A Grid-Adaptive Algebraic Hybrid RANS/LES Method

Kurzfassung

The present thesis considers the compressible Navier-Stokes equations to simulate the flow of air about basic and complex test cases. As numerical solution method the unstructured finite-volume solver DLR-TAU is used. The aim of the work is to provide a hybrid RANS/LES simulation strategy for the reliable numerical prediction of the stall behavior of high-lift airfoils under the influence of turbulent inflow. The focus is on the development of an improved modeling technique based on the Detached Eddy Simulation (DES) method. The DES combines two complementary modeling concepts: the Large Eddy Simulation (LES) with high fidelity at a high computational effort, which is directly coupled to the flow Reynolds number, and the statistical approach to solve the Reynolds-Averaged Navier-Stokes (RANS) equations with lower fidelity for separated flows but at a considerably lower computational effort. In the present thesis the Algebraic Delayed DES (ADDES) is extended, improved, and validated for several fundamental flow cases and application challenges. In the ADDES the distinction between RANS and LES zones is controlled by algebraic sensors, which detect the flow state by evaluating boundary layer velocity profiles. To allow for complex application cases, the evaluation of the boundary-layer properties is implemented in a fully parallelized algorithm, which can handle complex geometries. Furthermore, the ADDES is coupled with wall-modeled LES capabilities to provide a model for attached boundary layers with turbulent onflow. In order to mitigate the so-called grey-area problem at the RANS-to-LES interface, a vorticity-based LES filter width was adopted and reformulated for the unstructured dual-grid approach of TAU, in order to stimulate the generation of resolved turbulent structures. Moreover, a grid-resolution sensor for Large-Eddy Simulations is proposed, which enables assessing the grid from a single LES solution. This sensor can be used to control an automatic local grid adaptation in order to provide an appropriate spatial resolution for the respective flow problem. In the target application of the present thesis, the interaction of a generic airfoil generated vortex with a two-element high-lift airfoil is simulated. In a preliminary investigation the generation and transport of the onflow disturbance is isolated to determine the required level of modeling. In combination with the improved high-fidelity ADDES approach, the mean influence of the disturbance on the high-lift airfoil is successfully reproduced in the final target application. During the development of the improved simulation strategy, intermediate results were published at several work stages, as listed below. The publications [A]-[F] with major own contributions are attached in the appendix of the thesis.