Date: 03/05/09

Speaker: R. Bourguet 

Title: Hierarchical modeling of compressible turbulent unsteady flows around
bodies

Abstract:
In the context of realistic aerodynamic flow prediction, the elaboration of a
hierarchical modeling strategy allows to consider both precise numerical
simulation of physical phenomena by a "High-Fidelity" (HF) approach, and
integration of low numerical complexity models into optimization or control
procedures. The present study contributes to the development of such a
methodology for the modeling of compressible and turbulent unsteady flows
around bodies. The structural properties of non-equilibrium turbulence are
examined in high Reynolds number parietal flows. On the basis of this physical
analysis, a constitutive law is suggested for turbulent stress modeling within
the statistical framework of the Organised Eddy Simulation. The non-linearities
occurring between mean strain and turbulent stress anisotropy tensors can be
captured by a tensorial eddy-viscosity. The components of the anisotropic
eddy-viscosity are determined by a specific turbulence model issued from
projections of a second-order closure. Jointly, a reduced-order modeling
approach issued from the Galerkin projection of the compressible flow
Navier-Stokes equations onto a low-dimensional basis extracted by Proper
Orthogonal Decomposition (POD), is developed. The POD-Galerkin method is
applied in the case of slightly compressible and transonic flows around wings
initially predicted by direct numerical simulation or the previous HF
approach. This leads to an efficient prediction of main flow space-time
evolutions while a strong reduction of the number of degrees of freedom is achieved.
The robustness of the POD-Galerkin model towards parameter changes in the flow
configuration is quantified. A method based on Hadamard formulation of Navier-Stokes
equations is suggested to take into account wing shape modification in the reduced-order
model, in the prospect of its application to optimal shape design.