- Email: [email protected]
Effect of turbulence on drop breakup in counter air flow
International Journal of Multiphase Flow 120 (2019) 103108
Contents lists available at ScienceDirect
International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow
Effect of turbulence on drop breakup in counter air flow Hui Zhao a,b,c, Dung Nguyen c, Daniel J. Duke c, Daniel Edgington-Mitchell c, Julio Soria c, Hai-Feng Liu a,b,∗, Damon Honnery c a
Shanghai Engineering Research Center of Coal Gasification, East China University of Science and Technology, Shanghai 200237, China Shanghai Engineering Research Center of Space Engine, Shanghai Institute of Space Propulsion, Shanghai 201112, China c Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Victoria 3800, Australia b
a r t i c l e
i n f o
Article history: Received 30 November 2018 Revised 30 August 2019 Accepted 5 September 2019 Available online 5 September 2019 Keywords: Secondary atomization Drop breakup Instability Turbulence
a b s t r a c t Understanding the factors that lead to breakup of liquid droplets is of interest in many applications. Liquid droplet breakup processes are typically broken into regimes based on a Weber number calculated based on an average flow velocity (Solsvik et al., 2013). In turbulent flows, the instantaneous velocity may differ significantly from the average velocity. Here an experimental investigation on the role of turbulence in the breakup process is undertaken, whose continuous phase is gas. The turbulence is produced by confined counterflow into which the droplets fall. Droplet breakup mode is visualized by high speed camera, and the turbulence of counterflow is measured by Particle Image Velocimetry. The experimental results show that the breakup morphology and mode frequency varies with the turbulence intensity of the counterflow. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction Atomization is a subject of practical interest in nature (Villermaux and Bossa, 2009) and numerous applications, such as combustion (Ma et al., 2013; Broumand and Birouk, 2016), gasification (Jampolski et al., 2016; Strasser and Battaglia, 2017), agriculture (Koizumi, 2012), medicine (Xie et al., 2017), material preparation (Sasaki et al., 2008) and spray drying (Sahu et al., 2013; Sakuma et al., 2018). A liquid droplet with a speed differential with respect to the ambient medium will experience aerodynamic forces that may cause the drop to deform and break apart into fragments. This process is referred to as secondary atomization (Guildenbecher et al., 2009; Jain et al., 2015; Sichani and Emami, 2015). The performance of many systems is dependent on the final droplet size and hence controlled atomization of the fluid is essential. This desire for control over droplet sizes motivates a deeper understanding of droplet breakup processes. Secondary atomization is typically characterized by two nondimensional numbers, the Weber number (We) and the Ohnesorge number (Oh). The Weber number represents the ratio of disruptive hydrodynamic forces to the stabilizing surface tension force,
W e = ρg (ug −ul )2 D0 /σ
∗
Corresponding author. E-mail address: hfl[email protected] (H.-F. Liu).
https://doi.org/10.1016/j.ijmultiphaseflow.2019.103108 0301-9322/© 2019 Elsevier Ltd. All rights reserved.
(1)
where ρ g is the air density, ug is the mean gas velocity, ul is the drop velocity, D0 is the initial diameter of drop, σ is the surface tension. Based on morphological classification, as the Weber number increases, bag breakup, bag-stamen breakup, dual-bag breakup, bag/plume breakup, etc. occur in turn. These breakup types which have the characteristic bag structure are all governed by the Rayleigh-Taylor instability. These breakup types can be named as Rayleigh-Taylor piercing (or the combined RT/aerodynamic drag mechanism, general bag breakup, et al.) (Guildenbecher et al., 2009; Zhao et al., 2010; Theofanous, 2011, Flock et al., 2012). Critical Weber number is the beginning of bag breakup, which establishes the criteria for the onset of secondary atomization. Many studies have reported the critical Weber number of water is approximately constant in secondary atomization, W ec = 11 ± 2 (Krzeczkowski, 1980; Pilch and Erdman, 1987; Hsiang and Faeth, 1995; Chou and Faeth, 1998; Zhao et al., 2011; Kulkarni and Sojka, 2014). The Ohnesorge number is a dimensionless number that relates the viscous forcesto inertial and surface tension forces, which is defined as Oh = μ/ ρl σ D0 , where μ is the liquid viscosity, ρ l is the liquid density. So the larger Oh indicate a greater influence of liquid viscosity on atomization. Critical Weber number will increase with the increase of Oh (Aliseda et al., 2008; Tavangaret et al., 2015). While Weber number is typically calculated based on a mean fluid velocity, in a turbulent flow the mean velocity does not necessarily capture the instantaneous hydrodynamic forces experienced by the droplet (Solsvik et al., 2013). A model for breakup
2
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Notation a arms b CD D0 Dm H I N NB Oh T t ug ul u We WeB Wec Werms Werms ,B WeT W
ρg ρl σ μ λ λ λc ε
drop average acceleration (drop acceleration obtained by the average gas velocity) rms acceleration caused by turbulence a coefficient for the modified influence of turbulence drag coefficient the initial diameter of drop the maximum drop diameter (mother size) the height of drop relative turbulence intensity the number of RT waves per drop disk diameter the number of RT waves per drop disk diameter based on the data of Plate No. B Ohnesorge number dimensionless characteristic time real time mean gas velocity drop velocity mean velocity Weber number by mean gas velocity Weber number by mean gas velocity based on the data of Plate No. B critical Weber number, the beginning of bag breakup Weber number by rms velocity Weber number by rms velocity based on the data of Plate No. B the drop Weber number in the turbulent jet based on Prevish and Santavicca (1998) the width of drop air density liquid density surface tension liquid viscosity RT wavelength instantaneous RT wavelength critical RT wavelength the rate of energy dissipation per unit mass
in turbulent flow and a turbulent Weber number was proposed by Kolmogorov (1949) and Hinze (1955). Here the characteristic velocity of turbulent Weber number u2 = C1 (ε D0 )2/3 , where C1 is constant, ɛ is the energy input per unit mass and unit time. Here the velocity given is not equal to the fluctuating velocity or the rms velocity. There exist models for the structure function for the whole spectrum of turbulence as explained in the review of Solsvik and Jakobsen (2016). Hinze (1955) also observed that droplets deform differently in the presence of turbulence; rather than deforming into an oblate ellipsoid as in the case of laminar flow, drop deformation and fragmentation is irregular. Sevik and Park (1973) suggested an additional mechanism for breakup in turbulent flows: a resonance process driven by a match between the characteristic turbulence frequency and the fundamental resonant frequency of droplet. Drops or bubbles would deform very violently if the exciting frequency corresponds to one of their resonant frequencies. The progressively smaller bubble sizes that are generated when the lowest critical Weber number is exceeded appears to be related to the higher characteristic frequency of the turbulence which excites higher order modes of vibration of a drop or bubble, thus leading to the formation of smaller parts. Furthermore, this classical theory could also be modified by including the effect of intermittency in the turbulent field (Baldyga and Bourne, 1993). Prevish and San-
tavicca (1998) found that critical Weber number decreases as the turbulence intensity of the ambient flow increases using hydrocarbon droplets at elevated pressures. The breakup mode is predominantly bag breakup for laminar flow, the mixture of bag and bulgy for turbulence flow. Bulgly deformation mode is as follows. As the surface of the globule is deformed locally, bulges and protuberances occur, and thus parts of the globule become bodily separated. The bag breakup mode is composed of a thin hollow bag attached to a toroidal rim. The bag disintegrates first, followed by the rim. The former results in a larger number of small fragments; the latter a smaller number of large fragments. The combination of the bulk velocity and the fluctuating velocities of eddies with scales on the order of the initial droplet diameter may be responsible for breakup in turbulent flowfields. For methanol drops, critical conditions for initial breakup, based on mean (bulk) velocity, decrease from 11 in laminar flow to 4 in a moderately turbulent (Relative turbulence intensity I=30%) flowfield, and to 3 for a highly turbulent (I = 45%) flowfield. The mechanism of breakup is predominantly bag for laminar folwfield, a mixture of bag and bulgy in the I = 30% flowfield, and predominantly bulgy when I = 45%. Andersson and Andersson (2006a,b) study the role of turbulence length scale relative to the droplet size in terms of inducing further drop breakup. Their model predicts that turbulent structures close in size to the fluid particle contribute most to the breakup. There exists abundant literature on secondary atomization, and summaries are available in several detailed review articles (Guildenbecher et al., 2009; Theofanous, 2011). In secondary atomization, the turbulent droplet breakup modes are bag and bulgly breakup mainly. On the physical mechanisms of secondary atomization, turbulence within the two fluids may create additional forces that destabilize drops. In addition, unsteady ambient flow could be considered by accounting for the time that the disruptive forces act on the drop and/or accounting for the rate of change of these forces. Turbulence adds randomness to the breakup process. Some drops experience low local velocities and therefore break up slowly, or do not break up at all. Other drops experience local velocities higher than the average and therefore break up faster and at lower We (based on the mean velocity). However, at present the morphological characteristics and physical mechanisms of droplet breakup in the presence of turbulence remain very poorly understood (Guildenbecher et al., 2009; Lefebvre and Mcdonell, 2017). Rayleigh-Taylor instability occurs when the lighter fluid is pushing the heavier fluid (Sharp, 1984). In general bag breakup, the Rayleigh-Taylor instability plays a leading role, which is an instability of an interface between two fluids of different densities (Theofanous, 2011). In the initial stage, the amplitude of perturbations is growing with time. The turbulence can have great effect on the drop breakup by the initial perturbations, etc. In this test, we notice that the breakup morphology and mode frequency varies with the turbulence intensity of the airflow. Thus the purpose of this paper is to investigate the effect of counterflow turbulence on droplet breakup at Weber numbers moderately higher than the critical value. The rest of the paper is organized as follows. In Part 2, we describe the details of experimental methods. Results are presented and discussed in Part 3, followed by concluding remarks in Part 4. 2. Experimental set-up Experiments are conducted in a drop tower as shown Fig. 1 using water and air as the liquid and gas phases. Drops of 3.7 mm diameter are formed on the nozzle, fall through the tube in quiescent air before entering the test section (80 × 80 mm) and being subjected to a confined turbulent counterflow. Four perforated plates are used to provide different initial conditions for the turbulence in the counterflow. Specifications for the plates are shown
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Fig. 1. Sketch of drop breakup experimental apparatus.
3
Fig. 3. Photo of PIV experimental apparatus.
PCO40 0 0 camera. The resulting images had an optical resolution of 20 μm/pixel. The laser runs with an interframing time between images of 40 μs. We use the 105 mm Micro-Nikkor lens set to an aperture of f/5.6. The tests are conducted with a 32 × 32 interrogation window and a 50% overlap. 3. Results and discussion 3.1. Characterization of turbulent counterflow
Fig. 2. Turbulence inducing plate. Table 1 Perforated turbulence inducing plate specifications. No.
Solidity
Hole diameter (mm)
Thickness (mm)
A B C D
90% 64% 60% 53%
2.4 1.6 3.2 8.0
0.67 0.52 1.53 1.63
in Table 1 and Fig. 2. A MotionPro X3 high speed camera with a 105 mm Micro-Nikkor lens is used to capture drop breakup events at the framerate 1600 fps. The light source is a pulsed CBT-120 (green) LED (Willert et. al 2012), whose exposure time is 1 μs and LED facula width is 42 mm. All the images of the droplets obtained by high speed camera have the same magnification factor. The image resolution is 64.8 μm per pixel. Particle Image Velocimetry (PIV) jet experiments were conducted in the Laboratory for Turbulence Research in Aerospace and Combustion at Monash University. The complete description of the algorithm used can be found in previous work (Soria, 1996; Soria et al., 2003). PIV is used to characterize the turbulence in the test section as shown Fig. 3. Oil particles are introduced into the counter flow gas upstream of the test section using a VisCount Smoke Generator (Daniel et al., 2011, 2014; Tan et al., 2017). The particles are illuminated with a EverGreen Nd:YAG laser at a 532 nm wavelength, and particle images recorded on a
Nine configurations for the turbulent counterflow are considered. PIV is used to characterize the variation in mean velocity and turbulence intensity for these different counterflow configurations as shown in Table 2. Representative velocity profiles over a typical droplet trajectory are shown in Fig. 4; mean velocity and turbulence intensity are largely invariant with axial position. When mean velocity is held constant, the turbulence intensity of Plate No. A is the highest, likely due to its high solidity. When the solidities (Plates B, C and D) and mean velocities are similar, the turbulence intensity increases with plate hole diameter. 3.2. Morphological characteristics of drop breakup The diameter of the initial droplet on exiting the drop tower is 3.7 mm, an example image is shown in Fig. 5(a). Depending on both the mean velocity and turbulence intensity, this initially spherical droplet may undergo a number of different breakup modes. First, Fig. 5 presents a comparison of breakup modes for two flows with similar mean velocities, and similar characteristic length scales, but different turbulence intensities. Here, mean velocity is obtained from the data of flow meter and experimental device size. The characteristic length scale is the drop diameter. Turbulent intensity is obtained from the data of PIV. Both cases exhibit the classical bag breakup mode, however comparing Fig. 5(b) and (c) there are significant differences in morphology beyond the typical randomness (small morphological changes of each test) observed in breakup behaviour. Turbulence also has great effect on the drop breakup morphology. The growth of drop (width W and height H) with time for a low and high intensity case of turbulence is shown in Fig. 6(a) and (b). The dimensionless characteristic time t·u of drop is T = √ g , where ug is the mean velocity, t is the real D0
ρl /ρg
time (Nicholls and Ranger, 1969). The origin of time is the beginning of drop breakup. The beginning of drop breakup refers to the time when droplets enter the airflow (the exit of tube in Fig. 1).
4
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Fig. 4. Representative turbulent statistcs obtained by PIV. The origin of the position is the exit of tube as shown in Fig. 1.
Fig. 5. (a) The diameter D0 of initial drop is 3.7 mm, all the images of the droplets obtained by high speed camera have the same magnification factor. (b) and (c) Experimental photos of drop bag breakup at low mean velocity.
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
5
Table 2 Flow statistics. No.
Plate no.
Mean velocity (m/s)
Rms velocity (m/s)
Turbulence intensity
1 2 3 4 5 6 7 8 9
A B C D A B C D A
13.9 10.5 10.9 10.7 11.3 8.78 8.79 8.79 8.90
2.7 0.4 0.4 0.7 2.5 0.2 0.3 0.5 2.1
19.2% 3.4% 3.8% 6.1% 22.0% 2.7% 3.6% 5.7% 23.7%
Table 3 Representative RT wave number N of breakup mode (Zhao et al., 2010).
N
No breakup
Bag
Bag-stamen
Multi-bag
0
1
2
3
smaller number of large fragments. So the energy from turbulence can obtain more small fragments, which is beneficial to atomization performance. Fig. 7 also shows the experimental photos of drop bag breakup morphology when the mean velocity is bigger than Fig. 6. The size of bag structure increases with the increase of mean velocity at low turbulence intensity significantly. In general, the bag structure is smoother in high turbulence intensity than low turbulence intensity before the breakup. This is an interesting phenomenon, which may be due to the rapid expansion of bag. This situation is similar to the flapping liquid sheet (Villermaux and Clanet, 2002), the wrinkle on the bag is the development of instability. Fig. 8 shows the experimental photos of drop bag-stamen breakup morphology, whose mean velocity is equal to Fig. 7. Turbulence will add the randomness of the drop breakup process, which will be studied in Part 3.3 in detail. The stamen structure increases with the increase of turbulence intensity observably. At the same time, the bag structure decreases with the increase of turbulence intensity slightly. 3.3. Physical mechanism
Fig. 6. The growth of drop with time for a low and high intensity case.
Here we describe the drop deformation before breakup, so T is the negative value. The bag structure will increase with the increase of turbulence intensity, and the ring structure will decrease with the increase of turbulence intensity. After breakup, the bag structure results in a larger number of small fragments; the ring structure results in a
The typical experimental photos of drop bag, bag-stamen and multi-bag breakup obtained in this test are shown in Fig. 9. Based on Rayleigh–Taylor piercing (also known as the combined RT/aerodynamic drag mechanism) mode (Zhao et al., 2010; Theofanous, 2011), the RT wave number N of drop breakup mode is shown in Table 3 and Fig. 9 approximately. Note that N for the given breakup mode has a range, not a specific value. RT instability is the instability of an interface between two fluids of different densities, which occurs when the lighter fluid is pushing the heavier fluid. In the airflow, the drop is deformed into a flat disk firstly. Therefore the simplified RT analysis predicts RT wavelengths will form on the leading surface of a deformed drop. When the diameter of drop is less than the critical wavelength of RT instability, the drops could not be fragmented by RT instability. And the number of bag increases with the increase of RT wave number per drop disk diameter, N. That is to say, the drop breakup process is strongly affected by RT wave number in the region of maximum cross stream dimension, N. Here to simplify, we choose a representative value. Drop breakup statistics involve over 20 0 0 objects in this test, which has been shown in Table 4. Here the final RT wave number N is equal to the sum of product of the wave number of each breakup mode and its probability. Turbulence can add randomness to the breakup process. Some local gas velocities are lower than
6
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Fig. 7. Experimental photos of drop bag breakup at high mean velocity.
the average velocity, while others are higher than the average velocity. We can find that turbulence will add the randomness of drop breakup mode, particularly at high mean velocity. In addition the final RT wave number N increases with the increase of turbulence intensity. RT wave is induced by aerodynamic force in secondary atomization. Turbulence will make the wavelength of RT wave different because of the change of velocity in turbulence. In the turbulent flow field, we propose that the instantaneous RT wavelength λ is affected by the velocity fluctuation. Once the instantaneous RT wavelength λ is smaller than the maximum drop diameter (mother size) Dm , the perturbation caused by turbulence will begin to develop into the RT wave. If the average RT wavelength λ is also smaller than Dm , the RT wave will induce the drop breakup finally. If λ is bigger than Dm , surface tension will stabilize the perturbations. Schematic of the development of RT instability on drop interface is shown in Fig. 10.
When the mean velocity is high (For example bag-stamen breakup and multi-bag breakup. In secondary atomization, the bag-stamen and multi-bag breakup modes appear at higher mean gas velocity than bag breakup modes.), there is Dm > λ, the perturbation induced by turbulence will develop into the RT wave. Turbulence has significant impact on the drop breakup mode and morphology. The critical wavelength of RT instability (Chandrasekhar, 1961) is defined as
λc =2π
σ ρl a
(2)
where ρ l is the liquid density, a is the drop average acceleration (drop acceleration obtained by the average gas velocity), σ is the surface tension. The average wavelength of the most unstable RT wave is expressed as
λ=2π
3σ ρl a
(3)
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Fig. 8. Experimental photos of drop bag-stamen breakup at high mean velocity.
Table 4 Experimental results of breakup mode statistics. No.
Plate no.
mean We
turbulent We
No breakup
Bag
Bag-stamen
Multi-bag
1 2 3 4 5 6 7 8 9
A B C D A B C D A
19.8 13.0 13.7 13.3 14.4 10.1 10.1 10.1 10.3
0.45 0.0076 0.011 0.026 0.38 0.0035 0.0061 0.016 0.27
0.0% 0.0% 0.0% 0.0% 0.0% 4.6% 0.4% 4.7% 2.6%
0.0% 96.0% 70.7% 66.5% 0.0% 95.4% 99.6% 95.3% 85.1%
30.7% 4.0% 29.3% 33.5% 77.5% 0.0% 0.0% 0.0% 12.3%
69.3% 0.0% 0.0% 0.0% 22.5% 0.0% 0.0% 0.0% 0.0%
7
8
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Fig. 9. Schematic of experimental photos breakup mode and RT wave number.
Based on our previous work (Zhao et al., 2011), the drop average acceleration is
a=
3ρg u2CD D2m 4D30 ρl
(4)
where CD is the drag coefficient. In secondary atomization, CD of liquid drops has been studied in detail which is approximately constant in the range of test Reynolds number under the condition of similar shape (Liu et al., 1993; Chou and Faeth, 1998; Zhao et al., 2010, 2011; Theofanous, 2011). RT wave in Eq. (3) and acceleration in Eq. (4) can be considered as constant approximately when turbulence intensity is small. This is also a common method in literature. When the effect of turbulence is significant, turbulence could add randomness to the breakup process. Some drops experience local velocities higher than the average and therefore break
up faster and at lower We (based on the mean velocity) based on Eqs. (5) and (6). So Eqs. (5) and (6) can be considered as the modified equation of Eqs. (3) and (4). When considering the effects of turbulence, the instantaneous RT wavelength is
λ =2π
3σ ρl (a + arms )
(5)
The rms acceleration caused by turbulence is given by
3ρg (b · urms ) CD D2m 4D30 ρl 2
arms =
(6)
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
9
Fig. 10. Schematic of the development of RT instability on drop interface.
Fig. 12. Effect of turbulence on morphology in bag breakup regime. Fig. 11. Effect of turbulence on morphology in multi-mode breakup regime.
where b is a coefficient. The correlation of the RT wave number N is
N=
Dm
= λ
2π
Dm 3σ ρl (a+arms )
=
D2m
CD
D20 4π
W e + b2W erms
(7)
where We is introduced in Eq. (1), W erms = ρg u2rms D0 /σ . The rms velocity is obtained by PIV. The drag coefficient is obtained by the drop shape in literature in detail (Zhao et al., 2010, 2011). The result which is transformed by dimensionless (The minimum turbulence intensity, Plate No. B) is
N = NB
W e + b2W erms W eB + b2W erms,B
(8)
where WeB , Werms ,B and NB is based on the data of Plate No. B. The best fit correlation of the experimental results is b = 12.3. The fitting results are shown in Fig. 11. Based on Rayleigh–Taylor piercing (also known as the combined RT/aerodynamic drag mechanism) mode (Zhao et al., 2010; Theofanous, 2011), In bag breakup regime, there is Dm = λ, the perturbation induced by turbulence is stable, which will be hard to grow in time. Turbulence has smaller effect on the drop breakup mode
as shown in Fig. 12. The best fit correlation of the experimental results is b = 3.37. Prevish and Santavicca (1998) define the drop Weber number in the turbulent jet, which is W eT = ρg (u + b · urms )2 D0 /σ based on theoretical analysis. The factor of b = 3 is intended to account for the statistical maximum of a probability curve comprising all values. That is very close to our experimental results (b = 3.37) when the velocity is low. However b is not an invariant constant, which increases with the increase of velocity rapidly (b = 12.3). So it indicates that the effect of turbulence may increase non-linearly. Here this discrepancy on the definition of We is due to the difference of analysis ideas. The definition in literature (Prevish and Santavicca, 1998) is from statistical maximum of the probability curve. In this paper, we try to study this topic by the Rayleigh– Taylor instability. Based on the Rayleigh–Taylor piercing or the combined RT/aerodynamic drag mechanism, the small perturbations and fluctuations could induce and promote the appearance and development of RT instability, which is not limited to the similar scale as droplets. Then the drag force from airflow would further promote the development of RT wave. So in the breakup process of drop, the influence of turbulence should be complex, which may have multiple roles. The roles of different turbulence scales will be
10
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
interesting and significant. In general, the value of b should be close to 1. However, the interesting thing is that b2 >> 1. Here the turbulence plays a more important role than expected. The influence of turbulence on b may indicate this physical mechanism should be researched in detail in the future. 4. Conclusions In this study, we have investigated the effect of turbulence on drop breakup in counter air flow. Photos obtained by high speed camera show that turbulence has great effect on the drop breakup morphology. The bag structure increases with the increase of turbulence intensity in bag breakup regime; the stamen structure increases with the increase of turbulence intensity when the average velocity is high. The statistical data show that: at high mean velocity, turbulence has great effect on the drop breakup mode, RT wave number N increases with the increase of turbulence intensity (b = 12.3). However, turbulence has smaller effect on the drop breakup mode in bag breakup regime (b = 3.37). Overall, the experimental results from the PIV system and high speed camera show that: the high fluctuating velocity at high mean velocity will predominantly shift the topology of drop breakup; however the high fluctuating velocity at low mean velocity will predominantly modify the topology of drop breakup. Acknowledgments This research was supported by the National Key R&D Program of China (2018YFC0808502-02), the Shanghai Engineering Research Center of Space Engine (17DZ2280800), the Fundamental Research Funds for the Central Universities, and the scholarship from China Scholarship Council. References Aliseda, A., Hopfinger, E.J., Lasheras, J.C., Kremer, D.M., Berchielli, A., Connolly, E.K., 2008. Atomization of viscous and non-newtonian liquids by a coaxial, high-speed gas jet. experiments and droplet size modeling.. Int. J. Multiphase Flow 34 (2), 161–175. Andersson, R., Andersson, B., 2006a. On the breakup of fluid particles in turbulent flows. AIChE J. 52, 2021–2030. Andersson, R., Andersson, B., 2006b. Modeling the breakup of fluid particles in turbulent flows. AIChE J. 52, 2031–2038. Baldyga, J., Bourne, J., 1993. Drop break-up and intermittent turbulence. J. Chem. Eng. Jpn. 26, 738–741. Broumand, M, Birouk, M, 2016. Liquid jet in a subsonic gaseous crossflow: Recent progress and remaining challenges. Prog. Energy Combust. Sci. 57, 1–29. Chandrasekhar, S., 1961. Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford. Chou, W.H., Faeth, G.M., 1998. Temporal properties of secondary drop breakup in the bag breakup regime. Int. J. Multiphase Flow 24 (6), 889–912. Daniel, E.M., Honnery, D., Soria, J., 2011. Particle relaxation and its influence on the particle image velocimetry cross-correlation function. Exp. Fluids 51 (4), 933–947. Daniel, E.M., Kilian, O., Honnery, D.R., Julio, S., 2014. Coherent structure and sound production in the helical mode of a screeching axisymmetric jet. J. Fluid Mech. 748 (2), 822–847. Flock, A.K., Guildenbecher, D.R., Chen, J., Sojka, P.E., Bauer, H.J., 2012. Experimental statistics of droplet trajectory and air flow during aerodynamic fragmentation of liquid drops. Int. J. Multiphase Flow 47 (3), 37–49. Guildenbecher, D.R., López-Rivera, C., Sojka, P.E., 2009. Secondary atomization. Exp. Fluids 46 (3), 371. Hinze, J.O., 1955. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289–295.
Hsiang, L P, Faeth, G M, 1995. Drop deformation and breakup due to shock wave and steady disturbances. Int. J. Multiphase Flow 21 (4), 545–560. Jain, M., Prakash, R.S., Tomar, G., Ravikrishna, R.V., 2015. Secondary breakup of a drop at moderate Weber numbers. Proc. R. Soc. Lond. 471 (2177), 20140930. Jampolski, L., Sänger, A., Jakobs, T., Guthausen, G., Kolb, T., Willenbacher, N., 2016. Improving the processability of coke water slurries for entrained flow gasification. Fuel 185, 102–111. Koizumi, T., 2012. Development of engineering and the direction in transition from land consolidation to agricultural infrastructure improvement and rural development. Int. J. Multiphase Flow 47 (3), 37–49. Kolmogorov, A.N., 1949. On the disintegration of drops in a turbulent flow. Dokl. Akad. Nauk SSSR 66, 825–828. Krzeczkowski, S.A., 1980. Measurement of liquid droplet disintegration mechanisms. Int. J. Multiphase Flow 6 (3), 227–239. Kulkarni, V., Sojka, P.E., 2014. Bag breakup of low viscosity drops in the presence of a continuous air jet. Phys. Fluids 26 (7), 545–560. Lefebvre, A., Mcdonell, V., 2017. Atomization and Sprays, Second Ed. CRC Press. Liu, A.B, Mather, D., Reitz, R.D., 1993. Modeling the Effects of Drop Drag and Breakup on Fuel Sprays SAE Technical Report No. 930072. Ma, X., Duan, Y., Liu, M., 2013. Atomization of petroleum-coke sludge slurry using effervescent atomizer. Exp. Thermal Fluid Sci. 46 (4), 131–138. Nicholls, J.A., Ranger, A.A., 1969. Aerodynamic shattering of liquid drops. AIAA J. 7 (2), 285–290. Pilch, M, Erdman, C.A., 1987. Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Int. J. Multiphase Flow 13 (6), 741–757. Prevish, T., Santavicca, D., 1998. Turbulent breakup of hydrocarbon droplets at elevated pressures. ILASS Americas. In: 11th Annual Conference on Liquid Atomization and Spray Systems, Sacramento, CA, pp. 246–250. Sahu, R.P., Sinha-Ray, S., Yarin, A.L., Pourdeyhimi, B., 2013. Blowing drops off a filament. Soft Matter 9 (26), 6053–6071. Sakuma, H, Tamura, K, Minagawa, K., 2018. Doughnut"-like clay microparticles fabricated using a hybrid method of spray drying and centrifugal disc atomization. Chem. Lett. 47 (1), 68–70. Sasaki, E, Kurayama, F, Ida, J I, et al., 2008. Preparation of microcapsules by electrostatic atomization. J. Electrostat. 66 (5), 312–318. Sevik, M., Park, S.H., 1973. The splitting of drops and bubbles by turbulent fluid flow. J. Fluids Eng. 95, 53–60. Sharp, D.H., 1984. An overview of Rayleigh–Taylor instability. Physica D 12 (1–3), 3–18. Sichani, A.B., Emami, M.D., 2015. A droplet deformation and breakup model based on virtual work principle. Phys. Fluids 27 (3), 1001–1048. Solsvik, J, Jakobsen, H.A., 2016. A review of the statistical turbulence theory required extending the population balance closure models to the entire spectrum of turbulence. AIChE J. 62 (5), 1795–1820. Solsvik, J, Tangen, S, Jakobsen, H.A., 2013. On the constitutive equations for fluid particle breakage. Rev. Chem. Eng. 29 (5), 241–356. Soria, J., 1996. An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Exp. Thermal Fluid Sci. 12 (2), 221–233. Soria, J., New, T.H., Lim, T.T., Parker, K., 2003. Multigrid CCDPIV measurements of accelerated flow past an airfoil at an angle of attack of 30°. Exp. Thermal Fluid Sci. 27 (5), 667–676. Strasser, W., Battaglia, F., 2017. The effects of pulsation and retraction on non-Newtonian flows in three-stream injector atomization systems. Chem. Eng. J. 309, 532–544. Tan, D.J., Soria, J., Honnery, D., Edgington-Mitchell, D., 2017. Novel method for investigating broadband velocity fluctuations in axisymmetric screeching jets. AIAA J. 55 (7), 1–14. Tavangar, S., Hashemabadi, S.H., Saberimoghadam, A., 2015. CFD simulation for secondary breakup of coal-water slurry drops using OpenFOAM. Fuel Process. Technol. 132 (1), 153–163. Theofanous, T.G., 2011. Aerobreakup of Newtonian and viscoelastic liquids. Annu. Rev. Fluid Mech. 43 (1), 661–690. Villermaux, E., Bossa, B., 2009. Single-drop fragmentation determines size distribution of raindrops. Nat. Phys. 5 (9), 697–702. Villermaux, E., Clanet, C., 2002. Life of a flapping liquid sheet. J. Fluid Mech. 462 (462), 341–363. Willert, C.E., Mitchell, D.M., Soria, J., 2012. An assessment of high-power light-emitting diodes for high frame rate schlieren imaging. Exp. Fluids 53 (2), 413–421. Xie, Z, Shen, W, Lin, J, et al., 2017. Sedation effects of intranasal dexmedetomidine delivered as sprays versus drops on pediatric response to venous cannulation. Am. J. Emerg. Med. 35 (8), 1126–1130. Zhao, H., Liu, H.F., Cao, X.K., Li, W.F., Xu, J.L., 2011. Breakup characteristics of liquid drops in bag regime by a continuous and uniform air jet flow. Int. J. Multiphase Flow 37 (5), 530–534. Zhao, H., Liu, H.F., Li, W.F., Xu, J.L., 2010. Morphological classification of low viscosity drop bag breakup in a continuous air jet stream. Phys. Fluids 22 (11), 4.
Contents lists available at ScienceDirect
International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow
Effect of turbulence on drop breakup in counter air flow Hui Zhao a,b,c, Dung Nguyen c, Daniel J. Duke c, Daniel Edgington-Mitchell c, Julio Soria c, Hai-Feng Liu a,b,∗, Damon Honnery c a
Shanghai Engineering Research Center of Coal Gasification, East China University of Science and Technology, Shanghai 200237, China Shanghai Engineering Research Center of Space Engine, Shanghai Institute of Space Propulsion, Shanghai 201112, China c Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Victoria 3800, Australia b
a r t i c l e
i n f o
Article history: Received 30 November 2018 Revised 30 August 2019 Accepted 5 September 2019 Available online 5 September 2019 Keywords: Secondary atomization Drop breakup Instability Turbulence
a b s t r a c t Understanding the factors that lead to breakup of liquid droplets is of interest in many applications. Liquid droplet breakup processes are typically broken into regimes based on a Weber number calculated based on an average flow velocity (Solsvik et al., 2013). In turbulent flows, the instantaneous velocity may differ significantly from the average velocity. Here an experimental investigation on the role of turbulence in the breakup process is undertaken, whose continuous phase is gas. The turbulence is produced by confined counterflow into which the droplets fall. Droplet breakup mode is visualized by high speed camera, and the turbulence of counterflow is measured by Particle Image Velocimetry. The experimental results show that the breakup morphology and mode frequency varies with the turbulence intensity of the counterflow. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction Atomization is a subject of practical interest in nature (Villermaux and Bossa, 2009) and numerous applications, such as combustion (Ma et al., 2013; Broumand and Birouk, 2016), gasification (Jampolski et al., 2016; Strasser and Battaglia, 2017), agriculture (Koizumi, 2012), medicine (Xie et al., 2017), material preparation (Sasaki et al., 2008) and spray drying (Sahu et al., 2013; Sakuma et al., 2018). A liquid droplet with a speed differential with respect to the ambient medium will experience aerodynamic forces that may cause the drop to deform and break apart into fragments. This process is referred to as secondary atomization (Guildenbecher et al., 2009; Jain et al., 2015; Sichani and Emami, 2015). The performance of many systems is dependent on the final droplet size and hence controlled atomization of the fluid is essential. This desire for control over droplet sizes motivates a deeper understanding of droplet breakup processes. Secondary atomization is typically characterized by two nondimensional numbers, the Weber number (We) and the Ohnesorge number (Oh). The Weber number represents the ratio of disruptive hydrodynamic forces to the stabilizing surface tension force,
W e = ρg (ug −ul )2 D0 /σ
∗
Corresponding author. E-mail address: hfl[email protected] (H.-F. Liu).
https://doi.org/10.1016/j.ijmultiphaseflow.2019.103108 0301-9322/© 2019 Elsevier Ltd. All rights reserved.
(1)
where ρ g is the air density, ug is the mean gas velocity, ul is the drop velocity, D0 is the initial diameter of drop, σ is the surface tension. Based on morphological classification, as the Weber number increases, bag breakup, bag-stamen breakup, dual-bag breakup, bag/plume breakup, etc. occur in turn. These breakup types which have the characteristic bag structure are all governed by the Rayleigh-Taylor instability. These breakup types can be named as Rayleigh-Taylor piercing (or the combined RT/aerodynamic drag mechanism, general bag breakup, et al.) (Guildenbecher et al., 2009; Zhao et al., 2010; Theofanous, 2011, Flock et al., 2012). Critical Weber number is the beginning of bag breakup, which establishes the criteria for the onset of secondary atomization. Many studies have reported the critical Weber number of water is approximately constant in secondary atomization, W ec = 11 ± 2 (Krzeczkowski, 1980; Pilch and Erdman, 1987; Hsiang and Faeth, 1995; Chou and Faeth, 1998; Zhao et al., 2011; Kulkarni and Sojka, 2014). The Ohnesorge number is a dimensionless number that relates the viscous forcesto inertial and surface tension forces, which is defined as Oh = μ/ ρl σ D0 , where μ is the liquid viscosity, ρ l is the liquid density. So the larger Oh indicate a greater influence of liquid viscosity on atomization. Critical Weber number will increase with the increase of Oh (Aliseda et al., 2008; Tavangaret et al., 2015). While Weber number is typically calculated based on a mean fluid velocity, in a turbulent flow the mean velocity does not necessarily capture the instantaneous hydrodynamic forces experienced by the droplet (Solsvik et al., 2013). A model for breakup
2
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Notation a arms b CD D0 Dm H I N NB Oh T t ug ul u We WeB Wec Werms Werms ,B WeT W
ρg ρl σ μ λ λ λc ε
drop average acceleration (drop acceleration obtained by the average gas velocity) rms acceleration caused by turbulence a coefficient for the modified influence of turbulence drag coefficient the initial diameter of drop the maximum drop diameter (mother size) the height of drop relative turbulence intensity the number of RT waves per drop disk diameter the number of RT waves per drop disk diameter based on the data of Plate No. B Ohnesorge number dimensionless characteristic time real time mean gas velocity drop velocity mean velocity Weber number by mean gas velocity Weber number by mean gas velocity based on the data of Plate No. B critical Weber number, the beginning of bag breakup Weber number by rms velocity Weber number by rms velocity based on the data of Plate No. B the drop Weber number in the turbulent jet based on Prevish and Santavicca (1998) the width of drop air density liquid density surface tension liquid viscosity RT wavelength instantaneous RT wavelength critical RT wavelength the rate of energy dissipation per unit mass
in turbulent flow and a turbulent Weber number was proposed by Kolmogorov (1949) and Hinze (1955). Here the characteristic velocity of turbulent Weber number u2 = C1 (ε D0 )2/3 , where C1 is constant, ɛ is the energy input per unit mass and unit time. Here the velocity given is not equal to the fluctuating velocity or the rms velocity. There exist models for the structure function for the whole spectrum of turbulence as explained in the review of Solsvik and Jakobsen (2016). Hinze (1955) also observed that droplets deform differently in the presence of turbulence; rather than deforming into an oblate ellipsoid as in the case of laminar flow, drop deformation and fragmentation is irregular. Sevik and Park (1973) suggested an additional mechanism for breakup in turbulent flows: a resonance process driven by a match between the characteristic turbulence frequency and the fundamental resonant frequency of droplet. Drops or bubbles would deform very violently if the exciting frequency corresponds to one of their resonant frequencies. The progressively smaller bubble sizes that are generated when the lowest critical Weber number is exceeded appears to be related to the higher characteristic frequency of the turbulence which excites higher order modes of vibration of a drop or bubble, thus leading to the formation of smaller parts. Furthermore, this classical theory could also be modified by including the effect of intermittency in the turbulent field (Baldyga and Bourne, 1993). Prevish and San-
tavicca (1998) found that critical Weber number decreases as the turbulence intensity of the ambient flow increases using hydrocarbon droplets at elevated pressures. The breakup mode is predominantly bag breakup for laminar flow, the mixture of bag and bulgy for turbulence flow. Bulgly deformation mode is as follows. As the surface of the globule is deformed locally, bulges and protuberances occur, and thus parts of the globule become bodily separated. The bag breakup mode is composed of a thin hollow bag attached to a toroidal rim. The bag disintegrates first, followed by the rim. The former results in a larger number of small fragments; the latter a smaller number of large fragments. The combination of the bulk velocity and the fluctuating velocities of eddies with scales on the order of the initial droplet diameter may be responsible for breakup in turbulent flowfields. For methanol drops, critical conditions for initial breakup, based on mean (bulk) velocity, decrease from 11 in laminar flow to 4 in a moderately turbulent (Relative turbulence intensity I=30%) flowfield, and to 3 for a highly turbulent (I = 45%) flowfield. The mechanism of breakup is predominantly bag for laminar folwfield, a mixture of bag and bulgy in the I = 30% flowfield, and predominantly bulgy when I = 45%. Andersson and Andersson (2006a,b) study the role of turbulence length scale relative to the droplet size in terms of inducing further drop breakup. Their model predicts that turbulent structures close in size to the fluid particle contribute most to the breakup. There exists abundant literature on secondary atomization, and summaries are available in several detailed review articles (Guildenbecher et al., 2009; Theofanous, 2011). In secondary atomization, the turbulent droplet breakup modes are bag and bulgly breakup mainly. On the physical mechanisms of secondary atomization, turbulence within the two fluids may create additional forces that destabilize drops. In addition, unsteady ambient flow could be considered by accounting for the time that the disruptive forces act on the drop and/or accounting for the rate of change of these forces. Turbulence adds randomness to the breakup process. Some drops experience low local velocities and therefore break up slowly, or do not break up at all. Other drops experience local velocities higher than the average and therefore break up faster and at lower We (based on the mean velocity). However, at present the morphological characteristics and physical mechanisms of droplet breakup in the presence of turbulence remain very poorly understood (Guildenbecher et al., 2009; Lefebvre and Mcdonell, 2017). Rayleigh-Taylor instability occurs when the lighter fluid is pushing the heavier fluid (Sharp, 1984). In general bag breakup, the Rayleigh-Taylor instability plays a leading role, which is an instability of an interface between two fluids of different densities (Theofanous, 2011). In the initial stage, the amplitude of perturbations is growing with time. The turbulence can have great effect on the drop breakup by the initial perturbations, etc. In this test, we notice that the breakup morphology and mode frequency varies with the turbulence intensity of the airflow. Thus the purpose of this paper is to investigate the effect of counterflow turbulence on droplet breakup at Weber numbers moderately higher than the critical value. The rest of the paper is organized as follows. In Part 2, we describe the details of experimental methods. Results are presented and discussed in Part 3, followed by concluding remarks in Part 4. 2. Experimental set-up Experiments are conducted in a drop tower as shown Fig. 1 using water and air as the liquid and gas phases. Drops of 3.7 mm diameter are formed on the nozzle, fall through the tube in quiescent air before entering the test section (80 × 80 mm) and being subjected to a confined turbulent counterflow. Four perforated plates are used to provide different initial conditions for the turbulence in the counterflow. Specifications for the plates are shown
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Fig. 1. Sketch of drop breakup experimental apparatus.
3
Fig. 3. Photo of PIV experimental apparatus.
PCO40 0 0 camera. The resulting images had an optical resolution of 20 μm/pixel. The laser runs with an interframing time between images of 40 μs. We use the 105 mm Micro-Nikkor lens set to an aperture of f/5.6. The tests are conducted with a 32 × 32 interrogation window and a 50% overlap. 3. Results and discussion 3.1. Characterization of turbulent counterflow
Fig. 2. Turbulence inducing plate. Table 1 Perforated turbulence inducing plate specifications. No.
Solidity
Hole diameter (mm)
Thickness (mm)
A B C D
90% 64% 60% 53%
2.4 1.6 3.2 8.0
0.67 0.52 1.53 1.63
in Table 1 and Fig. 2. A MotionPro X3 high speed camera with a 105 mm Micro-Nikkor lens is used to capture drop breakup events at the framerate 1600 fps. The light source is a pulsed CBT-120 (green) LED (Willert et. al 2012), whose exposure time is 1 μs and LED facula width is 42 mm. All the images of the droplets obtained by high speed camera have the same magnification factor. The image resolution is 64.8 μm per pixel. Particle Image Velocimetry (PIV) jet experiments were conducted in the Laboratory for Turbulence Research in Aerospace and Combustion at Monash University. The complete description of the algorithm used can be found in previous work (Soria, 1996; Soria et al., 2003). PIV is used to characterize the turbulence in the test section as shown Fig. 3. Oil particles are introduced into the counter flow gas upstream of the test section using a VisCount Smoke Generator (Daniel et al., 2011, 2014; Tan et al., 2017). The particles are illuminated with a EverGreen Nd:YAG laser at a 532 nm wavelength, and particle images recorded on a
Nine configurations for the turbulent counterflow are considered. PIV is used to characterize the variation in mean velocity and turbulence intensity for these different counterflow configurations as shown in Table 2. Representative velocity profiles over a typical droplet trajectory are shown in Fig. 4; mean velocity and turbulence intensity are largely invariant with axial position. When mean velocity is held constant, the turbulence intensity of Plate No. A is the highest, likely due to its high solidity. When the solidities (Plates B, C and D) and mean velocities are similar, the turbulence intensity increases with plate hole diameter. 3.2. Morphological characteristics of drop breakup The diameter of the initial droplet on exiting the drop tower is 3.7 mm, an example image is shown in Fig. 5(a). Depending on both the mean velocity and turbulence intensity, this initially spherical droplet may undergo a number of different breakup modes. First, Fig. 5 presents a comparison of breakup modes for two flows with similar mean velocities, and similar characteristic length scales, but different turbulence intensities. Here, mean velocity is obtained from the data of flow meter and experimental device size. The characteristic length scale is the drop diameter. Turbulent intensity is obtained from the data of PIV. Both cases exhibit the classical bag breakup mode, however comparing Fig. 5(b) and (c) there are significant differences in morphology beyond the typical randomness (small morphological changes of each test) observed in breakup behaviour. Turbulence also has great effect on the drop breakup morphology. The growth of drop (width W and height H) with time for a low and high intensity case of turbulence is shown in Fig. 6(a) and (b). The dimensionless characteristic time t·u of drop is T = √ g , where ug is the mean velocity, t is the real D0
ρl /ρg
time (Nicholls and Ranger, 1969). The origin of time is the beginning of drop breakup. The beginning of drop breakup refers to the time when droplets enter the airflow (the exit of tube in Fig. 1).
4
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Fig. 4. Representative turbulent statistcs obtained by PIV. The origin of the position is the exit of tube as shown in Fig. 1.
Fig. 5. (a) The diameter D0 of initial drop is 3.7 mm, all the images of the droplets obtained by high speed camera have the same magnification factor. (b) and (c) Experimental photos of drop bag breakup at low mean velocity.
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
5
Table 2 Flow statistics. No.
Plate no.
Mean velocity (m/s)
Rms velocity (m/s)
Turbulence intensity
1 2 3 4 5 6 7 8 9
A B C D A B C D A
13.9 10.5 10.9 10.7 11.3 8.78 8.79 8.79 8.90
2.7 0.4 0.4 0.7 2.5 0.2 0.3 0.5 2.1
19.2% 3.4% 3.8% 6.1% 22.0% 2.7% 3.6% 5.7% 23.7%
Table 3 Representative RT wave number N of breakup mode (Zhao et al., 2010).
N
No breakup
Bag
Bag-stamen
Multi-bag
0
1
2
3
smaller number of large fragments. So the energy from turbulence can obtain more small fragments, which is beneficial to atomization performance. Fig. 7 also shows the experimental photos of drop bag breakup morphology when the mean velocity is bigger than Fig. 6. The size of bag structure increases with the increase of mean velocity at low turbulence intensity significantly. In general, the bag structure is smoother in high turbulence intensity than low turbulence intensity before the breakup. This is an interesting phenomenon, which may be due to the rapid expansion of bag. This situation is similar to the flapping liquid sheet (Villermaux and Clanet, 2002), the wrinkle on the bag is the development of instability. Fig. 8 shows the experimental photos of drop bag-stamen breakup morphology, whose mean velocity is equal to Fig. 7. Turbulence will add the randomness of the drop breakup process, which will be studied in Part 3.3 in detail. The stamen structure increases with the increase of turbulence intensity observably. At the same time, the bag structure decreases with the increase of turbulence intensity slightly. 3.3. Physical mechanism
Fig. 6. The growth of drop with time for a low and high intensity case.
Here we describe the drop deformation before breakup, so T is the negative value. The bag structure will increase with the increase of turbulence intensity, and the ring structure will decrease with the increase of turbulence intensity. After breakup, the bag structure results in a larger number of small fragments; the ring structure results in a
The typical experimental photos of drop bag, bag-stamen and multi-bag breakup obtained in this test are shown in Fig. 9. Based on Rayleigh–Taylor piercing (also known as the combined RT/aerodynamic drag mechanism) mode (Zhao et al., 2010; Theofanous, 2011), the RT wave number N of drop breakup mode is shown in Table 3 and Fig. 9 approximately. Note that N for the given breakup mode has a range, not a specific value. RT instability is the instability of an interface between two fluids of different densities, which occurs when the lighter fluid is pushing the heavier fluid. In the airflow, the drop is deformed into a flat disk firstly. Therefore the simplified RT analysis predicts RT wavelengths will form on the leading surface of a deformed drop. When the diameter of drop is less than the critical wavelength of RT instability, the drops could not be fragmented by RT instability. And the number of bag increases with the increase of RT wave number per drop disk diameter, N. That is to say, the drop breakup process is strongly affected by RT wave number in the region of maximum cross stream dimension, N. Here to simplify, we choose a representative value. Drop breakup statistics involve over 20 0 0 objects in this test, which has been shown in Table 4. Here the final RT wave number N is equal to the sum of product of the wave number of each breakup mode and its probability. Turbulence can add randomness to the breakup process. Some local gas velocities are lower than
6
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Fig. 7. Experimental photos of drop bag breakup at high mean velocity.
the average velocity, while others are higher than the average velocity. We can find that turbulence will add the randomness of drop breakup mode, particularly at high mean velocity. In addition the final RT wave number N increases with the increase of turbulence intensity. RT wave is induced by aerodynamic force in secondary atomization. Turbulence will make the wavelength of RT wave different because of the change of velocity in turbulence. In the turbulent flow field, we propose that the instantaneous RT wavelength λ is affected by the velocity fluctuation. Once the instantaneous RT wavelength λ is smaller than the maximum drop diameter (mother size) Dm , the perturbation caused by turbulence will begin to develop into the RT wave. If the average RT wavelength λ is also smaller than Dm , the RT wave will induce the drop breakup finally. If λ is bigger than Dm , surface tension will stabilize the perturbations. Schematic of the development of RT instability on drop interface is shown in Fig. 10.
When the mean velocity is high (For example bag-stamen breakup and multi-bag breakup. In secondary atomization, the bag-stamen and multi-bag breakup modes appear at higher mean gas velocity than bag breakup modes.), there is Dm > λ, the perturbation induced by turbulence will develop into the RT wave. Turbulence has significant impact on the drop breakup mode and morphology. The critical wavelength of RT instability (Chandrasekhar, 1961) is defined as
λc =2π
σ ρl a
(2)
where ρ l is the liquid density, a is the drop average acceleration (drop acceleration obtained by the average gas velocity), σ is the surface tension. The average wavelength of the most unstable RT wave is expressed as
λ=2π
3σ ρl a
(3)
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Fig. 8. Experimental photos of drop bag-stamen breakup at high mean velocity.
Table 4 Experimental results of breakup mode statistics. No.
Plate no.
mean We
turbulent We
No breakup
Bag
Bag-stamen
Multi-bag
1 2 3 4 5 6 7 8 9
A B C D A B C D A
19.8 13.0 13.7 13.3 14.4 10.1 10.1 10.1 10.3
0.45 0.0076 0.011 0.026 0.38 0.0035 0.0061 0.016 0.27
0.0% 0.0% 0.0% 0.0% 0.0% 4.6% 0.4% 4.7% 2.6%
0.0% 96.0% 70.7% 66.5% 0.0% 95.4% 99.6% 95.3% 85.1%
30.7% 4.0% 29.3% 33.5% 77.5% 0.0% 0.0% 0.0% 12.3%
69.3% 0.0% 0.0% 0.0% 22.5% 0.0% 0.0% 0.0% 0.0%
7
8
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
Fig. 9. Schematic of experimental photos breakup mode and RT wave number.
Based on our previous work (Zhao et al., 2011), the drop average acceleration is
a=
3ρg u2CD D2m 4D30 ρl
(4)
where CD is the drag coefficient. In secondary atomization, CD of liquid drops has been studied in detail which is approximately constant in the range of test Reynolds number under the condition of similar shape (Liu et al., 1993; Chou and Faeth, 1998; Zhao et al., 2010, 2011; Theofanous, 2011). RT wave in Eq. (3) and acceleration in Eq. (4) can be considered as constant approximately when turbulence intensity is small. This is also a common method in literature. When the effect of turbulence is significant, turbulence could add randomness to the breakup process. Some drops experience local velocities higher than the average and therefore break
up faster and at lower We (based on the mean velocity) based on Eqs. (5) and (6). So Eqs. (5) and (6) can be considered as the modified equation of Eqs. (3) and (4). When considering the effects of turbulence, the instantaneous RT wavelength is
λ =2π
3σ ρl (a + arms )
(5)
The rms acceleration caused by turbulence is given by
3ρg (b · urms ) CD D2m 4D30 ρl 2
arms =
(6)
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
9
Fig. 10. Schematic of the development of RT instability on drop interface.
Fig. 12. Effect of turbulence on morphology in bag breakup regime. Fig. 11. Effect of turbulence on morphology in multi-mode breakup regime.
where b is a coefficient. The correlation of the RT wave number N is
N=
Dm
= λ
2π
Dm 3σ ρl (a+arms )
=
D2m
CD
D20 4π
W e + b2W erms
(7)
where We is introduced in Eq. (1), W erms = ρg u2rms D0 /σ . The rms velocity is obtained by PIV. The drag coefficient is obtained by the drop shape in literature in detail (Zhao et al., 2010, 2011). The result which is transformed by dimensionless (The minimum turbulence intensity, Plate No. B) is
N = NB
W e + b2W erms W eB + b2W erms,B
(8)
where WeB , Werms ,B and NB is based on the data of Plate No. B. The best fit correlation of the experimental results is b = 12.3. The fitting results are shown in Fig. 11. Based on Rayleigh–Taylor piercing (also known as the combined RT/aerodynamic drag mechanism) mode (Zhao et al., 2010; Theofanous, 2011), In bag breakup regime, there is Dm = λ, the perturbation induced by turbulence is stable, which will be hard to grow in time. Turbulence has smaller effect on the drop breakup mode
as shown in Fig. 12. The best fit correlation of the experimental results is b = 3.37. Prevish and Santavicca (1998) define the drop Weber number in the turbulent jet, which is W eT = ρg (u + b · urms )2 D0 /σ based on theoretical analysis. The factor of b = 3 is intended to account for the statistical maximum of a probability curve comprising all values. That is very close to our experimental results (b = 3.37) when the velocity is low. However b is not an invariant constant, which increases with the increase of velocity rapidly (b = 12.3). So it indicates that the effect of turbulence may increase non-linearly. Here this discrepancy on the definition of We is due to the difference of analysis ideas. The definition in literature (Prevish and Santavicca, 1998) is from statistical maximum of the probability curve. In this paper, we try to study this topic by the Rayleigh– Taylor instability. Based on the Rayleigh–Taylor piercing or the combined RT/aerodynamic drag mechanism, the small perturbations and fluctuations could induce and promote the appearance and development of RT instability, which is not limited to the similar scale as droplets. Then the drag force from airflow would further promote the development of RT wave. So in the breakup process of drop, the influence of turbulence should be complex, which may have multiple roles. The roles of different turbulence scales will be
10
H. Zhao, D. Nguyen and D.J. Duke et al. / International Journal of Multiphase Flow 120 (2019) 103108
interesting and significant. In general, the value of b should be close to 1. However, the interesting thing is that b2 >> 1. Here the turbulence plays a more important role than expected. The influence of turbulence on b may indicate this physical mechanism should be researched in detail in the future. 4. Conclusions In this study, we have investigated the effect of turbulence on drop breakup in counter air flow. Photos obtained by high speed camera show that turbulence has great effect on the drop breakup morphology. The bag structure increases with the increase of turbulence intensity in bag breakup regime; the stamen structure increases with the increase of turbulence intensity when the average velocity is high. The statistical data show that: at high mean velocity, turbulence has great effect on the drop breakup mode, RT wave number N increases with the increase of turbulence intensity (b = 12.3). However, turbulence has smaller effect on the drop breakup mode in bag breakup regime (b = 3.37). Overall, the experimental results from the PIV system and high speed camera show that: the high fluctuating velocity at high mean velocity will predominantly shift the topology of drop breakup; however the high fluctuating velocity at low mean velocity will predominantly modify the topology of drop breakup. Acknowledgments This research was supported by the National Key R&D Program of China (2018YFC0808502-02), the Shanghai Engineering Research Center of Space Engine (17DZ2280800), the Fundamental Research Funds for the Central Universities, and the scholarship from China Scholarship Council. References Aliseda, A., Hopfinger, E.J., Lasheras, J.C., Kremer, D.M., Berchielli, A., Connolly, E.K., 2008. Atomization of viscous and non-newtonian liquids by a coaxial, high-speed gas jet. experiments and droplet size modeling.. Int. J. Multiphase Flow 34 (2), 161–175. Andersson, R., Andersson, B., 2006a. On the breakup of fluid particles in turbulent flows. AIChE J. 52, 2021–2030. Andersson, R., Andersson, B., 2006b. Modeling the breakup of fluid particles in turbulent flows. AIChE J. 52, 2031–2038. Baldyga, J., Bourne, J., 1993. Drop break-up and intermittent turbulence. J. Chem. Eng. Jpn. 26, 738–741. Broumand, M, Birouk, M, 2016. Liquid jet in a subsonic gaseous crossflow: Recent progress and remaining challenges. Prog. Energy Combust. Sci. 57, 1–29. Chandrasekhar, S., 1961. Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford. Chou, W.H., Faeth, G.M., 1998. Temporal properties of secondary drop breakup in the bag breakup regime. Int. J. Multiphase Flow 24 (6), 889–912. Daniel, E.M., Honnery, D., Soria, J., 2011. Particle relaxation and its influence on the particle image velocimetry cross-correlation function. Exp. Fluids 51 (4), 933–947. Daniel, E.M., Kilian, O., Honnery, D.R., Julio, S., 2014. Coherent structure and sound production in the helical mode of a screeching axisymmetric jet. J. Fluid Mech. 748 (2), 822–847. Flock, A.K., Guildenbecher, D.R., Chen, J., Sojka, P.E., Bauer, H.J., 2012. Experimental statistics of droplet trajectory and air flow during aerodynamic fragmentation of liquid drops. Int. J. Multiphase Flow 47 (3), 37–49. Guildenbecher, D.R., López-Rivera, C., Sojka, P.E., 2009. Secondary atomization. Exp. Fluids 46 (3), 371. Hinze, J.O., 1955. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289–295.
Hsiang, L P, Faeth, G M, 1995. Drop deformation and breakup due to shock wave and steady disturbances. Int. J. Multiphase Flow 21 (4), 545–560. Jain, M., Prakash, R.S., Tomar, G., Ravikrishna, R.V., 2015. Secondary breakup of a drop at moderate Weber numbers. Proc. R. Soc. Lond. 471 (2177), 20140930. Jampolski, L., Sänger, A., Jakobs, T., Guthausen, G., Kolb, T., Willenbacher, N., 2016. Improving the processability of coke water slurries for entrained flow gasification. Fuel 185, 102–111. Koizumi, T., 2012. Development of engineering and the direction in transition from land consolidation to agricultural infrastructure improvement and rural development. Int. J. Multiphase Flow 47 (3), 37–49. Kolmogorov, A.N., 1949. On the disintegration of drops in a turbulent flow. Dokl. Akad. Nauk SSSR 66, 825–828. Krzeczkowski, S.A., 1980. Measurement of liquid droplet disintegration mechanisms. Int. J. Multiphase Flow 6 (3), 227–239. Kulkarni, V., Sojka, P.E., 2014. Bag breakup of low viscosity drops in the presence of a continuous air jet. Phys. Fluids 26 (7), 545–560. Lefebvre, A., Mcdonell, V., 2017. Atomization and Sprays, Second Ed. CRC Press. Liu, A.B, Mather, D., Reitz, R.D., 1993. Modeling the Effects of Drop Drag and Breakup on Fuel Sprays SAE Technical Report No. 930072. Ma, X., Duan, Y., Liu, M., 2013. Atomization of petroleum-coke sludge slurry using effervescent atomizer. Exp. Thermal Fluid Sci. 46 (4), 131–138. Nicholls, J.A., Ranger, A.A., 1969. Aerodynamic shattering of liquid drops. AIAA J. 7 (2), 285–290. Pilch, M, Erdman, C.A., 1987. Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Int. J. Multiphase Flow 13 (6), 741–757. Prevish, T., Santavicca, D., 1998. Turbulent breakup of hydrocarbon droplets at elevated pressures. ILASS Americas. In: 11th Annual Conference on Liquid Atomization and Spray Systems, Sacramento, CA, pp. 246–250. Sahu, R.P., Sinha-Ray, S., Yarin, A.L., Pourdeyhimi, B., 2013. Blowing drops off a filament. Soft Matter 9 (26), 6053–6071. Sakuma, H, Tamura, K, Minagawa, K., 2018. Doughnut"-like clay microparticles fabricated using a hybrid method of spray drying and centrifugal disc atomization. Chem. Lett. 47 (1), 68–70. Sasaki, E, Kurayama, F, Ida, J I, et al., 2008. Preparation of microcapsules by electrostatic atomization. J. Electrostat. 66 (5), 312–318. Sevik, M., Park, S.H., 1973. The splitting of drops and bubbles by turbulent fluid flow. J. Fluids Eng. 95, 53–60. Sharp, D.H., 1984. An overview of Rayleigh–Taylor instability. Physica D 12 (1–3), 3–18. Sichani, A.B., Emami, M.D., 2015. A droplet deformation and breakup model based on virtual work principle. Phys. Fluids 27 (3), 1001–1048. Solsvik, J, Jakobsen, H.A., 2016. A review of the statistical turbulence theory required extending the population balance closure models to the entire spectrum of turbulence. AIChE J. 62 (5), 1795–1820. Solsvik, J, Tangen, S, Jakobsen, H.A., 2013. On the constitutive equations for fluid particle breakage. Rev. Chem. Eng. 29 (5), 241–356. Soria, J., 1996. An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Exp. Thermal Fluid Sci. 12 (2), 221–233. Soria, J., New, T.H., Lim, T.T., Parker, K., 2003. Multigrid CCDPIV measurements of accelerated flow past an airfoil at an angle of attack of 30°. Exp. Thermal Fluid Sci. 27 (5), 667–676. Strasser, W., Battaglia, F., 2017. The effects of pulsation and retraction on non-Newtonian flows in three-stream injector atomization systems. Chem. Eng. J. 309, 532–544. Tan, D.J., Soria, J., Honnery, D., Edgington-Mitchell, D., 2017. Novel method for investigating broadband velocity fluctuations in axisymmetric screeching jets. AIAA J. 55 (7), 1–14. Tavangar, S., Hashemabadi, S.H., Saberimoghadam, A., 2015. CFD simulation for secondary breakup of coal-water slurry drops using OpenFOAM. Fuel Process. Technol. 132 (1), 153–163. Theofanous, T.G., 2011. Aerobreakup of Newtonian and viscoelastic liquids. Annu. Rev. Fluid Mech. 43 (1), 661–690. Villermaux, E., Bossa, B., 2009. Single-drop fragmentation determines size distribution of raindrops. Nat. Phys. 5 (9), 697–702. Villermaux, E., Clanet, C., 2002. Life of a flapping liquid sheet. J. Fluid Mech. 462 (462), 341–363. Willert, C.E., Mitchell, D.M., Soria, J., 2012. An assessment of high-power light-emitting diodes for high frame rate schlieren imaging. Exp. Fluids 53 (2), 413–421. Xie, Z, Shen, W, Lin, J, et al., 2017. Sedation effects of intranasal dexmedetomidine delivered as sprays versus drops on pediatric response to venous cannulation. Am. J. Emerg. Med. 35 (8), 1126–1130. Zhao, H., Liu, H.F., Cao, X.K., Li, W.F., Xu, J.L., 2011. Breakup characteristics of liquid drops in bag regime by a continuous and uniform air jet flow. Int. J. Multiphase Flow 37 (5), 530–534. Zhao, H., Liu, H.F., Li, W.F., Xu, J.L., 2010. Morphological classification of low viscosity drop bag breakup in a continuous air jet stream. Phys. Fluids 22 (11), 4.