods to airframe-generated noise has not received as much attention even though airframe-generated noise competes nowadays with engine noise as modern engines have become significantly more quiet. This is especially true during aircraft approach and landing, when engines operate at reduced thrust, and airframe components such as high-lift devices are in a deployed state.

In this thesis, a general framework is developed to calculate the gradient of a cost function in a nonlinear unsteady flow environment using the adjoint method. The flow is governed by the unsteady two-dimensional compressible Navier-Stokes equations (URANS) in conjunction with a one-equation turbulence model. The unsteady optimization algorithm developed in this work utilizes a Newton-Krylov approach: Newton’s method is applied to solve the nonlinear flow problem; the gradient-based optimizer uses the quasi-Newton method BFGS; and the Krylov subspace method solvers GMRES and Bi-CGSTAB are used to solve the resulting linear forward and adjoint problems, respectively. The efficacy 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.

Finally, to calculate the 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 optimize the shape of airfoils based on their calculated far-field noise. 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.

Refereed Journal Papers

M.P. Rumpfkeil and D.J. Mavriplis "Efficient Hessian Calculations using Automatic Differentiation and the Adjoint Method with Applications", AIAA Journal, 2010. Accepted.

M. P. Rumpfkeil and D.W. Zingg "A Hybrid Algorithm for Far-Field Noise Minimization", Computers and Fluids, doi:10.1016/j.compfluid.2010.05.006, Volume 39, Issue 9, pp. 1516-1528, 2010.

M. P. Rumpfkeil and D.W. Zingg "The optimal control of unsteady flows with a discrete adjoint method", Journal of Optimization and Engineering, doi: 10.1007/s11081-008-9035-5, Volume 11, Issue 1, pp. 5-22, 2010.

Refereed Conference Papers

M.P. Rumpfkeil, W. Yamazaki, and D.J. Mavriplis "Uncertainty Analysis Utilizing Gradient and Hessian Information", Sixth International Conference on Computational Fluid Dynamics (ICCFD6), St. Petersburg, Russia, July 2010 (100KB).

W. Yamazaki, M.P. Rumpfkeil, and D.J. Mavriplis "Design Optimization Utilizing Gradient/Hessian Enhanced Surrogate Model", 28th AIAA Applied Aerodynamics Conference, Chicago, Illinois, USA, June 2010. AIAA paper 2010-4363 (2.6MB).

M. P. Rumpfkeil and D.J. Mavriplis "Efficient Hessian Calculations using Automatic Differentiation and the Adjoint Method", 48th AIAA Aerospace Meeting and Exhibit, Orlando, Florida, USA, January 2010. AIAA paper 2010-1268 (648KB).

M. P. Rumpfkeil and D.W. Zingg "Far-Field Noise Minimization Using an Adjoint Approach", Fifth International Conference on Computational Fluid Dynamics (ICCFD5), Seoul, Korea, July 2008 (208KB).

M. P. Rumpfkeil and D.W. Zingg "Unsteady Optimization Using a Discrete Adjoint Approach Applied to Aeroacoustic Shape Design", 46th AIAA Aerospace Meeting and Exhibit, Reno, Nevada, USA, January 2008. AIAA paper 2008-18 (268KB).

M. P. Rumpfkeil and D.W. Zingg "Optimal Aeroacoustic Shape Design Using a Discrete Adjoint Approach". In Proceedings of the 15th Annual Conference of the CFD Society of Canada, Toronto, Ontario, May 2007. Paper 1106, pp. 221-228 (140KB).

M. P. Rumpfkeil and D.W. Zingg "The Remote Inverse Shape Design of Airfoils in Unsteady Flows". In Proceedings of the 12th Annual CASI Aerodynamics Symposium, Toronto, Ontario, April 2007. Paper 318 (820KB).

M. P. Rumpfkeil and D.W. Zingg "A General Framework for the Optimal Control of Unsteady Flows with Applications", 45th AIAA Aerospace Meeting and Exhibit, Reno, Nevada, USA, January 2007. AIAA paper 2007-1128 (1.2MB).