Calculation of Wake-Induced Unsteady Flow in a Turbine Cascade

Numerical predictions are reported of two-dimensional unsteady flow in a linear turbine cascade, where the unsteadiness is caused by passing wakes generated by the preceding row of blades. In particular, an experiment is simulated in which the passing wakes were generated by cylinders moving on a rotating squirrel cage. Blade-to-blade calculations were carried out by solving the unsteady 2D flow equations with an accurate finite-volume procedure, thereby resolving the periodic unsteady motion. The effects of stochastic turbulent fluctuations are simulated with a two-layer turbulence model, in which the standard k-ε model is applied in the bulk of the flow and a one-equation model in the near-wall region. This involves also a transition model based on an empirical formula due to Abu-Ghannam and Shaw (1980), which was adapted for the unsteady situation by applying it in a Lagrangean way, following fluid parcels in the boundary layer underneath disturbed and undisturbed free stream on their travel downstream. The calculations are compared with experiments for various wake-passing frequencies. On the whole, the complex unsteady flow behaviour is simulated realistically, including the moving forward of transition when the wake-passing frequency increases, but not all details can be reproduced.