Session: 37-02 CFD Solver Methods

Paper Number: 82959

82959 - Analysis of Turbomachinery Averaging Techniques 

In this paper, various approaches to average non-uniform flow in turbomachinery are analyzed. Special emphasis is put on the flux, entropy and work averaging techniques. It is shown how the latter relates to Miller's mechanical work potential. Moreover, it is shown that work averaging is consistent with Hartsel's cooled turbine efficiency in that it can be computed from a standard formula for isentropic turbine efficiency if the stagnation pressures are based on the work average.

Circumferential and temporal averages are distinguished from radial averaging techniques. Dzung and Prasad suggest to compute a so-called complete equilibrium state which can be considered a radial flux averaging. Our analysis, however, shows that this approach, as opposed to circumferential flux averaging, lacks a physical rationale and can cause overly pessimestic radial mixing losses. It is therefore recommended to combine circumferential flux averaging with one of the other, more optimistic, approches to obtain integral quantities.

In this paper, it is shown that by means of a generalization of the second-order approximation of the mixing entropy associated to averaging, the averages discussed here can be compared to each other in terms of their mixing loss asymptotics. It is found that the work average is as optimistic as the entropy average for vorticity and acoustic modes, but as pessimistic as the flux averaging for entropy modes. This last observation is a simple way to explain 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.

Our findings are illustrated by means of the analysis of steady and unsteady flow simulations of a turbine stage. The implementational issues, in particular for the post processing of unsteady flows in the time and frequency domains, are highlighted.

Presenting Author: Christian Frey German Aerospace Center (DLR)

Presenting Author Biography: 1995-2001: Studies of Mathematics at Humboldt University of Berlin<br/>2001: Diploma in Mathematics<br/>2001-2005: Scientist at University of Cologne<br/>2005: Doctoral Degree in Mathematics<br/>2005-today: Scientist at Institute of Propulsion Technology of German Aerospace Center (DLR)<br/>2010-today: Head of Team “New Methods” within department Numerical Methods

Authors:

Christian Frey German Aerospace Center (DLR)
Graham Ashcroft German Aerospace Center (DLR)
Michael Müller German Aerospace Center (DLR)
Jens Wellner German Aerospace Center (DLR)