multi phase flow regimes

8/4/2019 Multi Phase Flow Regimes

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Multiphase Flow Regimes andApproaches in CFD Simulation

By:

Amir Heidari ([email protected])

Academic webpage:

http://www.webpages.iust.ac.ir/amirheidari


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Multiphase flow regimes can be grouped into four categories:

gas-liquid or liquid-liquid flows; gas-solid flows; liquid-solid flows; and three-phase flows.

Gas-Liquid or Liquid-Liquid Flows: (see Figure 1)

Bubbly flow: This is the flow of discrete gaseous or fluid bubbles in a continuousfluid.

Droplet flow: This is the flow of discrete fluid droplets in a continuous gas. Slug flow: This is the flow of large bubbles in a continuous fluid. Stratified/free-surface flow: This is the flow of immiscible fluids separated by a

clearly-defined interface.

Gas-Solid Flows: (see Figure 1)

Particle-laden flow: This is flow of discrete particles in a continuous gas. Pneumatic transport: This is a flow pattern that depends on factors such as solid

loading, Reynolds numbers, and particle properties. Typical patterns are dune flow,

slug flow, packed beds, and homogeneous flow.

Fluidized bed: This consists of a vertical cylinder containing particles, into which agas is introduced through a distributor. The gas rising through the bed suspends the

particles. Depending on the gas flow rate, bubbles appear and rise through the bed,

intensifying the mixing within the bed.

Liquid-Solid Flows:


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Slurry flow: This flow is the transport of particles in liquids. The fundamentalbehavior of liquid-solid flows varies with the properties of the solid particles relative

to those of the liquid. In slurry flows, the Stokes number (see Equation 23.2-4) is

normally less than 1. When the Stokes number is larger than 1, the characteristic of

the flow is liquid-solid fluidization. Hydrotransport: This describes densely-distributed solid particles in a continuous

liquid

Sedimentation: This describes a tall column initially containing a uniform dispersedmixture of particles. At the bottom, the particles will slow down and form a sludge

layer. At the top, a clear interface will appear, and in the middle a constant settling

zone will exist.

Figure 1


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Three-Phase Flows:

Three-phase flows are combinations of the other flow regimes listed in the previoussections.

Bubbly flow examples include absorbers, aeration, air lift pumps, cavitation,evaporators, flotation, and scrubbers.

Droplet flow examples include absorbers, atomizers, combustors, cryogenic pumping,dryers, evaporation, gas cooling, and scrubbers.

Slug flow examples include large bubble motion in pipes or tanks. Stratified/free-surface flow examples include sloshing in offshore separator devices and

boiling and condensation in nuclear reactors.

Particle-laden flow examples include cyclone separators, air classifiers, dust collectors,and dust-laden environmental flows.

Pneumatic transport examples include transport of cement, grains, and metal powders. Fluidized bed examples include fluidized bed reactors and circulating fluidized beds. Slurry flow examples include slurry transport and mineral processing Hydrotransport examples include mineral processing and biomedical and

physiochemical fluid systems

Sedimentation examples include mineral processing.


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The first step in solving any multiphase problem is:

to determine which of the regimes provides some broad guidelines for determining

appropriate models for each regime, and how to determine the degree of interphase

coupling for flows involving bubbles, droplets, or particles, and the appropriate model

for different amounts of coupling.

Approaches to Multiphase ModelingApproaches to Multiphase ModelingApproaches to Multiphase ModelingApproaches to Multiphase Modeling

In FLUENT, three different Euler-Euler multiphase models are available:

o The volume of fluid (VOF) model,o The mixture model,o and the Eulerian model.

The VOF ModelThe VOF ModelThe VOF ModelThe VOF ModelThe VOF model is a surface-tracking technique applied to a fixed Eulerian mesh.

It is designed for two or more immiscible fluids where the position of the interface

between the fluids is of interest. In the VOF model, a single set of momentum

equations is shared by the fluids, and the volume fraction of each of the fluids in each

computational cell is tracked throughout the domain. Applications of the VOF model

include stratified flows, free-surface flows, filling, sloshing, the motion of large

bubbles in a liquid, the motion of liquid after a dam break, the prediction of jet

breakup (surface tension), and the steady or transient tracking of any liquid-gas

interface.


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The Mixture ModelThe Mixture ModelThe Mixture ModelThe Mixture ModelThe mixture model is designed for two or more phases (fluid or particulate). As in

the Eulerian model, the phases are treated as interpenetrating continua. The mixture

model solves for the mixture momentum equation and prescribes relative velocities todescribe the dispersed phases. Applications of the mixture model include particle-

laden flows with low loading, bubbly flows, sedimentation, and cyclone separators.

The mixture model can also be used without relative velocities for the dispersed

phases to model homogeneous multiphase flow.

The Eulerian ModelThe Eulerian ModelThe Eulerian ModelThe Eulerian ModelThe Eulerian model is the most complex of the multiphase models in FLUET. It

solves a set ofn momentum and continuity equations for each phase. Coupling is

achieved through the pressure and interphase exchange coefficients. The manner in

which this coupling is handled depends upon the type of phases involved; granular

(fluid-solid) flows are handled differently than nongranular (fluid-fluid) flows. For

granular flows, the properties are obtained from application of kinetic theory.

Momentum exchange between the phases is also dependent upon the type of mixture

being modeled. FLUET's user-defined functions allow you to customize the

calculation of the momentum exchange. Applications of the Eulerian multiphase

model include bubble columns, risers, particle suspension, and fluidized beds.

Model Comparisons

For bubbly, droplet, and particle-laden flows in which the phases mix and/or

dispersed-phase volume fractions exceed 10%, use either the mixture model or the

Eulerian model.

For slug flows, use the VOF model.For stratified/free-surface flows, use the VOF model.

For pneumatic transport, use the mixture model for homogeneous flow or the Eulerian

model for granular flow.

For fluidized beds, use the Eulerian model for granular flow.

For slurry flows and hydrotransport , use the mixture or Eulerian model


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For sedimentation, use the Eulerian model.

For general, complex multiphase flows that involve multiple flow regimes, select the

aspect of the flow that is of most interest, and choose the model that is most

appropriate for that aspect of the flow. ote that the accuracy of results will not be as

good as for flows that involve just one flow regime, since the model you use will be

valid for only part of the flow you are modeling.

To choose between the mixture model and the Eulerian model:

If there is a wide distribution of the dispersed phases (i.e., if the particles vary in size

and the largest particles do not separate from the primary flow field), the mixture

model may be preferable (i.e., less computationally expensive). If the dispersed phases

are concentrated just in portions of the domain, you should use the Eulerian model

instead.

If interphase drag laws that are applicable to your system are available (either within

FLUENT or through a user-defined function), the Eulerian model can usually provide

more accurate results than the mixture model. Even though you can apply the same

drag laws to the mixture model, as you can for a nongranular Eulerian simulation, if

the interphase drag laws are unknown or their applicability to your system is

questionable, the mixture model may be a better choice. For most cases with spherical

particles, then the Schiller-aumann law is more than adequate. For cases with

nonspherical particles, then a user-defined function can be used.

If you want to solve a simpler problem, which requires less computational effort, the

mixture model may be a better option, since it solves a smaller number of equations


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than the Eulerian model. If accuracy is more important than computational effort, the

Eulerian model is a better choice.

Keep in mind, however, that the complexity of the Eulerian model can make it less

computationally stable than the mixture model.

The process of solving a multiphase system is inherently difficult, and you may encounter

some stability or convergence problems. If a time-dependent problem is being solved, and

patched fields are used for the initial conditions, it is recommended that you perform a few

iterations with a small time step, at least an order of magnitude smaller than the

characteristic time of the flow. You can increase the size of the time step after performing a

few time steps. For steady solutions it is recommended that you start with a small under-

relaxation factor for the volume fraction, it is also recommended not to start with a patch

of volume fraction equal to zero. Another option is to start with a mixture multiphase

calculation, and then switch to the Eulerian multiphase model.

Overview of the VOF Model:

The VOF model can model two or more immiscible fluids by solving a single set of

momentum equations and tracking the volume fraction of each of the fluids throughout


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the domain. Typical applications include the prediction of jet breakup, the motion of

large bubbles in a liquid, the motion of liquid after a dam break, and the steady or

transient tracking of any liquid-gas interface.

The VOF formulation in FLUET is generally used to compute a time-dependent solution, but

for problems in which you are concerned only with a steady-state solution, it is possible to

perform a steady-state calculation. A steady-state VOF calculation is sensible only when your

solution is independent of the initial conditions and there are distinct inflow boundaries for the

individual phases. For example, since the shape of the free surface inside a rotating cup depends

on the initial level of the fluid, such a problem must be solved using the time-dependent

formulation. On the other hand, the flow of water in a channel with a region of air on top and a

separate air inlet can be solved with the steady-state formulation.

Surface Tension

The VOF model can also include the effects of surface tension along the interface

between each pair of phases. The model can be augmented by the additional

specification of the contact angles between the phases and the walls. You can specifya surface tension coefficient as a constant, as a function of temperature, or through

a UDF. The solver will include the additional tangential stress terms (causing what

is termed as Marangoni convection) that arise due to the variation in surface tension

coefficient. Variable surface tension coefficient effects are usually important only in

zero/near-zero gravity conditions.

Wall AdhesionAn option to specify a wall adhesion angle in conjunction with the surface tension

model is also available in the VOF model. The model is taken from work done by

Brackbill et al. [40]. Rather than impose this boundary condition at the wall itself,


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the contact angle that the fluid is assumed to make with the wall is used to adjust the

surface normal in cells near the wall. This so-called dynamic boundary condition

results in the adjustment of the curvature of the surface near the wall.

Overview of Mixture Model

The mixture model is a simplified multiphase model that can be used to model

multiphase flows where the phases move at different velocities, but assume local

equilibrium over short spatial length scales. The coupling between the phases should

be strong. It can also be used to model homogeneous multiphase flows with very

strong coupling and the phases moving at the same velocity. In addition, the mixture

model can be used to calculate non-ewtonian viscosity.

The mixture model can model n phases (fluid or particulate) by solving the

momentum, continuity, and energy equations for the mixture, the volume fraction

equations for the secondary phases, and algebraic expressions for the relative

velocities. Typical applications include sedimentation, cyclone separators, particle-

laden flows with low loading, and bubbly flows where the gas volume fraction

remains low.

The mixture model is a good substitute for the full Eulerian multiphase model in

several cases. A full multiphase model may not be feasible when there is a wide

distribution of the particulate phase or when the interphase laws are unknown or

their reliability can be questioned. A simpler model like the mixture model can

perform as well as a full multiphase model while solving a smaller number ofvariables than the full multiphase model.

The mixture model allows you to select granular phases and calculates all properties

of the granular phases. This is applicable for liquid-solid flows.


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The mixture model, like the VOF model, uses a single-fluidapproach. It differs from the

VOF model in two respects:

The mixture model allows the phases to be interpenetrating.

The mixture model allows the phases to move at different velocities, using the

concept of slip velocities. (ote that the phases can also be assumed to move at the

same velocity, and the mixture model is then reduced to a homogeneous multiphase

model.)

Overview of Eulerian Model

The Eulerian multiphase model in FLUENT allows for the modeling of multiple

separate, yet interacting phases. The phases can be liquids, gases, or solids in nearly

any combination. An Eulerian treatment is used for each phase, in contrast to the

Eulerian-Lagrangian treatment that is used for the discrete phase model.

With the Eulerian multiphase model, the number of secondary phases is limited only

by memory requirements and convergence behavior. Any number of secondary

phases can be modeled, provided that sufficient memory is available. For complex

multiphase flows, however, you may find that your solution is limited by

convergence behavior.

FLUENT's Eulerian multiphase model does not distinguish between fluid-fluid and

fluid-solid (granular) multiphase flows. A granular flow is simply one that involves

at least one phase that has been designated as a granular phase.

multi phase flow regimes

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