The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbomachines

The extension of a well-established three-dimensional flow calculation method to calculate the flow through multiple turbomachinery blade rows is described in this paper. To avoid calculating the unsteady flow, which is inherent in any machine containing both rotating and stationary blade rows, a mixing process is modeled at a calculating station between adjacent blade rows. The effects of this mixing on the flow within the blade rows may be minimized by using extrapolated boundary conditions at the mixing plane. Inviscid calculations are not realistic for multistage machines and so the method includes a range of options for the inclusion of viscous effects. At the simplest level such effects may be included by prescribing the spanwise variation of polytropic efficiency for each blade row. At the most sophisticated level viscous effects and machine performance can be predicted by using a thin shear layer approximation to the Navier–Stokes equations and an eddy viscosity turbulence model. For high-pressure-ratio compressors there is a strong tendency for the calculation to surge during the transient part of the flow. This is overcome by the use of a new technique, which enables the calculation to be run to a prescribed mass flow. Use of the method is illustrated by applying it to a multistage turbine of simple geometry, a two-stage low-speed experimental turbine, and two multistage axial compressors.