Title: Identification of model and grid parameters for incompressible turbulent flows
Abstract: The present thesis studies the behavior of turbulence models for incompressible flows based on the DLR-THETA-code and calibrates relevant model and grid parameters arising in the numerical simulations. Large-eddy simulation (LES) is a popular approach dealing with the turbulent flow governed by the Navier-Stokes equations (NSE). Due to the requirement of high resolution of the near-wall region at high Reynolds number flow hybrid approaches, e.g. detached-eddy simulation (DES) and wall modeled LES, are developed to use LES model in separated flow region and Reynolds averaged Navier-Stokes (RANS) model or wall functions in the near-wall region. In LES large scales are resolved and the effect of small scales are modeled, while only mean values are solved in RANS. The model and grid parameters are often flow type dependent and affected by the numerical schemes, e.g. the constant Cs in the Smagorinsky subgrid-scale (SGS) model and the location y(1) of the first grid point away from the wall. The parameter identification problems for incompressible turbulent flow using an adjoint optimization approach are still open. As an alternative the least-square fitting combining a Newton-type method is used to compute the optimized parameter.The DLR-THETA-code is a solver for incompressible flow of finite volume method on collocated grids using projection method. The Smagorinsky SGS model and hybrid methods are implemented into this code. Three benchmark problems with increasing complexity, decaying homogeneous isotropic turbulence (DHIT), plane channel flow and flow over a backward-facing step, are considered. The performance of discretization schemes are first tested with DHIT using the Smagorinsky SGS model. The model parameter Cs is identified with the schemes which provide best results in comparison with the experimental data. Further numerical results are presented for plane channel flow at moderate Reynolds number Re=395 based on friction velocity and channel half width and the grid parameter y(1) is another quantity to identify by comparing the results with the DNS data. For DES based on the Spalart-Allmaras model (SADES), DHIT and plane channel flow at moderate Reynolds number Re=395 are reconsidered. The influence of the model constant in SADES is demonstrated. Moreover, the channel flow at a higher Reynolds number Re=4800 is studied with two hybrid approaches, i.e. LES and SADES with wall functions, that is, wall functions are used to provide approximate boundary condition for the outer layer flow instead of resolving the near-wall region. A correction to the turbulent viscosity in the near-wall region is considered. Finally first results of the instantanous velocity for flow over a backward-facing step are shown.