A CFD code for three-dimensional viscous flows, in particular for those in turbomachinery, has been developed based on Favre-averaged compressible Navier-Stokes equations and one-equation Spalart-Allmaras turbulence closure. The model equation of Spalart-Allmaras turbulence closure is converted into conservative form and discretized in the same manner as that for mean flow equations. A two-dimensional transonic diffuser flow and a two-dimensional transonic nozzle flow which feature pressure-gradient induced separation and shock wave/boundary layer interaction respectively are used to validate the code and application of the Spalart-Allmaras model (hereafter the S-A model) in internal flows. It is shown that the S-A model can give fairly good results compared to the experimental data. Some modifications of model equation are introduced for improving the grid insensitivity of the turbulence model. To validate the applicability of the code to the complex flows in transonic turbomachines, flows through two transonic compressor rotors, NASA Rotors 67 and 37 are calculated, and numerical results are compared with the well documented experimental data. The calculated results agree reasonably well with the experiments, and as expected, the S-A model, which is primarily developed for external flows, can also be effectively applied to internal flows. Discrepancies between the experimental data and calculations and the possible causes are also discussed.
Contribution to the Optimal Shape Design of Two-Dimensional Internal Flows with Embedded Shocks
