The calculation of the entropy generation rate ds/dt in turbomachinery passages is a straightforward task once the velocity and temperature fields are known. The global entropy generation rate in the passage, dS/dt = ∫V(x,y,z)(ds/dt)dxdydz, is of course directly related to the cascade efficiency, but its functional dependence on the local characteristics of the flowfield is not immediately detectable: the left-hand side is a single-valued quantity that cannot, as such, be used as the objective function of an inverse design procedure (because a local modification of a single detail of the blade geometry invariably produces non-negligible effects on the entire flow domain). On the contrary, knowledge of the local entropy generation rate in each point of a channel provides immediate useful insight into the relative importance of the different sources of irreversibility in the process. There are numerous examples of the application of entropy generation maps as a diagnostic design tool, i.e., to locate problematic areas that demand for design “improvements”: these are, though, basically heuristic and intrinsically non-systematic approaches. On the other hand, the adoption of a functional based on the local entropy generation rates is difficult both from a theoretical and from a practical point of view, and there is no example yet of a blade profile optimization in which the objective function is V(x,y,z)(ds/dt)dxdydz, to be minimized over the design domain V. This paper presents a rational derivation of the relationships between the local and global entropy generation and the local features of the flow, and illustrates them by means of two examples derived from applications developed in the last years by the Turbomachinery Group led by the author at the University of Roma 1. The merits and limits of the use of such a “local” approach are critically discussed, and in the Conclusions a procedure is proposed for the development of an inverse design approach based on a properly constrained objective function based on ds/dt: though quite intensive from a computational point of view, there are indications that such an approach may become feasible on realistic geometries in the near future.

1.
A. Bejan: Entropy generation in heat and fluid flow, J. Wiley, 1982
2.
E. Casartelli et al.: Numerical Flow Analysis in a Subsonic Vaned Radial Diffuser With Leading Edge Redesign, J. Turbom., v. 121, January 1999.
3.
R. Cerini: Application of a LES model to the 2D and 3D simulation of a vaned diffuser for a radial compressor, M. Eng. Thesis, U. of Romal, 2000 (in Italian)
4.
W.N. Dawes: A Simulation of the Unsteady Interaction of a Centrifugal Compressor with Its Vaned Diffuser, J. Turbom., v. 107, April 1995.
5.
J.D. Denton: Loss mechanisms in turbo-machines, J. Turbom., v. 114, Oct. 1993
6.
D.J. Dorney, J.R. Schwab: Unsteady Numerical Simulations of Radial Temperature Profile Redistribution in a Single-Stage Turbine, J. Turbom., v.118, October 1996.
7.
H. Harada: Performance Characteristics of Two- and Three-Dimensional Impellers in Centrifugal Compressors, J. Turbom., v. 110, January 1988
8.
M.D. Hathaway et al.: NASA Low-Speed Centrifugal Compressor for Three-Dimensional Viscous Code Assessment and Fundamental Flow Physic Research, J. Turbom., v.114, April 1992.
9.
C.L. Iandoli, E.Sciubba: 3-D numerical calculation of the local entropy generation rates in a radial compressor stage, Submitted to Int. J. of Thermodynamics, 2004
10.
M. Inoue, N.A. Cumpsty: Experimental Study of Centrifugal Impeller Discharge Flow in Vaneless and Vaned Diffusers, J. Eng. for Gas Turb. & Power, v. 106, April 1984.
11.
H. Krain: A Study on Centrifugal Impeller and Diffuser Flow, J. Turbom., v.103, October 1981.
12.
G. Natalini, E. Sciubba: Minimization of the local rates of entropy production in the design of air-cooled gas turbine blades, ASME J. Eng. for GT & Power, v.121, July 1999
13.
M. Peeters, M. Sleiman: A Numerical Investigation of the Unsteady Flow in Centrifugal Stages, ASME 2000-GT-426, May 2000.
14.
P. Roccetti: Application of a LES model to the 2D and 3D simulation of an axial gas turbine stage, M. Eng. Thesis, U. of Romal, 2000 (in Italian)
15.
E. Sciubba: Entropy production rates as a true measure of viscous and thermal losses in thermo-mechanical components. Proc. NATO W. shop on Heat- & Mass Transfer, Bucharest, 1994
16.
Y.K.P. Shum, N.A. Cumpsty: Impeller-Diffuser Interaction in Centrifugal Compressor, ASME 2000-GT-428, May 2000
17.
R.G. Stabe: Performance of a High-Work Low Aspect Ratio Turbine Tested with a Realistic Inlet Radial Temperature Profile, NASA Technical Memorandum 83655, June 1984.
18.
H. Tennekes, J.L. Lumley: A first course in Turbulence, MIT Press, 1972
This content is only available via PDF.
You do not currently have access to this content.