Turbulence models for non-circular ducts and channels
This thesis describes the development and application of numerical predictive procedures for flows in which turbulence-driven secondary motion plays an important role. The focus is on fully-developed flows in closed ducts and open channels of various cross-sectional geometries. Two different turbulence models were evaluated: a complete Reynoldsstress- transport model and a two-equation k-f model used in conjunction with a nonlinear stress-strain relationship. Detailed consideration was given to the various approximations utilized in closing the Reynoldsstress equations, particularly to the difficult pressure-strain-correlation term which proved crucial for the accurate prediction of the turbulencedriven secondary motion. The thesis also considers the validity of such models to flows influenced by the presence of a free surface. Appropriate numerical procedures were developed to handle the variety of geometries likely to be encountered in engineering practice. Particular attention was placed on the development of the numerical procedure which utilizes the nonlinear k-e model in conjunction with body fitted coordinates. The performance of each model was assessed through detailed comparisons with published data from a very wide range of flows in non-circular ducts and channels. Both models succeeded in predicting the secondary flow and its effects on the mean-velocity field in rectangular and com - pound ducts. For flows in rectangular channels, the Reynolds-stress model proved capable of accurately predicting the strength and location of secondary-flow cells and their role in displacing the position of the mean-velocity maximum to below the free surface. In contrast, the nonlinear model failed to reproduce this result for reasons discussed in some detail in the thesis. Both models predicted equally well the shear stress over wetted perimeter indicating that the defect of the nonlinear model encountered near to the free surface was rather localized. The Reynolds-stress model also proved to be particularly accurate in the prediction of flows in compound channels. The nonlinear k-f model was found to be less accurate there but, due to its economy and robustness, this model seems to be an acceptable alternative to Reynolds-stress models for the practical prediction of flows in simple and compound open channels.