This document introduces key terminology used in multiphase flow modeling. It defines a continuous phase/primary phase as the bulk carrier fluid and dispersed phase/secondary phase as the discrete particles, droplets, or bubbles suspended in the continuous phase. Volume fraction and densities are also defined for both phases. Velocities include superficial velocities based on mass flow rates and phase velocities relating the actual velocity to volume fraction. Other terms introduced are mass concentration, quality, phase loading, and Stokes number which indicates particle independence from the continuous phase flow.

1. Introduction to Multiphase Flow Modeling
learncax.com /blog/2012/05/21/multiphase-f low-modelingterminologies/
Ganesh Visavale
Terminologies:
The fundamental terminologies used in the study of multiphase flows are as follows:
Cont inuous phase or Primary phase:
This is basically the carrier fluid, that is
present in bulk.
Dispersed phase or Secondary
phase: This is the discrete phase which
is usually in the form of particles,
droplets, or bubbles. The secondary
phase may or may not have a distinct
velocity field i.e. it will at some times follow
the continuous phase or at times will have
its own velocity field and affect the
continuous phase flow.
Volume f ract ion:
+ Volume fraction of a dispersed phase: It is
defined as the ratio of volume of dispersed
phase to the volume of the medium or the total
volume. Mathematically represented by
Where del Vd is the volume of the dispersed
phase in volume del V .
Unlike a continuum, the volume fraction cannot
be defined at a point and is defined based on
the volume.
+ Volume fraction of a continuous phase: Similarly, defined as the ratio of volume of
continuous phase to the volume of the medium or the total volume. Mathematically
represented by
where del Vc is the volume of the continuous phase in the volume. By definition the sum of
the volume fraction must be unity i.e.
Densit ies: In multiphase we have two terms for densities, the bulk density and the
material density. The bulk density is defined as the mass of the dispersed phase per
unit volume of mixture, mathematically given by,
del Md mass of dispersed phase. This bulk density is related to the material density rho(d) by,
The sum of the bulk densities for the dispersed and continuous phases is the mixture density.
Velocit ies: There are generally two terms used to define velocities, the
superficial velocity and the phase velocity.
+ Superficial Velocities: It is mostly associated with pipe flow and is the mass flow rate, of
the respective phase divided by the pipe area A and material density. So in case of
dispersed phase this superficial velocity is given by:
+ Phase velocities: The phase velocity Ud is the actual velocity of the phase. The volume
fraction relates the phase velocity with the superficial velocity as follows:
The phase velocity or the bulk density, are generally defined for our convenience purpose
in study of multiphase flow and different from the actual velocity and density of the phase.
They are obtained by multiplying actual velocity or density with volume fraction.

2. Mass concent rat ion of dispersed phase: It is the ratio of the mass of dispersed
phase to that of the continuous phase in a mixture.
Qualit y: It is the measure of the quantity of dispersed phase in the medium (both the
dispersed and continuous phase).
Phase Loading: It is the ratio of mass flux of the dispersed phase to that of continuous
phase.
Disperse Flows: In such flows the phase loading of dispersed flows is comparatively
lower (by mass) than the continuous phase. The bulk of the flow is occupied by the
continuous phase and dominates the flow phenomena. In dispersed flow the particle
motion is mainly controlled by the fluid forces (like drag and lift).
Dense Flows: Such flows are generally associated with high phase loadings of dispersed
phase. Here the interparticle collisions play a dominant role in the flow field controlling the
overall particle motion. The dense flows are classified into two main categories namely,
+ Collision dominated: Collisions between the particles control the overall flow features.
+ Contact dominated: Continuous particle to particle contact controls the overall flow features.
St okes Number: It is a non- dimensional number, given by the ratio of particle (dispersed phase) relaxation
time to the characteristic time scale of the flow. Mathematically represented by:
+ Significance of Stokes Number:
If Stk , then particles follow the continuous phase flow closely.
If Stk> 1 , then dispersed phase particles will move independent of the continuous phase flow.
coming up… Fundamentals of Multiphase Flow Modeling
scrolling="no" frameborder="0" style="border:none; overflow:hidden;
width:100px; height:27px;" allowTransparency="true">
Share