A robust and accurate Navier-Stokes algorithm for three-dimensional applications adopting arbitrary modelling of the Reynolds stresses

In this thesis a new Navier-Stokes solver for complex three-dimensional geometries, adopting arbitrary modelling of the Reynolds stresses, is presented. Ak-s model, adopting a modelling of the turbulent transport not based on the eddy viscosity, has been written in generalised coordinates and solved with a finite volume approach, using both a GMRES solver and a direct solver for the solution of the linear systems of equations. The results presented show that the modification adopted for the modelling of'the turbulent transport also provides a more accurate value of the physical diffusion and, as a consequence, improves the increase in accuracy when using higher-order convection schemes. A simple non-linear modelling of the Reynolds stresses has been designed introducing an additional term, quadratic in the main strain rate, to the basic Boussinesq's form; the corresponding constant has been evaluated through comparison with experimental data. The computational procedure is implemented for the flow analysis in a 90 ° square section bend and the obtained results show that with the non- linear modelling a much better agreement with the measured data is obtained, both for the velocity and the pressure. The importance of the convection scheme is also discussed, showing how the effect of the non-linear correction added to the Reynolds stresses is effectively hidden by the additional numerical diffusion introduced by a low- order convection scheme as the first-order Upwind, thus making necessary the use of higher-order schemes. Some results for centrifugal turbo machinery are also presented, giving some initial indications on the effects of the proposed modification in the modelling of the turbulent diffusion on the prediction of the flow in rotating passages.