Zhineng Wang ,Yong Kang *,Xiaochuan Wang Shijing Wu ,Xiaoyong Li

1 Key Laboratory of Hydraulic Machinery Transients,Ministry of Education,Wuhan University,Wuhan 430072,China

2 Hubei Key Laboratory of Waterjet Theory and New Technology,Wuhan University,Wuhan 430072,China

3 School of Power and Mechanical Engineering,Wuhan University,Wuhan 430072,China

Keywords:Airlift pump Flow regimes Bubble Mass transfer Hydrodynamics

A B S T R A C T A slug flow model considering the dispersed bubbles entrained from the tail of Taylor bubble(TB)and recoalesced with the successive TB was proposed.Experiment was conducted to test the validity of this model by using a high-speed camcorder and particle image velocimetry(PIV).It was found that the model was valid for predicting the characteristics of slug flow in airlift pump within average error of 14%.Moreover,large pipe diameter was found to accelerate the rise velocity of TB and decreases void fraction in liquid slug by a small margin.

1.Introduction

may affect the shape of the trailing bubble.Hanafizadeh et al.[7]evaluated the data of bubble velocity in slug flow obtained by the high-speed camera.Seshadri et al.[8]measured the thickness of the liquid film around a TB by various image processing techniques and found that the thickness of liquid film is dependenton the inertial and surface tension effects.Xia et al.[9]conducted experiment to measure the slug length in vertical pipe by using the optical probes.Lu et al.[10]studied the pressure drop of slug flow in vertical pipes and found that the pressure drop is greatly affected by the pipe diameter and the phase flow rates.

Based on these experimental data,many researchers tried to propose empirical correlations.Brauner and Taitel[11]developed a model for slug length distribution in slug flow and found that the mean slug length of fully developed slug flow is about 1.5 times the minimum stable slug length.For gas and liquid velocities,Nicklin et al.[12]proposed a drift model by considering the effect of gravitational acceleration and fluid properties.Taitel et al.[13,14]presented a model to predict the hydrodynamics of the liquid film around TB.The above models show good agreement with the corresponding experimental data,but have no ability to evaluate the overall hydrodynamic characteristics of slug flow,because most of them simply focus on single flow parameters based on specific assumptions.

For better predicting the overall hydrodynamics of slug flow,Fernandes et al.[15]tried to develop an overall model based on some empirical correlations proposed by former researchers.To simplify the calculation,they considered an idealized unit cell which is consisting of a TB,a water falling film,an adjacent liquid slug under the condition of fully developed flow.Based on this specialunitcell,they analyzed the flow characteristics and constructed the model equations.To close the equations,a mass balance model of discrete bubbles was introduced.It was reported that this overall model could calculate the pressure drop,phase velocity,void fraction for slug flow,but there still existed some prediction errors as stated in their conclusion[15].

In fact,there are a lot of small discrete bubbles being embedded in slug flow.These bubbles could shed from the tail of TB and also recoalesce with the successive TB,which greatly affects the hydrodynamics of slug flow.Fernandes et al.[15]had considered this problem and proposed a simple model on the entrainment of gas bubbles from TB.But the gas entrainment in[15]was not accurate enough as commented by Brauner and Ullmann[16],who thought the effect of surface tension,which plays a role in bubble fragmentation,was ignored in that model.Based on the overall model[16,17]the flux of small bubbles was further modified by considering the effect of surface tension and an overall model of slug flow was proposed,by which some parameters of slug flow,such as void fraction and TB velocity,could be calculated.The derivation of their model in[16]was difficult because the liquid slug was divided into two parts:a wake region and a far wake region.However,there is still no way to clearly distinguish the two different regions.

Moreover,the discrete bubbles could also increase the velocity of TB due to their re-coalescence with the successive TB as pointed in[18].Few researchers considered about this phenomenon when constructing their models,which would result in a big error for predicting the characteristics of slug flow.Thus,to construct a high precision model,it is a necessity to consider the re-coalescence of small discrete bubbles with TB.In this study,an overall model taking account of bubbles entrained from the tail of TB and re-coalesced with the successive TB was developed to predict the hydrodynamics of slug flow.An experimental study is carried out to observe the slug flow and measure its velocity field by using a high-speed camcorder and PIV,respectively.

2.Modeling for Slug Flow

Fig.1.A slug unit.

An idealized unit cell of slug flow consisting of a TB,a water falling film,and a liquid slug is shown in Fig.1 by assuming a stable slug flow in an airlift pump.To analyze the hydrodynamics of slug flow,a fixed coordinate system(x0–z0)and a moving coordinate system(x–z)attached to the nose of TB were used as shown in Fig.1.It is worth noting that the moving coordinate system was only used to describe the axial variation of film thickness relative to the TB nose.In Fig.1,the TB moves at a velocity of UGTBwhich is more quickly than that of liquid slug.Thus,a little liquid is shed from the bottom of the liquid slug,forming a film falling around TB with a velocity of ULf.Small bubbles in the wake of TB with a velocity of UGEare en-trained from the tail of TB.Among these,part of small bubbles could re-coalesce with the tail of TB at a velocity of UGBand the other will flow out of the TB tail at a net rate of UGE-UGB.In the stable slug flow,the length of liquid slug and TB almost remained constant,which means the net gas flow(UGS=UGE-UGB)shed from the tail of TB will eventually be absorbed into the nose of the trailing TB.The recurrent bubble entrainment from the tail of TB and the re-coalescence with the trailing TB will result in an effective increase of TB rise velocity,UTB.

2.1.Rise velocity of TB

It is noted that there is a difference between the two velocities of UGTBand UTB.UGTBis the true velocity of gas inside a TB as shown in Fig.2,which ignores small bubble fusion with TB,while UTBis the observed rising velocity,which is superposition of the gas velocity in TB(UGTB)and an additional velocity increment(ΔUG-ent)due to small bubble coalescence with TB:

Fernandes et al.[15]ignored this additional velocity(ΔUG-ent)because it was too complex to calculate.That is also one of the reasons why an error exists when predicting the hydrodynamics of slug flow.To calculate the TB rise velocity,Mao and Dukler[18]estimated the additional velocity by supposing this additional velocity is proportional to the velocity difference between TB and bubbles in liquid slug.They proposed a simple theoretically equation for this additional velocity[18]:

where εLSis the void fraction in liquid slug,εTBis the void fraction in the TB segment,and UGLSis the gas velocity in liquid slug.

Combining Eqs.(1)and(2),the rise velocity of TB could be rewritten as follows:

For UGTBin Eq.(3),Van Hout et al.[19]and Braunerand Ullmann[16]estimated it as a superposition of the TB velocity in a stagnantliquid and a mixture velocity:

where C0TBis the velocity distribution parameter,and it is suggested to equal to 1.2 for fully developed turbulent flow in gas–liquid flow.U0TBis the TB velocity in stagnant liquid.Umis the mixture velocity.

In a vertical pipe,Zukoski[20]found that the drift velocity of TB in stagnant liquid is related to the liquid viscosity,surface tension and pipe diameter.He suggested a correlation to describe the TB velocity in stagnant liquid:

where D is pipe diameter,ρLis the liquid density,ρGis the gas density,and g the gravity acceleration.

Fig.2.A sketch for the model of TB rise velocity.

2.2.Bubble entrainment

The entrainment is caused by a plunging jet from the falling film entering the gas–liquid mixture of a liquid slug,which eventually entrains a mass of gas in the trailing TB and generates small bubbles in the liquid slug.Most of the researchers[21,22]stated the disturbances on the jet surface are responsible for the flux of small bubbles.Brauner and Ullmann[16]further investigated the expression of the entrainment flux(UGE)and found that it is proportional to the flux of turbulent energy supply by the penetrating liquid film “jet”at a rate U jet:

where CJis a constant,its value is about 1 for slug flow,as estimated by Brauner[16],σ is the surface tension,dmaxis the maximal bubble size,Ujetis a relative velocity between the water falling film and the liquid slug,and u′,v′,and w′are the velocities of compound shear layer in three directions.And

where ULfis the velocity of liquid film.

The flux of turbulent energy is associated with the collision between the liquid film(ULf)and the liquid slug(ULLS).Brauner and Ullmann[16]had estimated its conservative values according to recent data of the velocity field in the wake of a single TB rising in a vertical pipe:

Gas entrainment was substantiated to occur only if the turbulent energy is big enough.A critical Weber number was usually employed as a threshold value to judge bubble entrainment[23]:extended their study by introducing the effect of fluid properties,pipe diameter and pipe inclination on the breakage of continuous gas flow.All of their study shows that the dimensionless bubble size greatly depends on the Eotvos number.For a vertical pipe,Brauner and Ullmann[16,17,26]suggesta simple correlation for estimating the dimensionless maximal bubble size as follows:

From Eqs.(10)–(11),the maximal bubble size could be calculated by

For a vertical pipe with ID 40 mm,the maximal bubble size is 1.7 mm.This value is very reasonable compared with the result of Brauner[16]who estimated the maximal size is about1.68 mm in diversified flow patterns for pipe diameter of 51 mm.

For the value of the critical Weber number,it could be deduced from the maximal bubble size and the critical flux of turbulent energy(Eq.(9)),in theory.However,the flux of turbulent energy is not easy to be measured.Sevik and Park[27]had investigated the critical Weber number for the breakage of air bubble in water in a rectangular tank.Brauner and Ullmann[16]further estimated the critical Weber number for bubble breakage from the tail of TB in a circular pipe.They proposed the value of critical Weber number is 0.667.

Inserting Eqs.(8)–(11)in Eq.(6)results in

For the maximal bubble size(dmax)in Eq.(9),Calderbank[24]and Brodkey[25]tried to predict the maximal size of the stable spherical bubbles entrained from continuous gas phase.Brauner[26]further

Part of the small bubbles en-trained from TBmay re-coalesce with its tail resulting in a bubble back flow.The back flow is generated due to the velocity difference between small bubbles and TB.Brauner and Ullmann[16]had an expression for the rate of this back flow as

where U0is the drift velocity of small bubbles in liquid slug.This drift velocity had been estimated by Harmathy[28]:

Thus,the net gas rate flowing out of TB tail could be calculated by

The net gas flow forms a series of dispersed bubbles in liquid slug resulting in a void fraction in liquid slug.Moreover,these dispersed bubbles coalescing with the successive TB at its nose produce a rise velocity.In a developed slug flow,the net gas flow is proportional to the difference between the rise velocity and the TB velocity[29]:

2.3.Gas and liquid velocities in liquid slug

The drift- flux model as one of the most accurate models for bubbly flow in the slug regime has been used for solving many engineering problems[30].This model could be given as

where C0is the distribution parameter,ULLSthe liquid velocity in liquid slug.The value of C0is greatly dependent on bubble concentration and velocity distributions in liquid slug.For an axisymmetric concentration of small bubble in vertical pipes,the range of this value is about 1.05–1.3[16].To simplify the calculation,it is approximately equal to a mean value of 1.175.

2.4.The liquid film

In the segment of TB(Fig.1),the mixture velocity could be regarded as the sum of the apparent film velocity and the apparent gas velocity,according to the overall mass balance:

Thus,the apparent film velocity(εLFULf)could be obtained from the mixture velocity and the apparent gas velocity(εTBUGTB)[16,17],where εLFis the film holdup,which could be calculated from its film thickness:

According to the derivations in[16],the gradient of the film holdup could be written as follows:

where τfand τiare the shear stressesbetween the liquid and the wall,the gas–liquid interface,respectively,=z/D the dimensionless axial coordinate.

It should be noted that Eq.(24)proposed by Brauner and Ullmann[16]describes the variation of film thickness along TB.From Fig.1,it was easy to be observed that the film holdup is εGLSat the top of TB nose.Thus,in the moving coordinate system,the boundary condition of Eq.(24)is as follows:

Moreover,the shear stress in Eq.(24)could be estimated according to its slip velocity and the corresponding friction coefficients.Thus,the above two stresses in Eq.(24)could be calculated by

where ffand fiare friction coefficients between the liquid and the wall,the gas–liquid interface.The friction coefficient of gas liquid interface could be estimated based on Wallis correlation[31]:

where C=16,n=1,for laminar flow,and C=0.046,n=2 for turbulent flow,and Re is the Reynolds number,which is defined as

where ηLis liquid viscosity.Dhis the liquid hydraulic diameter and it is about 4 h for liquid film.

2.5.The TB length

The TB length could be obtained from the mass balance of gas in a slug unit.

where JGis a super ficial gas velocityin airlift pump,is the dimensionless TB length(=LTB/D),and is the dimensionless slug length

From Eq.(31),the TB length could be rewritten as follows:

As compared with the models of Fernandes[15]and Mao-Dukler[18],the present model consisted by a series of Eqs.(1)–(19)can detailedly reflect the hydrodynamics of dispersed bubbles entrained from TB tail and re-coalesced with TB nose.This may make the current model closer to actual slug flow.

The numerical solution for this model is similar to that proposed by Brauner and Ullmann[16].To solve this model,a solution of three nonlinear equations(Eqs.(3),(19),(24))for the unknown parameters(UTB,εLS,εLf)was required,while the other equations are explicit auxiliary equations.For a certain length of TB,the most common method is to discretize the differential Eq.(24)in the axial direction.For a discrete element,the remaining two nonlinear equations with other auxiliary equations need to be solved by a nonlinear equation algorithm.After solution of this element,a new boundary condition for another one should be updated.However,the length of TB(in Eq.(32))depends on some unknown parameters,such as,UGLS,εLS,and εTB,which means the TB length should also be updated to a stable one in this calculation.This would result in complex iteration and big calculation error,which greatly depends on the number of discrete units.For this problem,Brauner and Ullmann[16]proposed a two stage procedure according to the following steps.

The first stage is to replace Eq.(24)with a prescribed value of film thickness.It is approximately equal to a mean film holdup,which could be measured from the images captured by a high speed camera,as said in[16].Thus,by setting the operation condition of slug flow(Um),two implicit Eqs.(3)and(19)for unknowns(UTB,εLS)are much easier to be solved by a least square method.In the second stage,Eq.(24)could be solved by using a Runge–Kutta method.Thus,the distribution of film holdup along TB could also be estimated.To verify the correctness of the algorithm,a comparison between the prescribed value of film thickness and the calculated one by Eq.(24)could be done.It was found that solving this complex model using the two stage algorithm is more convenient and accurate.

3.Experimental

3.1.Experimental setup and data acquisition

The experimental apparatus is shown in Fig.3.It mainly consists of a 40 mm inner diameter lifting tube(2500 mm long)made of transparent plexiglass to visually observe the flow structure.A centrifugal pump was used to controlling the submergence ratio defined asγ=L2/L(in Fig.3)by regulating the height of water in the storage tank.

In this experiment,the submergence ratio was 0.9,and the air discharge varies from 0 to 20 m3·h-1.A gas turbine flow meter with an accuracy of±1%was mounted near the air injector to get the inlet air flow rate(QG).A water flow meter with an accuracy of±0.5%was employed to get the water flow rate(QL).The mixture velocity could be calculated as follows:

A high-speed camcorder(Phantom M310-12G,VRI,USA)was employed to visually examine the hydrodynamics of slug flow in airlift pump.This camcorder with a 1280×800 pixel resolution was mounted at a height of 2000 mm above the air injector by using a shooting frequency of 1500 frames·s-1.In addition,a couple of cold light sources of LED were used to get a better lighting effect.

To better capture the hydrodynamics of slug flow,a PIV as shown in Fig.4 was also used to measure the velocity field in slug flow.It is noted that the PIV measurement was not synchronized with the recorder by high-speed camcorder,because PIV measurement was conducted at night to avoid the effects of natural light.The light source was supplied by a double pulse Nd:YAG laser(Type Vlite350)with a pulse energy of 350 mJ.Image capture system was a 630090 Powerview 4MP-LS Camera(SR-CMOS,12 bit,1024 × 1024 pixels,5.5 μm pixel pitch),which was mounted normal to the laser sheet.The central plane of the riser pipe,which was illuminated by the laser sheet,was chosen as a measured plane.Al2O3particle was adopted as the tracer according to[32].The main settings of PIV systems were:data acquisition frequency was 20 frame pairs per second,the time interval between two pulses was from 500 to 1000 μs for different air flow rates.

Fig.3.The schematic of airlift pump.

Fig.5.Measurement for TB velocity.(a)Schematic diagram,(b)an example.

3.2.Data processing

3.2.1.TB velocity

Fig.5(a)shows the two positions of TB at a time interval Δt.The distance(Δz)between the noses of two successive TBs could be measured with a ruler.Thus,the velocity of TB could be estimated as follows:

Fig.5(b)shows an example photo for measuring TB velocity.We measured 10 TB to determine the average velocity under each experimental condition.

3.2.2.Liquid velocity

The liquid velocity in liquid slug could be calculated from the velocity field in liquid slug.The mean value of liquid velocity in a slug could be calculated as follows:

where viis the vertical velocity in velocity plot,m is the number of velocities in liquid slug.

It should be noted that mean values of liquid velocity should be a volume-averaged velocity in theory.Moreover,the velocity distribution of water film should also be an average in the whole radius sampled for the local liquid velocity.However,there is still no way to obtain its volumetric velocity field for a long pipe due to the difficulty for the spatial arrangement of PIV cameras and laser lens.For this problem,multiple velocity fields at the same flow condition were used to calculate their mean values for water velocities in slug and in water film.

3.2.3.Velocity of water film

The velocity of water film could also be estimated from the velocity field around TB.As we know,the falling film accelerates in the vertical direction due to the effect of gravity.Thus,we need to know the velocity profile along the length of TB.In the velocity field around TB,we calculated the mean velocity of water film at the same horizontal position and recorded the corresponding distance from the nose of TB.

3.3.Uncertainty analysis

The main parameters extracted from the experimental data are TB velocity(UTB),liquid velocity(ULLS)and liquid film velocity(ULf).Their uncertainties were analyzed as follows:

(1)The error of UTB.The value of TB velocity was measured from the images as shown in Fig.5.Thus,the error was determined by measured displacement(Δz)and the corresponding time(Δt).According to Eq.(34),the error of TB velocity could be estimated by

The uncertainty error of measurement time interval is equal to half of the camera frame exposure time accuracy(0.5×10-6s),while the error of measured distance is equal to the minimum scale of a ruler(0.001 m).In this experiment,the time interval Δt is in a range of 0.1 s–0.3 s.According to the calculation method,the maximum error of could be estimated to be 0.2%.

(2)The errors of ULLSand ULf.ULLSand ULfwere estimated from PIV results.However,the uncertainty of the PIV results is very complex to calculate.By comparing the PIV results in airlift pump with that measured by LDV,which has a high measuring accuracy(0.7%),it could be estimated that the maximal error between PIV results and LDV results is about 5.1%,indicating the PIV results in this work is acceptable.From the above,we could conclude that the errors of ULLSand ULfare about 5.8%.

4.Results

For airlift pump,water is pumped by the buoyancy force of gas flow.The superficial water velocity(JL)at different superficial gas velocity(JG)was shown in Fig.6.For superficial gas velocity in a range of 0–4 m·s-1,the airlift pump of 40 mm ID operates in a slug flow regime.

4.1.Visual observations

Fig.7 shows the slug flow for JG=0.3 m·s-1.It is characterized by Taylor bubbles with a diameter approximately equal to the tube diameter.Small bubbles in liquid slug are presented mainly due to the fragmentation of the bubble tail as shown in Fig.7(a)and(b).Part of small bubble can re-coalesce with the next TB as shown in Fig.7(c)and(d).

4.2.PIV results

Fig.8 shows the instantaneous vector plot of the velocity field round a TB at JG=0.74 m·s-1.Fig.8(a)shows the velocity field in the region around the nose of TB.The axial component of velocity reaches its maximum at the top of TB.Fig.8(b)shows the velocity field around the tail of TB at JG=0.74 m·s-1.It could be found that some complex vortex structures in velocity field.In general,a pair of symmetrical vortexes was reported to be formed at the lower corner of a TB in its average flow field by many investigators[32].However,vortex structure in the instantaneous vector plot is more complex than that of average flow field.Fig.8(c)and(d)shows the velocity field in the wake of TB at JG=0.74 m·s-1.It could be found that some vortexes could also be observed between-4＜z/D＜-3.6.This kind of vortex was induced by the small bubbles in liquid slug.For instantaneous vector plot,liquid also has a complex motion.

5.Model Predictions and Discussion

5.1.Validity of the predicted model

The TB velocity could be estimated from the images captured by the high-speed camcorder,while the liquid velocity and the film velocity are obtained from PIV results.Thus,these velocities(TB velocity,liquid velocity and film velocity)are used as experimental data to verify the model.

Fig.9(a)shows the calculated TB rise velocity at different gas superficial velocities,and the linearity is obvious as reported in many experiments[33–34].Fig.9(b)shows the liquid velocity in the liquid slug versus the gas superficial velocity.Fig.9(c)shows the velocity of liquid film versus the dimensionless distance from TB nose at three gas velocities(JG=0.7 m·s-1,1.4 m·s-1,2.1 m·s-1).The above comparisons in Fig.9 testify well the validity of the present model of slug flow.Moreover,their errors of UTB,ULLS,and ULfbetween calculated and tested data are about 6.1%,14%,and 12.4%,respectively.Thus,the uncertainty of this model is about 14%.

5.2.Prediction of characteristics of slug flow

Fig.10 shows the rise velocity of TB versus gas superficial velocity for different diameters.The rise velocity increases slightly with increasing diameter.This is because the drift velocity of TB in stagnant liquid is higher in a large diameter(see Eq.(5)).Another phenomenon is that this velocity increment at larger diameter is more obvious in a high gas superficial velocity,which indicates that the bubble coalescence at the nose of TB is more serious at high gas superficial velocity.

Fig.6.Superficial water velocity versus superficial gas velocity.

Fig.7.Photos of slug flow for J G=0.3 m·s-1 at different time.(a)t=0,(b)t=0.1 s,(c)t=1.222 s,(d)t=1.226 s.

Fig.8.Velocity vector plots in slug flow at J G=0.74 m·s-1 and J L=0.26 m·s-1.(a)Around TB nose,(b)around TB wake,(c)in liquid slug,-3.3＜z/D＜-2.2,(d)in liquid slug,-4.1＜z/D＜-3.3.

Fig.9.Comparison of the model predictions with the present experimental data.(a)TB velocity,(b)velocity of liquid in liquid slug,(c)liquid film velocity at different operations.

Fig.10.TB rise velocity versus gas superficial velocity.

Fig.12.Void fraction in liquid slug versus gas superficial velocity.

From Fig.11,it can be seen that the net gas flow of small bubbles increases with increasing gas superficial velocity after a threshold value(JG＞0.7 m·s-1).When JG＜0.7 m·s-1,no bubble is generated in the tail of TB due to the effect of surface tension which tries to keep a stable interface.When JG＞0.7 m·s-1,the turbulence in the wake of TB becomes stronger which deforms the tail of TB and produces a lot of small bubbles.The large diameter can increase the net gas flow at the same gas superficial velocity which indicates the fragmentation of TB tail becomes more serious since the Weber number increases with diameter as seen in Eq.(14).

Fig.12 shows the void fraction versus gas superficial velocity for different diameters.It can be seen that the gas superficial velocity must exceed a minimum threshold value before gas can be en-trained into the slug body.The void fraction is mainly a function of the gas superficial velocity.Nydal et al.[35]also found this phenomenon in their experiment,the void fraction was mainly a function of gas velocity,and a weaker effect of liquid velocity on void faction can be observed.The void faction increases linearly with the gas superficial velocity in a range of 0.7–0.8 m·s-1.While in a large gas superficial velocity(JG＞0.8 m·s-1),void fraction then slowly increases.This is due to the distribution of small bubbles in liquid slug.From the high speed camcorder,it could be observed that a swarm of bubbles,in which bubbles interact with each other,is formed after the gas superficial velocity exceeds 0.8 m·s-1.Moreover,the diameter has a small effect on the void faction in a high gas superficial velocity(JG＞0.8 m·s-1).The large diameter can decrease the void fraction slightly,as shown in Fig.12,due to the quick increment of volume of liquid slug but slow increment of bubble flow rate.

Fig.11.Net gas flow rate of small bubbles versus gas superficial velocity.

Fig.13.Liquid velocity in liquid slug versus gas superficial velocity.

Fig.14.Film thickness distribution along.

Fig.13 shows the liquid velocity in slug versus gas superficial velocity.It could be found that liquid velocity steeply increases with gas superficial velocity within a low velocity range(JG＜0.7 m·s-1).When JG＞0.7 m·s-1,it slowly increases with gas superficial velocity.This may be due to the variation of void fraction in liquid slug.It could be deduced from Fig.12 that no small bubbles exist in liquid slug for JG＜0.7 m·s-1as void fraction is almost 0 under this condition,which indicates liquid is totally driven by TB.In this case,the liquid flow is stable and its velocity increases linearly with the increasing gas superficial velocity.When gas superficial velocity is large enough,small bubbles shed from TB could disturb liquid flow.Under this condition,liquid velocity would not be linear with the gas superficial velocity.Moreover,the large diameter could increase liquid velocity in liquid slug.This is also consistent with the result in[36]that more liquid is required to obtain slug flow in large diameter pipes.

Fig.14 shows the dimensionless thickness of liquid film versus dimensionless length of TB at JG=1.4 m·s-1.Fig.15 shows the film velocity versus length of dimensionless length of TB at JG=1.4 m·s-1.It could be seen that large diameter increases the thickness of liquid film but decreases the film velocity.As shown in Eq.(27),large diameter increases the drift velocity of TB in stagnant liquid resulting in a larger interface friction between gas and liquid.Therefore,the large interface friction hinders the motion of falling film and increases the thickness of falling film.

Fig.15.Film velocity distribution along TB.

6.Conclusions

A model of the slug flow taking into account the bubble entrainment was proposed.A high-speed camcorder was employed to observe the motion of Taylor bubble at different mixture velocities.Furthermore,a PIV was also used to measure the velocity field of liquid around Taylor bubble.The conclusions are obtained as follows:

(1)The model of slug flow was valid to predict the hydrodynamics of slug flow in airlift pump.Errors of TB velocity,liquid velocity,and film velocity between predicted and experimental data are below 14%.

(2)Large pipe diameter could increase the rise velocity of Taylor bubble and decrease void fraction in liquid slug by a small margin.

(3)Liquid velocity in slug drastically increases with superficial gas velocity in a low range(0.7 m·s-1＜JG＜0.8 m·s-1),and slowly increases with superficial gas velocity in a high range(JG＞0.8 m·s-1).

Nomenclature

C0distribution parameter of small bubble

C0TBdistribution parameter of Taylor bubble

D pipe diameter,m

Dhhydraulic diameter,m

dmaxmaximal bubble size

EoDEotvos number

fffriction coefficient of liquid-wall

fifriction coefficient of gas–liquid

g gravity acceleration,m·s-2

h film thickness,m

JGsuperficial gas velocity,m·s-1

JLsuperficial liquid velocity,m·s-1

L length of riser pipe,m

L2static depth of liquid,m

LTBlength of Taylor bubble,m

LLSlength of liquid slug,m

m number of data in velocity plot

PIV particle image velocimetry

QGgas flow rate,m3·s-1

QLliquid flow rate,m3·s-1

Re Reynolds number

TB Taylor Bubble

U0drift velocity of small bubble,m·s-1

U0TBTB velocity in stagnant liquid,m·s-1

UGEentrainment velocity,m·s-1

UGBrate of bubble back flow,m·s-1

UGLSgas velocity in liquid slug,m·s-1

UGSnet gas rate,m·s-1

UGTBgas velocity inside TB,m·s-1

Ujetrelative rate of film jet,m·s-1

ULfvelocity of liquid film,m·s-1

ULLSliquid velocity in liquid slug,m·s-1

Ummixture velocity,m·s-1

UTBrise velocity of TB,m·s-1

vivelocity in velocity plot,m·s-1

We Weber number

γ submergence ratio

ΔUG-entadditional velocity,m·s-1

εLffilm holdup

εTBvoid fraction in TB segment

εLSvoid fraction in liquid slug ηLliquid viscosity

ρLliquid density

ρGgas density

σ the surface tension

τfshear stress of liquid-wall

τishear stress of gas–liquid