On the Challenges of Validation Exercises of Two-Dimensional Models

The assessment of the modeling error of computational simulations (validation) requires the comparison of quantities of interest obtained from simulations and experiments, which are supposed to be obtained for similar conditions (geometry, boundary conditions, material properties, heat transfer coefficients, etc.). It is not unusual to find validation exercises assuming two-dimensional geometries. Such assumption implies that it is not possible to strictly satisfy the similarity of experimental and simulations conditions. In the recent AVT- 349 project, a two-dimensional validation exercise was proposed for boundary-layers developing on the Virginia Tech wind-tunnel wall with pressure gradients imposed by a rectangular wing with a NACA 0012 airfoil section in the middle of the tunnel at angles of attack between −10 deg and 12 deg. Modifications of the wind-tunnel geometry and boundary conditions were proposed for the simulations to take into account the effect of the displacement thickness of the “side walls” boundary-layers. Furthermore, no information was available to specify inflow and outflow boundary conditions, and so the length of the domain for the simulations is extended to allow the use of simplified boundary conditions. In his paper, we use the Virginia Tech test case for an angle of attack of −10 deg to illustrate the effects of changing geometry and boundary conditions in two-dimensional validation exercises. The mathematical/computational models are the Reynolds-averaged Navier–Stokes (RANS) equations using four different turbulence models (three eddy- viscosity models and a Reynolds-stress model). Sets of geometrically similar grids are used to allow the estimation of the quantities of interest that include the pressure and friction
coefficients, displacement thickness, momentum thickness, and mean velocity profiles of the boundary-layer on the bottom wall of the wind-tunnel. Input uncertainties generated by the approximate boundary conditions used in the simulations are estimated using sensitivity coefficients. We also address the consequences of the postprocessing techniques used to determine the quantities of interest, especially the shear-stress at the wall, displacement thickness, and momentum thickness of the bottom wall boundary-layer. The ASME V&V20 point-wise validation metric and a multivariate metric, which take into account experimental, numerical, and input uncertainties, are used to quantify the modeling error of the selected mathematical/computational models.