Docstoc

CFD Simulation of Immiscible Liquid Dispersions

Document Sample
CFD Simulation of Immiscible Liquid Dispersions Powered By Docstoc
					CFD Simulation of Immiscible
     Liquid Dispersions

        Srinath Madhavan

   Department of Chemical Engineering
                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.

6th July 2005       CFD Simulation of Immiscible Liquid Dispersions   2
                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.




6th July 2005                 CFD Simulation of Immiscible Liquid Dispersions              3
                Interfacial Area of Contact
          For a unit volume of the Liquid-Liquid
           dispersion,
                                     dispersed phase holdup
                Interfacia l area 
                                    dispersed phase diameter
          A combination of smaller drop sizes and
           larger dispersed phase holdup is usually
           sought.

6th July 2005           CFD Simulation of Immiscible Liquid Dispersions   4
                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.
6th July 2005             CFD Simulation of Immiscible Liquid Dispersions   5
                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.

6th July 2005             CFD Simulation of Immiscible Liquid Dispersions                   6
                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.
6th July 2005              CFD Simulation of Immiscible Liquid Dispersions   7
                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.

6th July 2005                CFD Simulation of Immiscible Liquid Dispersions    8
                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.

6th July 2005                CFD Simulation of Immiscible Liquid Dispersions   9
                Two-fluid Approach to
                Multi-fluid CFD Modeling

                                                                   Dispersed phase 1 (e.g. air bubbles)


                                                                   Dispersed phase 2 (e.g. oil drops)


                                                                   Continuous phase (e.g. water)


                Reality             Two-fluid model

           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.

6th July 2005             CFD Simulation of Immiscible Liquid Dispersions                           10
                Two-fluid Model:
                Governing Equations
           Conservation of mass:
                                                  n           d  
                     q q      q qvq    
                                           
                                                    m pq   q q q 
                 t                                p 1         dt 

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

                     q v q   0
                           


6th July 2005             CFD Simulation of Immiscible Liquid Dispersions   11
                Two-fluid Model:
                Governing Equations (2)
            Conservation of Momentum:
                                                                       
                    q  q vq      q  q vq vq     qp   q   q  q g
                                                                                  
                t
                 Fq  Flift ,q  Fvm, q    K pq v p  vq   m pq v pq 
                                                 n
                                                                        
                                                                     
                                                       p 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:
                                                                        
               q  q v q v q 
                                                                      
                                                 q p              q   
                 
                                            
                                                                   
                                                                     
    Change of momentum per unit volume                                Pressure force per unit volume    Viscous force per unit volume

                       
                                                      F                                  K v
                                                                                                
                                                                                                     v q 
                                                                                                      
                                                                                            n
                 q q g
                
                                          
                                                       lift , q                        
                                                                                          p 1
                                                                                               pq p

    Gravitational force per unit volume       Lift force per unit volume                  
                                                                               Turbulent dispersion & drag force per unit volume

6th July 2005                       CFD Simulation of Immiscible Liquid Dispersions                                                 12
                The closure problem
                                                                                                                                     
                        q  q v q v q 
                                                                                                                                   
                                                                                             q p                               q                
                          
                                                                                       
                                                                                                                                
                                                                                                                                  
              Change of momentum per unit volume                                  Pr essure force per unit volume       Viscous force per unit volume

                                
                                                                                                   K v
                                                                                                           
                                                                                                                v q 
                                                                                                                 
                                                                                                       n
                          q q g
                         
                                                                F
                                                                  lift , q                         
                                                                                                     p 1
                                                                                                          pq p

              Gravitational force per unit volume       Lift force per unit volume                   
                                                                                         Turbulent dispersion and drag force per unit volume




                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.

6th July 2005                            CFD Simulation of Immiscible Liquid Dispersions                                                                    13
                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).

6th July 2005               CFD Simulation of Immiscible Liquid Dispersions                      14
                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.
6th July 2005            CFD Simulation of Immiscible Liquid Dispersions         15
                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.
6th July 2005        CFD Simulation of Immiscible Liquid Dispersions   16
                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.

6th July 2005            CFD Simulation of Immiscible Liquid Dispersions         17
                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).


6th July 2005                     CFD Simulation of Immiscible Liquid Dispersions                 18
                Review of the Interphase
                Drag Force
                                                                In dispersed multiphase systems, the
                                                                 force that opposes the relative velocity
                                                                 between the phases is called the drag
            
                    Drag force (FD)                              force,
            C                       3 C D d  cVS2
                               FD                              Drag force on drops is different from
                                    4     de                     the drag force on rigid spheres. This is
  Dispersed                                                      attributed to two factors:
  entity
                                                                   Internal circulation,
                                                CA                  Shape deformation.

                                                             Drag force on a drop is affected in the
  A                             A      C                         presence of adjacent drops. Again,
                                                                 there are two factors responsible for
      Fluid velocity vectors                  Direction of       this behavior:
                                              relative               Reduced buoyancy force on the drop,
                                              velocity
                                                                     Apparent increase in medium viscosity.

6th July 2005                         CFD Simulation of Immiscible Liquid Dispersions                          19
                Expressions for the Drag
                Coefficient of a Single Drop
       For single rigid spheres, the                                    0.35
                                                                                    Klee and Treybal
        expression proposed by Schiller                                             Hu and Kintner             Rigid sphere
        and Naumann (1935) is widely
                                                                         0.30       Grace et al.
                                                                                    Ishii and Zuber
        used,                                                                       Schiller and Naumann
                                                                         0.25




                                               Relative velocity (m/s)
       For     single   drops,    several
        expressions     for    the   drag                                0.20
        coefficient have been proposed:
            Hu and Kintner (1955)                                       0.15

            Klee and Treybal (1956)
                                                                         0.10
            Grace et al. (1976)
            Ishii and Zuber (1979)                                      0.05
                                                                                                           Single drops
       It can be seen that significant
        differences between the two are                                  0.00

        observed at higher equivalent                                           0   2      4       6       8     10   12   14    16

        drop diameters (i.e. greater                                                           Equivalent diameter (mm)

        than 3 mm).
6th July 2005             CFD Simulation of Immiscible Liquid Dispersions                                                       20
                Expressions for the Drag Coefficient
                of a Drop in the Presence of Adjacent
                Drops
                                                                          0.16
       medium = μc   medium > μc                                        0.14




                                                Relative velocity (m/s)
       ρmedium = ρc   ρmedium < ρc                                        0.12                                                    us
                                                                           0.1
                                                                          0.08
                                                                          0.06
                                                                          0.04               um
                                                                          0.02                                           de = 5 mm
           us                                                               0
                        um                                                       0     0.1        0.2     0.3      0.4      0.5        0.6
                                                                                             Dispersed phase holdup (-)


         drop = μd    drop = μd                                            Ishii and Zuber (Dense fluid particles)

         ρdrop = ρd    ρdrop = ρd                                            Ishii and Zuber (corrected w ith Rusche and Issa (2000)
                                                                             Kumar and Hartland
                                                                             Ishii and Zuber (Single drop)
If (drop > μc) and (ρdrop < ρc) => um < us

6th July 2005            CFD Simulation of Immiscible Liquid Dispersions                                                               21
                                   Review of the Interphase
                                   Lift Force – Inviscid Lift
                                    Axis                                     When a dispersed phase entity moves
                                                                              through a non-uniform flow field, it will
Fluid velocity vectors




                                                                              experience a lift force due to the vorticity
                                                                             or shear in the continuous phase field,
                                    A                            
                                                                C           The lift force acts on the dispersed entities
                                B   Dispersed entity                          in a direction perpendicular to the relative
                                                                              motion between the two phases.
                                                                                                                  
                                                                                                                  
                                    Wall                                       Flift   C L  q  p v q  v p    v q
                                                                                                                   Axis
                                                                            Low velocity  High Pressure
                                                                              
                               A                      B                      CA
                                                                     
                                        C                            C
                                                                                            Inviscid                      Inviscid
                                                                                                                    Lift force
                                                                             CB            Lift force
                               CA                         CB
                                                                                                                   Wall
                                                                             High velocity  Low pressure
                         Calculation of Relative Velocity

6th July 2005                                          CFD Simulation of Immiscible Liquid Dispersions                                 22
                Review of the Interphase Lift
                Force – Vortex-shedding Lift
                                                   Recent studies indicate that the
                                                    inviscid lift force may not be the only
                Axis                                lift force experienced by a dispersed
                                                    entity in shear flow (Taeibi-Rahni
                                                    and Loth, 1996; Loth et al., 1997;
                                                    Moraga et al., 1999),
                         Wake-induced Lift
                         force
                                                   Larger dispersed entities moving
                Wake                                much faster than the fluid shed
                         Inviscid Lift force        vortices as they move,

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




6th July 2005          CFD Simulation of Immiscible Liquid Dispersions                   23
                Expressions for the Lift
                Coefficient (CL)
          Constant lift coefficient,
                                                      0.7
          The expression for lift                    0.5
           coefficient proposed by
           Moraga et al. (1999),
                                                      0.3

          An approach similar to                     0.1
           that of Moraga et al.
           (1999) in which validity          CL (-)
                                                      -0.1
           limits    for    the    lift                          Moraga et al. (1999)
           coefficient     expression                            CL = 0.0
                                                      -0.3
           have been modified in
           accordance     with    the
                                                                 Troshko et al. (2001)


           recommendations made
                                                                 ReReÑ = 183897
                                                      -0.5
           by Troshko et al. (2001).
                                                                 Moraga et al. (1999) applied to drops
                                                                 and bubbles
                                                      -0.7
                                                             1        100                10000           1000000   100000000

                                                                                  Re Re 

6th July 2005               CFD Simulation of Immiscible Liquid Dispersions                                             24
                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
     In the           In the                           (1990)
     absence of       presence of                               Dp            Dq         
                                                       
     Turbulent        Turbulent                        v dr         p           q 
     Dispersion       Dispersion                                           pq q      
                                                                pq p                     
  Very high DPN      Very low DPN
                                                                 Dispersion Prandtl Number (DPN)

                                          
                                  
    K pq v p  v q   K pq U p  U q
                                                                 
                                                             K pq v dr
                            
                                                        
                         Drag force                    Turbulent dispersion force
                         per unit volume               per unit volume

6th July 2005            CFD Simulation of Immiscible Liquid Dispersions                           25
                Data Sets used for CFD
                Validation                                                                                           1 mm  de  5 mm

                                                   Continuous phase superficial   Dispersed phase superficial   Average dispersed phase
                   Data Set           Data Point
                                                          velocity (m/s)                velocity (m/s)                holdup (-)

                                         F20                 0.4935                         0.1363                      0.1912
78 mm ID
            Farrar and Bruun (1996)      F25                 0.4634                         0.1637                      0.2275
                                         F30                 0.4263                         0.1972                      0.2783
                                         H10                 0.5855                         0.0651                      0.0873
              Hamad et al. (2000)
                                         H20                 0.5855                         0.1464                      0.1764
                                         A5                  0.5441                         0.0286                      0.0493

              Al-Deen and Bruun          A10                 0.5441                         0.0605                      0.0917
                    (1997)               A20                 0.5441                         0.1360                      0.1872
                                         A30                 0.5441                         0.2332                      0.2992
                                        L20A                 0.4000                         0.1000                      0.1851
16 mm ID
                                        L20B                 1.2000                         0.3000                      0.1809
                 Lang (1999)
                                         L40                 0.3000                         0.2000                      0.3692
                                         L60                 0.2000                         0.3000                      0.5474

200 mm ID                                V5                  0.2268                         0.0119                      0.0323
                                         V10                 0.2149                         0.0239                      0.0661
            Vigneaux et al. (1988)
                                         V30                 0.1671                         0.0716                      0.2350
                                         V50                 0.1194                         0.1194                      0.4308

6th July 2005                           CFD Simulation of Immiscible Liquid Dispersions                                                   26
                Comparative Evaluation of Drag
                Coefficient Expressions for Single Entities
                (using CFD Simulations)
                                                                              Experimental conditions of Al-
                                                                               Deen and Bruun (1997) were
            Expression for CD0         de = 2 mm   de = 5 mm   de = 8 mm
                                                                               used as an example – phase
                                                                               ratio of the dispersed phase =
       Schiller and Naumann (1935)
                                        0.04429     0.03894     0.03651
                                                                               5 %,
             – Rigid sphere
                                                                              All expressions for single
                                                                               entities predict similar holdups
       Ishii and Zuber (1979)           0.04405     0.04095     0.04094        at low equivalent diameters
                                                                               (de  2 mm),
                                                                              As the equivalent diameter
       Grace et al. (1976)              0.04405     0.04023     0.04055
                                                                               increases, the single drop
                                                                               holdup predictions start to
       Hu and Kintner (1955)            0.04432     0.04014     0.04032
                                                                               deviate from the rigid sphere
                                                                               predictions,
                                                                              The drag model proposed by
       Klee and Treybal (1956)          0.04428     0.04208     0.04204        Ishii and Zuber (1979) was
                                                                               chosen as a representative for
                                                                               single drops.
6th July 2005                        CFD Simulation of Immiscible Liquid Dispersions                          27
                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                  Expression for CDM              de = 2 mm   de = 5 mm
            example – phase ratio of the
            dispersed phase = 30 %,
                                                       Ishii and Zuber - Dense fluid
           All expressions predict similar            particles (1979)
                                                                                               0.2855      0.2751
            holdups at de = 2 mm and at de = 5
            mm,
                                                       Kumar and Hartland (1985)               0.2890      0.2797
           When compared to the average
            holdup    as     reported    in    the
            experiment ( 29 %), it is seen that       Ishii and Zuber (1979) drag
            accounting for the presence of             expression    for   single    drops,
            adjacent entities results in a slightly    modified to account for the presence
                                                                                               0.2902      0.2812
            better prediction,                         of adjacent drops using the
                                                       correction factor proposed by
           The expression proposed by Kumar           Rusche and Issa (2000)
            and Hartland (1985) suitably
            accounts for the presence of               Ishii and Zuber (1979)         drag
            adjacent drops as its holdup               expression for single drops
                                                                                               0.2824      0.2707
            predictions lie between the other
            two approaches.
6th July 2005                CFD Simulation of Immiscible Liquid Dispersions                                        28
                Comparative Evaluation of Lift
                Coefficient Expressions/Values
                (using CFD Simulations)
      Experimental conditions of                                            0.5
       Farrar and Bruun (1996) are                                                     Phase    ratio   of    the
       chosen as an example,                                                0.45                                            de = 5 mm
                                                                                       dispersed phase = 30 %,




                                               Dispersed phase holdup (-)
      The     expression     for   lift                                     0.4       no turbulent dispersion
       coefficient     proposed     by                                      0.35
       Moraga et al. (1999) was
       found to give numerical                                               0.3
       instabilities and/or unphysical
                                                                            0.25
       predictions,
                                                                                            Troshko et al. (2001)         CL = + 0.01
      Positive constants for CL                                             0.2
       predict wall peaks whereas                                           0.15            CL = + 0.005                  CL = + 0.001
       negative constants predict
       ‘coring’ and/or ‘near-wall                                            0.1            CL = 0.0                      CL = - 0.001
       peaking’ trends,                                                     0.05            CL = - 0.005                  CL = - 0.01
      All constant lift coefficients
       and the expression proposed                                            0
       by Troshko et al. (2001)                                                    0       0.2           0.4          0.6          0.8    1
       predict     non-zero     volume
       fractions at the wall.                                                                          Normalized radius (-)

                                                                            Drag coefficient expression used: Kumar and Hartland (1985)

6th July 2005                  CFD Simulation of Immiscible Liquid Dispersions                                                           29
                Comparative Evaluation of Turbulent
                Dispersion Coefficient Values (using
                CFD Simulations)
       Turbulent dispersion effects
                                                                                 0.4
        were simulated using the
        approach proposed by Simonin                                                       Phase    ratio  of   the
        and Viollet (1990), which                                               0.35       dispersed phase = 30 %
        accounts for the response of




                                                   Dispersed phase holdup (-)
                                                                                 0.3
        drops to turbulent eddies in the
        continuous phase,
                                                                                0.25
       The experimental conditions of
        Farrar and Bruun (1996) are                                                          Drag coefficient expression used:
                                                                                 0.2
        used as an example. A ‘data                                                          Kumar and Hartland (1985)
        point’ featuring a ‘near-wall’                                          0.15
        peak was chosen to demonstrate
        the     effect    of     turbulent                                       0.1              DPN 0.075           DPN 0.75
        dispersion,
       The expression for lift coefficient                                     0.05              DPN 7.5             DPN 0.0075
        as proposed by Troshko et al.
        (2001) was used,                                                          0
       High DPN values (e.g. 7.5)                                                     0        0.2       0.4       0.6        0.8         1
        decrease the degree of turbulent                                                              Norm alized radius (-)
        dispersion and vice-versa.
                                                                                                                               de = 5 mm
6th July 2005                   CFD Simulation of Immiscible Liquid Dispersions                                                                30
                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.
6th July 2005                      CFD Simulation of Immiscible Liquid Dispersions                                     31
                Data set of Farrar and
                Bruun (1996)
                                                                              0.4

         Experimental conditions:
               Pipe ID = 78 mm,                                             0.35

                Length = 1.5 m ( 20
                pipe diameters),                                              0.3




                                                Dispersed phase holdup (-)
               QT = 0.00308 m3/s,                                           0.25
                phase ratios of the
                dispersed phase (20, 25                                       0.2
                & 30%),
                                                                             0.15
         Simulation conditions:                                                           F20 - SIM          F20 - EXP

               de = 5 mm,                                                    0.1
                                                                                           F25 - SIM          F25 - EXP

               Lift coefficient proposed
                by Troshko et al. (2001),
                                                                             0.05          F30 - SIM          F30 - EXP

               DPN = 7.5.                                                     0
                                                                                    0   0.01           0.02          0.03   0.04
                                                                                               Radial position (m)



6th July 2005               CFD Simulation of Immiscible Liquid Dispersions                                                   32
                Data set of Hamad et al.
                (2000)
                                                                                    0.4

          Experimental conditions:
                   Pipe ID = 78 mm,                                               0.35
                                                                                                      H10 - SIM             H10 - EXP
                    Length = 4.2 m ( 53
                    pipe diameters),




                                                      Dispersed phase holdup (-)
                                                                                    0.3

                   QT = 0.00310 (H10) and                                                            H20 - SIM             H20 - EXP
                    0.00348 (H20) m3/s,                                            0.25
                    phase ratios of the
                    dispersed phase (10,                                            0.2
                    20%),
                                                                                   0.15
          Simulation conditions:
                   Lift coefficient proposed                                       0.1
                    by Troshko et al. (2001),
                   H10: de = 3.25 mm &                                            0.05
                    DPN = 0.01,
                   H20: de = 3.50 mm &                                              0
                    DPN = 0.075.                                                          0   0.005   0.01   0.015   0.02     0.025     0.03   0.035   0.04
                                                                                                             Radial position (m)


6th July 2005                    CFD Simulation of Immiscible Liquid Dispersions                                                                       33
                Data set of Al-Deen and
                Bruun (1997)
           Experimental conditions:                                             0.6
                   Pipe ID = 78 mm,                                                       A5 - SIM               A5 - EXP
                    Length = 1.5 m ( 20                                                   A10 - SIM              A10 - EXP
                    pipe diameters),                                             0.5
                   QT = 0.00272 – 0.00369                                                 A20 - SIM              A20 - EXP




                                                    Dispersed phase holdup (-)
                    m3/s, phase ratios of the                                              A30 - SIM              A30 - EXP
                    dispersed phase (5, 10,                                      0.4
                    20 & 30%),
                                                                                 0.3
           Simulation conditions:
                   Lift coefficient proposed
                    by Troshko et al. (2001),                                    0.2
                   A5: de = 3.0 mm &
                    DPN = 0.024,                                                 0.1
                   A10: de = 3.5 mm &
                    DPN = 0.075,
                   A20: de = 4.0 mm &                                            0
                    DPN = 0.412,                                                       0   0.01          0.02           0.03   0.04
                   A30: de = 4.0 mm &                                                            Radial position (m)
                    DPN = 7.5.
6th July 2005                   CFD Simulation of Immiscible Liquid Dispersions                                                   34
                                              Data set of Lang (1999),
                                              Pipe ID: 16 mm, Length  65 pipe
                                              diameters
                              0.3                                                                                                       0.9

                                                                                                                                        0.8                  L20A - SIM                L20A - EXP
                             0.25




                                                                                                           Dispersed phase holdup (-)
                                                                                                                                        0.7
Dispersed phase holdup (-)




                                                                                                                                                             L40 - SIM                 L40 - EXP
                              0.2                                                                                                       0.6

                                                                                                                                        0.5
                             0.15
                                                    L20B - SIM                                                                          0.4

                              0.1                                                                                                       0.3

                                                                                                                                        0.2
                             0.05                   L20B - EXP
                                                                                                                                        0.1
                                                                          QT = 0.00030 m3/s                                                       QT = 0.00010 m3/s
                               0                                                                                                         0
                                    0     0.001   0.002   0.003   0.004    0.005   0.006   0.007   0.008                                      0          0.002            0.004         0.006       0.008
                                                          Radial position (m)                                                                                    Radial position (m)

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

6th July 2005                                                             CFD Simulation of Immiscible Liquid Dispersions                                                                            35
                Data set of Vigneaux et al.
                (1988)
      Experimental conditions:                                          0.8
            Pipe ID = 200 mm, Length                                                     V5 - SIM                 V5 - EXP
             = 14 m ( 70 pipe                                           0.7
             diameters),                                                                  V10 - SIM                V10 - EXP

             QT = 0.0075 m3/s, phase                                                      V30 - SIM                V30 - EXP




                                            Dispersed phase holdup (-)
                                                                        0.6
             ratios of the dispersed                                                      V50 - SIM                V50 - EXP
             phase (5, 10, 30 & 50%),                                    0.5

      Simulation conditions:                                            0.4
            V5: de = 2.00 mm,
             CL = -0.05 & DPN = 1.593,                                   0.3
            V10: de = 2.75 mm,
             CL = -0.05 & DPN = 0.328,                                   0.2
            V30: de = 5.00 mm,
             Troshko et al. (2001) &                                     0.1
             DPN = 4.125,
            V50: de = 5.00 mm,                                           0
             Troshko et al. (2001) &                                           0   0.02          0.04       0.06         0.08   0.1
             DPN = 4.125.                                                                      Radial position (m)

6th July 2005               CFD Simulation of Immiscible Liquid Dispersions                                                     36
                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.
6th July 2005               CFD Simulation of Immiscible Liquid Dispersions          37
                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.



6th July 2005                  CFD Simulation of Immiscible Liquid Dispersions       38
                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%).

6th July 2005                  CFD Simulation of Immiscible Liquid Dispersions                  39
                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.
6th July 2005              CFD Simulation of Immiscible Liquid Dispersions         40
                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.


6th July 2005              CFD Simulation of Immiscible Liquid Dispersions   41

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:157
posted:4/15/2011
language:English
pages:41