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Breakup morphology of annular liquid sheet with an inner round air stream
Chemical Engineering Science 137 (2015) 412–422
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Breakup morphology of annular liquid sheet with an inner round air stream Hui Zhao a,b, Jian-Liang Xu a,b, Ju-Hui Wu a,b, Wei-Feng Li a,b, Hai-Feng Liu a,b,n a Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, East China University of Science and Technology, Shanghai 200237, People's Republic of China b Shanghai Engineering Research Center of Coal Gasification, East China University of Science and Technology, Shanghai 200237, People's Republic of China
H I G H L I G H T S
Annular liquid sheet breakup can be divided into shell, cellular and fiber regime. Dimensionless cellular size is proportional to We 0.5. Breakup regime of annular liquid sheet has been made in h/D2–We map.
art ic l e i nf o
a b s t r a c t
Article history: Received 5 March 2015 Received in revised form 9 June 2015 Accepted 21 June 2015 Available online 9 July 2015
Experiments were performed on the deformation and breakup of annular liquid sheet of nine coaxial twin-fluid air-blast atomizers with water–air systems by using a high speed camera. Due to the morphological difference, the annular sheet breakup could be classified into three regimes, which were bubble (shell) breakup, Christmas tree (cellular) breakup and fiber breakup. The roles of atomizer size and Rayleigh–Taylor instability in the annular sheet breakup were studied. The correlations on the instability wavelength and the size of cellular structure were deduced. The results showed that the dimensionless cellular size was proportional to We 0.5, which were in good agreement with the experimental results. In order to have an overview of the different breakup mechanisms taking place over the wide range, we suggested categorizing these breakup regimes in a Weber number and dimensionless sheet thickness map. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Air-blast Coaxial Sprays Atomization Breakup
1. Introduction The transformation of liquid into spray is of importance in agriculture, meteorology and many industrial processes. Liquid atomization is also a fundamental research topic in multiphase flow, which has been studied extensively both theoretically and experimentally (Wang et al., 2014; Kulkarni and Sojka, 2014; Kekesi et al., 2014; Prakash et al., 2014; Xiao et al., 2014). As a common type of atomization, coaxial jets are utilized in a number of devices, including as burners in industrial furnaces and gasifiers, propellant injectors in rockets, and the exhaust of modern large bypass turbofan engines (Schumaker and Driscoll, 2012). In these applications, the complex near-field structure plays a critical role in determining how well the system performs (Lasheras and
n Corresponding author at: Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, East China University of Science and Technology, Shanghai 200237, People's Republic of China. Tel.: þ 86 21 64251418. E-mail address: hfl[email protected] (H.-F. Liu).
http://dx.doi.org/10.1016/j.ces.2015.06.062 0009-2509/& 2015 Elsevier Ltd. All rights reserved.
Hopfinger, 2000; Villermaux, 2007; Gorokhovski and Herrmann, 2008; Dumouchel, 2008; Theofanous, 2011). There are two basic types on coaxial gas–liquid jets: (I) a cylindrical liquid jet surrounded by an annular gaseous stream and (II) an annular liquid sheet with an inner round gaseous stream. The properties of above two basic types are the foundation of three or multi-channels coaxial jets (Carvalho and Heitor, 1998; Wahono et al., 2008; Duke et al., 2010, 2012; Liu et al., 2006; Leboucher et al., 2010, 2012, 2014), which are also helpful in the research of monodisperse microbubbling by capillary flow focusing (Gañán-Calvo and Gordillo , 2001; Gañán-Calvo, 2004, GañánCalvo et al., 2006). In this paper, we focus on the latter type (II). Annular liquid sheets are typically generated with circular slit nozzles or by diverging nozzle configurations which are common in many applications. So the distortion and disintegration of annular liquid sheets are of both fundamental and practical interest. The theoretical analysis on the instability of an annular liquid jet has been studied by Meyer and Weihs (1987), Oguz and Prosperetti (1993), Shen and Li (1996), Mehring and Sirignano (2000a, 2000b), Sevilla
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Table 1 The ranges of experimental parameters in coaxial jets, type (II).
Kendall (1986) Lee and Chen (1991) Martínez-Bazán et al. (1999a, 1999b) Adzic et al. (2001) Li and Shen (2001) Choi and Lee (2005) Sevilla et al. (2005a, 2005b) Leboucher et al. (2010, 2012, 2014) This study
Gas velocity (m/s)
Liquid velocity (m/s)
Dimensionless sheet thickness (h/D2), where h is the width of the annulus, D2 is the outside diameter of annulus exit.
1.5–13.7 5.5–32.0 1.07, 4.48, 8.88, 9.84 0–40 3.85–45 136–283 2.7–58.5 25–155 4.4–154.7
0.5–4.75 0.96 17 0.86 1.73–3.47 1.6–21.5 1.85–9.65 2 0.17–3.03
0.19 0.21 0.30, 0.40, 0.43 0.11 0.024 0.04–0.13 0.36, 0.39, 0.42 0.125 0.06–0.37
liquid liquid air
liquid liquid air
liquid liquid air
Fig. 1. Simple schematic diagrams illustrating the shape of the different regimes. (a) bubble breakup (shell breakup) (b) Christmas tree breakup (cellular breakup) (c) fiber breakup.
et al. (2002), Chen et al. (2003) etc. The experimental characteristics of annular sheet distortion and disintegration have also been investigated, whose atomizer sizes are as shown in Table 1. These data show various breakup morphologies and properties of coaxial jets, which are very interesting and useful. Kendall (1986) observed the bubble (shell) regime at low air velocity and studied the formation of liquid shells firstly. The breakup morphologies of annular sheet were also observed by Lee and Chen (1991), Martínez-Bazán et al. (1999a, 1999b), Adzic et al. (2001), Li and Shen (2001), Choi and Lee (2005), Sevilla et al. (2005a, 2005b) and Leboucher et al. (2010, 2012, 2014). A series of simple schematic diagrams illustrating the shape of the different regimes are shown in Fig. 1.
There are some high-quality papers on the atomization of liquid annulus around a central gas core. However, some papers only focus on the single breakup regime; other papers only focus on the single nozzle. The influence of atomizer sizes on breakup morphology and transition of different regimes is also absent. There are some correlations on the ranges of the breakup regimes in the literature. Unfortunately, these correlations are purely empirical or apply to the single nozzle. To overcome this, a theoretical model is needed which is based on the underlying physics. Here in order to have an overview of the different breakup mechanisms taking place over the wide ranges, this paper focuses on the ranges of different breakup regimes which can apply to
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Table 2 Summary of experimental conditions and parameters. Atomizer no.
air water
water
1 2 3 4 5 6 7 8 9
D0 (mm)
D1 (mm)
D2 (mm)
9.02 9.02 4.08 2.00 5.10 2.00 6.96 2.00 4.02
11.08 11.14 6.28 4.24 7.12 4.24 9.04 4.24 6.08
12.56 14.92 9.30 7.30 14.92 9.30 23.88 14.92 23.88
D1
0.06 0.13 0.16 0.21 0.26 0.27 0.31 0.36 0.37
Water velocity ul (m/s)
Air velocity ug (m/s)
1.01–3.03 0.18–1.44 0.75–3.01 1.00–3.00 0.21–0.82 0.52–1.55 0.29–0.58 0.17–0.69 0.27–0.53
4.4–86.9 6.5–76.1 5.3–138.1 22.1–154.7 20.4–102.0 22.1–154.7 18.3–109.5 22.1–154.7 21.9–131.3
3
2
D0
h/ D2
Water
5 2
4
1
D2 Fig. 2. Experimental atomizer configuration.
1-Air Blower 2-Flow Meter 3-Experimental Atomizer 4-High-speed Camera 5-Computer
Fig. 3. Flow chart of experiment process.
different nozzles. The influence of atomizer sizes on breakup morphology of annular liquid sheet with an inner round air stream has been studied in detail. We deduce the simplified theoretical formulas for predicting the transitions between breakup modes, which agrees well with our experimental results and the data of the literature. As discussed above, the present research is aimed at better understanding of the breakup morphologies and mechanisms of annular liquid sheet, especial for the effect of atomizer sizes. Some correlations are also reported for predicting deformation and breakup characteristics of annular sheet. In order to have an overview of the different breakup processes taking place over the wide range, an attempt to establish a diagram on various breakup regimes has been made.
2. Experimental apparatus and methodology The coaxial two-fluid air-blast atomizer geometry is shown schematically in Fig. 2, which is similar to our earlier work (Zhao et al., 2012, 2014a–c), consisting of the geometrically simple case of a round air jet surrounded by a co-flowing annular liquid stream. D0 is the internal diameter of central orifice exit, D1 is the internal diameter of annulus exit, and D2 is the outside diameter of annulus exit. There are nine kinds of atomizers used in this experiment, and their dimensions and experimental conditions are shown in Table 2. The results of atomizer diameter reported in Table 2 are measured by the Vernier caliper, whose uncertainty is 70.02 mm. Gas phase air passed through the central passage, while the liquid phase water flow passed through the annular space. The experiments were conducted at atmospheric pressure and room temperature, and the working fluids were water and air. The experimental apparatus is sketched in Fig. 3. The gas and liquid velocities are obtained by the flow meters. The type of flow meters employed is LZB glass tube rotameter flow meter, whose uncertainty is 71:5%. The high-speed digital camera (Fastcam APX-RS, Photron limited) was used combined with a continuous 1 kW halogen light. The digital images are analyzed and measured with
NIH Image software ImageJ, which is often used to analyze digital images of atomization in the literature. There are more than 1000 images recorded and analyzed per case. The width of the annulus in the exit is h ¼ ðD2 D1 Þ=2.
3. Results and discussion At low air velocity all atomizers are in bubble (shell) regime, whose experimental photographs are shown in Fig. 4. An additional feature of bubble (shell) regime is the formation of small ligaments as shown in Fig. 5, which is also observed by Li and Shen (2001). The small ligaments eject usually right after the bubble pinches off. We suggest that this phenomenon is due to the impingement of liquid sheet. As shown in Fig. 6, these small ligaments appear in different atomizers, which is a common phenomenon. At high air velocity, when the sheet is thin (The transitions between “thin” and “thick” sheets is ðh=D2 Þ ¼ 0:24, the corresponding analysis is close to the part near Fig. 15), the cell-like structures appear in the surface of annular liquid, which is shown in Fig. 7. This regime due to the striking appearance of cells is termed the Christmas tree regime. The cause of Christmas tree (cellular) regime is due to R–T instability, which is similar to the bag breakup in secondary breakup and the membrane breakup in air-blast cylindrical jets. The bag or membrane structures often appear in the breakup process of Christmas tree (cellular) regime as shown in Fig. 7(b). This Christmas tree (cellular) regime was mentioned by Adzic et al. (2001), Choi and Lee (2005) and Leboucher et al. (2010, 2012, 2014). This similar phenomenon was also been found in the breakup of planar liquid sheet (Stapper and Samuelsen, 1990; Stapper et al., 1992; Park et al., 2004). This illustrates that the cellular structure is a common phenomenon in both flat sheet and annular sheet experiments. Besides bubble (shell) breakup, wave structure can also be found in Christmas tree (cellular) breakup, whose evolvement is illustrated in Figs. 8 and 9. The wave structure is the primary destabilization of annular liquid sheet. The evolvement of cell-like structures is as shown in Fig. 8. At initial stage, the surface of liquid
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Fig. 4. Photographs of bubble (shell) breakup at low air velocity. (a) Atomizer 1, ul ¼ 1.01m/s, ug ¼ 4.4m/s, (b) Atomizer 2, ul ¼0.36m/s, ug ¼ 10.9m/s, (c) Atomizer 3, ul ¼ 0.75m/s, ug ¼5.3m/s, (d) Atomizer 4, ul ¼1.00m/s, ug ¼ 22.1m/s, (e) Atomizer 5, ul ¼ 0.21m/s, ug ¼ 20.4m/s. (f) Atomizer 6, ul ¼ 0.52m/s, ug ¼ 22.1m/s, (g) Atomizer 7, ul ¼ 0.51m/s, ug ¼ 18.3m/s, (h) Atomizer 8, ul ¼ 0.17m/s, ug ¼ 22.1m/s, (i) Atomizer 9, ul ¼ 0.27m/s,ug ¼ 21.9m/s.
impingement of liquid sheet
small ligaments
Fig. 5. The impact of annular liquid sheet gives rise to small ligaments. The interval separating each snapshot of this sequence is 2.68 ms. (Atomizer 2, ul ¼ 0.18 m/s, ug ¼ 6.5 m/s).
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Atomizer 1, ul =1.01m/s, ug
Atomizer 3, ul =1.50m/s, ug
Atomizer 6, ul =0.52m/s, ug
=4.4m/s
=10.6m/s
=22.1m/s
Atomizer 7, ul =0.29m/s, ug
Atomizer 8, ul =0.17m/s, ug
Atomizer 9, ul =0.40m/s, ug
=18.3m/s
=22.1m/s
=21.9m/s
Fig. 6. The impingement of annular liquid sheet gives rise to small ligaments which are shown in circle.
sheet near the nozzle outlet is smooth. Then under the action of airflow, the liquid sheet expands and the cell-like structures are formatted gradually. The breakup of cell would lead to the breakup of liquid sheet. Finally near the nozzle outlet there would be next initial stage. So in this breakup mode the cell-like structures play an important role in the breakup of annular liquid sheet with an inner round air stream. Fig. 8 shows experimental photographs of Christmas tree (cellular) breakup whose time interval is 1.33 ms. Fig. 10 shows the breakup structure in far field. Due to the surface tension, the annular sheet will contract if there is no airflow. This will lead to the decrease of airflow export, so the airflow has to push the sheet to move. This sheet acceleration results from the push of airflow. So the cellular structure is the secondary destabilization of annular liquid sheet. In the study of annular sheet, there are some different definitions of the Weber number, the one we used in this paper is given by Meyer and Weihs (1987) (the symbol is Wh in their paper)
ρg u2r h ; We ¼ σ
ð1Þ
where σ is the surface tension, ur is the relative velocity. The liquid Reynolds number is defined by Re ¼
ρl u l h ; μl
ð2Þ
where μl is the viscosity of liquid. Following the dimensionless wavelength of Lozano et al. (2005), we obtained an empirical correlation on the wavelength of bubble (shell) breakup and Christmas tree (cellular) breakup. Based on the multivariate analysis performed on
the data, the best fit correlation of present measurements is given by 0:64 λ ¼ 12:29D0:36 Re0:09 We 0:36 ; 0 h
ð3aÞ
or 0:14 λ h pffiffiffiffiffiffiffiffiffiffiffiffi ¼ 12:29 Re0:09 We 0:36 D0 h UD0
ð3bÞ
The correlation coefficient of the fit (Eqs. 3a and 3b) is 0.95. And the simpler equation without Re number would still sufficiently capture the measured results, 0:64 λ ¼ 22:98D0:36 We 0:34 ; 0 h
ð3cÞ
or 0:14 λ h pffiffiffiffiffiffiffiffiffiffiffiffi ¼ 22:98 We 0:34 D0 h UD0
ð3dÞ
The correlation coefficient of the fit (Eqs. 3c and 3d) is 0.93. Wavelength value calculated using this correlation is plotted against the measured values in Fig. 11. Here the wavelength is the perpendicular distance between two wave crests on the liquid sheet interface near the nozzle outlet. The wavelength is obtained by the help of NIH Image software ImageJ, which is a public domain, Java-based image processing program. ImageJ can display, edit, analyze, process, save, and print images. The Rayleigh–Taylor (R–T) instability is the instability of an interface between two fluids of different densities, which occurs when the lighter fluid is pushing the heavier fluid (Rayleigh, 1883; Taylor, 1950). Recently R–T instability is often used in the study of atomization (Varga et al., 2003; Marmottant and Villermaux, 2004; Zhao et al.,
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Fig. 7. Photographs of Christmas tree (cellular) breakup at high air velocity. (a) Atomizer 1, ul ¼2.02m/s, ug ¼ 65.2m/s, (b) Atomizer 2, ul ¼1.08m/s, ug ¼ 65.2m/s, (c) Atomizer 3, ul ¼ 1.50m/s, ug ¼ 95.6m/s, (d) Atomizer 4, ul ¼3.00m/s, ug ¼ 154.7m/s.
2010, 2011, 2013). Here the lighter fluid is airflow; the heavier fluid is water sheet. The push of high-speed airflow triggers R–T instability, producing cell-like structures. The diameter of circular perforations represents the typical length scale of cellular structures, which should be equal to the wavelength of R–T instability. A part of sheet is taken as the analysis object which is shown in Fig. 12. The simplified force balance on this part sheet can be written as: 1 F ¼ C 1 C D ρg u2r S ¼ ml a; 2
ð4Þ
ð5Þ
By combining Eqs. (4) and (5), the acceleration of the sheet is a¼
C 1 C D ρg u2r 2hρl
ð8Þ As the length scale of cellular structures can be estimated by d p λmax
ð9Þ
By combining Eqs. (8) and (9), the calculation is
where C D is the drag coefficient, S is the surface area of the sheet facing the airflow, ml and a are the mass and acceleration of the sheet, respectively. As the airflow and the sheet are not perpendicular, a correction factor C 1 is introduced. The mass of the sheet is ml ¼ Shρl
By combining Eqs. (6) and (7), we can obtain sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3σ 6σ h 6h 6 ¼ 2π λmax ¼ 2π ¼ 2π ¼ 2π h C 1 C D We C 1 C D We ρl a C 1 C D ρg u2r
ð6Þ
As the classic linear stability analysis (Chandrasekhar, 1961), the R–T wavelength of the most unstable wave is expressed as: sffiffiffiffiffiffiffi 3σ ; ð7Þ λmax ¼ 2π ρl a
d ¼ C 2 We 0:5 ; h
ð10Þ
where C2 is a coefficient. Here d is the mean of two mutually perpendicular lengths of cell. The cellular sizes are obtained by the photographs as shown in Fig. 13(a), which is the average value of CS1 and CS2. The experimental results are shown in Fig. 13, which is in well agreement with the R–T instability theory. The line in Fig. 13 is the following theoretical fit: d ¼ 19:91We 0:5 h
ð11Þ
The correlation coefficient of the fit is 0.97. By the theoretical analysis of perturbation growth rate Meyer and Weihs (1987) found that when the annulus thickness was big, the annular jet behaves liked a full liquid jet; when the annulus thickness was small, the jet behaves liked a two-dimensional liquid sheet. We found in our experiment that on the deformation
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Fig. 8. The wave in Christmas tree (cellular) breakup in near field, Δt¼ 0.67 ms. (Atomizer 4, ul ¼ 2.00 m/s, ug ¼ 110.5 m/s). (a)t, (b)t þ Δt, (c)t þ 2Δt, (d)tþ 3Δt, (e)t þ 4Δt, (f) t þ5Δt, (g)t þ6Δt, (h)t þ 7Δt.
and breakup morphology of annular sheet there was the similar phenomenon. When the sheet is thick, the surface of sheet displays transverse azimuthal modulations instead of cellular structures (Zhao et al., 2014c). Above a critical air velocity, the digitations appear which is shown in Fig. 14. So it is in the fiber breakup regime. With the increase of air velocity, the number of digitations also increases gradually and eventually generates in large numbers of liquid ligaments. The Christmas tree regime identified by Leboucher et al. (2010, 2012, 2014) is the cellular regime. The name of Christmas tree regime focuses on the whole structure of spray, while the name of cellular regime focuses on the local structure near the nozzle outlet. And the fiber regime is different from the Christmas tree regime, which is another new breakup regime. The appearance of spray in the fiber regime is not close to the Christmas tree. In the fiber regime the sheet bursts suddenly, and then it generates plenty of jet (ligament) structures irregularly. Due to the similarity between the primary and secondary breakup mechanisms, the drop breakup mechanism in secondary breakup can be used to study the annular sheet breakup. According to “Rayleigh–Taylor piercing” mechanism (Theofanous, 2011) or “the combined R–T/aerodynamic drag” mechanism (Guildenbecher et al., 2009), the influence of wave number (the number of R–T wave in the characteristic scale) on the appearance of liquid breakup is great. When the wave number is smaller than a constant, the instability of interface is negligible; while when the
wave number is bigger than the constant, the instability of interface will be remarkable. Near the nozzle outlet, the fiber and cell structures are the feature of the instability of interface. So we can obtain the boundary of bubble (shell) regime, the transition is expected when D2
λmax
¼ C3;
ð12Þ
where C 3 is a constant. By combining Eqs. (9), (10) and (12), we can obtain h 1 ¼ We0:5 D2 C 2 C 3
ð13Þ
For the range of parameters and atomizer geometry studied C 2 U C 3 ¼ 25 was found to agree favorably with experimental data, so the limit of bubble (shell) breakup is given by h 1 ¼ We0:5 D2 25
ð14aÞ
So if there is D2 We0:5 =h o 25;
ð14bÞ
the shell regime exists. The surface energy per unit mass of thin sheet is bigger than thick sheet. When the energy of liquid is large enough, liquid sheet will break up easily. Thin sheet expands and breaks up easily; however thick sheet expands initially then contracts finally, which breaks up hardly. The surface energy per
H. Zhao et al. / Chemical Engineering Science 137 (2015) 412–422
419
25
h D0
20
Measured
λ
.
Atomizer 1 Atomizer 2 Atomizer 3 Atomizer 4 Atomizer 5 Atomizer 6 Atomizer 7 Atomizer 8 Atomizer 9
15 10 5 0
0
5
10
15
Calculated
20
25
λ h . D0
Fig. 11. Comparison of measured wavelength to wavelength predicted by Eq. (3b).
h sheet
airflow
Fig. 12. Sketch of part sheet.
Fig. 9. The wavelength in Christmas tree (cellular) breakup in far field, (Atomizer 4, ul ¼ 2.00 m/s, ug ¼ 110.5 m/s).
Cell generation zone CS2
Cell breakup zone
CS1
10 Atomizer1 Atomizer2 Atomizer3 Atomizer4
d/h
8 6 4 Fig. 10. The breakup structures in far field, (Atomizer 2, ul ¼ 1.44 m/s, ug ¼54.3 m/s).
2
unit mass of liquid sheet is
0
e¼
Es π ðD1 þD2 Þσ L 4σ 2σ ¼ ¼ ¼ ml π D2 D2 Lρ ðD2 D1 Þρl hρl 4
2
1
ð15Þ
l
where L is the length of sheet. When the central air flow disappears, it will be a liquid round cylindrical jet, which can be thought as the extreme state. The surface energy per unit mass of
0.0
0.1
0.2
0.3
0.4
We -0.5 Fig. 13. (a) Sketch of measure of cellular sizes; (b) The dimensionless cellular sizes as a function of We.
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Fig. 14. Photographs of fiber breakup at high air velocity. (a) Atomizer 5, ul ¼0.62m/s, ug ¼102.0m/s, (b) Atomizer 6, ul ¼ 1.55m/s, ug ¼154.7m/s, (c) Atomizer 7, ul ¼ 0.58m/s, ug ¼ 109.5m/s, (d) Atomizer 8, ul ¼ 0.69m/s, ug ¼154.7m/s, (e) Atomizer 9, ul ¼0.53m/s, ug ¼ 131.3m/s.
liquid jet is e0 ¼
Es π D2 σ L 4σ ¼ ¼ ml π D22 Lρl D2 ρl
ð16Þ
4
So the dimensionless transition between thin sheet and thick sheet would be e0 2h ¼ ¼ C4 e D2
ð17Þ
where C 4 is a constant. Experimental results show that Christmas tree (cellular) breakup appears when the dimensionless sheet thickness is small, and fiber breakup appears when the dimensionless sheet thickness is big. For the range of parameters and atomizer geometry studied C 4 ¼ 0:48 was found to agree favorably with experimental data, so the limit is given by h D1 ¼ 0:24 or ¼ 0:52 D2 D2
ð18Þ
In order to have an overview of the different breakup processes taking place over the wide range of liquid and gas conditions, it is useful to establish a regime diagram. Here, an attempt to establish such a diagram has been made. Fig. 15 shows three breakup regimes of annular sheet breakup in the parameter space h/D2– We. It should be noted that the Weber number in our study is defined as We ¼ ρg u2r h=σ . The experimental results of Kendall (1986), Adzic et al. (2001), Sevilla et al. (2005a, 2005b), Choi and Lee (2005) and Zhao et al. (2014c) are also shown in Fig. 15, respectively. The estimated limit Eqs. (14) and (18) which are
shown in Fig. 15 are in well agreement with experimental results and those reports in literature. The Weber number We has a great influence on the limit of bubble (shell) breakup regime, however, the limit between fiber breakup regime and Christmas tree (cellular) breakup regime is hardly affected by We.
4. Conclusions In this paper, the deformation and breakup of annular liquid sheet in a coaxial air stream have been investigated in a wide range of dimensionless sheet thickness and Weber number. The major conclusions are as follows: (1) Due to the morphological difference, the annular liquid sheet breakup could be divided into three regimes: bubble (shell) regime, Christmas tree (cellular) regime and fiber regime. (2) The empirical correlation on wavelength in shell regime and cellular regime was developed from the measured data. And the size of cellular structures is measured and analyzed. The results show that the dimensionless cellular size is proportional to We 0.5, which is consistent with the R–T instability theory. (3) The breakup regime of annular liquid sheet has been made in the parameter space dimensionless sheet thickness and Weber number. The experimental results and those reports in literature are in well agreement with the range of breakup regimes we suggested.
H. Zhao et al. / Chemical Engineering Science 137 (2015) 412–422
ρg σ μl λ λmax
0.5 0.4
421
ambient air density surface tension liquid dynamic viscosity wavelength Rayleigh–Taylor wavelength of the most unstable wave
h/D2
0.3 0.2
Acknowledgments
0.1 0.0 -1 10
0
10
1
2
10
10
3
10
4
10
We Fig. 15. Breakup regimes in the parameter space h/D2–We. Experiment results: ■ Bubble (shell) regime; ○ Christmas tree (Cellular) regime; △ Fiber regime; Predicted critical values: Eq. (14); Eq. (18); Bubble (shell) regime, Kendall (1986); Bubble (shell) regime, Lee and Chen (1991); Bubble (shell) regime, Li and Shen (2001); Bubble (shell) regime, Sevilla et al. (2005a, 2005b); Bubble (shell) regime, Leboucher et al. (2010, 2012, 2014); Christmas tree (Cellular) regime, Lee and Chen (1991); Christmas tree (Cellular) regime, Adzic et al. (2001); Christmas tree (Cellular) regime, Li and Shen (2001); Christmas tree (Cellular) regime, Choi and Lee (2005); Christmas tree (Cellular) regime, Leboucher et al. (2010, 2012, 2014); Fiber regime, Zhao et al. (2014c).
The properties of breakup morphology and fragment distribution in different regimes are different. In order to obtain the desired results of atomization in the industrial scale, the suitable range of nozzle size and operating condition could be determined with the help of the regime map.
Nomenclature a C1 C2 C3 C4 CD d D0 D1 D2 e e0 Es h L ml Re S t Δt ug ul ur We
ρl
This study was supported by the National Natural Science Foundation of China, China (U1402272), Fundamental Research Funds for the Central Universities (WB1314046), and Shanghai Natural Science Foundation, China (15ZR1409500).
acceleration correction factor correction factor correction factor correction factor drag coefficient length scale of cellular structure diameter of central circular orifice inner diameter of coaxial air annular orifice outer diameter of coaxial air annular orifice surface energy per unit mass of liquid sheet surface energy per unit mass of liquid jet surface energy sheet thickness, the width of the annulus of nozzle outlet length of liquid sheet mass of liquid sheet liquid Reynolds number the surface area of the sheet facing the airflow time time interval air velocity liquid velocity relative velocity between the two fluids Weber number liquid density
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Theofanous, T.G., 2011. Aerobreakup of Newtonian and viscoelastic liquids. Annu. Rev. Fluid Mech. 43, 661–690. Varga, C.M., Lasheras, J.C., Hopfinger, E.J., 2003. Initial breakup of a small-diameter liquid jet by a high-speed gas stream. J. Fluid Mech. 497, 405–434. Villermaux, E., 2007. Fragmentation. Annu. Rev. Fluid Mech. 39, 419–446. Wahono, S., Honnery, D., Soria, J., Ghojel, J., 2008. High-speed visualisation of primary break-up of an annular liquid sheet. Exp. Fluids 44, 451–459. Wang, Y., Qiu, L., Reitz, R.D., Diwakar, R., 2014. Simulating cavitating liquid jets using a compressible and equilibrium two-phase flow solver. Int. J. Multiph. Flow 63, 52–67. Xiao, F., Dianat, M., McGuirk, J.J., 2014. LES of turbulent liquid jet primary breakup in turbulent coaxial air flow. Int. J. Multiph. Flow 60, 103–118. 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, 114103. 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. Multiph. Flow 37, 530–534. Zhao, H., Liu, H.F., Xu, J.L., Li, W.F., Cheng, W., 2012. Breakup and atomization of a round coal water slurry jet by an annular air jet. Chem. Eng. Sci. 78, 63–74. Zhao, H., Liu, H.F., Xu, J.L., Li, W.F., Lin, K.F., 2013. Temporal properties of secondary drop breakup in the bag–stamen breakup regime. Phys. Fluids 25, 054102. Zhao, H., Liu, H.F., Tian, X.S., Xu, J.L., Li, W.F., Lin, K.F., 2014a. Influence of atomizer exit area ratio on the breakup morphology of coaxial air and round water jets. AIChE J. 60, 2335–2345. Zhao, H., Hou, Y.B., Liu, H.F., Tian, X.S., Xu, J.L., Li, W.F., Liu, Y., Wu, F.Y., Zhang, J., Lin, K.F., 2014b. Influence of rheological properties on air-blast atomization of coal water slurry. J. Non-Newton. Fluid Mech. 211, 1–15. Zhao, H., Liu, H.F., Tian, X.S., Xu, J.L., Li, W.F., Lin, K.F., 2014c. Outer ligamentmediated spray formation of annular liquid sheet by an inner round air stream. Exp. Fluids 55 (8), 1–13.
Contents lists available at ScienceDirect
Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Breakup morphology of annular liquid sheet with an inner round air stream Hui Zhao a,b, Jian-Liang Xu a,b, Ju-Hui Wu a,b, Wei-Feng Li a,b, Hai-Feng Liu a,b,n a Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, East China University of Science and Technology, Shanghai 200237, People's Republic of China b Shanghai Engineering Research Center of Coal Gasification, East China University of Science and Technology, Shanghai 200237, People's Republic of China
H I G H L I G H T S
Annular liquid sheet breakup can be divided into shell, cellular and fiber regime. Dimensionless cellular size is proportional to We 0.5. Breakup regime of annular liquid sheet has been made in h/D2–We map.
art ic l e i nf o
a b s t r a c t
Article history: Received 5 March 2015 Received in revised form 9 June 2015 Accepted 21 June 2015 Available online 9 July 2015
Experiments were performed on the deformation and breakup of annular liquid sheet of nine coaxial twin-fluid air-blast atomizers with water–air systems by using a high speed camera. Due to the morphological difference, the annular sheet breakup could be classified into three regimes, which were bubble (shell) breakup, Christmas tree (cellular) breakup and fiber breakup. The roles of atomizer size and Rayleigh–Taylor instability in the annular sheet breakup were studied. The correlations on the instability wavelength and the size of cellular structure were deduced. The results showed that the dimensionless cellular size was proportional to We 0.5, which were in good agreement with the experimental results. In order to have an overview of the different breakup mechanisms taking place over the wide range, we suggested categorizing these breakup regimes in a Weber number and dimensionless sheet thickness map. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Air-blast Coaxial Sprays Atomization Breakup
1. Introduction The transformation of liquid into spray is of importance in agriculture, meteorology and many industrial processes. Liquid atomization is also a fundamental research topic in multiphase flow, which has been studied extensively both theoretically and experimentally (Wang et al., 2014; Kulkarni and Sojka, 2014; Kekesi et al., 2014; Prakash et al., 2014; Xiao et al., 2014). As a common type of atomization, coaxial jets are utilized in a number of devices, including as burners in industrial furnaces and gasifiers, propellant injectors in rockets, and the exhaust of modern large bypass turbofan engines (Schumaker and Driscoll, 2012). In these applications, the complex near-field structure plays a critical role in determining how well the system performs (Lasheras and
n Corresponding author at: Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, East China University of Science and Technology, Shanghai 200237, People's Republic of China. Tel.: þ 86 21 64251418. E-mail address: hfl[email protected] (H.-F. Liu).
http://dx.doi.org/10.1016/j.ces.2015.06.062 0009-2509/& 2015 Elsevier Ltd. All rights reserved.
Hopfinger, 2000; Villermaux, 2007; Gorokhovski and Herrmann, 2008; Dumouchel, 2008; Theofanous, 2011). There are two basic types on coaxial gas–liquid jets: (I) a cylindrical liquid jet surrounded by an annular gaseous stream and (II) an annular liquid sheet with an inner round gaseous stream. The properties of above two basic types are the foundation of three or multi-channels coaxial jets (Carvalho and Heitor, 1998; Wahono et al., 2008; Duke et al., 2010, 2012; Liu et al., 2006; Leboucher et al., 2010, 2012, 2014), which are also helpful in the research of monodisperse microbubbling by capillary flow focusing (Gañán-Calvo and Gordillo , 2001; Gañán-Calvo, 2004, GañánCalvo et al., 2006). In this paper, we focus on the latter type (II). Annular liquid sheets are typically generated with circular slit nozzles or by diverging nozzle configurations which are common in many applications. So the distortion and disintegration of annular liquid sheets are of both fundamental and practical interest. The theoretical analysis on the instability of an annular liquid jet has been studied by Meyer and Weihs (1987), Oguz and Prosperetti (1993), Shen and Li (1996), Mehring and Sirignano (2000a, 2000b), Sevilla
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Table 1 The ranges of experimental parameters in coaxial jets, type (II).
Kendall (1986) Lee and Chen (1991) Martínez-Bazán et al. (1999a, 1999b) Adzic et al. (2001) Li and Shen (2001) Choi and Lee (2005) Sevilla et al. (2005a, 2005b) Leboucher et al. (2010, 2012, 2014) This study
Gas velocity (m/s)
Liquid velocity (m/s)
Dimensionless sheet thickness (h/D2), where h is the width of the annulus, D2 is the outside diameter of annulus exit.
1.5–13.7 5.5–32.0 1.07, 4.48, 8.88, 9.84 0–40 3.85–45 136–283 2.7–58.5 25–155 4.4–154.7
0.5–4.75 0.96 17 0.86 1.73–3.47 1.6–21.5 1.85–9.65 2 0.17–3.03
0.19 0.21 0.30, 0.40, 0.43 0.11 0.024 0.04–0.13 0.36, 0.39, 0.42 0.125 0.06–0.37
liquid liquid air
liquid liquid air
liquid liquid air
Fig. 1. Simple schematic diagrams illustrating the shape of the different regimes. (a) bubble breakup (shell breakup) (b) Christmas tree breakup (cellular breakup) (c) fiber breakup.
et al. (2002), Chen et al. (2003) etc. The experimental characteristics of annular sheet distortion and disintegration have also been investigated, whose atomizer sizes are as shown in Table 1. These data show various breakup morphologies and properties of coaxial jets, which are very interesting and useful. Kendall (1986) observed the bubble (shell) regime at low air velocity and studied the formation of liquid shells firstly. The breakup morphologies of annular sheet were also observed by Lee and Chen (1991), Martínez-Bazán et al. (1999a, 1999b), Adzic et al. (2001), Li and Shen (2001), Choi and Lee (2005), Sevilla et al. (2005a, 2005b) and Leboucher et al. (2010, 2012, 2014). A series of simple schematic diagrams illustrating the shape of the different regimes are shown in Fig. 1.
There are some high-quality papers on the atomization of liquid annulus around a central gas core. However, some papers only focus on the single breakup regime; other papers only focus on the single nozzle. The influence of atomizer sizes on breakup morphology and transition of different regimes is also absent. There are some correlations on the ranges of the breakup regimes in the literature. Unfortunately, these correlations are purely empirical or apply to the single nozzle. To overcome this, a theoretical model is needed which is based on the underlying physics. Here in order to have an overview of the different breakup mechanisms taking place over the wide ranges, this paper focuses on the ranges of different breakup regimes which can apply to
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Table 2 Summary of experimental conditions and parameters. Atomizer no.
air water
water
1 2 3 4 5 6 7 8 9
D0 (mm)
D1 (mm)
D2 (mm)
9.02 9.02 4.08 2.00 5.10 2.00 6.96 2.00 4.02
11.08 11.14 6.28 4.24 7.12 4.24 9.04 4.24 6.08
12.56 14.92 9.30 7.30 14.92 9.30 23.88 14.92 23.88
D1
0.06 0.13 0.16 0.21 0.26 0.27 0.31 0.36 0.37
Water velocity ul (m/s)
Air velocity ug (m/s)
1.01–3.03 0.18–1.44 0.75–3.01 1.00–3.00 0.21–0.82 0.52–1.55 0.29–0.58 0.17–0.69 0.27–0.53
4.4–86.9 6.5–76.1 5.3–138.1 22.1–154.7 20.4–102.0 22.1–154.7 18.3–109.5 22.1–154.7 21.9–131.3
3
2
D0
h/ D2
Water
5 2
4
1
D2 Fig. 2. Experimental atomizer configuration.
1-Air Blower 2-Flow Meter 3-Experimental Atomizer 4-High-speed Camera 5-Computer
Fig. 3. Flow chart of experiment process.
different nozzles. The influence of atomizer sizes on breakup morphology of annular liquid sheet with an inner round air stream has been studied in detail. We deduce the simplified theoretical formulas for predicting the transitions between breakup modes, which agrees well with our experimental results and the data of the literature. As discussed above, the present research is aimed at better understanding of the breakup morphologies and mechanisms of annular liquid sheet, especial for the effect of atomizer sizes. Some correlations are also reported for predicting deformation and breakup characteristics of annular sheet. In order to have an overview of the different breakup processes taking place over the wide range, an attempt to establish a diagram on various breakup regimes has been made.
2. Experimental apparatus and methodology The coaxial two-fluid air-blast atomizer geometry is shown schematically in Fig. 2, which is similar to our earlier work (Zhao et al., 2012, 2014a–c), consisting of the geometrically simple case of a round air jet surrounded by a co-flowing annular liquid stream. D0 is the internal diameter of central orifice exit, D1 is the internal diameter of annulus exit, and D2 is the outside diameter of annulus exit. There are nine kinds of atomizers used in this experiment, and their dimensions and experimental conditions are shown in Table 2. The results of atomizer diameter reported in Table 2 are measured by the Vernier caliper, whose uncertainty is 70.02 mm. Gas phase air passed through the central passage, while the liquid phase water flow passed through the annular space. The experiments were conducted at atmospheric pressure and room temperature, and the working fluids were water and air. The experimental apparatus is sketched in Fig. 3. The gas and liquid velocities are obtained by the flow meters. The type of flow meters employed is LZB glass tube rotameter flow meter, whose uncertainty is 71:5%. The high-speed digital camera (Fastcam APX-RS, Photron limited) was used combined with a continuous 1 kW halogen light. The digital images are analyzed and measured with
NIH Image software ImageJ, which is often used to analyze digital images of atomization in the literature. There are more than 1000 images recorded and analyzed per case. The width of the annulus in the exit is h ¼ ðD2 D1 Þ=2.
3. Results and discussion At low air velocity all atomizers are in bubble (shell) regime, whose experimental photographs are shown in Fig. 4. An additional feature of bubble (shell) regime is the formation of small ligaments as shown in Fig. 5, which is also observed by Li and Shen (2001). The small ligaments eject usually right after the bubble pinches off. We suggest that this phenomenon is due to the impingement of liquid sheet. As shown in Fig. 6, these small ligaments appear in different atomizers, which is a common phenomenon. At high air velocity, when the sheet is thin (The transitions between “thin” and “thick” sheets is ðh=D2 Þ ¼ 0:24, the corresponding analysis is close to the part near Fig. 15), the cell-like structures appear in the surface of annular liquid, which is shown in Fig. 7. This regime due to the striking appearance of cells is termed the Christmas tree regime. The cause of Christmas tree (cellular) regime is due to R–T instability, which is similar to the bag breakup in secondary breakup and the membrane breakup in air-blast cylindrical jets. The bag or membrane structures often appear in the breakup process of Christmas tree (cellular) regime as shown in Fig. 7(b). This Christmas tree (cellular) regime was mentioned by Adzic et al. (2001), Choi and Lee (2005) and Leboucher et al. (2010, 2012, 2014). This similar phenomenon was also been found in the breakup of planar liquid sheet (Stapper and Samuelsen, 1990; Stapper et al., 1992; Park et al., 2004). This illustrates that the cellular structure is a common phenomenon in both flat sheet and annular sheet experiments. Besides bubble (shell) breakup, wave structure can also be found in Christmas tree (cellular) breakup, whose evolvement is illustrated in Figs. 8 and 9. The wave structure is the primary destabilization of annular liquid sheet. The evolvement of cell-like structures is as shown in Fig. 8. At initial stage, the surface of liquid
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Fig. 4. Photographs of bubble (shell) breakup at low air velocity. (a) Atomizer 1, ul ¼ 1.01m/s, ug ¼ 4.4m/s, (b) Atomizer 2, ul ¼0.36m/s, ug ¼ 10.9m/s, (c) Atomizer 3, ul ¼ 0.75m/s, ug ¼5.3m/s, (d) Atomizer 4, ul ¼1.00m/s, ug ¼ 22.1m/s, (e) Atomizer 5, ul ¼ 0.21m/s, ug ¼ 20.4m/s. (f) Atomizer 6, ul ¼ 0.52m/s, ug ¼ 22.1m/s, (g) Atomizer 7, ul ¼ 0.51m/s, ug ¼ 18.3m/s, (h) Atomizer 8, ul ¼ 0.17m/s, ug ¼ 22.1m/s, (i) Atomizer 9, ul ¼ 0.27m/s,ug ¼ 21.9m/s.
impingement of liquid sheet
small ligaments
Fig. 5. The impact of annular liquid sheet gives rise to small ligaments. The interval separating each snapshot of this sequence is 2.68 ms. (Atomizer 2, ul ¼ 0.18 m/s, ug ¼ 6.5 m/s).
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Atomizer 1, ul =1.01m/s, ug
Atomizer 3, ul =1.50m/s, ug
Atomizer 6, ul =0.52m/s, ug
=4.4m/s
=10.6m/s
=22.1m/s
Atomizer 7, ul =0.29m/s, ug
Atomizer 8, ul =0.17m/s, ug
Atomizer 9, ul =0.40m/s, ug
=18.3m/s
=22.1m/s
=21.9m/s
Fig. 6. The impingement of annular liquid sheet gives rise to small ligaments which are shown in circle.
sheet near the nozzle outlet is smooth. Then under the action of airflow, the liquid sheet expands and the cell-like structures are formatted gradually. The breakup of cell would lead to the breakup of liquid sheet. Finally near the nozzle outlet there would be next initial stage. So in this breakup mode the cell-like structures play an important role in the breakup of annular liquid sheet with an inner round air stream. Fig. 8 shows experimental photographs of Christmas tree (cellular) breakup whose time interval is 1.33 ms. Fig. 10 shows the breakup structure in far field. Due to the surface tension, the annular sheet will contract if there is no airflow. This will lead to the decrease of airflow export, so the airflow has to push the sheet to move. This sheet acceleration results from the push of airflow. So the cellular structure is the secondary destabilization of annular liquid sheet. In the study of annular sheet, there are some different definitions of the Weber number, the one we used in this paper is given by Meyer and Weihs (1987) (the symbol is Wh in their paper)
ρg u2r h ; We ¼ σ
ð1Þ
where σ is the surface tension, ur is the relative velocity. The liquid Reynolds number is defined by Re ¼
ρl u l h ; μl
ð2Þ
where μl is the viscosity of liquid. Following the dimensionless wavelength of Lozano et al. (2005), we obtained an empirical correlation on the wavelength of bubble (shell) breakup and Christmas tree (cellular) breakup. Based on the multivariate analysis performed on
the data, the best fit correlation of present measurements is given by 0:64 λ ¼ 12:29D0:36 Re0:09 We 0:36 ; 0 h
ð3aÞ
or 0:14 λ h pffiffiffiffiffiffiffiffiffiffiffiffi ¼ 12:29 Re0:09 We 0:36 D0 h UD0
ð3bÞ
The correlation coefficient of the fit (Eqs. 3a and 3b) is 0.95. And the simpler equation without Re number would still sufficiently capture the measured results, 0:64 λ ¼ 22:98D0:36 We 0:34 ; 0 h
ð3cÞ
or 0:14 λ h pffiffiffiffiffiffiffiffiffiffiffiffi ¼ 22:98 We 0:34 D0 h UD0
ð3dÞ
The correlation coefficient of the fit (Eqs. 3c and 3d) is 0.93. Wavelength value calculated using this correlation is plotted against the measured values in Fig. 11. Here the wavelength is the perpendicular distance between two wave crests on the liquid sheet interface near the nozzle outlet. The wavelength is obtained by the help of NIH Image software ImageJ, which is a public domain, Java-based image processing program. ImageJ can display, edit, analyze, process, save, and print images. The Rayleigh–Taylor (R–T) instability is the instability of an interface between two fluids of different densities, which occurs when the lighter fluid is pushing the heavier fluid (Rayleigh, 1883; Taylor, 1950). Recently R–T instability is often used in the study of atomization (Varga et al., 2003; Marmottant and Villermaux, 2004; Zhao et al.,
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Fig. 7. Photographs of Christmas tree (cellular) breakup at high air velocity. (a) Atomizer 1, ul ¼2.02m/s, ug ¼ 65.2m/s, (b) Atomizer 2, ul ¼1.08m/s, ug ¼ 65.2m/s, (c) Atomizer 3, ul ¼ 1.50m/s, ug ¼ 95.6m/s, (d) Atomizer 4, ul ¼3.00m/s, ug ¼ 154.7m/s.
2010, 2011, 2013). Here the lighter fluid is airflow; the heavier fluid is water sheet. The push of high-speed airflow triggers R–T instability, producing cell-like structures. The diameter of circular perforations represents the typical length scale of cellular structures, which should be equal to the wavelength of R–T instability. A part of sheet is taken as the analysis object which is shown in Fig. 12. The simplified force balance on this part sheet can be written as: 1 F ¼ C 1 C D ρg u2r S ¼ ml a; 2
ð4Þ
ð5Þ
By combining Eqs. (4) and (5), the acceleration of the sheet is a¼
C 1 C D ρg u2r 2hρl
ð8Þ As the length scale of cellular structures can be estimated by d p λmax
ð9Þ
By combining Eqs. (8) and (9), the calculation is
where C D is the drag coefficient, S is the surface area of the sheet facing the airflow, ml and a are the mass and acceleration of the sheet, respectively. As the airflow and the sheet are not perpendicular, a correction factor C 1 is introduced. The mass of the sheet is ml ¼ Shρl
By combining Eqs. (6) and (7), we can obtain sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3σ 6σ h 6h 6 ¼ 2π λmax ¼ 2π ¼ 2π ¼ 2π h C 1 C D We C 1 C D We ρl a C 1 C D ρg u2r
ð6Þ
As the classic linear stability analysis (Chandrasekhar, 1961), the R–T wavelength of the most unstable wave is expressed as: sffiffiffiffiffiffiffi 3σ ; ð7Þ λmax ¼ 2π ρl a
d ¼ C 2 We 0:5 ; h
ð10Þ
where C2 is a coefficient. Here d is the mean of two mutually perpendicular lengths of cell. The cellular sizes are obtained by the photographs as shown in Fig. 13(a), which is the average value of CS1 and CS2. The experimental results are shown in Fig. 13, which is in well agreement with the R–T instability theory. The line in Fig. 13 is the following theoretical fit: d ¼ 19:91We 0:5 h
ð11Þ
The correlation coefficient of the fit is 0.97. By the theoretical analysis of perturbation growth rate Meyer and Weihs (1987) found that when the annulus thickness was big, the annular jet behaves liked a full liquid jet; when the annulus thickness was small, the jet behaves liked a two-dimensional liquid sheet. We found in our experiment that on the deformation
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Fig. 8. The wave in Christmas tree (cellular) breakup in near field, Δt¼ 0.67 ms. (Atomizer 4, ul ¼ 2.00 m/s, ug ¼ 110.5 m/s). (a)t, (b)t þ Δt, (c)t þ 2Δt, (d)tþ 3Δt, (e)t þ 4Δt, (f) t þ5Δt, (g)t þ6Δt, (h)t þ 7Δt.
and breakup morphology of annular sheet there was the similar phenomenon. When the sheet is thick, the surface of sheet displays transverse azimuthal modulations instead of cellular structures (Zhao et al., 2014c). Above a critical air velocity, the digitations appear which is shown in Fig. 14. So it is in the fiber breakup regime. With the increase of air velocity, the number of digitations also increases gradually and eventually generates in large numbers of liquid ligaments. The Christmas tree regime identified by Leboucher et al. (2010, 2012, 2014) is the cellular regime. The name of Christmas tree regime focuses on the whole structure of spray, while the name of cellular regime focuses on the local structure near the nozzle outlet. And the fiber regime is different from the Christmas tree regime, which is another new breakup regime. The appearance of spray in the fiber regime is not close to the Christmas tree. In the fiber regime the sheet bursts suddenly, and then it generates plenty of jet (ligament) structures irregularly. Due to the similarity between the primary and secondary breakup mechanisms, the drop breakup mechanism in secondary breakup can be used to study the annular sheet breakup. According to “Rayleigh–Taylor piercing” mechanism (Theofanous, 2011) or “the combined R–T/aerodynamic drag” mechanism (Guildenbecher et al., 2009), the influence of wave number (the number of R–T wave in the characteristic scale) on the appearance of liquid breakup is great. When the wave number is smaller than a constant, the instability of interface is negligible; while when the
wave number is bigger than the constant, the instability of interface will be remarkable. Near the nozzle outlet, the fiber and cell structures are the feature of the instability of interface. So we can obtain the boundary of bubble (shell) regime, the transition is expected when D2
λmax
¼ C3;
ð12Þ
where C 3 is a constant. By combining Eqs. (9), (10) and (12), we can obtain h 1 ¼ We0:5 D2 C 2 C 3
ð13Þ
For the range of parameters and atomizer geometry studied C 2 U C 3 ¼ 25 was found to agree favorably with experimental data, so the limit of bubble (shell) breakup is given by h 1 ¼ We0:5 D2 25
ð14aÞ
So if there is D2 We0:5 =h o 25;
ð14bÞ
the shell regime exists. The surface energy per unit mass of thin sheet is bigger than thick sheet. When the energy of liquid is large enough, liquid sheet will break up easily. Thin sheet expands and breaks up easily; however thick sheet expands initially then contracts finally, which breaks up hardly. The surface energy per
H. Zhao et al. / Chemical Engineering Science 137 (2015) 412–422
419
25
h D0
20
Measured
λ
.
Atomizer 1 Atomizer 2 Atomizer 3 Atomizer 4 Atomizer 5 Atomizer 6 Atomizer 7 Atomizer 8 Atomizer 9
15 10 5 0
0
5
10
15
Calculated
20
25
λ h . D0
Fig. 11. Comparison of measured wavelength to wavelength predicted by Eq. (3b).
h sheet
airflow
Fig. 12. Sketch of part sheet.
Fig. 9. The wavelength in Christmas tree (cellular) breakup in far field, (Atomizer 4, ul ¼ 2.00 m/s, ug ¼ 110.5 m/s).
Cell generation zone CS2
Cell breakup zone
CS1
10 Atomizer1 Atomizer2 Atomizer3 Atomizer4
d/h
8 6 4 Fig. 10. The breakup structures in far field, (Atomizer 2, ul ¼ 1.44 m/s, ug ¼54.3 m/s).
2
unit mass of liquid sheet is
0
e¼
Es π ðD1 þD2 Þσ L 4σ 2σ ¼ ¼ ¼ ml π D2 D2 Lρ ðD2 D1 Þρl hρl 4
2
1
ð15Þ
l
where L is the length of sheet. When the central air flow disappears, it will be a liquid round cylindrical jet, which can be thought as the extreme state. The surface energy per unit mass of
0.0
0.1
0.2
0.3
0.4
We -0.5 Fig. 13. (a) Sketch of measure of cellular sizes; (b) The dimensionless cellular sizes as a function of We.
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Fig. 14. Photographs of fiber breakup at high air velocity. (a) Atomizer 5, ul ¼0.62m/s, ug ¼102.0m/s, (b) Atomizer 6, ul ¼ 1.55m/s, ug ¼154.7m/s, (c) Atomizer 7, ul ¼ 0.58m/s, ug ¼ 109.5m/s, (d) Atomizer 8, ul ¼ 0.69m/s, ug ¼154.7m/s, (e) Atomizer 9, ul ¼0.53m/s, ug ¼ 131.3m/s.
liquid jet is e0 ¼
Es π D2 σ L 4σ ¼ ¼ ml π D22 Lρl D2 ρl
ð16Þ
4
So the dimensionless transition between thin sheet and thick sheet would be e0 2h ¼ ¼ C4 e D2
ð17Þ
where C 4 is a constant. Experimental results show that Christmas tree (cellular) breakup appears when the dimensionless sheet thickness is small, and fiber breakup appears when the dimensionless sheet thickness is big. For the range of parameters and atomizer geometry studied C 4 ¼ 0:48 was found to agree favorably with experimental data, so the limit is given by h D1 ¼ 0:24 or ¼ 0:52 D2 D2
ð18Þ
In order to have an overview of the different breakup processes taking place over the wide range of liquid and gas conditions, it is useful to establish a regime diagram. Here, an attempt to establish such a diagram has been made. Fig. 15 shows three breakup regimes of annular sheet breakup in the parameter space h/D2– We. It should be noted that the Weber number in our study is defined as We ¼ ρg u2r h=σ . The experimental results of Kendall (1986), Adzic et al. (2001), Sevilla et al. (2005a, 2005b), Choi and Lee (2005) and Zhao et al. (2014c) are also shown in Fig. 15, respectively. The estimated limit Eqs. (14) and (18) which are
shown in Fig. 15 are in well agreement with experimental results and those reports in literature. The Weber number We has a great influence on the limit of bubble (shell) breakup regime, however, the limit between fiber breakup regime and Christmas tree (cellular) breakup regime is hardly affected by We.
4. Conclusions In this paper, the deformation and breakup of annular liquid sheet in a coaxial air stream have been investigated in a wide range of dimensionless sheet thickness and Weber number. The major conclusions are as follows: (1) Due to the morphological difference, the annular liquid sheet breakup could be divided into three regimes: bubble (shell) regime, Christmas tree (cellular) regime and fiber regime. (2) The empirical correlation on wavelength in shell regime and cellular regime was developed from the measured data. And the size of cellular structures is measured and analyzed. The results show that the dimensionless cellular size is proportional to We 0.5, which is consistent with the R–T instability theory. (3) The breakup regime of annular liquid sheet has been made in the parameter space dimensionless sheet thickness and Weber number. The experimental results and those reports in literature are in well agreement with the range of breakup regimes we suggested.
H. Zhao et al. / Chemical Engineering Science 137 (2015) 412–422
ρg σ μl λ λmax
0.5 0.4
421
ambient air density surface tension liquid dynamic viscosity wavelength Rayleigh–Taylor wavelength of the most unstable wave
h/D2
0.3 0.2
Acknowledgments
0.1 0.0 -1 10
0
10
1
2
10
10
3
10
4
10
We Fig. 15. Breakup regimes in the parameter space h/D2–We. Experiment results: ■ Bubble (shell) regime; ○ Christmas tree (Cellular) regime; △ Fiber regime; Predicted critical values: Eq. (14); Eq. (18); Bubble (shell) regime, Kendall (1986); Bubble (shell) regime, Lee and Chen (1991); Bubble (shell) regime, Li and Shen (2001); Bubble (shell) regime, Sevilla et al. (2005a, 2005b); Bubble (shell) regime, Leboucher et al. (2010, 2012, 2014); Christmas tree (Cellular) regime, Lee and Chen (1991); Christmas tree (Cellular) regime, Adzic et al. (2001); Christmas tree (Cellular) regime, Li and Shen (2001); Christmas tree (Cellular) regime, Choi and Lee (2005); Christmas tree (Cellular) regime, Leboucher et al. (2010, 2012, 2014); Fiber regime, Zhao et al. (2014c).
The properties of breakup morphology and fragment distribution in different regimes are different. In order to obtain the desired results of atomization in the industrial scale, the suitable range of nozzle size and operating condition could be determined with the help of the regime map.
Nomenclature a C1 C2 C3 C4 CD d D0 D1 D2 e e0 Es h L ml Re S t Δt ug ul ur We
ρl
This study was supported by the National Natural Science Foundation of China, China (U1402272), Fundamental Research Funds for the Central Universities (WB1314046), and Shanghai Natural Science Foundation, China (15ZR1409500).
acceleration correction factor correction factor correction factor correction factor drag coefficient length scale of cellular structure diameter of central circular orifice inner diameter of coaxial air annular orifice outer diameter of coaxial air annular orifice surface energy per unit mass of liquid sheet surface energy per unit mass of liquid jet surface energy sheet thickness, the width of the annulus of nozzle outlet length of liquid sheet mass of liquid sheet liquid Reynolds number the surface area of the sheet facing the airflow time time interval air velocity liquid velocity relative velocity between the two fluids Weber number liquid density
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