Nonlinear Mixing Length Model for Prediction of Secondary Currents in Uniform Channel Flows

A nonlinear turbulence model for numerical solution of uniform channel flow is presented. Turbulent stresses are evaluated from a nonlinear mixing length model that relates turbulent stresses to quadratic products of the mean rate of strain and the mean vorticity. The definition of the mixing length, based on a three-dimensional integral measure of boundary proximity, eliminates the need for solution of additional transport equations for the turbulence quantities. Experimental data from the literature for closed and open-channel flows are utilized to validate the model. The model produced the secondary flow vortices successfully. Velocity field and wall shear stresses affected by secondary flow vortices are accurately computed. Bulging of velocity contour lines toward the corners and dipping phenomena of maximum velocity are successfully simulated.