Computing the Entropy Generation Rate for Turbomachinery Design Applications: Can a Diagnostic Tool Become a Predictive One?

Abstract

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.