Optimisation of Turbomachinery Components by Constrained Minimisation of the Local Entropy Production Rate

Abstract

This Lecture presents some reflections on the practical measure of thermodynamic irreversibilities affecting the interactions of a process fluid with a part of a turbomachine: the main contention here being that the entropy generation rate is the only thermodynamic quantity that can be used to correctly estimate viscous and thermal losses, and to compare both the absolute and the relative performance of different configurations. An entropic analysis (i.e., the calculation of the entropy generation rates associated with the various types of “losses”) can be performed at a bulk, at a microscopic and at a macroscopic level. The bulk level is the one usually employed in lumped formulations, where either the entire system or portions thereof are considered as a control volume, and the entropy generation rate is computed via the usual thermodynamic expressions derived by direct manipulation of the constitutive relations. The microscopic or local level is the method advocated here: it consists of separating the two different forms of irreversible entropy production in fluid flow, due to thermal (st) and viscous (sv) effects respectively, and of expressing them as functions of the local velocity- and temperature gradients and of the local temperature. The macroscopic or global level consists in integrating the results of the microscopic analysis over the domain of interest: it produces a value of the total entropy generation rate quantitatively very close to that obtained by the bulk method, but different in principle from it, because calculations at the global level take explicitly into account the non-uniformity of the medium.