Discontinuous Galerkin Method for the numerical investigation of the effects of an active Gurney flap on the characteristics of an airfoil

In the last two decades in fluid dynamics it has been reported an increasing attention toward higher order methods because of their capability to simulate with great accuracy some phenomena involving wave propagation and/or turbulence which are of great practical interest. At the same time the methods based on a Discontinuous Galerkin formulation for the spatial discretization have been investigated with increasing interest since the correspondent high order versions of the methods traditionally employed in fluid dynamics (Finite Elements Methods, Finite Volumes and Finite Differences) have shown important drawbacks in terms of efficiency or their implementation is hard. Nowadays the Discontinuous Galerkin Method can be considered mature as a great amount of numerical studies are available in literature in which the properties of this discretization such as robustness and stability are investigated. However studies regarding complex applications of practical interest are still missing. In this work an efficient Discontinuous Galerkin method is proposed for the solution of the Favre averaged Navier Stokes equations written adopting an Arbitrary Lagrangian Eulerian formulation, for turbulent compressible flows in two dimensions and for bodies whose velocity with respect to the mean flow field is not constant. The turbulence model is based either on the Spalart Allmaras equation or the k-ω. To partially mitigate its intrinsic high computational cost, a nodal formulation of the Discontinuous Galerkin Method was adopted. The integration in time of the governing equations is carried out either with an explicit Runge-Kutta fourth order scheme or with an implicit time discretization based on a preconditioned Generalized Minimal RESidual algorithm for the solution of the Newton linearized system. The numerical model is applied to the solution of unsteady flows associated to an actively controlled Gurney Flap (or micro-tab) located in proximity of the trailing edge of an airfoil, with oscillations up to 20Hz. Several configurations of deployment motions are considered under different free stream conditions in order to demonstrate the capability of the solver to predict accurately unsteady non-linear problems at high Reynolds numbers. Moreover the numerical calculations are compared with experimental data in the case of the NACA 0012 airfoil, and of a modified version of the base shape employed in the experiments whose trailing edge is slightly thickened in order to accommodate the Gurney flap and the mechanism for the active flap tests. The results are in good agreement with the experimental data. The flow scenarios proposed in literature in the case of a static Gurney flap, under different flow conditions and flap geometries, are confirmed. The dynamic case is investigated for different motion frequencies and flap heights, and compared with available experimental data. Extensive numerical simulations of active Gurney flaps are still missing, and the present work represents an attempt to give an insight into the effectiveness of active flaps