Reference solutions for compressible single-phase flows in heated and cooled ducts

• Published in: Physics of fluids (1994) 2024-05, Vol.36 (5)
• Main Authors: Schropff, S., Petitpas, F., Daniel, E.
• Format: Article
• Language: English
• Subjects: Compressible flow; Cooling; Critical pressure; Exact solutions; Heat flux; Heat transfer; Heating; Mathematical analysis; Pressure ratio; Single-phase flow
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0209500

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.