A coupled time-reversal/complex differentiation method for aeroacoustic sensitivity analysis: towards a source detection procedure

Abstract

Defining and identifying the aeroacoustic sources in a turbulent flow is a great challenge especially for noise control strategy. The purpose of the present study consists in proposing a new methodology to localize regions associated with sound generation. These regions are associated, in the present work, with those of high sensitivity of the acoustic field, using the heuristic argument that modifying the flow in these regions would lead to a very significant change in the radiated noise. The proposed method relies on the efficient coupling between the time-reversal theory applied to the Euler equations and the complex differentiation method to compute the sensitivity variable. To the knowledge of the authors, this is the first time that the time-reversal technique is applied to vectorial hydrodynamic equations, in place of the classical scalar wave equation. Subsequently, regions associated with sound generation are related to spatiotemporal events which exhibit the maximum of sensitivity to acoustical disturbances measured in far field. The proposed methodology is then successively tested on three cases for which the nature of the source is different: injection of mass, vibrating surfaces and flow instabilities arising in a plane mixing layer flow. For each test case, the two-dimensional Euler equations are solved using a numerical solver based on a pseudo-characteristics formulation. During these computations flow, variables are stored only at the computational boundaries. These variables are time reversed and relevant information concerning the acoustical disturbances is tagged using complex differentiation in order to lead the sensitivity analysis. The same numerical solver is used to access the evolution of the time-reversed variables. In each test case, the proposed methodology allows to localize successfully zones associated with noise generation.