Large Eddy simulation for dispersed bubbly flows : a review · Large Eddy simulation for dispersed...

Large Eddy simulation for dispersed bubbly flows a review

Citation for published version (APA)Dhotre M T Deen N G Niceno B Khan Z amp Joshi J B (2013) Large Eddy simulation for dispersedbubbly flows a review International Journal of Chemical Engineering 2013 [343276]httpsdoiorg1011552013343276

DOI1011552013343276

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Hindawi Publishing CorporationInternational Journal of Chemical EngineeringVolume 2013 Article ID 343276 22 pageshttpdxdoiorg1011552013343276

Review ArticleLarge Eddy Simulation for Dispersed Bubbly Flows A Review

M T Dhotre1 N G Deen2 B Niceno3 Z Khan4 and J B Joshi45

1 ABB Switzerland Ltd 5400 Baden Switzerland2Multiphase Reactors Group Department of Chemical Engineering and ChemistryEindhoven University of Technology The Netherlands

3 Laboratory for Thermal-Hydraulics Nuclear Energy and Safety Department Paul Scherrer Institute Switzerland4 Institute of Chemical Technology Matunga Mumbai 400 019 India5Homi Bhabha National Institute Anushakti Nagar Mumbai 400 094 India

Correspondence should be addressed to M T Dhotre maheshdhotregmailcom

Received 14 June 2012 Revised 31 October 2012 Accepted 18 November 2012

Academic Editor Nandkishor Nere

Copyright copy 2013 M T Dhotre et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Large eddy simulations (LES) of dispersed gas-liquid flows for the prediction of flow patterns and its applications have beenreviewed The published literature in the last ten years has been analysed on a coherent basis and the present status has beenbrought out for the LES Euler-Euler and Euler-Lagrange approaches Finally recommendations for the use of LES in dispersed gasliquid flows have been made

1 Introduction

Gas-liquid flows are often encountered in the chemicalprocess industry but also numerous examples can be found inpetroleum pharmaceutical agricultural biochemical foodelectronic and power-generation industries The modellingof gas-liquid flows and their dynamics has become increas-ingly important in these areas in order to predict flowbehaviour with greater accuracy and reliabilityThere are twomain flow regimes in gas-liquid flows separated (eg annularflow in vertical pipes stratified flow in horizontal pipes) anddispersed flow (eg droplets or bubbles in liquid) In thiswork we consider only dispersed bubbly flows

Dispersed Bubbly Flow The description of bubbly flowsinvolves modelling of a deformable (gas-liquid) interfaceseparating the phases discontinuities of properties across thephase interface the exchange between the phase and turbu-lence modelling Most of the dispersed flowmodels are basedon the concept of a domain in the static (Eulerian) referenceframe for description of the continuous phase with additionof a reference frame for the description of the dispersed phaseThe dispersed phase may be described in the same staticreference frame as the continuous leading to the Eulerian-Eulerian (E-E) approach or in a dynamic (Lagrangian)

reference frame leading to the Eulerian-Lagrangian (E-L)approach

In the E-L approach the continuous liquid phase ismodelled using an Eulerian approach and the dispersed gasphase is treated in a Lagrangian way that is the individualbubbles in the system are tracked by solving Newtonrsquos secondlaw while accounting for the forces acting on the bubblesAn advantage here is the possibility to model each individualbubble also incorporating bubble coalescence and breakupdirectly Since each bubble path can be calculated accuratelywithin the control volume no numerical diffusion is intro-duced into the dispersed phase computation However adisadvantage is the larger the system gets the more equationsneed to be solved that is one for every bubble

The E-E approach describes both phases as two continu-ous fluids each occupying the entire domain and interpene-trating each other The conservation equations are solved foreach phase together with interphase exchange termsThe E-Eapproach can suffer from numerical diffusion However withthe aid of higher order discretization schemes the numericaldiffusion can be reduced sufficiently and can offer the sameorder of accuracy as with E-L approach (Sokolichin et al[1]) The advantage here is that the computational demandsare far lower compared to the E-L approach particularly for

2 International Journal of Chemical Engineering

systemswith higher dispersed void fractionsWe review theseapproaches here with respect to the turbulence descriptions

Turbulence Modelling The major difficulty in modellingmultiphase turbulence is the wide range of length and timescales on which turbulent mixing occurs The largest eddiesare typically comparable in size to the characteristic lengthof the mean flow The smallest scales are responsible forthe dissipation of turbulence kinetic energy The DirectNumerical Simulation (DNS) approach with no modellingresolves all the scales present in turbulence However it isnot feasible for practical engineering problems involving highReynolds number flows The Reynolds-Averaged NavierndashStrokes (RANS) approach ismore feasible itmodels the time-averaged velocity field either by using turbulent viscosity orby modelling the Reynolds stresses directly

The large eddy simulation (LES) falls between DNS andRANS in terms of the fraction of the resolved scales In LESlarge eddies are resolved directly that is on a numerical gridwhile small unresolved eddies are modelled The principlebehind LES is justified by the fact that the larger eddiesbecause of their size and strength carry most of the flowenergy (typically 90) while being responsible for mostof the transport and therefore they should be simulatedprecisely (ie resolved) On the other hand the small eddieshave relatively little influence on the mean flow and thuscan be approximated (ie modelled) This approach toturbulence modelling also allows a significant decrease in thecomputational cost over direct simulation and captures moredynamics than a simple RANS model

In RANS models often the assumption of isotropicturbulence is made for the core of the flow which is not validin dispersed bubbly flows that is the velocity fluctuations inthe gravity direction are typically twice those in the otherdirections This assumption is not made in LES for largestructures of the flow giving LES an advantage over RANSfor the core regions of the flow However the situationis different close to the walls where LESrsquo assumption ofisotropic turbulence is heavily violated due to the absence oflarge eddies close to the walls

2 LES for Dispersed Bubbly Flows

In dispersed bubbly flows the large-scale turbulent structuresinteract with bubbles and are responsible for themacroscopicbubble motion whereas small-scale turbulent structuresonly affect small-scale bubble oscillations Since large scales(carrying most of the energy) are explicitly captured in LESand the less energetic small scales are modelled using asubgrid-scale (SGS)model LES can reasonably reproduce thestatistics of the bubble-induced velocity fluctuations in theliquid

There are three important considerations formodelling ofdispersed bubbly flows

(1) Separation of length scales of the interface thatis micro- meso- and macroscales The separationof these scales forms the basis for ldquofilteringrdquo theNavierndashStokes equations and applying proper model

equations for multiphase situation Important fordispersed flow is to identify the scales at which thegoverning equations are to be applied microscalesthat is scales which are small enough to describeindividual bubble shapes mesoscales which are com-parable to bubble sizes andmacroscales which entailenough bubbles for statistical representation

(2) The grid-scale equations Depending on the ratio ofthe length scales introduced above with the grid res-olution we can afford on a given computer hardwarea proper form of the governing equations must bechosen For instance if the mesh size is in the micro-scale order one can use single-fluid interface trackingtechniques to solve the problem If on the other handthe grid size is large enough for statistical descriptionof bubbles the E-E approach can be used Should thegrid size be comparable to the meso-scales we arein a limiting area for both approaches and specialcare must be taken in order to solve equations whichdescribe the underlying physics consistently

(3) The physical models Depending on the selected grid-scale equations physical models of various complex-ities must be employed The options here are numer-ous whether they concern turbulence modelling orinterphase modelling but these models are generallysimpler in case more of the microscales are resolved

In the following sections we describe each of these threeelements to model turbulent dispersed bubbly flow

21 FilteringOperation Theaimof filtering theNavier-Stokesequations is to separate the resolved scales from the SGS(nonresolved)The interface between the phases and the levelof detail required in its resolutionmodelling defines the filterin a multiphase flow

When LES is applied at a micro-scale filtering of turbu-lent fluctuations needs to be combinedwith interface trackingmethods These methods have been developed and used inboth dispersed flow and free surface flow by Bois et al [2]Toutant et al [3 4] Magdeleine et al [5] Lakehal [6] andLakehal et al [7] These methods require that all phenomenahaving an influence on space and time position of the inter-face are also simulated For the amount of details required andthe large size of practical problems of interest these types ofmodels should merely be seen as a support for the modellingand validation of more macroscopic approaches and cannotaddress a real industrial-scale problem (Bestion [8])

When LES is applied at a macro-scale the interface res-olution is not considered However in practical simulationsthese would require too coarse grids leading to poor reso-lution of turbulence quantities Much more often we are inthe meso-scale region in which the mesh size is comparableto bubble sizes This pushes the main assumptions of the E-E approach to its limit of validity and the grid is not fineenough for full interface tracking In other words the meshrequirement for E-E multiphase modelling conflicts with therequirements by LES approaches [9]

International Journal of Chemical Engineering 3

h

db

Figure 1 Milelli condition (from Niceno et al [10])

The issue of the requirement of the mesh size was firstaddressed by Milelli et al [11] who carried out a systematicanalysis and performed a parametric study with differentmesh sizes and bubble diameters They showed that for caseof a shear layer laden with bubbles it was possible to providean optimum filter width 12 lt Δ119889119887 lt 15 where Δ is thefilter width and 119889119887 is the bubble diameter (shown in Figure 1)This means that the grid space should be at least 50 largerthan the bubble diameterThe constraint imposed on the ratioΔ119889119887 implies that the interaction of bubbles with the smallestresolved scales is captured without additional approximation

22 Grid-Scale Equations The principle of the LES formula-tion is to decompose the instantaneous flow field into large-scale and small-scale components via a filtering operationIf 120601119891denotes the filtered or grid-scale component of the

variable 120601119891 that represents the large-scale motion then

120601119891 = 120601119891⏟⏟⏟⏟⏟⏟⏟

resolved

+ 1206011015840

119891⏟⏟⏟⏟⏟⏟⏟

subgrid

(1)

where 120601 is the variable of interest subscript 119891 refers either tothe liquid or the gas phase In the remainder of this paper weomit the bars of all resolved variables for the sake of simplicityThe following filtered equations are obtained

120597

120597119905(120572119891120588119891u119891) + Δ sdot (120572119891120588119891u119891) = 0 (2)

120597

120597119905(120572119891120588119891u119891) + Δ sdot (120572119891120588119891u119891u119891)

= minusnabla sdot (120572119891120591119891) minus 120572119891nabla119901 + 120572119891120588119891119892 + M119891(3)

The right hand side terms of (3) are respectively thestress the pressure gradient gravity and the momentumexchange between the phases due to interface forces

The SGS stress tensor which reflects the effect of theunresolved scales on the resolved scales is modelled as

120591119891 = minus120583eff119891 (nablau119891 + (nablau119891)119879

minus2

3119868 (nabla sdot u119891)) (4)

where 120583119890ff119891 is the effective viscosityIn the E-E approach separate equations are required for

each phase (see (3) 119891 = 119897 119892) together with interphaseexchange terms (for details Drew [12]) In most of the

investigations turbulence is taken into consideration for thecontinuous phase by SGS models The dispersed gas phaseis modelled as laminar but influence of the turbulence inthe continuous phase is considered by a bubble-inducedturbulence (BIT) model

In the E-L approach there are two coupled parts a partdealing with the liquid phase motion and a part describingthe bubbles motionThe dynamics of the liquid are describedin a similar way as in the E-E approach whereas the bubblemotion is modelled through the second law of Newton

Since the governing equations for the liquid and gasphase are expressed in the Eulerian and Lagrangian referenceframes respectively amapping technique is used to exchangeinterphase coupling quantities Depending upon the volumefraction of the dispersed phase one-way (eg 120572119892 lt 10

minus6) ortwo-way coupling between gas phase to liquid phase (10minus6 lt120572119892 lt 10

minus3) prevails In both cases bubble-bubble interactions

(ie collisions) can be neglected but the effect of the bubbleson the turbulence structure in the continuous phase has to beconsidered for higher volume fraction and does not play anyrole in lower volume fraction of gas phase Elgobashi [13]Thework reviewed here considers the two-way coupling whichconsists of the following

221 Forward Coupling (Liquid to Bubble) In the forwardcoupling calculated liquid velocities velocity gradients andpressure gradients on an Eulerian grid are interpolated todiscrete bubble locations for solving the Lagrangian bubbleequation motion

222 Backward or Reversed Coupling (Bubble to Liquid)The forces available at each bubblersquos centroid need to bemapped back to the Eulerian grid nodes in order to evaluatethe reaction force 119865 The two-way interaction (forward andbackward) is accomplished with a mapping method forexample PSI-cell method [14] modified PSI-wall-method[15] or mapping functions discussed by Deen et al [16]

23 Interfacial Forces The motion of a single bubble withconstant mass can be written according to Newtonrsquos secondlaw

119898119887

119889v119889119905

= sum F (5)

The bubble dynamics are described by incorporating allrelevant forces acting on a bubble rising in a liquid It isassumed that the total forcesum F is composed of separate anduncoupled contributions originating from pressure gravitydrag lift virtual mass wall lubrication and wall deformationturbulent dispersion

sum F = F119875 + F119866 + F119863 + F119871 + FVM + FTD + FWL + FWD

(6)

For each force the analytical expression or a semiempir-ical model is used based on bubble behaviour observed inexperiment or in DNS

To summarize the influencecontribution of these forcesare as follows


(1) The modeling of the lift force for capturing bub-ble plume meandering and bubble dispersion isimportant However there is an uncertainty regard-ing appropriate value or correlation representing liftcoefficientThere is also recommendation that bubblesize-dependent lift coefficient should be chosen [17]

(2) The value of the lift coefficient can be different thanthe one used in RANS approach It is because ofdifferent handling of factors responsible for bubbledispersion that is the interaction between the bub-bles and influence of turbulent eddies in the liquidphase In RANS approach they are considered bymeans of the lift and turbulent dispersion force withuncertainty of exact contribution of the individualforces Most of the investigators use a constant valueof the lift coefficient (119862119871 = 05) while the value ofthe turbulent dispersion coefficient is varied (01 to10) to get good agreementwith the experimental dataHowever in LES bubble dispersion caused by liquidphase turbulent eddies is implicitly calculated anda more realistic contribution of the lift force can beused The coefficient for the effective lift force thusmay vary between the two approaches [18]

(3) The virtual mass force is proportional to the relativeacceleration between the phases and is negligible oncea pseudosteady state is reached It has little influenceon the simulation results for bubble plumes [19]Milelli [20] It is mainly because of the accelerationand deceleration effects are restricted to small endregions of the column A constant coefficient is usedin almost all investigations

(4) In LES through filtering velocities are decomposedinto a resolved and a SGSpartThe resolved part of theturbulent dispersion is implicitly computedHoweverin case of a bubble size smaller than the filter sizeturbulent transport can be present at SGS level andshould be considered [9] This can be done using aone-equation model wherein it can be modelled byreplacing the total kinetic energy by SGS contribution(119896SGS) By the same argument other forces also needmodelling at SGS level

The values or expressions for the coefficient of drag liftand virtualmass force used by different investigators are givenin Tables 1 and 3

24 SGS Models It is well known that in turbulent flowenergy generally cascades from large to small scales Theprimary task of the SGS model therefore is to ensure that theenergy drain in the LES is same as obtained with the cascadefully resolved as one would have in a DNS The cascadinghowever is an average process Locally and instantaneouslythe transfer of energy can be much larger or much smallerthan the average and can also occur in the opposite direction(ldquobackscatterrdquo)

241 Smagorinsky [21] Model The simplest well-knownand mostly used Smagorinsky [21] model is based on the

Boussinesq hypothesis It requires the definition of time andlength scales and a model constant Smagorinsky used thefollowing expression to calculate the turbulent viscosity thatis the SGS viscosity

120583eff119897 = 120583lam119897 + 120588119897(119862119878Δ)2radicS2 (7)

where 120583lam119897 is the (laminar) dynamic viscosity 119862119878 is theSmagorinsky constant S is the characteristic strain tensor offiltered velocity and Δ is the filter width usually taken as thecubic root of the cell volume

In the single-phase flow literature the value of theconstant used is in the range from119862119878 = 0065 (Moin and Kim[22]) to119862119878 = 025 (Jones andWille [23])The value of119862119878 usedin gas-liquid flows varies from that of single phase flow and isin the range of 008 to 012 [11 20 24 25] The lower range of119862119878 value compared to single phase could be attributed to theinterphase coupling term which acts as a form of SGS modeland can make contribution to the turbulent kinetic energydissipation The sensitivity analysis carried out for 119862119878 valueshows that larger 119862119878 values can produce excessive dampingeffect to the liquid velocity field and eventually leads to asteady-state solution [26 27]

The main reason for the frequent use of the Smagorinskymodel is its simplicity Its drawbacks are that the constant119862119878 has to be calibrated and its optimal value may vary withthe type of flow or the discretization scheme Moreover themodel is purely dissipative and hence does not account eitherfor the small-scale effect on the large scales adequately (byneglecting the ldquobackscatterrdquo of turbulent energy) while it actspurely as a drain for the turbulent kinetic energy

The dynamic model originally proposed by Germanoet al [28] eliminates some of these disadvantages by calcu-lating the Smagorinsky constant as a function of space andtime from the smallest scales of the resolved motion

242 Dynamic SGSModel Thedynamic SGSmodel assumesSGS turbulent energy to be in local equilibrium (ie produc-tion = dissipation) The eddy viscosity is estimated from (7)but with a 119862119878 as a local time-dependent variable

The basic idea is to apply a second test filter to theequations The new filter width twice the size of the gridfilter produces a resolved flow field The difference betweenthe two resolved fields is the contribution of the small scaleswhose size is in between the grid filter and the test filterThe information related to these scales is used to computethe model constant The advantage here is that no empiricalconstant is needed and that the procedure allows the negativeturbulent viscosity implying energy transfer from smaller tolarger scales (energy back-scatter) This effect in principleallows both an enhancement and attenuation of the turbulentintensity introduced by the bubbles

The model has a few drawbacks wide fluctuations indynamically computed constants can cause stability issuesalong with additional computational expense

243 One-Equation Model In spite of the fact that dynamicSGS model calculates model constant 119862119878 thus making aconstant-free model it lacks the information on the amount


Table1Com

paris

onof

LESsim

ulations

No

Author

Colum

nD(times

W)times

H(m

)Sparger

desig

nBu

bble

diam

eter

Rangeo

f119881119866m

sNum

bero

fgrid

cells

Filter

SGSMod

elBIT

closure

mod

els+

Interfa

cialforcec

oefficientclosures++

Drag

119862119863

Lift

119862119871

Virtual

mass

119862VM

(1)

Deenetallowast[19

]015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

32times

32times

90

Δ=5ndash10mm

Smagorinsky

119862119878=01

(1)

(4)

05

05

(2)

Bove

etal

[29]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

9times

6times

30

Δ=10ndash17m

mSm

agorinsky

119862119878=005ndash0

2mdash

(24)

05

05

(3)

Zhangetal

[26]

015times015times045ndash0

90

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

15times

15times

90

mdashSm

agorinsky

119862119878=008ndash0

20

(123)

(2)

(4)

Tabibetal

[17]

015times

10

Perfo

rated

plate

5mm

200

times10minus3

1500

00Δ

=3m

mSm

agorinsky

119862119878=01

(1)

(1)

(5)

Dho

treetal

[20]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus5

15times

15times

50

15times

15times

100

119889119861lt

Δ

Smagorinsky

119862119878=012

Germano

(1)

(1)

05

05

(6)

Nicenoetal

[9]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

30times

30times

90

Δisequaltothe

grid

spacing

Δ119889119887=15

Smagorinsky

119862119878=012

OEM

(12)

(15)

05

05

(7)

Dho

treetal

[18]

20

times34

Perfo

rated

plate

26m

m49

times10minus3

mdash28m

mlt

Δlt

40m

mSm

agorinsky

119862119878=012

(1)

(5)

05

05

(8)

Nicenoetal

[10]

015times

015times

10

Perfo

rated

plate

4mm

49

times10minus3

30times

30times

100

Δ=5m

mOEM

Germano

(12)

(45)

05

05

(9)

TabibandSchw

arz

[30]

015times

10

Perfo

rated

plate

3ndash5m

m200

times10minus3

mdashmdash

OEM

(2)

Max

[(1)(6

)]

minus005

mdash

(10)

vandenHengel

etal[31]

015times

10

Perfo

rated

plate

3mm

49

times10minus3

15times

15times

45

Δ=

10mm

Smagorinsky

(1)

(3)

05

05

(11)

HuandCelik

[32]

015times

008times

10

Pipe

sparger

16mm

0660times

10minus3

96times

50times

8

120times

80times

10

PSI-ballmetho

d2m

mSm

agorinsky

119862119878=0032

(4)

(3)

05

05

(12)

Lain

[27]

014times

10

Porous

mem

brane

26m

m0272times

10minus3

30times

30times

50

45times

45times

10

Δ119889119887=18

Smagorinsky

119862119878=01

(4)

05

(13)

Darmanae

tal

[33]

02

times003times

10

Multip

oint

gas

injection

4mm

70

times10minus3

80times

12times

400

Δ=

25mm

Vrem

an

119862119878=01

mdash(3)

05

(14)

Sung

korn

etal

[34]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

30times

30times

90

Δisequaltothe

grid

spacing

Δ119889119887=12

5

Smagorinsky

119862119878=010ndash0

12(6)

(3)

05

(15)

Baietal[35]B

aietal[36]

015times

015times

045

Perfo

rated

plate

5mm

50

times10minus3

100

times10minus3

150

times10minus3

250

times10minus3

15times

15times

45

20times

20times

60

30times

30times

90

mdashVrem

anSm

agorinsky

119862119878=01

mdash(3)

05

05

Thea

utho

rshave

studied

thee

ffectof

thisforceo

vera

range

+Num

bersindicatedarer

efered

toTable2

++Num

bersindicatedarer

efered

toTable3


Table 2 Bubble-induced turbulence models

No Author 120583BIT 119878119896BIT 119878

120598BIT Assumptions

(1) Sato and Sekoguchi[37]

120583BIT =

120588119871120572119866119862120583BIT1198891198611003816100381610038161003816U119866 minus U119871

1003816100381610038161003816

0 0

(2) Pfleger and Becker[38] 0 120572119871119862119896

1003816100381610038161003816M1198701003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

120572119871

119896119871

119862120598119878119896BIT

(3) Troshko and Hassan[39] 0 1003816100381610038161003816M119863119871

1003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

0453119862119863

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

2119862VM119889119861

119878119896BIT

(4) Crowe et al[14] PSI cellball approximation

(5) Sommerfeld [40] Stochastic interparticlecollision model

(6) Sommerfeld et al [41] Langevin equation model

of SGS turbulent kinetic energy a datum which may proveuseful inmodelling some aspects of dispersed flows (eg SGSbubble-induced turbulence)

The essence of the one-equation model is to solve addi-tional transport equation for SGS turbulent kinetic energy

120597119896SGS120597119905

= nabla [(120583 + 120583SGS) nabla119896SGS] + 119875119896SGSminus 119862120576

11989632

SGSΔ

(8)

Here 119875119896SGSis production of SGS turbulent kinetic energy and

is defined as

119875119896SGS= 120583SGS

10038161003816100381610038161003816119878119894119895

10038161003816100381610038161003816 (9)

and SGS viscosity is obtained from

120583SGS = 119862119896Δ11989612

SGS (10)

The availability of the SGS turbulent kinetic energy allowsfor modelling of SGS interphase sorces such as bubble-induced turbulence and turbulent dispersion at SGS Theapplication of one-equation SGS model for bubbly flows isillustrated in more detail in sections below

25 Effect of Bubble-Induced Turbulence (BIT) In the E-Eapproach the turbulent stress in the liquid phase is con-sidered to have two contributions one due to the inherentthat is shear-induced turbulence that is assumed to beindependent of the relative motion of bubbles and liquid andthe other due to the additional bubble-induced turbulence(Sato and Sekoguchi [37]) For BIT there are two modellingapproaches The first approach is proposed by Sato andSekoguchi [37] and Sato et al [42]

120583BI119897 = 120588119891 119862120583BI 120572119892 11988911988710038161003816100381610038161003816u119892minusu119897

10038161003816100381610038161003816 (11)

with 119862120583BI as a model constant which is equal to 06 and 119889119887

as the bubble diameter Milelli et al [11 24] found that themodelling of the bubble-induced turbulence did not improvethe results They tried two different formulations the Tranmodel and the Satomodel and found that they have negligibleeffect This was attributed to fact that the bubble-inducedviscosity (and turbulence) is not crucial the turbulence beingmainly driven by the liquid shear and a low void fraction

(asymp2 leading to 120583BI119897 asymp 10minus2 kg(ms)) did not significantly

modify the situation It was thought that in a case in whichthe bubbles actually drive the turbulence (via buoyancyandor added mass forces) the situation would be differentHowever in subsequent studies similar observations weremade in bubble plumes simulated by Deen et al [19] Dhotreet al [20] Niceno et al [9]

The second approach for the modelling of BIT allowsfor the advective and diffusive transport of turbulent kineticenergy This model incorporates the influence of the gasbubbles in the turbulence bymeans of additional source termsin the 119896SGS equation and is taken to be proportional to theproduct of the drag force and the slip velocity between thetwo phases This approach was used in work of Niceno et al[10] through the use of a one-equation model They foundsignificant influence of the additional source terms as usedby Pfleger et al [43] as shown in Figure 2

Figure 2 shows the comparison of the liquid kineticenergy obtained for the case of a bubble plume rising in asquare column It can be seen that the simulation withoutBIT underpredicts the turbulent kinetic energyTheuse of theSato model reproduced the double-peaked profile for kineticenergy The Pfleger model also reproduced the experimentaldata very well Figure 2(b) shows the ratio of the modelledSGS energy to the resolved energy With no BIT this ratiohas the lowest value whereas the Sato model yields moreSGS energy while the Pfleger model gives a ratio that isroughly twice as high which is particularly pronounced inthe middle of the column Table 2 gives a summary of BITmodels proposed by various investigators

3 Numerical Details

Crucial parameters for obtaining reliable LES results are thetime step selection the total time for gathering good statisticsof the averaged variables and discretization schemes for thevariables The time step choice is determined by the criterionthat the maximum Courant-Fredrichs-Levy (CFL) numbermust be less than one (119873CFL = Δ119905119906maxΔ119909min lt 1)

For flow variables central difference should be usedfor discretization of advection terms and avoid using diffu-sive upwind schemes However for scalars variables high-order schemes (MUSCL QUICK or Second-Order) may be


Table 3 Drag force models

No Author Equation

(1) Ishii and Zuber [44] 119862119863

=24Re

(1 + 01Re075)

(2) Tomiyama [45]119862119863

=(83) 119864119900 (1 minus 119864

2)

11986423

119864119900 + 16 (1 minus 1198642) 11986443

119865(119864)minus2

119864 =1

1 + 01631198641199000757

(Wellek et al [46])

119865 (119864) =sinminus1radic1 minus 119864

2minus 119864radic1 minus 119864

2

(1 minus 1198642)

(3) Tomiyama [47] (pure system) 119862119863

= max [min [16

Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]

(4) Ishii and Zuber [44] (distorted regime)119862119863 =

2

311986411990012

119864119900 = 119892Δ1205881198892

119866120590

(5) Clift et al [48]119862119863 =

24

Re(1 + 015Re0687

119875) Re119875 le 800

044 Re119875 gt 800

(6) Tomiyama [47] (contaminated system) 119862119863 = max [min [24

Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]

003

0025

002

0015

001

0005

00 005 01 015

Column width (m)

No BITSato

PflegerExperiment

2s

2)

Turb

ule

nt

kin

etic

en

ergy

(m

(a)

024

022

02

018

016

014

012

01

008

006

004

SGS

reso

lved

en

ergy

0 005 01 015

Column width (m)

No BITSato

Pfleger

(b)

Figure 2 (a) Resolved (dashed) and total (continuous) liquid kinetic energy and (b) ratio of the modelled and resolved parts of the turbulentkinetic for various BIT models (from Niceno et al [9])

tolerable to avoid nonphysical solutions (eg negative vol-ume fractions) An alternative to high-order schemes arethe bounded central differences The risk with use of all butcentral scheme is their diffusivityTheir influence on LESmayexceed the modelled SGS transport

It is necessary to follow the initial phase of the simulationwherein the turbulent strutures develop starting from initialcondition and to reach a statistiacally steady state Theduration of this phase depends on the flow characteristics

The simulation must be run for a total time long enoughto allow all turbulent instabilities that develop during thisphase to be convected across the region of interest Howeverthe convecting velocities of the turbulent structures and theregions of interest are not always known as a priori This iswhy it is recommended to run the simulation a multitude(typically 5 times) of the slowest integral time scales whichoften is the flow through time defined as the ratio of thesystem height over the bulk (superficial) velocity


4 LES Prediction of the Flow Pattern forDispersed Bubbly Flows

Here we review different LES studies that were performedusing theE-E andE-L approaches for simulating flowpatternsin gas-liquid bubbly flows Table 1 gives a summary of keynumerical parameters (filter size number of grids SGSmodel bubble diameter coefficient for interfacial forces) andexperimental details (geometrical dimension sparger designrange of superficial gas velocity) used by investigators

41 Euler-Eulerian (E-E) Approach

411 Milelli et al [11 24 49] Milelli et al reported forthe first time two-phase LES with E-E approach They firstinvestigated statistically 2D flow configuration and then freebubble plume

They addressed important concerns related to the two-phase LES simulation For instance they found that theoptimum ratio of the cutoff filter width (ie the grid) to thebubble diameter (119889119887Δ) should be around 15 That meansmesh size should be at least 50 larger than the bubblediameter (Figure 1) so that (a) bubble size determines thelargest scalemodelled (b) and its interactionwith the smallestcalculated scale above the cut-off is captured This is alsosupported by the scale-similarity principle of Bardina et al[50]

Milelli [49] investigated LES for a free bubble plume andcompared their predictions with the experiment of Anagboand Brimacombe [51] Here they found that the meanquantities were not strongly affected by the different SGSmodels Moreover they found little impact of the dispersedphase on the liquid turbulence from the turbulent energyspectrum taken in the bubbly flow region which revealeda power-law distribution oscillating between minus53 and minus83in the inertial subrange The results conform to previousstudies which attributed the more dissipative spectrum tothe presence of the dispersed phase Hence they found noinfluence of modifying the SGSmodel to account for bubble-induced dissipation

Further they observed in simulation that the lift coef-ficient value plays a major role in capturing the plumespreading and the used lift coefficient may differ for an LEScompared to the one that is justified in an RANS approachThe plausible explanation here is from different handlingof two factors responsible for bubble dispersion that isinteraction between the bubbles and influence of turbulenteddies in the liquid phase

412 Deen et al [19] Deen et al [19] reported LES for gas-liquid flow in a square cross-sectional bubble column forthe first time They investigated the performance of RANSand LES approaches influence of the interphase forces andbubble-induced turbulence

They found that RANS approach (k-120576 model) overesti-mated the turbulent viscosity and could only predict lowfrequency unsteady flow On other hand LES as shown inFigure 3 reproduced high frequency experimental data and

0

02

04

06

08

100 110 120 130 140 150

Time (s)

LDA

LES

minus02

uy

L(m

s)

119896-ε

Figure 3 Time history of the axial liquid velocity at the centrelineof the column at a height of 025m (from Deen et al [19])

predicted the strong transient bubble plume movements asin an experiment

Furthermore they also identified that the lift force isresponsible for transient spreading of the bubble plume andin absence of it only with drag force the bubble plumeshowed no transverse spreading

They considered the effective viscosity of the liquidphase with three contributions the molecular shear-inducedturbulent (modelled using Smagorinsky model) and bubble-induced turbulent viscosities [37] Like in the work ofMilelli they confirmed the marginal effect of the BIT on thepredictions The effect of virtual mass force on the simulatedresults was also found to be negligible

413 Bove et al [29] Bove et al [29] reported LES withE-E approach for the same square cross-sectional bubblecolumn as used by Deen et al [19]They studied the influenceof numerical modelling of the advection terms and theinlet conditions on LES performanceThe upwind first-orderand higher-order Flux Corrected Transport (FCT) schemesfor both the phase fraction equations and the momentumequations were employed The simulations using a second-order FCT scheme showed relatively good agreement withthemeasurement data of Deen et al [19]The authors showedthat the proper discretization of the momentum and volumefraction equations is essential for correct prediction of theflow field

Further the LES results were found to be very sensitiveto inlet boundary conditions (Figure 4) Three different inletconfigurations simulated showed that the inlet modellinginfluences the predicted fluid flow velocity (as in Figure 4(a))and an important fluid flowparameter the turbulent viscosity(Figure 4(b)) In this work the sparger (a perforated plate)was not modelled due to the difficulty in adapting the meshgrid to the geometry They also suggested that near wall


03

025

02

015

01

005

0

minus005

minus010 01 02 03 04 05 06 07 08 09 1

(ms

)

xD

Deen exp dataInlet 1

Inlet 2Inlet 3

(a)

Inlet 1

Inlet 2

Inlet 3

25

2

15

1

05

00 005 01 015 02 025 03 035 04 045

yH

(kg

m s)

(b)

Figure 4 Comparison of (a) averaged axial liquid velocity profile at 119910119867 = 056 (b) instantaneous viscosity profile along the height of thecolumn (120 s) for three inlet conditions (from Bove et al [29])

region description in the SGS models is important andthe lack of the near wall modelling can lead to erroneousprediction of frictional stresses at the wall

They used drag model for the contaminated water whichgave a better prediction of the slip velocity however thevelocity profile was underestimated for both gas and liquidphase Reason for the underprediction was not clear whetherit was due to drag model or an improper value of the liftcoefficient used or an error in the near wall modelling Needfor further work in this direction was suggested

414 Zhang et al [26] Zhang et al [26] reported LES in asquare cross-sectional bubble column They investigated theSmagorinsky model constant and carried out a sensitivityanalysis It was found that higher119862119878 values led to higher effec-tive viscosity which dampens the bubble plume dynamicsleading to a steepmean velocity profile (as shown in Figure 5)They obtained a good agreement with themeasurements with119862119878 in range of 008ndash010 They also confirmed that the liftforce plays a critical role for capturing the dynamic behaviourof the bubble plume

They extended the work of Deen et al [19] and predictedthe dynamic behaviour in the square bubble column using ak-120576 turbulence model extended with BIT

415 Tabib et al [17] Tabib et al [17] reported LES usingE-E approach in a cylindrical column for a wide range ofsuperficial gas velocity In accordance with the earlier workthey confirmed the importance of a suitable lift coefficientand drag lawMoreover they studied the influence of differentspargers (perforated plate sintered plate and single hole)and turbulence models (k-120576 RSM and LES) using theexperimental data of Bhole et al [52]Themain findings fromthe study were that the RSM performs better than the k-120576 model the LES was successful in predicting the averaged

flow behaviour and was able to simulate the instantaneousvortical-spiral flow regime in the case of a sieve plate columnas well as the bubble plume dynamics in case of single-holesparger Finally they concluded that LES can be effectivelyused for the study of the flow structures and instantaneousflow profiles

416 Dhotre et al [20] Dhotre et al [20] reported LES withan E-E approach for a gas-liquid flow in a square cross-sectional bubble column They studied the influence of SGSmodels Smagorinky and Dynamic models of Germano et al[28] It was found that both the Smagorinsky model (119862119878 =012) and the Germano model predictions compared wellwith the measurements

They further investigated the value of 119862119878 obtained fromthe Germanomodel Reason for similar performance of bothmodels was clear from the probability density function of 119862119878(from Germano model) over the entire column As shownin Figure 6 the value of 119862119878 has the highest probability inthe range of 012ndash013 Like Zhang et al [26] the authorsconfirmed that with a proper BIT model RANS also per-formed well for mean quantities of flow variables Figure 7shows the comparison of the predicted instantaneous vectorflow field for axial liquid velocity from all the three models(Smagorinky Germano and RANS)

It was further concluded that the Germano model cangive correct 119862119878 estimates for the configuration under consid-eration and in general can be used for other systems where119862119878 is not known as ldquoa priorirdquo from previous analysis

417 Niceno et al [10] Niceno et al [10] investigated LESwith E-E approach for a gas-liquid flow in a square cross-sectional bubble columnTheydemonstrated the applicabilityof a one-equation model for the SGS kinetic energy (119896SGS)


0 02 04 06 08 1

0

01

02

03

04

05

v mL

(ms

)

xD

= 008= 01

= 015

= 02Exp (yH = 063)

minus01

(mdash)

119862119878 119862119878

119862119878

119862119878

(a) Axial liquid velocity

0

01

02

03

04

05

06

07

0 02 04 06 08 1

= 008= 01

= 015

= 02Exp (yH = 063)

v mG

(ms

)

xD (mdash)

119862119878 119862119878

119862119878

119862119878

(b) Axial gas velocity

Figure 5 Comparison of the prediction and measurement of mean velocity of the both phases the predicted profiles were obtained withdifferent 119862119878 values used in the SGS model (Zhang et al [26])

0

0002

0004

0006

0008

001

0012

0 005 01 015 02 025 03

PD

F

CS

Figure 6 Probability density function for computed constant 119862119878 inGermano model over entire column (from Dhotre et al [9])

The predictions showed that the one-equation SGS modelgives superior results to the Germano model with the addi-tional benefit of having information on the modelled SGSkinetic energy

120583eff119897 = 120583lam119897 + 120588119897119862119896Δradic119896SGS (12)

with 119862119896 = 007 a model constant They studied the influenceof two approaches for bubble-induced turbulence approachof an algebraic model (Sato et al 1975) and extra source terms(as used in Pflger et al 1999) in the transport equation for SGSkinetic energy approach It was found that the latter approachimproved the quantitative prediction of the turbulent kinetic

energy (as shown in Figure 2(a)) The modelled SGS kineticenergy for the Pfleger model found to be much higher thanfor the Satomodel (Figure 2(b)) indicating the Pflegermodelneeds a more appropriate constant for LES

They suggested that the modelled SGS information canbe used to access the SGS interfacial forces in particular theturbulent dispersion force In their work the effect of SGSturbulent dispersion force could not be determined as thebubble size was almost equivalent to the mesh size

418 Dhotre et al [18] Dhotre et al [18] extended LES withE-E approach for a gas-liquid flow in a large-scale bubbleplume The predictions at three elevations were comparedwith themeasurement data of Simiano [55] and anRANSpre-diction The LES approach was shown superior in capturingthe transient behaviour of the plume (Figure 8) and predictssecond-order statistics of the liquid phase accurately

They emphasized the crucial role of the lift force in theprediction of the lateral behaviour of the bubble plumes Inthe RANS approach the turbulent dispersion force is requiredto reproduce the bubble dispersion however in LES bubbledispersion is implicitly calculated by resolving the large-scale turbulentmotion responsible for bubble dispersionThedependence of the bubble dispersion with the value of liftcoefficient was also observed in Milelli et al [11 24] Deenet al [19] Lain and Sommerfeld [56] Van den Hengel et al[31] Tabib et al (2008) and Dhotre et al [20])

Dhotre et al [18] found good agreement with the mea-surement data at higher elevation while discrepancies wereobserved at lower elevation near the injector The reason forthe discrepancies was attributed to the absence of modellingbubble coalescence and breakup This was also found in the


Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS

Figure 7 Predicted instantaneous vector flow field for axial liquid velocity after 150 s for all three models (from Dhotre et al [20])

0e+00

25eminus03

5eminus03

75eminus03

1eminus02Air void fraction

(a)

Averaged Instantaneous

(b)

Figure 8 Comparison of k-120598model and EELES predictions vector plot of axial velocity coloured with the void fraction in the midplane (a)k-120598 model (b) EELES (from Dhotre et al [18])

work of Van den Hengel et al [31] wherein the authorsshowed that most of the coalescence occurs in the lowerpart of the column and recommended to consider bubblesize distribution and coalescence and breakup models forreproducing the bubble behaviour near the sparger

419 Niceno et al [10] Niceno et al [10] reported LESwith E-E approach for a gas-liquid flow in a square cross-sectional bubble columnThey compared two different codes(CFX-4 and Neptune) and two subgrid-scale models (as inFigure 9)The prediction from the Smagorinsky model in the


0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)

NeptuneCFX4Experiment

Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)

Figure 9 Comparison of liquid turbulent kinetic energy obtainedwith CFX-4 using one-equation model and Neptune CFD withSmagorinsky model and experimental data The blue dashed line isthe resolved the blue continuous line is the total (resolved plus SGS)kinetic energy (from Niceno et al [10])

Neptune CFD code and the one-equation model of CFX-4was compared with the measurement data of Deen et al [19]Agreement between the predictions from the two SGSmodelswas found to be good and it was concluded that the influenceof the SGS model was small This is in contradiction withearlier work of Van den Hengel et al [31] where they showedsignificant contribution of the SGS model (Figure 10) whichis discussed in more detail in section (42) It remains to beseen if this was due to the fine mesh used by the authors(Δ119889119887 = 12) Niceno et al [10] argued that with the knownflow pattern in a bubble column that is a dominant bubbleplume meandering between the confining walls the biggesteddy having most energy is of the size of the domain crosssection Thus the grid used in their work was a compromisebetween sufficiently fine to capture themost energetic eddiesand sufficiently coarse to stay close to the Milelli criterion[11 24] Furthermore they pointed out the limitations of LESwith E-L or E-E approach without resolving interface theyindicated that themost influential interfacial forces (drag andlift) aremodelled for the large-scale field and their effect fromthe small scale remains a question On the other hand theyrecommend large-scale simulation as in theworks of Lakehalet al [25] which explicitly resolves the large-scale part ofthe interfacial forces and models the part at the SGS levelwhere the effects are smaller and hence less influential on theaccuracy of the results

4110 Tabib and Schwarz [30] Tabib and Schwarz [30]extended the work of Niceno et al [9] and attempted toquantify the effect of SGS turbulent dispersion force fordifferent particle systems where the particle sizes would besmaller than the filter sizeThey used LES with E-E approach

They used the formulation of Lopez de Bertodano [57]to approximate the turbulent diffusion of the bubbles by theSGS liquid eddies for a gas-liquid bubble column system [17]The bubble size was in range of 3ndash5mm The mesh used insimulationswas coarser than the bubble diameterThey founda high contribution from the SGS turbulent dispersion forcewhen compared with the magnitude of the other interfacialforces (like drag force lift force resolved turbulent dispersionforce and force due to momentum advection and pressure)Finally Tabib and Schwarz concluded that for LES with E-Eapproach when the mesh size is bigger than bubble size theSGS turbulent dispersion force should be used and a one-equation SGS-TKE model overcomes a conceptual drawbackof E-E LES model

42 Euler-Lagrangian (E-L) Approach421 Van den Hengel et al [31] Van den Hengel et al [31]reported LES with E-L approach for a gas-liquid flow ina square cross-sectional bubble column The liquid phasewas computed using LES and a Lagrangian approach wasused for the dispersed phase They used a discrete bubblemodel (DBM) originally developed by Delnoij et al [58 59]and extended it to incorporate models describing bubblebreakup and coalescenceThemean and fluctuating velocitiespredicted in the simulations showed a good agreement withthe experimental data of Deen et al [19]

Authors studied the influence of the SGS model on thepredictions and found that without SGS model the averageliquid velocity and liquid velocity fluctuations aremuch lowercompared to the case with a SGS model This was due tothe lower effective viscosity in this case which led to lessdampening of the bubble plume dynamics and subsequentlyto flattermean liquid velocity profiles (as shown in Figure 10)

In this work also the authors confirmed the importantrole of the lift coefficient in capturing the plume dynamicsThey considered two lift coefficients (119862119871 = 05 and 03) andfound that a smaller value of the lift coefficient led to higheraverage velocity and velocity fluctuations and less spreadingof the plume which resulted in overprediction of the averagevelocity in the centre of the column

422 Hu and Celik [32] Hu and Celik [32] studied LESwith an E-L approach for the gas-liquid flow in a flatbubble column The liquid phase was computed using LESand a Lagrangian approach was used for the dispersedphase The authors developed a mapping technique calledparticle-source-in-ball (PSI-ball) for coupling the Eulerianand Lagrangian reference frames The concept is a general-ization of the conventional particle-source-in-cell (PSI-cell)method as well as a template-function-based treatment [14]

They reported second-order statistics of the pseudo-turbulent fluctuations and demonstrated that a single-phaseLES along with a point-volume treatment of the dispersedphase could serve as a viable closure model

Hu and Celik reported that the predictedmean quantities(such as mean liquid velocity field) were in good agreementwith the experimental data of Sokolichin and Eigenberger[54] as shown in Figure 11 and further gave an accurate


0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)

Figure 10 Comparison of the simulated and experimental liquid velocity and velocity fluctuations for cases with and without SGS model ata height of 0255m and a depth of 0075m Effect of the SGS model (from Van den Hengel et al [31])

prediction of the instantaneous flow features including liquidvelocity fluctuations and unsteady bubble dispersion patternHu and Celik also studied the influence of the Smagorinskyconstant and found that the constant for multiphase systemsfalls in a relatively smaller range than for single-phase flowsHigher values of the 119862119878 showed an excessive damping effectto the liquid field which led to a steady-state solutionThis observation is in accordance with other investigators[26 31] Furthermore authors proposed to use 119862119878 as amodeling parameter rather than a phyiscal constant as theinterphase coupling terms used as well as the high frequencyturbulent fluctuations contribute to the turbulent kineticenergy dissipation

423 Lain [27] Lain [27] reported an LESwith E-L approachfor a gas-liquid flow in a cylindrical bubble column He usedLES for the liquid phase and a Lagrangian approach for thedispersed gas phase The interaction terms between liquidand gas phases was calculated using the particle-source-in-cell (PSI-cell) approximation of Crowe et al [14]The bubbleswere considered as a local source of momentum and sourceterm was added

A simple model for the subgrid liquid fluctuating velocityto account for the BIT considered in this work was foundto have no influence on the predictions As in previousworks authors confirmed a strong dependency of the bubbledispersion in the column on the value of transverse lift


(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)

Figure 11 Long-time averaged liquid velocity field onmiddepth plane (a) E-L approach (b) LDAmeasurement of Becker et al [53] (c) LDAmeasurement of Sokolichin and Eigenberger [54] and (d) 3D E-E simulations of Sokolichin and Eigenberger [54] (from Hu and Celik [32])

force coefficient used He concluded that the lift coefficientdepends on the bubble-liquid relative velocity and was themain mechanism responsible for the spreading of bubblesacross the column crosssection He further compared thesimulation results with particle image velocimetry (PIV)measurements (Border and Sommerfeld [60]) and k-120576 calcu-lations

424 Darmana et al [33] Darmana et al [33] used the LESwith E-L approach for simulating the gas-liquid flow in a flatbubble column and validated the model with experimentaldata of Harteveld et al [61] They investigated seven spargerdesigns and their influence on the flow structure It was foundthat themodel captures the influence of different gas spargingvery well (eg Figure 12 shows one such case simulated)However in all cases simulated authors found systematicoverprediction of dispersed phase distribution (25) whichwas attributed to an inaccuracy of the drag force and theturbulence model at high gas void fractions

425 Sungkorn et al [34] Sungkorn et al [34] reported LESwith the E-L approach for a gas-liquid flow in a square cross-sectional bubble column They modelled the continuousliquid phase using a lattice-Boltzmann (LB) scheme and aLagrangian approach was used for the dispersed phase Forthe bubble phase the Langevin equationmodel [41] was usedfor estimating the effect of turbulence The bubble collisionswere described by a stochastic interparticle collision model

based on the kinetic theory developed by Sommerfeld [40]The predictions showed a very good agreement with theexperimental data for the mean and fluctuating velocitycomponents Figure 13 shows the sanpshots of predicted thebubble dispersion patterns

It was also found that their collision model leads totwo benefits the computing time is dramatically reducedcompared to the direct collision method and secondly it alsoprovides an excellent computational efficiency on parallelplatforms Sungkorn et al [34] claim that the methodologycan be applied to a wide range of problemsThe investigationsare valid for lower global void fraction and further work isrequired to consider it for higher void fraction systems

5 Application of LES

51 Preamble The investigations discussed in earlier sectionsdealt with the use of LES for predicting the flow patterns Inthe published literature the knowledge of flow pattern hasbeen employed for the estimation of equipment performancesuch as mixing (Joshi and Sharma [62] Joshi [63] Ranadeand Joshi [64] Ranade et al [65] and Kumaresan and Joshi[66]) heat transfer (Joshi et al [67] Dhotre and Joshi [68])Sparger design (Dhotre et al [69] Kulkarni et al [70]) gasinduction (Joshi and Sharma [71] Murthy et al [72]) andsolid suspension (Raghava Rao et al [73] Rewatkar et al[74] and Murthy et al [75]) Joshi and Ranade [76] havediscussed the perspective of computational fluid dynamics


700

650

600

550

500

450

400

350

z(m

m)

z(m

m)

minus150minus100minus50 0 50 100 150

x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)

Figure 12 Instantaneous flow structure comparison between experiment (a) and simulation (b) From left to right bubble positions bubblevelocity and liquid velocity (from Darmana et al [33])

(CFD) in designing process equipment with their viewson expectations current status and path forward The LESsimulations provide substantially improved understanding ofthe flow pattern Therefore in this section the applicationof LES for design objectives like mixing heat transfer andchemical reactions by some investigators will be reviewedThe LES simulations have also been used in the identificationof turbulent structures their dynamics and the role of

structure dynamics in the estimation of design parametersThe LES simulations have also been used in the estimations ofterms in k-120576 and RSMmodels such as generation dissipationand transport of turbulent kinetic energy (k) the turbulentenergy dissipation rate (120576) and Reynolds stresses Theseestimations have improved the understanding of RANS (k-120576 and RSM) models These two applications of LES are alsodescribed briefly


(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)

Figure 13 Snapshots of the bubble dispersion pattern after 20 50 100 and 150 s The bubbles are coloured by the local magnitude of theliquid fluctuations (from Sungkorn et al [34])

52 Mass Transfer and Chemical Reaction

521 Darmana et al [77 78] Darmana et al [77 78] usedLES with E-L approach to simulate flow mass transfer andchemical reaction in flat bubble column They consideredmass transfer rate in liquid-phase momentum equation andreaction interfacial forces in the bubble motion equation

Also the presence of various chemical species wasaccounted through a transport equation for each speciesDarmana et al estimated the mass transfer rate from theinformation of the individual bubbles directly They used themodel to simulate the reversible two-step reactions foundin the chemisorption process of CO2 in an aqueous NaOHsolution in a lab-scale pseudo-2D bubble column reactor(eg Figure 14) They found good agreement between sim-ulation and measurement for the case without mass transferIn absence of an accurate mass transfer closure the authorsfound that the overall mass transfer rate was lower comparedto the measurement However the influence of the masstransfer on the flow agreed well with experimental data

522 Zhang et al [79] Zhang et al [79] followed a proceduresimilar to that used by Darmana et al [78] although inthis case an E-E approach was used to simulate flow masstransfer and chemical reactions in square cross-sectionalbubble column [19] Zhang et al studied physical andchemical absorption of CO2 bubbles in water and in anaqueous sodium hydroxide (NaOH) solution They used abubble number density equation for coupling of flow masstransfer and chemical reaction The authors demonstratedthe influence of the mass transfer and chemical reaction onthe hydrodynamics bubble size distribution and gas holdup

53 Mixing and Dispersion

531 Bai et al [36] Bai et al [36] used LES with E-Lapproach to investigate the effect of the gas sparger and gasphase mixing in a square cross-sectional bubble columnTheliquid phase was computed using LES and a Lagrangianapproach was used for the dispersed phase They usedthe DBM and investigated the effect of two SGS modelsSmagorinsky [21] and Vreman [80] They compared thevertical liquid velocity and turbulent kinetic energy of theliquid phase at three different heights with PIV data andfound that the model proposed by Vreman performed betterthan Smagorinsky model

They further investigated the effect of the gas spargerproperties (sparged area and its location) on the hydrody-namics in a bubble column and characterized the macromix-ing of the gas phase in the column in terms of an axialdispersion coefficient They compared the predicted liquidphase dispersion coefficient with the literature correlationsas shown in Figure 15 The range of superficial gas velocityinvestigated in work is low compared to what is commonin industrial application For large-scale reactors at highsuperficial velocities Bai et al recommended to extendthe discrete bubble modelling with bubble coalescence andbreakup

54 Estimation of the Turbulent Dispersion Force In theRANS approach the drag and lift forces depend on theactual relative velocity between the phases but the ensembleequations of motion for the liquid only provide informationregarding the mean flow field The random influence ofthe turbulent eddies is considered by modelling a turbulentdispersion force By analogy with molecular movement the


1242 1248 2 4 1 2 3 05 1 15

times10minus5 times10minus5times10minus3

Figure 14 Instantaneous solution 10 s after the CO2 gas is introduced From left to right bubble positions gas velocity liquid velocity pHrespectively and concentration of dissolved CO

2 HCOminus and CO

2

minus (kmol mminus3) (from Darmana et al [77])

Ohki (1970) Towell (1972)

Deckwer (1974) Hikita (1974) Zehner (1986) Heijnen (1984)

DBM (Tracer0) DBM (Tracer1)

0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

Figure 15 Comparison of the simulated liquid phase dispersioncoefficient with the literature correlations (from Bai et al [36])

force is set proportional to the local bubble concentration gra-dient (or void fraction) with a diffusion coefficient derivedfrom the turbulent kinetic energy The value of the turbulentdispersion coefficient is chosen to get an agreement with themeasurement data and is not known as a priori

In LES the resolved part of the turbulent dispersion isimplicitly computed and hence one can use informationfrom LES for calculating the magnitude of this force Themethodology depends on scales at which LES is to be appliedFor instance at the mesoscale in the E-L approach bubblesdispersed by drag and lift through turbulent eddies can becomputed At micro-scale LES one might need to consider

bubble coalescence and breakup phenomena along with areasonable number of bubbles It can be computationallyexpensive but in view of increasing available computerpower this should become feasible soon

55 Dynamics of Turbulent Structures and the Estimation ofDesign Parameters The turbulent flows contain flow struc-tures with a wide range of length and time scales whichcontrol the transport processes The length scales of thesestructures can range from column dimensions (highest) toKolmogorov scales (lowest) However not all the scales ofturbulence contribute equally to different transport rates andmixing If only mixing is the important design criterionthen the knowledge about the mean flow pattern (large-scalestructures) would generally suffice the purpose (Ekambaraand Joshi [81]) However for the prediction of the gas holdupbubble size distribution true mass transfer coefficient andheat transfer coefficient the knowledge about all the scalesis important [82 83] Hence it is imperative to identify thescales and dynamics of turbulent flow structures and theirrelationship with the rates of different transport processThe present empirical design practices do not considerthese basic mechanisms and conceales the detailed localinformation about the relationship between the turbulenceand the equipment performance

The subject of quantification of local turbulent flowstructures and reliable estimation of transport propertieshas been reviewed by Joshi et al [84] and [82 83] Thevelocity and pressure data from LES were analyzed usingthemathematical techniques such asmultiresolution analysis[85] wavelet transforms (discrete and continuous) properorthogonal decomposition (POD) and hybrid POD-wavelettechniques (Tabib and Joshi [86] Tabib et al [87] Sathe etal [88] and Mathpati et al [89]) These techniques give thesize shape penetration depth and energy content of all the


flow structure in the system This flow structure informationcan also be used for the construction of energy spectrumand for examining the scaling laws for turbulence in bubblecolumns Such understanding of turbulence is expected toprovide better insights into the transport phenomena Onesuch attempt has been reported by Deshpande et al [90 91]

56 Comparison of Turbulence Models CFD providesdetailed flow information within single- and multiphasereactors Most popular and computationally inexpensivemodels such as k-120576 model and Reynolds stress model(RSM) are widely used to predict the mean flow patternThese models can give reliable estimation about the liquidphase mixing However they do not accurately predict theturbulence parameters such as turbulent kinetic energy andthe dissipation rate due to inbuilt modelling assumptions aswell as complexity of flow [11 24] These models are timeaveraged and hence the information related to differentturbulent structures is lost

It is known that a large number of simplifying assump-tions are made while deriving the k-120576 and RSM modelsTherefore it is important to understand the gravity of theseassumptions on the quantitative values of transport ratesof k and 120576 due to convection diffusion and turbulentdispersion It is also important to know the quantitativeestimation of production and dissipation rates of k and 120576Therefore it is important to estimate these five terms usingk-120576 RSM and LES models From the LES simulations thetime series of velocity and pressure can be stored Theseare subsequently used for the detailed comparison of k-120576RSM and LES models in terms of the rates of transport(convection molecular and turbulent diffusion) and the ratesof production and the dissipation of k and 120576 for the case ofdispersed bubbly flows [92]

6 Summary and Suggestions for Future Work

(1) E-E and E-L LES are promising approaches forpredicting unsteady buoyancy-driven flow inducinglarge-scale coherent structures for gas-liquid dis-persed flow Care should be taken to clearly identifythe scales (micro macro or meso) at which LESshould be applied in order to decide the level ofinterface resolution and modelling required Theapproach of LES at mesoscales (ie without explicitlytracking interface) using E-E and E-L description hasbeen reviewed for gas-liquid dispersed flow

(2) Pioneering work of Milelli et al [11 24] has initiatedthe LES approach for gas-liquid dispersed flows Themain contribution comes from insights in the cutofffilter requirement and SGS modelling

(3) The simulation and the experimental measurementof Deen et al [19] in a square cross-sectional bubblecolumn have triggered a systematic development ofthe two-phase LES for both E-E and E-L approaches

(4) The concept behind the LES is very simple butcharacterized by a large number of choices (regard-ing numerical and physical modelling) that all havesignificant influence on the results However it offersgreat potential in terms of determination of statisti-cal quantities and instantaneous information aboutflow structures This information can be extremelyuseful for the prediction of other physical processesbehaviour (eg transport of scalar (temperatureconcentration) chemical reactions)

(5) From LES simulation with E-EE-L approaches thatwere reviewed in this work it is recommended that

(a) The grid or filter size selection based on filtersize to bubble diameter ratio Δ119889119887 of 12 givesreasonable results

(b) The Smagorinsky constant 119862119878 is a modellingparameter rather than a physical constantAlthough the constant value of the parametergives satisfactory results for unknown config-uration it should be estimated with Germanodynamic procedure (using the overall distribu-tion of the constant through probability den-sity)

(c) The lift force is the main mechanism for thedispersion and the lift coefficient should beestimated though sensitivity of interfacial forceson values of slip velocity and gas holdupThe liftcoefficient in LES can be different from that inRANS

(d) The central difference scheme should be usedfor the discretization of advection terms for flowvariables and high-order schemes (MUSCLQUICK or Second-Order) can be used forscalar variables

(e) The minimum time for gathering statisticsshould be at least one flow through time (asdefined as ratio of the system height over thebulk (superficial) velocity)

(6) In advent of computer hardware the E-L approachappears very promising for the near future Furtherwork in mapping functions for two-way coupling canexpedite the development of this approach that canbe used as a means of both predicting the propertiesof specific turbulent flows and providing flow detailsthat can be used like data to test and refine otherturbulence-closure models

(7) The approach for BIT with extra production termsinto the SGS-turbulent kinetic energy equation (fol-lowing the procedure described by Pfleger and Becker[38]) has shown to be more effective than theapproach involving a bubble-induced viscosity [37]It can be that the enhanced eddy viscosity in LESdoes not represented as realistic physical model asthe SGS turbulent kinetic energy Nonetheless it is aninteresting issue and more work in investigating theBIT should be undertaken


(8) Treatment of the interphase forces needs more atten-tion

(a) The drag and nondrag forces (lift virtual massforce) can be modelled using resolved fieldapproaches The modelling of these forces forthe SGS and their effect on the overall simula-tion results need to be evaluated

(b) One finds strong dependency of the bubbledispersion on the value of transverse lift forcecoefficient The transverse lift which dependson the bubble-liquid relative velocity seems tobe the main mechanism responsible for thespreading of the bubbles It will help if one canestimate the separate contributions of each ofthese forces

(c) The virtual mass force has little influence onsimulation results So far a constant coefficienthas been used in all the investigations howeverdependence on void fraction has been shownin experiments It would be good to have acorrect description in order to improve resultsnear the inlet where bubble acceleration effectsare important

(9) The strong coupling between subgrid-scale (SGS)modelling and the truncation error of the numericaldiscretization can be exploited by developing dis-cretization methods where the truncation error itselffunctions as an implicit SGS model Such attempt canbe useful and go in the direction of finding a universalSGS model

(10) In order to use LES for reliable predictions at min-imum computational costs understanding of theinfluence of discretization methods boundary con-ditions wall models and numerical parameters (egconvergence criterion time steps etc) is essentialThe contribution focusing on these aspects should beundertaken for both E-EE-L approaches

(11) Substantial development has been achieved in LES inthe last decade for understanding bubbly gas-liquiddispersed flow However it is mainly restricted tolow superficial gas velocities and gas fractions Futurework should focus on industrially relevant large-scale reactors at high superficial gas velocity Themodelling of bubble coalescence and breakup mightbe necessary along with further clarity in filteringoperations

(12) Joshi and coworkers have used LES for the identifi-cation of flow structures and their dynamics Theyhave proposed a procedure to use this informationfor the estimation of design parameters Substantialadditional work is needed for finding 3D informationon the structure characteristics such as size shapevelocity and energy distributions

Nomenclature

119862119863 Drag force coefficient119862119871 Lift force coefficient119862VM Virtual mass coefficient119862TD Turbulent dispersion coefficient1198621205981 Model parameter in turbulent dissipation

energy equation (=144)1198621205982 Model parameter in turbulent dissipation

energy equation (=192)119862119878 Smagorinsky model constant119862120583BI Model constant (Sato and Seguchi

[37] model) (=06)119889119887 Mean bubble diameter119863 Diameter of the column (m)119865119875 Force originating due to pressure (Nm3)119865119866 Gravitational force per unit volume of

dispersion (Nm3)119865119871 Lift forceper unit volume of dispersion

(Nm3)119865VM Virtual mass force per unit volume of

dispersion (Nm3)119865TD Turbulent dispersion force per unit

volume of dispersion (Nm3)119865WL Wall lubrication force per unit volume of

dispersion (Nm3)119865WD Wall deformation force per unit volume of

dispersion (Nm3)119867 Height of column (m)119870 Turbulent kinetic energy per unit mass

(m2s2)119870SGS Subgrid-scale turbulent kinetic energy

(m2s3)S Characteristic of strain tensor of filtered

velocityu Instantaneous axial velocity (ms)119882 Width of column (m)

Greek Symbols

Δ Filter widthΔ119905 Simulation time step120601119891 Grid-scale component of scalar

120601119891 Resolved component of scalar

1206011015840

119891 Filtered component of scalar

120576 Turbulent energy dissipation rate per unitmass (m2s3)

120572 Fractional phase holdup120572119892 Fractional gas phase holdup120588 Density (kgm3)120588119897 Density of liquid (kgm3)120583eff119891 Effective viscosity of phase119891 (Pa s)120583eff119897 Effective viscosity of liquid phase 119891(Pa s)120583lam119897 Molecular viscosity of liquid phase 119891(Pa s)120583BI119897 Bubble-induced viscosity (Pa s)

Subscripts

F Phase 119892 = gas phase 119897 = liquid phaseBI Bubble-induced


Abbreviations

BIT Bubble-induced turbulenceE EulerianL LagrangianSGS Subgrid-scale

Acknowledgment

NGDeenwould like to thank the EuropeanResearchCoun-cil for its financial support under its Starting InvestigatorGrant scheme contract number 259521 (cutting bubbles)

References

[1] A Sokolichin G Eigenberger A Lapin and A LubbertldquoDynamic numerical simulation of gas-liquid two-phase flowsEulerEuler versus EulerLagrangerdquo Chemical Engineering Sci-ence vol 52 no 4 pp 611ndash626 1997

[2] G Bois D Jamet and O Lebaigue ldquoTowards large eddy sim-ulation of two-phase flow with phase-change direct numericalsimulation of a pseudo-turbulent two-phase condensing flowrdquoin Proceedings of the 7th International Conference onMultiphaseFlow (ICMF rsquo10) Tampa Fla USA May-June 2010

[3] A Toutant M Chandesris D Jamet and O Lebaigue ldquoJumpconditions for filtered quantities at an under-resolved discon-tinuous interfacemdashpart 1 theoretical developmentrdquo Interna-tional Journal of Multiphase Flow vol 35 no 12 pp 1100ndash11182009

[4] A Toutant M Chandesris D Jamet and O Lebaigue ldquoJumpconditions for filtered quantities at an under-resolved discon-tinuous interfacemdashpart 2 a priori testsrdquo International Journalof Multiphase Flow vol 35 no 12 pp 1119ndash1129 2009

[5] S Magdeleine B Mathieu O Lebaigue and C Morel ldquoDNSup-scaling applied to volumetric interfacial area transportequationrdquo in Proceedings of the 7th International Conference onMultiphase Flow (ICMF rsquo10) p 12 Tampa Fla USA May-June2010

[6] D Lakehal ldquoLEIS for the prediction of turbulent multi-fluidflows applied to thermal hydraulics applicationsrdquo in Proceedingsof the XFD4NRS Grenoble France September 2008

[7] D Lakehal M Fulgosi S Banerjee and G Yadigaroglu ldquoTur-bulence and heat exchange in condensing vapor-liquid flowrdquoPhysics of Fluids vol 20 no 6 Article ID 065101 2008

[8] D Bestion ldquoApplicability of two-phase CFD to nuclear reactorthermalhydraulics and elaboration of best practice guidelinesrdquoNuclear Engineering and Design vol 253 pp 311ndash321 2012

[9] B Niceno M T Dhotre and N G Deen ldquoOne-equation sub-grid scale (SGS) modelling for Euler-Euler large eddy simula-tion (EELES) of dispersed bubbly flowrdquo Chemical EngineeringScience vol 63 no 15 pp 3923ndash3931 2008

[10] B Niceno M Boucker and B L Smith ldquoEuler-Euler large eddysimulation of a square cross-sectional bubble column usingthe Neptune CFD coderdquo Science and Technology of NuclearInstallations vol 2009 Article ID 410272 2009

[11] M Milelli B L Smith and D Lakehal ldquoLarge-eddy simulationof turbulent shear flows laden with bubblesrdquo in Direct andLarge-Eddy Simulation IV B J Geurts R Friedrich andO Metais Eds pp 461ndash470 Kluwer Academic PublishersAmsterdam The Netherlands 2001

[12] D A Drew ldquoAveraged field equations for two-phase mediardquoStudies in Applied Mathematics vol 50 no 2 pp 133ndash165 1971

[13] S Elgobashi ldquoParticle-laden turbulent flows direct simulationand closuremodelsrdquoApplied Scientific Research vol 48 no 3-4pp 301ndash314 1991

[14] C T Crowe M P Sharma and D E Stock ldquoThe particle-source-in cell (PSI-CELL) model for gas-droplet flowsrdquo Journalof Fluids Engineering vol 99 no 2 pp 325ndash332 1977

[15] GHuTowards large eddy simulation of dispersed gas-liquid two-phase turbulent flows [PhD thesis] Mechanical and AerospaceEngineering Department West Virginia University Morgan-town WVa USA 2005

[16] N G Deen M V S Annaland and J A M Kuipers ldquoMulti-scale modeling of dispersed gas-liquid two-phase flowrdquo Chemi-cal Engineering Science vol 59 pp 1853ndash1861 2004

[17] M V Tabib S A Roy and J B Joshi ldquoCFD simulation ofbubble columnmdashan analysis of interphase forces and turbulencemodelsrdquo Chemical Engineering Journal vol 139 no 3 pp 589ndash614 2008

[18] M T Dhotre B Niceno B L Smith and M Simiano ldquoLarge-eddy simulation (LES) of the large scale bubble plumerdquo Chemi-cal Engineering Science vol 64 no 11 pp 2692ndash2704 2009

[19] N G Deen T Solberg and B H Hjertager ldquoLarge eddysimulation of the gas-liquid flow in a square cross-sectionedbubble columnrdquo Chemical Engineering Science vol 56 no 21-22 pp 6341ndash6349 2001

[20] MTDhotre BNiceno andB L Smith ldquoLarge eddy simulationof a bubble column using dynamic sub-grid scale modelrdquoChemical Engineering Journal vol 136 no 2-3 pp 337ndash3482008

[21] J Smagorinsky ldquoGeneral circulation experiments with theprimitive equationsrdquo Monthly Weather Review vol 91 pp 99ndash165 1963

[22] P Moin and J Kim ldquoNumerical investigations of turbulentchannel flowrdquo Journal of Fluid Mechanics vol 118 pp 341ndash3771982

[23] W Jones andMWille ldquoLarge eddy simulation of a jet in a crossflowrdquo in Proceedings of the 10th Symposium on Turbulent ShearFlows pp 41ndash46 The Pennsylvania State University 1995


[25] D Lakehal B L Smith and M Milelli ldquoLarge-eddy simulationof bubbly turbulent shear flowsrdquo Journal of Turbulence vol 3pp 1ndash20 2002

[26] D Zhang N G Deen and J A M Kuipers ldquoNumericalsimulation of the dynamic flow behavior in a bubble column astudy of closures for turbulence and interface forcesrdquo ChemicalEngineering Science vol 61 no 23 pp 7593ndash7608 2006

[27] D Lain ldquoDynamic three-dimensional simulation of gas liquidflow in a cylindrical bubble column Latin Americanrdquo AppliedResearch vol 39 pp 317ndash329 2009

[28] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[29] S Bove T Solbergt and B H Hjertager ldquoNumerical aspects ofbubble column simulationsrdquo International Journal of ChemicalReactor Engineering vol 2 no A1 pp 1ndash22 2004


[30] M V Tabib and P Schwarz ldquoQuantifying sub-grid scale (SGS)turbulent dispersion force and its effect using one-equation SGSlarge eddy simulation (LES) model in a gas-liquid and a liquid-liquid systemrdquo Chemical Engineering Science vol 66 no 14 pp3071ndash3086 2011

[31] E I V van den Hengel N G Deen and J A M KuipersldquoApplication of coalescence and breakup models in a discretebubble model for bubble columnsrdquo Industrial and EngineeringChemistry Research vol 44 no 14 pp 5233ndash5245 2005

[32] G Hu and I Celik ldquoEulerian-Lagrangian based large-eddysimulation of a partially aerated flat bubble columnrdquo ChemicalEngineering Science vol 63 no 1 pp 253ndash271 2008

[33] D Darmana N G Deen J A M KuipersW K Harteveld andR F Mudde ldquoNumerical study of homogeneous bubbly flowinfluence of the inlet conditions to the hydrodynamic behaviorrdquoInternational Journal of Multiphase Flow vol 35 no 12 pp1077ndash1099 2009

[34] R Sungkorn J J Derksen and J G Khinast ldquoModeling ofturbulent gas-liquid bubbly flows using stochastic Lagrangianmodel and lattice-Boltzmann schemerdquo Chemical EngineeringScience vol 66 no 12 pp 2745ndash2757 2011

[35] W Bai N G Deen and J A M Kuipers ldquoNumerical analysisof the effect of gas sparging on bubble column hydrodynamicsrdquoIndustrial and Engineering Chemistry Research vol 50 no 8 pp4320ndash4328 2011

[36] W Bai N G Deen and J A M Kuipers ldquoNumerical investiga-tion of gas holdup and phasemixing in bubble column reactorsrdquoIndustrial amp Engineering Chemistry Research vol 51 no 4 pp1949ndash1961 2012

[37] Y Sato and K Sekoguchi ldquoLiquid velocity distribution in two-phase bubble flowrdquo International Journal of Multiphase Flowvol 2 no 1 pp 79ndash95 1975

[38] D Pfleger and S Becker ldquoModelling and simulation of thedynamic flow behaviour in a bubble columnrdquo Chemical Engi-neering Science vol 56 no 4 pp 1737ndash1747 2001

[39] A A Troshko and Y A Hassan ldquoA two-equation turbulencemodel of turbulent bubbly flowsrdquo International Journal ofMultiphase Flow vol 27 no 11 pp 1965ndash2000 2001

[40] M Sommerfeld ldquoValidation of a stochastic Lagrangian mod-elling approach for inter-particle collisions in homogeneousisotropic turbulencerdquo International Journal of Multiphase Flowvol 27 no 10 pp 1829ndash1858 2001

[41] M Sommerfeld G Kohnen and M Rueger ldquoSome openquestions and inconsistencies of Lagrangian particle dispersionmodelsrdquo inProceedings of the 9th SymposiumonTurbulent ShearFlows Kyoto Japan 1993 paper no 15-1

[42] Y Sato M Sadatomi and K Sekoguchi ldquoMomentum andheat transfer in two-phase bubble flow-I Theoryrdquo InternationalJournal of Multiphase Flow vol 7 no 2 pp 167ndash177 1981

[43] D Pfleger S Gomes N Gilbert and H G Wagner ldquoHydro-dynamic simulations of laboratory scale bubble columns fun-damental studies of the Eulerian-Eulerian modeling approachrdquoChemical Engineering Science vol 54 no 21 pp 5091ndash50991999

[44] M Ishii and N Zuber ldquoDrag coefficient and relative velocity inbubbly droplet or particulate flowsrdquo AIChE Journal vol 25 no5 pp 843ndash855 1979

[45] A Tomiyama ldquoDrag lift and virtual mass forces acting on a sin-gle bubblerdquo in Proceedings of the 3rd International Symposiumon Two-Phase Flow Modeling and Experimentation Pisa ItalySeptember 2004

[46] R M Wellek A K Agrawal and A H P Skelland ldquoShape ofliquid drops moving in liquid mediardquo AIChE Journal vol 12no 5 pp 854ndash862 1966

[47] A Tomiyama ldquoStruggle with computional bubble dynamicsrdquo inProceedings of the 3rd International Conference on Multi-PhaseFlow (ICMF rsquo98) Lyon France June 1998

[48] R Clift J R Grace and M E Weber Bubbles Drops andParticles Academic Press New York NY USA 1978

[49] M Milelli A numerical analysis of confined turbulent bubbleplume [Diss EH no 14799] Swiss Federal Institute of Technol-ogy Zurich Switzerland 2002

[50] J Bardina J H Ferziger and W C Reynolds ldquoImprovedsubgridmodels for large eddy simulationrdquo AIAApaper 80-13581980

[51] P E Anagbo and J K Brimacombe ldquoPlume characteristicsand liquid circulation in gas injection through a porous plugrdquoMetallurgical Transactions B vol 21 no 4 pp 637ndash648 1990

[52] M R Bhole S Roy and J B Joshi ldquoLaser doppler anemometermeasurements in bubble column effect of spargerrdquo Industrialand Engineering Chemistry Research vol 45 no 26 pp 9201ndash9207 2006

[53] S Becker A Sokolichin and G Eigenberger ldquoGas-liquid flowin bubble columns and loop reactorsmdashpart II comparison ofdetailed experiments and flow simulationsrdquoChemical Engineer-ing Science vol 49 no 24 part 2 pp 5747ndash5762 1994

[54] A Sokolichin and G Eigenberger ldquoApplicability of the standardk-120576 turbulence model to the dynamic simulation of bubblecolumnsmdashpart I detailed numerical simulationsrdquo ChemicalEngineering Science vol 54 no 13-14 pp 2273ndash2284 1999

[55] M Simiano Experimental investigation of large-scale threedimensional bubble plume dynamics [Dissertation no 16220]Swiss Federal Institute of Technology Zurich Switzerland2005

[56] S Lain and M Sommerfeld ldquoLES of gas-liquid flow in acylindrical laboratory bubble columnrdquo in Proceedings of the5th International Conference on Multiphase Flow (ICMF rsquo04)Yokohama Japan 2004 paper no 337

[57] M Lopez de Bertodano Turbulent bubbly two-phase flow in atriangular duct [PhD thesis] Rensselaer Polytechnic InstituteTroy NY USA 1992

[58] E Delnoij F A Lammers J A M Kuipers and W P Mvan Swaaij ldquoDynamic simulation of dispersed gas-liquid two-phase flowusing a discrete bubblemodelrdquoChemical EngineeringScience vol 52 no 9 pp 1429ndash1458 1997

[59] E Delnoij J A M Kuipers and W P M Van Swaaij ldquoAthree-dimensional CFD model for gas-liquid bubble columnsrdquoChemical Engineering Science vol 54 no 13-14 pp 2217ndash22261999

[60] D Broder and M Sommerfeld ldquoAn advanced LIF-PLV systemfor analysing the hydrodynamics in a laboratory bubble columnat higher void fractionsrdquoExperiments in Fluids vol 33 no 6 pp826ndash837 2002

[61] W K Harteveld J E Julia R F Mudde and H E A vanden Akker ldquoLarge scale vortical structures in bubble columnsfor gas fractions in the range of 5ndash25rdquo in Proceedings of the16th International Congress of Chemical and Process Engineering(CHISA rsquo04) Prague Czech Republic 2004

[62] J B Joshi and M M Sharma ldquoA circulation cell model forbubble columnsrdquo Transactions of the Institution of ChemicalEngineers vol 57 no 4 pp 244ndash251 1979


[63] J B Joshi ldquoAxial mixing in multiphase contactorsmdasha unifiedcorrelationrdquo Transactions of the Institution of Chemical Engi-neers vol 58 no 3 pp 155ndash165 1980

[64] V V Ranade and J B Joshi ldquoFlow generated by pitched bladeturbines 1 Measurements using laser Doppler anemometerrdquoChemical Engineering Communications vol 81 pp 197ndash2241989

[65] V V Ranade J R Bourne and J B Joshi ldquoFluid mechanics andblending in agitated tanksrdquo Chemical Engineering Science vol46 no 8 pp 1883ndash1893 1991

[66] T Kumaresan and J B Joshi ldquoEffect of impeller design on theflow pattern and mixing in stirred tanksrdquo Chemical EngineeringJournal vol 115 no 3 pp 173ndash193 2006

[67] J B Joshi M M Sharma Y T Shah C P P Singh M Allyand G E Klinzing ldquoHeat transfer in multiphase contactorsrdquoChemical Engineering Communications vol 6 no 4-5 pp 257ndash271 1980

[68] M T Dhotre and J B Joshi ldquoTwo-dimensional CFD model forthe prediction of flow pattern pressure drop and heat transfercoefficient in bubble column reactorsrdquo Chemical EngineeringResearch and Design vol 82 no 6 pp 689ndash707 2004

[69] M T Dhotre K Ekambara and J B Joshi ldquoCFD simulationof sparger design and height to diameter ratio on gas hold-upprofiles in bubble column reactorsrdquo Experimental Thermal andFluid Science vol 28 no 5 pp 407ndash421 2004

[70] A V Kulkarni S V Badgandi and J B Joshi ldquoDesign ofring and spider type spargers for bubble column reactorexperimental measurements and CFD simulation of flow andweepingrdquoChemical Engineering Research andDesign vol 87 no12 pp 1612ndash1630 2009

[71] J B Joshi andMM Sharma ldquoMass transfer and hydrodynamiccharacteristics of gas inducing type of agitated contactorsrdquoCanadian Journal of Chemical Engineering vol 55 no 6 pp683ndash695 1977

[72] B N Murthy N A Deshmukh A W Patwardhan and J BJoshi ldquoHollow self-inducing impellers flow visualization andCFD simulationrdquo Chemical Engineering Science vol 62 no 14pp 3839ndash3848 2007

[73] K S M S Raghava Rao V B Rewatkar and J B Joshi ldquoCriticalimpeller speed for solid suspension in mechanically agitatedcontactorsrdquo AIChE Journal vol 34 no 8 pp 1332ndash1340 1988

[74] V B Rewatkar K S M S Raghava Rao and J B JoshildquoCritical impeller speed for solid suspension in mechanicallyagitated three-phase reactors 1 Experimental partrdquo Industrialand Engineering Chemistry Research vol 30 no 8 pp 1770ndash1784 1991

[75] B N Murthy R S Ghadge and J B Joshi ldquoCFD simulations ofgas-liquid-solid stirred reactor prediction of critical impellerspeed for solid suspensionrdquo Chemical Engineering Science vol62 no 24 pp 7184ndash7195 2007

[76] J B Joshi and V V Ranade ldquoComputational fluid dynamics fordesigning process equipment expectations current status andpath forwardrdquo Industrial and Engineering Chemistry Researchvol 42 no 6 pp 1115ndash1128 2003

[77] D Darmana N G Deen and J A M Kuipers ldquoDetailed mod-eling of hydrodynamics mass transfer and chemical reactionsin a bubble column using a discrete bubble modelrdquo ChemicalEngineering Science vol 60 no 12 pp 3383ndash3404 2005

[78] D Darmana R L B Henket N G Deen and J A M KuipersldquoDetailed modelling of hydrodynamics mass transfer andchemical reactions in a bubble column using a discrete bubble

model chemisorption of CO2 into NaOH solution numericaland experimental studyrdquo Chemical Engineering Science vol 62no 9 pp 2556ndash2575 2007

[79] D Zhang N G Deen and J A M Kuipers ldquoEuler-eulermodeling of flow mass transfer and chemical reaction in abubble columnrdquo Industrial and Engineering Chemistry Researchvol 48 no 1 pp 47ndash57 2009

[80] A W Vreman ldquoAn eddy-viscosity sub-grid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[81] K Ekambara and J B Joshi ldquoAxial mixing in laminar pipeflowsrdquo Chemical Engineering Science vol 59 no 18 pp 3929ndash3944 2004

[82] C S Mathpati S S Deshpande and J B Joshi ldquoComputationaland experimental fluid dynamics of jet loop reactorrdquo AIChEJournal vol 55 no 10 pp 2526ndash2544 2009

[83] C S Mathpatii M V Tabib S S Deshpande and J B JoshildquoDynamics of flow structures and transport phenomena 2Relationship with design objectives and design optimizationrdquoIndustrial and Engineering Chemistry Research vol 48 no 17pp 8285ndash8311 2009

[84] J B Joshi V S Vitankar A A Kulkarni M T Dhotre andK Ekambara ldquoCoherent flow structures in bubble columnreactorsrdquo Chemical Engineering Science vol 57 no 16 pp 3157ndash3183 2002

[85] S S Deshpande J B Joshi V R Kumar and B D Kulka-rni ldquoIdentification and characterization of flow structures inchemical process equipment using multiresolution techniquesrdquoChemical Engineering Science vol 63 no 21 pp 5330ndash53462008

[86] MV Tabib and J B Joshi ldquoAnalysis of dominant flow structuresand their flow dynamics in chemical process equipment usingsnapshot proper orthogonal decomposition techniquerdquo Chem-ical Engineering Science vol 63 no 14 pp 3695ndash3715 2008

[87] M V Tabib M J Sathe S S Deshpande and J B JoshildquoA hybridized snapshot proper orthogonal decomposition-discrete wavelet transform technique for the analysis of flowstructures and their time evolutionrdquo Chemical EngineeringScience vol 64 no 21 pp 4319ndash4340 2009

[88] M J Sathe I HThaker T E Strand and J B Joshi ldquoAdvancedPIVLIF and shadowgraphy system to visualize flow structurein two-phase bubbly flowsrdquo Chemical Engineering Science vol65 no 8 pp 2431ndash2442 2010

[89] C S Mathpati M J Sathe and J B Joshi ldquoReply to lsquocommentson dynamics of flow structures and transport phenomenamdashpartI experimental and numerical techniques for identification andenergy content of flow structuresrsquordquo Industrial and EngineeringChemistry Research vol 49 no 9 pp 4471ndash4473 2010

[90] S S Deshpande C S Mathpati S S Gulawani J B Joshi andV Ravi kumar ldquoEffect of flow structures on heat transfer insingle and multiphase jet reactorsrdquo Industrial and EngineeringChemistry Research vol 48 no 21 pp 9428ndash9440 2009

[91] S S Deshpande M V Tabib J B Joshi V Ravi Kumar andB D Kulkarni ldquoAnalysis of flow structures and energy spectrain chemical process equipmentrdquo Journal of Turbulence vol 11article N5 pp 1ndash39 2010

[92] Z Khan C S Mathpati and J B Joshi ldquoComparison ofturbulence models and dynamics of turbulence structures inbubble column reactors effects of sparger design and superficialgas velocityrdquo Chemical Engineering Science In press

Hindawi Publishing CorporationInternational Journal of Chemical EngineeringVolume 2013 Article ID 343276 22 pageshttpdxdoiorg1011552013343276

Review ArticleLarge Eddy Simulation for Dispersed Bubbly Flows A Review

M T Dhotre1 N G Deen2 B Niceno3 Z Khan4 and J B Joshi45

1 ABB Switzerland Ltd 5400 Baden Switzerland2Multiphase Reactors Group Department of Chemical Engineering and ChemistryEindhoven University of Technology The Netherlands

3 Laboratory for Thermal-Hydraulics Nuclear Energy and Safety Department Paul Scherrer Institute Switzerland4 Institute of Chemical Technology Matunga Mumbai 400 019 India5Homi Bhabha National Institute Anushakti Nagar Mumbai 400 094 India

Correspondence should be addressed to M T Dhotre maheshdhotregmailcom

Received 14 June 2012 Revised 31 October 2012 Accepted 18 November 2012

Academic Editor Nandkishor Nere

Copyright copy 2013 M T Dhotre et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Large eddy simulations (LES) of dispersed gas-liquid flows for the prediction of flow patterns and its applications have beenreviewed The published literature in the last ten years has been analysed on a coherent basis and the present status has beenbrought out for the LES Euler-Euler and Euler-Lagrange approaches Finally recommendations for the use of LES in dispersed gasliquid flows have been made

1 Introduction

Gas-liquid flows are often encountered in the chemicalprocess industry but also numerous examples can be found inpetroleum pharmaceutical agricultural biochemical foodelectronic and power-generation industries The modellingof gas-liquid flows and their dynamics has become increas-ingly important in these areas in order to predict flowbehaviour with greater accuracy and reliabilityThere are twomain flow regimes in gas-liquid flows separated (eg annularflow in vertical pipes stratified flow in horizontal pipes) anddispersed flow (eg droplets or bubbles in liquid) In thiswork we consider only dispersed bubbly flows

Dispersed Bubbly Flow The description of bubbly flowsinvolves modelling of a deformable (gas-liquid) interfaceseparating the phases discontinuities of properties across thephase interface the exchange between the phase and turbu-lence modelling Most of the dispersed flowmodels are basedon the concept of a domain in the static (Eulerian) referenceframe for description of the continuous phase with additionof a reference frame for the description of the dispersed phaseThe dispersed phase may be described in the same staticreference frame as the continuous leading to the Eulerian-Eulerian (E-E) approach or in a dynamic (Lagrangian)

reference frame leading to the Eulerian-Lagrangian (E-L)approach

In the E-L approach the continuous liquid phase ismodelled using an Eulerian approach and the dispersed gasphase is treated in a Lagrangian way that is the individualbubbles in the system are tracked by solving Newtonrsquos secondlaw while accounting for the forces acting on the bubblesAn advantage here is the possibility to model each individualbubble also incorporating bubble coalescence and breakupdirectly Since each bubble path can be calculated accuratelywithin the control volume no numerical diffusion is intro-duced into the dispersed phase computation However adisadvantage is the larger the system gets the more equationsneed to be solved that is one for every bubble

The E-E approach describes both phases as two continu-ous fluids each occupying the entire domain and interpene-trating each other The conservation equations are solved foreach phase together with interphase exchange termsThe E-Eapproach can suffer from numerical diffusion However withthe aid of higher order discretization schemes the numericaldiffusion can be reduced sufficiently and can offer the sameorder of accuracy as with E-L approach (Sokolichin et al[1]) The advantage here is that the computational demandsare far lower compared to the E-L approach particularly for


















h

db





120601119891 = 120601119891⏟⏟⏟⏟⏟⏟⏟

resolved

+ 1206011015840

119891⏟⏟⏟⏟⏟⏟⏟

subgrid

(1)


120597

120597119905(120572119891120588119891u119891) + Δ sdot (120572119891120588119891u119891) = 0 (2)

120597

120597119905(120572119891120588119891u119891) + Δ sdot (120572119891120588119891u119891u119891)





minus2

3119868 (nabla sdot u119891)) (4)












119898119887

119889v119889119905

= sum F (5)



(6)












120583eff119897 = 120583lam119897 + 120588119897(119862119878Δ)2radicS2 (7)










Table1Com

paris

onof

LESsim

ulations

No

Author

Colum

nD(times

W)times

H(m

)Sparger

desig

nBu

bble

diam

eter

Rangeo

f119881119866m

sNum

bero

fgrid

cells

Filter

SGSMod

elBIT

closure

mod

els+

Interfa

cialforcec


Drag

119862119863

Lift

119862119871

Virtual

mass

119862VM

(1)

Deenetallowast[19

]015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

32times

32times

90

Δ=5ndash10mm

Smagorinsky

119862119878=01

(1)

(4)

05

05

(2)

Bove

etal

[29]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

9times

6times

30

Δ=10ndash17m

mSm

agorinsky

119862119878=005ndash0

2mdash

(24)

05

05

(3)

Zhangetal

[26]


90

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

15times

15times

90

mdashSm

agorinsky

119862119878=008ndash0

20

(123)

(2)

(4)

Tabibetal

[17]

015times

10

Perfo

rated

plate

5mm

200

times10minus3

1500

00Δ

=3m

mSm

agorinsky

119862119878=01

(1)

(1)

(5)

Dho

treetal

[20]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus5

15times

15times

50

15times

15times

100

119889119861lt

Δ

Smagorinsky

119862119878=012

Germano

(1)

(1)

05

05

(6)

Nicenoetal

[9]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

30times

30times

90

Δisequaltothe

grid

spacing

Δ119889119887=15

Smagorinsky

119862119878=012

OEM

(12)

(15)

05

05

(7)

Dho

treetal

[18]

20

times34

Perfo

rated

plate

26m

m49

times10minus3

mdash28m

mlt

Δlt

40m

mSm

agorinsky

119862119878=012

(1)

(5)

05

05

(8)

Nicenoetal

[10]

015times

015times

10

Perfo

rated

plate

4mm

49

times10minus3

30times

30times

100

Δ=5m

mOEM

Germano

(12)

(45)

05

05

(9)

TabibandSchw

arz

[30]

015times

10

Perfo

rated

plate

3ndash5m

m200

times10minus3

mdashmdash

OEM

(2)

Max

[(1)(6

)]

minus005

mdash

(10)

vandenHengel

etal[31]

015times

10

Perfo

rated

plate

3mm

49

times10minus3

15times

15times

45

Δ=

10mm

Smagorinsky

(1)

(3)

05

05

(11)

HuandCelik

[32]

015times

008times

10

Pipe

sparger

16mm

0660times

10minus3

96times

50times

8

120times

80times

10

PSI-ballmetho

d2m

mSm

agorinsky

119862119878=0032

(4)

(3)

05

05

(12)

Lain

[27]

014times

10

Porous

mem

brane

26m

m0272times

10minus3

30times

30times

50

45times

45times

10

Δ119889119887=18

Smagorinsky

119862119878=01

(4)

05

(13)

Darmanae

tal

[33]

02

times003times

10

Multip

oint

gas

injection

4mm

70

times10minus3

80times

12times

400

Δ=

25mm

Vrem

an

119862119878=01

mdash(3)

05

(14)

Sung

korn

etal

[34]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

30times

30times

90

Δisequaltothe

grid

spacing

Δ119889119887=12

5

Smagorinsky

119862119878=010ndash0

12(6)

(3)

05

(15)

Baietal[35]B

aietal[36]

015times

015times

045

Perfo

rated

plate

5mm

50

times10minus3

100

times10minus3

150

times10minus3

250

times10minus3

15times

15times

45

20times

20times

60

30times

30times

90

mdashVrem

anSm

agorinsky

119862119878=01

mdash(3)

05

05

Thea

utho

rshave

studied

thee

ffectof

thisforceo

vera

range

+Num

bersindicatedarer

efered

toTable2

++Num

bersindicatedarer

efered

toTable3



No Author 120583BIT 119878119896BIT 119878



120583BIT =

120588119871120572119866119862120583BIT1198891198611003816100381610038161003816U119866 minus U119871

1003816100381610038161003816

0 0


1003816100381610038161003816M1198701003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

120572119871

119896119871

119862120598119878119896BIT


1003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

0453119862119863

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

2119862VM119889119861

119878119896BIT






120597119896SGS120597119905


11989632

SGSΔ

(8)


is defined as

119875119896SGS= 120583SGS

10038161003816100381610038161003816119878119894119895

10038161003816100381610038161003816 (9)


120583SGS = 119862119896Δ11989612

SGS (10)



120583BI119897 = 120588119891 119862120583BI 120572119892 11988911988710038161003816100381610038161003816u119892minusu119897

10038161003816100381610038161003816 (11)







3 Numerical Details





No Author Equation

(1) Ishii and Zuber [44] 119862119863

=24Re

(1 + 01Re075)

(2) Tomiyama [45]119862119863

=(83) 119864119900 (1 minus 119864

2)

11986423

119864119900 + 16 (1 minus 1198642) 11986443

119865(119864)minus2

119864 =1

1 + 01631198641199000757

(Wellek et al [46])



2

(1 minus 1198642)


= max [min [16

Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]


2

311986411990012

119864119900 = 119892Δ1205881198892

119866120590

(5) Clift et al [48]119862119863 =

24

Re(1 + 015Re0687

119875) Re119875 le 800

044 Re119875 gt 800


Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]

003

0025

002

0015

001

0005

00 005 01 015

Column width (m)

No BITSato

PflegerExperiment

2s

2)

Turb

ule

nt

kin

etic

en

ergy

(m

(a)

024

022

02

018

016

014

012

01

008

006

004

SGS

reso

lved

en

ergy

0 005 01 015

Column width (m)

No BITSato

Pfleger

(b)















0

02

04

06

08

100 110 120 130 140 150

Time (s)

LDA

LES

minus02

uy

L(m

s)

119896-ε








03

025

02

015

01

005

0

minus005

minus010 01 02 03 04 05 06 07 08 09 1

(ms

)

xD


Inlet 2Inlet 3

(a)

Inlet 1

Inlet 2

Inlet 3

25

2

15

1

05

00 005 01 015 02 025 03 035 04 045

yH

(kg

m s)

(b)













0 02 04 06 08 1

0

01

02

03

04

05

v mL

(ms

)

xD

= 008= 01

= 015

= 02Exp (yH = 063)

minus01

(mdash)

119862119878 119862119878

119862119878

119862119878


0

01

02

03

04

05

06

07

0 02 04 06 08 1

= 008= 01

= 015

= 02Exp (yH = 063)

v mG

(ms

)

xD (mdash)

119862119878 119862119878

119862119878

119862119878



0

0002

0004

0006

0008

001

0012

0 005 01 015 02 025 03

PD

F

CS











Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS


0e+00

25eminus03

5eminus03

75eminus03


(a)


(b)





0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

















































































































h

db





120601119891 = 120601119891⏟⏟⏟⏟⏟⏟⏟

resolved

+ 1206011015840

119891⏟⏟⏟⏟⏟⏟⏟

subgrid

(1)


120597

120597119905(120572119891120588119891u119891) + Δ sdot (120572119891120588119891u119891) = 0 (2)

120597

120597119905(120572119891120588119891u119891) + Δ sdot (120572119891120588119891u119891u119891)





minus2

3119868 (nabla sdot u119891)) (4)












119898119887

119889v119889119905

= sum F (5)



(6)












120583eff119897 = 120583lam119897 + 120588119897(119862119878Δ)2radicS2 (7)










Table1Com

paris

onof

LESsim

ulations

No

Author

Colum

nD(times

W)times

H(m

)Sparger

desig

nBu

bble

diam

eter

Rangeo

f119881119866m

sNum

bero

fgrid

cells

Filter

SGSMod

elBIT

closure

mod

els+

Interfa

cialforcec


Drag

119862119863

Lift

119862119871

Virtual

mass

119862VM

(1)

Deenetallowast[19

]015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

32times

32times

90

Δ=5ndash10mm

Smagorinsky

119862119878=01

(1)

(4)

05

05

(2)

Bove

etal

[29]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

9times

6times

30

Δ=10ndash17m

mSm

agorinsky

119862119878=005ndash0

2mdash

(24)

05

05

(3)

Zhangetal

[26]


90

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

15times

15times

90

mdashSm

agorinsky

119862119878=008ndash0

20

(123)

(2)

(4)

Tabibetal

[17]

015times

10

Perfo

rated

plate

5mm

200

times10minus3

1500

00Δ

=3m

mSm

agorinsky

119862119878=01

(1)

(1)

(5)

Dho

treetal

[20]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus5

15times

15times

50

15times

15times

100

119889119861lt

Δ

Smagorinsky

119862119878=012

Germano

(1)

(1)

05

05

(6)

Nicenoetal

[9]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

30times

30times

90

Δisequaltothe

grid

spacing

Δ119889119887=15

Smagorinsky

119862119878=012

OEM

(12)

(15)

05

05

(7)

Dho

treetal

[18]

20

times34

Perfo

rated

plate

26m

m49

times10minus3

mdash28m

mlt

Δlt

40m

mSm

agorinsky

119862119878=012

(1)

(5)

05

05

(8)

Nicenoetal

[10]

015times

015times

10

Perfo

rated

plate

4mm

49

times10minus3

30times

30times

100

Δ=5m

mOEM

Germano

(12)

(45)

05

05

(9)

TabibandSchw

arz

[30]

015times

10

Perfo

rated

plate

3ndash5m

m200

times10minus3

mdashmdash

OEM

(2)

Max

[(1)(6

)]

minus005

mdash

(10)

vandenHengel

etal[31]

015times

10

Perfo

rated

plate

3mm

49

times10minus3

15times

15times

45

Δ=

10mm

Smagorinsky

(1)

(3)

05

05

(11)

HuandCelik

[32]

015times

008times

10

Pipe

sparger

16mm

0660times

10minus3

96times

50times

8

120times

80times

10

PSI-ballmetho

d2m

mSm

agorinsky

119862119878=0032

(4)

(3)

05

05

(12)

Lain

[27]

014times

10

Porous

mem

brane

26m

m0272times

10minus3

30times

30times

50

45times

45times

10

Δ119889119887=18

Smagorinsky

119862119878=01

(4)

05

(13)

Darmanae

tal

[33]

02

times003times

10

Multip

oint

gas

injection

4mm

70

times10minus3

80times

12times

400

Δ=

25mm

Vrem

an

119862119878=01

mdash(3)

05

(14)

Sung

korn

etal

[34]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

30times

30times

90

Δisequaltothe

grid

spacing

Δ119889119887=12

5

Smagorinsky

119862119878=010ndash0

12(6)

(3)

05

(15)

Baietal[35]B

aietal[36]

015times

015times

045

Perfo

rated

plate

5mm

50

times10minus3

100

times10minus3

150

times10minus3

250

times10minus3

15times

15times

45

20times

20times

60

30times

30times

90

mdashVrem

anSm

agorinsky

119862119878=01

mdash(3)

05

05

Thea

utho

rshave

studied

thee

ffectof

thisforceo

vera

range

+Num

bersindicatedarer

efered

toTable2

++Num

bersindicatedarer

efered

toTable3



No Author 120583BIT 119878119896BIT 119878



120583BIT =

120588119871120572119866119862120583BIT1198891198611003816100381610038161003816U119866 minus U119871

1003816100381610038161003816

0 0


1003816100381610038161003816M1198701003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

120572119871

119896119871

119862120598119878119896BIT


1003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

0453119862119863

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

2119862VM119889119861

119878119896BIT






120597119896SGS120597119905


11989632

SGSΔ

(8)


is defined as

119875119896SGS= 120583SGS

10038161003816100381610038161003816119878119894119895

10038161003816100381610038161003816 (9)


120583SGS = 119862119896Δ11989612

SGS (10)



120583BI119897 = 120588119891 119862120583BI 120572119892 11988911988710038161003816100381610038161003816u119892minusu119897

10038161003816100381610038161003816 (11)







3 Numerical Details





No Author Equation

(1) Ishii and Zuber [44] 119862119863

=24Re

(1 + 01Re075)

(2) Tomiyama [45]119862119863

=(83) 119864119900 (1 minus 119864

2)

11986423

119864119900 + 16 (1 minus 1198642) 11986443

119865(119864)minus2

119864 =1

1 + 01631198641199000757

(Wellek et al [46])



2

(1 minus 1198642)


= max [min [16

Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]


2

311986411990012

119864119900 = 119892Δ1205881198892

119866120590

(5) Clift et al [48]119862119863 =

24

Re(1 + 015Re0687

119875) Re119875 le 800

044 Re119875 gt 800


Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]

003

0025

002

0015

001

0005

00 005 01 015

Column width (m)

No BITSato

PflegerExperiment

2s

2)

Turb

ule

nt

kin

etic

en

ergy

(m

(a)

024

022

02

018

016

014

012

01

008

006

004

SGS

reso

lved

en

ergy

0 005 01 015

Column width (m)

No BITSato

Pfleger

(b)















0

02

04

06

08

100 110 120 130 140 150

Time (s)

LDA

LES

minus02

uy

L(m

s)

119896-ε








03

025

02

015

01

005

0

minus005

minus010 01 02 03 04 05 06 07 08 09 1

(ms

)

xD


Inlet 2Inlet 3

(a)

Inlet 1

Inlet 2

Inlet 3

25

2

15

1

05

00 005 01 015 02 025 03 035 04 045

yH

(kg

m s)

(b)













0 02 04 06 08 1

0

01

02

03

04

05

v mL

(ms

)

xD

= 008= 01

= 015

= 02Exp (yH = 063)

minus01

(mdash)

119862119878 119862119878

119862119878

119862119878


0

01

02

03

04

05

06

07

0 02 04 06 08 1

= 008= 01

= 015

= 02Exp (yH = 063)

v mG

(ms

)

xD (mdash)

119862119878 119862119878

119862119878

119862119878



0

0002

0004

0006

0008

001

0012

0 005 01 015 02 025 03

PD

F

CS











Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS


0e+00

25eminus03

5eminus03

75eminus03


(a)


(b)





0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References









































































































120583eff119897 = 120583lam119897 + 120588119897(119862119878Δ)2radicS2 (7)










Table1Com

paris

onof

LESsim

ulations

No

Author

Colum

nD(times

W)times

H(m

)Sparger

desig

nBu

bble

diam

eter

Rangeo

f119881119866m

sNum

bero

fgrid

cells

Filter

SGSMod

elBIT

closure

mod

els+

Interfa

cialforcec


Drag

119862119863

Lift

119862119871

Virtual

mass

119862VM

(1)

Deenetallowast[19

]015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

32times

32times

90

Δ=5ndash10mm

Smagorinsky

119862119878=01

(1)

(4)

05

05

(2)

Bove

etal

[29]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

9times

6times

30

Δ=10ndash17m

mSm

agorinsky

119862119878=005ndash0

2mdash

(24)

05

05

(3)

Zhangetal

[26]


90

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

15times

15times

90

mdashSm

agorinsky

119862119878=008ndash0

20

(123)

(2)

(4)

Tabibetal

[17]

015times

10

Perfo

rated

plate

5mm

200

times10minus3

1500

00Δ

=3m

mSm

agorinsky

119862119878=01

(1)

(1)

(5)

Dho

treetal

[20]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus5

15times

15times

50

15times

15times

100

119889119861lt

Δ

Smagorinsky

119862119878=012

Germano

(1)

(1)

05

05

(6)

Nicenoetal

[9]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

30times

30times

90

Δisequaltothe

grid

spacing

Δ119889119887=15

Smagorinsky

119862119878=012

OEM

(12)

(15)

05

05

(7)

Dho

treetal

[18]

20

times34

Perfo

rated

plate

26m

m49

times10minus3

mdash28m

mlt

Δlt

40m

mSm

agorinsky

119862119878=012

(1)

(5)

05

05

(8)

Nicenoetal

[10]

015times

015times

10

Perfo

rated

plate

4mm

49

times10minus3

30times

30times

100

Δ=5m

mOEM

Germano

(12)

(45)

05

05

(9)

TabibandSchw

arz

[30]

015times

10

Perfo

rated

plate

3ndash5m

m200

times10minus3

mdashmdash

OEM

(2)

Max

[(1)(6

)]

minus005

mdash

(10)

vandenHengel

etal[31]

015times

10

Perfo

rated

plate

3mm

49

times10minus3

15times

15times

45

Δ=

10mm

Smagorinsky

(1)

(3)

05

05

(11)

HuandCelik

[32]

015times

008times

10

Pipe

sparger

16mm

0660times

10minus3

96times

50times

8

120times

80times

10

PSI-ballmetho

d2m

mSm

agorinsky

119862119878=0032

(4)

(3)

05

05

(12)

Lain

[27]

014times

10

Porous

mem

brane

26m

m0272times

10minus3

30times

30times

50

45times

45times

10

Δ119889119887=18

Smagorinsky

119862119878=01

(4)

05

(13)

Darmanae

tal

[33]

02

times003times

10

Multip

oint

gas

injection

4mm

70

times10minus3

80times

12times

400

Δ=

25mm

Vrem

an

119862119878=01

mdash(3)

05

(14)

Sung

korn

etal

[34]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

30times

30times

90

Δisequaltothe

grid

spacing

Δ119889119887=12

5

Smagorinsky

119862119878=010ndash0

12(6)

(3)

05

(15)

Baietal[35]B

aietal[36]

015times

015times

045

Perfo

rated

plate

5mm

50

times10minus3

100

times10minus3

150

times10minus3

250

times10minus3

15times

15times

45

20times

20times

60

30times

30times

90

mdashVrem

anSm

agorinsky

119862119878=01

mdash(3)

05

05

Thea

utho

rshave

studied

thee

ffectof

thisforceo

vera

range

+Num

bersindicatedarer

efered

toTable2

++Num

bersindicatedarer

efered

toTable3



No Author 120583BIT 119878119896BIT 119878



120583BIT =

120588119871120572119866119862120583BIT1198891198611003816100381610038161003816U119866 minus U119871

1003816100381610038161003816

0 0


1003816100381610038161003816M1198701003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

120572119871

119896119871

119862120598119878119896BIT


1003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

0453119862119863

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

2119862VM119889119861

119878119896BIT






120597119896SGS120597119905


11989632

SGSΔ

(8)


is defined as

119875119896SGS= 120583SGS

10038161003816100381610038161003816119878119894119895

10038161003816100381610038161003816 (9)


120583SGS = 119862119896Δ11989612

SGS (10)



120583BI119897 = 120588119891 119862120583BI 120572119892 11988911988710038161003816100381610038161003816u119892minusu119897

10038161003816100381610038161003816 (11)







3 Numerical Details





No Author Equation

(1) Ishii and Zuber [44] 119862119863

=24Re

(1 + 01Re075)

(2) Tomiyama [45]119862119863

=(83) 119864119900 (1 minus 119864

2)

11986423

119864119900 + 16 (1 minus 1198642) 11986443

119865(119864)minus2

119864 =1

1 + 01631198641199000757

(Wellek et al [46])



2

(1 minus 1198642)


= max [min [16

Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]


2

311986411990012

119864119900 = 119892Δ1205881198892

119866120590

(5) Clift et al [48]119862119863 =

24

Re(1 + 015Re0687

119875) Re119875 le 800

044 Re119875 gt 800


Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]

003

0025

002

0015

001

0005

00 005 01 015

Column width (m)

No BITSato

PflegerExperiment

2s

2)

Turb

ule

nt

kin

etic

en

ergy

(m

(a)

024

022

02

018

016

014

012

01

008

006

004

SGS

reso

lved

en

ergy

0 005 01 015

Column width (m)

No BITSato

Pfleger

(b)















0

02

04

06

08

100 110 120 130 140 150

Time (s)

LDA

LES

minus02

uy

L(m

s)

119896-ε








03

025

02

015

01

005

0

minus005

minus010 01 02 03 04 05 06 07 08 09 1

(ms

)

xD


Inlet 2Inlet 3

(a)

Inlet 1

Inlet 2

Inlet 3

25

2

15

1

05

00 005 01 015 02 025 03 035 04 045

yH

(kg

m s)

(b)













0 02 04 06 08 1

0

01

02

03

04

05

v mL

(ms

)

xD

= 008= 01

= 015

= 02Exp (yH = 063)

minus01

(mdash)

119862119878 119862119878

119862119878

119862119878


0

01

02

03

04

05

06

07

0 02 04 06 08 1

= 008= 01

= 015

= 02Exp (yH = 063)

v mG

(ms

)

xD (mdash)

119862119878 119862119878

119862119878

119862119878



0

0002

0004

0006

0008

001

0012

0 005 01 015 02 025 03

PD

F

CS











Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS


0e+00

25eminus03

5eminus03

75eminus03


(a)


(b)





0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































Table1Com

paris

onof

LESsim

ulations

No

Author

Colum

nD(times

W)times

H(m

)Sparger

desig

nBu

bble

diam

eter

Rangeo

f119881119866m

sNum

bero

fgrid

cells

Filter

SGSMod

elBIT

closure

mod

els+

Interfa

cialforcec


Drag

119862119863

Lift

119862119871

Virtual

mass

119862VM

(1)

Deenetallowast[19

]015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

32times

32times

90

Δ=5ndash10mm

Smagorinsky

119862119878=01

(1)

(4)

05

05

(2)

Bove

etal

[29]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

9times

6times

30

Δ=10ndash17m

mSm

agorinsky

119862119878=005ndash0

2mdash

(24)

05

05

(3)

Zhangetal

[26]


90

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

15times

15times

90

mdashSm

agorinsky

119862119878=008ndash0

20

(123)

(2)

(4)

Tabibetal

[17]

015times

10

Perfo

rated

plate

5mm

200

times10minus3

1500

00Δ

=3m

mSm

agorinsky

119862119878=01

(1)

(1)

(5)

Dho

treetal

[20]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus5

15times

15times

50

15times

15times

100

119889119861lt

Δ

Smagorinsky

119862119878=012

Germano

(1)

(1)

05

05

(6)

Nicenoetal

[9]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

15times

15times

45

30times

30times

90

Δisequaltothe

grid

spacing

Δ119889119887=15

Smagorinsky

119862119878=012

OEM

(12)

(15)

05

05

(7)

Dho

treetal

[18]

20

times34

Perfo

rated

plate

26m

m49

times10minus3

mdash28m

mlt

Δlt

40m

mSm

agorinsky

119862119878=012

(1)

(5)

05

05

(8)

Nicenoetal

[10]

015times

015times

10

Perfo

rated

plate

4mm

49

times10minus3

30times

30times

100

Δ=5m

mOEM

Germano

(12)

(45)

05

05

(9)

TabibandSchw

arz

[30]

015times

10

Perfo

rated

plate

3ndash5m

m200

times10minus3

mdashmdash

OEM

(2)

Max

[(1)(6

)]

minus005

mdash

(10)

vandenHengel

etal[31]

015times

10

Perfo

rated

plate

3mm

49

times10minus3

15times

15times

45

Δ=

10mm

Smagorinsky

(1)

(3)

05

05

(11)

HuandCelik

[32]

015times

008times

10

Pipe

sparger

16mm

0660times

10minus3

96times

50times

8

120times

80times

10

PSI-ballmetho

d2m

mSm

agorinsky

119862119878=0032

(4)

(3)

05

05

(12)

Lain

[27]

014times

10

Porous

mem

brane

26m

m0272times

10minus3

30times

30times

50

45times

45times

10

Δ119889119887=18

Smagorinsky

119862119878=01

(4)

05

(13)

Darmanae

tal

[33]

02

times003times

10

Multip

oint

gas

injection

4mm

70

times10minus3

80times

12times

400

Δ=

25mm

Vrem

an

119862119878=01

mdash(3)

05

(14)

Sung

korn

etal

[34]

015times

015times

045

Perfo

rated

plate

4mm

49

times10minus3

30times

30times

90

Δisequaltothe

grid

spacing

Δ119889119887=12

5

Smagorinsky

119862119878=010ndash0

12(6)

(3)

05

(15)

Baietal[35]B

aietal[36]

015times

015times

045

Perfo

rated

plate

5mm

50

times10minus3

100

times10minus3

150

times10minus3

250

times10minus3

15times

15times

45

20times

20times

60

30times

30times

90

mdashVrem

anSm

agorinsky

119862119878=01

mdash(3)

05

05

Thea

utho

rshave

studied

thee

ffectof

thisforceo

vera

range

+Num

bersindicatedarer

efered

toTable2

++Num

bersindicatedarer

efered

toTable3



No Author 120583BIT 119878119896BIT 119878



120583BIT =

120588119871120572119866119862120583BIT1198891198611003816100381610038161003816U119866 minus U119871

1003816100381610038161003816

0 0


1003816100381610038161003816M1198701003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

120572119871

119896119871

119862120598119878119896BIT


1003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

0453119862119863

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

2119862VM119889119861

119878119896BIT






120597119896SGS120597119905


11989632

SGSΔ

(8)


is defined as

119875119896SGS= 120583SGS

10038161003816100381610038161003816119878119894119895

10038161003816100381610038161003816 (9)


120583SGS = 119862119896Δ11989612

SGS (10)



120583BI119897 = 120588119891 119862120583BI 120572119892 11988911988710038161003816100381610038161003816u119892minusu119897

10038161003816100381610038161003816 (11)







3 Numerical Details





No Author Equation

(1) Ishii and Zuber [44] 119862119863

=24Re

(1 + 01Re075)

(2) Tomiyama [45]119862119863

=(83) 119864119900 (1 minus 119864

2)

11986423

119864119900 + 16 (1 minus 1198642) 11986443

119865(119864)minus2

119864 =1

1 + 01631198641199000757

(Wellek et al [46])



2

(1 minus 1198642)


= max [min [16

Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]


2

311986411990012

119864119900 = 119892Δ1205881198892

119866120590

(5) Clift et al [48]119862119863 =

24

Re(1 + 015Re0687

119875) Re119875 le 800

044 Re119875 gt 800


Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]

003

0025

002

0015

001

0005

00 005 01 015

Column width (m)

No BITSato

PflegerExperiment

2s

2)

Turb

ule

nt

kin

etic

en

ergy

(m

(a)

024

022

02

018

016

014

012

01

008

006

004

SGS

reso

lved

en

ergy

0 005 01 015

Column width (m)

No BITSato

Pfleger

(b)















0

02

04

06

08

100 110 120 130 140 150

Time (s)

LDA

LES

minus02

uy

L(m

s)

119896-ε








03

025

02

015

01

005

0

minus005

minus010 01 02 03 04 05 06 07 08 09 1

(ms

)

xD


Inlet 2Inlet 3

(a)

Inlet 1

Inlet 2

Inlet 3

25

2

15

1

05

00 005 01 015 02 025 03 035 04 045

yH

(kg

m s)

(b)













0 02 04 06 08 1

0

01

02

03

04

05

v mL

(ms

)

xD

= 008= 01

= 015

= 02Exp (yH = 063)

minus01

(mdash)

119862119878 119862119878

119862119878

119862119878


0

01

02

03

04

05

06

07

0 02 04 06 08 1

= 008= 01

= 015

= 02Exp (yH = 063)

v mG

(ms

)

xD (mdash)

119862119878 119862119878

119862119878

119862119878



0

0002

0004

0006

0008

001

0012

0 005 01 015 02 025 03

PD

F

CS











Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS


0e+00

25eminus03

5eminus03

75eminus03


(a)


(b)





0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References


































































































No Author 120583BIT 119878119896BIT 119878



120583BIT =

120588119871120572119866119862120583BIT1198891198611003816100381610038161003816U119866 minus U119871

1003816100381610038161003816

0 0


1003816100381610038161003816M1198701003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

120572119871

119896119871

119862120598119878119896BIT


1003816100381610038161003816

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

0453119862119863

1003816100381610038161003816U119866 minus U1198711003816100381610038161003816

2119862VM119889119861

119878119896BIT






120597119896SGS120597119905


11989632

SGSΔ

(8)


is defined as

119875119896SGS= 120583SGS

10038161003816100381610038161003816119878119894119895

10038161003816100381610038161003816 (9)


120583SGS = 119862119896Δ11989612

SGS (10)



120583BI119897 = 120588119891 119862120583BI 120572119892 11988911988710038161003816100381610038161003816u119892minusu119897

10038161003816100381610038161003816 (11)







3 Numerical Details





No Author Equation

(1) Ishii and Zuber [44] 119862119863

=24Re

(1 + 01Re075)

(2) Tomiyama [45]119862119863

=(83) 119864119900 (1 minus 119864

2)

11986423

119864119900 + 16 (1 minus 1198642) 11986443

119865(119864)minus2

119864 =1

1 + 01631198641199000757

(Wellek et al [46])



2

(1 minus 1198642)


= max [min [16

Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]


2

311986411990012

119864119900 = 119892Δ1205881198892

119866120590

(5) Clift et al [48]119862119863 =

24

Re(1 + 015Re0687

119875) Re119875 le 800

044 Re119875 gt 800


Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]

003

0025

002

0015

001

0005

00 005 01 015

Column width (m)

No BITSato

PflegerExperiment

2s

2)

Turb

ule

nt

kin

etic

en

ergy

(m

(a)

024

022

02

018

016

014

012

01

008

006

004

SGS

reso

lved

en

ergy

0 005 01 015

Column width (m)

No BITSato

Pfleger

(b)















0

02

04

06

08

100 110 120 130 140 150

Time (s)

LDA

LES

minus02

uy

L(m

s)

119896-ε








03

025

02

015

01

005

0

minus005

minus010 01 02 03 04 05 06 07 08 09 1

(ms

)

xD


Inlet 2Inlet 3

(a)

Inlet 1

Inlet 2

Inlet 3

25

2

15

1

05

00 005 01 015 02 025 03 035 04 045

yH

(kg

m s)

(b)













0 02 04 06 08 1

0

01

02

03

04

05

v mL

(ms

)

xD

= 008= 01

= 015

= 02Exp (yH = 063)

minus01

(mdash)

119862119878 119862119878

119862119878

119862119878


0

01

02

03

04

05

06

07

0 02 04 06 08 1

= 008= 01

= 015

= 02Exp (yH = 063)

v mG

(ms

)

xD (mdash)

119862119878 119862119878

119862119878

119862119878



0

0002

0004

0006

0008

001

0012

0 005 01 015 02 025 03

PD

F

CS











Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS


0e+00

25eminus03

5eminus03

75eminus03


(a)


(b)





0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References


































































































No Author Equation

(1) Ishii and Zuber [44] 119862119863

=24Re

(1 + 01Re075)

(2) Tomiyama [45]119862119863

=(83) 119864119900 (1 minus 119864

2)

11986423

119864119900 + 16 (1 minus 1198642) 11986443

119865(119864)minus2

119864 =1

1 + 01631198641199000757

(Wellek et al [46])



2

(1 minus 1198642)


= max [min [16

Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]


2

311986411990012

119864119900 = 119892Δ1205881198892

119866120590

(5) Clift et al [48]119862119863 =

24

Re(1 + 015Re0687

119875) Re119875 le 800

044 Re119875 gt 800


Re(1 + 015Re0687) 48

Re]

8

3

119864119900

119864119900 + 4]

003

0025

002

0015

001

0005

00 005 01 015

Column width (m)

No BITSato

PflegerExperiment

2s

2)

Turb

ule

nt

kin

etic

en

ergy

(m

(a)

024

022

02

018

016

014

012

01

008

006

004

SGS

reso

lved

en

ergy

0 005 01 015

Column width (m)

No BITSato

Pfleger

(b)















0

02

04

06

08

100 110 120 130 140 150

Time (s)

LDA

LES

minus02

uy

L(m

s)

119896-ε








03

025

02

015

01

005

0

minus005

minus010 01 02 03 04 05 06 07 08 09 1

(ms

)

xD


Inlet 2Inlet 3

(a)

Inlet 1

Inlet 2

Inlet 3

25

2

15

1

05

00 005 01 015 02 025 03 035 04 045

yH

(kg

m s)

(b)













0 02 04 06 08 1

0

01

02

03

04

05

v mL

(ms

)

xD

= 008= 01

= 015

= 02Exp (yH = 063)

minus01

(mdash)

119862119878 119862119878

119862119878

119862119878


0

01

02

03

04

05

06

07

0 02 04 06 08 1

= 008= 01

= 015

= 02Exp (yH = 063)

v mG

(ms

)

xD (mdash)

119862119878 119862119878

119862119878

119862119878



0

0002

0004

0006

0008

001

0012

0 005 01 015 02 025 03

PD

F

CS











Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS


0e+00

25eminus03

5eminus03

75eminus03


(a)


(b)





0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References










































































































0

02

04

06

08

100 110 120 130 140 150

Time (s)

LDA

LES

minus02

uy

L(m

s)

119896-ε








03

025

02

015

01

005

0

minus005

minus010 01 02 03 04 05 06 07 08 09 1

(ms

)

xD


Inlet 2Inlet 3

(a)

Inlet 1

Inlet 2

Inlet 3

25

2

15

1

05

00 005 01 015 02 025 03 035 04 045

yH

(kg

m s)

(b)













0 02 04 06 08 1

0

01

02

03

04

05

v mL

(ms

)

xD

= 008= 01

= 015

= 02Exp (yH = 063)

minus01

(mdash)

119862119878 119862119878

119862119878

119862119878


0

01

02

03

04

05

06

07

0 02 04 06 08 1

= 008= 01

= 015

= 02Exp (yH = 063)

v mG

(ms

)

xD (mdash)

119862119878 119862119878

119862119878

119862119878



0

0002

0004

0006

0008

001

0012

0 005 01 015 02 025 03

PD

F

CS











Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS


0e+00

25eminus03

5eminus03

75eminus03


(a)


(b)





0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































03

025

02

015

01

005

0

minus005

minus010 01 02 03 04 05 06 07 08 09 1

(ms

)

xD


Inlet 2Inlet 3

(a)

Inlet 1

Inlet 2

Inlet 3

25

2

15

1

05

00 005 01 015 02 025 03 035 04 045

yH

(kg

m s)

(b)













0 02 04 06 08 1

0

01

02

03

04

05

v mL

(ms

)

xD

= 008= 01

= 015

= 02Exp (yH = 063)

minus01

(mdash)

119862119878 119862119878

119862119878

119862119878


0

01

02

03

04

05

06

07

0 02 04 06 08 1

= 008= 01

= 015

= 02Exp (yH = 063)

v mG

(ms

)

xD (mdash)

119862119878 119862119878

119862119878

119862119878



0

0002

0004

0006

0008

001

0012

0 005 01 015 02 025 03

PD

F

CS











Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS


0e+00

25eminus03

5eminus03

75eminus03


(a)


(b)





0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































0 02 04 06 08 1

0

01

02

03

04

05

v mL

(ms

)

xD

= 008= 01

= 015

= 02Exp (yH = 063)

minus01

(mdash)

119862119878 119862119878

119862119878

119862119878


0

01

02

03

04

05

06

07

0 02 04 06 08 1

= 008= 01

= 015

= 02Exp (yH = 063)

v mG

(ms

)

xD (mdash)

119862119878 119862119878

119862119878

119862119878



0

0002

0004

0006

0008

001

0012

0 005 01 015 02 025 03

PD

F

CS











Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS


0e+00

25eminus03

5eminus03

75eminus03


(a)


(b)





0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































Free surface

06 ms

(a) Germano

Free surface

06 ms

(b) Smagorinsky

Free surface

06 ms

(c) RANS


0e+00

25eminus03

5eminus03

75eminus03


(a)


(b)





0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































0 005 01 0150

0005

001

0015

002

0025

003

Column width (m)


Turb

ule

nt

kin

etic

en

ergy

(m

2s

2)












0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































0

005

01

015

02

025

0 005 01 015

StandardPIV

minus01

minus005

uzL

(ms

)

No LES no uSGS

(a)

0 005 01 0150

005

01

015

02

025

u zL

(ms

)

StandardPIV

No LES no uSGS

(b)

0

002

004

006

008

01

012

0 005 01 015

StandardPIV

No LES no uSGS

u xL

(ms

)

(c)






(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































(a)

15

14

13

12

11

1

09

08

07

06

05

04

03

02

01

00 01 02 03 04 05

(b) (c) (d)










700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x(mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

700

650

600

550

500

450

400

350

z(m

m)

z(m

m)


x (mm)


x (mm)

350

300

250

200

150

100

50

0

1 ms

1 ms

(a)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

07

06

05

04

03

02

01

00 01005 015 02

z(m

)

x (m)

1 ms 1 ms

(b)





(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































(a) (b) (c)

Flu

ctu

atio

n v

eloc

ity

(ms

)

0025

0019

0013

0006

0

(d)











1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































1242 1248 2 4 1 2 3 05 1 15



2 HCOminus and CO

2





0

001

002

003

004

0 0005 001 0015 002 0025 003

ug (ms)

Dl

(m2s

)

































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References


























































































































Nomenclature














Greek Symbols



1206011015840




Subscripts



Abbreviations


Acknowledgment


References

































































































Abbreviations


Acknowledgment


References
































































































Large Eddy simulation for dispersed bubbly flows : a review · Large Eddy simulation for dispersed...

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Transcript of Large Eddy simulation for dispersed bubbly flows : a review · Large Eddy simulation for dispersed...