cfd simulation of immiscible liquid dispersions srinath madhavan department of chemical engineering

CFD Simulation of Immiscible Liquid

Dispersions

Srinath Madhavan

Department of Chemical Engineering

6th July 2005 CFD Simulation of Immiscible Liquid Dispersions 2

Outline

Introduction to liquid-liquid dispersions, Motivation driving the current study, Objectives of the present investigation, Research methodology, Simulation results and discussion, Conclusions and recommendations.


Liquid-Liquid Dispersions

Immiscible liquid dispersions are commonly encountered in CPI,

For instance in liquid-liquid extraction, emulsification and homogenization, direct contact heat transfer, polymerization etc.

Enhanced heat/mass transfer rates are desirable in most processes,

These depend on the heat/mass transfer coefficient, the driving force and the interfacial area of contact,

It is relatively easier to manipulate the contact area when compared to the driving force or the heat/mass transfer coefficient.


Interfacial Area of Contact

For a unit volume of the Liquid-Liquid dispersion,

A combination of smaller drop sizes and larger dispersed phase holdup is usually sought.

diameterphasedispersed

holdupphasedispersedarealInterfacia


Importance of Dispersed Phase Holdup

Holdup is a fundamental multiphase characteristic which: Influences the overall performance, Affects the pressure drop, Determines the global residence time, Can significantly modify the flow

structure, Is therefore an important design

parameter.


Holdup Distribution

For improved design and efficient contacting, correlations that relate the system performance to the local flow characteristics need to be developed,

While the average dispersed phase holdup can reasonably predict certain parameters such as the pressure drop, it cannot accurately predict local heat/mass transfer rates,

It therefore becomes important to carry out experiments to determine the local holdup distribution in the system.


The need for CFD studies

Although extensive experiments can provide enough information to develop empirical correlations, there are certain inherent limitations such as: The limited range of application, Simplifying assumptions used in their development, Scale-up issues, Use of intrusive measurement techniques, Inability to develop expressions suited for complex

geometries, Time consuming and often expensive, Safety concerns etc.

Hence there is a growing need for alternatives to experimental analysis.


Computational Fluid Dynamics (CFD)

Accurate simulation of fluid flows by solving the basic conservation equations (mass, momentum and energy) is the primary objective of CFD,

Although CFD cannot entirely replace experiments, it features several lucrative advantages when compared to conventional experimental analysis: Low cost, Prompt analysis devoid of any scale-up issues, Simulation of certain situations which cannot be

handled experimentally, Advanced visualization of technical results that helps to

better understand flow features etc.


CFD and Dispersed Multi-fluid Systems

There are quite a few approaches to dispersed Multi-fluid modeling using CFD: Discrete phase (Eulerian-Lagrangian), Two-fluid (Eulerian-Eulerian), Interface tracking (Volume of Fluid), Mixture (Algebraic Slip Mixture Model).

Among these, the two-fluid approach is widely used owing to the adequate flow detail it provides (even at high dispersed phase volume fractions) in exchange for a reasonable amount of computation power.


Two-fluid Approach to Multi-fluid CFD Modeling

Realized by averaging the local instantaneous equations (mass, momentum and energy), which reduces computational power requirements,

Concept of interpenetrating continua and phasic velocities and volume fractions.

Reality Two-fluid model

Dispersed phase 2 (e.g. oil drops)

Continuous phase (e.g. water)

Dispersed phase 1 (e.g. air bubbles)


Two-fluid Model: Governing Equations

Conservation of mass:

n

p

qqqpqqqqqq dt

dmv

t 1

0 qqv

For steady-state incompressible flow in the absence of mass transfer this simplifies to:


Two-fluid Model: Governing Equations (2)

Conservation of Momentum:

n

ppqpqqppqqvmqliftq

qqqqqqqqqqq

vmvvKFFF

gpvvvt

1,,

Again, for steady-state incompressible flow in the absence of mass transfer, external body forces (Fq), and virtual/added mass effects (Fvm), the momentum conservation equation simplifies to:

volumeunitperforcedragdispersionTurbulent

n

pqppq

volumeunitperforceLift

qlift

volumeunitperforcenalGravitatio

qq

volumeunitperforceViscous

q

volumeunitperforcePressure

q

volumeunitpermomentumofChange

qqqq

vvKFg

pvv

&

1,


The closure problem

volumeunitperforcedraganddispersionTurbulent

n

pqppq

volumeunitperforceLift

qlift

volumeunitperforcenalGravitatio

qq

volumeunitperforceViscous

q

volumeunitperforceessure

q

volumeunitpermomentumofChange

qqqq

vvKFg

pvv

1,

Pr

Turbulent stresses (viscous force per unit volume) and interphase forces (drag, lift and turbulent dispersion forces per unit volume) are unknown.

In order to obtain a closed set of equations, these terms need to be supplied.


Turbulence Closure Terms

Viscous stresses in turbulent flows can be supplied through the specification of a turbulent viscosity calculated using an appropriate turbulence model,

In the context of multi-fluid turbulence models, the standard k- turbulence model is most extensively studied. With specific reference to liquid-liquid dispersions, it has been found to be numerically robust and gives reasonable predictions for an affordable computational cost,

Turbulence quantities for the dispersed phase can be modeled using Tchen’s theory of dispersion of discrete particles by homogeneous turbulence (TChen, 1947),

Effect of dispersed phase on the flow structure of the continuous phase can be accounted for using turbulence modulation. This aspect is nonetheless, still under active research,

It is however, a generally accepted fact that more research is required to accurately predict turbulence in multi-fluid systems (Ranade, 2002).


Interphase Closure Terms

Although several interphase forces are encountered in liquid-liquid dispersions, experimental observations indicate that turbulent dispersion, drag and lift forces are the most significant (Farrar and Bruun, 1996; Domgin et al., 1997; Soleimani et al., 1999),

With reference to immiscible liquid dispersions, a large number of investigations pertaining to interphase forces (particularly the drag force) are available in the open literature,

Nevertheless, there has been no attempt to analyze and evaluate the different expressions for the interphase forces,

Non-drag forces such as turbulent dispersion and lift forces dictate the lateral movement of the dispersed phase and thus influence the dispersed phase distribution.


Research Objective The objective of the present study is to

identify and quantify the various significant interphase forces encountered in turbulent bubbly flows of immiscible liquid dispersions.

The knowledge so gained can be beneficially employed to develop generally applicable CFD guidelines for interphase closure in dispersed liquid-liquid systems.


Overall Approach

Selection of a liquid-liquid contactor that can be used to achieve the current research objectives,

Review of previous work related to interphase forces in liquid-liquid systems,

Selection of data sets for CFD validation, Preliminary simulations of liquid-liquid turbulent bubbly

flows to compare and evaluate various formulations for drag and lift forces and turbulent dispersion,

Identifying drag, lift and turbulent dispersion coefficient expressions and/or values which yield a good agreement with experimental data,

To propose guidelines for inter-phase closure on the basis of the above simulation results.


Choice of L-L Contactor – Vertical pipe

Why pipes?

Simple hydrodynamics when compared to other contacting units such as stirred tanks or mechanically agitated columns,

Turbulence characteristics of the continuous phase are very well investigated,

Can be expected to yield accurate predictions of the fundamental two-phase flow characteristics (e.g. local dispersed phase holdup, relative velocity between the phases etc.) without recourse to a large degree of empiricism and know-how.

As pipes are ubiquitous in chemical, process and petroleum industries, an extensive database of detailed experimental results is also available. This is particularly true for the case of dispersed liquid-liquid pipeline flow (Foussat and Hulin, 1984; Farrar, 1988; Farrar and Bruun, 1988; Vigneaux et al., 1988; Simonian, 1993; Farrar and Bruun, 1996; Lang and Auracher, 1996; Al-Deen and Bruun, 1997; Ali et al., 1999; Lang, 1999; Soleimani et al., 1999; Fordham et al., 1999; Hamad et al., 2000).


Review of the Interphase Drag Force

In dispersed multiphase systems, the force that opposes the relative velocity between the phases is called the drag force,

Drag force on drops is different from the drag force on rigid spheres. This is attributed to two factors: Internal circulation, Shape deformation.

Drag force on a drop is affected in the presence of adjacent drops. Again, there are two factors responsible for this behavior: Reduced buoyancy force on the

drop, Apparent increase in medium

viscosity.

Fluid velocity vectors

Dispersed entity

A

C

AC

C

A

Direction of relative velocity

Drag force (FD)

e

ScdDD d

VCF

2

4

3


Expressions for the Drag Coefficient of a Single Drop

For single rigid spheres, the expression proposed by Schiller and Naumann (1935) is widely used,

For single drops, several expressions for the drag coefficient have been proposed: Hu and Kintner (1955) Klee and Treybal (1956) Grace et al. (1976) Ishii and Zuber (1979)

It can be seen that significant differences between the two are observed at higher equivalent drop diameters (i.e. greater than 3 mm).

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 2 4 6 8 10 12 14 16

Equivalent diameter (mm)

Re

lati

ve

ve

loc

ity

(m

/s)

Klee and Treybal

Hu and Kintner

Grace et al.

Ishii and Zuber

Schiller and Naumann

Single drops

Rigid sphere


Expressions for the Drag Coefficient of a Drop in the Presence of Adjacent Drops

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.1 0.2 0.3 0.4 0.5 0.6

Dispersed phase holdup (-)R

ela

tive v

elo

cit

y (

m/s

)

Ishii and Zuber (Dense f luid particles)

Ishii and Zuber (corrected w ith Rusche and Issa (2000)

Kumar and Hartland

Ishii and Zuber (Single drop)

μmedium = μc

ρmedium = ρc

ρdrop = ρd

μdrop = μd

ρdrop = ρd

μdrop = μd

μmedium > μc

ρmedium < ρc

usum

If (μdrop > μc) and (ρdrop < ρc) => um < us

um

us

de = 5 mm


Review of the Interphase Lift Force – Inviscid Lift

When a dispersed phase entity moves through a non-uniform flow field, it will experience a lift force due to the vorticity or shear in the continuous phase field,

The lift force acts on the dispersed entities in a direction perpendicular to the relative motion between the two phases.

BC

B

C

A

B C

Dispersed entity

Wall

Axis

A

C

AC

High velocity Low pressure

Low velocity High Pressure

Inviscid Lift force

AC

BC

Flu

id v

elo

city

vect

ors

Calculation of Relative Velocity

Wall

Axis

Inviscid Lift force

qpqpqLlift vvvCF


Review of the Interphase Lift Force – Vortex-shedding Lift

Recent studies indicate that the inviscid lift force may not be the only lift force experienced by a dispersed entity in shear flow (Taeibi-Rahni and Loth, 1996; Loth et al., 1997; Moraga et al., 1999),

Larger dispersed entities moving much faster than the fluid shed vortices as they move,

An asymmetric wake behind the dispersed entity can give rise to significant lateral forces that oppose the inviscid lift force.

Wall

Axis

Inviscid Lift force

Wake-induced Lift force

Wake


Expressions for the Lift Coefficient (CL)

Constant lift coefficient,

The expression for lift coefficient proposed by Moraga et al. (1999),

An approach similar to that of Moraga et al. (1999) in which validity limits for the lift coefficient expression have been modified in accordance with the recommendations made by Troshko et al. (2001).

-0.7

-0.5

-0.3

-0.1

0.1

0.3

0.5

0.7

1 100 10000 1000000 100000000

Re Re

CL

(-)

Moraga et al. (1999)

CL = 0.0

Troshko et al. (2001)

ReReÑ = 183897

Moraga et al. (1999) applied to dropsand bubbles


Review of Turbulent Dispersion

A pseudo-force which induces a diffusive flux that accounts for dispersion (or spread) of dispersed phase entities due to the random influence of the turbulent eddies present in the continuous phase.

In the absence of Turbulent Dispersion

In the presence of Turbulent Dispersion

volumeunitperforcedispersionTurbulent

drpq

volumeunitperforceDrag

qppqqppq vKUUKvvK

q

qpq

qp

ppq

pdr

DDv

Dispersion Prandtl Number (DPN)

Very high DPN

Very low DPN

Model proposed by Simonin and Viollet (1990)


Data Sets used for CFD Validation

Data Set Data PointContinuous phase superficial

velocity (m/s)Dispersed phase superficial

velocity (m/s)Average dispersed phase

holdup (-)

Farrar and Bruun (1996)

F20 0.4935 0.1363 0.1912

F25 0.4634 0.1637 0.2275

F30 0.4263 0.1972 0.2783

Hamad et al. (2000)H10 0.5855 0.0651 0.0873

H20 0.5855 0.1464 0.1764

Al-Deen and Bruun (1997)

A5 0.5441 0.0286 0.0493

A10 0.5441 0.0605 0.0917

A20 0.5441 0.1360 0.1872

A30 0.5441 0.2332 0.2992

Lang (1999)

L20A 0.4000 0.1000 0.1851

L20B 1.2000 0.3000 0.1809

L40 0.3000 0.2000 0.3692

L60 0.2000 0.3000 0.5474

Vigneaux et al. (1988)

V5 0.2268 0.0119 0.0323

V10 0.2149 0.0239 0.0661

V30 0.1671 0.0716 0.2350

V50 0.1194 0.1194 0.4308

16 mm ID

78 mm ID

200 mm ID

1 mm de 5 mm


Comparative Evaluation of Drag Coefficient Expressions for Single Entities (using CFD Simulations)

Expression for CD0 de = 2 mm de = 5 mm de = 8 mm

Schiller and Naumann (1935) – Rigid sphere

0.04429 0.03894 0.03651

Ishii and Zuber (1979) 0.04405 0.04095 0.04094

Grace et al. (1976) 0.04405 0.04023 0.04055

Hu and Kintner (1955) 0.04432 0.04014 0.04032

Klee and Treybal (1956) 0.04428 0.04208 0.04204

Experimental conditions of Al-Deen and Bruun (1997) were used as an example – phase ratio of the dispersed phase = 5 %,

All expressions for single entities predict similar holdups at low equivalent diameters (de 2 mm),

As the equivalent diameter increases, the single drop holdup predictions start to deviate from the rigid sphere predictions,

The drag model proposed by Ishii and Zuber (1979) was chosen as a representative for single drops.


Comparative Evaluation of Drag Coefficient Expressions that account for the presence of other Drops (using CFD Simulations)

Experimental conditions of Al-Deen and Bruun (1997) were used as an example – phase ratio of the dispersed phase = 30 %,

All expressions predict similar holdups at de = 2 mm and at de = 5 mm,

When compared to the average holdup as reported in the experiment ( 29 %), it is seen that accounting for the presence of adjacent entities results in a slightly better prediction,

The expression proposed by Kumar and Hartland (1985) suitably accounts for the presence of adjacent drops as its holdup predictions lie between the other two approaches.

Expression for CDM de = 2 mm de = 5 mm

Ishii and Zuber - Dense fluid particles (1979)

0.2855 0.2751

Kumar and Hartland (1985) 0.2890 0.2797

Ishii and Zuber (1979) drag expression for single drops, modified to account for the presence of adjacent drops using the correction factor proposed by Rusche and Issa (2000)

0.2902 0.2812

Ishii and Zuber (1979) drag expression for single drops

0.2824 0.2707


Comparative Evaluation of Lift Coefficient Expressions/Values (using CFD Simulations)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.2 0.4 0.6 0.8 1

Normalized radius (-)

Dis

pers

ed p

hase

hol

dup

(-)Troshko et al. (2001) CL = + 0.01

CL = + 0.005 CL = + 0.001

CL = 0.0 CL = - 0.001

CL = - 0.005 CL = - 0.01

Experimental conditions of Farrar and Bruun (1996) are chosen as an example,

The expression for lift coefficient proposed by Moraga et al. (1999) was found to give numerical instabilities and/or unphysical predictions,

Positive constants for CL predict wall peaks whereas negative constants predict ‘coring’ and/or ‘near-wall peaking’ trends,

All constant lift coefficients and the expression proposed by Troshko et al. (2001) predict non-zero volume fractions at the wall.

de = 5 mmPhase ratio of the dispersed phase = 30 %, no turbulent dispersion

Drag coefficient expression used: Kumar and Hartland (1985)


Comparative Evaluation of Turbulent Dispersion Coefficient Values (using CFD Simulations)

Turbulent dispersion effects were simulated using the approach proposed by Simonin and Viollet (1990), which accounts for the response of drops to turbulent eddies in the continuous phase,

The experimental conditions of Farrar and Bruun (1996) are used as an example. A ‘data point’ featuring a ‘near-wall’ peak was chosen to demonstrate the effect of turbulent dispersion,

The expression for lift coefficient as proposed by Troshko et al. (2001) was used,

High DPN values (e.g. 7.5) decrease the degree of turbulent dispersion and vice-versa.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.2 0.4 0.6 0.8 1

Normalized radius (-)

Dis

per

sed

ph

ase

ho

ldu

p (

-)

DPN 0.075 DPN 0.75

DPN 7.5 DPN 0.0075

Drag coefficient expression used: Kumar and Hartland (1985)

Phase ratio of the dispersed phase = 30 %

de = 5 mm


Summary of Simulation Details

CFD package: Pre-processor: Gambit 2.1.2, Solver and Post-processor: Fluent 6.1.22,

Hardware: GNU/Linux workstation (Pentium IV 2.53 GHz CPU, 1 GB DDR SDRAM, 1 GB swap space) running Red

Hat Linux 9, Simulation time (20 minutes to 5 hours),

Computation grid: Axisymmetric structured grid with 1:1 cell aspect ratios (6,000 to 80,000 cells), Near-wall treatment: Y+ 30 for Standard wall functions and Y+ 5 for Enhanced wall treatment,

Solver configuration: Eulerian multiphase model, k-ε turbulence model for the continuous phase, TChen (1947) theory of dispersion by homogeneous turbulence for the dispersed phase, Mono-dispersed drop sizes in the range (1 to 5 mm), Drag coefficient expression proposed by Kumar and Hartland (1985), Lift coefficient expression proposed by Troshko et al. (2001) and constant (negative) lift coefficients, Turbulent dispersion using the Simonin and Viollet (1990) approach, Steady state solution approach.

RSS (Residual sum of sqaures) was used to compare simulations with experimental data wherever possible.


Data set of Farrar and Bruun (1996)

Experimental conditions: Pipe ID = 78 mm,

Length = 1.5 m ( 20 pipe diameters),

QT = 0.00308 m3/s, phase ratios of the dispersed phase (20, 25 & 30%),

Simulation conditions: de = 5 mm, Lift coefficient

proposed by Troshko et al. (2001),

DPN = 7.5.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.01 0.02 0.03 0.04

Radial position (m)

Dis

pe

rse

d p

ha

se

ho

ldu

p (

-)F20 - SIM F20 - EXP

F25 - SIM F25 - EXP

F30 - SIM F30 - EXP


Data set of Hamad et al. (2000)

Experimental conditions:

Pipe ID = 78 mm, Length = 4.2 m ( 53 pipe diameters),

QT = 0.00310 (H10) and 0.00348 (H20) m3/s, phase ratios of the dispersed phase (10, 20%),

Simulation conditions: Lift coefficient


H10: de = 3.25 mm & DPN = 0.01,

H20: de = 3.50 mm & DPN = 0.075.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Radial position (m)

Dis

per

sed

ph

ase

ho

ldu

p (

-)

H10 - SIM H10 - EXP

H20 - SIM H20 - EXP


Data set of Al-Deen and Bruun (1997)


Length = 1.5 m ( 20 pipe diameters),

QT = 0.00272 – 0.00369 m3/s, phase ratios of the dispersed phase (5, 10, 20 & 30%),

Simulation conditions: Lift coefficient


A5: de = 3.0 mm &DPN = 0.024,

A10: de = 3.5 mm & DPN = 0.075,

A20: de = 4.0 mm & DPN = 0.412,

A30: de = 4.0 mm & DPN = 7.5.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.01 0.02 0.03 0.04

Radial position (m)

Dis

per

sed

ph

ase

ho

ldu

p (

-)

A5 - SIM A5 - EXP

A10 - SIM A10 - EXP

A20 - SIM A20 - EXP

A30 - SIM A30 - EXP


Data set of Lang (1999), Pipe ID: 16 mm, Length 65 pipe diameters

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Radial position (m)

Dis

pers

ed p

hase

hol

dup

(-)

L20B - SIM

L20B - EXP

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.002 0.004 0.006 0.008

Radial position (m)

Dis

per

sed

ph

ase

ho

ldu

p (

-)

L20A - SIM L20A - EXP

L40 - SIM L40 - EXP

(DPN = 0.06; CL = -0.050; de = 2 mm)L20A (DPN = 0.75; CL = -0.075; de = 1 mm)L40 (DPN = 3.00; CL = -0.050; de = 1 mm)

QT = 0.00010 m3/sQT = 0.00030 m3/s


Data set of Vigneaux et al. (1988)


Length = 14 m ( 70 pipe diameters),

QT = 0.0075 m3/s, phase ratios of the dispersed phase (5, 10, 30 & 50%),

Simulation conditions: V5: de = 2.00 mm,

CL = -0.05 & DPN = 1.593,

V10: de = 2.75 mm,CL = -0.05 & DPN = 0.328,

V30: de = 5.00 mm, Troshko et al. (2001) & DPN = 4.125,

V50: de = 5.00 mm, Troshko et al. (2001) & DPN = 4.125.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.02 0.04 0.06 0.08 0.1

Radial position (m)

Dis

pe

rse

d p

ha

se

ho

ldu

p (

-)

V5 - SIM V5 - EXP

V10 - SIM V10 - EXP

V30 - SIM V30 - EXP

V50 - SIM V50 - EXP


Conclusions from CFD Simulations

Following conclusions can be drawn based on the numerical study of liquid-liquid up-flows in vertical pipes spanning a wide range of experimental conditions: Liquid-Liquid bubbly up-flows in vertical pipes typically

feature ‘Wall peaking’, ‘Near-wall peaking’ and ‘Coring’ trends for the dispersed phase holdup distribution. In order to successfully predict such inhomogeneous phase distributions, accounting for drag and lift forces and turbulent dispersion is imperative,

An analysis of several drag coefficient expressions clearly reveals that the drag on drops differs significantly from the drag on rigid spheres, particularly at larger equivalent drop diameters. Also, at high dispersed phase holdups, accounting for the presence of adjacent drops yields slightly better predictions. However, the drag force alone cannot predict the local holdup accurately.


Conclusions from CFD Simulations (2)

Non-drag lateral forces such as the lift force and turbulent dispersion dictate the overall phase distribution: The expression for lift coefficient proposed by Troshko et

al. (2001) yields very good predictions when bubble Reynolds numbers greater than 250 are encountered. However, for bubble Reynolds numbers lower than 250, constant (negative) values for the lift coefficients were found to yield the best predictions,

Turbulent dispersion is found to be more significant at lower dispersed phase holdups when compared to higher dispersed phase holdups,

The equivalent drop diameter (de) has to be increased as the dispersed phase holdup increases.


Interphase Closure Guidelines for Liquid-Liquid Systems

The following closure guidelines are recommended for application in dispersed liquid-liquid flows: Drag force:

The drag coefficient expression proposed by Kumar and Hartland (1985) should be used to account for the drag force in immiscible liquid dispersions,

Lift force: The expression for lift coefficient proposed by Troshko et al. (2001)

should be used when bubble Reynolds numbers greater than 250 are encountered. At lower bubble Reynolds numbers, constant (negative) lift coefficients in the range (-0.05 to -0.075) are recommended,

Turbulent dispersion: For the model proposed by Simonin and Viollet (1990), Dispersion

Prandtl Numbers (DPN) in the range 0.01 DPN 0.075 are recommended for use at low dispersed phase holdups (< 10%) and Dispersion Prandtl Numbers in the range 0.075 DPN 7.5 are recommended for use at high dispersed phase holdups (i.e. up to 50%).


Recommendations for Future Work

For dispersed flows featuring low Reynolds numbers (Re 250), expressions which directly estimate the lift coefficient based on local flow properties should be identified and tested,

Various approaches to account for turbulent dispersion should be analyzed. In particular, models such as the one proposed by Lopez de Bertodano (1998) where the dispersion coefficient is expressed as a function of the locally evaluated, turbulent Stokes number should be tested,

The effect of turbulence modulation (both enhancement and suppression) should be included in future simulations,

The ability of the models to predict turbulence intensities in the continuous phase should then be tested,

The effect of accounting for a dynamic size distribution of drops should also be investigated. Various drop breakage and coalescence models should be reviewed, and selected models ought to be suitably coupled to the multi-fluid CFD framework in order to study this effect properly.


Acknowledgements Thanks to:

Supervisors Dr. Al Taweel and Dr. Murat Koksal. Guiding committee members: Dr. Gupta, Dr.

Dabros and Dr. Chuang. Fellow colleagues at the Mixing and Separation

Research Laboratory. Guidance from the 'Academic Support

Team' at Fluent is gratefully acknowledged.

cfd simulation of immiscible liquid dispersions srinath madhavan department of chemical engineering

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