The effect of two inclined circular plunging jets on air entrainment in an aeration tank

Computational Methods in Multiphase Flow III 229 The effect of two inclined circular plunging jets on air entrainment in an aeration tank M. S. Baawain, M. Gamal El-Din & D. W. Smith Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada Abstract Air entrainment occurs when two or more flowing fluids plunge into each other, or when some sort of turbulence is introduced in a water body. In this study, experiments were conducted to explore some properties of bubble plumes of two inclined circular plunging water jets on a water surface in a cubic tank utilizing particle image velocimetry (PIV). Different combinations of two inclined water jet sizes operating under different flow rates and plunging angles were used to study air entrainment in the aeration tank. The PIV system was used to measure the two-phase jet velocities in both lateral and axial positions. Other parameters of interest, such as penetration depths and the height and width of the two-phase mixture due to the air entrainment, were monitored using a photographic technique. The gas hold-up (ε G ) and the bubble average diameter (d b ) were consequently obtained. Using ε G and d b, the specific interfacial area (a) and the overall mass transfer coefficient (k L a) under each operating condition were determined. The obtained results were compared with results obtained under similar operating conditions for vertically aligned jets. Keywords: air entrainment, plunging jets, particle image velocimetry, gas holdup, specific interfacial area, overall mass transfer coefficient. 1 Introduction Liquid plunging jets are moving columns of liquid (water) that pass through some gaseous headspace before impinging into a free surface of the receiving liquid. At the intersection of the plunging jet and the liquid surface, free-surface instabilities develop and gas entrainment may be observed. In order for the gas entrainment to take place, the jet impact velocity has to exceed a characteristic

230 Computational Methods in Multiphase Flow III velocity (onset or threshold velocity) that is a function of the plunging flow conditions [1]. Other factors that control the mechanisms of air entrainment include: physical properties of the liquid, the design of the jet nozzle, the distance from the jet outlet to the liquid surface, and the turbulence of the jet [2, 3]. Air entrainment by plunging liquid jets in water bodies has potential applications in many chemical and waste treatment processes. Examples of such processes include minerals-processing flotation cells and wastewater treatment. This process, referred to as plunging jet entrainment and aeration, can also be observed in natural systems such as self-purification (re-aeration) of rivers and waterfalls [2, 3, 4]. When aeration systems are used in wastewater treatment plants, the ultimate goal is to obtain high mass transfer of oxygen by having the most effective bubbles (i.e. bubbles with small diameter and long residence time). The process of mass transfer of gas to water with time (t) can be expressed using the following equation: dc dt ( C C) = k a (1) L where C is the dissolved oxygen concentration in water (mg/l), k L a is the overall mass transfer coefficient (s -1 ), and C s is the saturation concentration of oxygen in water. The determination of k L a is very important for the design and performance evaluation of gas-liquid mass transfer processes. This study explores air entrainment resulted from the use of two inclined circular plunging jets intersecting at the surface of water tank in comparison to the commonly used vertical jets. The research aims at utilizing particle image velocimetery (PIV), which is a well established non-intrusive measuring technique that can provide simultaneous measurements of velocity components of different phases of fluids [5, 6], to evaluate the two-phase jet velocity components in the tank. In addition to the impingement angle, this research work evaluates the use of different jets nozzle size, free jet lengths, and jet outlet velocities. 2 Materials and methods Air entrainment experiments were performed using a clear walled tank, vertical jet, and a particle image velocimetery, as shown in fig. 1. The inside dimensions of the tank had a width of 0.67 m, a length of 0.67 m, and a depth of 0.67 m. An overflow weir was located on one side to maintain a constant depth in the tank. The water overflow drained into a storage barrel and re-circulated using an electric pump, which also provided a means of varying the discharge. Water was directed by the pump to two inclined (or vertical) circular jets mounted above the water surface of the tank. This alignment allowed the jets to be moved in three directions and to be rotated from 0 o to 90 o. The diameter of these jets was varied from 2.5 x 10-3 to 0.01 m. Air bubbles entrained by jets s

Computational Methods in Multiphase Flow III 231 Jets Overflow weir Drain/ recirculate CCD cameras Aeration tank PIV preprocessor Nd:Yag laser To PC Figure 1: Experimental setup. were then observed through the transparent tank walls. Two measuring tapes were secured to the tank horizontal and vertical sides in order to monitor the depth and width of the bubble plumes. The PIV system consisted of a laser source, two charge coupled device (CCD) cameras, and processing units. This study used an Nd:Yag dual cavity laser with a power level of 100 mj. The emitted wavelength of the Nd:Yag laser was 532 nm with a pulse duration of 10 ns. The time between pulses was set to 100 µs with a maximum repetition rate of 8.0 Hz. The two CCD cameras were configured to use double frames for PIV measurements (velocity measurements) of the two phases (water and air). Melamine-formaldehyde (MF) spheres, coated with Rhodium B (RhB), were used as seeding particles during the liquid velocity measurements. A FlowMap System Hub from Dantec Dynamics was used to record and transfer the data to a PC where FlowMap software was used to analyze the images and export the resulted files to a desired format for further analysis. Two PIV measurements were conducted simultaneously: one for obtaining liquid jet velocity components in the tank and the second for measuring the air (bubble) jet velocity components in the tank. The images captured for the bubble plumes by the CCD camera were used to estimate the average bubble size under each experimental condition.

232 Computational Methods in Multiphase Flow III Table 1: Summary of the experimental operating conditions. Run # Q L x 10-5 (m 3 /s) d o x 10-3 (m) α (deg) H x 10-2 (m) 1 3.15 2.50 90 5.00 2 3.15 2.50 15 7.00 3 3.15 2.50 22.5 8.45 4 6.30 5.00 90 5.00 5 6.30 5.00 15 7.00 6 6.30 5.00 22.5 8.45 7 9.45 5.00 90 5.00 8 12.6 5.00 90 5.00 9 9.45 5.00 15 7.00 10 12.6 5.00 15 7.00 11 6.30 5.00 15 8.60 12 9.45 5.00 15 8.60 13 12.6 5.00 15 8.60 14 6.3 5.00 15 11.20 15 9.5 5.00 15 11.20 16 12.6 5.00 15 11.2 17 9.45 5.00 22.5 8.45 18 12.6 5.00 22.5 8.45 19 9.45 7.50 90 5.00 20 9.45 7.50 15 7.00 21 9.45 7.50 22.5 8.45 22 12.6 10.0 90 5.00 23 12.6 10.0 15 7.00 24 12.6 10.0 22.5 8.45 A summary of the experimental runs conducted for this work is provided in table 1. The jet nozzles were made of copper with an inlet diameter (d i ) of 0.025 m and a cylindrical length (l i ) of 0.015 m. Nozzles outlet diameter (d o ) used in this study ranged from 2.5 x 10-3 to 0.01 m yielding a range for the aspect ratio (l i /d o ) of 1.5 and 6. The monitored water temperature during all experiments was 23 o C ± 1 o C. The Liquid flowrate (Q L ) was varied from 3.15 x 10-3 to 12.6 x 10-3 m 3 /s, with the angle at which the jets plunge the surface (α) of 67.5 o, 75 o (resulted angle between the two jets are 45 o and 30 o, respectively) and 90 o. The vertical distance from the jets outlet to the free water surface (H) was varied from 0.05 to 0.11 m. The rage of H and α used in this study resulted in a free jet length (L o ) that ranged from 0.05 to 0.13 m. The mean outlet jet velocity (u o ) has to be greater than a threshold value (u e ) at which gas entrainment inaugurates. A rough estimate of u e in m/s can be obtained using the following relationship [2]: e 0.534 5L o u = (2)

Computational Methods in Multiphase Flow III 233 Equation (2) is valid for L o ranging from 0.015 to 0.4 m. The required u e for this study ranged from 1.0 to 1.7 m/s. The used u o was always more than the required u e in order to ensure air entrainment in the tank under every experimental condition throughout the course of this study. In addition to satisfying the threshold velocity criterion, the water temperature was 23 o C (i.e. kinematic water viscosity of 9.34 x 10-7 m 2 /s) and at the mentioned flow rates and nozzle diameters, the diameter-based Reynolds number (Re d ) was greater than 1.71 x 10 4 indicating turbulent flow conditions which are favourable for air entertainment [2]. Some parameters of interest such as the maximum penetration depth (z p ), the width of the bubble plume, and the height and the width of the two-phase mixture (gas and water) due to the air entrainment were observed using a digital photographic technique and by eye inspection utilizing the measuring tapes fixed to the sides of the tank. The height and width of the two-phase mixture can be used to estimate the gas holdup (ε G ) as follows: WL G ( H L G H L ) W L ε G = (3) H L G where W L-G is the width of the two-phase mixture (m), W L is the inside width of the tank under no air entrainment (m), H L-G is the height of the two-phase mixture (m), and H L is the inside depth of the tank under no air entrainment (m). Once ε G is obtained and the average bubble diameter (d b ) is obtained from the CCD camera images, the specific interfacial area (a) of the bubbles can be determined using the following relationship [7]: a = 6 ε G 1 ε G d b (4) 3 Results and discussion 3.1 Velocity measurements All PIV measurements obtained for the velocity components of the two phase flow conditions were taken below the region of the break-up length (z b ) (length after which bubbles start to be formed in the water body) of the two-phase jet. The reason for taking the measurements below z b is related to the inability of the scattered laser sheet from reaching the CCD cameras. Therefore, the CCD cameras were moved up and down to overcome this problem. Measurements of the lateral (radial) distributions (x) of water and bubble jets velocity components were taken at different axial positions (z). At each z, the axial velocity (v) was normalized by its centreline value (v m ), and plotted against the normalized lateral

234 Computational Methods in Multiphase Flow III v/v m 1.0 0.8 0.6 0.4 0.2 0.0 do =5mm do =7.5mm do =10mm Gaussian -0.2 (a) -0.4 0.0 1.0 2.0 3.0 4.0 5.0 6.0 x/d o v/v m 1.0 0.8 do = 5mm do = 7.5mm 0.6 do = 10mm 0.4 Gaussian 0.2 0.0 (b) -0.2 0.0 1.0 2.0 3.0 4.0 5.0 6.0 x/d o Figure 2: Lateral distributions of the axial mean velocity: (a) gas-phase, (b) liquid-phase. distance (x/d 0 ). The data shown in Figure 2 is a result of using same value of Re d and varying d o and θ (the angle between the two plunging jets).fig. 2a, representing the gas phase, shows a fairly good agreement with the Gaussian distribution. However, as d o decreases (i.e. water jet velocity increases), the deviation from the Gaussian distribution increases. The negative values of v/v m in the region of x/d o > 2 could be attributed to the fact that bubbles rise up when their buoyancy force overcomes the impingement force. On the other hand, the water phase jet, fig. 2b, showed a very good agreement with the Gaussian distribution in the region of x/d o < 2, which is supported by the observations made by Iguchi et al [8], and McKeogh and Ervine [9]. The negative values observed as x/d o increased further could be related to the effect of the rising bubble. 3.2 Penetration depth The performance of the aeration process resulted from air entrainment due to plunging jets is highly affected by the residence time of the entrained bubbles. Therefore, the residence time is related to the bubble penetration depth (z p ) into the aeration tank. During all experimental conditions (table 1), penetration depth was always less than the water depth in the tank. Figure 3a illustrates that under the same turbulence condition and different α, as d o increases, z p also increases. It also shows that under the same d o, z p at α = 75 o (θ = 30 o ) is greater than the ones related to the other two cases (α = 67.5 o and α = 90 o ). Figure 3b shows the variation of z p at different water jet outlet velocity at d o = 5.0 x 10-3 m and different α values. Results showed that as jet outlet velocity increases, z p also increases. For a specific velocity, the highest z p was obtained when α = 75 o and L o /d o ratio was relatively small. The relatively high z p value under α = 75 o (θ = 30 o ) could be related to the combined energy of the two plunging jets that intersect at the surface of the water without much dissipation.

Computational Methods in Multiphase Flow III 235 Penetration depth, m 0.40 0.35 alpha = 75 alpha = 67.5 0.30 0.25 alpha = 90 0.20 0.15 0.10 0.05 0.00 0.000 0.002 0.004 0.006 0.008 0.010 0.012 Nozzle diameter, m 0.35 Penetration depth, m 0.30 0.25 0.20 0.15 alpha = 75, Lo/do = 16 alpha = 75, Lo/do = 20 0.10 alpha = 75, Lo/do = 25 alpha = 67.5, Lo/do = 22 0.05 alpha = 67.5, Lo/do = 10 0.00 0.0 2.0 4.0 6.0 8.0 Nozzle outlet velocity, m/s Figure 3: Variation of the penetration depth with nozzles diameter and nozzle outlet velocity. In the case of α = 67.5 o, the intersecting jets could be dissipating the energy as the angle of intersection was too wide. 3.3 Gas hold-up and mass transfer coefficient Gas hold-up (ε G ) is another important parameter in evaluating gas-liquid mass transfer. ε G was obtained using the measured parameters and applying them to eqn (3). As d o increases (outlet velocity decreases for the same Re d ), ε G decreases (see fig. 4a). This can be explained by the reduced amount of bubble entrained under such conditions. On the contrary, for the same d o as shown in fig. 4b, ε G increases as outlet velocity increases. This result is expected as for the same nozzle diameter, increasing the jet outlet velocity will increase the turbulence

236 Computational Methods in Multiphase Flow III 0.003 Gas holdup 0.003 0.002 0.002 0.001 0.001 alpha=75 alpha = 67.5 alpha = 90 0.000 0.000 0.002 0.004 0.006 0.008 0.010 0.012 Nozzle diameter, m Gas holdup 0.008 0.007 alpha = 75, Lo/do = 16 0.006 alpha = 75, Lo/do = 20 0.005 alpha = 75, Lo/do = 25 0.004 alpha = 67.5, Lo/do = 22 0.003 alpha = 67.5, Lo/do = 10 0.002 0.001 0.000 0.0 2.0 4.0 6.0 8.0 Nozzle outlet velocity, m/s Figure 4: Variation of the gas hold-up with nozzles diameter and nozzle outlet velocity. further (initial experimental condition was turbulent with Re d > 1.7 x 10 4 ). Hence as the turbulence increases, the free-surface instabilities will increase and therefore leading to more air entrainment and eventually higher gas hold-up. After ε G was obtained and the average bubble diameter was determined from the CCD images captured during the PIV processing, the specific interfacial area (a) was calculated using eqn (4). The local mass transfer coefficient was then assumed to be 2.0 x 10-4 m/s according to Bin [2] and multiplied by eqn (4) in order to evaluate the overall mass transfer coefficient (k L a). Figure 5 shows the variation of k L a with jet nozzle diameter under the same turbulent condition. The mass transfer mechanism is expected to decrease in this case as the amount of gas entrained decreased under similar conditions (fig. 4a).

Computational Methods in Multiphase Flow III 237 k L a, s -1 2.00E-06 1.60E-06 1.20E-06 8.00E-07 4.00E-07 alpha =75 alpha = 67.5 alpha = 90 0.00E+00 0 0.002 0.004 0.006 0.008 0.01 0.012 Nozzle diameter, m Figure 5: Variation of the overall mass transfer coefficient with nozzles diameter. 4 Conclusions Gas entrainment utilizing liquid plunging jets has seen many practical applications in chemical and waste treatment processes. The phenomenon can be observed in natural systems such as re-aeration of rivers and streams. Although, such systems can entrain air in water bodies, the process has to be optimized in order to achieve the most effective bubble in the system. This study explored the air entrainment resulted from the use of two inclined circular plunging jets intersecting at the surface of a water tank with different angles and nozzle diameters in comparison to the vertical plunging jets. Particle image velocimetery (PIV), a non-intrusive measuring technique, was used to measure the lateral and axial velocities of the two-phase jet. Images captured during the PIV process using the charge coupled device (CCD) cameras were used to estimate the average bubble size under each operating condition. Other important parameters such as the maximum penetration depth, the width of the bubble plume, and the height and the width of the two-phase mixture (gas and water) due to the air entrainment were observed using a digital photographic technique and by eye inspection utilizing the measuring tapes fixed to the sides of the tank. PIV measurements of the normalized axial velocity for the gas and water jets were plotted against normalized lateral distance. Results of both phases showed good agreement with the Gaussian distribution which agrees with the literature. The variation from the Gaussian distribution is related to the amount of bubbles that may block the CCD camera from capturing the scattered laser sheet. The bubble penetration depth was measured to evaluate the jet combination that will provide the longest bubble residence time. Results obtained under the same turbulence condition and different plunging angle (α) showed that as the

238 Computational Methods in Multiphase Flow III nozzle diameter (d o ) increased the penetration depth (z p ) also increased. Also, under the same d o, z p at α = 75 o (θ = 30 o ) was found to be higher than the ones obtained under other cases (α = 67.5 o and α = 90 o ). Gas hold-up (ε G ) was found to decrease as d o increases (outlet velocity decreases for the same Re d ). This was related to the reduced amount of bubble entrained under such conditions. On the other hand, when same d o is used, ε G increases as outlet velocity increases. This was explained as increasing the jet outlet velocity will increase the turbulence condition further and hence the freesurface instabilities will increase leading to more air entrainment and eventually higher gas hold-up. After ε G was obtained and the average bubble diameter was determined from the CCD images captured during the PIV processing, the specific interfacial area (a) and the overall mass transfer coefficient (k L a) were calculated. References [1] Cummings, P.D., & Chanson, H., An experimental study of individual air bubble entrainment at a planar plunging jet. Chem. Eng. Res. Des., 77 (A2), pp. 159 164, 1999. [2] Bin, A.K., Gas entrainment by plunging liquid jets. Chem. Eng. Sci., 48(21), 3585 3630, 1993. [3] Chanson, H., Air Bubble Entrainment in Free-Surface Turbulent Shear Flows. Academic Press: London, 1997. [4] Evans, G.M., Jameson, G.J, & Rielly, C.D., Free jet expansion and gas entrainment characteristics of a plunging jet, Exp. Therm. Fluid Mech., 12, 142 149, 1996. [5] Raffel, M., Willert, C. & Kompenhans, J., Particle Image Velocimetry: A Practical Guide, Springer-Velag: Berlin Heidelberg, N. Y., 1998. [6] Stanislas, M., Kompenhans, J., & Westerweel, J., Particle Image Velocimetry: Progress Towards Industrial Application, Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000. [7] Jakubowski, C.a., Atkinson, B.W., Dennis, P., & Evans, G.M., Ozone Mass Transfer in a confined plunging liquid jet contactor, Ozone Sci. & Eng. 25, 1 12, 2003. [8] Iguchi, M., Okita, K., & Yamamoto, F., Mean velocity and turbulence characteristics of water flow in the bubble dispersion region induced by plunging water jet. Int. J. Multiphase Flow, 24(4), 523 537, 1998. [9] McKeogh, E.J., & Ervine, D.A., Air entrainment rate and diffusion pattern of plunging liquid jets. Chem. Eng. Sci. 36, 1161 1172, 1981.