[Article from the PHOENICS Encyclopaedia]

[See also Numerical Computation of Multi-phase Flows; a Lecture Course"

- Definitions
- IPSA for two inter-penetrating continua
- multiple inter-penetrating continua
- separated (
*i.e.*free-surface) flows - the Lagrangian (
*i.e.*particle-group tracking option)

Multi-phase-flow phenomena are, for PHOENICS, those in which, within the smallest element of space which is considered (

Examples are:-

- suspensions of oil droplets in water, or of water droplets in oil;
- the air-snow mixture in an avalanche;
- the sand-air mixture in a sandstorm;
- the "mushy zone" of mixed solid and liquid metal in a casting mould;
- the water-air mixture in a shower bath;
- the gas-oil-water mixture, in the pores within rock, in a petroleum-recovery process;
- droplets of fuel oil, mixed with hot gases, in a combustion chamber.

**Definition of a phase**

The above examples employ the word "phase" in the sense customary in
thermodynamics, where the liquid, solid and gas phases are
distinguished.

However, a broader definition of phase is used in PHOENICS. This allows sand particles of different densities, or steam bubbles of different sizes, or gas eddies of different temperatures, also to be regarded as different phases.

Often, the multiple phases in the complete domain become sharply separated. This happens, for example, when the gas flame beneath a domestic kettle is switched off; for the bubbles rise, the suspended droplets fall, and a plane unbroken surface forms between the steam and the water.

The flow is then often called a fully-separated or free-surface flow.

Both intermingled and separated flows are considered in this encyclopaedia article.

Multi-phase-flow phenomena can be simulated by PHOENICS in four distinct ways. These are:

- as two inter-penetrating continua, each having at each point in
the space-time domain under consideration, its own:
- velocity components,
- temperature,
- composition,
- density,
- viscosity,
- volume fraction,
- etc;

- as multiple inter-penetrating continua having the same variety of properties;
- as two non-interpenetrating continua, separated by a free surface; or
- as a particulate phase for which the particle trajectories are computed as they move through a continuous fluid.

[Section 3 of the PHOENICS Encyclopaedia article on multi-phase flow. Click here for the start of the article]

When many phases are present, it is impractical to solve full sets of Navier-Stokes equations for all of them.

In this method, therefore, only one set of differential equations
is solved, to give the **mixture-mean** velocities at each point and
time.

Then separate sets of equations are solved, one for each phase,
which govern its relative velocities, *i.e.*their differences from the
mean.

The latter equations are algebraic ones, which are derived from the Navier-Stokes equations by neglect of second-order terms.

This entails that the relative velocities are computed by reference only to the local pressure gradients, the body forces and the inter- phase friction.

The volume fractions occupied by each phase, at each point and time, are calculated at the same time.

This method is referred to in the PHOENICS documentation as the "algebraic-slip" method, with the abbreviation ASLP. Elsewhere in the scientific literature, it is sometimes called the "drift-flux" method.

It is embodied in the Advanced Multi-Phase Flow option of PHOENICS; and it makes use of the open-source Fortran file GXASLP.FOR .

Click here for a lecture on the algebraic-slip method

This method is especially useful for simulating sedimentation and other processes, for example the separation of oil, gas and water in a centrifuge.

An example of this kind now follows.

The axi-symmetrical grid: 38 * 50

The axis is along the lower edge of the picture border
The flow is from right to left.
The cylindrical vessel is rotating at high speed, so that the
liquids are flung to the outside, *i.e.*upward on the diagram.

Note the sharpness of the gas-liquid interface. This is of course realistic; but not all numerical-simulation schemes are capable of producing it.

Contours of total oil concentration

Contours of light oil concentration

Contours of heavier oil concentration

Contours of heaviest oil concentration

See also the following Applications Album entry

[Section 4 of the PHOENICS Encyclopaedia article on multi-phase flow. Click here for the start of the article]

Method (3) treats the two (or more) fluids as a single fluid subject to discontinuities of density, viscosity and composition.

These discontinuities, *i.e.*the inter-fluid surfaces, are tracked as
they move through the domain of interest, by solution of the
individual continuity equations of each fluid.

Three tracking procedures are available, namely:

- (a) the height-of-liquid method,

Click here for a lecture on HOL - (b) the scalar-equation method,

Click here for a lecture on SEM - (c) the particle-on-surface method.

Click here for the Encyclopaedia article on this

The first of these is the most economical of computer time; but it cannot handle "breaking-wave" situations, in which the free-surface height at any horizontal position becomes multi-valued.

Both (b) and (c) can handle such phenomena; but only method (b) is easily usable for three-dimensional phenomena.

[Section 5 of the PHOENICS Encyclopaedia article on multi-phase flow. Click here for the start of the article]

Method (4) is embodied in the GENTRA (*i.e.*GENeral TRAcking) option
of PHOENICS.

The particles (or groups of particles) are tracked by solving the Lagrangian equations of motion, with full interactivity between the particulate and the continuous phases.

Heat, mass and momentum transfer can take place between the particulate and continuous phases; and the particles can undergo phase change and chemical reaction. They may also radiate.

Allowance is made for the particles to stick to walls which they hit, to slide along them subject to friction, or to bounce off with various coefficients of restitution.

GENTRA has found many applications in chemical engineering, power
engineering and aeronautics, *e.g.*the icing of aircraft-engine
intakes.

Examples of the application of the above methods to industrial and scientific flow simulations will be found in the Application Album.

For further information, see the PHOENICS Encyclopaedia entries: IPSA, ASLP, HOL, SEM, GENTRA, and also the Lectures on PHOENICS at the top level of POLIS.

See also the Encyclopaedia article on Multi-Fluid Models of Turbulence, and the lectures accessible from the top POLIS menu.

Body-fitted grid for a spray dryer

Contours of vapor mass fraction

It is worth noting that the particle-tracking method can also be used for computing the motion of free surfaces.

Click here for the Encyclopaedia article on this

This is illustrated by the following Applications Album entry, which compares the scalar-equation and the particle-tracking method. Agreement is good, as of course it should be.