Ning Mao,Can Kang,*,Wisdom Opare,2,Yang Zhu

1School of Energy and Power Engineering,Jiangsu University,Zhenjiang 21213,China

2Faculty of Engineering,Takoradi Technical University,Takoradi,P.O.Box 256,Ghana

Keywords:Bubble Ventilation Wake flow PIV Photography Bubble size distribution

A B S T R A C T An experimental study was conducted to investigate the 2D bubbly flow downstream of a cylinder.Sparsely distributed bubbles were produced using the ventilation method.The carrier flow was measured using the particle image velocimetry(PIV)technique.The shadow imaging technique was used to capture instantaneous bubbly flow images.An image-processing code was compiled to identify bubbles in acquired image,calculate the bubble equivalent diameter and the bubble velocity.The effects of Reynolds number and the flow rate of the injected air were considered.The result indicates that the carrier flow is featured by distinct flow structures and the wake region is suppressed as the upstream velocity increases.Regarding the bubbles trapped in the wake flow,the number of small bubbles increases with the upstream velocity.On the whole,the bubble velocity is slightly lower than that of the carrier flow.The consistency between small bubbles and the carrier flow is high in terms of velocity magnitude,which is justified near the wake edge.The difference between the bubble velocity and the carrier flow velocity is remarkable near the wake centerline.For certain Reynolds number,with the increase in the air flow rate,the bubble equivalent diameter increases and the bubble void fraction is elevated.

1.Introduction

Bubbly flows facilitate the heat and mass transfer between different phases and therefore assume an important function in chemical and environmental engineering[1–3].Fundamentally,the inter-phase interaction involved in the bubbly flow depends significantly on both bubble parameters and the traits of the carrier flow.Some bubbly flows are characterized by scattered bubbles.In this context,the deviation of bubble behavior from general pseudo-single phase model is appreciable.At present,regarding the available knowledge of the bubbly flow,empirical relationship instead of quantitative conclusions is prevalent.Bubbles trapped in liquid flow are subjected to the influence of multiple factors such as gas volume fraction,liquid density and flow parameter distribution.An accurate acquisition of bubble size and its spatial distribution enables the understanding of bubble dynamics under specific flow conditions.Meanwhile,the identification of bubbles is a prerequisite for tracing the essence of the carrier flows,particularly the flows featured by high velocity gradients and strong turbulence.

Non-intrusive flow measurement and visualization techniques,such as X-ray technique and high speed photography(HSP)[4–8],lend sound support in bubbly flow research.Kong et al.[9]used the γ-CT measurement technique to investigate the gas content in the gas–liquid two-phase flow stirred by a Rushton rotor,and the influence of ventilation position and air flow rate on the gas content was explained.Shollenberger et al.[10]used γ-ray to measure bubble rising behavior at different air flow rates.X-ray tracking particle velocimetry(XPTV)was employed by Seeger et al.[11]to measure the flow field in the bubble column at high air void fraction and both flow field characteristics and cross-sectional air content were presented.Xu et al.[12]used ultrasonic tomography to detect instantaneous phenomena in the gas–liquid two-phase flow and developed a real-time monitoring system.High speed photography(HSP)serves as another useful tool in the study of the gas–liquid two-phase flow.Triplett et al.[13]depicted the gas–liquid two-phase flow pattern based on image processing technology.With particle image velocimetry(PIV),Hernandez-Alvarado et al.[14]measured bubble void fraction,bubble size and interfacial area in cocurrent down flow bubble column reactor using HSP.Image processing techniques are critical for extracting information from captured images.Lau et al.[15]attempted to separate overlapping bubbles in bubbly flows with large void fraction by means of a watershed algorithm.These studies take the understanding of bubbly flow to a new height.With the development of bubbly flow measurement and visualization techniques,the amount of data has been enhanced considerably.In this context,measurements of high quality deserve more attention.Nevertheless,studies in this aspect are rather limited hitherto.

The purpose of the present study is to seek bubbly flow characteristics in the wake flow downstream of a cylinder.An experimental work is conducted with the cylinder deployed in the 2D test segment of a water tunnel.Bubbles are produced with a ventilation device installed upstream of the cylinder.The emphasis is placed on the bubbles entrapped in the wake flow downstream of the cylinder.Under the condition of no ventilation,the pure water flow downstream is measured using PIV.With ventilation,the bubbly flow in the wake of the cylinder is visualized with the shadow imaging technique,and then the bubble images acquired are processed with an in-house code.Statistics on the bubbles are extracted from consecutive images.The influence of the upstream velocity and the air flow rate on bubble size and bubble kinematic characteristics is investigated.

2.Experimental

2.1.PIV measurement set-up

A particle image velocimetry system manufactured by LaVision Company of Germany was used in the experiment.The PIV system is composed of a low-frequency double-pulse laser,a CCD camera with the double-frame and double-exposure modes,a time synchronization controller,a set of laser beam guiding arms and lenses,and Davis software for data acquisition and process.The configuration of primary components of the PIV experiment is displayed in Fig.1.Hollow glass particles,with diameters ranging from 20 to 50 μm,served as tracing particles in the experiment.The depth of view(DOV)plane for the measurement was set to overlap with the mid-span plane of the cylinder.According to the operation parameters of the camera,the depth of view was 8.1 mm.In this context,the monitored zone is sufficiently thick to accommodate the moving bubbles.

2.2.Water tunnel test segment and cylinder

The experiment was carried out based on the platform of a water tunnel,and the attainable water flow velocity with this water tunnel is 13 m·s-1.In the present study,upstream velocities of 1.25 m·s-1,1.61 m·s-1,1.98 m·s-1,2.35 m·s-1were selected.The characteristic length was defined as the width of the test segment,so the corresponding Reynolds number,Re,are 37425,48203,59281,and 70060,respectively.The test segment illustrated in Fig.2,with dimensions of 700 mm(length)×50 mm(width)×350 mm(height),is made from plexiglass and used to accommodate the cylinder.The height H and diameter D of the cylinder are 50 mm and 30 mm,respectively.Therefore,the block ratio of the test segment is 0.086.The flow region monitored with PIV is shown in Fig.2 as well.

A convergent segment is mounted upstream of the test section and the profile of this segment conforms to the Witozinsky curve,and connects the stabilization segment with identical cross sections of 390 mm×390 mm and the inlet of the test section(315 mm×50 mm).To examine the influence of the test section geometry on velocity distributions,PIV measurement was conducted with the cylinder removed.Velocity profiles at various Reynolds numbers are plotted in Fig.3.Through changing the optical configuration,the velocity distributions in both xoy and xoz planes were obtained.Along y direction,namely the height of the test section,obvious velocity gradients occur near the upper and lower walls of the test section.In the middle part,the velocity distributions are rather uniform,as shown in Fig.3(a).Along z direction,similar velocity distribution tendencies are demonstrated.The shape of the velocity profile is insensitive to the variation in Reynolds number;therefore,high quality of the carrier flow eliminates the disturbance of unexpected factors on the bubbles that would be involved.

2.3.Shadow imaging system

In view of the deficiency of PIV in studying scattered bubbles,shadow imaging technique was used here to acquire bubble information.This technique is based on backlight illumination and the high magnification imaging.The shadow of bubbles in the focal plane of the optical lenses is recorded.Relative to PIV,the sheet light source of PIV is replaced with the volumetric light source;moreover,the rigid laser arm is replaced with the flexible optical fiber.The schematic view of the shadow imaging system and the major facilities are shown in Fig.4.A CCD camera with the double frame and double exposure shooting mode was used to capture consecutively bubble images.The depth of view plane was geared to the midspan plane of the test section.The dimensions of the monitored area are 3D×2D.The window size depends on the image resolutions and the accuracy of bubble edge detection.Considering the bubbly flow downstream of the cylinder,as shown in Fig.2,such a window is advantageous for observing the influence of the wake on bubbles.The acquisition frequency is 6.9 Hz,and each data group was composed of 200 instantaneous images.For each Reynolds number,the final results were averaged based on three data groups.

Fig.1.Primary components of the PIV experiment rig.

Fig.2.Schematic diagram of the test section and monitored area.

2.4.Ventilation system

An air compressor was used to provide stable air flow for the ventilation experiment with the flow rate varied from 25 to 250 L·h-1.A buffer tank was connected to the air compressor to enhance the steadiness of air flow.The air flow rate was measured with a rotor flow meter.A copper tube with the outer diameter of 1.0 mm and inner diameter of 2 mm served as the ventilation tube,which was mounted upstream the cylinder as shown in Fig.2.The stream wise distance between the tube and the cylinder axis is 250 mm.Along the wall of the tube,seven holes with the identical diameter of 0.3 mm are evenly distributed to generate air bubbles.The distance between neighboring air holes is 10 mm.The air pressures at each hole are equal and stable.

Fig.3.Cross-sectional velocity distributions in the test section.

Fig.4.Shadow imaging experiment rig.

2.5.Image processing

An image-processing code was developed based on the Matlab software to identify bubble edge and to calculate bubble velocity.There are several algorithms such as Sobel algorithm and Wallis algorithm that can be used to detect bubble edge[16].Here,the Canny algorithm was transplanted into the image-processing code as a bubble-identification module.The advantages of Canny algorithm are low error rate,high positioning accuracy and strong denoising capability.

The primary steps of bubble image processing are illustrated in Fig.5.The no-ventilation flow field,as shown in Fig.5(a),is taken as the background,and the background is subtracted from the raw bubble image in Fig.5(b).Then the Canny algorithm is used to recognize the bubble profile.Several studies have been dedicated to the separation of overlapping bubbles[17,18].Here,the method of tracing the bubble edge curvature is adopted to reconstruct the shielded bubble edge.

The bubble edge s in the two-dimensional plane is given by:

where x and y represent the horizontal and vertical coordinates of a point on bubble edge,respectively,and t is an independent variable.The curvature k(t)is expressed as:

The bubble is assumed to be ellipsoidal or spherical. The curvature of the bubble edge is calculated according to Eq.(2).Both single bubble profiles and overlapping bubble profiles are seen in Fig.5(d).The coincidence point of two overlapping bubbles is reached as the curvature changes sharply, as indicated in Fig. 5(e). Provided that the number of coincidence points is equal to or greater than 2,the nonlinear least squares method is used to fit the ellipse edge which contains the hidden bubble edge segment,as displayed in Fig.5(f).

With the shooting mode of double frame and double exposure,the camera can furnish spatially and temporally correlated image pairs.The time interval between two neighboring frames is denoted by dt.Each bubble associated with the first frame is recognized in the second frame based on the cross-correlation algorithm.Therefore,bubble velocity can be derived based on the displacement of the bubble centroid and the time interval between neighboring images.

3.Wake Flow under No-ventilation Condition

The carrier flow exerts a significant influence on bubbles,so it is necessary to study the flow structures in the carrier flow under noventilation condition.During the PIV experiment,since the cylinder is not transparent,local flows above and below the cylinder cannot be measured concurrently,but the flows above and below the cylinder are symmetrical with respect to the cylinder[19].Therefore,only the measurement scheme with the incident light lens deployed under the cylinder was practiced.

3.1.Instantaneous flow field

As flow travels around the cylinder in a certain range of Reynolds number,a shear layer will be produced at the interface between the wake region and the outer stream adjacent to the wake region[20,21].Meanwhile,the shear layer fosters an environment for the generation of vorticity,and as the wake develops,the overall vorticity decays.At Re=59281,transient vorticity distribution and wake flow pattern are shown in Fig.6.It is seen that two rows of vortices shed from the upper and lower sides of the cylinder.The maximum vortex scale is even comparable with the cylinder diameter.It is noticeable that the vortex scales are diverse and the mixing of the upper and lower shear layers is intensified immediately downstream of the cylinder.Provided that bubbles are trapped in the wake flow shown in Fig.6,bubble shape or even bubble survival is anticipated to be affected by the flow structure.Additionally,because the tracing particles accumulate in the wake region,the collision between these particles may alter the particle traveling routes;therefore,streamlines in the wake region are not smooth,some streamlines are even distorted due to the velocity component in the z direction.

3.2.Time-averaged vorticity field

Time-averaged vorticity distributions at Re=37425,48203,59281 and 70060 are shown in Fig.7.It is seen that pairs of large scale vortices with opposite rotation are symmetrically distributed on the upper and lower sides of the wake region.It is deducible that the vorticity magnitude exhibits dual-peak distribution patterns in the cross sections vertical to the streamwise direction.As the Reynolds number increases,the vorticity diffusion in the transverse direction is intensified.Particularly,in Fig.7(d),immediately downstream of the cylinder,vorticity spreads distinctly towards the wake centerline,facilitating the production of small-scale vortices.

Fig.5.Bubble recognition process.

Fig.6.Transient vorticity distribution and streamlines at Re=59281.

Fig.7.Time-averaged vorticity and velocity distributions.

Fig.8.Overview of the bubbly flow pattern.

Cross-sectional streamwise velocity distributions over Cross sectional segments A–A′(x/D=2.5),B–B′(x/D=3.5)and C–C′(x/D=4.5)are displayed in Fig.7.From Fig.7(a)to(d),the wake width reduces continuously,as is ascribed to the suppression of the wake in transverse direction by the outer stream.The fluctuations of velocity along the segments arise because the three cross-sectional segments are exposed to the strong effects of the meandering wake flow.As the wake progresses,velocity difference between wake region and the outer stream is minimized,and the cross-sectional velocity distribution curves are flattened,as is the common feature shared by the four different Reynolds numbers.

Fig.9.Bubble velocity distribution at Re=37425.

4.Bubbly Wake Flow Downstream of the Cylinder

An overview of the transiently captured bubbly flow pattern is presented in Fig.8.As can be seen,bubbles are sparsely distributed and the overlapping between bubbles is slight,facilitating the implementation of image processing.As bubbles pass by the cylinder,both the shape and the kinematic characteristics of the bubble differ over the entire flow region.Meanwhile,the influence of the wake flow on the bubbles trapped in is significant,and it is clearly evident that the disparity in the bubble size as well as the bubble shape exists for bubbles residing near the wake centerline and at the wake edge.Moreover,it is noticeable that the movement of the bubbles immediately downstream of the cylinder is in accordance with the meandering wake flow.This means that the bubbles are inevitably influenced by the carrier flow.Nevertheless,physical traits of bubbles differ substantially from those of the water flow,necessitating a comprehensive investigation of bubble geometry and bubble velocity.

4.1.Bubble streamwise velocity

At Re=37425 and 70060,distributions of the streamwise bubble velocity over cross-sections A–A′,B–B′,and C–C′at different air flow rates are shown in Figs.9 and 10,respectively.The velocity magnitudes were obtained through averaging the bubble velocity over 800 bubble images.As shown in Fig.9,for the same cross section,low velocity arises near the wake centerline,as is shared by all cross sections inspected.At the wake edge,the velocity profiles are fairly smooth.Compared to Fig.7(a),the distribution patterns of bubble velocity are similar with those of the carrier flow;meanwhile,the bubble velocity magnitudes are relatively small.As the wake develops from Cross-sections A–A′to C–C′,the overall bubble velocity magnitude increases,which is in accordance with the evolution of the carrier flow velocity.

Near the wake edge,the bubble velocity is slightly lower than that of the carrier flow,as is shared by the four cases shown in Fig.9.As the air flow rate increases,no remarkable deviation between the velocities of the two phases is seen.In comparison,near the wake centerline,although the velocity distributions of the two phases remain similar,the velocity difference between the bubbles and the carrier flow is apparent.Moreover,with the increase in the air flow rate,the velocity difference is reinforced.In this context,immediately downstream of the cylinder,bubbles are directly exposed to the effects of diverse vortices and other large-scale flow structures confined in the wake flow.Therefore,the streamwise motion of the bubbles is undermined,which leads to a fairly large deviation between the velocities of the two phases.

As Reynolds number increases,the agreement between crosssectional bubble velocity distribution and water flow velocity distribution is retained.Meanwhile,the bubble velocity increases with Reynolds number.In Cross-section A–A′,near the centerline of the wake,bubble velocity is apparently lower than that of water,which can be deduced from Fig.7(d).Moreover,velocity fluctuations in the transverse direction are apparent,demonstrating the strong effect of the flow structures on bubble motion.In comparison,the difference in the velocity magnitude is minimized near the wake edge,as is common for the three cross sections and similar to the results shown in Fig.9.

Fig.10.Bubble velocity distribution at Re=70060.

Table 1Streamwise velocity along the wake centerline at Re=37425

Along the wake centerline,averaged streamwise velocity of water,Vl,obtained under no-ventilation is compared with the averaged streamwise velocity of bubble,VB,under the ventilation condition at Re=37425,and the comparison is described in Table 1.It can be found that VBis lower than Vlin the same cross section.With the same ventilation air flow rate,VBincreases along the flow direction,which is similar to the variation trend associated with the no-ventilation situation.As the air flow rate increases,the bubble velocity magnitudes at each cross section are close to each other. Such a tendency proves that bubble velocity depends to a large extent on the velocity of the carrier flow.In this context,the effect of the air flow rate on bubble velocity is relatively mitigated.

4.2.Bubble equivalent diameter

Bubble equivalent diameter dAis employed to denote bubble size:

where Apis the projected area of the bubble in the image.

Under various Re conditions,bubble diameter distributions are shown in Figs.11 and 12.It is apparent that bubble equivalent diameter increases from external sides towards the center of wake region,which is due to the inertial effect of bubbles[22].At Re=37425,bubble equivalent diameter values are concentrated in the range of 1.0–1.5 mm.At Re=70060,the majority of bubble equivalent diameter values are within the range of 0.8–1.3 mm.Bubbles with relatively small size are located primarily in the zone of-5 mm＜y＜5 mm.Bubble equivalent diameter increases along the flow direction.In addition,bubble size at lower Reynolds number is larger than that at higher Reynolds number.At certain upstream velocity,bubble size increases with the increase in the air flow rate.Consequently the space that is not occupied by bubbles is suppressed.Near the wake centerline,some large-size bubbles are split into smaller ones.

A comparison of the errors in the calculation of the bubble equivalent diameter is illustrated in Fig.13.As can be seen,for the middle part,near the centerline of the wake,relatively large errors arise,as is common for the two Reynolds numbers.Essentially,this is related to the influence of the unsteady wake flow on the bubble geometry.In contrast,away from the middle part,the errors decrease clearly.In this case,a slight variation in the bubble shape is expected because the bubbles have escaped from the strong effect of the wake. The overall errors for the two Reynolds numbers are close to one another;moreover,the largest error in the calculation of the bubble equivalent diameter is less than 5%.

4.3.Distribution of bubble void fraction

Fig.11.Bubble equivalent diameter distribution at Re=37425.

Fig.12.Bubble equivalent diameter distribution at Re=70060.

Since the images captured are two-dimensional,the bubble void fraction,α,is calculated based on the volume fraction of the bubbles in the acquisition volume.The calculation formula takes the form:where Viis the volume of individual bubble,which was obtained under the assumption of that the bubble is a sphere and the bubble equivalent diameter defined in Eq.(3)was used.V is the total cuboid acquisition volume,which was calculated through the depth of view and the monitored area,namely the zone of 4D×2D,2D from the center of the cylinder,as illustrated in Fig.2.In this context,the depth of view is 8.1 mm according to the operation parameters of the camera.

Fig.13.Errors in the calculation of the bubble equivalent diameter.

It is seen from Eq.(4)that the accuracy of the calculation of the bubble void fraction depends largely on the accuracy of the bubble volume calculation,because the dimensions of the monitored volume are accurately known.A preliminary experiment was conducted to validate the accuracy of the bubble area detection;single bubbles were produced in a transparent water tank with a syringe pump which furnished a constant air flow rate of 20 L·h-1.The maximum uncertainty of±2.78%with the image processing code used was obtained.Here,the bubble void fraction under different operation conditions was calculated based on 800 bubbly flow images,which contain totally approximately 240000 bubbles.The result is plotted in Fig.14.It is seen that as the air flow rate keeps invariant,bubble void fraction increases gradually with the upstream velocity.This is reasonable since the bubble number increases in individual images as the upstream velocity increases.Nevertheless,the increase is not linear,which is related to the disturbance of the carrier flow on the bubbles.For certain Reynolds number,bubble void fraction is augmented consistently with the increase in the air flow rate from 100 to 175 L·h-1.In this context, the influence of the air flow rate on the bubble void fraction is significant.

Fig.14.Bubble void fraction under various operation conditions.

In view of the bubble size and the bubble void fraction obtained,the effect of bubbles on the turbulent characteristics of the carrier deserves an explanation.With existing techniques,the difficulty of measuring turbulent parameters in the liquid wake of the cylinder is appreciable.It has been reported that as Reynolds number is fairly low and the bubble size is small,the presence of bubbles would lower turbulent intensity,but the turbulent intensity distributions remain similar[23].It should be noted that the previous works emphasized pipe flows or channel flows,and the wall exerts an important effect on the distribution of turbulent intensity[24].In the bubbly wake flow considered here,the distribution of bubbles is not uniform and the bubble void fraction is relatively low compared to that reported in previous studies.In the wake region,bubbles are accumulated and the interaction between bubbles and the unsteady wake is intensified,as can be justified from the distributions of bubble size.In this case,the turbulent intensity of the carrier flow is reduced.In contrast,regarding the branches of flows above or under the wake region,no obvious disturbance on turbulent fluctuations is anticipated in view of the orderly motion of bubbles.

5.Conclusions

(1)Under no-ventilation condition,the wake flow downstream of the cylinder manifests distinct flow structures.As the upstream velocity increases,both velocity and vorticity in the wake region increase,while the streamwise development of the wake is suppressed.In the transverse direction,velocity near the wake centerline is lower than that at the wake edge.The overall velocity increases in the streamwise direction,signifying the attenuation of the wake.

(2)For certain air flow rate,the size of the bubbles trapped in the wake flow decreases as Reynolds number increases.The bubble size distribution curve is characterized by a minimum near the wake center line,irrespective of Reynolds number.With the increase in the air flow rate,the bubblevoid fraction is consistently augmented.As Reynolds number keeps invariant,the increase in the bubble void fraction with the augment of the air flow rate is evidenced.

(3)The overall distribution of the bubble velocity is in accordance with its counterpart associated with the carrier flow. The velocity magnitudes of bubbles are lower than those of the carrier flow.At the wake edge,slight velocity difference arises between bubbles and water.In comparison,near the wake centerline,bubble velocity is apparently lower than that ofwater;moreover,severe fluctuations of bubble velocity in transverse direction are witnessed.