Compressible single-phase flows in heated and cooled ducts

TL;DR

This paper develops analytical solutions for steady, compressible single-phase flows in heated and cooled ducts, classifying flow regimes and providing tools for flow characterization based on pressure ratios and heat flux.

Contribution

It introduces a methodology to analyze non-adiabatic compressible flows, including a classification based on critical pressure ratios and an abacus for flow characterization.

Findings

Critical pressure ratio distinguishes subsonic and supersonic regimes.

No steady shock-wave can occur in the studied configuration.

Analytical solutions agree closely with numerical simulations.

Abstract

Analytical/quasi-analytical solutions are proposed for a steady, compressible, single-phase flow in a rectilinear duct subjected to heating followed by cooling. The flow is driven by the pressure ratio between an upstream tank and a variable outlet pressure. The article proposes a methodology to determine the full flow behavior, as a function of pressure ratio and heat-flux distribution. Following an analogy done with the study of compressible flows in nozzles, a behavioral classification of non-adiabatic compressible flows is proposed through the definition of critical pressure ratios. It is demonstrated that a critical pressure ratio distinguishes subsonic and supersonic outlet regimes and that there cannot be a steady shock-wave in such configuration. The behavior of this critical pressure ratio is studied for limit cases of heat-flux, delineating physical boundaries. An abacus is also proposed for a given couple of heating and cooling powers, as both values are needed to characterize the flow. Results are studied for parameters such as pressure ratio and outlet heat power. A short validation of a numerical simulation tool is provided, yielding excellent results and very small relative errors.