Numerical simulation of shock oscillations over airfoil using a wall law approach

Eric Goncalvès da Silva (1) , Robert Houdeville

1 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]

Shock-induced oscillations (SIO) are a pure aerodynamic problem that can occur over rigid airfoils as a result of the development of instabilities caused by the boundary-layer separation and the shock-wave interaction. This problem is extremely important because it can lead to the buffeting phenomenon through the mechanical response of the wing structure. A detailed description of the physical features of SIO is given by Lee. Computations have been essentielly done over thick airfoils to investigate the SIO problem. Numerically, the local time-step technique, which is efficient to accelerate the convergence towards the steady state, cannot be applied for unsteady computations that imperatively need a global time step. This constraint drastically reduces the method efficiency because of the Courant-Friedrichs-Lewy stability criterion. To overcome this difficulty, the dual time-stepping approach has been proposed by Jameson. It has also been used recently by Furlano and Renaud for SIO computations. In the present study a wall law approach is used to relax the mesh refinement near the wall and therefore to increase the value of the global time step. Then, the computational efficiency of the explicit method is restored. Providing large CPU cost savings, the wall law approach has also proved to be attractive for the quality of its results in computing separated flows and for the robustness improvment it brings. Moreover, the eddy viscosity models based on the linear Boussinesq relation are known to be unable to capture the boundary layer separation and unable to take into consideration the nonequilibrium effects. A consequence of these weakness observed for unsteady computations is the over production of eddy viscosity,which limits the development of natural unsteadiness and modifies the flow topology. In this Note, we show that the turbulence model behavior can be remarkably improved by limiting the eddy viscosity with the shear-stress-transport (SST) correction associated with a wall law approach.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Eric Goncalvès da Silva, Robert Houdeville. Numerical simulation of shock oscillations over airfoil using a wall law approach. AIAA Journal, 2003, 41 (9), pp.1829-1832. ⟨10.2514/2.7303⟩. ⟨hal-00217677⟩