Master thesis and internship[BR]- Master's thesis : A Wall Model for LES of Flows with Laminar-Turbulent Transition[BR]- Integration Internship : TU Delft

Abstract

Large Eddy Simulations (LES) offer a better reliability than the Reynolds-Averaged Navier-Stokes method and a more acceptable computational cost compared to Direct Numerical Simulations. Nevertheless, with such an approach, wall-bounded flows at high Reynolds numbers require an excessively fine mesh resolution to fully resolve the energetic turbulent structures within the inner boundary layer. Consequently, the related computational cost is a major obstacle for most practical engineering settings. To overcome this, Wall-Modeled Large Eddy Simulations (WMLES) estimate instead of resolve the effect of the inner layer. Considering the wall-stress modeling approach, this is achieved by providing the wall-shear stress as a Neumann boundary condition and enforcing the impermeability instead of imposing a no-slip condition over the wall. In this context, a wall-stress model is built for incompressible flows including laminar-turbulent transition. As a first step, a laminar wall model (LWM) is established by assuming a self-similar boundary layer based on the Falkner-Skan equation. The model is able to provide a friction estimate from the knowledge of the pressure at the wall vicinity. A validation with respect to wall-resolved solutions is then carried out by considering a flat plate and the Hiemenz flow. The robustness and accuracy of the LWM are demonstrated in both cases, except near the leading edge of the flat plate where the self-similarity assumption is not appropriate.

Then, a method for calculating distances on irregular triangular meshes is developed in order to apply the LWM to curved surfaces. The resulting algorithm provides the shortest distance over the surface with respect to an imposed set of stagnation points. A succession of convergence studies for different test cases demonstrates that the process leads to a distance field with a sufficiently good accuracy and smoothness for wall-modeling applications.

A hybrid wall model (HWM) is finally built by combining the LWM with a turbulent wall model based on the general wall function. In order to validate it, different flows over an extruded wing are considered: the NACA0012 with (Re = 10.25 x 10^6 ; AoA = 0°) and the A-airfoil with (Re = 3.1 x 10^6 ; AoA = 3.4°) and (Re = 2.1 x 10^6 ; AoA = 13.3°). The HWM is first applied by hard-coding the transition between the two wall functions. The resulting wall-shear stress shows a good match with the empirical data for fully attached flows. Lastly, a sensor measuring the turbulent kinetic energy is used at each point of the surface to automatically determine the type of regime and impose the wall treatment accordingly. As long as the imposed sensor threshold is suitable and the mesh resolution sufficiently fine, the sensor is able to predict a transition corresponding relatively well with the experiment. However, the results show that these sensor parameters are case dependent.