CFD Simulation of Immiscible Liquid Dispersions

1
CFD Simulation of Immiscible Liquid Dispersions

• Srinath Madhavan
• Department of Chemical Engineering

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.

3
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.

4
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.

5
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.

6
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.

7
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.

8
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.

9
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.

10
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.

11
Two-fluid Model Governing Equations

• Conservation of mass

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

12
Two-fluid Model Governing Equations (2)

• Conservation of Momentum

• 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

13
The closure problem

• 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.

14
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 Tchens 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).

15
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.

16
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.

17
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.

18
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).

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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.

Drag force (FD)
Dispersed entity
Fluid velocity vectors
Direction of relative velocity
20
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).

Rigid sphere
Single drops
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Expressions for the Drag Coefficient of a Drop in
the Presence of Adjacent Drops
µmedium gt µc
µmedium µc
?medium lt ?c
?medium ?c
us
um
de 5 mm
us
um
µdrop µd
µdrop µd
?drop ?d
?drop ?d
If (µdrop gt µc) and (?drop lt ?c) gt um lt us
22
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.

Fluid velocity vectors
Dispersed entity
Low velocity ? High Pressure
Inviscid Lift force
Inviscid Lift force
High velocity ? Low pressure
Calculation of Relative Velocity
23
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.

24
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).

25
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.

• Model proposed by Simonin and Viollet (1990)

In the absence of Turbulent Dispersion
In the presence of Turbulent Dispersion
Very low DPN
Very high DPN
Dispersion Prandtl Number (DPN)
26
Data Sets used for CFD Validation
1 mm ? de ? 5 mm
Data Set Data Point Continuous 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
Farrar and Bruun (1996) F25 0.4634 0.1637 0.2275
Farrar and Bruun (1996) F30 0.4263 0.1972 0.2783
Hamad et al. (2000) H10 0.5855 0.0651 0.0873
Hamad et al. (2000) H20 0.5855 0.1464 0.1764
Al-Deen and Bruun (1997) A5 0.5441 0.0286 0.0493
Al-Deen and Bruun (1997) A10 0.5441 0.0605 0.0917
Al-Deen and Bruun (1997) A20 0.5441 0.1360 0.1872
Al-Deen and Bruun (1997) A30 0.5441 0.2332 0.2992
Lang (1999) L20A 0.4000 0.1000 0.1851
Lang (1999) L20B 1.2000 0.3000 0.1809
Lang (1999) L40 0.3000 0.2000 0.3692
Lang (1999) L60 0.2000 0.3000 0.5474
Vigneaux et al. (1988) V5 0.2268 0.0119 0.0323
Vigneaux et al. (1988) V10 0.2149 0.0239 0.0661
Vigneaux et al. (1988) V30 0.1671 0.0716 0.2350
Vigneaux et al. (1988) V50 0.1194 0.1194 0.4308
78 mm ID
16 mm ID
200 mm ID
27
Comparative Evaluation of Drag Coefficient
Expressions for Single Entities (using CFD
Simulations)

• 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.

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
28
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
29
Comparative Evaluation of Lift Coefficient
Expressions/Values (using CFD Simulations)

• 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.

• Phase ratio of the dispersed phase 30 , no
  turbulent dispersion

de 5 mm
Drag coefficient expression used Kumar and
Hartland (1985)
30
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.

Phase ratio of the dispersed phase 30
Drag coefficient expression used Kumar and
Hartland (1985)
de 5 mm
31
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 11 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-e 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,

32
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.

33
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 proposed by Troshko et al.
  (2001),
• H10 de 3.25 mm DPN 0.01,
• H20 de 3.50 mm DPN 0.075.

34
Data set of Al-Deen and Bruun (1997)

• Experimental conditions
• Pipe ID 78 mm, 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 proposed by Troshko et al.
  (2001),
• 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.

35
Data set of Lang (1999), Pipe ID 16 mm, Length
? 65 pipe diameters
QT 0.00010 m3/s
QT 0.00030 m3/s
L20A (DPN 0.75 CL -0.075 de 1 mm) L40
(DPN 3.00 CL -0.050 de 1 mm)
(DPN 0.06 CL -0.050 de 2 mm)
36
Data set of Vigneaux et al. (1988)

• Experimental conditions
• Pipe ID 200 mm, 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.

37
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.

38
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.

39
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 (lt 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).

40
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.

41
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.