Computation of the Unsteady Transonic Flow in Harmonically Oscillating Turbine Cascades Taking Into Account Viscous Effects

Abstract

This paper presents the numerical results of a code for computing the unsteady transonic viscous flow in a two-dimensional cascade of harmonically oscillating blades. The flow field is calculated by a Navier–Stokes code, the basic features of which are the use of an upwind flux vector splitting scheme for the convective terms (Advection Upstream Splitting Method), an implicit time integration, and the implementation of a mixing length turbulence model. For the present investigations, two experimentally investigated test cases have been selected, in which the blades had performed tuned harmonic bending vibrations. The results obtained by the Navier–Stokes code are compared with experimental data, as well as with the results of an Euler method. The first test case, which is a steam turbine cascade with entirely subsonic flow at nominal operating conditions, is the fourth standard configuration of the “Workshop on Aeroelasticity in Turbomachines.” Here the application of an Euler method already leads to acceptable results for unsteady pressure and damping coefficients and hence this cascade is very appropriate for a first validation of any Navier–Stokes code. The second test case is a highly loaded gas turbine cascade operating in transonic flow at design and off-design conditions. This case is characterized by a normal shock appearing on the rear part of the blades’s suction surface, and is very sensitive to small changes in flow conditions. When comparing experimental and Euler results, differences are observed in the steady and unsteady pressure coefficients. The computation of this test case with the Navier–Stokes method improves to some extent the agreement between the experiment and numerical simulation.