On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations

This paper presents a throughflow analysis tool developed in the context of the average-passage flow model elaborated by Adamczyk. The Adamczyk's flow model describes the 3D time-averaged flow field within a blade row passage. The set of equations that governs this flow field is obtained by performing a Reynolds averaging, a time averaging, and a passage-to-passage averaging on the Navier–Stokes equations. The throughflow level of approximation is obtained by performing an additional circumferential averaging on the 3D average-passage flow. The resulting set of equations is similar to the 2D axisymmetric Navier–Stokes equations, but additional terms resulting from the averages show up: blade forces, blade blockage factor, Reynolds stresses, deterministic stresses, passage-to-passage stresses, and circumferential stresses. This set of equations represents the ultimate throughflow model provided that all stresses and blade forces can be modeled. The relative importance of these additional terms is studied in the present contribution. The stresses and the blade forces are determined from 3D steady and unsteady databases (a low-speed compressor stage and a transonic turbine stage) and incorporated in a throughflow model based on the axisymmetric Navier–Stokes equations. A good agreement between the throughflow solution and the averaged 3D results is obtained. These results are also compared to those obtained with a more “classical” throughflow approach based on a Navier–Stokes formulation for the endwall losses, correlations for profile losses, and a simple radial mixing model assuming turbulent diffusion.