CAA simulation requires the calculation of the propagation of acoustic waves with low numerical dissipation and dispersion error, and to take into account complex geometries. To give, at the same time, an answer to both challenges, a Discontinuous Galerkin Method is developed for Computational AeroAcoustics. Euler's linearized equations are solved with the Discontinuous Galerkin Method using flux splitting technics. Boundary conditions are established for rigid wall, non-reflective boundary and imposed values. A first validation, for induct propagation is realized. Then, applications illustrate: the Chu and Kovasznay's decomposition of perturbation inside uniform flow in term of independent acoustic and rotational modes, Kelvin-Helmholtz instability and acoustic diffraction by an air wing.

The analysis of aeroacoustics propagation is required to solve many practical problems. As an alternative to Euler’s linearized equations, an equation was established by Galbrun in 1931. It assumes the flow verifies Euler’s equations and the perturbation is small and adiabatic. It is a linear second-order vectorial equation based on the displacement. Galbrun’s equation derives from a Lagrangian density and provides conservative expressions of the aeroacoustics intensity and energy density. A (CAA) method dealing with the numerical resolution of Galbrun’s equation using the finite-element method (FEM) is presented. The exact solution for the propagation of acoustic modes inside an axisymmetric straight-lined duct in the presence of a shear flow is known and compared with the FEM solution. Comparisons are found to be in good agreement and validate a first step in the development of a CAA method based on the FEM and Galbrun’s equation. The FEM is then applied to an axisymmetric duct including a varying cross section and a nonuniform flow with respect to both the axial and the radial coordinates. The expression of the aeroacoustics intensity implemented in the FEM provides an accurate in-duct power balance.

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We investigate the effect of the wall-scalar fluctuations on passive scalar turbulent fields for a moderate Reynolds number Rτ = 395 and for several Prandtl numbers ranging from the very low value Pr = 0.01 to the high value Pr = 10 by means of direct numerical simulation (DNS) simulations. Several cases of plane channel flows are considered. Case I is a channel flow heated on both walls with a constant imposed heat flux qw. We consider for this case two different types of boundary conditions. For the first one, the isoscalar boundary condition θw = 0 is imposed at the wall implying that its fluctuation and therefore its rms scalar fluctuations θrms=⟨θ′θ′⟩ is zero at the wall whereas in the second type, θw is not prescribed to a fixed value so that it is fluctuating in time at the wall leading to nonzero rms fluctuations. In this latter case, as the heat flux is maintained constant in time at the wall, the fluctuating heat flux q′w reduces to zero at the wall. For illustration purpose, in addition to case I, we also consider case II, which is a plane channel heated only from one wall but cooled from the other one at the same rate taking into account of the freestream scalar boundary condition at the wall θ′w≠0 with q′w=0. The distributions of the mean scalar field, root-mean-square fluctuations, turbulent heat flux, correlation coefficient, turbulent Prandtl number, and Nusselt number are examined in detail. Moreover, some insights into the flow structure of the scalar fields are provided. As a result of interest, it is found that the mean scalar field ⟨θ⟩ is not affected by the scalar fluctuations at the wall. But owing to the different boundary conditions applied at the wall, significant differences in the evolution of the rms scalar fluctuations θrms are observed in the immediate vicinity of the wall. Surprisingly, the maximum rms intensity remains almost unchanged in the near wall region whatever the type of boundary condition is applied at the wall. In addition, the turbulent heat fluxes that play a major role in heat transfer are found to be independent of the wall scalar fluctuations. This study demonstrates that the impact of the wall scalar fluctuations is appreciable mainly in the near wall region. This outcome must be taken into account when simulating industrial flows with thermal boundary conditions involving different fluid/solid combinations.

A two-way coupling on unstructured meshes between a flow and a high-order acoustic solvers for jet noise prediction is considered. The flow simulation aims at generating acoustic sources in the near field while the acoustic simulation solves the full Euler equations, thanks to a discontinuous Galerkin method, in order to take into account nonlinear acoustic propagation effects. This methodology is firstly validated on academic cases involving nonlinear sound propagation, shock waves and convection of aerodynamic perturbations. The results are compared to analytical solutions and direct computations. A good behaviour of the coupling is found regarding the targeted space applications. An application on a launch pad model is then simulated to demonstrate the robustness and reliability of the present approach.

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