Zonal computational method for turbulent plane cascade flow

Summary

A zonal method is presented for computing the incompressible flow through plane cascades with blunt trailing edges. The flow field is divided into three distinct regions, i.e. the potential flow region, the turbulent boundary layers, and the region of the turbulent flow near the trailing edge and in the near wake. The potential flow is computed by a panel method that accounts for the periodicity of the cascade flow in an exact manner. A finite-difference scheme is applied to solve the boundary-layer equations together with a classical mixing-length formula. In the trailing edge and near wake region, a local solution of the time-averaged Navier-Stokes equations is obtained by a finite-element method, which incorporates a k-ε model for the Reynolds stresses. To match the potential-flow solution to the Navier-Stokes solution, the circulation is determined iteratively such that the pressure difference across the wake at the outflow boundary becomes zero. A relaxation procedure is applied to stabilize the iteration process. Numerical results for the flow through a plate cascade, as a test case, show fair agreement with experimental data for the static pressure difference. The computed outflow angle, however, is smaller than the value given in the literature. The discrepancy seems to be due to the fact that in recirculation zones the k-ε model predicts values of the turbulent normal stresses that are too large.