Closure modeling and numerical simulation for turbulent flows: Wall roughness model, realizability, and turbine blade heat transfer

RANS simulations are widely used in industrial applications. However, computations by closure models sometimes are inaccurate. The main objective of our study is to develop and test turbulence closure models for three areas: wall roughness model, realizability, and turbine blade heat transfer.; The first part of this research develops wall roughness models. We followed the strategy by Durbin et al. (2001) to develop k - o and v2 - f wall roughness models. The boundary conditions for turbulence variables were modified from smooth wall and log law behavior. In several test cases, the proposed model and the Wilcox k - o model produce almost the same results. These two k - o rough wall models often predict that the surface roughness decreases the separation bubble size, but this is opposite to the experiments. A v 2 - f wall function model is developed to test the log law formulations used in the v2 - f rough wall formulations. The v2 - f rough wall model remains unfinished.; The second part of this thesis discuss the realizability problems of turbulence models. Schumann (1977) introduced two realizability conditions in Reynolds stresses: non-negative eigenvalues and Schwartz's inequality from the statistics. However, in eddy viscosity models, the realizability problem is a phenomenal problem---energy over-production. This study surveyed several realizability models and tested them in several cases on turbulent energy and heat transfer. The results show that realizability models eliminate over-production of turbulent energy and over-estimation of heat transfer, but they do not guarantee accurate results. Reynolds stress models have no energy over-production problem.; The last part of this research simulates turbine blade heat transfer. The v2 - f model, the k - &egr; 2-layer model, and the k - &egr; wall function model simulated the transonic turbine for ReCx = 0.5 and 1.0 x 106 and with and without inlet turbulence grid. The heat transfer rates on the endwall and blade surface were compared with the experimental results. The experimental results show that grid turbulence weakens the coherent vortices and removes the transition, but the models do not predict the turbulence grid effects. The models that were tested predict increase of heat transfer by reduction of Reynolds number.