Far-field properties of aerated water jets in air

International Journal of Multiphase Flow 76 (2015) 158–167

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International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w

Far-field properties of aerated water jets in air Wenming Zhang a, David Z. Zhu a,b,⇑ a b

Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB T6G 2W2, Canada Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China

a r t i c l e

i n f o

Article history: Received 2 March 2015 Received in revised form 13 July 2015 Accepted 14 July 2015 Available online 26 July 2015 Keywords: Air Diameter Drops Jets Rain intensity Spreading Two-phase flow Trajectory Velocity Water

a b s t r a c t This paper presents an experimental investigation on aerated water jets at a 45° angle into air. Different amount of air was injected into the water jets upstream of a circular nozzle. The focus was on the bulk trajectories of the aerated jets, as well as the intensity, size and velocity of the water drops in the far-field. It was found that, the injection of air into water jets will significantly accelerate water jet breakup in air, causing the water jet to spread much wider and more uniform. Meanwhile, water drop size became substantially smaller, but drop velocity only became slightly smaller. On the horizontal plane at the same elevation of the nozzle, intensity of falling water drops was noticed to have a Gaussian distribution in the transverse direction, while a left-skewed Gaussian distribution in the longitudinal direction. At the location of maximum intensity, drop size and velocity distributions also approximated Gaussian distributions, while the size distribution could be more complex in a pure water jet. Terminal water drop velocity was correlated with drop diameter, and its value was 20% smaller in an aerated jet than in a pure water jet for the drops with diameters of 2–10 mm. The energy dissipation of these jets was significant as these jets broke down to drops with relatively small terminal velocities. Ó 2015 Elsevier Ltd. All rights reserved.

Introduction Liquid jets in air have been studied extensively as they have wide applications in hydraulic structures (Chanson, 2009; Pfister et al., 2014), sewer dropshafts (Zhang et al., 2014; Camino et al., 2015), fountains, irrigation, fire extinction, atmosphere cleaning, industrial painting or printing, chemical reactors, atomization and spray, among others (Lefebvre, 2000; Surma and Friedel, 2004; Dumouchel, 2008; Chanson, 2009; Gowing et al., 2010; Osta et al., 2012). Most of the studies concentrated on liquid–air multiphase flow properties near the injection nozzle (near-field) such as liquid jet breakup, instability analysis, drop or spray formation, and multiphase flow dynamics (e.g., Bogy, 1979; Hoyt et al., 1974; Faeth et al., 1995; Sallam et al., 2002; Birouk and Lekic, 2009; Portillo et al., 2011). Only limited studies examined the far-field behavior of liquid jets: Rajaratnam et al. (1994) and Rajaratnam and Albers (1998) studied high-speed (85–160 m/s) water jets in air up to 2500 times of the nozzle diameter but without details on water drop properties such as size and its distribution. Guha et al. (2010) numerically simulated these high-speed jets. ⇑ Corresponding author at: Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB T6G 2W2, Canada. E-mail addresses: [email protected] (W. Zhang), [email protected] (D.Z. Zhu). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2015.07.006 0301-9322/Ó 2015 Elsevier Ltd. All rights reserved.

A water jet mixed with a certain amount of air at the injection point, called an aerated water jet in this study, is of particular interest. In dam spillways, high-speed water jets quickly become aerated by entraining the ambient air. After leaving spillways, the aerated jets eject into the air at certain angles and then impinge into the plunging pool (Vischer and Hager, 1995; Pfister et al., 2014). The breakup of the jets in air can directly impact on the level of total dissolved gases in the downstream rivers and fish-kill (Geldert et al., 1998; Orlins and Gulliver, 2000; Politano et al., 2009). Compared to pure liquid jets, aerated jets in air are expected to have different behavior. Aerated liquid jets are usually produced using two types of artificial aeration in addition to the self-aeration as in dam spillways. The first type is to mix air and liquid in a mixing chamber/injector upstream of the injection nozzle (Surma and Friedel, 2004; Gowing et al., 2010; Wu et al., 2012). In Surma and Friedel (2004), aerated water jets were injected horizontally via a nozzle into a test chamber. Drop velocity was measured by using a phase Doppler anemometer within a distance of approximately 140 times of the nozzle diameter. Longitudinal and radial distributions of axial drop velocity were presented. However, their study was close to the nozzle, and no results were reported on drop sizes, drop concentration and water-phase/rain intensity. Gowing et al. (2010) and Wu et al. (2012) experimentally and numerically studied aerated water jets in air, but they focused on the bubbly flow inside the nozzles

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and on the augment of thrust due to air injection for marine propulsion devices. The second type of artificial aeration is to mix air and liquid outside of the nozzle using coflowing (co-axial) two-phase jets. Coflowing two-phase jets are mostly related with twin-fluid atomization, in which a fast air jet is coflowing with a liquid jet and its kinetic energy is used to aid the breakup of liquid-phase. Extensive studies have been reported (Lin and Reitz, 1998; Lasheras and Hopfinger, 2000; Morozumi and Fukai, 2004; Sevilla et al., 2005; Matas and Cartellier, 2013). Recently Avulapati and Venkata (2013) reported a variant of coflowing two-phase jets, in which a gas flow was injected on to the impinging point of two liquid jets to assist atomization. Similarly, most of these studies were near the nozzle with a focus on the liquid breakup and drop properties. Relevant to the studies of aerated jets in air, some studies on aerated jets in liquid have been reported: Lima Neto et al. (2008) in stagnant ambient water, and Zhang and Zhu (2013, 2014) in crossflowing water. They found that, compared to pure air injection, the introduction of liquid phase into the gas phase prior to the nozzle exit was found to significantly decrease bubble diameter. Lima Neto et al. (2008) and Zhang and Zhu (2013) also reported a criterion for producing small gas bubbles with relatively uniform sizes. Based on the above studies, one would expect that, for water jets in air, adding air into the water jets upstream of the nozzle will be able to promote the breakup of water jets and produce smaller and more uniform water drops. This might be a useful alternative to the traditional way of liquid atomization using small orifices (Sharma and Fang, 2014), non-circular nozzles (Kasyap et al., 2009; Farvardin and Dolatabadi, 2013; Sharma and Fang, 2014) and other specially-designed nozzles (e.g., varying the injector length/diameter ratio in Osta et al., 2012). This study reports an experimental study on aerated water jets at an angle into the air. The focus is on far-field drop properties in the horizontal plane at the same elevation of the nozzle, including longitudinal and transverse distributions of water/rain intensity, drop size and drop velocity. Effect of increasing initial gas volume fractions of aerated jets on these drop properties were examined in two groups of experiments: fixing the water flow rate in the first group, and fixing the water jet exit velocity in the second group.

Experimental setup and procedure The experiments of aerated water jets in air were conducted in the T. Blench Hydraulics Laboratory at the University of Alberta (see Fig. 1 for the setup). All the ventilation openings in the laboratory were closed to avoid any wind effect on the jets. Air and water were pre-mixed using a Venturi injector (Model 2081-A, Mazzei Injector Corp.) before the mixture exited the nozzle. The air was supplied from a gas line in the laboratory and its gauge pressure was controlled at 5 atm using a pressure-regulating value. The air flow rate was controlled using an air rotameter with an accuracy of 3% (FL-2044, Omega Engineering Inc.). The water was supplied by using a pump controlled with a variable frequency drive. The water flow rate was measured using a magnetic flow meter. A brass nozzle was specially made as shown in the insert of Fig. 1. The nozzle’s inner diameter contracted from 25.4 mm (same as the inner diameter of the PVC pipe that connected the nozzle and the Venturi injector) to d0 = 6 mm (d0 is the nozzle exit diameter). This gradual change prevented any significant disturbance to the jets by the nozzle itself. Different ratios of air–water mixtures were injected at an angle of 45° into the air. Table 1 lists five experimental conditions, which can be divided into two groups. In the first group (Expt. #1–3), the water flow rate Qw was kept constantly at 18 liters per minute (LPM), while the air flow rate Qa was changed from 0 to 30 LPM. Therefore, the initial gas volume fraction of aerated jets C0 = Qa/(Qa + Qw) was changed from 0% (pure water jet) to 63%. In the second group (Expt. #4–5), the liquid-phase (water) velocity at the nozzle exit Uw0 = 4Qw/[(1  C0)pd20] was maintained the same (16.5 m/s) as in Expt. #2, while C0 was similarly changed from 0% to 63%. The liquid-phase velocity is an estimate of velocity of the liquid exiting the nozzle under the assumption that the area ratio occupied by the liquid-phase at the exit is the same as the liquid volume fraction (1  C0). The two groups of experiments were designed to examine the effect of changing C0 on jet properties while keeping a constant value of Qw and Uw0, respectively. Rain of falling water drops was collected in the horizontal plane (xy plane in Fig. 1) at the same elevation of the nozzle exit and 2 m above the ground to avoid any backsplash of water from the ground. In each experiment, the study plane was divided into two or three regions based on rain intensity. And

25.4 mm

15.7 mm

6 mm

Bulk Jet z

25.4 mm Brass Nozzle

Mists y x

Venturi Injector

Study Plane (2 m above Ground)

ImageWindow

PVC Pipe Wall

Valve

High-speed Camera Rotameter

Flow Meter

Air

Pump

To Computer

Pressure Pressure Meter Valve

Water Fig. 1. Schematic of the experimental setup. Details of the nozzle are shown in the insert.

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Table 1 Experimental conditions and brief results for aerated water jets in air. Nozzlea

Rainb

Dropsc

Experiments

Qa (LPM)

Qw (LPM)

C0

Uw0 (m/s)

Re

Imax (mm/hr)

Conservation ratio (%)

d (mm)

U (m/s)

e (%)

#1 #2 #3

0 10 30

18 18 18

0 0.36 0.63

10.61 16.50 28.29

4213 6554 11,235

25815.0 356.8 184.9

100.8 88.1 111.8

7.15 4.68 2.75

7.46 7.10 6.10

50.5 81.5 95.3

#4 #2 #5

0 10 17.64

28 18 10.36

0 0.36 0.63

16.50 16.50 16.50

6554 6554 6554

977.5 356.8 412.8

92.0 88.1 102.4

6.47 4.68 3.59

8.49 7.10 5.94

73.5 81.5 87.1

a At the nozzle exit, the initial gas volume fraction C0 = Qa/(Qa + Qw); the liquid-phase (water) exit velocity Uw0 = 4Qw/[(1-C0)pd20], where d0 is the nozzle diameter; Re = Uw0d0/mc, where mc is the kinematic viscosity of the continuous phase (i.e., air in this study). b Imax is the maximum rain intensity in the study plane (see Fig. 1); also presented is the ratio of total rain flux collected in the study plane to Qw. c Ensemble-averaged equivalent drop diameter, velocity and energy dissipation rate at the location of Imax in the study plane.

in each region, up to 400 glass bottles (25 mL with a bottle-neck diameter 1.52 cm) were used simultaneously to collect rain within a period varying from several minutes to an hour depending on the rain intensity in that region. The glass bottles were tested to give the same (3% difference) result of rain intensity distribution as those of much larger plastic bottles (250 mL with a bottle-neck diameter 3.26 cm). The glass bottles were placed at various transects spacing 0.3–1 m apart in the longitudinal (x in Fig. 1) direction, and 0.1 m apart in the transverse (y) direction. In the pure water jet of Expt. #1, majority of rain was found to fall within a narrow area at a much higher rain intensity. In this case, sampling rake of brass tubes with an inner diameter of 5.48 mm were selected to collect rain based on the testing results of tubes with several other diameters. The bottom of each tube was connected vertically via a plastic tube into a bottle, which was sheltered from rain. The tubes were arranged at 2 cm apart from each other in the rake. The rake was first placed at one transect for collecting rain within a period of 10–30 min, then the entire rake was moved 15 cm in the longitudinal direction to the next transect. In the region outside the high-intensity rain in Expt. #1, glass bottles were used as described above. In each experiment, the total rain flux in the horizontal plane was integrated and compared to the water injection rate at the nozzle. The total water/rain flux was calculated from R þ1 R þ1 Idxdy, where I is the measured rain intensity. 1 1 Comparisons of the integrated values with the water injection rates at the nozzle are listed in Table 1. The conservation ratio of rain flux, on average, is (99.0 ± 9.3)%, for all experiments. In Expt. #2 or #3, the loss of rain flux is slightly larger (±11.8%), which might be related with the fact that the rain has a wider range in the experiment and the assumed linear interpolation between measurement points (and sections) tends to produce a relatively larger error in estimating rain flux. Nevertheless, the above comparison shows the reliability of the measurements. The properties of water drops such as size and velocity were obtained using a high-speed camera (Phantom V211, Vision Research Inc.). The camera was set to take images at a resolution of 1280  800 pixels2, with an exposure time of 20 ls, at a speed of 500 frames per seconds and for a period of 10–15 s. To clearly capture drops, a 75–300 mm Nikon zooming lens was used. Background light was provided by 2  1000 W halogen lamps in a softbox of 1.2 m  0.9 m. Image window size varied from 11.2 cm  7 cm to 16 cm  10 cm depending on the distance to the camera. The smallest drops that can be clearly captured were around 0.5 mm in diameter, and the image recorded the drops within ±5 cm from the camera’s focus plane. In all experiments, the camera was set to focus on the vertical plane of xz at the location of the maximum rain intensity Imax

(see Fig. 1). In Expt. #1–3, to study the distribution of drop properties in the transverse (y) direction at the section of Imax, the focus plane was also set at every 20 cm from the vertical plane of xz. To further study their longitudinal distributions in the vertical plane, Expt. #1 and #3 were selected as an example for pure water jets and aerated jets, respectively, and images were taken every 1–2 m in the longitudinal (x) direction. Images were post-processed in Matlab. Edge of drops was detected first, and the equivalent diameter of each drop was calculated assuming a spherical shape. Drop velocity was calculated from the displacement of centroid of the drop. Results and discussions Bulk jet trajectory As schematically shown in Fig. 1, after the jet was ejected into the air, majority of the water-phase was constrained in the jet region determined by the jet momentum and the gravitational force. Underneath the bulk jet, mists or tiny drops were always observed even in the case of pure water jets. These drops were believed to be peeled off from the jet boundary. It can be observed that the breakup of aerated water jets occurred right after they exited the nozzle. That is, the breakup length is zero in this case. For the pure water jets, the breakup occurred at some distance away from the nozzle and before the jets reached their maximum rise heights. The breakup length was roughly estimated from photos to be 150d0 in Expt. #1 and 215d0 in Expt. #4. These values are generally in agreement with the predictions of 140–200d0 for Expt. #1 and 200–315d0 for Expt. #4 according to Chen and Davis (1964), Grant and Middleman (1966), and Sallam et al. (2002). Note that the predictions in these studies are for liquid jets injected vertically down, while in this study the jets were injected upwards at a 45° angle. Trajectories of the jets’ upper boundary are shown in Fig. 2. The jets’ lower boundaries are not shown due to the fact that the falling of mists underneath of the bulk jet makes it difficult to accurately determine them. Fig. 2 suggests that both Qa and Qw are controlling parameters for the upper boundary of aerated jets. For example, in terms of the maximum rise height and maximum traveling distance of the jets (upper boundary), in the first group of experiments, they both increased due to the increase in Uw0 (Table 1) when C0 was increased from 0% (Expt. #1) to 36% (Expt. #2) and further to 63% (Expt. #3). In the second group of experiments (Expt. #4, 2 and 5), when C0 was increased from 0% to 63% while Uw0 was maintained at 16.5 m/s, they both decreased due to the jet breakup in air and hence the increase of air resistance. Without air resistance, the theoretical jet’s maximum rise height in the z direction, Hmt, and the maximum traveling distance

W. Zhang, D.Z. Zhu / International Journal of Multiphase Flow 76 (2015) 158–167

7 6

Expt #1

Expt #2

Expt #3

Expt #4

Expt #5

Expt #2 - Modeled

z (m)

5 #3

4 #4

3 #2 #5

2 Expt #1

1 0 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16

x (m) Fig. 2. Measured upper boundaries of aerated jets in air. An example of jet trajectory modeling is also shown for Expt. #2.

in the x direction, Lmt, can be determined assuming the jet is similar to a projectile in air:

Hmt ¼ ðU w0 sin hÞ =ð2gÞ

2

ð1Þ

Lmt ¼ U 2w0 sin 2h=g

ð2Þ

where h is the angle of the injection from the horizontal plane; and g is the acceleration due to gravity. The results show that the measured values are always smaller than the predictions. A coefficient b is introduced herein as the ratio of the measured value to the prediction value, i.e., b ¼ Hm =Hmt or Lm =Lmt . The b values was found to be similar for Hm and Lm in all the five experiments, indicating the jet trajectory is equally affected by air resistance in both the longitudinal x and vertical z directions. In the first group of experiment, b = 0.80 for the pure water jet in Expt. #1. With the increase of C0 from 0% to 36% and further to 63%, b value decreases substantially from b = 0.80 to 0.44 (Expt. #2) and then 0.22 (Expt. #3). This suggests that air injection at the nozzle will significantly cause jet energy loss due to jet breakup and resistance of ambient air. In the second group of experiments, b = 0.60 for the pure water jet in Expt. #4, and 0.36 for the aerated jet in Expt. #5. From the above analysis, air resistance is important for aerated jets in air. With air resistance, the following equation can be written for a projectile (Cohen et al., 2013):

M

! dU 2 ! ! 1 ¼ M g  qC D pd U U dt 8

ð3Þ

! where M, d and U and are the mass, diameter and velocity vector of the projectile (water drops in our study; refer to Table 1 for d values and initial values of U); q is the air density; CD is the drag coefficient; and t is time. Eq. (3) can be numerically integrated to obtain the velocity in the x and z directions and therefore the trajectory. A typical example of modeling results using Eq. (3) for Expt. #2 is shown in Fig. 2, in which CD = 0.47 is used. Cohen et al. (2013) used a CD value of 0.44 in modeling trajectory of water jets in air from fire hoses. Although this modeling approach is rather crude, satisfying agreement is obtained between the modeling results and measurements of the jet upper boundary. The discrepancy might be caused by the assumption that the jet is similar to a single projectile while in fact the former contains numerous drops and is in the form of continuous jet before jet breakup. For all the four jets, similar results can be obtained with CD = 0.4–0.5. Rain intensity Distribution of falling water drops (rain) in the horizontal xy plane is shown in Fig. 3 for all the experiments. In each contour of rain intensity, two edges are shown: one is the intensity of

161

9 mm/hr, which was the low detection/measurement level; the other is 5% of Imax. In addition, the edge of jet impinging region is also shown, which was estimated from the jet width (discussed below). Primary of the rain, 60–85%, fell within the jet impinging region, and the rest fell in the mist region upstream of it (see Fig. 1). This ratio appears to decrease with C0: it decreased from 85% to 80% and further to 60% when C0 increased from 0 to 0.63, respectively, in Expt. #1–3. In all five experiments, the width (in the y direction) of rain first gradually increases due to jet spreading and then gradually decreases as a result of jet-edge fallout. The longitudinal distance to the widest rain region, Lw, is only 4–5 m (666d0–833d0) for aerated jets, while it is 8–11 m (1333d0–1833d0) for pure water jets. Compared with the jet maximum traveling distance, Lw/Lm is 43–56% for an aerated jet, while it is 79–88% for a pure water jet. In the first group of experiments (Expt. #1–3), rain distribution changes significantly with the increase of Qa while Qw was maintained the same. For the pure water jet, rain is distributed within a narrow area with an extremely uneven rain intensity (Imax > 20,000 mm/hr); while for the aerated jets, the rain range becomes substantially larger in both x and y directions and rain distribution becomes much more even (Imax = 180–360 mm/hr). It is also interesting to note that the pure water jet has a much smaller mist region compared to the aerated jets. Moreover, the pure water jet has one peak of rain intensity, while the aerated jets have two peaks, caused by jet impingement and mist falling. This phenomenon is expected to be related with jet breakup mechanism. In the pure water jet, jet breakup and subsequent ligament/water pocket/drop breakup occur at relatively large distance away from the nozzle, while in the aerated jets, these breakups occur immediately at the nozzle due to air injection. In the latter case, drops of different velocities tend to differentiate their falling locations with larger travel distance, causing more than one peak of rain intensity. Further from Expt. #2 and #3, the two peaks become more apart from each other with the increase of C0. In the second group of experiments (#4, #2 and #5), rain intensity values are not directly comparable because Qw changes. With the increase of C0 from 0 to 36%, rain region increases, suggesting that the effect of increasing Qa on enlarging the rain region is more effective than the effect of decreasing Qw on reducing the rain region. Further increase of C0 from 36% to 63% results in a reduction of rain region, suggesting that the effect of decreasing Qw becomes dominant. The aerated jet of Expt. #5 only has one peak of rain intensity, which might be associated with its small rain region. Comparison of the results of two pure water jets (Expt. #1 and #4) shows that, although Qw increases from 18 LPM to 28 LPM, rain region increases substantially, resulting in the peak value of rain intensity decreases by 25.4 times (from 25,815 mm/hr to 978 mm/hr). In all experiments, the rain intensity along y direction at any transect in the xy plane was found to follow a Gaussian distribution. Two typical examples are presented in Fig. 4: one for pure water jets and the other for aerated jets. The difference in the Gaussian distributions for a pure water jet and an aerated jet only lies in the peak value and width of the distribution: pure water jet has a much larger peak but a smaller width. Fig. 5(a) shows the change of local (sectional) maximum rain intensity, Imax,s, in the longitudinal direction. In all experiments, its longitudinal distribution can be approximated as a left-skewed (negatively-skewed) Gaussian distribution. The overall Gaussian distribution originates from the jet property, while the left-skewness is generated from the falling of tiny drops/mists peeled from the jet edge. In the first group of experiments (Expt. #1–3), with the increase of C0, the skewness becomes more substantial as the peeling off is easier due to the more intense breakup of the water jet. In Expt. #3, the peeling off becomes comparable to

162

W. Zhang, D.Z. Zhu / International Journal of Multiphase Flow 76 (2015) 158–167 I (mm/hr)

(a ) Expt #1

1 20009

y (m)

0.5

5% Imax

15009

0

10009

K5%=0.19

-0.5

5009

-1

0

2

4

6

8

10

12

14

16

9

x (m)

Expt #2

1

5% Imax

y (m)

0.5

2bx

0 -0.5

K5%=0.20

-1 0

2

2by

Mist Region 4

6

8

Jet Impinging Region 10

12

14

16

x (m)

Expt #3

1

339 309 279 249 219 189 159 129 99 69 39 18 9

189 169

0.5

y (m)

1291

149 129

0

109 89

-0.5

K5%=0.20 0

2

69

5% Imax (9mm/hr)

-1

4

6

8

10

49

12

14

16

x (m)

29 9

I (mm/hr)

(b) Expt #4

809

1 0.5

y (m)

709

5% Imax

609 509

0

409 309

-0.5

K5%=0.23

209

-1

109

0

2

4

6

8

10

12

14

16

x (m)

Expt #2

1

9

5% Imax

y (m)

0.5 0

2bx

-0.5

K5%=0.20

-1 0

2

4

Jet Impinging Region

2by

Mist Region 6

8

10

12

14

16

x (m)

Expt #5

1

5% Imax y (m)

0.5 0 -0.5

K5%=0.19

-1 0

2

4

6

8

x (m)

49

10

12

14

16

339 309 279 249 219 189 159 129 99 69 39 18 9

399 369 339 309 279 249 219 189 159 129 99 69 39 21 9

Fig. 3. Rain intensity distribution in the xy plane, (a) in Experiments #1–3 and (b) in Experiments #4, 2 and 5. Also shown are contour indicting 5% of Imax that is defined as rain edge, and the spreading rate of the rain edge till the widest rain location. Dashed oval indicates the impinging region of a bulk jet.

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W. Zhang, D.Z. Zhu / International Journal of Multiphase Flow 76 (2015) 158–167

(a) Expt #1 6000

(b) Expt #3 at x = 9.67 m 200

Expt Data

5000

Expt Data

Fied Gaussian

Fied Gaussian

Imax (mm/hr)

Imax (mm/hr)

at x = 8.70 m

4000 3000 2000

150 100 50

1000 0 -0.2

-0.1

0

0.1

0 -1.5

0.2

-1

-0.5

y (m)

0

0.5

1

1.5

y (m)

Fig. 4. Typical examples of rain intensity distribution in the transverse y direction, (a) for pure water jets, in which rain was collected by sampling rake of tubes and (b) for aerated jets, in which rain was collected by sampling bottles.

1200

Expt #1 Expt #2 Expt #3

1000 100 10

Expt #4 Expt #2 Expt #5

1000

Imax,s (mm/hr)

10000

Imax, s (mm/hr)

(a)

800 600 400 200

1

0 0

5

10

0

15

5

x (m)

(b)

80

80

Expt #1 Expt #2 Expt #3

70 60

15

Expt #4 Expt #2 Expt #5

70 60

50

b /d0

b /d0

10

x (m)

40 30

50 40 30

20

20

10

10

0

0 0

1000

2000

3000

x /d0

0

1000

2000

3000

x /d0

Fig. 5. (a) Longitudinal distribution of sectional maximum rain intensity in the x-axis and (b) half-width of rain intensity in the xy plane.

that of the jet’s primary flow, causing the two peaks of rain intensity in Fig. 4. In the second group of the experiments (#4, #2 and #5), Expt. #5 has a comparable skewness as in Expt. #2 although C0 increases from 36% to 63%, which is because Qw decreases from 18 LPM to 10 LPM and hence less drops are peeled off in Expt. #5. In order to describe the extent of the rain region, half-width b is defined as where the rain intensity is 50% of the maximum value at a transect. Fig. 5(b) shows the longitudinal distribution of b in the xy plane. As can be seen, b first increases and then decreases with x, which agrees with the general observation from Fig. 3. In the first group of experiments (Expt. #1–3), comparison of Expt. #1 and #2 shows that the introduction of air (C0 increases from 0% to 36%) substantially enlarges the value of b. Further increase of C0 to 63% in Expt. #3 makes the b more uniformly distributed along x. In the second group of experiments (Expt. #4, #2 and #5), since Uw0 is kept the same, an increase of C0 results in a decrease of Qw and therefore smaller value of b. The jets’ spreading/growth rates in the mist region are first examined. If the rain edge is defined using 5% of Imax, the spreading/growth rate of rain edge from a virtual origin to the widest rain location, k5%, is directly drawn in the mist region in Fig. 3 assuming a linear growth. It is interesting to notice that k5% is quite consist

(0.19–0.23) in all five experiments. The virtual origin is close to the nozzle location for an aerated jet because of the zero jet breakup length; while it is far away from the nozzle for a pure water jet, which might be related with the larger jet breakup length. Based on k5%, the spreading rate of half-width b from the virtual origin to the widest rain location, k50% = 0.10–0.12, which is close to the spreading rate of approximately 0.10 for a single-phase jet (Zhang et al., 2012). The jets’ spreading rates in the jet impinging region are next examined. The half-widths of the jet impinging region in the x and y directions, bx and by, are defined as shown in Fig. 3. The values of by can be directly read from Fig. 5(b). The value of bx was estimated by fitting a certain range of the experimental data in Fig. 5(a) with a Gaussian distribution. The range was selected from a certain point upstream of the peak value of Imax,s to the farthest point to exclude the effect of falling mists on the Gaussian distribution (e.g., in Expt. #3, data between x = 9 m and 15 m were used). The results of bx and by are shown in Fig. 6(a), and bx values are much larger (5–10 times) than by values, which is expected and can also be seen from Fig. 3. From Fig. 6(a), the present data on both pure water jets and aerated jets suggest that both bx and by increases linearly with Uw0. Since Uw0 is related with Lm, the

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(a)

600

(b)

bx /d0 bx by /d0 by

500

500 400

b/d0

b/d0

400

600

300

300

200

200

100

100

0 0

10

20

0 1000

30

Uw0 (m/s)

bx /d0 bx by by /d0 bx/d0 = 0.29Lm/d0 -134.30 R² = 0.90

by/d0 = 0.026Lm/d0 -0.277 R² = 0.94

1250

1500

1750

2000

Lm/d0

Fig. 6. Half-width of the jet impinging region (a) versus the jet exit velocity at the nozzle for both the pure water and aerated jets and (b) versus the jet centerline’s maximum traveling distance in the x direction for the aerated jets.

relations of bx and by versus Lm are shown in Fig. 6(b). The present data of by can be well-fitted with:

by =d0 ¼ 0:026Lm =d0  0:277 R2 ¼ 0:94

ð4Þ

The coefficients 0.026 is the spreading rate of by for an aerated jet from the nozzle location to the center of jet impinging region. Drop size Typical photos of drops at the location of Imax in Expt. #1–3 are shown in Fig. 7 (see Fig. 1 for the schematic image-taken location). Photos in Expt. #4–5 not shown in the figure as they are similar to Expt. #2–3 (only differ in drop sizes). In the pure water jet of Expt. #1, the water-phase is composed of large water pockets, ligaments, as well as drops and droplets of different sizes. The water-phase breakup was sometimes captured by the high-speed camera, indicating the breakup is still continuing even at the location of

Imax that is over 9 m away from the nozzle. In Expt. #2–5, however, the water-phase is only composed of drops and droplets – no ligaments or water pockets. It is interesting to mention that a drop may contain a bubble inside it. Such phenomenon is more commonly seen in an aerated jet, which is probably related with the gas injection at the nozzle and the complex water-phase breakup in air. Table 1 lists the ensemble-averaged equivalent drop diameter d at the location of Imax. It should be noted that all drops have reached their terminal sizes (and velocities) in the image window, as their values do not change even the drops are photographed more than 10 times in the same window. In both groups of experiments, d appears to decrease with C0, for instance, d decreases from 7.15 mm in Expt. #1 to 2.75 mm in Expt. #3 when C0 increases from 0% to 63%. Drop size distribution at the location of Imax is presented in Fig. 8(a) for all experiments. In general, drop size distribution can be approximated as Gaussian in most of the experiments. The only exception is Expt. #1, in which there are

(a) Expt #1

10 mm

10 mm

10 mm

10 mm

10 mm

10 mm

(b) Expt #2

(c) Expt #3

Fig. 7. Typical photos of drops at the location of Imax in Expt. #1–3.

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0.4

(a)

0.4

Expt #1

Expt #4 Expt #2

Expt #2

0.3

Expt #3

Pdf

Pdf

0.3 0.2 0.1

Expt #5

0.2 0.1

0

0 0

2

4

6

0

8 10 12 14 16 18 20

2

4

6

d (mm) 0.6

(b)

0.6

Expt #4

0.5

Expt #2 Expt #3

Expt #2 Expt #5

0.4

Pdf

0.4

Pdf

d (mm)

Expt #1

0.5

8 10 12 14 16 18 20

0.3

0.3

0.2

0.2

0.1

0.1

0

0 0

1

2

3

4

5

6

7

8

9 10

0

1

2

3

U (m/s)

4

5

6

7

8

9 10

U (m/s)

Fig. 8. Probability density functions, Pdf, at the location of Imax, for (a) drop size and (b) drop velocity.

two peaks: one for d = 0–6 mm; and the other for d = 6–16 mm. This is not surprising given the fact that the water-phase in Expt. #1 is composed of small-to-large drops, ligaments and water pockets (see Fig. 7). Transverse distributions of ensemble-averaged drop diameter for Expt. #1–3 are shown in Fig. 9(a) in the y direction at the location of Imax. The distribution for the pure water jet of Expt. #1 appears to be a triangle, which is expected to be Gaussian if more measurements could be made. The distribution in Expt. #2–3 is more approximately a top-hat, suggesting a more or less uniform size distribution in the transverse direction. The longitudinal 8 7 6 5 4 3 2 1 0

Drop velocity Ensemble-averaged drop velocity U at the location of Imax is listed in Table 1. Similar to drop diameter, U also decreases with the increase of C0 in both groups of experiments. Fig. 8(b) presents

(b)

Expt #1 Expt #2 Expt #3

8 6

U (m/s)

d (mm)

(a)

distributions of ensemble-averaged drop diameter along the x-axis for Expt. #1 and Expt. #3 are shown in Fig. 10(a). It is clear that d increases with x from the nozzle. This is probably because smaller drops are easier to peel off from the jet edge and therefore fall closer to the nozzle.

4 Expt #1 Expt #2 Expt #3

2 0 0

0.2

0.4

0.6

0.8

0

0.2

0.4

y (m)

0.6

0.8

y (m)

Fig. 9. Transverse distributions of ensemble-averaged (a) drop diameter and (b) drop velocity along the transect of Imax in Experiments #1–3.

(a)

8

(b)

Expt #1

7

Expt #3

Expt #1 Expt #3

8

6

Imax Locaon

5

U (m/s)

d (mm)

10

4 3 2

Imax Locaon

1

6 4 2

Imax Locaon

0

0 0

5

10

x (m)

15

0

5

10

15

x (m)

Fig. 10. Longitudinal distributions of ensemble-averaged (a) drop diameter and (b) drop velocity along x-axis in Experiments #1 and 3.

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the drop velocity distribution at the location of Imax. The distribution may be approximated as Gaussian as for drop diameter d, but its trend is much less clear than d because U is mostly distributed in a few narrow bins. The values of U are comparable in different experiments, and the difference is much smaller than that of d. This phenomenon generally agrees with the trend shown in Table 1: U only decreases by 18.2% (from 7.46 m/s to 6.10 m/s) from Expt. #1 to Expt. #3, while d decreases by 61.5% (from 7.15 mm to 2.75 mm). The velocity distribution in Expt. #1 is skewed, which is related with the complex distribution of d as shown in Fig. 8(a). Transverse distributions of ensemble-averaged drop velocity are shown in Fig. 9(b) at the location of Imax for Expt. #1–3. Generally all the jets have approximate top-hat distributions, although the trend is less clear for the pure water jet of Expt. #1. The longitudinal distributions of ensemble-averaged U along the x-axis for Expt. #1 and Expt. #3 are shown in Fig. 10(b). Similar to drop diameter, U increases with x. In Expt. #1, U is expected to further decrease with the decrease of x in the region x < 6.7 m if measurements were conducted there. The relation of terminal drop velocity UT versus drop diameter d at the location of Imax is shown in Fig. 11. Also plotted in Fig. 11 is Ferro (2001)’s prediction for UT based on his summary of previous experimental measurements of rain drops in air:

U T ¼ 9:5½1  expð0:6dÞ

ð5Þ

where UT and d are in m/s and mm, respectively. Clift et al. (1978) also summarized some complex equations for the terminal velocity of any liquid drops in gas. They reported that when the Eötvös num2

ber Eo ¼ g Dqd =r < 0.5, the relation of UT for spheres in air (see their Fig. 5.14) may be used, where Dq is the density difference and r is the surface tension. When EO P 0.5, the following equation (re-arranged from their Eqs. (7)–(11)  (7)–(13)) can be used:

UT ¼

ag b0:25 Dqb0:25

rb0:75 q0:5

2b1

d

ð6Þ

in which SI units are used. The coefficients of a and b are as follows: a = 1.62 and b = 0.755 when 0.5 6 EO 6 1.84; a = 1.83 and b = 0.555 when 1.84 6 EO 6 5.0; a = 2.00 and b = 0.500 when EO P 5.0. Clift et al. (1978)’s predictions almost overlap that of Ferro (2001) and thus they are not shown in Fig. 11 for clarity. Overall, the trend from the present results agrees with the prediction of Ferro (2001) or Clift et al. (1978): UT first increases rapidly with d for d = 0–2 mm, then increases gradually for d = 2– 8 mm, and finally reaches a stable value for d = 8–20 mm. This indicates that the dependence of UT on d becomes weaker with the increase of d, which can be also inferred from Eq. (5) or (6). The present results of UT  8.1 m/s for d P 8 mm is similar to the

12 10

U (m/s)

8 6

Expt #1 Expt #2

4

Expt #3

Fig. 12. Relation of energy dissipation rate at the location of Imax, with jet exit velocity.

value of 9.4 m/s from Eq. (5) or (6), suggesting that, while drop shape might change, terminal drop velocity is the same as long as d P 8 mm. In the range of d = 0–2 mm, the present results of all five experiments are fairly close to the prediction. Note that some of the present UT values are as high as 7–8 m/s (mostly in the pure water jet of Expt. #1), which are almost double of the prediction. Further examination of the drop images shows that these high-speed drops are mostly associated with the breakup of large water ligaments or drops, and therefore their velocities are still close to the velocities of large drops. For d = 2–10 mm, the present UT values appear to differentiate for the cases of pure water jets and aerated jets. In the former case (Expt. #1 and #4), the UT values are, generally, still close (around 10% difference) to the prediction of Ferro (2001) or Clift et al. (1978), especially in Expt. #4. The slightly larger difference in Expt. #1, compared to Expt. #4, might be related with its complex jet/ligament/drop breakup in air. In the case of aerated jets, the UT values are roughly 25% smaller than the prediction. That is, from the present measurements, the UT values of aerated jets are roughly 20% smaller than that in pure water jets for the same value of d. This is possibly related with the interesting phenomenon of air bubble trapped in water drops in the case of aerated jets (discussed earlier in Fig. 7) and thus smaller gravity force for the water drops. Energy dissipation rate e is examined at the location of Imax by comparing the terminal kinetic energy with the initial value, i.e., e = (1  U2/Uw02)  100%. The results are listed in Table 1. Overall, the values of e is high, 51–95%. In both groups of experiments, e appears to increase with C0. For instance, in the first group of experiments, e increases from 51% in Expt. #1 to 82% in Expt. #2 and further to 95% in Expt. #3, where C0 increases from 0 to 0.36 and further to 0.63. Similar conclusion can be made from the second group of experiments. This implies that substantial amount of the jet energy is dissipated due to the introduction of air at the nozzle. Fig. 12 shows the relation of e with Uw0 at the location of Imax. There is a clear trend that e increases with Uw0. This can be explained by the fact that the difference is small in terminal drop velocities in different experiments (see Table 1) and therefore a larger initial jet energy (Uw02) will end up with a larger energy dissipation rate.

Expt #4

2

Expt #5

Conclusions

Ferro (2001)

0 0

5

10

15

20

d (mm) Fig. 11. Relation of drop size versus terminal drop velocity at the location of Imax for all experiments.

This paper presents an investigation of aerated water jets injected at 45° into still air, with a focus on far-field jet properties including bulk trajectories of the jets, intensity of falling water drops (rain intensity), as well as drop size and velocity in the

W. Zhang, D.Z. Zhu / International Journal of Multiphase Flow 76 (2015) 158–167

horizontal plane at the same elevation of the nozzle. Main conclusions are as follows: (1) Air injection at the nozzle significantly changed the jet properties. The rain fell mostly (60–85%) in the jet impinging region; and the rest in the upstream mist region, which increased with the air injection. The jet breakup length was (150–250)d0 for the pure water jets, while it was zero for the aerated jets. Longitudinal distance of the widest rain region was 43–56% of the jet maximum travel distance for an aerated jet, while it was 79–88% for a pure water jet. Jet trajectories of both pure water jets and aerated jets were then modeled satisfactorily using a projectile model with air resistance. (2) With the increase of air injection, rain became larger in range and smaller in peak intensity. The cross-sectional peak of rain intensity generally followed a left-skewed Gaussian distribution in the longitudinal x direction. Along the transverse y direction, rain intensity was found to be perfectly Gaussian distribution. The spreading/growth rate of the Gaussian distribution’s half-width from a virtual origin to the rain’s widest location was quite consistent (0.10–0.12) in all five experiments. The spreading rate from the nozzle to the jet impinging location was found to be 0.03 in the y direction, while it was 9 times larger in the x direction. (3) With the increase of air injection, both water drop diameter d and velocity U decreased, although the decrease of U was much less than that of d. Transverse distribution of d at the location of maximum rain intensity was found to be Gaussian in a pure water jet and a top-hat in an aerated jet, while the distribution of U was top-hat in both cases. Moreover, both d and U was found to increase with x. Probability density functions of both d and U were Gaussian in most experiments, except in the pure water jet of Expt. #1 where both large and small drops existed and the size distribution had two peaks. (4) Overall, the present results of water drop terminal velocity UT agreed with predictions of Ferro (2001) and Clift et al. (1978). UT was found to first increase rapidly with d for d = 0–2 mm, then increase slowly for d = 2–8 mm, and finally reach a stable value of 8.1 m/s for d = 8–20 mm. The present measurement also suggests that UT values appear to be 20% smaller in an aerated jet than in a pure water jet for d = 2– 10 mm. Finally, jet energy dissipation rate was examined: 50–74% for the pure water jets and 82–95% for the aerated jets. The high dissipation rate was because the jets broke down to drops with relatively small terminal velocities.

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