Fabien Petitpas

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.

Analytical/quasi-analytical solutions are proposed for a steady, compressible, two-phase flow in mechanical equilibrium in a rectilinear duct subjected to heating followed by cooling. The flow is driven by the pressure ratio between a variable outlet pressure and an upstream tank. A critical pressure ratio distinguishes subsonic and supersonic outlet regimes: the article proposes a methodology to determine the full flow behaviour, as a function of pressure ratio and heat-flux distribution. Going forward, these analytical reference solutions will help validate numerical codes for more complex industrial applications. Specific results are studied for a mixture of liquid water and water vapour.

Analytical/quasi-analytical solutions are proposed for a steady, compressible, two-phase flow in mechanical equilibrium in a rectilinear duct subjected to heating followed by cooling. The flow is driven by the pressure ratio between a variable outlet pressure and an upstream tank. A critical pressure ratio distinguishes subsonic and supersonic outlet regimes: the article proposes a methodology to determine the full flow behaviour, as a function of pressure ratio and heat-flux distribution. Going forward, these analytical reference solutions will help validate numerical codes for more complex industrial applications. Specific results are studied for a mixture of liquid water and water vapour.

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.

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.

In this paper, a new model is built to treat two-phase flows with a carrier phase laden with compressible liquid droplets. In some applications, the pressure in the carrier phase varies so much that it obviously should impact the droplet’s specific mass and temperature. This may be the case, for example, in solid rocket motors, where liquid droplets of aluminum at high temperature are ejected through a nozzle and endure pressure variations from 50 bar to atmospheric pressure or less. The same kind of problem may be observed in physics of explosive or in astrophysics. In these cases, a more precise description of the dispersed phase may be useful. Moreover, in extreme cases, it may become irrelevant to continue using a pressureless model for the dispersed phase, especially if a phase change or chemical reaction occurs. Therefore, a new thermodynamically consistent model is built for two-phase compressible dilute flows. Pressure in dispersed flow is reintroduced through the use of an equation of state. The ...