Evaluation of turbulence variable distributions for fully rough pipe flow

The specific turbulent kinetic energy, root-mean-square fluctuating vorticity, and mean-vortex-wavelength distributions are presented for fully rough pipe flow. The distributions of these turbulence variables are obtained from a proposed turbulence model. Many of the turbulence models commonly used for computational fluid dynamics are based on an analogy between molecular and turbulent transport. However, traditional k-epsilon and k-&ohgr; models fail to exhibit proper dependence on the molecular viscosity. Based on a rigorous application of the Boussinesq's hypothesis, Phillips proposed a vorticity-based transport equation for the turbulent kinetic energy. The foundation for this vorticity-based transport equation is presented. In future development of this model, a transport equation for the fluctuating vorticity is needed. In order to assess the model and evaluate closure coefficients, the resulting turbulent vorticity distribution must be compared to reference distributions. This dissertation presents reference distributions for the mean fluctuating vorticity and mean turbulent wavelength obtained for fully rough pipe flow. These distributions are obtained from a turbulence model, which involves the proposed transport equation for the turbulent kinetic energy and an empirical relation for the mean vortex wavelength. The empirical relation for the mean vortex wavelength requires numerous closure coefficients. These closure coefficients are determined through gradient-based optimization techniques. The current model gives excellent agreement with well established relations obtained for both the friction factor and velocity distribution.