Analysis of Turbomachinery Averaging Techniques

Abstract

In this paper, various averaging techniques commonly used in turbomachinery applications are analyzed. It is shown how the work average relates to Miller’s mechanical work potential and that it is, in a certain way, consistent with Hartsel’s cooled turbine efficiency. It is found that a key to understand these approaches is to analyze the impact that entropy variations at inflows have on them. Second-order asymptotics of mixing entropy are used to establish a close relationship between flux and work averages. It is found that the mixing entropy asymptotic due to entropy modes is identical for both averages. The work average, along with Miller’s mechanical work potential analysis, is as optimistic as the entropy average for vorticity and acoustic modes, but as pessimistic as the flux averaging for entropy variations. This explains why mechanical work potential-based analysis is pessimistic about the inflow and thus optimistic about the efficiency of a turbine for high entropy variations in the inflow, e.g., in the presence of hot streaks or film cooling. Radial averaging techniques are discussed and their impact on turbine performance is shown. Our findings are illustrated by means of the analysis of steady and unsteady flow simulations of a 1.5 stage turbine configuration.