Assessment of Equation Solvers and Optimization Techniques for Nonaxisymmetric Liners

Abstract

CPU times and memory requirements for a commonly used solver are compared to that of a state-of-the-art, parallel, sparse solver. The sparse solver is then used in conjunction with three optimization methodologies (genetic algorithm, contour deformation, and Davidon‐Fletcher‐Powell) to assess the usefulness of these methodologies for designing optimized nonaxisymmetric liners. This assessment is performed using a multimodal noise source in a finite length rectangular duct without flow. The sparse solver is found to reduce memory requirements by a factor of 5 and processing time by a factor of 11 when compared with the commonly used solver. All three optimization techniques give nearly the same optimum impedance for uniform liners, and this impedance approaches the Cremer optimum impedance at low frequency where only the plane wave mode is cuton. For nonaxisymmetric liners, the genetic algorithm gives improvements in optimum attenuation over the other optimization methodologies because of the presence of multiple local optima. Another important result is the discovery that, when optimized, a spanwise segmented liner with two segments gives attenuations equal to or substantially greater than an optimized axially segmented liner with the same number of segments.