• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Experimental detection of bubble-wall interactions in a vertical gas-liquid flow☆

    2017-05-29 01:39:36XingWangJiaoSunJieZhaoWenyiChen

    Xing Wang ,Jiao Sun ,3,Jie Zhao ,Wenyi Chen ,*

    1 Department of Process Equipment and Control Engineering,Hebei University of Technology,Tianjin 300130,China

    2 Research Center of Engineering Fluid and Process Enhancement,Hebei University of Technology,Tianjin 300130,China

    3 Department of Mechanics,School of Mechanical Engineering,Tianjin University,Tianjin 300350,China

    4 State Key Laboratory of Coal-based Low Carbon Energy,ENN Science&Development Co.,Ltd.,Langfang 065001,China

    1.Introduction

    Bubble dispersion near wall plays a central role in many industries like chemical engineering,petroleum,food,and pharmaceutical industry.Bubble distribution has a significant effect on strengthening mass and heat transfers and mixing the gas and the liquid in bubble columns,bioreactors and wastewater treatment,etc.It is well known that the wall effect,combined with the wake instability,may cause a more complex path instability forthe rising bubbles.Therefore,ithas practical significance to study the motion of near-wall bubbles and flow characteristics in gas-liquid flow systems for the design and optimization of the processes accompanied with bubble flows.

    The rise of a bubble driven by buoyancy in a still liquid has been investigated mainly for the trajectory and shape.The inertia,viscosity,surface tension,and also the contamination of the bubble surface were key factors for the bubble movementwhich were successfully explained by Clift[1].In stagnant and clean water,a small bubble whose diameter was less than 1.3 mm could keep a spherical shape and rise in a straight line.Zenit&Magnaudet[2]found that the so-called path instability was attributed to the asymmetry of the vortical structures in the wake.However,as the bubble size increased,its shape began to deform to ellipsoidal,oblate ellipsoidal,or cap shape,and proceeded in a zigzagging,helical,or more complex movement.In many practical situations,the rising bubbles would encounter incline or vertical wall.Some scholars researched bubbles near inclined wall in the past many years[3-8].Recent theoretical and experimental studies on the near-wall bubbles in gas-liquid flow attracted widespread attention.Chen binet al.[9,10]focused on the trajectory of near-wall bubbles in low and high viscosity liquids.They demonstrated that the existence of the wall could restrain the velocity component by direct numerical simulation.Sygioka and Komori[11,12]developed a new mathematical model and numerical simulation procedures aboutnear-wall bubbles.De Vries[13]explained the motion characteristic of a spherical bubble near a plane wall in pure water using direct numerical simulation and optical experiments.According to their reports,the wake vortex gradually evolved into vortex blob when the bubble collided with a vertical wall.The parameter determining the transition from a straight ascending to a zigzag trajectory was the Weber number.Takemura and Magnaudet[14,15]investigated the motion of a spherical bubble moving near a plane wall in a quiescent water and silicone oils at small Reynolds number(Re≤30),in which the viscous effect was dominant,the rising bubble migrated away from the wallunderrepulsive liftforce caused by diffusion of the vortex in the interaction between the walland bubble wake.But asReincreased,the boundary layer on bubble surface became thinner and liquid velocity was reduced between the bubble and the wall.Due to the velocity distribution,wall-normal pressure gradient around the bubble caused the bubble to be attracted towards the wall.In recent years,based on the conclusions of Takemura and Sugiyama[16]showed that a deformed bubble near the vertical plane had lateral migration in viscous liquid numerically.When the gap between the wall and the bubble became narrower,the bubble bounced off the wall because of the interaction effects of attraction and repulsive lift.Zenget al.[17,18]discussed lift and drag coefficient of a rigid sphere near wall.They revealed that lift coefficient decreased withReand the distance between the wall and the bubble forRe<100,while the lift coefficient increased forRe>100.Sugioka and Tsukada[19]obtained similar conclusions by numerical calculation hereafter.

    In summary,the main research approaches of flow structure about near wall gas-liquid two-phase flow were numerical simulations and the conclusions were limited to continuous phase around single bubble.The optical experiments of predecessors were primarily interested in the bubbles'trajectory and the effects of attraction and repulsion in the process of bubble rising.Few scholars cared for the motion characteristics of bubble chains and the velocity field around bubbles near the vertical plane wall.Therefore,in the present study,the bubbles'motion characteristics rising with an in finitesimal deformation were discussed by high speed photography technology and the statistical characteristics ofthe flow field around the bubbles were experimentally investigated by the particle image velocimetry(PIV)measurement.The effect of bubble injecting frequency and the distance between the bubble and the plane wall on bubble motions and flow field characteristics such as statistical bubbles'trajectories,average velocity distributions of flow field and Reynolds shear stress,were analyzed.

    2.Experimental Set-up and Method

    As illustrated in Fig.1,an acrylic cube container(220×220×350 mm3)with a stainless steel nozzle(inner diameter of 0.8 mm)located at the center of the bottom and a detachable glass vertical plane was used in the experiment.The 40%glycerin aqueous solution(ρl=1087.1 kg·m-3,γ =0.0666 N·m-1,μ =3.203 × 10-3Pa·s)has already been filtered,because contaminated liquid would affectbubbles'dynamic characteristics[20-22].A chain of bubbles,generated from compressed air through the nozzle,rose due to buoyancy in quiescent liquid.The frequency ofbubble generation was controlled by a pressure regulatorin the following two situations:bubbles rising freely and near the vertical wall.The four differentinjecting frequencies ofbubbles weref1=47 Hz,f2=126 Hz,f3=157 Hz andf4=210 Hz.The vertical wall was moved horizontally to change the distanceSbetween the nozzle and the wall,asS1=1.5 mm,S2=3 mm andS3=4.5 mm.Therefore,there were totally 16 working conditions in the experiment.The illumination of the test region was provided by an LED light behind the rectangular tank,installed with a piece of sulfuric acid paperas a lightdiffuse.The bubble behavior was recorded by a high-speed camera(2048×2048 pixels),and 10,000 images were obtained continuously at a frame rate of 100 Hz.The image sequences obtained were analyzed by a digital image processing algorithm based on MATLAB software.Fig.2 showed the original photos of two bubbles taken in the experiment.The circle in Fig.2 around the bubble was the result of ellipse fitting of the bubble after processing with MATLAB.

    Fig.2.The original photo of bubbles taken in the experiment.

    Fig.1.Sketches of experiment system:1.Air pump,2.Press regulator,3.Diffuser plate,4.Water tank,5.CCD camera,6.Laser,7.LED light,8.Vertical plane wall,9.Nozzle.

    To investigate the flow field ofgas-liquid flow,time-resolved particle image velocimetry(TR-PIV)system(LA Vision)was implemented.The laser(100 mJ)plane was aligned vertically to induced fluorescence of Red fluorescent polymer microspheres seeded in the flow,with the density of1050 kg·m-3and the diameterof20-50μm.Particle images were recorded by a high-speed camera with a resolution of2048×2048 pixels at the sampling rate of 100 Hz.10,000 samples data and 9999 instantaneous velocity fields were obtained in the experiment.The final interrogation window had a size of 32×32 pixels and an overlap ratio of 75%.Table 1 showed the details of different experimental conditions,thatRe=Vtdeρlμ-1,Eo=g(ρl- ρg)de2γ-1andMo=(ρl- ρg)gμ4/γ3ρl2.Here,ρland ρgare the density of glycerin aqueous solution and air,respectively,gis the gravitational acceleration,Vtis the terminal rising velocity of bubble,γ and μ are the surface tension and kinematic viscosity of glycerin aqueous solution,respectively.The original PIV images of rising bubbles in the condition off2=126 Hz were showed in Fig.3,where the bubble was shown to be within a broken red line in the pictures.

    Table 1Experimental conditions

    3.Results and Discussion

    3.1.Rising behavior of the near wall bubble train

    Normally,dimensionless parametersEo,MoandRecan be used to describe the characteristics of bubbles in a stagnant liquid,different shapes of bubbles have differentEoandMo[23-25].Clift[1]researched bubbles in liquids with different physical properties and drew a classic diagram,shown in Fig.4,which could describe differentbubbles related to differentEo,MoandRe.There were three types of bubble rising,i.e.rectilinear,zigzag and spiral trajectory[2,10,24-28],both of the last two unsteady motion was mainly caused by asymmetric distributions of the vortical structures behind the bubbles.Subsequently,some researchers studied the relation of dimensionless parameters in different viscosity liquids by numerical simulation and experimental method.The results were in good agreement with the result of Clift[10,29,30].In the experiment,a suitable inner diameter of nozzle and glycerin aqueous solution with special concentration were prepared to ensure bubbles ascending in a straight line.The enlarged black points in Fig.4 represented four different emission frequencies in the experiment,from which it could be seen that the bubbles in this region were nearly elliptical.

    Fig.5(a)showed the statistical trajectory of a chain of bubbles rising without wall under the condition of four different frequencies.In the figure,x=0 represented the location of nozzle,andy-axis represented the vertical distance above the nozzle surface.As can be seen in Fig.5(b),there were three different stages in the process of bubbles rising:acceleration,deceleration and constant velocity.Fig.5(b)showed thatthe bubble terminalvelocity increased with the advance ofthe bubble frequency.The reason was that the bubble frequency was increased by the higher pressure in the gas pipeline,which caused the bubble to have more inertial energy when escaping from the nozzle.So the bubbles with higher frequency had a larger terminal velocity.

    Fig.3.The original PIV images of rising bubbles:(a)freely rising bubbles without the plane;(b)S*≈ 1.2;(c)S*≈ 2.3;(d)S*≈ 3.6.

    The presence of rigid wall affected the forms of bubble movement,gas hold-up and the structure of the flow field around bubbles.When bubbles rising in straight were affected by rigid wall,not only the surface of bubbles would deform,but also the form of original motion would change.The main forms of nearwall bubble motion included migrating away from the wall,moving towards the wall and bouncing along the wall.The lift force on the bubble played an important role in the movement of the bubble.When the direction of the lift force on the bubble was away from the wall,bubble moved away from the wall.In turn,bubble moved close to the wall.Meanwhile bouncing motion was caused by the direction change in the lift force.

    Fig.4.Shape regions of different frequency bubbles in unhindered gravitational motion through stagnant liquids in the experiment[1].

    Fig.5.Statistical trajectories(a)and speed curve(b)of freely rising bubbles with four different frequencies.

    Bubble motion characteristics were compared under the conditions of different distanceSbetween the vertical plane and the nozzle.When the normalized initial distanceS*≈1.2,bubbles ascended in zigzag trajectory and the trajectory of all bubbles overlapped greatly,as shown in Fig.6.The vertical wall was located in the negativex-axis.The first bouncing happened when the bubble collided with the wall after escaping from the nozzle and then bubbles ascended in zigzag trajectory.Meanwhile,all bubbles with different frequencies had a tendency to migrate away from the wall.Theoretically,bubble motion characteristic was in fluenced by the combined effect of both inertial force and lift force when the bubble escaped from the nozzle.In the experiment,the frequency of the bubbles was controlled by adjusting the pressure regulator.With the augment of pressure,the frequency of the bubbles would gradually increase.From the perspective of qualitative analysis,the speed of bubbles escaping from the nozzle must be increase gradually,and therefore the inertial force would increase gradually.About the effect of lift force which caused by the wall on bubble motion characteristics,evidence can be found in the literature.Many scholars have used direct numerical simulation to numerically demonstrate the change in the direction of lift force.Zenget al.[17,18]discussed lift and drag coefficient of a rigid sphere near wall.At lowRe,the moment coefficient was negative,but it rapidly increased and became positive even with a small increase inRe.The lift coefficient decreased withReand the distance between the wall and the bubble forRe<100,while the lift coefficient increased forRe>100.In addition,vorticity generated on the particle surface was not symmetrically distributed in the wake due to the presence of the nearby wall.The asymmetry in the vorticity distribution contributed to an asymmetric induced flow,whose effectwas to generate a liftforce on the particle directed away from the wall.Sugioka and Tsukada[19]calculated the drag and lift forces acting on a spherical bubble moving near a plane wall over a wide range ofRefrom 1 to 300,and to numerically demonstrate the change in the direction ofliftforce.The main resultsshowed thatthe direction of the lift force on the bubble changed from towards the wall to away from the wall betweenL/d=0.6 and 0.7 when the Reynolds number was larger than 100.Whatcan be con firmed was thatthe direction of the lift force was away from the wall in the present condition.So with the combined effect of inertial force and lift force,all bubbles with different frequencies tended to migrate away from the wall.This was also consistent with the result from the experiment.

    Fig.7 showed bubble trajectory with different frequencies whenS*≈ 2.3 andS*≈ 3.6,respectively.WhenS*≈ 2.3,Fig.7(a)revealed that all the bubbles of different frequencies had a tendency to move close to the wallafterescaping from the nozzle when the rising distancey<20 mm.However,in the location of 20 mm<y<60 mm,bubbles moved away from the wall obviously.Furthermore,low-frequency bubbles ascended in straight lines wheny>60 mm and the distance between the rising bubble and the wall increased gradually.But the increase of that distance was not obvious for bubbles with higher frequency(f4=210 Hz).In Fig.7(b),underS*≈3.6,low-frequency bubbles ascended in straight lines,and also gradually migrated away from the wall,but with the frequency increasing,the bubbles gradually moved towards to the wall.By contrasting Fig.7(a)to(b),at the same frequency,with the increase ofS*,the lateral migration distance of the bubbles decreased gradually.At the sameS*,the lateral migration distance of the bubble also decreased with the increase of the frequency.The wall effect would decrease as the initial distance from the bubbles to the wall increased.WhenS*became larger,the wall effect acting on the bubble would decrease,thatis,the effectofliftforce would decrease,and the increase of frequency caused the inertial force of the bubble to increase.AstheS*and the frequency increased,the proportion ofthe inertial force increased gradually in the combined action of the inertial force and the lift force.If the proportion of the inertial force was greaterthan the lift force,the trajectory of the bubble showed the reduction of lateral migration distance,.i.e.,the bubble moved close to the wall.In summary,the bubble frequency and the normalized initial distance between the bubble and the wall commonly affect the movement of bubbles,so the bubbles also appeared in different motion states in different frequencies and distances.

    Fig.7.Statistical trajectories of bubbles with(a)S*≈2.3;(b)S*≈3.6.

    3.2.Flow characteristics around the near wall bubble

    In stagnant liquids,the average flow fields around the bubbles were symmetrical if the bubble ascended in a straight line without wall.When the ejection frequency of bubbles was increased,the average velocity of the liquid around the bubbles became larger,since the higher terminal velocity of bubbles could continuously drive liquid around them,as shown in Fig.8.

    The average velocity distributions of flow field in the case ofS*≈1.2 were shown in Fig.9,where the vertical wall was also located in the negativex-axis.Under the in fluence of bubbles ascending in zigzag trajectory,high and low average velocity flow appeared on both sides of the bubbles,alternating with each other.Furthermore,the liquid was extruded when bubbles moved towards the wall,and the compression effectmade the liquid obtain acceleration.So both drive function of bubbles and compression effect of wall collectively led to high-speed fluid existed in the region between the wall and the nozzle.

    The average velocity distributions of flow field with four different bubble frequencies atS*≈2.3 were shown in Fig.10.The regularities of flow field distribution for bubbles moving towards the wall or away from the wall were almost similar.The liquid near wall had relative high velocity,while on the side of far away from the wall it had relative low speed.Because of repressive effect of the wall,the liquid driven by rising bubbles could only change little momentum with low-speed liquid,even including stagnantliquidsin the region between the bubble and the wall.However,the liquid on the side far away from the wall could change more momentum with low-speed and stagnant liquid by the driven of bubbles.Therefore,there was a phenomenon of asymmetrical velocity distribution on both sides of the bubbles.

    In the present,the schemes only considered the flow distributions in the laser sheet,and the results could show the flow regularity around the bubbles[31,32].However,the flow- fields information out of the lasersheetshould notbe ignored.So in the future itshould be measured by other means,e.g.Tomographic PIV,which could help us to see more details of the two-phase flow near the vertical wall.

    3.3.Reynolds shear stress and turbulent intensity around the near wall bubble

    It was well known that Reynolds stress was generated by turbulent fluctuation.In industry production,the size and the distribution of shear stress affected the efficiency of heat exchange and mass transfer.Therefore,itwas significantto study Reynolds shearstress characteristic of near wall gas-liquid two-phase flow.

    The shear stress distributions on both sides of bubbles were symmetrical when bubbles rose without plane wall,as shown in Fig.11.In the wake vortex behind bubbles,the fluid flow directions were opposite,which led positive and negative magnitude of shear stress.As the bubble frequencies increased,liquid surrounding bubbles was driven more frequently,which made higher shear stress of the liquids around bubbles.

    Fig.8.The average velocity distribution of flow field around freely rising bubbles:(a)f1=47 Hz;(b)f2=126 Hz;(c)f3=157 Hz;(d)f4=210 Hz.

    Fig.12 showed the shear stress distribution for different bubble frequencies atS*≈1.2.In this condition,bubbles rose at the zigzag trajectory,and the shapes of the stress distribution looked like blobs.The Reynolds stress distributions were characterized by the alternate positive and negative variations,which were accorded with bubbles ascending in zigzag trajectory.Meanwhile,shear stress magnitudes in the vicinal region near wall were higher than that far from the wall.The blob structure of shear stress was generated only when bubbles ascended atzigzag trajectory nearthe wallbecause thiskind ofsituation could form alternative vortex motion in the wake of bubbles.Although the shear stress magnitude with bubbles at low frequency was small,the blob structures were obvious.The reason for this phenomenon was that the interval between two bubbles of low frequency was bigger than that of high frequency.Thus the vortex structure induced by the first bubble could exist a long time without being destroyed by the next bubble.Nevertheless,the vortex structures induced in the risingprocess of high frequency bubbles were easily destroyed by later bubbles.Thus there were regularities of distribution for Reynolds shear stress in Fig.12.

    Fig.9.The average velocity distribution of flow field around rising bubbles at S*≈1.2:(a)f1=47 Hz;(b)f2=126 Hz;(c)f3=157 Hz;(d)f4=210 Hz.

    With the increase of bubble frequencies,there were large-scale Reynolds stresses in unsteady stage(20 mm<y<60 mm)of the rising bubbles atS*≈2.3,which was seen in Fig.13.It illustrated that there was higher pulsation speed of liquid between the vertical wall and the bubble when near wall rising bubbles lose its stability.In the following rising process,the Reynolds stresses far away from the wallwere higher than that in the region of near wall.It was because that repressive effect of rigid wall would cause the fluid layer to have high mean velocity,while the liquid far away from the wall was less affected by repressive effect and high-speed fluid was easy to move into the fluid layer with smaller mean velocity.Owing to this mechanism,the low-velocity fluid layer was accelerated and higher Reynolds stresses appeared in away from the wall.

    Fig.11.The shear stress distribution for freely rising bubbles:(a)f1=47 Hz;(b)f2=126 Hz;(c)f3=157 Hz;(d)f4=210 Hz.

    Fig.12.The shear stress distribution for rising bubbles at S*≈1.2:(a)f1=47 Hz;(b)f2=126 Hz;(c)f3=157 Hz;(d)f4=210 Hz.

    Fig.14 showed the in fluence of normalized initial distanceS*and bubble ejecting frequency on the turbulent intensity profiles.It was noted that the turbulent intensity profiles were almost symmetrical aboutx=0 for freely rising bubbles with different frequencies.In Fig.14 the peaks became higher as the bubble frequency increased and it was also seen that the turbulent intensities in theydirection were greater than that in thexdirection.Furthermore,the turbulent intensity in thexdirection whenS*=1.2 was higher than other cases,which suggested that the bubbles rising in zigzag trajectory facilitated the uniformity ofturbulence distribution.Butthe value ofturbulentintensity inydirection had no obvious change in different situations in Fig.14.

    4.Conclusions

    Fig.14.Turbulence intensity profiles in different cases.

    The near-wall rising characteristic of bubbles in a chain has been studied and analyzed while varying the normalized initial distance(S*)and bubble frequency(f).In the present experiment,the rising bubbles in a straight line without the wall and more complex path variations due to the wall effectand frequency variation were observed.It is found that near-wall bubble rising trajectory changes from a zigzag path to a smoothly straightline with the increase ofS*.The average flow fields around the bubbles and the turbulentintensity profiles are almost symmetricalwhen bubble ascends in a straightline without wall.When near-wall bubbles ascended in zigzag trajectory,high and low average velocity would alternately appear on both sides of the bubbles,and as well as the positive and negative Reynolds shear stress.For near wall bubbles ascended in analogous straight trajectory,bubbles'trajectory tend to far away or close to the wall,and the fluid between bubbles and the wall has higher velocity and lower Reynolds shear stress.

    [1]R.Clift,J.R.Grace,M.E.Weber,Bubbles,Drops,and Particles,Courier Corporation,2005.

    [2]R.Zenit,J.Magnaudet,Path instability of rising spheroidal air bubbles:A shapecontrolled process,Phys.Fluids20(2008)061702.

    [3]T.Maxworthy,Bubble rise under an inclined plate,Phys.Fluids229(1991)659-674.

    [4]A.Perron,L.I.Kiss,S.Poncsák,An experimental investigation of the motion of single bubbles under a slightly inclined surface,Int.J.Multiphase Flow32(2006)606-622.

    [5]B.Donnelly,T.S.O'Donovan,D.B.Murray,Surface heat transfer due to sliding bubble motion,Appl.Therm.Eng.29(2009)1319-1326.

    [6]B.Chen,Direct numerical simulation of a single bubble rising along an inclination wall,J.Eng.Thermophys.28(2007)965-967(in Chinese).

    [7]H.Ju,G.Chen,G.D.Li,et al.,Experimental study on motion behavior of single bubble rising along inclined plane in still water,Chin.J.Hydrodyn.26(2011)327-332(in Chinese).

    [8]S.M.Dong,G.D.Li,R.Xue,et al.,Experimental research on collision and rebound of single bubble with inclined wall in stationary liquid,J.Water Resour.Archit.Eng.6(2008)50-52(in Chinese).

    [9]B.Chen,Direct numerical simulation of a single bubble rising in still water,J.Eng.Thermophys.26(2005)980-982(in Chinese).

    [10]B.Chen,Direct numerical simulation of a single bubble rising in high viscosity fluid,J.Eng.Thermophys.27(2006)255-258(in Chinese).

    [11]K.I.Sugioka,S.Komori,Drag and lift forces acting on a spherical water droplet in homogeneous linear shear air flow,J.Fluid Mech.570(2007)155-175.

    [12]K.I.Sugioka,S.Komori,Drag and lift forces acting on a spherical gas bubble in homogeneous shear liquid flow,J.Fluid Mech.629(2009)173-193.

    [13]A.W.G.De Vries,A.Biesheuvel,L.Van Wijngaarden,Notes on the path and wake of a gas bubble rising in pure water,J.Multiphase Flow28(2002)1823-1835.

    [14]F.Takemura,J.Magnaudet,The transverse force on clean and contaminated bubbles rising near a vertical wall at moderate Reynolds number,J.Fluid Mech.495(2003)235-253.

    [15]F.Takemura,S.Takagi,J.Magnaudet,et al.,Drag and lift forces on a bubble rising near a vertical wall in a viscous liquid,J.Fluid Mech.461(2002)277-300.

    [16]K.Sugiyama,F.Takemura,On the lateral migration of a slightly deformed bubble rising near a vertical plane wall,J.Fluid Mech.662(2010)209-231.

    [17]L.Zeng,S.Balachandar,P.Fischer,Wall-induced forces on a rigid sphere at finite Reynolds number,J.Fluid Mech.536(2005)1-25.

    [18]L.Zeng,F.Najjar,S.Balachandar,et al.,Forces on a finite-sized particle located close to a wall in a linear shear flow,Phys.Fluids21(2009)033302.

    [19]K.Sugioka,T.Tsukada,Direct numerical simulations of drag and lift forces acting on a spherical bubble near a plane wall,J.Multiphase Flow71(2015)32-37.

    [20]B.Cuenot,J.Magnaudet,B.Spennato,The effects of slightly soluble surfactants on the flow around a spherical bubble J,J.Fluid Mech.339(1997)25-53.

    [21]J.Magnaudet,I.Eames,The motion of high-Reynolds-number bubbles in inhomogeneous flows,Annu.Rev.Fluid Mech.32(2000)659-708.

    [22]S.Takagi,Y.Matsumoto,Surfactant effects on bubble motion and bubbly flows,Annu.Rev.Fluid Mech.43(2011)615-636.

    [23]L.Liu,H.J.Yan,G.J.Zhao,Experimental studies on the shape and motion of air bubbles in viscous liquids,Exp.Thermal Fluid Sci.62(2015)109-121.

    [24]D.Mikaelian,A.Larcy,A.Cockx,etal.,Dynamics and morphology of single ellipsoidal bubbles in liquids,Exp.Thermal Fluid Sci.64(2015)1-12.

    [25]D.Mikaelian,A.Larcy,S.Dehaeck,A new experimental method to analyze the dynamics and the morphology of bubbles in liquids:Application to single ellipsoidal bubbles,Chem.Eng.Sci.100(2013)529-538.

    [26]A.Tomiyama,G.P.Celata,S.Hosokawa,et al.,Terminal velocity of single bubbles in surface tension force dominant regime,Int.J.Multiphase Flow28(2002)1497-1519.

    [27]L.J.Xu,G.Chen,J.B.Shao,et al.,Study on motion behavior of bubbles with different diameters in still water,Chin.J.Hydrodyn.27(2012)582-588(in Chinese).

    [28]R.Zenit,J.Magnaudet,Measurements of the streamwise vorticity in the wake of an oscillating bubble,Int.J.Multiphase Flow35(2009)195-203.

    [29]H.R.Wang,Y.P.Li,D.Yang,et al.,On the shape feature of a single bubble rising in viscous liquids,J.Eng.Thermophys.9(2009)1492-1494(in Chinese).

    [30]M.Wu,M.Gharib,Experimental studies on the shape and path of small air bubbles rising in clean water,Phys.Fluids14(2002)49-52.

    [31]Z.L.Liu,Y.Zheng,PIV study of bubble rising behavior,Powder Technol.168(1)(2006)10-20.

    [32]Z.L.Liu,Y.Zheng,L.Jia,et al.,Study of bubble induced flow structure using PIV,Chem.Eng.Sci.60(13)(2005)3537-3552.

    男人舔奶头视频| 在线a可以看的网站| 精品一区二区三区四区五区乱码| 亚洲乱码一区二区免费版| netflix在线观看网站| 嫁个100分男人电影在线观看| 欧美又色又爽又黄视频| 欧美一级a爱片免费观看看 | xxxwww97欧美| 丰满的人妻完整版| 国产亚洲精品av在线| x7x7x7水蜜桃| 午夜福利免费观看在线| 欧美一区二区精品小视频在线| 国产伦在线观看视频一区| 中出人妻视频一区二区| 日韩大码丰满熟妇| 国产一区在线观看成人免费| 一本综合久久免费| 黄色丝袜av网址大全| 欧美乱妇无乱码| 国产精品一区二区三区四区久久| 麻豆久久精品国产亚洲av| 欧美乱码精品一区二区三区| 欧美中文日本在线观看视频| 久久中文字幕一级| 国产av一区二区精品久久| 日韩中文字幕欧美一区二区| 看黄色毛片网站| 国产精品久久电影中文字幕| 一进一出抽搐动态| 91成年电影在线观看| avwww免费| 此物有八面人人有两片| 又黄又爽又免费观看的视频| 国模一区二区三区四区视频 | 国产成人av教育| 亚洲av成人av| 午夜视频精品福利| 亚洲av中文字字幕乱码综合| 午夜激情福利司机影院| 极品教师在线免费播放| 精品久久久久久,| 国产激情欧美一区二区| 亚洲欧美激情综合另类| 欧美成人一区二区免费高清观看 | 成人一区二区视频在线观看| 国产精华一区二区三区| 1024香蕉在线观看| 日韩欧美 国产精品| 久久精品国产综合久久久| 性欧美人与动物交配| 久久亚洲真实| 99久久精品热视频| 国产亚洲精品久久久久久毛片| 夜夜躁狠狠躁天天躁| 精品久久久久久久末码| 国产野战对白在线观看| 99精品在免费线老司机午夜| 一本久久中文字幕| 亚洲狠狠婷婷综合久久图片| 19禁男女啪啪无遮挡网站| 伊人久久大香线蕉亚洲五| 九色国产91popny在线| 久久久精品欧美日韩精品| av中文乱码字幕在线| 不卡av一区二区三区| 观看免费一级毛片| 成人av在线播放网站| 丝袜美腿诱惑在线| 色综合亚洲欧美另类图片| 亚洲人成网站在线播放欧美日韩| 人妻丰满熟妇av一区二区三区| 日本 欧美在线| 久久天堂一区二区三区四区| 动漫黄色视频在线观看| 一级毛片高清免费大全| 午夜激情福利司机影院| 亚洲狠狠婷婷综合久久图片| 无遮挡黄片免费观看| 超碰成人久久| 精品一区二区三区av网在线观看| 香蕉国产在线看| 国产一区二区在线av高清观看| 精品一区二区三区视频在线观看免费| 国产精品一区二区免费欧美| 婷婷丁香在线五月| 欧美zozozo另类| 午夜福利18| 国产精品久久久久久久电影 | 欧美另类亚洲清纯唯美| 搡老熟女国产l中国老女人| 国产精品久久久久久人妻精品电影| 久久香蕉国产精品| 久久久国产欧美日韩av| 国产午夜福利久久久久久| 757午夜福利合集在线观看| 啦啦啦观看免费观看视频高清| 成人国语在线视频| 色播亚洲综合网| 99国产精品一区二区蜜桃av| 91av网站免费观看| 久久香蕉国产精品| 亚洲精品久久成人aⅴ小说| 真人做人爱边吃奶动态| 国产成人一区二区三区免费视频网站| 少妇被粗大的猛进出69影院| www.自偷自拍.com| 麻豆成人av在线观看| 在线国产一区二区在线| 国内久久婷婷六月综合欲色啪| 成年免费大片在线观看| 久久精品国产99精品国产亚洲性色| 国产亚洲av嫩草精品影院| 亚洲国产欧美人成| 国产高清激情床上av| 国产精品免费视频内射| 欧美中文日本在线观看视频| 午夜精品在线福利| 1024视频免费在线观看| 18禁美女被吸乳视频| 亚洲成人国产一区在线观看| 国产一区二区在线观看日韩 | 久9热在线精品视频| 国产黄色小视频在线观看| 淫秽高清视频在线观看| 美女大奶头视频| 两个人的视频大全免费| 搡老熟女国产l中国老女人| 高潮久久久久久久久久久不卡| 国产成人啪精品午夜网站| 少妇的丰满在线观看| 可以在线观看的亚洲视频| 在线观看午夜福利视频| or卡值多少钱| 久久香蕉国产精品| 国产高清激情床上av| 麻豆成人av在线观看| 色综合婷婷激情| 日本一本二区三区精品| 国产aⅴ精品一区二区三区波| 久久精品国产99精品国产亚洲性色| 亚洲人成伊人成综合网2020| 亚洲色图 男人天堂 中文字幕| a在线观看视频网站| 日日干狠狠操夜夜爽| 国产一区二区三区在线臀色熟女| 亚洲精品色激情综合| 日韩精品免费视频一区二区三区| 他把我摸到了高潮在线观看| 国产在线观看jvid| 国产爱豆传媒在线观看 | 亚洲电影在线观看av| 亚洲成av人片在线播放无| 国产aⅴ精品一区二区三区波| 免费看日本二区| 在线观看午夜福利视频| 变态另类丝袜制服| 色噜噜av男人的天堂激情| 一进一出抽搐gif免费好疼| 亚洲精品一卡2卡三卡4卡5卡| 黑人操中国人逼视频| 国产精品电影一区二区三区| 久久伊人香网站| 非洲黑人性xxxx精品又粗又长| 国产精品久久视频播放| 听说在线观看完整版免费高清| АⅤ资源中文在线天堂| 天天躁狠狠躁夜夜躁狠狠躁| 嫩草影视91久久| 亚洲人成网站在线播放欧美日韩| 国产精品亚洲一级av第二区| 国产精品一区二区精品视频观看| 一区二区三区激情视频| 中文资源天堂在线| 少妇熟女aⅴ在线视频| 99久久久亚洲精品蜜臀av| 女人高潮潮喷娇喘18禁视频| 欧美黑人精品巨大| 深夜精品福利| 成年版毛片免费区| 婷婷亚洲欧美| 欧美精品亚洲一区二区| 精品不卡国产一区二区三区| 亚洲欧美日韩东京热| 精品不卡国产一区二区三区| 亚洲精品在线观看二区| 免费在线观看完整版高清| 欧美一区二区国产精品久久精品 | 欧美日韩乱码在线| 国产精华一区二区三区| 日本a在线网址| 国产亚洲精品久久久久5区| АⅤ资源中文在线天堂| 日韩精品青青久久久久久| 国产伦一二天堂av在线观看| 黑人欧美特级aaaaaa片| 级片在线观看| 亚洲av中文字字幕乱码综合| 狂野欧美激情性xxxx| 中文字幕精品亚洲无线码一区| 日本 欧美在线| 高清毛片免费观看视频网站| 国产真实乱freesex| 国产精华一区二区三区| а√天堂www在线а√下载| 欧美成人性av电影在线观看| 两个人视频免费观看高清| 亚洲aⅴ乱码一区二区在线播放 | 国产伦人伦偷精品视频| 制服丝袜大香蕉在线| av视频在线观看入口| 51午夜福利影视在线观看| 亚洲乱码一区二区免费版| 国产野战对白在线观看| 国产精品亚洲美女久久久| 欧美不卡视频在线免费观看 | 好看av亚洲va欧美ⅴa在| 亚洲精品一卡2卡三卡4卡5卡| 亚洲中文日韩欧美视频| 可以在线观看毛片的网站| 国产精品 欧美亚洲| 日韩欧美国产在线观看| 国产精品久久电影中文字幕| 级片在线观看| 午夜福利成人在线免费观看| 午夜激情福利司机影院| 久久精品国产99精品国产亚洲性色| 欧美日韩亚洲国产一区二区在线观看| 久久草成人影院| 人成视频在线观看免费观看| 欧美zozozo另类| 岛国在线免费视频观看| 久久久久久大精品| 深夜精品福利| 国产精品久久久久久精品电影| 国产真人三级小视频在线观看| 精品人妻1区二区| 少妇粗大呻吟视频| 亚洲专区国产一区二区| 亚洲电影在线观看av| 老司机靠b影院| 欧美+亚洲+日韩+国产| 亚洲精品在线观看二区| 亚洲全国av大片| 国产精品电影一区二区三区| 亚洲avbb在线观看| 久99久视频精品免费| 久久久国产成人免费| 18禁裸乳无遮挡免费网站照片| 又大又爽又粗| 亚洲色图 男人天堂 中文字幕| 国产成人aa在线观看| 嫁个100分男人电影在线观看| 成年人黄色毛片网站| 禁无遮挡网站| 麻豆av在线久日| 一边摸一边抽搐一进一小说| 精品久久久久久久末码| 一本久久中文字幕| 青草久久国产| 国产欧美日韩一区二区精品| 亚洲一卡2卡3卡4卡5卡精品中文| 一级作爱视频免费观看| 99精品久久久久人妻精品| 女警被强在线播放| xxxwww97欧美| 成在线人永久免费视频| 51午夜福利影视在线观看| 日韩欧美免费精品| 嫩草影院精品99| 最近最新中文字幕大全免费视频| 亚洲九九香蕉| 亚洲国产精品成人综合色| 日韩av在线大香蕉| 老司机福利观看| 午夜激情av网站| 少妇粗大呻吟视频| 国产精品一及| 1024视频免费在线观看| 蜜桃久久精品国产亚洲av| 亚洲欧美日韩高清在线视频| 欧美不卡视频在线免费观看 | 在线免费观看的www视频| 我要搜黄色片| 成人手机av| 女人被狂操c到高潮| 国产1区2区3区精品| 国产高清视频在线播放一区| 亚洲国产精品999在线| 长腿黑丝高跟| 一级片免费观看大全| 成人手机av| 一本精品99久久精品77| 成人高潮视频无遮挡免费网站| 2021天堂中文幕一二区在线观| 99在线人妻在线中文字幕| 亚洲五月婷婷丁香| 免费看日本二区| 搡老熟女国产l中国老女人| 天天躁夜夜躁狠狠躁躁| 亚洲狠狠婷婷综合久久图片| 1024手机看黄色片| 国产片内射在线| 曰老女人黄片| 国产真人三级小视频在线观看| 亚洲精品中文字幕一二三四区| 成年免费大片在线观看| 韩国av一区二区三区四区| 国产高清视频在线播放一区| 美女黄网站色视频| a级毛片在线看网站| 久久草成人影院| 欧美乱码精品一区二区三区| 欧美又色又爽又黄视频| 女生性感内裤真人,穿戴方法视频| 国模一区二区三区四区视频 | 国产熟女午夜一区二区三区| 两个人看的免费小视频| 妹子高潮喷水视频| 91麻豆精品激情在线观看国产| 五月玫瑰六月丁香| 国产伦人伦偷精品视频| 在线观看日韩欧美| 精品第一国产精品| 国产精品亚洲一级av第二区| 中文字幕人成人乱码亚洲影| 亚洲av熟女| 日韩欧美在线二视频| 国产精品98久久久久久宅男小说| 少妇被粗大的猛进出69影院| 在线观看免费日韩欧美大片| 久久久久精品国产欧美久久久| 欧美成人午夜精品| 亚洲激情在线av| 亚洲五月天丁香| 黄色丝袜av网址大全| 国产精品98久久久久久宅男小说| 欧美日本亚洲视频在线播放| 天天添夜夜摸| 最近在线观看免费完整版| 亚洲欧洲精品一区二区精品久久久| 天天一区二区日本电影三级| 久久国产乱子伦精品免费另类| 久久精品综合一区二区三区| 亚洲一卡2卡3卡4卡5卡精品中文| 淫妇啪啪啪对白视频| 国产视频一区二区在线看| 亚洲精品久久成人aⅴ小说| 亚洲欧美一区二区三区黑人| 法律面前人人平等表现在哪些方面| av福利片在线观看| avwww免费| 久久中文字幕人妻熟女| 少妇的丰满在线观看| 国产亚洲av高清不卡| 久久精品影院6| 99久久国产精品久久久| 欧美乱色亚洲激情| 国产真人三级小视频在线观看| 最近最新中文字幕大全免费视频| 日韩欧美在线二视频| 黑人巨大精品欧美一区二区mp4| 亚洲国产欧洲综合997久久,| 99久久国产精品久久久| 久久 成人 亚洲| 成人特级黄色片久久久久久久| 久久亚洲精品不卡| 亚洲性夜色夜夜综合| 国产亚洲欧美98| 国产亚洲av高清不卡| 一个人免费在线观看的高清视频| 法律面前人人平等表现在哪些方面| 99久久久亚洲精品蜜臀av| 一个人观看的视频www高清免费观看 | 精品熟女少妇八av免费久了| 成人18禁高潮啪啪吃奶动态图| 欧美日韩精品网址| 麻豆久久精品国产亚洲av| 国产精品爽爽va在线观看网站| 少妇的丰满在线观看| 曰老女人黄片| 欧美在线黄色| 久久精品成人免费网站| 老司机午夜福利在线观看视频| av免费在线观看网站| 久久天堂一区二区三区四区| 成年人黄色毛片网站| 国产又黄又爽又无遮挡在线| 人人妻,人人澡人人爽秒播| 人成视频在线观看免费观看| 亚洲欧美精品综合久久99| 黄色成人免费大全| 宅男免费午夜| 午夜精品久久久久久毛片777| 亚洲精品av麻豆狂野| 婷婷精品国产亚洲av在线| 欧美日韩亚洲综合一区二区三区_| aaaaa片日本免费| 亚洲免费av在线视频| 日日夜夜操网爽| 婷婷精品国产亚洲av在线| 日韩欧美免费精品| 亚洲第一欧美日韩一区二区三区| 搡老熟女国产l中国老女人| 久久精品人妻少妇| 亚洲人成77777在线视频| 一进一出抽搐动态| 国产精品亚洲美女久久久| 久久精品aⅴ一区二区三区四区| 日韩大码丰满熟妇| 成人精品一区二区免费| 好男人电影高清在线观看| 中文字幕人妻丝袜一区二区| 久99久视频精品免费| 老司机深夜福利视频在线观看| 一级a爱片免费观看的视频| 69av精品久久久久久| 一本一本综合久久| 级片在线观看| 在线观看www视频免费| 亚洲精品色激情综合| 精品熟女少妇八av免费久了| 欧美激情久久久久久爽电影| 欧美黑人精品巨大| 给我免费播放毛片高清在线观看| 日韩国内少妇激情av| 国产精品免费一区二区三区在线| 桃色一区二区三区在线观看| 精品一区二区三区视频在线观看免费| 听说在线观看完整版免费高清| 黑人欧美特级aaaaaa片| 国产亚洲精品第一综合不卡| 亚洲色图 男人天堂 中文字幕| 亚洲成av人片在线播放无| 色在线成人网| av免费在线观看网站| 91麻豆精品激情在线观看国产| 久久草成人影院| 999精品在线视频| 性色av乱码一区二区三区2| www.熟女人妻精品国产| 国产午夜福利久久久久久| 精品久久久久久久毛片微露脸| 一卡2卡三卡四卡精品乱码亚洲| 欧美一区二区精品小视频在线| 一夜夜www| 日韩大尺度精品在线看网址| 天天躁狠狠躁夜夜躁狠狠躁| 国产成人影院久久av| 欧美日本视频| 五月伊人婷婷丁香| 成人手机av| 一本综合久久免费| 午夜免费观看网址| 久99久视频精品免费| 看黄色毛片网站| www.999成人在线观看| 人妻久久中文字幕网| 精品一区二区三区视频在线观看免费| videosex国产| 色尼玛亚洲综合影院| 成人国产一区最新在线观看| 亚洲黑人精品在线| 国产av麻豆久久久久久久| 人人妻,人人澡人人爽秒播| 最近最新免费中文字幕在线| 亚洲av中文字字幕乱码综合| 欧美黑人精品巨大| 精品熟女少妇八av免费久了| 婷婷亚洲欧美| 久久久精品欧美日韩精品| 99热6这里只有精品| 国产亚洲av高清不卡| 我要搜黄色片| 国产精品电影一区二区三区| 久久精品夜夜夜夜夜久久蜜豆 | 极品教师在线免费播放| 国产aⅴ精品一区二区三区波| 亚洲国产精品sss在线观看| 日韩有码中文字幕| 99国产精品99久久久久| 色综合亚洲欧美另类图片| 老司机福利观看| 女人高潮潮喷娇喘18禁视频| 真人一进一出gif抽搐免费| av免费在线观看网站| 亚洲七黄色美女视频| 亚洲成av人片在线播放无| 他把我摸到了高潮在线观看| 成人亚洲精品av一区二区| 欧美日韩黄片免| 天天添夜夜摸| xxx96com| 亚洲国产看品久久| 最近最新中文字幕大全免费视频| 可以在线观看毛片的网站| 在线视频色国产色| 精品欧美国产一区二区三| 手机成人av网站| 欧美一区二区国产精品久久精品 | 国产熟女xx| 久久这里只有精品中国| 欧美人与性动交α欧美精品济南到| 激情在线观看视频在线高清| 亚洲av电影在线进入| 国产人伦9x9x在线观看| 亚洲精品一区av在线观看| 成人手机av| 天天一区二区日本电影三级| 国产精品日韩av在线免费观看| 精品久久久久久久久久久久久| 免费看a级黄色片| 午夜福利视频1000在线观看| 欧美日韩精品网址| 欧美性猛交╳xxx乱大交人| 免费在线观看日本一区| 国内揄拍国产精品人妻在线| 国产v大片淫在线免费观看| 色噜噜av男人的天堂激情| 精品欧美国产一区二区三| 国产精品1区2区在线观看.| 午夜亚洲福利在线播放| 国产激情偷乱视频一区二区| 视频区欧美日本亚洲| 亚洲在线自拍视频| 国产高清激情床上av| 亚洲欧美精品综合久久99| 美女午夜性视频免费| 国产成人欧美在线观看| 18禁黄网站禁片免费观看直播| 老司机午夜十八禁免费视频| 黑人巨大精品欧美一区二区mp4| 高清毛片免费观看视频网站| 全区人妻精品视频| 青草久久国产| 亚洲中文字幕日韩| 亚洲五月婷婷丁香| 在线观看www视频免费| 一本一本综合久久| av福利片在线观看| 久久精品成人免费网站| 久久久久久免费高清国产稀缺| 毛片女人毛片| 欧美日韩精品网址| 香蕉丝袜av| 欧美高清成人免费视频www| 亚洲精品国产精品久久久不卡| 午夜久久久久精精品| 美女午夜性视频免费| 久久久久久亚洲精品国产蜜桃av| 18禁观看日本| 国产av又大| 日本黄色视频三级网站网址| 一个人观看的视频www高清免费观看 | 男女午夜视频在线观看| 99精品久久久久人妻精品| 又紧又爽又黄一区二区| 夜夜爽天天搞| 麻豆成人av在线观看| 俺也久久电影网| 欧美日韩精品网址| 一个人观看的视频www高清免费观看 | 久久久国产精品麻豆| 免费在线观看日本一区| 91麻豆精品激情在线观看国产| 在线播放国产精品三级| 一区福利在线观看| 中出人妻视频一区二区| 亚洲国产精品999在线| e午夜精品久久久久久久| 此物有八面人人有两片| 黄色片一级片一级黄色片| 成人av一区二区三区在线看| 欧美成狂野欧美在线观看| 精品国产亚洲在线| 两性夫妻黄色片| 精品国产超薄肉色丝袜足j| 午夜福利在线观看吧| 变态另类成人亚洲欧美熟女| 男女视频在线观看网站免费 | 精品国产乱码久久久久久男人| 无限看片的www在线观看| а√天堂www在线а√下载| 欧美日韩精品网址| av视频在线观看入口| 国产精品98久久久久久宅男小说| а√天堂www在线а√下载| 99国产精品一区二区三区| 国产黄色小视频在线观看| 亚洲国产精品合色在线| 日韩大码丰满熟妇| 全区人妻精品视频| 99在线视频只有这里精品首页| 男人舔奶头视频| 又爽又黄无遮挡网站| 大型黄色视频在线免费观看| 嫁个100分男人电影在线观看| 国产亚洲精品久久久久久毛片| 制服诱惑二区| av中文乱码字幕在线| 欧美中文日本在线观看视频| 99re在线观看精品视频| 蜜桃久久精品国产亚洲av| 国产91精品成人一区二区三区| xxx96com| 亚洲精品国产精品久久久不卡| 亚洲国产欧美网| 在线观看美女被高潮喷水网站 | 真人一进一出gif抽搐免费| 男人舔女人的私密视频| 成年女人毛片免费观看观看9| 久久婷婷人人爽人人干人人爱| 黄色a级毛片大全视频| 欧美性猛交╳xxx乱大交人|