A Simple Analytical Theory for Interpreting Measured Total Pressure in Multiphase Flows

Abstract

This paper presents a simple, analytical theory for determining total pressure in multiphase flows, a subject of theoretical interest as well as of practical importance. It is shown here that the nonequilibrium processes occurring in the vicinity of a measuring device have a significant influence on the magnitude of flow velocity inferred from Pitot measurements. The present theory predicts that, depending on the size of the particles or droplets, the total pressure 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 toward the stagnation point) and the equilibrium total pressure (when the dispersed phase, either liquid droplets, or solid particles, is always at inertial and thermodynamic equilibrium with the continuous vapour phase). The presented analytical theory is a relation between nondimensional total pressure and Stokes number, representing particle size or inertia, and specifies the total pressure under different nonequilibrium conditions. One simple equation applies to diverse multiphase mixtures, solid particle laden gas as well as vapour-droplet mixtures, and at a wide range of flow conditions, both subsonic and supersonic. The associated issue of interpreting total temperature, and the relation between measured total pressure and entropy production in multiphase flows have been discussed at length by Guha (1998).