Numerical Method

The 2D airfoil simulations are performed with the Navier-Stokes solver DLR-TAU [2, 3] using hybrid grids. This flow solver is a finite-volume solver for the Reynolds – averaged Navier-Stokes equations on hybrid grids. The convective fluxes can be dis­cretized either with upwind or central schemes, the latter being used in conjunction with scalar artificial dissipation for the present simulations. Time discretization is done implicitly using a backward Euler scheme [4] in connection with a LU-SGS linear solver.

1.1 Analysis in 2D

For the analysis of low speed cases, the airfoil NLF(0)416 by Somers [5] was chosen. This airfoil is a natural laminar flow airfoil with a very thin trailing edge. A wide base of experimental data at different flow conditions is available. These range from Re = 2 • 106, 4 • 106 and 6 • 106 for Ma = 0.1 as well as Ma = 0.2, 0.3 und 0.4 for Re = 6 • 106. This airfoil was chosen because in addition to the original airfoil with the very thin trailing edge, a version with a blunt trailing edge was also measured experimentally. The bluntness was generated by attaching a wedge on the original airfoil. Thus, numerical simulations with different trailing-edge geometries can be validated using the experimental values.

The subsequent flow solutions were obtained for Re = 4 • 106 at Ma = 0.1, using the Spalart-Almaras turbulence model [6]. The transition was fixed according to the locations given in [5]. All versions of the airfoil were discretized using 210 grid points on the upper surface and 150 grid points on the lower surface. Besides changing the topology of the grid at the wake, the number of grid points along the trailing edges was also varied. Parts of this study have been published in [7].