A unified theory for the interpretation of total pressure and temperature in two-phase flows at subsonic and supersonic speeds

Abstract

This paper presents a unified theory on the interpretation of total pressure and total temperature in multiphase flows. The present approach applies to both vapourdroplet mixtures and solid-particle laden gases, and at subsonic as well as supersonic velocities. It is shown here that the non-equilibrium processes occurring in the vicinity of a stagnation point are important. These processes may be responsible for the generation of entropy and affect the pressure and temperature at the stagnation point. They should be properly considered while inferring, say, flow velocity or entropy generation from Pitot measurements. By proper non-dimensionalization of the relevant parameters, it is possible to find a single (theoretically obtained) calibration curve for the total pressure as a function of the particle size, which is almost independent of the constituents of the multiphase mixture and of the flow conditions. The calibration curve is a plot of a pressure recovery factor versus Stokes number and specifies the total pressure under different non-equilibrium conditions. The total pressure, predicted by the present theory, varies monotonically between the two limiting values: the frozen total pressure (when there is no interphase mass, momentum and energy transfer in the decelerating flow towards the stagnation point) and the equilibrium total pressure (when the dispersed phase, either the liquid droplets or the solid particles, is always at inertial and thermodynamic equilibrium with the continuous vapour phase). The equilibrium total pressure is always higher than the frozen total pressure. It is shown that the equilibrium total temperature, on the other hand, may be higher or lower than the frozen total temperature. In addition, unlike the case of total pressure, the calibration curve for total temperature is not so universal, and the total temperature under non-equilibrium conditions is not necessarily bounded between the frozen and equilibrium values. It is further shown that the entropy of a multiphase mixture has to be carefully interpreted and is not unequivocally related to the total pressure even in steady adiabatic flow.

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