Finite element solution of the Navier-Stokes equations for 3-D turbulent free shear flows

A half-equation model of turbulence has been developed to describe three-dimensional turbulent free shear flows. The model is used in a general purpose finite element procedure using primitive variables. The penalty function method is used, in a generalized Galerkin weak formulation of the Navier-Stokes equations, to enforce the conservation of mass. In this procedure the pressure does not explicitly appear, thus significantly reducing the computation time when compared to the velocity-pressure approach. Numerical solutions are obtained for four problems: a round jet issuing from a wall into still surroundings, a three-dimensional square jet issuing from a wall into still surroundings, a uniform flow past a free running propeller, and a shear flow past a free running propeller. An actuator disk with variable radial distribution of thrust and torque is used to model the propeller. Very good agreement between prediction and experiments is observed for the jet problems.