Spectral element/smoothed profile method for turbulent flow simulations of waterjet propulsion systems

Abstract

We have developed fast numerical algorithms [1] for flows with complex moving domains, e.g. propellers in free-space and impellers in waterjets, by combining the smoothed profile method (SPM, [2, 3, 4]) with the spectral element method [5]. The new approach exhibits high-order accuracy with respect to both temporal and spatial discretizations. Most importantly, the method yields great computational efficiency as it uses fixed simple Cartesian grids and hence it avoids body-conforming mesh and remeshing. To simulate high Reynolds number flows, we incorporate the Spalart-Allmaras turbulence model and solve the unsteady Reynolds-averaged Navier-Stokes (URANS) equations. We present verification of the method by studying the turbulent boundary layer over a flat plate. We show that both the eddy viscosity and velocity fields are resolved very accurately within the boundary layer. Having developed and validated our numerical approach, we apply it to study transitional and turbulent flows in an axial-flow waterjet propulsion system. The efficiency and robustness of our method enable parametric study of many cases which is required in design phase. We present performance analysis and show the agreement with experimental data for waterjets.