INTRODUCTION TO

MULTIPHASE FLOW Mekanika Fluida II

-Haryo Tomo-

1

Definitions

• Multiphase flow is simultaneous flow of • Matters with different phases( i.e. gas, liquid or solid).

• Matters with different chemical substances but with the same phase (i.e. liquid-liquid like oil-water).

• Primary and secondary phases • One of the phases is considered continuous (primary) and others

(secondary) are considered to be dispersed within the continuous phase. • A diameter has to be assigned for each secondary phase to calculate its

interaction (drag) with the primary phase (except for VOF model).

• Dilute phase vs. Dense phase; • Refers to the volume fraction of secondary phase(s)

• Volume fraction of a phase =

Volume of the phase in a cell/domain

Volume of the cell/domain

2

Why model multiphase flow?

• Multiphase flow is important in

many industrial processes:

• Riser reactors.

• Bubble column reactors.

• Fluidized bed reactors.

• Scrubbers, dryers, etc.

• Typical objectives of a modeling

analysis:

• Maximize the contact between

the different phases, typically

different chemical compounds.

• Flow dynamics.

Rushton CD-6 BT-6

3

Two-phase Flow Applications

The practical importance in many common engineering and industrial applications are:

• Steam generators and condensers, steam turbines ( Power

Plants ).

• Refrigeration .

• Coal fired furnaces .

• Fluidized bed reactors .

• Liquid sprays .

• Separation of contaminants from a carrier fluid

• Free surface flows, where sharp interfaces exist .

• pumping of slurries .

• pumping of flashing liquids .

• raining bed driers .

• oil industry two phase flow occurs in pipelines carrying oil and

natural gas.

• energy conversion .

• paper manufacturing .

• food manufacturing .

• medical applications .

The laws governing two phase flow are identical

to those for single phase flow. However, the

equations are more complex and/or more

numerous than those of single phase flow.

The description of the two-phase flow is complicated due to the existence of interface between the phases depending on a large number of variables such as :

1. quality (x).

2. phase physical properties .

3. flow patterns .

4. pipe geometry .

5. orientation of flow .

A general classifications divide two-phase flow into four

groups depending on the mixtures of phases in the flow.

The four groups are the flow of gas-liquid, gas-solid,

liquid-solid and immiscible liquid-liquid mixtures. The last

case is technically not a two-phase mixture, it is rather a

single phase two-component flow, but for all practical

purposes it can be considered as a two-phase mixture.

Flow Regimes In Horizontal Flow

1. Bubble flow .

2. Plug flow .

3. Stratified flow (layered, separated) .

4. Wavy flow (ripple flow, cresting) .

5. Slug flow .

6. Semi-annular flow .

7. Annular flow (ringed) .

8. Spray flow (mist, froth, dispersed) .

Flow Regimes in Vertical Flow

• Multiphase flow can be classified by the following regimes: 1. Bubbly flow: Discrete gaseous or fluid

bubbles in a continuous fluid

2. Droplet flow: Discrete fluid droplets in a continuous gas

3. Particle-laden flow: Discrete solid particles in a continuous fluid

4. Slug flow: Large bubbles (nearly filling cross-section) in a continuous fluid

5. Annular flow: Continuous fluid along walls, gas in center

6. Stratified/free-surface flow: Immiscible fluids separated by a clearly-defined interface

bubbly flow

droplet flow

particle-laden

flow

slug flow

annular flow free-surface flow

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Slug Bubble Separated Annular

Two Phase Flow Regimes Mapping

Mapping of flow patterns that occur in pipe flow has

always been a popular means of describing the

behaviors of flow at different conditions. The

superficial velocity of the gas and liquid are usually

put on the two different axes, and supply an efficient

method of comparing and contrasting the effects of

different flow conditions .

Flow regimes: vertical gas-liquid flow

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15

Multiphase flow regimes

• User must know a priori the characteristics of the flow.

• Flow regime, e.g. bubbly flow, slug flow, annular flow, etc.

• Only model one flow regime at a time.

• Predicting the transition from one regime to another

possible only if the flow regimes can be predicted by the

same model. This is not always the case.

• Laminar or turbulent.

• Dilute or dense.

• Secondary phase diameter for drag considerations.

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• Empirical correlations.

• Lagrangian.

• Track individual point particles.

• Particles do not interact.

• Algebraic slip model.

• Dispersed phase in a continuous phase.

• Solve one momentum equation for the mixture.

• Two-fluids theory (multi-fluids).

• Eulerian models.

• Solve as many momentum equations as there are phases.

• Discrete element method.

• Solve the trajectories of individual objects and their collisions, inside a continuous phase.

• Fully resolved and coupled.

Incre

ased c

om

ple

xity

Modeling approach

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Coupling between phases

• One-way coupling:

• Fluid phase influences particulate phase via aerodynamic drag and

turbulence transfer.

• No influence of particulate phase on the gas phase.

• Two-way coupling:

• Fluid phase influences particulate phase via aerodynamic drag and

turbulence transfer.

• Particulate phase reduces mean momentum and turbulent kinetic

energy in fluid phase.

• Four-way coupling:

• Includes all two-way coupling.

• Particle-particle collisions create particle pressure and viscous

stresses.

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Modeling multiphase flows

Flow Specific

bubbly

droplet

particle-laden

slug

annular

stratified/free surface

rapid granular flow

Model Specific

Lagrangian Dispersed

Phase Algebraic Slip

Eulerian

Eulerian Granular

Volume of Fluid

? Process Specific

Separation

Filtration

Suspension

Evaporation

Reaction

• What is the goal of the simulation?

• Which effects are important?

• Controlled by which hydrodynamic effects?

• Controlled by which other transport

phenomena effects?

• All these factors influence which model to

choose for the analysis.

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Physical effects in dispersed systems

• Hydrodynamics: • Change in shape.

• Diameter.

• Particle-wall collision.

• Particle-particle collision.

• Coalescence.

• Dispersion and breakup.

• Turbulence.

• Inversion.

• Other transport phenomena: • Heat transfer.

• Mass transfer.

• Change in composition.

• Heterogeneous reactions.

20

Multiphase formulation

• Two phases

• Three phases

Fluid

Solids

Solids - 1

Solids - 2

Fluid

21

I. Classification of sediment load

The sediment that is transported by a current.

Two main classes:

Wash load: silt and clay size material that remains in suspension even during low flow

events in a river.

Bed material load: sediment (sand and gravel size) that resides in the bed but goes into

transport during high flow events (e.g., floods).

Bed material load makes up many arenites and rudites in the geological record.

Sediment transport under unidirectional flows

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Three main components of bed material load.

Contact load: particles that move in contact with the bed by sliding or rolling over it.

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Saltation load: movement as a series of “hops”

along the bed, each hop following a ballistic

trajectory.

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When the ballistic trajectory is disturbed by turbulence the motion is referred to as

Suspensive saltation.

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Intermittent suspension load: carried in suspension by turbulence in the flow.

“Intermittent” because it is in suspension only during high flow events and otherwise

resides in the deposits of the bed.

Bursting is an important process in initiating suspension transport.

26

In the section on grain size distributions we

saw that some sands are made up of several

normally distributed subpopulations.

These subpopulations can be interpreted in

terms of the modes of transport that they

underwent prior to deposition.

II. Hydraulic interpretation of grain size

distributions

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The finest subpopulation represents the wash

load.

Only a very small amount of wash load is ever

stored within the bed material so that it makes

up a very small proportion of these deposits.

28

The coarsest subpopulation represents the

contact and saltation loads.

In some cases they make up two

subpopulations (only one is shown in the

figure).

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The remainder of the distribution, normally

making up the largest proportion, is the

intermittent suspension load.

This interpretation of the subpopulations gives

us two bases for quantitatively determining

the strength of the currents that transported

the deposits.

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The grain size “X” is the coarsest sediment

that the currents could move on the bed.

If the currents were weaker, that grain size

would not be present.

If the currents were stronger, coarser

material would be present.

This assumes that there were no limitations

to the size of grains available in the system.

In this case, X = -1.5 f or

approximately 2.8 mm.

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The grain size “Y” is the coarsest sediment

that the currents could take into suspension.

Therefore the currents must have been just

powerful enough to take the 0.41 mm

particles into suspension.

In this case, Y = 1.3 f or

approximately 0.41 mm.

If the currents were stronger the coarsest

grain size would be larger.

This assumes that there were no limitations

to the size of grains available in the system.

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To quantitatively interpret “X” we need to

know the hydraulic conditions needed to just

begin to move of that size.

This condition is the “threshold for sediment

movement”.

To quantitatively interpret “Y” we need to

know the hydraulic conditions needed to just

begin carry that grain size in suspension.

This condition is the “threshold for

suspension”.

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The threshold for grain movement on the bed.

Grain size “X” can be interpreted if we know what flow strength is required to just move

a particle of that size.

That flow strength will have transported sediment with that maximum grain size.

Several approaches have been taken to determine the critical flow strength to initiate

motion on the bed.

34

Hjulstrom’s Diagram

Based on a series of experiments using unidirectional currents with a flow depth of 1

m.

The diagram (below) shows the critical velocity that is required to just begin to move

sediment of a given size (the top of the yellow field).

It also shows the critical velocity for deposition of sediment of a given size (the bottom

of the yellow field).

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Note that for grain sizes coarser than 0.5 mm the velocity that is required for transport

increases with grain size; the larger the particles the higher velocity that is required for

transport.

For finer grain sizes (with cohesive clay minerals) the finer the grain size the greater the

critical velocity for transport.

This is because the more mud is present the greater the cohesion and the greater the

resistance to erosion, despite the finer grain size.

36

The problem is that the forces that are required to move sediment are not only related

to flow velocity.

Boundary shear stress is a particularly important force and it varies with flow depth.

to = rgDsinq

Therefore, Hjulstrom’s diagram is reasonably accurate only for sediment that has been

deposited under flow depths of 1 m.

37

Shield’s criterion for the initiation of motion

Based on a large number of experiments Shield’s criterion considers the problem in

terms of the forces that act to move a particle.

The criterion applies to beds of spherical particles of uniform grain size.

Forces that are important to initial motion:

2. to which causes a drag force that acts to

move the particle down current.

3. Lift force (L) that reduces the effective

submerged weight.

1. The submerged weight of the particle ( ) which

resists motion.

3( )6

s gd

r r

38

What’s a Lift Force?

The flow velocity that is “felt” by the particle varies from approximately zero at its base to

some higher velocity at its highest point.

39

Pressure (specifically “dynamic pressure” in contrast to static pressure) is also imposed

on the particle and the magnitude of the dynamic pressure varies inversely with the

velocity:

Higher velocity, lower dynamic pressure.

Maximum dynamic pressure is

exerted at the base of the particle

and minimum pressure at its highest

point.

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The dynamic pressure on the particle varies symmetrically from a minimum at the top to

a maximum at the base of the particle.

41

This distribution of dynamic pressure results in a net pressure force that acts upwards.

Thus, the net pressure force (known as the Lift Force) acts oppose the weight of the

particle (reducing its effective weight).

This makes it easier for the flow to

roll the particle along the bed.

The lift force reduces the drag

force that is required to move the

particle.

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If the particle remains immobile to the flow and the velocity gradient is large enough so

that the Lift force exceeds the particle’s weight….it will jump straight upwards away from

the bed.

Once off the bed, the pressure

difference from top to bottom of the

particle is lost and it is carried down

current as it falls back to the bed….

following the ballistic trajectory of

saltation.

A quick note on saltation…… 43

2 < L/D < 20

UG,sup up to 50 cm/s

UG,sup >> UL,sup

Liquid

Gas

Gas Inlet

Liquid/Slurry Inlet

Gas

Liquid

Pool

Sparger

A bubble column is a liquid pool sparged by a process stream.

Example: bubble column design

44

Flow Regime Map (Deckwer, 1980)

Bubbly Flow Churn-Turbulent Flow (“Heterogeneous”)

Bubble columns: flow regimes

45

Bubble column design issues • Design parameters:

• Gas holdup. Directly related to rise velocity. Correlations of the form

a ~ usgarl

bscmld are commonly used.

• Mass transfer coefficient kla. Correlations of the form

kla ~ usgarl

bscmld mg

eDfDrg are commonly used.

• Axial dispersion occurs in both the liquid and gas phase, and

correlations for each are available.

• Mixing time. Correlations are available for a limited number of systems.

• Volume, flow rates and residence time.

• Flow regime: homogeneous, heterogeneous, slug flow.

46

Bubble column design issues - cont’d

• Accurate knowledge of the physical properties is

important, especially the effects of coalescence and mass

transfer affecting chemicals.

• Although good correlations are available for commonly

studied air-water systems, these are limited to the ranges

studied.

• Correlations may not be available for large scale systems

or systems with vessel geometries other than cylinders

without internals.

• Furthermore, experimental correlations may not

accurately reflect changes in performance when flow

regime transitions occur.

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Bubble size

• At present, bubble column reactors are modeled using a

single effective bubble size.

• Coalescence and breakup models are not yet mature.

• Statistical approach. Solve equation for number density.

• Population balance approach.

• Application of population balance with two-fluid models with initial

focus on gas-liquid.

• The gas phase is composed of n bubble bins and share the same

velocity as the second phase.

• The death and birth of each bubble bin is solved from the above

models.

48

Example - gas-liquid mixing vessel

• Combinations of multiple

impeller types used.

• Bottom radial flow turbine

disperses the gas.

• Top hydrofoil impeller provides

good blending performance in

tall vessels.

49

Eulerian-granular/fluid model features

• Solves momentum equations for each phase and additional volume fraction equations.

• Appropriate for modeling fluidized beds, risers, pneumatic lines, hoppers, standpipes, and particle-laden flows in which phases mix or separate.

• Granular volume fractions from 0 to ~60%.

• Several choices for drag laws. Appropriate drag laws can be chosen for different processes.

• Several kinetic-theory based formulas for the granular stress in the viscous regime.

• Frictional viscosity based formulation for the plastic regime stresses.

• Added mass and lift force.

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Eulerian-granular/fluid model features

• Solves momentum equations for each phase and

additional volume fraction equations.

• Appropriate for modeling fluidized beds, risers, pneumatic

lines, hoppers, standpipes, and particle-laden flows in

which phases mix or separate.

• Granular volume fractions from 0 to ~60%.

• Several choices for drag laws. Appropriate drag laws can

be chosen for different processes.

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Elastic Regime Plastic Regime Viscous Regime

Stagnant Slow flow Rapid flow

Stress is strain Strain rate Strain rate dependent independent dependent

Elasticity Soil mechanics Kinetic theory

Granular flow regimes

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• When a fluid flows upward through a bed of solids, beyond a certain fluid velocity the solids become suspended. The suspended solids:

• has many of the properties of a fluid,

• seeks its own level (“bed height”),

• assumes the shape of the containing vessel.

• Bed height typically varies between 0.3m and 15m.

• Particle sizes vary between 1 mm and 6 cm. Very small particles can agglomerate. Particle sizes between 10 mm and 150 mm typically result in the best fluidization and the least formation of large bubbles. Addition of finer size particles to a bed with coarse particles usually improves fluidization.

• Superficial gas velocities (based on cross sectional area of empty bed) typically range from 0.15 m/s to 6 m/s.

Fluidized-bed systems

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Fluidized bed example

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Fluidized bed uses

• Fluidized beds are generally used for gas-solid contacting. Typical uses include:

• Chemical reactions:

• Catalytic reactions (e.g. hydrocarbon cracking).

• Noncatalytic reactions (both homogeneous and heterogeneous).

• Physical contacting:

• Heat transfer: to and from fluidized bed; between gases and solids; temperature control; between points in bed.

• Solids mixing.

• Gas mixing.

• Drying (solids or gases).

• Size enlargement or reduction.

• Classification (removal of fines from gas or fines from solids).

• Adsorption-desorption.

• Heat treatment.

• Coating.

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Gas

Dust

Gas distributor or constriction plate Windbox or plenum chamber

Dust

Separator

Gas and entrained solids

Gas in

Solids Feed

Fre

ebo

ard

Bed

dep

th

Solids Discharge

Disengaging Space

(may also contain a

cyclone separator)

Fluidized Bed

Typical fluidized bed systems - 1

56

Uniform Fluidization

Bed with central jet Gas

Solids

Gas + solids

Riser section of

a recirculating

fluidized bed

Typical fluidized bed systems - 2

57

Increasing Gas Velocity

Fixed

Bed

Particulate

Regime

Bubbling

Regime

Slug Flow

Regime

Turbulent

Regime

Fast

Fluidization

Pneumatic

Conveying

Gas

So

lid

s R

etu

rn

So

lid

s R

etu

rn

So

lid

s R

etu

rn

Uch

U

Umf Umb

U

Fluidization regimes

58

Fluidized bed design parameters

• Main components are the fluidization vessel (bed portion, disengagement space, gas distributor), solids feeder, flow control, solids discharge, dust separator, instrumentation, gas supply.

• There is no single design methodology that works for all applications. The design methodologies to be used depend on the application.

• Typical design parameters are bed height (depends on gas contact time, solids retention time, L/D for staging, space required for internal components such as heat exchangers).

• Flow regimes: bubbling, turbulent, recirculating, slugs. Flow regime changes can affect scale-up.

• Heat transfer and flow around heat exchanger components.

• Temperature and pressure control.

• Location of instrumentation, probes, solids feed, and discharges.

59

Fluidized bed - input required for CFD

• CFD can not be used to predict the:

• minimum fluidization velocity,

• and the minimum bubbling velocity.

• These depend on the:

• particle shape,

• particle surface roughness,

• particle cohesiveness, and the

• particle size distribution.

• All of these effects are lumped into the drag term. Hence

we need to fine tune the drag term to match the

experimental data for minimum fluidization or minimum

bubbling velocity.

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• bed expansion

• gas flow pattern

• solid flow pattern

• bubbling size, frequency and

population

• short circuiting

• effects of internals

• effects of inlet and outlets

• hot spots

• reaction and conversion rates

• mixing of multiple particle size

• residence times of solids and gases

• backmixing and downflows (in risers)

• solids distribution/segregation

Fluidized bed - when to use CFD • If the drag term is tuned to match the minimum fluidization

velocity, CFD then can be used to predict:

61