Some Remarks About the Computation of the Entropy Generation Rate in Turbomachinery
The entropy generation rate s. = ds/dt in turbo-machinery passages is an important indicator of the effectiveness of the energy exchange in the machine. The calculation of s. is straightforward once the velocity and temperature fields are known in detail. At each instant in time, the global entropy generation rate 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 flow field is not immediately detectable, because the left-hand side depends not only on the instantaneous flow characteristics, but also on the history of its development. This is indeed the profound reason why an accurate knowledge of the local entropy generation rate in each point of a channel provides immediate and very useful insight into the different sources of irreversibility in the process. There are numerous examples of application of entropy generation maps as a diagnostic design tool, i.e., to locate problematic areas that demand for design “improvements”, but there are only a few comprehensive studies on the theoretical validity of the numerical approach to the computation of the local entropy generation rate. This paper presents a rational derivation of the relationships between the local and global entropy generation and the local features of the flow, and discusses some issues about the influence of the turbulence modeling on the results. The merits and limits of the use of such a “local” approach are also critically discussed with a simple example of a specific application to the k-ε model.
Keywords: Entropy transport equation, entropy generation rate, k-ε model, turbulent models, spectral analysis, turbomachinery.