Validation of a Discontinuous Galerkin Implementation of the Time-Domain Linearized Navier–Stokes Equations for Aeroacoustics

The propagation of small perturbations in complex geometries can involve hydrodynamic-acoustic interactions, coupling acoustic waves and vortical modes. A propagation model, based on the linearized Navier–Stokes equations, is proposed. It includes the mechanism responsible for the generation of vorticity associated with the hydrodynamic modes. The linearized Navier–Stokes equations are discretized in space using a discontinuous Galerkin formulation for unstructured grids. Explicit time integration and non-reflecting boundary conditions are described. The linearized Navier–Stokes (LNS) model is applied to two test cases. The first one is the time-harmonic source line in an incompressible inviscid two-dimensional mean shear flow in an infinite domain. It is shown that the proposed model is able to capture the trailing vorticity field developing behind the mass source and to represent the redistribution of the vorticity. The second test case deals with the analysis of the acoustic propagation of an incoming perturbation inside a circular duct with a sudden area expansion in the presence of a mean flow and the evaluation of its scattering matrix. The computed coefficients of the scattering matrix are compared to experimental data for three different Mach numbers of the mean flow, M0 = 0.08, 0.19 and 0.29. The good agreement with the experimental data shows that the proposed method is suitable for characterizing the acoustic behavior of this kind of network

Proper orthogonal decomposition as surrogate model for aerodynamic optimization

A surrogate model based on the proper orthogonal decomposition is developed in order to enable fast and reliable evaluations of aerodynamic fields. The proposed method is applied to subsonic turbulent flows and the proper orthogonal decomposition is based on an ensemble of high-fidelity computations. For the construction of the ensemble, fractional and full factorial planes together with central composite design-of-experiment strategies are applied. For the continuous representation of the projection coefficients in the parameter space, response surface methods are employed. Three case studies are presented. In the first case, the boundary shape of the problem is deformed and the flow past a backward facing step with variable step slope is studied. In the second case, a two-dimensional flow past a NACA 0012 airfoil is considered and the surrogate model is constructed in the (Mach, angle of attack) parameter space. In the last case, the aerodynamic optimization of an automotive shape is considered. The results demonstrate how a reduced-order model based on the proper orthogonal decomposition applied to a small number of high-fidelity solutions can be used to generate aerodynamic data with good accuracy at a low cost

Broadband trailing-edge noise prediction with a stochastic source model

A RANS-based numerical technique for the prediction of the airfoil trailing-edge broadband noise is presented. The definition of the sound sources from RANS turbulence statistics is based on a stochastic reconstruction of the turbulent velocity fluctuations. The method, named Eulerian Solenoidal Digital Filter, accounts for the convective transport and for the solenoidality of the velocity field. The acoustic near field is computed solving the Acoustic Perturbation Equations in the frequency domain. The integral formulation of Ffowcs Williams and Hawkings is used to evaluate the far-field radiation. The ESDF method is validated for the case of homogeneous isotropic turbulence and it is applied to the calculation of the broadband trailing-edge noise of a NACA 0012 airfoil. Near-field and far-field results are compared with analytical and experimental dat