Evaluation of an incompressible energy-vorticity turbulence model for fully rough pipe flow

Traditional methods of closing the Boussinesq-based Reynolds-averaged Navier-Stokes equations are considered, and suggestions for improving two-equation turbulence models are made. The traditional smooth-wall boundary conditions are shown to be incorrect, and the correct boundary conditions are provided along with sample solutions to traditional models. The correct boundary condition at a smooth wall for dissipation-based turbulence models is that which forces both the turbulent kinetic energy and its first derivative to zero. Foundations for an energy-vorticity model suggested by Phillips are presented along with the near-smooth-wall behavior of the model. These results show that at a perfectly smooth wall, the turbulent kinetic energy may approach the wall at a higher order than is generally accepted. The foundations of this model are used in the development of a k-lambda model for fully rough pipe flow. Closure coefficients for the model are developed through gradient-based optimization techniques. Results of the model are compared to results from the Wilcox 1998 and 2006 k-o models as well as four eddy-viscosity models. The results show that the Phillips k-lambda model is much more accurate than other models for predicting the relationship between Reynolds number and friction factor for fully rough pipe flow. However, the velocity profiles resulting from the model deviate noticeably from the law of the wall.