Entropy transport for quasi-one-dimensional flow

Abstract

The study of entropy in the context of quasi-one-dimensional flow is expanded in this work. Specifically, a new entropy transport equation is derived and integrated into a closed-form algebraic expression for entropy change. The derivation identifies the respective components of the entropy change and is valid for flows with an arbitrary combination of area change, heat transfer, and friction. The irreversibility is identified and found to be composed of frictional dissipation, irreversible heat transfer, and irreversible flow work. The irreversible flow work is a new term that results from the restriction to quasi-one-dimensional flows. The algebraic expression for each component of the entropy change is first validated using several canonical flows (i.e., isentropic, Fanno, Rayleigh, and a normal shock). A unique entropy production mechanism is identified for each of the entropy producing canonical flows (e.g., Fanno, Rayleigh, and a normal shock). Two additional cases, sudden expansion and contraction, are then considered and show that irreversible flow work is the sole entropy production mechanism. Finally, simultaneous friction and heat transfer are examined, and the overall entropy change is decomposed into the respective contributions from frictional dissipation and the heat transfer terms. In all cases, the net entropy change from the newly derived expressions agrees with known solutions to within numerical precision.