Numerical optimization for airframe noise reduction

Airframe noise, which is primarily generated by the nose and main landing gears as well as the high-lift devices such as the leading-edge slats and trailing-edge flaps, is the dominant noise source for an aircraft in landing approach. In this work, two noise reduction strategies are explored, namely porous trailing-edge treatment and optimal shape design. To that end, a discrete adjoint framework based on algorithmic differentiation (AD) is developed to study airframe noise minimization via both shape and topology optimization. This framework is first applied to identify the optimal distribution of porous material of a flat plate with a porous trailing edge in subsonic flow resolved with a high resolution large-eddy simulation (LES) method. The AD-based noise adjoint is shown to be highly accurate and allows for efficient evaluation of the entire design sensitivity vec- tor in one stroke, at a cost comparable to that of a single primal LES simulation. Noise minimization is performed to determine the optimal distribution of the design variables that govern the porosity and permeability of the trailing edge. The optimal design obtained is found to attain a maximum noise reduction of 12dB from a flat plate with solid trailing edge and 3dB from the baseline design with a linear porosity variation respectively. Comparison of far-field noise spectra reveals that the optimization has little effect on the broadband noise component compared to its baseline level. The design space of this optimization problem is also shown to be multi-modal. Next, a hybrid noise prediction framework is developed in which a permeable surface Ffowcs Williams and Hawkings (FW-H) Equation solver is implemented and coupled with an unsteady Reynolds-Averaged Navier-Stokes (URANS) solver. The accuracy of this hybridframework was verified using a canonical problem of a circular cylinder in cross flow. Next, an AD-based consistent discrete adjoint solver is developed which directly inherits the convergence properties of the primal flow solver due to the differentiation of the entire nonlinear fixed-point iterator. This framework is applied to a number of 2-D and 3-D noise minimization cases via shape optimization. The lift and noise design objectives were shown to be competing in all cases studied - noise minimization always leads to a marked loss of lift. Lift-constrained noise minimization were performed for all 2-D cases and shown to be able to successfully constrain the mean lift at its baseline level while still reducing noise. A number of unconventional optimal designs were obtained, including an airfoil design with wavy surfaces to reduce wake interaction noise. In the 3-D case, the baseline and optimized designs were also analyzed using a turbulence-resolving delayed detached-eddy simulation (DDES). The results indicate that the optimal configuration determined by the URANS-based optimization also performs well when analyzed with DDES and even exceeds the prediction of the original URANS simulation