Hybrid aeroacoustic computation of a low Mach number non-isothermal shear layer

• A hybrid aeroacoustic formulation is developed for low Mach heated flows.
• The hydrodynamic solver belongs to the Low Mach Number Approximation class.
• Several source terms are compared to obtain the acoustic field.
• Links to Ribner’s and Lilley’s analogies are provided.
• The noise of isothermal or non-isothermal shear layers is computed.

Direct numerical simulation of noise generated by low speed flows requires strong numerical constraints related to the different scales in space and time for the dynamics of the flow and the propagation of sound waves. At low Mach numbers, the aeroacoustic hybrid approaches initiated by Hardin and Pope (1994) [5] based on separate calculations for the flow and for the acoustic radiation, are therefore attractive. In this paper, we show that such methods can be used for the general case of non-constant density or temperature. The starting point is an asymptotic expansion of the full Navier–Stokes equations that gives a set of equations that retain the presence of density and temperature inhomogeneities, allowing access to the dynamic quantities without the stability constraints related to acoustic waves. Then starting from the solutions of flow fluctuating quantities, we propose several possible developments of the equations to obtain the acoustic field. They lead to different sets of equations and source terms depending on the level of simplifying assumptions: the Perturbed Low Mach Number Approximation (PLMNA) or the linearized Euler equations (LEE) linearized with respect to the mean flow. An isothermal and a non-isothermal spatially evolving mixing layer are taken as test problems. The solutions of the proposed hybrid methods show a satisfactory behavior compared with the reference solution given by a compressible DNS.