An Approach for Multi-Stage Calculations Incorporating Unsteadiness

Abstract

This paper describes a mathematical approach to the calculation of unsteady flow in multi-stage turbomachinery. An asymptotic formulation is used, with the small asymptotic parameter being the level of unsteadiness in each blade row. The baseline flow is the nonlinear steady flow that is computed by many existing multi-stage calculation methods. The first order linear perturbation is the unsteady flow field arising from stator/rotor interactions between neighboring blade rows. The second order correction contains the information about the time-averaged effect of unsteadiness on the mean flow. The advantage of this asymptotic approach is that it leads to a set of equations which can be solved numerically very much more cheaply than the full nonlinear unsteady flow equations, while still retaining the key features of the flow.