A Method for Optimizing Non-Axisymmetric Liners for Multimodal Sound Sources

Central processor unit 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 constrained optimization methodologies to assess the relative merits of non-axisymmetric versus axisymmetric liner concepts for improving liner acoustic suppression. This assessment is performed with a multimodal noise source (with equal mode amplitudes and phases) in a finite-length rectangular duct without flow. The sparse solver is found to reduce memory requirements by a factor of five and central processing time by a factor of eleven when compared with the commonly used solver. Results show that the optimum impedance of the uniform liner is dominated by the least attenuated mode, whose attenuation is maximized by the Cremer optimum impedance. An optimized, four-segmented liner with impedance segments in a checkerboard arrangement is found to be inferior to an optimized spanwise segmented liner. This optimized spanwise segmented liner is shown to attenuate substantially more sound than the optimized uniform liner and tends to be more effective at the higher frequencies. The most important result of this study 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.