Experimental Investigation of the Interaction between Rising Bubbles and Swirling Water Flow

This study experimentally investigates the interaction between rising bubbles and swirling water flow imposed around the central (vertical) axis of a bubble plume in a cylindrical water tank. Small air bubbles are successively released from the bottom of the tank to generate a bubble plume, and a stirring disc at the bottom of the tank is rotated to impose a swirling water flow around the central axis of the bubble plume.The bubbles disperse further with the increasing rotational speedω of the stirring disc. Some bubbles shift toward the central axis of the swirling flow when ω is high. The nondimensional swirling velocity of water reduces with increasing bubble flow rate when ω is lower than a certain value. However, it is less affected by the bubbles when ω is higher. The precessional amplitude for the upper end of the vortex core increases due to the presence of the bubbles. With increasing ω, the nondimensional precessional velocity decreases, and the bubble effect also reduces.


Introduction
Gas bubbles successively released into a liquid induce liquid flow as they rise, due to the buoyancy force.Such bubbledriven flow (bubble plume) is utilized in various engineering devices concerning matter and heat transfer, mixing, and chemical reactions.A number of studies have previously been performed on bubble plumes, and methods to predict entrained liquid flow rate [1,2] and plume characteristics [3,4] have been proposed.The relation between the meandering motion of rising bubbles and bubble flow rate has also been investigated [5].The authors [6,7] developed simulation methods and carried out numerical simulations for bubble plumes.The simulations successfully analyzed bubble meandering motion and large-scale vortical structures induced by the bubbles.Bubble motion is one of the important and elementary phenomena governing the plume characteristics, and it is closely related to the performance of the device incorporating a bubble plume.Therefore, the control of bubble motion promises to optimize device performance.
Investigations of the bubble behavior in a mixing layer [8] and in jets [9][10][11] showed that bubble motion in such shear flows is dominated by large-scale eddies.It is well known that vortex rings, which represent large-scale eddies, have a higher ability to transport matter through their convection process with a self-induced velocity.Therefore, the authors [12] experimentally explored the possibility of controlling bubble motion in a bubble plume with a vortex ring.A vortex ring launcher, composed of a cylinder and a piston, is mounted at the bottom of a water tank.Small hydrogen bubbles are generated by the electrolysis of water (cathode is wound around the cylinder outlet) and released into still water in the tank.The bubbles rise because of buoyancy forces and induce a bubble plume.Water in the cylinder is discharged into the bubble plume by the piston, resulting in a vertically upward vortex ring convection in the plume.The bubble entrainment in the vortex ring and the transport of the entrained bubbles by the convection of vortex ring were clarified.The effect of the bubbles on the behavior of the vortex ring was also explained.Bubbles rising because of buoyancy forces are considered to be greatly affected by a large-scale eddy with a vertical axis or a swirling flow around the bubbles.Thus, the swirling flow can be employed for controlling bubble motion in a bubble plume.Some attempts to apply swirling flows to remove bubbles from liquid [13] as well as to generate microbubbles [14] were undertaken, and bubble motion was studied.The motion of a bubble in a swirling water flow inside a circular pipe was explored by experimental and numerical approaches [15].However, the interaction between rising bubbles and a swirling flow imposed around the central (vertical) axis of a bubble plume has not been investigated.
The objective of this study is to experimentally investigate the interaction between rising bubbles and swirling flow around a bubble plume.The experiment is performed in a cylindrical water tank.A stirring disc, including a magnet, is mounted at the center of the tank bottom.Small air bubbles are successively released from two tubules mounted near the stirring disc to generate a bubble plume.The stirring disc is rotated to generate swirling water flow around the bubble plume.The diameter and water depth are five times the diameter of the stirring disc.The bubble motion and characteristics of the swirling water flow are explored, and the effects of bubble volume flow rate and the rotational speed of the stirring disc are discussed.

Experimental
2.1.Experimental Setup. Figure 1 shows a schematic of the experimental setup.To obtain basic knowledge on the interaction between bubbles and swirling water flow, the experiment is conducted in a cylindrical water tank made of transparent acrylic resin.In this tank, bubble plumes are generated and swirling water flow is imposed around the central (vertical) axis.The tank diameter  1 is 300 mm, and the height is 455 mm.The top of the tank is open to the atmosphere, and the tank is installed in a rectangular tank made of transparent acrylic resin.The width and depth of the rectangular tank are 350 mm.To accurately visualize the bubbles and water flow in the cylindrical tank, the effect of refractive index at the cylindrical tank wall is eliminated by filling the gap between the two tanks with water.The origin of coordinates is set at the center of the tank bottom.The - plane is horizontal, and the -axis is considered to be vertical.
A cylindrical casing, the top of which is open to the water, is mounted on the bottom of the cylindrical tank, as shown in Figure 2. The inner and outer diameters are 62 mm and 70 mm, respectively, and the height is 20 mm.On the outer wall, two tubules having inner diameter of 0.5 mm are attached, and each of the tubules is connected to an air pump through a flow meter.Air bubbles, which are successively released from the tubules into the water, rise as a result of buoyancy force and generate a bubble plume.A cylindrical stirring disc with diameter  0 of 60 mm and height of 13 mm is installed in the casing.The stirring disc, including a magnet, is rotated around the central (vertical) axis of the tank by the magnetic force imposed by a magnetic stirrer.The rotation produces swirling water flows around the plume centerline.
This study clarifies the fundamental mechanism of the interaction between bubbles and swirling water flow.Therefore, it would provide useful insights for the analysis and prediction of the interaction in industrial devices such as cyclonic separators and heat exchangers.

Experimental Method and Conditions. The water depth
is 300 mm, and the water velocity in the horizontal crosssections of the tank is measured by a PIV system.Nylon particles (mean diameter: 80 m, specific weight: 1.02) are included as tracers for the PIV system.Particle images,  Rotation number, Ω 0 5.9 × 10 4 7.9 × 10 4 9.9 × 10  produced on a horizontal laser light sheet (power: 100 mW, wavelength: 532 nm, and thickness: 1 mm), are acquired by a high-speed camera.The frame rate, shutter speed, view area, and spatial resolution of the camera are 200 fps, 1/200 s, 150 mm × 200 mm, and 480 × 640 pixels, respectively.The laser light sheet used in the PIV system is employed to measure bubble distribution in the horizontal cross-sections of the tank.In addition, it is also used to explore the behavior of the vortex core on the water surface.
The rotational speed of the stirring disc and the bubble flow rate are the experimental parameters varied in this study.To express rotational speed, the nondimensional rotation number Ω = ( 0 /2) 2 /V is defined, where  is the angular velocity of the stirring disc and V is the kinematic viscosity of the water.The present experiment is performed with the rotation numbers listed in Table 1.The volumetric flow rate of the bubbles released from the tubules,   , is set to 12 mm 3 /s or 24 mm 3 /s.Table 1 also shows the rotational frequency of the stirring disc  at a temperature of 293 K.   core remains almost steady around the central axis of the tank at elevations higher than half the water depth, / ≥ 0.5.However, it markedly swirls or precesses just above the stirring disc.Similar behavior of the vortex core is observed at each rotation number.The precessional amplitude has no significant dependences on Ω, as discussed later.

Results and Discussion
When the water velocity over the horizontal section is measured at / 0 = 4.17, the time-averaged velocity distribution occurs as shown in Figure 4.The swirling velocity increases with increasing Ω, and the velocity field is almost axisymmetric.The velocity is extremely low around the central axis ( =  = 0).This is because the vortex core remains almost steady along the central axis, as shown in Figure 3.
The circumferential component   of the water velocity over the section at / 0 = 4.17 shown in Figure 4 changes in a radial direction, as presented in Figure 5, where   is expressed in the nondimensional form using the peripheral speed  0 /2 of the stirring disc.At / 0 ≥ 0.4, the velocity distributions for each rotation number Ω are similar.These distributions are approximately fitted by   /( 0 /2) = 0.16/(/ 0 ) at / 0 ≥ 0.57, indicating the occurrence of a free-vortex type velocity field.

Bubble Motion.
Bubble diameters are measured just above the outlet of the bubble-releasing tubules.The equivalent diameter   , expressed in the nondimensional form   / 0 , is plotted against the rotation number Ω in Figure 6, where  0 is the diameter of the stirring disc.The   / 0 value in the swirling flow is less than 0.033, or   ≤ 2mm.It decreases with increasing Ω.The bubbles grow at the outlet of the tubules because of the air fed from the air pump and are detached from the outlet due to the drag force exerted by the swirling water flow.Increasing Ω leads to an increase in swirling water velocity, which heightens the drag force, therefore causing detachment of smaller bubbles from the tubule outlet.When the bubble flow rate   is lower,   is smaller and the decrease with increasing Ω is larger.After the detachment of a bubble from the tubule outlet, the subsequent bubble begins to grow at the outlet.When   is lower, the growth rate is also smaller; therefore, the bubble is easily detached even when the diameter is smaller.At the impeller inlet of a turbopump operated for gas-liquid twophase flow, the bubbles are reduced in size by the rotating blades.Murakami and Minemura [16] derived an empirical formula   ∝  −3/4 , where  is the rotational frequency of the impeller.The solid line in Figure 6  of   / 0 = 124 −3/4 , approximating the result at   = 12 mm 3 /s.Figure 7 shows the bubble behavior when   = 24 mm 3 /s.In the quiescent water (Ω = 0), the released bubbles rise with meandering motion in the region higher than a certain elevation.This is attributable to the eddies appearing just behind each bubble.When the stirring disc is rotated clockwise, swirling water flow is induced.The rising bubbles are affected by the swirling flow, and hence they are rotated clockwise around the central (vertical) axis of the tank.The bubbles exhibit helical motions.With increasing Ω, the bubble rotation angle increases.
Bubble behavior at the lower bubble flow rate   = 12 mm 3 /s is shown in Figure 8.The bubble distribution is almost similar to the case of   = 24mm 3 /s shown in Figure 7.In this case, the effect of   is not significant.
Figure 9 shows the bubble distributions over the horizontal section (/ 0 = 0.83) just above the stirring disc, where the positions of the bubbles passing through the section for fifteen seconds are plotted.The bubble-releasing tubules are indicated by red circles.The bubbles rise almost vertically when Ω = 0.In the case when Ω > 0, the bubbles are rotated clockwise around the central axis ( =  = 0).Their rotation angle and dispersion increase with increasing Ω.
Figure 10 presents the bubble distributions on the higher horizontal section at / 0 = 2.5.When compared with the result at / 0 = 0.83 shown in Figure 9, the rotation angle and the dispersion are larger.One can observe the bubble  swirling motion caused by the swirling water flow.Increasing Ω induces larger bubble dispersion.It should be noted that some bubbles shift toward the central axis when Ω ≥ 9.9×10 4 .This is because a negative pressure gradient toward the central axis is produced by the swirling water flow, and accordingly it drives the bubbles to the axis.Magaud et al. [15] investigated the motion of a bubble in swirling water flow inside a circular pipe.They found that the bubble migrates to the central axis of the pipe when the swirling angular velocity is higher than a critical value.The current study reveals that such bubble migration also occurs in bubble plume generated in swirling water flow.Figure 15: Effect of bubbles on the circumferential velocity of water at / 0 = 4.17.

Velocity of Swirling Water Flow.
The time-averaged water velocity over the horizontal section at / 0 = 4.17 is shown in Figure 11, where the nondimensional velocity u/( 0 /2) at Ω = 7.9 × 10 4 is plotted.The velocity reduces around the central axis with increasing the bubble flow rate   .A local reduction occurs at two locations when   = 24 mm 3 /s, thus producing nonaxisymmetric velocity field.This is because a number of bubbles exist at these locations.The circumferential velocity   of the water flow field shown in Figure 11 is presented in Figure 12.The velocity reduction due to increasing   is reconfirmed.Marked reduction occurs at / 0 ≤ 0.5.The density of the two-phase mixtures in the tank is lowered owing to the released bubbles, and therefore the stirring disc does not sufficiently rotate the mixtures.The velocity reduction is also caused by the friction between the two phases.
When the rotation number Ω is increased to 11.7 × 10 4 , the time-averaged water velocity is distributed over the horizontal section at / 0 = 4.17 as shown in Figure 13.In contrast with the abovementioned result for Ω = 7.9 × 10 4 , the bubble flow rate does not significantly affect the water velocity, and the velocity fields remain almost axisymmetric.
Figure 14 shows the change in circumferential velocity when Ω = 11.7 × 10 4 .One can reconfirm that the velocity is less affected by   , except around the central axis (/ 0 ≤ 0.21).This is because the angular momentum supplied to the water is larger, and accordingly the effect of the bubbles is relatively lessened.
Calculating the averaged circumferential velocity of the water in the region 0.1 ≤ / 0 ≤ 2, ⟨  ⟩, the nondimensional value changes with   as shown in Figure 15.Though the nondimensional velocity decreases with increasing   at Ω ≤ 7.9 × 10 4 , it remains almost unaltered at Ω ≥ 9.9 × 10 4 .It is observed that the released bubbles scarcely affect the nondimensional velocity of the swirling water flow when the rotational speed of the stirring disc is higher than a certain value.

Behavior of the Upper
End for the Vortex Core.The locus for the upper end of the vortex core is plotted in Figure 16, where the results at   = 0 and 12 mm 3 /s at Ω = 7.9 × 10 4 are compared.By setting the tracer particles used for the PIV afloat on the upper end of the vortex core, the coordinates r  = (  ,   ) are measured by visualizing the particles with a horizontal laser-light sheet.The coordinates measured every 0.2 s over a period of 15 s are plotted.The upper end of the vortex core moves around the central axis of the tank, exhibiting precessional motion.The bubbles cause a large amplitude of the precessional motion.
In the case of Ω = 11.7 × 10 4 , the precessional amplitude is amplified by the bubbles as shown in Figure 17.But the amplification is slightly smaller when compared with the result for Ω = 7.9 × 10 4 .
The standard deviation   for r  depends on Ω, as shown in Figure 18.The precessional amplitude increases due to the presence of the bubbles.A clear effect of Ω on   is not observed.
When estimating the precessional velocity for the upper end of the vortex core, k = r  /, the time-averaged velocity changes as a function of Ω, as shown in Figure 19.The nondimensional velocity V/( 0 /2) decreases with increasing Ω at the single-phase water flow condition (  = 0).A similar decrease is also observed at   = 12 mm 3 /s.It should be noted that the effect of   reduces with increasing Ω.When Ω is higher, the effect of the bubbles is less significant, as shown in Figure 15.Such a bubble effect also appears in the precessional velocity for the top end of the vortex core.

Conclusions
The interaction between rising bubbles and swirling water flow imposed around the central (vertical) axis of a bubble plume is experimentally explored.A stirring disc, including a magnet, is placed at the bottom of a water tank, and air bubbles are successively released from two tubules, mounted near the stirring disc, into the water to generate the bubble plume.The stirring disc is rotated by the magnetic force imposed with a magnetic stirrer to produce a swirling water flow around the plume centerline.The diameter of the stirring disc is 60 mm, and bubbles with a certain diameter are successively released at the volumetric flow rate   .The rotation number Ω of the stirring disc is less than 11.7 × 10 4 , and the bubble flow rate is lower than 24 mm 3 /s.The results are summarized as follows.
(1) The bubble diameter just above the outlet of the bubble-releasing tubules decreases with increasing Ω.
When   is lower, the diameter is smaller and the decrease with increasing Ω is larger.
(2) The dispersion of the bubbles rising in the swirling water flow increases with increasing Ω.Some bubbles  International Journal of Chemical Engineering shift toward the central axis of the tank when Ω ≥ 9.9 × 10 4 because of the pressure gradient caused by the swirling water flow.
(3) The nondimensional circumferential velocity of water reduces with increasing   when Ω ≤ 7.9 × 10 4 .The marked reduction occurs around the central axis of the tank where several bubbles exist.However,   does not significantly affect the velocity when Ω ≥ 9.9 × 10 4 .
(4) The precessional amplitude for the upper end of the vortex core increases due to the bubbles.The precessional velocity, expressed in the nondimensional form by the rotational speed of the stirring disc, decreases with increasing Ω.In addition, the effect of   is reduced.

Nomenclatures
0 : Diameter of stirring disc = 60 mm  1 : Diameter of cylindrical tank = 300 mm   : Bubblediameter : Water depth = 300 mm : Rotational frequency of stirring disc   : Standard deviation of r    : Volumetric flow rate of released bubbles : Distancefromthecentralaxisoftank r  : Position vector for the upper end of vortex core u: W atervelocity   : Circumferential component of u V: Time-averaged velocity of the upper end of vortex core , , : Spatial coordinates V: Kinematic viscosity of water : Angular velocity of stirring disc = 2/60 Ω: Nondimensional rotation number = ( 0 /2) 2 /.

3. 1 .
Swirling Water Flow without Bubbles.The single-phase swirling flow or the water flow at the bubble flow rate   = 0 is investigated.Figure3depicts the vortex core when the nondimensional rotation number Ω is 9.9 × 10 4 .This figure is acquired by injecting a small amount of milk with water paint in the swirling center on the water surface.The vortex D 0 = 124 Ω −3/4 Q g = 12 mm 3 /s Q g = 24 mm 3 /s
Figure 19: Precessional speed for the upper end of vortex core.

Table 1 :
Rotational speed of stirring disc.