Finite element method for computing turbulent propeller flow

A numerical procedure based on the primitive variable Navier-Stokes equations is applied to the simulation of the three-dimensional axisymmetric flow near a propeller in a uniform flow. The time-averaged Navier-Stokes equations are solved using both a mixed and a penalty function finite element method. A new model is developed to compute axisymmetric viscous throughflow past propellers. This is achieved by forcing the flow to be tangent to the mean stream surface between the blades. This condition is enforced by introducing a Lagrange multiplier that can be interpreted as the force applied by the blades on the fluid. Turbulence is modelled by a simple mixing length equation. Detailed comparison with wind tunnel measurements shows good prediction of velocity and pressure. The present approach represents a first step toward the development of a viscous quasi-three-dimensional capability.