| 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 present 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 (Proc. Roy. Soc. 1998). |
