ICLASS-2006 Aug.27-Sept.1, 2006, Kyoto, Japan

Paper ID ICLASS06-070

EXPERIMENTAL INVESTIGATION OF DROPLET BREAKUP IN SHEAR GAS FLOWS

Takashi SUZUKI, Koshi MITACHI

Department of Mechanical Engineering, Toyohashi University of Technology Tempaku-cho Toyohashi, Aichi 441-8580 Japan

E-mail: takashi@mech.tut.ac.jp ABSTRACT Aerodynamic breakup of liquid droplets in shear gas flows was studied experimentally to present basic data for the modeling of droplet breakup in practical spray processes. Two representative shear gas flows were employed; the simple shear flow and the conventional linear shear flow. The droplet breakup was first investigated in the simple shear flow. There were two types of breakup; vibrational breakup and film-type breakup. The critical velocity-gradient for breakup did not depend upon droplet diameter so much, but upon liquid properties. The breakup time of droplet was measured using high-speed video camera. The breakup time decreased with increase of the velocity-gradient. The breakup time did not depend so much upon the droplet diameter, but upon liquid properties. Then the droplet breakup was examined in the linear shear flow that had mean flow component and transverse velocity-gradient. The breakup manner of droplet depended upon both capillary number and Weber number, and the breakup pattern differed in every observation. It was concluded that the droplet breakup, as well as outcome of breakup, could not be predicted directly from Weber number when gas flow had large transverse velocity-gradient.

Key words: Droplet Breakup, Shear flow, Critical breakup condition, Breakup time, Photographic observation 1. INTRODUCTION

The numerical simulation of spray processes is of great significance in the development of spray systems. Many mathematical models are used to numerically describe spray processes [1]. Aerodynamic breakup of liquid droplet has been studied by numerous researchers [2,3]. Based on the results several breakup models have been developed. However most of the studies deal with breakup of isolated droplet suddenly exposed to uniform gas flow. In actual spray processes, gas flow may not be uniform. Further experimental data is necessary for better modeling of droplet breakup in spray processes.

In this study the droplet breakup in shear gas flow was investigated experimentally. Two representative flow fields were studied; simple shear flow (see figure 1(a)) and conventional linear shear flow that had mean flow component and transverse velocity-gradient (see figure 1(b)). Breakup motion of droplet was observed in detail by flash photography. The breakup manner of droplet in shear gas flow differed much from that in uniform gas stream. The breakup manner of droplet depended much upon capillary number based on velocity gradient. In the linear shear flow the breakup pattern of droplet depended upon both capillary number and Weber number. The critical breakup condition and the breakup time of droplet were examined. Data obtained here will provide useful hints for the development of droplet breakup models. 2. DROPLET BREAKUP IN SIMPLE SHEAR FLOW

2.1 Experimental Method Figure 2 shows experimental setup, which was

employed to observe droplet breakup in simple shear flow. A transparent rectangular duct of 60mm long was installed horizontally, and two planar duct for air injection were installed at both ends of the rectangular duct, as shown in the figure. The axes of two air jets were parallel each other. Test section was center of the

(a) Simple shear flow (b) Linear shear flow

Droplet Droplet

du/dy u– & du/dy

y y uu

Figure 1. Models of shear gas flows.

Table 1. Experimental conditions.

Test Liquid Distilled water, Ethanol, Butanol, Silicone oil #10 Diameter of droplet, d 1.0 – 3.5 mm Velocity-gradient, du/dy < 4000 1/s

Table 2. Physical properties of test liquid at 300K. Test Liquid density viscosity surface tension (kg/m3) (mPa⋅s) (mN/m)

Distilled water 997 0.85 71.7 Ethanol 791 1.00 22.2 Butanol 806 2.29 24.2

Silicone oil #10 935 9.35 20.1

rectangular duct. Above the rectangular duct PZT driven droplet generator was installed, and liquid droplet of demanded size was dropped one by one into the test section. Figure 3(a) shows the distribution of longitudinal air velocity measured by thermo-anemometer. The air flow field was almost two-dimensional. In the test section the air velocity was almost proportional to the

distance from the central plane. Based on the velocity distributions, the velocity-gradient, du/dy, of shear flow was set to demanded value by controlling air injection velocity, ujet. As shown in figure 3(b), the turbulent intensity in the test section was not small. Therefore the air flow should not be laminar.Breakup motion of droplet was observed in detail by flash photography. Breakup time, tB, of droplet was measured using high-speed video camera. Range of experimental conditions are summarized in table 1. Test liquid employed in this study was Distilled water, ethanol, butanol and silicone oil #10. Physical properties of test liquid are shown in table 2. Distilled water has large surface tension, and silicon oil #10 has large viscosity.

Figure 2. Experimental setup for simple shear flow. Figure 3. Air velocity distributions of simple shear flow.

Figure 4. Flash photographs of liquid droplets during breakup in simple shear flow (Butanol, d = 2mm).

0 2000 40000

2

4

0 2000 40000

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4

0 2000 40000

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4

0 2000 40000

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4du/dy 1/s

d m

md

mm

du/dy 1/s

(a) Ethanol

(c) Silicon Oil #10

du/dy 1/s

d m

md

mm

du/dy 1/s

(b) Butanol

(d) Water

Vibrational

Onset of film type

Vibrational

Onset of film type

Vibrational

Onset of film typeVibrational

Onset offilm type

FilmVibrational & FilmVibrationalNo breakup

Figure 5. Map of observed breakup pattern of droplet in simple shear flow.

10–3 10–2 10–1

10–3

10–2

WaterEthanol Butanol Oil #10Breakup patternNo breakupVibrational

Vibrational & FilmFilm

Onset of Film Type Breakup

Ca g

[ =

µg (d

u/dy

) d /σ

]

Oh [ = µl / (ρl d σ)1/2 ]

Cag = 0.0044 Oh0.16

Figure 6. Critical capillary number for onset of

film-type breakup in simple shear flow.

2.2 Breakup Behavior Breakup motion of droplet was first observed in simple shear flow. Flash photographs of droplets were shown in figure 4. The breakup pattern of droplet differed much from that in uniform gas stream. There were two types of breakup; vibrational breakup and film-type breakup. Droplet did not breakup at

sufficiently small velocity-gradient (a). When the velocity-gradient became large, vibrational breakup was observed (b). Film-type breakup, as well as vibrational breakup, was observed at larger velocity-gradient. In case of film-type breakup, the droplet was extended into a plane liquid film with bold rim by the aerodynamic shear force, then the film disintegrated into many small droplets as shown in figure 4(c) and (d). Vibrational breakup was seldom observed at still larger velocity-gradient. Figure 5 shows breakup regimes of droplet in the simple shear flow. The critical velocity-gradient for droplet breakup did not depend so much upon diameter, d, of droplet within this experimental range. The critical velocity-gradient for onset of film-type breakup was larger than that for droplet breakup, and became large with decrease of droplet diameter. The critical velocity-gradient for droplet breakup and that for onset of film-type breakup depended upon liquid properties. As shown in figure 5(d), the critical velocity-gradients of water droplet were larger than those of other test liquid employed in this study. Large surface tension of water should prevent the deformation development of droplet. Contrary, the critical velocity-gradients of ethanol droplet did not differ much from those of silicon oil #10 droplet that had large viscosity. This result suggested that the viscosity of liquid did not play so important role in this experimental range. Data shown in figure 5 were made non-dimensional and shown in figure 6. Cag is capillary number and Oh is Ohnesorge number. The critical capillary number for onset of film-type breakup became large gradually with

1000

10

1000

10

1000

10

1000

10

du/dy 1/s

t B

ms

(a) Ethanol

(c) Silicon Oil #10

(b) Butanol

(d) Water

2000 50002

5

20

50

du/dy 1/s

t B

ms

2000 50002

5

20

50

du/dy 1/s

t B

ms

2000 50002

5

20

50

du/dy 1/s

t B

ms

2000 50002

5

20

50

D mm2.51.81.51.0

D mm2.61.91.51.3

D mm2.61.91.51.3

D mm3.53.12.62.1

Figure 7. Breakup time of droplet in simple shear flow.

0.001 0.01

1

WaterEthanol Butanol Oil #10Breakup patternNo breakupVibrational

Vibrational & FilmFilm

0.002 0.0050.2

0.5

2

Cag [ = µg (du/dy) d /σ ]

t B / t

* [

= t B

(du/

dy) (ρ g

/ρl )1/

2 ]

tB / t* ~– 0.4for Film Type Breakup

tB / t* ~– 1.0for Vibrational Breakup

Figure 8. Dimensionless breakup time of droplet

in simple shear flow.

increase of Ohnesorge number. Following empirical correlation for onset of film-type breakup was presented within this experimental range. Cag = 0.0044 Oh0.16 (1)

The study on deformation of suspended fluid drop in shear liquid flow revealed that the suspended drop broke up in similar manner to the film-type breakup, and the critical capillary number for breakup was order 0.1 [4]. The critical capillary number for film-type droplet breakup, obtained in this study, was much smaller than that for the suspended fluid drop. These results suggested that the turbulent viscosity played important role. If the turbulent viscosity was 100 times as large as viscosity of air, the turbulent-viscosity based capillary number should be 100 times larger than the value of Cag and the same order with the critical capillary number of suspended fluid drop. 2.3 Breakup Time

Figure 7 shows breakup time, tB, of droplet in the simple shear flow measured using high-speed video camera. As shown in the figure, the breakup time did not depended so much upon the droplet diameter. However the breakup time decreased with increase of the velocity-gradient. The breakup time also depended on liquid properties. The breakup time of water droplet was larger than that of other test liquid employed in this study, as shown in figure 7(d). Large surface tension of water should prevent the breakup of droplet. The breakup time data shown in figure 7 were made non-dimensional using the characteristic time, t*, and shown in figure 8. Data in the range of relatively small capillary number were the breakup time of vibrational breakup, and data in the range of relatively large capillary number were the breakup time of film-type

breakup. The dimensionless breakup time, tB/t*, for film-type breakup was about 0.4, and the dimensionless breakup time for vibrational breakup was about 1.0. That is, the dimensionless breakup time of vibrational breakup was much larger than that of film-type breakup. 3. DROPLET BREAKUP IN LINEAR SHEAR FLOW 3.1 Experimental Method

Figure 9 shows the experimental setup for droplet breakup in the linear shear flow, which had mean flow component and transverse velocity-gradient. A transparent rectangular duct of 180 mm long was installed horizontally, and an air injection duct was installed on the end of rectangular duct, as shown in the figure. The PZT driven droplet generator was installed above the rectangular duct, and liquid droplet of

demanded size was dropped one by one. Figure 10 shows the distributions of stream-wise air velocity measured by thermo-anemometer. The air flow field was almost two-dimensional. Conventional linear shear flow field was formed beside the planar air jet as shown in the figure. Based on the gas velocity distributions, the mean-flow component, u , and the transverse velocity-gradient, du/dy, around droplet were set to demanded values by controlling the stream-wise position, x, of the droplet generator and the air injection velocity, ujet,

Breakup motion of droplet was observed in detail by flash photography. Butanol was employed as test liquid. The droplet diameter was 2mm. The range of Weber number, Weg, based on the mean flow component was 0 – 30, and the range of capillary number, Cag, based on the transverse velocity-gradient was 0 – 0.006.

0 10 20 30

–40

–30

–20

–10

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–40

–30

–20

–10

0u– m/s

–y

mm A

ir Je

t

(a) Mean gas velocity (b) Turbulent intencity

RMS(u' ) m/s

ujet = 26 m/s110140

–y

mm

x = 50 mm

x mm8050

Droplet

ujet = 26 m/s

Figure 9. Experimental setup for linear shear flow. Figure 10. Gas velocity distributions of linear shear flow.

Figure 11. Sketch of typical breakup patterns in linear shear flow.

Figure 12. An example of breakup regimes of droplet in linear shear flow.

3.2 Experimental Results

Breakup motion of droplet was observed in linear shear flow. Figure 11 shows sketch of typical breakup patterns. When the velocity-gradient was sufficiently small, the breakup manner of droplet was almost similar to that droplet in uniform gas flow. Droplet did not breakup at sufficiently slow mean flow (a). When the mean flow became fast, the vibrational breakup was observed (b). At still faster mean-flow, bag-type breakup (c), as well as vibrational breakup, was observed. When the transverse velocity-gradient became large, deformed bag-type breakup was observed. The bag of liquid film was asymmetrical, as shown in figure 11(d). This type of breakup was called bag-oid in this study. At still larger velocity-gradient, deformed film-type breakup was observed. Upstream rim of liquid film was bold, as shown in figure 11(e). This breakup type was called film-oid in this study. Figure 12 shows breakup regimes of droplet in linear shear flow. Arrows beside horizontal axis indicate the breakup regimes of droplet in uniform gas flow [5], and arrows beside vertical axis indicate the breakup regimes of droplet in the simple shear flow described in previous chapter. Representative flash photographs of droplets are also shown in the figure.

As shown in the figure, The critical condition for breakup and the breakup pattern depended upon both capillary number and Weber number. Moreover the breakup pattern differed in every observation, e.g. vibrational breakup, bag-type breakup, film-type breakup and their variations were observed in condition (d) of figure 12. That is, we can not predict directly the droplet breakup, as well as outcome of breakup, from the dimensionless flow parameters.

4. SUMMARY

Aerodynamic breakup of liquid droplet in shear gas flows was investigated experimentally. Following were deduced on the droplet breakup in simple shear flow: (1) The breakup manner of droplet differed much from

that in uniform gas stream. There were two types of breakup; vibrational and film-type.

(2) The critical velocity-gradient for breakup did not depend so much upon droplet diameter, but upon liquid properties. The critical velocity-gradient of high surface-tension droplet was larger than that of low surface-tension droplet.

(3) The critical capillary number for onset of film-type breakup became large gradually with increase of Ohnesorge number. An empirical correlation for the critical capillary number was presented.

(4) The breakup time of droplet did not depended so much upon droplet diameter, but upon liquid properties. The breakup time of high surface-tension droplet was larger than that of low surface-tension droplet.

(5) The breakup time decreased with increase of the velocity-gradient. The dimension-less breakup time for vibrational breakup was larger than that for film-type breakup.

Furthermore, following were deduced on the droplet breakup in conventional linear shear gas flow: (6) The breakup pattern observed were those in

uniform stream, those in simple shear flow and their variations.

(7) The breakup pattern depended upon both capillary number and Weber number. The breakup pattern differed in every observation when gas flow had large transverse velocity-gradient.

Acknowledgements Some students have assisted with this work, and the authors give special thanks to K.Suzuki. NOMENCLATURES Cag capillary number; σµ dyuCa gg )dd(= d diameter of droplet du/dy velocity-gradient Oh Ohnesorge number; ( ) 2/1σρµ ll dOh = t* characteristic time; t* =(ρl/ρg)1/2/(du/dy) tB breakup time of droplet u air velocity u mean-flow component of linear shear flow ujet air injection velocity Weg Weber number; σρ /2duWe gg = (x,y) coordinate ρg gas density ρl liquid density µg gas viscosity µl liquid viscosity σ surface tension

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