Validation of closure models for interfacial drag and turbulence in numerical simulations of horizontal stratified gas–liquid flows

International Journal of Multiphase Flow 62 (2014) 1–16

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International Journal of Multiphase Flow

journal homepage: www.elsevier .com/ locate / i jmulflow

Validation of closure models for interfacial drag and turbulencein numerical simulations of horizontal stratified gas–liquid flows

http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.01.0120301-9322/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +49 351 260 2170.E-mail addresses: [email protected] (T. Höhne), [email protected]

(J.-P. Mehlhoop).

Thomas Höhne, Jan-Peter Mehlhoop ⇑Helmholtz-Zentrum Dresden – Rossendorf e.V. (HZDR), Institute of Fluid Dynamics, POB 51 01 19, 01314 Dresden, Germany

a r t i c l e i n f o

Article history:Received 6 August 2013Received in revised form 29 January 2014Accepted 30 January 2014Available online 18 February 2014

Keywords:CFDHorizontal flowAIADTwo-phase flowHAWACHZDR

a b s t r a c t

The development of general models closer to physics and including less empiricism is a long-term objec-tive of the activities of the HZDR research programs. Such models are an essential precondition for theapplication of CFD codes to the modeling of flow related phenomena in the chemical and nuclear indus-tries. The Algebraic Interfacial Area Density (AIAD) approach allows the use of different physical modelsdepending on the local morphology inside a macroscale multi-fluid framework. A further step ofimprovement of modeling the turbulence at the free surface is the consideration of sub-grid wave turbu-lence that means waves created by Kelvin–Helmholtz instabilities that are smaller than the grid size. Infact, the influence on the turbulence kinetic energy of the liquid side can be significantly large. The newapproach was verified and validated against horizontal two-phase slug flow data from the HAWAC chan-nel and smooth and wavy stratified flow experiments of a different rectangular channel. The resultsapprove the ability of the AIAD model to predict key flow features like liquid hold-up and free surfacewaviness. Furthermore an evaluation of the velocity and turbulence fields predicted by the AIAD modelagainst experimental data was done. The results are promising and show potential for further modelimprovement.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

In the last decade, applications of Computational Fluid Dynamic(CFD) methods for industrial applications received more and moreattention, as they proved to be a valuable complementary tool fordesign and optimization. The main interest towards CFD consists infact in the possibility of obtaining detailed 3D complete flow-fieldinformation on relevant physical phenomena at lower cost thanexperiments.

Stratified two-phase flows are relevant in many industrialapplications, e.g. pipelines, horizontal heat exchangers and storagetanks. Special flow characteristics as flow rate, pressure drop andflow regimes have always been of engineering interest. Wallisand Dobson (1973) analyzed the onset of slugging in horizontaland near horizontal gas–liquid flows. Flow maps which predicttransitions between horizontal flow regimes in pipes were intro-duced, e.g. by Taitel and Dukler (1976) and Mandhane et al.(1974). The most important flow regimes are smooth stratifiedflow, wavy flow, slug flow and elongated bubble flow. Taitel andDukler (1976) explained the formation of slug flow by the

Kelvin–Helmholtz instability. They also proposed a model for thefrequency of slug initiation (Taitel and Dukler, 1977). The viscousKelvin–Helmholtz analysis proposed by Lin and Hanratty (1986)generally gives better predictions for the onset of slug flow.

Typically free surfaces manifest as stratified, wavy or slug flowsin horizontal flow domain where gas and liquid are separated bygravity. The simulation of slug formation is a sensitive test casefor the model setup regarding the quality of the models for inter-facial friction respectively momentum transfer. A general overviewon the phenomenological modeling of slug flow was given byHewitt (2003) and Valluri et al. (2008). Various multidimensionalnumerical models were developed to simulate stratified flows:Marker and Cell (Harlow and Welch, 1965), Lagrangian grid meth-ods (Hirt et al., 1974), Volume of Fluid method (Hirt and Nichols,1981) and level set method (Osher and Sethian, 1988). These meth-ods can in principle capture accurately most of the physics of thestratified flows. However, they cannot capture all the morphologi-cal formations such as small bubbles and droplets, if the grid is notsufficiently small. One of the first attempts to simulate mixed flowswas presented by Cerne et al. (2001) who coupled the VOF methodwith a two-fluid model in order to bring together the advantages ofboth formulations.

Mouza et al. (2001) were numerically investigating the charac-teristics of horizontal wavy stratified flow in circular pipes and

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rectangular channels. They used the CFD code CFX for a simulationof the gas and liquid flow in separate domains, setting the timeaveraged values of interfacial velocity and shear as boundary con-dition at the free surface. They used the data set by Fabre et al.(1987) as test case for rectangular channel flows. In a validationstudy for a preliminary version of the NEPTUNE_CFD code, Yaoet al. (2003) conducted 2D-simulations of the experiments by Fabreet al. (1987) as one of three test cases. They report a qualitativelygood agreement of the calculated profiles of velocity, turbulencekinetic energy and turbulent shear stresses for the cases with zeroand medium gas velocity. But some quantitative deviations occur.In the case with high gas velocity (case 400), the code fails in pre-dicting the turbulence parameters, which they account to theinability of the 2D-model to capture the transverse flow reportedfor that experiment. Terzuoli et al. (2008) used the data set as testcase for a cross-code comparison of three different CFD codes andto validate the free surface flow models of the respective codes.They compared the scientific code NEPTUNE_CFD and the commer-cial codes ANSYS CFX and FLUENT. By comparing 2D and 3D simu-lations with the experiments they found that three-dimensionaleffects should not be neglected. Furthermore they pointed outthe fundamental role of the drag modeling at the free surface. Aseries of five different experiments were used by Coste et al.(2012) for the validation of the NEPTUNE_CFD code, the experi-mental cases 250 and 400 from Fabre et al. (1987) being amongthem. They were able to achieve a good agreement of their numer-ical data with the experimental data for velocity and turbulence incase 250. For case 400 they found a significant deviation betweentheir simulations and the experiment, which they account to theinability of the NEPTUNE_CFD code to predict the transverse flowsoccurring in case 400.

In general, CFD simulations for free surface flows require themodeling of the non-resolved scales. For modeling of interfacialtransfers it is necessary to select the adequate interfacial transfermodels and to determine the interfacial area. The numerical solu-tion can resolve the statistically averaged motion of the free sur-face (including waves) which may not be too small relatively tothe channel height and to the characteristic length of the spatialdiscretization. However, the detailed structure of interactingboundary layers of the separated continuous phases and surfaceripples cannot be resolved. Instead, its influence on the averageflow must be modeled.

Non-resolved small scale structures of the interface have influ-ence on mass, momentum and heat transfer between the phases.The type of required models depends on the general modeling ap-proach used. To model the momentum transfer, e.g. in the frame ofthe two-fluid model the correlations for the interfacial drag areused. In the past due to the lack of appropriate models often dragcorrelations valid for bubbly flows or correlations developed for 1Dcodes were used to simulate the interfacial momentum transfer atthe free surface. Such approaches do not properly reflect the phys-ics of the phenomena.

Table 1Time and space filtering of the methods applicable to free surface flow (Bestion, 2010a).

Type of model Pseudo-DNS Filtered approach

Time or ensemble averaging No NoSpace filtering No YesTreatment of eddies All eddies simulated Large eddies simu

Small eddies modTreatment of free surface waves All wavelength

simulatedLarge wavelengthSmall wavelength

Required turbulence models No model Sub-grid turbulenenergy

Required closure models at freesurface

No model Interfacial frictionEffects of sub-grid

From this point of view, in the framework of the two-fieldmodel, it is interesting to consider, close to the interface, ananisotropic momentum exchange between liquid and gas. This isdone for the Algebraic Interfacial Area Density (AIAD) model (Höhneand Vallée, 2010; Höhne et al., 2011) which allows using differentmodels to calculate the drag force coefficient and the interfacialarea density for the free surface and for bubbles or droplets.

A further step of improvement of modeling the turbulence is theconsideration of non-predicted free surface waves or so called‘‘sub-grid waves’’ that means waves created by Kelvin–Helmholtzinstabilities that are smaller than the grid size. So far in the presentcode versions they are neglected. However, the influence on theturbulence kinetic energy of the liquid side can be significantlylarge. A region of marginal breaking is defined according Brocchiniand Peregrine (2001). In addition turbulence damping functionsshould cover all the free surface flow regimes, from weak to strongturbulence.

2. Modeling free surface flows

2.1. The CFD approaches applicable to free surface flow

The three main types of two-phase CFD, namely the RANS ap-proach, the space-filtered approaches (such as LES methods), andthe pseudo-DNS approaches are in principle applicable to freesurface flow (see Bestion, 2010a,b). Table 1 shows the main char-acteristics of these methods. If only two continuous fields (contin-uous liquid and continuous gas) exist in the flow without anybubble below the free surface and without any droplet in thegas flow, a one-fluid approach (homogeneous model) is applicabletogether with an Interface Tracking Method (ITM) to predict thefree surface.

Since there may be some bubble entrainment below the freesurface, a two fluid approach was also used to be able to deal withvarious types of interface configurations including both large inter-faces (free surface) and interface of dispersed fields (bubbles, drop-lets). Detailed derivation of the two-fluid model can be found inthe book of Ishii and Hibiki (2006).

On both sides of the free surface, shear layers are expectedwhich require a specific attention since complex phenomena withturbulent transfers coupled to possible interfacial waves takeplace. It was found necessary to be able to track the interface posi-tion in order to treat this zone in a similar way as a wall boundarylayer using wall functions. When trying to use a two fluid ap-proach, the development of an interface recognition method wasfound necessary.

The AIAD method belongs to the third time and space filteringtype. Because the model can be directly applied for industrial casesit is classified as a macroscale model (Fox, 2013). A different ap-proach in this group for instance is done in the NEPTUNE code(see Coste et al., 2007; Coste and Laviéville, 2009).

es LES (VLES, LEIS) RANS (URANS, TRANS)

YesNo

lated No eddy simulatedeledsimulated No wavelength simulatedmodeled

t diffusion for momentum and Reynolds stress tensorTurbulent diffusion of energyInterfacial friction

wavelength on interfacial transfers Effects of non-predicted free surfacewaves

Fig. 1. Different morphologies under slug flow conditions.

T. Höhne, J.-P. Mehlhoop / International Journal of Multiphase Flow 62 (2014) 1–16 3

2.2. Algebraic Interfacial Area Density model

Fig. 1 shows different morphologies that occur under slug flowconditions. Separate models are necessary for droplets or bubblesand separated continuous phases (interfacial drag, etc.).

The basic idea of the AIAD model is:

� The interfacial area density allows the detection of the morpho-logical form and the corresponding switching of each correla-tion from one object pair to another.� It provides a law for the interfacial area density and the drag

coefficient for a full range of phase volume fractions from noliquid to no gas (Fig. 2).� The model improves the physical modeling in the asymptotic

limits of bubbly and droplet flows.� The interfacial area density in the intermediate range is set to

the interfacial area density for free surface (Fig. 2).

The approach used in the AIAD model is to define blendingfunctions depending on the volume fraction that enable switchingbetween the morphologies of dispersed droplets, dispersed bub-bles and the free surface. Based on these blending functions, differ-ent equations for the interfacial area density and the dragcoefficient can be applied according to the local morphology. Theblending functions are defined as Eqs. (1) and (2) for droplet andbubble region, respectively and Eq. (3) for the free surface.

fD ¼ 1þ eaDðaL�aD;limitÞ� ��1 ð1Þ

fB ¼ 1þ eaBðaG�aB;limit Þ� ��1 ð2Þ

fFS ¼ 1� fD � fB ð3Þ

With aD and aB being the blending coefficients for droplets andbubbles, respectively and aD,limit and aB,limit the volume fraction lim-iters. In the simulations presented here, values of aD = aB = 70 andaD;limit ¼ aB;limit ¼ 0:3 were used. For all model coefficients samevalues were used as in previous studies (Höhne and Vallée, 2010;Höhne, 2013). They were chosen independent of the actual geom-etry and flow regime and no tuning of the AIAD model was donefor the work presented here. The threshold value aB;limit ¼ 0:3 is acritical volume fraction before the coalescence rate increases shar-ply and is verified by experiments in both vertical and horizontal

Fig. 2. Air volume fraction and corresponding morphologies/models.

flows. Published data agree that bubbly flow rarely exceeds agaseous volume fraction of about 0.25–0.35 when the transitionto resolved structures occurs (Griffith and Wallis, 1961; Taitelet al., 1980; Murzyn and Chanson, 2009). Parameter studies alsoindicated that the model is not very sensitive towards a changeof the blending function parameters. In Fig. 3 the blending functionfor bubbles is plotted against the gas volume fraction for differentvalues of aB and aB,limit.

For simplicity bubbles and droplets are for now assumed to beof spherical shape, with a constant diameter of dB and dD, respec-tively. Non-drag forces in the regions of dispersed flow areneglected. The resulting formulation for the interfacial area densityfor droplets, AD, is given by

AD ¼6aL

dDð4Þ

in which aL is the volume fraction of the liquid phase. The IAD forbubbles, AB, is formulated analogous. The IAD of the free surface,AFS, is defined as the magnitude of the gradient of the liquid volumefraction aL, as given in Eq. (5), with n being the normal vector of thefree surface.

AFS ¼ jraLj ¼@aL

@nð5Þ

The local interfacial area density A is then calculated as the sumof Aj, weighted by the blending functions fj:

A ¼X

j

fjAj; j ¼ FS;B;D ð6Þ

2.3. Modeling the free surface drag

In the general case of a two-phase flow, there is a velocity dif-ference between the fluids, which is commonly called slip velocity.In contradiction to most Volume of Fluid (VOF) methods whereonly one velocity field is present, in the multifluid framework eachphase has its own velocity and turbulence model. Thereby a dragforce is induced at the phase boundary that is acting on both

Fig. 3. Blending function fB plotted for different values of aB and aB,limit.


phases. The drag force can be correlated with the slip velocity U,the fluid density q, the surface area a and the dimensionless dragcoefficient CD. For geometry independent modeling the drag forceis expressed as the volumetric force density FD and a is then re-placed by the area density. The magnitude of the drag force densityis given by Eq. (7).

jFDj ¼ CDA12qjUj2 ð7Þ

For a dispersed flow, the density of the continuous phase is usedin Eq. (7). In case of a free surface the phase averaged density isused, i.e.

q ¼ aGqG þ aLqL ð8Þ

with qG and qL being the density of the gas and the liquid,respectively.

In simulations of free surface flows, Eq. (7) does not represent arealistic physical model. It is reasonable to expect that the veloci-ties of both fluids in the vicinity of the interface are rather similar.In Höhne et al. (2011), it is assumed that the shear stress near thesurface behaves like a wall shear stress on both sides of the inter-face in order to reduce the velocity differences of both phases. It issupposed that the morphology region ‘‘free surface’’ is acting like awall and a wall like shear stress is introduced at the free surfacewhich influences the loss of gas velocity. The components of thenormal vector ~n at the free surface are taken from the gradientsof the void fraction.

To use these directions of the normal vectors the gradients ofgas/liquid velocities, which are used to calculate the wall shearstress onto the free surface are weighted with the components ofthe normal vector. From theory, shear stress is a symmetric tensors, if we have a surface normal vector ~n then the wall like free sur-face shear stress vector sW is the product of the viscous stress ten-sor and the surface normal vector:

sW ¼sxx sxy sxz

syx syy syz

szx szy szz

264

375 �

nx

ny

nz

264

375 ð9Þ

This results in the following equations:

sW;x ¼ sxxnx þ sxyny þ sxznz

sW;y ¼ syxnx þ syyny þ syznz

sW;z ¼ szxnx þ szyny þ szznz

sW ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisW;x2 þ sW;y2 þ sW;z2

p ð10Þ

With nx;ny;nz being the components of the normal vector, u, v,w the components of the velocity vector and l the dynamic viscos-ity of the fluid, it can also be written:

sW;x ¼ nx � l � ð2 @u@xÞ

� �þ ny � l � ð@u

@y þ @v@xÞ

h iþ nz � l � ð@u

@z þ @w@xÞ

� �sW;y ¼ nx � l � ð@u

@y þ @v@xÞ

h iþ ny � l � ð2 @v

@yÞh i

þ nz � l � ð@v@z þ @w@yÞ

h isW;z ¼ nx � l � ð@w

@x þ @u@zÞ

� �þ ny � l � ð@w

@y þ @v@zÞ

h iþ nz � l � ð2 @w

@zÞ� �

sW ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisW;x2 þ sW;y2 þ sW;z2

pð11Þ

It is assumed, that the drag force (7) is equal to the wall shearstress force acting at the free surface in the vicinity of the freesurface:

FW ¼ siA ¼ FD ð12Þ

As a result, the modified drag coefficient is dependent on theviscosities of both phases, the wall like shear stresses (local gradi-ents of gas/liquid velocities normal to the free surface), the mixturedensity and the slip velocity between the phases:

CD;FS ¼2ðaLsW ;L þ aGsW ;GÞ

qjUj2ð13Þ

The AIAD model uses the following three different drag coeffi-cients: CD,B = 0.44 (Newton) for bubbles, CD,D = 0.44 for the dropletsand CD,FS (Höhne and Vallée, 2010) according to Eq. (13) for the freesurface. The advantage of this definition is that the resulting dragforce is not depending on U anymore, since jUj2 is being eliminated,but instead the local velocity gradients and the viscosities of bothphases are included in the calculation. This is a more physical def-inition for the interfacial drag force in a shear driven flow. The totaldrag coefficient for a unit volume is calculated analogous to theinterfacial area density as the weighted sum of the drag coeffi-cients for all morphologies:

CD ¼X

j

fjCD;j; j ¼ FS;B;D ð14Þ

2.4. Sub-grid wave turbulence

Small waves (Fig. 4) created by Kelvin–Helmholtz instabilitiesthat are smaller than the grid size are neglected in traditionaltwo phase flow CFD simulations, but the influence on the turbu-lence kinetic energy of the liquid side can be significantly large.Brocchini and Peregrine (2001) try to quantify this in the L–q dia-gram (Fig. 5) which predicts the free surface shape as a function ofthe liquid turbulence (q ¼

ffiffiffiffiffiffiffi2 kp

) and a length scale L. They sup-posed, that both gravity and surface tension act at a liquid surfaceso the surface behavior depends on both the turbulent Froudenumber Fr ¼ q=ð2gLÞ1=2 and Weber number We ¼ q2Lq=2r (r isthe interfacial tension coefficient). Thus the value of both parame-ters must be considered. Their effect is discussed by seeking todelineate a critical region of parameter space between quiescentsurfaces and surfaces that break up completely.

The shaded area in Fig. 5 represents the region of marginalbreaking and has been obtained by using the two estimated valuesfor both the critical Weber number and the critical Froude number.So far we assume that the local length scale L can be obtained bylocal surface morphology created by the larger interface structures,which are resolved. The shaded area in the diagram also indicatesthe range of variations between surface that is no longer smooth orpossibly broken because of turbulent flow.

Depending on the values of the Froude and Weber numbers thefollowing four regimes can be classified:

– Weak turbulence Fr� 1, We� 1: The turbulence is not strongenough to cause significant surface disturbances

– ‘‘Knobbly’’ flow Fr� 1, We� 1: The turbulence is strong enoughto deform the surface against gravity, but its turbulent lengthscale is small. Surface tension causes the surface shape to bevery smooth and rounded.

– Turbulence is dominated by gravity Fr� 1, We� 1: Surface dis-tortions are primarily counters by gravity, resulting in a nearlyflat free surface. The turbulent energy is sufficient to disturb thesurface at relatively small scales, leading to small regions ofwaves, vortex dimples and scars.

– Strong turbulence Fr� 1, We� 1: The turbulence is strongenough to counter gravity and surface tension which is nolonger sufficient to prevent the surface from breaking up intodroplet and bubbles.

Since turbulence can have different lengths scales at the sametime, many of these regions can occur close to each other.

For an upper critical value Brocchini and Peregrine (2001) com-pared the turbulent kinetic energy density per unit volume of ablob that can disturb the surface with the energy of a surface

Fig. 4. Surface instabilities at the free surface (HAWAC).

1.00E-02

1.00E-01

1.00E+00

1.00E+01

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01

Lenght scale [m]

Turb

ulen

t Vel

ocity

q [m

/s]

Knobbly

Bubbly

RippledWavy

Breaking

Flat

Scarified

Ballistic

Fig. 5. Diagram of the (L, q)-plane for water (Brocchini and Peregrine, 2001).


disturbance per unit surface area (Fig 6). It is assumed, that a blobis just able to generate a spherical drop that touches the surfacewhen it has lost any overall motion. This leads to an estimate forthe upper bound of the transition zone of:

q2u �

p24

gnLþ pr2LqL

ð15Þ

with gn ¼~g �~nFS. The gravity vector normally stabilizes the free sur-face in horizontal flows. In cases of slug flows or vertical flows thevector can even destabilize the flow. Therefore the normal vector ofthe free surface is also taken into account. If gn turns into negativevalues the term is destabilizing the surface. The interface normalvector is formulated using the volume fraction gradient of the liquidphase:

~n ¼ ra1

jra1jð16Þ

With this formulation the interface normal vector is always point-ing into the liquid. The product becomes zero in the case of an inter-face located parallel to the gravity vector (~n perpendicular to ~gn).Additionally it becomes negative if the inward directed interfacenormal vector is pointing into the opposite direction compared to~g, which is the case occurring with Rayleigh–Taylor type ofinstabilities.

The model surface for the lower bound is derived at themolecular level from the continuum surface model fromShikhmurzaev (1997). Surface diffusion studies show that the firstindication of turbulence ‘‘breaking’’ the surface can be represented

lower bound

Fig. 6. Example for the upper and low

by the creation of fresh surface by the breaking of the surface skin(Fig. 6). It is considered as a linear down welling feature boundedby two, convex-upward quarter-circles. The result of the lowerbound of the transition region is then:

q2l �

53� p

2

� �gnL125þ ðp� 2Þr

5LqLð17Þ

We assume that we must add the potion of turbulent kinetic en-ergy created by the small waves at the liquid side which is so farmissing in the simulation to the overall turbulent kinetic energy(see Fig. 5 shaded area):

kSWT ¼ 0:5ðq2u � q2

l Þ ð18Þ

The result is depended on the local length scale L shown inFig. 7.

The consequence of the specific turbulent kinetic energy k isprescribed in the following source term:

Pk;SWT ¼ fFS23@Ui

@xiqLk ð19Þ

where the gradients of the local velocities and the liquid density arepresent and which is added to the total turbulent kinetic energy(k-x Model, Wilcox, 1994):

@ðqkÞ@tþr � ðqUkÞ ¼ r � lþ lt

rk

� �rk

� �þ Pk � b0qkx

þ Pk;SWT ð20Þ

The term Pk,SWT in Eq. (20) is blended only in the vicinity of thefree surface.

2.5. Turbulence damping

Damping of turbulence as the interface is approached – on bothsides- was found vital for the modeling of interface deformationsunder strong gas-side shear (Reboux et al., 2006). The phenomenonis similar to wall-turbulence decay, where it is known and rigor-ously derived that the eddy viscosity scales with the cube of thedistance to the wall. The same has been found via DNS for interfa-cial flows, on the gas side which obviously perceives the interfaceas a solid wall (Fulgosi et al., 2003); it was also found that theliquid side eddy viscosity scales with the square of the interfacedistance. In fact, it was found that when no damping is introduced,a spurious amount of eddy viscosity is generated at the interface,which tends to smear high frequency surface instabilities, likewrinkling and fingering, and introduce strong errors in estimating

upper bound

er bound of the transition zone.

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01Lenght scale [m]

Turb

ulen

t kin

etic

ene

rgy

1/2*

q2 [m

2 /s2 ]

turbulent kinetic energy of region ofmarginal breaking

Fig. 7. Diagram of the (L, k)-plane for water.

Table 2Flow rates and resulting mean liquid level and superficial velocities of theexperimental cases 250 and 400 (Fabre et al., 1987).

Case 250 400

Liquid flow rate _VL in l/s 3.0 3.0

Gas flow rate _VG in l/s 45.4 75.4

Mean liquid level hmean in mm 38 31.5Liquid superficial velocity ws,L in m/s 0.395 0.476Gas superficial velocity ws,G in m/s 3.66 5.50


the interfacial shear, which is the most important ingredient formass transfer modeling, as explained in the corresponding section.Furthermore, without any special treatment of the free surface, thehigh velocity gradients at the free surface, especially in the gaseousphase, generate levels of turbulence that are too high throughoutthe two-phase flow when using differential eddy viscosity modelslike the k-e or the k-x model. Therefore, a certain amount of damp-ing of turbulence is necessary in the region of the interface,because the mesh is too coarse to resolve the velocity gradient inthe gas phase at the interface.

A few empirical models have been suggested, which address theturbulence anisotropy at the free surface, see among others Celikand Rodi (1984). However, no model is applicable for a wide rangeof flow conditions, and all of them are non-local: they require forexample explicit specification of the liquid layer thickness, of theamplitude and period of surface waves, etc. Direct and Large-EddySimulations of turbulent multi-material flow have been applied tomodel surface waves. Specifically, Reboux et al. (2006) used DNS toquantify the damping of turbulence approaching the interface andincorporated this knowledge into the damping of LES turbulencemodels (Liovic and Lakehal, 2007a,b). Nourgaliev et al. (2008),Boeck and Zaleski (2005), Coward et al. (1997) reported represen-tations of surface instabilities that were obtained by DNS.

For the two-fluid formulation, Egorov (2004) proposed a sym-metric damping procedure. This procedure provides a solid wall-like damping of turbulence in both gas and liquid phases. It isbased on the standard x-equation, formulated by Wilcox (1994)as follows:

@@tðai �qi �xiÞþr�ða�iqi �Ui �xiÞ¼a �ai �qi �xi

ki�st;i � _Si�ai �b �qi �x2

i

þr½aiðliþrx �lt;iÞ �rxi�þSD;i

i¼g; l

ð21Þ

where a = 0.52 and b = 0.075 are the k-x model closure coefficientsof the generation and the destruction terms in the x-equation,rx = 0.5 is the inverse of the turbulent Prandtl number for x, st isthe Reynolds stress tensor, and _S is the strain-rate tensor. Asymp-totic analysis in the viscous sublayer near the wall shows, thatthe k-x model properly describes the turbulence damping in theinternal part of the boundary layer, if the following Dirichlet bound-ary condition is specified for x on the wall (subscript W):

xW;i ¼ B � 6li

bqi Dn2 ð22Þ

Here Dn is the near-wall grid cell height, B is a coefficient. In or-der to mimic the effect of this boundary condition near the freesurface, the following source terms have been introduced in theright hand side of the gas and liquid phase x-equations:

SD;i ¼ a � Dybqi B � 6li

bqiDn2

� �2

; i ¼ g; l ð23Þ

Here A is the interface area density, Dy the local characteristiclengths scale, Dn is the typical grid cell size across the interface,qi and li are density and viscosity of the corresponding phase i.The factor A activates this source term only at the free surface,where it cancels the standard x-destruction term of the x-equationð�aibqix2

i Þ and enforces the required high value of xi and thus theturbulence damping.

As a consequence there is a sink term and a source term in the kequation and probably the effect might cancel it out. Neverthelessthe physical effects of sub-grid turbulence and turbulence dampingdue to high velocity gradients are not the same and both should beconsidered.

3. Verification and validation

3.1. Horizontal wavy and stratified flow – Fabre channel

The second validation case of the AIAD model is an experimen-tal data set from Fabre et al. (1987). In a quasi-horizontal channelwith rectangular cross section, experiments with air and waterwere conducted. The flow regimes investigated were smooth andwavy co-current stratified flow. The channel consists of 6 segmentsmade of Plexiglas, with a total length of lc = 12.92 m and an innercross section of height and width of hc = 0.1 m and wc = 0.2 m,respectively. Water flows into the channel out of a tranquilizationtank. Air and water inlet are separated by a floating Plexiglas sheet.At the channel outlet, the water is discharged into a tank. Air andwater are recirculated in separate loops.

In Fabre et al. (1987) measurement data along the vertical axisat z = 9.1 m from the inlet are reported. The instantaneous inter-face height was measured with vertically mounted capacitancewires. Velocity in gas was measured using hot wire anemometryand velocity in liquid was measured with Laser Doppler Anemom-etry. A more detailed description of the experimental setup andmeasurement techniques can be found in Fabre et al. (1987).

Two of the experiments have been investigated in this work, thecases 250 and 400. Both of the measurements were done at thesame liquid flow rate of _VL ¼ 3:0 l

s. Gas flow rates were_VG ¼ 45:4 l

s and _VG ¼ 75:4 ls for cases 250 and 400, respectively.

The resulting mean liquid levels and corresponding superficialvelocities are summarized in Table 2. The specific cases were cho-sen, since case 250 was reported to be smooth stratified flow, whilecase 400 was in wavy stratified flow regime. Also, for case 400 adouble-vortex structure in the gas phase as well as in the liquidphase, revolving corkscrew-like along the channel (i.e. a rotationcan be measured in the plane normal to the main flow direction)was reported. Therefore both cases provide different characteristicconditions for a CFD model validation.

3.1.1. CFD setupSince transverse flows were observed in case 400 (cf. Section 3.1.), it

is strongly recommended to treat this test case as a three-dimensional

Table 3Number of nodes and cell width in each spatial direction of the meshes used in thegrid study.

Mesh No. of nodes Dx (mm) Dy (mm) Dz (mm)

Mesh 1 237,446 4.76 4.77 10.00Mesh 2 473,946 4.76 4.77 5.00Mesh 3 1,174,845 3.03 2.94 5.00

Fig. 9. Vertical profiles of the streamwise velocity w in air.

Fig. 10. Vertical profiles of the streamwise velocity w in water.


problem (Terzuoli et al., 2008). In the studies reported here, a short-ened 3D model of the channel with a length of 2.5 m and width andheight of 0.2 m and 0.1 m, respectively, was used for the simulationof both test cases. This way computational effort could be lowered toan acceptable level. Unstructured meshes with hexahedral cellswere used for both cases. The AIAD model was implemented intothe commercial CFD code ANSYS CFX 14.5 by CFX CommandLanguage (CCL). The data for the comparison with the experimentswere taken at a vertical center line 2.0 m from the inlet. To generateappropriate inlet boundary conditions, velocity profiles were takenfrom preliminary 2D simulations of the full length channel at 7.1 mfrom the inlet. The water level measured in the experiments wasspecified at the inlet and the boundary velocity profiles of air andwater were scaled accordingly. The same water level was specifiedas initial condition for the whole domain, together with thecorresponding gas and liquid superficial velocities and a hydrostaticpressure. As outlet boundary condition a constant pressure outletwas defined, with the volume fraction function and the hydrostaticpressure also used for the initial conditions. Fig. 8 shows an illustra-tion of the domain at the initial state for case 400.

The channel inclination was neglected in this study, since it isvery low. All simulations were run in transient mode. In a gridstudy three meshes were compared, using the setup of case 250.The number of nodes and the cell widths in all three spatialdirections are given in Table 3. For the coarsest mesh 1 conver-gence was not achieved and no results are presented. For mesh 2and mesh 3 the profiles of the velocity w in main flow directionfor air and water are shown in Figs. 9 and 10, respectively. Thereis no qualitative difference between the profiles and the quantita-tive deviation is sufficiently small to stop the grid study. Forfurther calculations the finest mesh 3 was used, since it showedbetter convergence behavior and allowed wider time steps.

3.1.2. Results and discussionThe focus of the analysis is put on the profiles of the velocity w

in flow direction and the profiles of the turbulence kinetic energy k,because in previous validation studies of the AIAD model theseparameters were not available. The time course of the water levelwas also evaluated. For case 250 (smooth stratified) calculationswith different turbulence models were done, which confirm thenecessity of turbulence damping in free surface flows.

3.1.2.1. Smooth stratified flow. The importance of turbulence mod-eling at the free surface was shown, e.g. by Fulgosi et al. (2003),so it is interesting and important to know how the use of differentturbulence models influences the solution and how the AIAD tur-bulence modeling performs in comparison to standard turbulencemodels. To get an insight into this, an assessment of turbulence

Fig. 8. Illustration of the initial volume fraction and t

models was done for case 250. The AIAD k-x model with turbu-lence damping and small wave turbulence is compared to threereference models. The models used as reference were k-e (Launder

he inlet velocity profile in case 400 (detail view).

Fig. 12. Scaled vertical profiles of the streamwise velocity w in air.

Fig. 13. Scaled vertical profiles of the streamwise velocity w in water.


and Sharma, 1974), unmodified k-x (Wilcox, 1994) and ShearStress Transport (SST) (Menter, 1994), all of which can be regardedas established standard models. All other parameters of the setupand the AIAD model were left unchanged.

The time dependent water levels at z = 2 m are shown in Fig. 11.Since no flow history data is reported in Fabre et al. (1987), thesimulation results are compared to the time averaged water levelreported for the experiment. For all setups an initial decrease ofthe water level occurs before a quasi-steady-state is reached. Thereis hardly any deviation in the course of the water level between k-eand k-x, which both show the poorest performance among themodels used. Also the SST model predicts water levels that aremuch lower than in the experiment. For the k-x model with turbu-lence damping, as used in the AIAD model, good agreement withthe experiment is achieved in the quasi-steady-state, but minordeviations leave room for further improvement. The results clearlyshow the necessity of turbulence damping at the free surface in or-der to correctly predict the liquid holdup.

The ability of the AIAD model to qualitatively predict the keyfeatures of free surface flows as well as liquid holdup was alreadydemonstrated in previous work. But in those studies measure-ment data on the kinematic structure of the flows was not avail-able from the experiments. Therefore the analysis of the velocityand turbulence data was the most important part of the workpresented here. Figs. 12 and 13 show the vertical profiles of thestreamwise velocity w for case 250 at the measurement locationfor the different turbulence models in comparison to the experi-mental data. To restore comparability of the velocity profiles de-spite the different water levels, the velocity values are scaledwith the superficial velocity ws;i ¼ _Vi=Aave;i of the phase i, whereAave,i is the average cross-sectional area occupied by phase i.The height is scaled with the average water level hmean in away that for water hL ¼ hL=hmean and for air hG ¼ðhG � hmeanÞ=ðhc � hmeanÞ.

In Fig. 12 especially the non-damped models expose a flattenedprofile in comparison to the experimental data, with the velocitymaximum shifted to the upper part of the channel close to the wall.This trend can also be observed for the AIAD k-x model in a weakerform, but in that case the qualitative agreement with the experi-ment is better in the upper part of the channel. Nonetheless thetrend in the free flow region is similar to the other turbulencemodels, but a steeper gradient is observed close to the free surface.

In water a satisfying agreement of the scaled velocity profiles isachieved between the SST model and the experiment, as can beseen in Fig. 13. The non-damped k-x and k-e models also delivergood results in the free flow region, but predict too low velocitiesin the vicinity of the free surface. When using the AIAD turbulencemodeling, the velocity close to the free surface is calculated toohigh. This inevitably distorts the profile also in the lower part ofthe channel. In order to further investigate this problem, the turbu-lence parameters are analyzed in the following.

Fig. 11. Development of the water level from the simulations of case 250 for different tu(1987).

The numerical coupling between the turbulence model and theconservation equations in RANS based eddy viscosity turbulencemodels is done via the turbulence viscosity or eddy viscosity lt,which is a function of turbulence kinetic energy and turbulencedissipation rate. For the k-x model and the k-e model the eddy vis-cosity is expressed by Eqs. (24) and (25), respectively, withCl = 0.99 being a constant.

lt;kx ¼ qkx

ð24Þ

lt;ks ¼ Clqk2

eð25Þ

rbulence models compared to the experimental mean water level from Fabre et al.


In the SST model, the eddy viscosity is expressed by Eq. (26).

lt;SST ¼ q � a1kmaxða1x;XF2Þ

ð26Þ

With a1 ¼ 59 being a SST model coefficient, X the absolute value of

the vorticity and F2 a blending function of the SST model:

F2 ¼ tanhðarg22Þ ð27Þ

Fig. 15. Vertical profiles of the turbulent viscosity lt in water.

arg2 ¼max2ffiffiffikp

b0xy0;500my2x

!ð28Þ

With y being the wall distance, m the kinematic viscosity of the fluidand b0 = 0.09 a SST model coefficient. Eddy viscosity and molecularviscosity of the fluid l are added up to the effective viscosityleff = l + lt.

Since the eddy viscosity is a numerical construct, no experimen-tal data is available to compare with the simulation results. But ananalysis of the eddy viscosity can give an insight on the influence ofthe turbulence modeling on the velocity field and the free surfaceposition. The effective viscosity acts as proportionality factor be-tween the viscous force Fl and the velocity gradient normal tothe flow direction @w

@h , as expressed in the standard shear stressEq. (29), with geff = Fl

A

seff ¼ leff@w@h

ð29Þ

Therefore, if the flow is incompressible and driven by a constantforce, an increase of the effective viscosity has the effect of a de-crease in the velocity gradient and vice versa. Since the molecularviscosity is assumed to be constant and is orders of magnitudesmaller than the turbulent viscosity in the case examined here,the latter one is the governing parameter of the effective viscosity.

Figs. 14 and 15 show the vertical profiles of the calculated eddyviscosity in air and water, respectively. For better comparability lt

is also correlated with h⁄. At the walls all models are more or less inagreement, but the deviations between the models grow drasti-cally towards the free surface. There the unmodified k-x and k-emodel reach the maximum lt, while with SST and AIAD k-x themaximum of lt is located in the free flow region and towards thefree surface lt decreases again. These trends are observed in bothphases. From these observations it can be explained why thereare such strong deviations between the velocity profiles and freesurface positions predicted by the different turbulence models.According to Eq. (29) an increase in turbulence viscosity has to re-sult in a decrease of the velocity gradient. The effect of this is a

Fig. 14. Vertical profiles of the turbulent viscosity lt in air.

smoothing of the velocity profile, as can be observed in Figs. 12and 13.

The velocity gradients also strongly affect the calculation of thefree surface drag, since the free surface drag force resulting fromthe combination of Eqs. (7) and (13) is only depending on the areadensity and the free surface shear stresses. The latter ones againare depending on the velocity gradients at the free surface accord-ing to Eq. (11). The result of the problems discussed above is there-fore a reduction in the calculated drag force, which forces areduction in the velocity difference between the phases. The onlyremaining degree of freedom is the interface position, with the re-sult of a shifting of the free surface towards the slower phase,which is the water in this case.

The above considerations in combination with the analysis ofthe eddy viscosity explain why the prediction of the holdup is poorwhen using the non-damped turbulence models. With the turbu-lence damping at the free surface used in the AIAD model, steepervelocity gradients at the free surface are allowed and this effect isweakened. This explains the better performance of the AIAD modelin predicting the liquid holdup.

To get a deeper insight into the turbulence structure of the flow,also the turbulence kinetic energy is analyzed, for which measure-ment data is available. The vertical profiles of k in the gas phase areplotted in Fig. 16. For comparability k is scaled with w2

s and corre-lated with h⁄. It is obvious that with all non-damped turbulencemodels k is strongly overestimated, up to one order of magnitudeclose to the free surface in case of the unmodified k-x. Accordingto Egorov (2004) this is a well-known problem and was the initial

Fig. 16. Profiles of the turbulence kinetic energy k in air.

Fig. 17. Profiles of the turbulence kinetic energy k in water. Fig. 19. Scaled vertical profiles of the streamwise velocity w in air for case 400.

Fig. 20. Scaled vertical profiles of the streamwise velocity w in water for case 400.


motivation for the development of turbulence damping functions.The k-x model with damping term predicts a turbulence kineticenergy profile much closer to the experimental one. But still thereare deviations, especially in the region below h⁄ = 0.5.

For the liquid phase the vertical profiles of the turbulencekinetic energy are shown in Fig. 17. The situation is comparableto the gas phase, the standard turbulence models fail in predictingk, while the k-x with damping is much closer. Noteworthy is thestrong increase of k close to the gas–liquid interface when usingdamped k-x and SST. Unfortunately there is no measurement dataavailable above h⁄ = 0.9, so it cannot be determined whether this isan artifact of the turbulence modeling or a realistic effect. From theexamination of the turbulence parameters it can be deduced thatthe free surface turbulence damping has an effect not only in thesmall region where the damping functions are blended in, but alsoinfluences a major part of the core flow. This effect is beneficial,because it leads to a more realistic calculation of the turbulencekinetic energy. But the problem remains that the performance ofthe k-x model away from the walls is not optimal, which is awell-known drawback (Menter, 1994).

3.1.2.2. Wavy stratified flow. To verify the results obtained for case250 for a wavy stratified flow as well, a simulation of case 400 wasconducted using the full AIAD model. Fig. 18 shows the time courseof the water level and the mean water level in the simulation com-pared to the mean water level in the experiment. The clearly pro-nounced zigzag course of the water level curve indicates that thewaviness of the flow is being captured by the simulation, but nomeasurement data is available for validation of wave amplitudesand frequency. The mean water level is predicted with a deviationof less than 6%, which is acceptable for now. The vertical velocityprofiles of the streamwise velocity w for air and water are shown

Fig. 18. Development of the water level and mean water level from the sim

in Figs. 19 and 20, respectively. They were, as above, scaled withws and correlated with h⁄. The overall trend is similar as for thesimulation of case 250. In air a good agreement between experi-mental and numerical results is achieved close to the wall, but inthe core flow the velocity is calculated too high. In water the trendobserved for case 250 is even more pronounced here and liquidvelocity close to the free surface is much higher in the simulationthan in the experiment. One reason for these deviations might bethe fact that the double-vortex structure reported for the experi-mental case 400 could not be captured in the simulation. Mostlikely the domain was too short for the transverse flow to developfrom the two-dimensional inlet velocity profile.

ulation of case 400 compared to the experimental mean water level.

Fig. 21. Schematic view of the horizontal channel with inlet device for a separate injection of water and air into the test-section.

Fig. 22. The HAWAC inlet device.

Fig. 23. Model and initial conditions of the volume fractions.


When comparing the kinematic structures in the cases 250 and400, not all aspects of the regime change marked by the transitionfrom a smooth to a wavy surface and by the occurrence of a trans-verse flow can be captured by the simulations. Although the wav-iness can be well captured by modeling the free surface dragdepending on the interfacial shear stresses, the velocity profilesare not fully congruent with the experimental data.

Future development of the AIAD model should therefore focuson the turbulence modeling. It has to be determined more in detail,how the free surface turbulence modeling takes effect on the coreflow and on the free surface drag. An asymmetric turbulencedamping should be considered to overcome the weaker perfor-mance of the model in the liquid phase, which was up to nownot done for reasons of numerical stability. Also a detailed assess-ment of the influence of the small wave turbulence is necessary.One prerequisite for these tasks are measurement data on thevelocity and turbulence fields close to the free surface, which arenot available in Fabre et al. (1987), as in most experimental studieson stratified flow, due to limitations in the measurement

techniques. A solution might be the analysis of DNS data as com-plement to experimental studies. As an alternative approach thedamping functions should be implemented with the SST model,since the k-x model is known to create problems in the free flowregion (Menter, 1994).

3.2. Horizontal slug flow – HAWAC channel

The Horizontal Air/Water Channel (HAWAC) (Fig. 21) is devotedto co-current flow experiments. A special inlet device provides de-fined inlet boundary conditions by separate injection of water andair into the test-section. A blade separating the phases can bemoved up and down to control the free inlet cross-section for eachphase, which influences the evolution of the two-phase flow re-gime. The cross-section of this channel is smaller than the channelused in an earlier study described by Vallée et al. (2008): itsdimensions are 100 30 mm2 (height width). The test-sectionis about 8 m long, and therefore the length-to-height ratio L/h is

Moving Wall 2m/sCase with gas velocity 10 m/s and liquid velocity 2 m/s with and without damping functions

Single phase case with only airflowing over moving wall

Fig. 24. Verification of the k-x turbulence model damping procedures.

Fig. 25. Results of the gas velocities over the channel height, k-x turbulence modelwith and without damping procedures using the AIAD model in comparison withsingle gas phase flow.


80. In terms of the hydraulic diameter, the dimensionless length ofthe channel is L/Dh = 173.

The inlet device (Fig. 22) is designed for separate injection ofwater and air into the channel. The air flows through the upperpart and the water through the lower part of this device. As the in-let geometry introduces many perturbations into the flow (bends,transition from pipes to rectangular cross-section), 4 wire-meshfilters are mounted in each part of the inlet device. The filters aremade of stainless steel wires with a diameter of 0.63 mm and havea mesh size of 1.06 mm. The wire-mesh filters are used to providehomogenous velocity profiles at the test-section inlet. Moreover,the filters produce a pressure drop that attenuates the effect ofthe pressure surge created by slug flow on the fluid supplysystems.

Air and water come in contact at the final edge of a 500 mmlong blade that divides both phases downstream of the filtersegment. The free inlet cross-section for each phase can be

Fig. 26. Measured picture sequence at JL = 1.0 m/s and JG = 5.0 m/s with

controlled by inclining this blade up and down. In this way, theperturbation caused by the first contact between gas and liquidcan be either minimized or, if required, a perturbation can be intro-duced (e.g. hydraulic jump). Both, filters and the inclinable blade,provide well-defined inlet boundary conditions for the CFD modeland therefore offer very good validation possibilities. Optical mea-surements were performed with a high-speed video camera.

3.2.1. CFD setupThe new approach was implemented via the command

language CCL into ANSYS CFX-14 (2012). An Euler–Euler multi-phase model using fluid dependent RANS k-x turbulence modelswas applied. The high-resolution discretization scheme was usedfor convection terms in the equations. For time integration, thefully implicit second order backward Euler method was appliedwith a constant time step of dt = 0.001 s and a maximum of 30coefficient loops per time-step. Convergence was defined in termsof the RMS values of the residuals, which was less than 10�4 mostof the time. An initial water level of half of the channel wasassumed for the entire model length. The inlet conditions are givenby both superficial velocities, a pressure distribution is set at thechannel outlet.

The grid consists of 1.2 106 hexahedral elements. A slug flowexperiment at a water velocity of 2.0 m/s and an air velocity of10.0 m/s was chosen for the CFD calculations. These velocities cor-respond to the following correlation proposed by Mishima andIshii (1980) for the evaluation of the onset of slugging in a horizon-tal pipe:

cG � cL ¼ 0:487ffiffiffiffiffiffiffiffiffiffiffiffigy0qL

qG

rð30Þ

where y0 = 50 mm is the height of the gas flow part of the chan-nel (the distance of the interface to the top) and ci the criticalvelocity of phase i.

In the experiment, the inlet blade was in the horizontal posi-tion. Accordingly, the model inlet was divided into two parts: inthe lower half of the inlet cross-section, water was injected with

Dt = 50 ms (depicted part of the channel: 0–3.2 m after the inlet).

Fig. 27. Calculated picture sequence at JL = 1.0 m/s and JG = 5.0 m/s with Dt = 50 ms (depicted part of the channel: 0.4–3.6 m after the inlet).

Fig. 28. Calculated picture sequences at JL = 1.0 m/s and JG = 5.0 m/s with isosurface at aL = 0.5, development of waves and slug formations in the channel.


air injected in the upper half. To allow for upstream flow develop-ment the inlet blade was modeled as shown in Fig. 10a. An initialwater level of y0 = 50 mm was assumed (Fig. 23b). In the simula-tion, both phases have been treated as isothermal and incompress-ible, at 25 �C and at a reference pressure of 1 bar. A hydrostaticpressure was assumed for the liquid phase. At the inlet, the turbu-lence properties were set using the ‘‘Medium intensity and Eddy

viscosity ratio’’ option of the flow solver. This is equivalent to a tur-bulence intensity of 5% in both phases. The inner surface of thechannel walls are defined as hydraulically smooth with a non-slipboundary condition applied to both gaseous and liquid phases. Thechannel outlet was modeled with a pressure controlled outletboundary condition. The parallel transient calculation of 15.0 s ofsimulation time on 8 processors took 21 CPU days.

Fig. 29. Sub-grid wave turbulence (W m�3), development of a slug formation in the channel.

Fig. 30. Comparison of air/water turbulence intensity (–) with and without sub-grid wave turbulence.


4.1.2. VerificationTo first verify the damping procedures, this slug flow experi-

ment of the HAWAC channel was used. The horizontal two phaseflow was modeled with and without the damping procedures. Inaddition, a single phase flow of the gaseous phase was modeledusing the upper part (50%) of the channel and a moving wall withconstant velocity of the liquid phase of 2 m/s at the lower wallboundary was utilized to mimic the free surface. Fig. 24 showsthe verification of the k-x turbulence models damping proceduresusing a HAWAC experiment. On the left side a case is shown withgas velocity 10 m/s and liquid velocity 2 m/s with and withoutdamping functions. On the right side a single phase case with onlyair flowing over a moving wall with 2 m/s is displayed. Fig. 25shows the results of the gas velocity field over the channel height.The simulations used the k-x turbulence model with and withoutdamping procedures inside the AIAD model framework in compar-ison to single gas phase flow. The damping functions have a strongeffect on the gas velocity field. It is obvious, that without modifica-tion of the turbulence at the free surface the velocity fields of a hor-izontal two phase flow are not predicted correctly.

Fig. 31. Power spectral density (PSD) of water level at the middle of the channel,CFD simulation.

5. Results and discussion

Picture sequences in Figs. 26 and 27 compare predictions of thephase distribution from the CFD calculation and comparable cam-era frames of slugging behavior observed in the experiment. Inboth cases, a slug is generated. The sequences show that the qual-itative behavior of the creation and propagation of the slug is sim-ilar in both the experiment and the CFD calculation.

In addition, Figs. 27 and 28 show the development of the slug.These slugs are induced only by instabilities generated in the sim-ulation and the single effects leading to slug formation that can besimulated in this model are:

� Instabilities and small waves randomly generated by the inter-facial momentum transfer. As a result, bigger waves aregenerated.� The waves can have different velocities and can merge together.� Bigger waves roll over smaller waves and can close the channel

cross-section.

The slug formation can also be induced by a perturbationappearing downstream at the inlet blade which separates thewater and the air flow. Fig. 28 gives a zoom of the interface whichclearly shows the instability propagation during the time leadingto the slug formation. In the simulation as well as in the experi-ment this perturbation is induced from the blade lip. Fig. 29 showsthe influence of the sub-grid wave turbulence during a slug devel-opment in the channel. In order to extract quantitative informationa local position was chosen 1.5 m after the blade position in themiddle of the channel over the channel height. The sub-grid waveturbulence exists only in the area of the free surface and followsthe slug formations. At the wavy front and back of the slugs thevalue of the sub-grid wave turbulence is the highest in the channel.

The turbulence intensity with and without sub-grid wave tur-bulence is displayed in Fig. 30. The turbulence intensity Tu is calcu-lated according to Eq. (31):

Tu ¼ffiffiffiffiffiffiffiffiffiffiffiffi2=3ki

pui

with i ¼ g; l ð31Þ

With the additional source term of the sub-grid wave turbu-lence in the water turbulence kinetic energy the value is slightlyhigher in the vicinity of the interface.

The slug frequency analysis was done using fast Fourier trans-form (FFT). The power spectral density (PSD), which describes


how the power of a signal or time series is distributed over differ-ent frequencies is used. The position of 2.5 m away from inlet bladein the middle of the channel (0.015 m, 0.05 m), where waves aregenerated, was utilized to describe the change of water level inthe channel. A characteristic slug frequency of around 2.0 Hz isseen Fig. 31, which corresponds roughly to the experimental valueof approximately 2.4 Hz.

6. Summary and conclusions

Stratified two-phase flows are relevant in many industrialapplications, e.g. pipelines, horizontal heat exchangers and storagetanks. Special flow characteristics as flow rate, pressure drop andflow regimes have always been of engineering interest. The numer-ical simulation of free surface flows can be performed using phase-averaged multi-fluid models, like the homogeneous and the two-fluid approaches, or non-phase-averaged variants. The approachshown in this paper within the two-fluid framework is the Alge-braic Interfacial Area Density (AIAD) model. It allows the macro-scopic blending between different models for the calculation ofthe interfacial area density and improved models for momentumtransfer in dependence on local morphology. An approach for thedrag force at the free surface was introduced. The model improvesthe physics of the existing two fluid approaches and is alreadyapplicable for a wide range of industrial two-phase flows. A furtherstep of improvement of modeling the turbulence was the consider-ation of sub-grid wave turbulence that means waves created byKelvin–Helmholtz instabilities that are smaller than the grid size.A first CFD validation of the approach was done for an adiabaticcase of the HAWAC channel. In addition two experimental testcases of the Fabre channel were simulated by using the AIAD mod-el as closure for stratified gas–liquid flows. For the first time theAIAD model was validated with a detailed set of velocity and tur-bulence data and its performance was compared with three stan-dard turbulence models. It was confirmed that with the AIADmodel it is possible to predict key flow features of stratified flowlike waviness of the free surface and liquid holdup with good accu-racy, where the established turbulence models fail. In predictingthe streamwise velocity and turbulence kinetic energy in the gasphase the AIAD model was also superior to the standard turbulencemodels, but there are still existing deviations to the experimentaldata. In calculating the liquid velocity, the SST turbulence modelis showing the best performance, although it again fails in predict-ing the turbulence kinetic energy, as well as the other standard tur-bulence models. The results show that a sophisticated modeling ofdrag and turbulence at the free surface is necessary in order to cor-rectly model stratified flow. The AIAD model is fulfilling theserequirements from a qualitative point of view. But further researchis necessary on the turbulence damping and its effect on the freesurface drag. More verification and validation of the approach isnecessary – more CFD grade experimental data are required forthe validation.

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