Rational study of incompressible turbulent flows

A new turbulence model is proposed in this dissertation for two-dimensional incompressible turbulent flows. The methodology used in the present study is a unilateral-statistical-average scheme with the concept of orthotropic eddy viscosity. This methodology has never been explored before in any research work of this nature. The distinguished feature of the unilateral-statistical-average scheme, compared to Reynolds averaging, is that the first-order information of the fluctuating velocity field is retained. This is achieved by dividing the fluctuating velocities into two groups and applying the average only to a single group. It is proved that the mean value of the fluctuating velocities of the first group solutions is not equal to zero. This non-zero quantity, together with a specified length vector, is used to define a 3 x 3 matrix of orthotropic eddy viscosity. In an off-streamline coordinate system, the eddy-viscosity matrix exhibits anisotropy characteristic, where each component of the turbulent stresses is related to all the components of the rate of strains of the mean fluid flow. The present model has been successfully applied to turbulent boundary-layer flow, turbulent free-shear jet flow, and turbulent wall-bounded separation flow without using empirical constants or wall-functions. Good agreements between the numerical results and experimental data or empirical predictions demonstrate that the unilateral-statistical-average scheme and the orthotropic non-linear eddy-viscosity formulation are robust and efficient in modeling basic turbulent flows. Applicability and predictability of the model to more complex engineering turbulence problems are worthy of further investigation in the future research.