INVESTIGATION OF DIFFERENT DISSIPATION MODELS FOR THE NUMERICAL SOLUTION OF THE NAVIER-STOKES EQUATIONS

Abstract

The aerodynamic design and optimization of flow-guiding components in the turboma-chines essentially require detailed knowledge of the complex three-dimensional flow field. At the Institute of Thermal Turbomachinery and Machine Laboratory, University of Stuttgart, the flow solver ITSM3D was developed for the numerical computation of turbomachinery flows. The spatial discretization is realized by central differences with an additional artificial dissipation term to ensure numerical stability. However, the quality of the numerical solution can be substantially affected by particular applied dissipation model. In the present work an effort is made to investigate various dissipation models for a wide range of flow regimes. Comparative calculations are accomplished and evalu-ated on the basis of different test cases belonging to subsonic, supersonic and transonic flow fields. In order to better understand the applicability, accuracy and limitations of different dissipation models, initially several model problems are considered. Test cases considered as model problems are ramped channel flow, flow through bumped channel and laminar boundary layer over flat plate. Afterward 2-D linear transonic and 3-D annular subsonic turbine cascades are considered as advanced test cases. For model problems, investigations are made in terms of boundary layer and shocks while for turbine cascades variety of flow parameters are used in order to investigate different dissipation models in depth. In case of two dimensional flows, matrix dissipation model gives more accurate results as compared to scalar dissipation model. On the other hand, for complex three dimensional flows, scalar dissipation model is able to provide a ro-bust and stable central differencing scheme for spatial discretization. Grid dependency studies are also made for model problems in the present investigation