A fast method For calculating sensitivities of acoustic propagation in ducts to small changes in geometry and mean flow

Hawkins, Rhiannon and Wilson, Alexander g. (2022) A fast method For calculating sensitivities of acoustic propagation in ducts to small changes in geometry and mean flow. In AIAA 2022. Aerospace Research Central.. (doi:10.2514/6.2022-3018).

Abstract

This paper introduces a computationally fast approximate method for calculating sensitivities of acoustic propagation in ducts to small changes in geometry and mean flow, although in this paper only changes to mean flow in one-dimensional and three-dimensional axisymmetric ducts are validated. A solution to the base (unperturbed) problem is first calculated by the eigen analysis in general curvilinear coordinates (EAGCC) method. The new method to calculate the sensitivities does not require any further eigen analysis beyond the base solution, and as a result is extremely fast to compute. The error in the method has been quantified for a range of test-cases and shown to be proportional to a single parameter combining the base flow Mach number, length of modified region, and a representative fractional increase in mean flow Mach number. As expected for a method based on linear approximation, the new method is shown to be accurate for small changes in mean flow over a limited region of the duct, but unsuitable for assessing widely varying geometries and mean flows. The new method is thus ideally suited to numerical optimisation and robust design studies, in which it can be used in an analogous manner to adjoint methods.

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