Analytical Closure of the Inviscid Blade Force Model

Abstract

A new formulation of the axisymmetric flow equations in turbomachinery is proposed, which inherently contains the additional blade force equations for simulation of the (de)swirling effect of the blade rows. Unlike in explicit blade force models, the blade force term does not need to be separately solved throughout the time-marching integration of the flow equations. The new formulation does not have an equation for the swirl momentum, but it describes instead a strictly two-dimensional flow with specific convective flux and source terms. The convective fluxes include the slope of the mean blade surface (i.e., the blade angle), whereas a blade load source term replaces the explicit blade force with the surface camber. Suitable leading/trailing edge boundary conditions are developed to match the new equations in bladed subdomains of the meridional flowpath with the conventional equations in those unbladed. These conditions are coupled to a discontinuous flux difference splitting technique for treatment of a range of transonic regimes. The numerical solution has capabilities to capture choking and passage shocks, which are first addressed theoretically and then shown by re-obtaining two simple exact solutions. The validation goes through comparison to experimental results, a full three-dimensional solution, and explicit blade force solutions.