| This paper presents a unified theory on the interpretation of
total
pressure and total temperature in multiphase flows. The present
approach
applies to both vapour-droplet 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 nonequilibrium 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 nonequilibrium 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. |
