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Effect of viscosity and surface tension on breakup and coalescence of bicomponent sprays
Chemical Engineering Science 131 (2015) 243–255
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Effect of viscosity and surface tension on breakup and coalescence of bicomponent sprays Ashkan Davanlou a, Joshua D. Lee a, Saptarshi Basu b, Ranganathan Kumar a,n a b
Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, USA Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
H I G H L I G H T S
G R A P H I C A L
A B S T R A C T
The effects of surface tension and viscosity are studied on spray behavior. Surface tension effect is more dominant at high Reynolds numbers. The spray cone angle increases with increase in pressure. At high pressures, viscous fluids have larger diameters in breakup zones. A correlation was developed to predict the SMD.
art ic l e i nf o
a b s t r a c t
Article history: Received 7 November 2014 Received in revised form 15 March 2015 Accepted 22 March 2015 Available online 14 April 2015
This work deals with an experimental study of the breakup characteristics of liquids with different surface tension and viscosity from a hollow cone hydraulic injector nozzle induced by pressure-swirl. The experiments were conducted at Reynolds numbers Rep ¼ 9500–23,000. The surface tension and viscosity of the surrogate fuels were altered from 72 to 30 mN/m and 1.1 to 1.6 mN s/m2, respectively. High speed photography and Phase Doppler Particle Anemometry were utilized to study the atomization process. Velocity and drop size measurements of the spray using PDPA in both axial and radial directions indicate a dependency on surface tension. However, these effects are dominant only at low Reynolds numbers and are negligible at high Reynolds number. Downstream of the nozzle, coalescence of droplets due to collision was also found to be significant and the diameters were compared for different liquids. For viscous fluids up to 1.6 cP, the independent effects of viscosity and injection pressure are studied. In general, the spray cone angle increases with increase in pressure. At high pressures, an increase in viscosity leads to higher drop sizes following primary and secondary breakup compared to water. This study will extend our understanding of surrogate fuel film breakup and highlight the importance of long and short wavelength instabilities. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Atomization Multiphase flow Pressure-swirl nozzle Coalescence Breakup Phase Doppler Anemometry
1. Introduction The most common atomizer used in the IC and aero-engines is the pressure-swirl nozzle (Simplex nozzle). Simplex nozzle has a swirl chamber that forces the liquid to leave the nozzle as an annular sheet. The sheet subsequently spreads out radially
n
Corresponding author. E-mail address: [email protected] (R. Kumar).
http://dx.doi.org/10.1016/j.ces.2015.03.057 0009-2509/& 2015 Elsevier Ltd. All rights reserved.
through a circular orifice and forms a hollow cone spray of finite film thickness (Lefebvre, 1989). The ejected liquid film undergoes different types of instabilities to disintegrate into ligaments and eventually droplets. In a simplex nozzle, with increase in injection pressure, the spray characteristics evolves through four stages of development; dribble stage, distorted pencil stage, onion stage, and Tulip stage (Lefebvre, 1989), where the last three stages are usually dominated by long wavelength film breakup. Once the spray becomes fully developed, short wavelength film breakup becomes dominant. This was shown analytically (Senecal et al.,
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Fig. 1. Experimental setup.
1999; Schmidt et al., 1999), using a linear instability analysis which allowed for the prediction of film length based on Weber number. Once the Kelvin–Helmholtz instabilities attain the maximum growth, the liquid sheet will shear off to produce liquid ligaments beginning the onset of the breakup process (Saha et al., 2012). Rangel and Sirignano (1988) used vortex-sheet discretization approach to investigate the effect of surface tension and density ratio on nonlinear growth of Kelvin–Helmholtz instability. A few articles have reviewed theories of distortion and disintegration of liquid jets (Senecal et al., 1999; Lin and Reitz, 1998; Sirignano and Mehring, 2000; Lasheras et al., 1998; Lasheras and Hopfinger, 2000; Dumouchel, 2008). The role of surfactants in coalescence of viscous drops is studied by Lu and Corvalan (2012). The breakup process consists of two steps: (a) a primary breakup regime induced by hydrodynamic instabilities and relatively large drag forces that cause the formation of ligaments or other irregular liquid elements and (b) a secondary breakup regime which is caused by aerodynamic instabilities resulting in larger droplets deforming and breaking up into smaller daughter droplets (Saha et al., 2012). The secondary breakup mechanism progresses until the aerodynamic breakup time becomes significantly large (mainly due to small droplet size and lower relative velocity), leading to higher coalescence probability. This increased coalescence change the spray characteristics exhibited by an increase in the average droplet size (Saha et al., 2012). In addition to breakup and coalescence, hollow cone sprays also display non-homogeneity in droplet number distribution in all spatial directions. Normally, dispersion of droplets occurs due to swirl induced centrifuging as well as large scale vortical structures in the surrounding gas flow field. Clark (1988) extended the Taylor’s model for drop breakup in a turbulent flow and suggested that drop size, viscosity and interfacial tension may influence the critical Weber number. Research performed in the last decade has been focused on developing and improving the numerical models which predict
Table 1 Liquid properties. Liquids
Surface tension (mN/m)
Density (kg/m3)
Dynamic viscosity (Ns/m2) 10 3
Water S1 S2 S3 V1 V2
72 60 48 30 71 69
958 962 955 962 955 954
1.11 1.13 1.14 1.15 1.3 1.6
the droplet distribution profiles for liquids. Experimental studies in swirling flows have reported contradictory results over the last few years (Shi and Kleinstreuer, 2007). More fundamental experimental works were conducted using optical diagnostics with water as the main fluid at different pressures (Saha et al., 2012; Davanlou et al., 2013). Ayres et al. (2001) developed a mathematical model to predict the joint distribution for both size and velocity of the droplets in sprays. Belhadef et al. (2012) developed an Eulerian model for liquid sheet atomization at high Weber numbers and Reynolds numbers. They validated their numerical results with Phase Doppler Anemometry (PDA). One of the key reasons for utilizing a simplex nozzle is the uniform distribution of liquid that is generated after primary breakup. This uniform distribution helps increase overall combustion efficiency in IC and aero-engines. Unfortunately, IC and aeroengines use hydrocarbon fuels with wide variations in thermophysical properties like surface tension, density, vapor pressure and viscosity. In fact, new generations of bio-fuels are highly viscous and multicomponent in nature. For this reason, the breakup and coalescence characteristics need to be investigated in more detail with liquids presenting starkly different physical
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Fig. 2. Change of spray angle for liquids S1, S2 and S3 at three pressures of 3, 7 and 14 bar.
Table 2 Comparison between two methods of spray edge detection. P (bar)
Image processing method (1)
Data rate method (2)
Difference between 1 and 2 (in %)
5 10 15 20
49.2217 0.5 65.1117 0.5 70.4717 0.5 75.8517 0.5
47.31 7 1 63.21 7 1 681 7 1 72.91 7 1
3.90 2.93 3.50 3.89
properties like surface tension and viscosity but in simple surrogate fluids first. The literature is limited in the experimental investigation of spray characteristics. Some fundamental research has been done to investigate the effects of various system parameters, i.e. viscosity, density, and surface tension on the distribution of droplet diameters and velocities (Park et al., 2009; Kim et al., 2008; Payri et al., 2008; Yao et al., 2012). For Newtonian liquids, it has been reported that system parameters, such as viscosity, density and nozzle diameter affect the spreading (cone) angle and breakup (Dorfner et al., 1995). Other studies investigated
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the impact of emulsification (Bolszo et al., 2010) or properties on pressure swirl atomization (Fan et al., 2014). Fan et al. (2014) investigated the effect of kinematic viscosity on droplet size distribution in Jetropha oil spray using laser diffraction method. They found five phases for spray cone evolution with viscosity variation, however, other aspects of breakup and coalescence of droplets were not investigated. In summary, even though studies have shown significant effect of liquid thermo-physical properties on the spray, these studies did not fully characterize the spray or provide an understanding of transition from secondary breakup to coalescence when physical properties are changed. Thus, the fundamentals of spray dynamics, such as spray formation, liquid breakup length, and droplet breakup regimes need further investigation. The main objective of this paper is to conduct experiments to understand the individual effects of surface tension and viscosity on the liquid breakup regimes including droplet coalescence compared to the base fluid, water. Droplet diameter and velocity profiles in the axial and radial directions will be characterized at different Reynolds numbers at different injection pressures for different surface tension and viscosity. This study will extend our understanding of surrogate fuel film breakup and highlight the importance of long and short wavelength instabilities for low and high Weber number ranges, respectively. The dependence of liquid breakup characteristics will be validated with experimental data for the first time in the context of high pressure swirling flow. Coalescence probability and swirl induced dispersion will also be studied in conjunction with breakup to provide a holistic view of droplet dynamics in these types of pressure atomizers for low surface tension and high viscosity fluids. Finally, a correlation will be provided for the new data based on the existing correlation given by Wang and Lefebvre (1987).
the Brewster effect on the surface of the liquid droplet for first order refraction angle. For measuring the spray angle and other spray characteristics a high speed Phantom V12.1 camera was used. Images were captured at 28,000 fps at full resolution. More details of the experimental setup can be found in Saha et al. (2012). The data reported in this section is recorded on the vertical plane (Z-axis) which passes through the center of the nozzle. For PDPA to make simultaneous diameter and velocity measurement, the two laser beams were allowed to intersect directly below and in the center of the nozzle exit by moving the nozzle with the traverse system. In order to gather data at different axial or radial distances with respect to the tip, the nozzle was moved using the traverse system without disturbing the optical setup. The autoclave was pressurized with both liquid solutions and air ranging from 0.3 to 2 MPa and was allowed to equilibrate for 20 min. The liquid was then injected into atmospheric conditions (25 1C and 101.325 kPa). Surfactant was added to water at different volumetric percentages to alter the surface tension. Polysorbate 80, 20, and soap were used to engineer three liquids S1, S2, and S3 with customized surface tension. Once the correct volume percentage was added to water, the mixture was placed in a sonicator for an hour to ensure adequate mixing. The solution was then allowed to rest until room temperature was reached before the surface tension was measured using a tensiometer with a 1% measurement uncertainty. Glycerol was used to alter the viscosity with limited change in the surface tension (V1 and V2) so comparisons can be made with available data in water. These values of surface tension and viscosity for the liquids S1–S3 and V1–V2 are so chosen to mimic the properties of real fuels. The properties of the solutions are compiled in Table 1.
2. Experimental setup The schematic diagram of the experimental setup utilized in this study is shown in Fig. 1. The system uses an autoclave (injection pressures up to 7.5 MPa), and a three axis transverse system which precisely controls the placement of the nozzle (25.4 mm increments) with respect to the diagnostic systems. The nozzle used in this study has a Flow number of 0.4 (ratio of the mass flow rate (lbm/h) and the square root of the differential pressure in psi) with orifice diameter 0.3 mm. This work utilizes the non-intrusive laser technique Phase Doppler Particle Anemometry (PDPA) to determine the velocity and diameter distributions. The PDPA setup uses a 632 nm He–Ne laser along with a photo-multiplier tube positioned at a receiving angle of 701 (Saha et al., 2012). The choice of the angle of collection is based on
Fig. 4. Reynolds number effect on spray angle for different surface tension liquids.
Fig. 3. Sample rate variation in the radial direction at Z¼ 10 mm and Z¼63 mm: (a) Liquid S2 compared to water, (b) liquid V1 compared to water.
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measurement volume. For PDPA, this was controlled by having a short fringe distance (Araneo et al., 2006). For the current experimental setup, the fringe spacing was 1.4 mm. The PDPA system had an accuracy of 4% for diameter measurements and 1% for velocity measurements with the spherically validated results corresponding to an aspect ratio range from 0.9 to 1.1. The spray cone angle was obtained using a Phantom V12.1 high speed camera coupled to a high power LED light source used for back lighting. The images were captured at 28,000 fps with 520 480 pixel resolutions. The images were analyzed using an edge detection algorithm in Matlab (Davanlou, 2014; Lee et al., 2013; Saha et al., 2012). The grey scale image was converted to a black and white image by generating the image matrix in binary form. To determine the spray cone angle, the intensity of the image was controlled by the edge detection function “canny” within Matlab with appropriate lower and upper bound limits that would determine how dark the pixel needed to be for it to be counted as 1 on the image matrix. These values were also compared with calculated values from geometric considerations.
3. Results and discussion For droplet velocity and diameter distribution along the axial and radial directions, results are reported in terms of Reynolds number. The Reynolds number can be determined using a velocity scale based on the pressure drop (Walzel, 2010), sffiffiffiffiffiffiffiffiffiffi 2 ΔP U Scale ¼ ð1Þ
ρl
sffiffiffiffiffiffiffiffiffiffi
ρ D 2ΔP Rep ¼ l μl ρl
ð2Þ
To fully characterize the flow and understand the spray dynamics for these liquids (see Table 1), axial and radial measurements were made throughout the spray at various Reynolds numbers (i.e. at different injection pressures). PDPA was the principal optical technique used for measuring droplet diameter and velocity, while high speed photography was used for general spray visualization. Note that the one-dimensional PDPA is capable of making only axial component of velocity measurements. This would have an effect on the velocity values especially towards the outer periphery of the spray where the radial velocity component is stronger than the inner locations. However, the physics that governs the flow can be estimated even with the availability of only axial velocity components. Fig. 5. Comparing the spray angle between water, V1 and V2: (a) Spray angle variation vs. pressure. (b) Spray angle variation vs. viscosity at 5, 10, 15 and 20 bar. (c) Spray angle variation vs. Reynolds number.
2.1. Uncertainty analysis To ensure a statistically significant distribution, a running average was done to determine how many droplets should be recorded to obtain an acceptable mean. It is determined that a minimum of 2000 droplet samples need to be taken in order to capture the true mean. For all PDPA measurement locations, a sample size of 10,000 spherically validated data points was gathered, which is consistent with Kim et al. (2002) and Lee et al. (2013). This data has been compared with data obtained from other techniques at the same location for cross-validation. For each measurement location, great care was taken to ensure accurate results. Since the droplets are small in size, and move at relatively high velocity, it is essential to have a small
3.1. Spray dynamics: Measurements and observations 3.1.1. Spray profile The spray cone angles were determined by high speed photographs (Fig. 2) at different pressures and also by traversing the PDPA probe volume radially. The edge of the spray is determined by the drop in the data rate (Fig. 3) due to the hollow cone swirl effect of the atomizer (Lee et al., 2013). The results of the two optical techniques for S2 fluid are provided in Table 2, and were within 7 4%. It can be clearly seen in Fig. 2 that by reducing the surface tension, the spray cone angle increases significantly. A reduction in the surface tension for pure liquids results in an increase in the growth rate of the most unstable modes, ultimately leading to earlier sheet breakup. The smaller droplet size in low surface tension fluids at the same spatial location leads to significant centrifugal dispersion due to lower inertia causing a wider spray cone angle (Butler Ellis et al., 2001). The spray
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cone angle for the low surface tension liquid (S3) shows almost a two fold increase for lower Reynolds number. At high Reynolds numbers, the difference in spray cone angle reduces for different liquids. Higher viscosity liquids V1 and V2 exhibit much lower Reynolds numbers, but show similar trends as surface tension. This maybe explained as follows. The lower Reynolds number indicates a comparable axial component of the velocity compared to the swirl or tangential velocity component. This leads to a dispersion of the droplets more towards the periphery causing wider cone angle. Figs. 4 and 5 show the spray cone angle variation as a function of Reynolds number for different liquids. Comparing S1–S3 with water shows that the decrease in surface tension results in larger spray angles. As Reynolds number is based on both injection pressure and liquid viscosity, for viscous cases (V1 and V2), the spray angle variation is plotted in terms of injection pressure for various
viscosity fluids (Fig. 5a) and in terms of viscosity for various injection pressures (Fig. 5b). Fig. 5a shows that initially both viscous liquids have greater angles compared to water. However, beyond 15 bar, the spray angle reaches a near-asymptotic value. Fig. 5b illustrates the effect of viscosity on cone angle. Totally, four pressures are compared. Here again, beyond 15 bar, V1 and V2 fluids do not display any noticeable difference in cone angles. Chen et al. (1992) reported that spray angle widens with increase in injection pressure or decrease in liquid viscosity. However, their fluid viscosity ranged from 1 cP to 12 cP, which is significantly greater than that reported here. Similarly, the nozzle orifice i.e., the flow number of atomizers reported by them is about one-twentieth of what is used here. The effect of nozzle geometry, e.g. orifice length, diameter and exit orifice area, are studied by Ballester and Dopazo (1994) for pressure-swirl atomizer.
Fig. 6. Discharge coefficient with respect to (a) pressure and (b) Reynolds number.
Fig. 7. Centerline measurements for the different surface tension liquids using PDPA at Rep 15,000: (a) Diameter, (b) velocity.
Fig. 8. Centerline diameter measurements for two different surface tension liquids using PDPA: (a) Rep 9500 (b) Rep 21,000
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Fig. 6 illustrates the discharge coefficient (CD) of viscous liquids _ compared ffiffiffiffiffiffiffiffiffiffiffiffiffiffi to water. Discharge coefficient is defined as C D ¼ m=A0 : p 2ρl ΔP , where A0 is the exit orifice area. It is seen that the discharge coefficient decreases after pressure increases from 5 bar to 36 bar, however it becomes near asymptotic at high pressures. In general the spray angle decreases with increase in discharge coefficient. Also when liquid viscosity is increased (e.g. V2), discharge coefficient decreases even though the variations are small. 3.1.2. Surface tension effects on diameter profile To determine the effects of surface tension and viscosity on the diameter profiles throughout the spray, several axial and radial locations were considered. Measurements were made at two axial locations, one relatively close to the nozzle at Z ¼10 mm and one far away at Z ¼ 63 mm. In Fig. 7a and b, a clear distinction in diameter and velocity can be seen between the three liquids with different surface tension and water for the axial cases at Rep ¼ 15,000. The diameters are nearly 20% less than that of pure water for solution S1 and nearly 50% less for solutions S2 and S3. However, for surface tension 48 mN/m and 30 mN/m (fluids S2 and S3), the average diameter is nearly the same beyond an axial location of 20 mm. The inflection point which distinguishes secondary breakup to coalescence shifts towards the nozzle for liquids with lower surface tension, indicating a slight relative change in the secondary breakup and coalescence zones. Near the nozzle, a significant decrease in velocity is noted for liquid solutions of lower surface tension (Fig. 7b). The velocity for all three liquid solutions is seen to be very similar, but lower than that for water in all axial locations. Since the diameter profile in the axial direction remains unchanged for S2 and S3, liquid S2 was tested to determine the effects of Reynolds number. The surface tension had little effect on the change in the diameter profile in the axial direction past σ ¼48 mN/m. Results for other Reynolds number are presented in Fig. 8. Fig. 8a and b shows the diameter profiles for Reynolds number Rep 9500 and 21,000, respectively. It can be noticed that at low Reynolds number a decrease in the diameter profile of 25–30% is seen by lowering the surface tension whereas at higher Reynolds number the values are very similar. With this observation it is reasonable to conclude that only at low injection pressures, the diameter of the droplets become affected by the change in the surface tension. This further indicates that at high Reynolds number, surface tension (i.e. We number) does not play a major role.
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affected by surface tension and viscosity. To fully understand its effects, a detailed analysis is done on the liquid film breakup and secondary breakup and coalescence part of the spray for solution S2 and compared to water as presented in our previous paper (Saha et al., 2012). 3.2.1. Theory of breakup and comparison with data The relative velocity between the liquid film and air creates an instability which allows the liquid film to break up into ligaments. The ligaments atomize to create more droplets and further break up into secondary droplets. Senecal et al. (1999) showed that a critical Weber number of 27/16 exists which delineates the long wavelength (WeoWec) and short wavelength (We4Wec) instability. Weber number is defined as We ¼ ρg U 2l t=σ , where ρg is gas phase density, Ul is liquid film velocity, t is half of film thickness (t¼h/2, h: film thickness) and σ is the surface tension of the liquid; t is given by _ μl Þ=ðΔP ρl ÞÞ0:25 where, Sivakumar and Kulkarni (2011) t ¼ 3:66ððmD ρl is liquid density, μl is liquid viscosity, t is half film thickness, ΔP is
3.1.3. Viscosity effects on droplet diameter The high viscosity liquids V1 and V2 were tested at three pressures of 5, 10 and 20 bar and compared with water. At low to medium pressures (5–10 bar), the trend in droplet diameters in the axial direction and transition points for all liquids seems almost identical (Fig. 9a and b) since the spray angles are considerably larger than that for water at these pressures (Fig. 7a and b) and the larger droplets end up on the periphery of the cone. At high injection pressures, increase in viscosity leads to higher drop sizes in primary and secondary breakup compared to water as shown in Fig. 9c. Similarly the coalescence regime is postponed for viscous cases compared to water, therefore the transition point from secondary breakup to coalescence shifts towards the nozzle. Next, these results will be corroborated by plotting the coalescence probability of liquids versus axial locations. 3.2. Breakup and coalescence phenomena All the results presented in Section 3.1.2 indicate that droplet breakup dynamics (primary and secondary) and coalescence are
Fig. 9. Viscosity effects on average droplet diameter profile at (a) P¼ 5 bar, (b) P ¼10 bar, (c) P¼ 20 bar.
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injection pressure and D is nozzle orifice diameter. The velocity of the liquid film is given by Ul ¼ kUscale, where Uscale is the velocity scale defined earlier and k¼0.7 from Senecal et al. (1999) and Saha et al. (2012). According to the film breakup theory, the instability grows very rapidly in a sinusoidal manner. The wavenumber of this instability can be expressed as, ) K s t ¼ We 2 ðfor Long wavelengthÞ ð3Þ K s t ¼ 2We 3 ðfor Short wavelengthÞ Using the relation between wavelength and wave number (Ks ¼2π/λ) one can write: λ ¼ 2π ðfor Long wavelengthÞ We
h
9 =
λ ¼ 3π ðfor Short wavelengthÞ ; 2We
h
ð4Þ
To determine the most unstable wavelength experimentally, shadowgraph technique was used. As shown in the inset of Fig. 10, pixel lengths were measured for each frame to obtain the wavelength for different fluids at different Reynolds numbers and Weber numbers. Most unstable wavelength (λ) denotes the distance from the peak of one wave to another wave just before the breakup of the liquid film. Small scale capillary waves on the surface of the liquid film have not been considered. Fig. 10 shows that the long wavelength for all engineered fluids decreases rapidly along the curve 2π/We up to the transition point of We¼27/16. At higher We in the short wavelength zone, the data for water and other fluids seem to follow the theoretical curve 3π/ (2.We) reasonably well. From the same data sets for all the fluids, the average droplet diameter is plotted in Fig. 11 in terms of dimensional and nondimensional quantities. Once again, in the long wavelength region, the diameter decreases with We up to Wec, and thereafter reaches
Fig. 10. Comparison between experimental results and theory for most unstable wavelengths. Different liquids are compared with water at 0–20 bar.
Fig. 11. Weber number effects on all liquids and Reynolds numbers: (a) average diameter, (b) average diameter non dimensionalized by film thickness.
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an asymptotic value in the short wavelength region. This shows that the initial size of the droplets is dependent on whether the spray is fully developed (short wavelength) or still developing (long wavelength). We noted already in Fig. 8b that the diameter does not change axially for fluids at lower surface tension if the Reynolds number is high enough.
Table 3 Reynolds number and Weber number for tested liquids. Liquid (bar)
Re
We
Water @ Water @ Water @ Water @ S1 @ 10 S1 @15 S1 @ 20 S2 @ 5 S2 @ 10 S2 @ 15 S3 @ 5 S3 @ 10 S3 @ 15 V1 @ 5 V1 @ 10 V1 @ 15 V2 @ 5 V2 @ 10 V2 @ 15
10,541 14,907 18,257 21,082 11,645 14,262 16,469 8,132 11,501 14,086 8,091 11,443 14,014 7,131 10,085 12,352 5,791 8,190 10,031
0.54 0.99 1.41 1.81 1.32 1.88 2.42 0.91 1.67 2.38 1.44 2.65 3.78 0.63 1.16 1.66 0.69 1.26 1.80
5 10 15 20
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In particular, when breakup takes place at high Reynolds number, the instability is in the short wavelength region where the diameter does not change. For these cases, the Weber number is larger than Wec of 27/16. This also suggests that in the short wavelength region, it is inertia and not surface tension that dominates. In the long wave length region, the wavelength decreases from about 0.75t linearly up to the transition of We ¼27/16. Beyond this transition, in the short wavelength region prior to coalescence, the diameter is seen to be constant at 0.4t. This region is dominated more by inertia and less by surface tension. Table 3 tabulates the calculated Reynolds number and Weber number of tested fluids at various injection pressures. 3.2.2. Radial distribution of droplet diameter The radial distribution of diameter at the two axial locations in Fig. 12a show that at Re¼9500, the two liquids display a linear decay in diameter at Z¼10 mm from the axis towards the tip of spray cone. This indicates that secondary breakup is still present and droplet dispersion towards the edge of the spray cone is low due to weak swirl at this low Reynolds number. However, down the axial location at Z¼63 mm, coalescence is dominant at all radial locations. The fact that water has larger average diameter at all radial locations is due to the fact that the diameter is consistently larger for water droplets after primary breakup. At higher Reynolds number (Rep ¼21,000) given in Fig. 12b, the droplet diameter increases at both axial locations near the nozzle and far away from it. At high Reynolds numbers, the swirl intensity
Fig. 12. Radial diameter measurements for liquid S2 compared to water at: (a) Rep ¼ 9500, (b) Rep ¼ 21,000.
Fig. 13. The coalescence probability for water and solution S2 at Rep 9000: (a) Measurements made along the centerline, (b) measurements made in the radial direction.
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Fig. 14. The coalescence probability for water and solution S2 at Rep 21,000: (a) measurements made along the centerline, (b) measurements made in the radial direction.
is high. Therefore, due to the combined effects of coalescence and centrifugal dispersion of larger droplets, the diameter increases even close to the nozzle. However, at Z¼ 63 mm, the increase of the diameter is caused by coalescence only. This can be conjectured from the velocity profile (not shown here) which increases radially at 10 mm, where coalescence does not occur. The presence of centrifugal dispersion of droplets causes the larger droplets to be swept towards the periphery. At Z¼63 mm however, the velocity decreases radially with an increase in diameter (not shown here), suggesting that the droplets coalesce.
coalescence, therefore the current calculations might overestimate the probability as soft merging and bouncing also occur at low Weber numbers. For head-on collision of the same size droplet, the relative velocity (Urel) would be twice that of the droplet velocity. Using PDPA data for 10,000 samples at each measurement location, Wecol and Wecrit were calculated for each individual droplets to evaluate the statistical probability of Wecol oWecrit, at which coalescence occurs (Saha et al., 2012). The coalescence probability is calculated as: Probability of coalescence ¼
Number of droplet with We rWecrit Toal number of droplets ð8Þ
3.3. Property effects on coalescence Secondary breakup consists of several types of breakup depending on the droplet Weber number. In this experimental investigation, Web o11 for all cases and at all locations. Here, the vibration-type secondary breakup mechanism is still dominant. In order to distinguish the end of secondary breakup and the beginning of coalescence, the breakup time and coalescence probability need to be considered. Using the PDPA data which encompassed 10,000 droplets, the breakup time can be calculated from t b =t n ¼ C
ð5Þ n
where C is constant and approximated as 5.0 and t is qffiffiffiffiffiffiffiffiffiffiffiffi do ρl =ρg tn ¼ Uo
ð6Þ
where d0 and U0 represent the droplet diameter and velocity (Hsiang and Faeth, 1992). In the chaotic nature of sprays, droplets are bound to interact with other droplets at all locations of the spray. To determine when the droplets will coalesce or bounce after they come in contact with one another is determined when the critical Weber number is reached. This critical Weber number was found by Qian and Law (1997) which is a function of Ohnesorge number. Wecrit ¼ 30:Ohcol þ 15 ð7Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi where Ohcol ¼ 16μl = ρl σ l do , defined as the collision Ohnesorge number. For coalescence probability calculations, only the head-on collision of same size droplets are considered, which would represent a lower bound. Coalescence will occur if the collision Weber number ðWecol ¼ ðρl U 2rel d0 =σ l ÞÞ is less than the critical Weber number (Eq. (7)). ρl and σl represent the density and surface tension of the liquid; d0 droplet diameter, and Urel the relative velocity between the two colliding droplets. Note that we used a critical Weber number that captures the transition from coalescence to separation after
3.3.1. Coalescence probability of low surface tension fluid S2 Fig. 13 provides the comparison of coalescence probability for water and solution S2 at Rep 9500 and Fig. 14 at Rep ¼21,000. The coalescence probability is low for the low Reynolds number case for the S2 fluid along the axis, and levels off at 50% at Re 21,000. As seen in the radial profiles of droplet diameter (Fig. 12), even though the coalescence probability increases towards the tip of the spray cone, the breakup time is still quite small allowing breakup to dominate. At Z¼ 63 mm, the probability is very high, therefore the increased diameter is predominantly due to coalescence. If coalescence probability is non-zero and the diameter decreases along the cone radius as in the low Reynolds number case, the breakup time needs to be considered to understand the reduction of drop diameter close to the nozzle. At the higher Reynolds number (Figs. 13 and 14), the results in both the axial and radial locations are similar which is in good agreement. At Re¼21,000, the coalescence probability peaked at 50% which is nearly twice as much as for Re 9500 in the axial direction. In the radial direction, similar profiles are seen with the coalescence probability at nearly 100% at Z¼63 mm. However, at Z¼10 mm, the opposite effect is seen where the coalescence probability is higher near the center of the spray than at the spray cone tip. This suggests that the increase in diameter in the radial direction at this particular axial location is due to the centrifugal droplet dispersion characteristics associated with these nozzles and not coalescence., which is also shown later from the breakup time. An interesting feature to note is that at both Reynolds numbers the trends are similar for liquid S2 but not for water. For water at Re 9500, the onion regime was observed and not for liquid S2. This suggests that after the flow has already encountered the pencil and distorted pencil spray regimes (Lefebvre, 1989) and is currently in the later stages of the spray regimes, i.e., onion, Tulip, and fully developed regimes.
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Considering the high Reynolds number case, Fig. 15 illustrates the breakup time using 10,000 droplet samples at different axial locations and radial conditions. At 10 mm, the coalescence probability
Fig. 16. The coalescence probability along the centerline for different viscosity liquids at Rep 15,000.
starts off high in the center of the spray and decreases radially even though the overall diameter is still increasing throughout the periphery. This is corroborated by the breakup time shown in Fig. 15b where at this particular location the breakup time is still very small. Therefore, it is possible to conclude that it is the swirl intensity and not the coalescence probability that increases the droplet diameter. The high swirl causes the majority of the larger droplets to be swept towards the outside of the spray cone. Further downstream in the axial direction in Fig. 15c, the breakup time for all radial locations is high. In addition, the coalescence probability is high throughout the radial direction, suggesting that the sole reason for the increased diameter is coalescence. 3.3.2. Coalescence probability of high viscosity fluids, V1 and V2 By calculating the coalescence probability for high viscosity fluids, V1 and V2, it can be seen from Fig. 16 that these liquids along with water display similar trends in that the percentage is low in the initial stages of breakup then increases before reaching a constant, although the viscous fluids show a high probability of coalescence compared to water. An interesting observation is that it takes liquid V2 longer to reach the asymptotic value than liquid V1. This is associated with the fact that as the viscosity increases, the transition zone gets larger, thus allowing liquid V2 to take a longer axial distance to reach the asymptotic value. Even though the coalescence probability is much higher, the increased diameter is about the same as that of water in the coalescence regime. This suggests that due to the increased injection velocity for the two engineered liquids, breakup could still occur, although not enough to dominate the coalescence process. The coalescence probability only suggests that if two droplets were able to collide in any form or even touch, then the probability of coalescence is higher than bounce-off. Thus, coalescence is the sole reason for the increase in droplet diameter. 3.4. Sauter mean diameter prediction
Fig. 15. PDF for breakup time tb at Rep 21,000, (a) measurements made along the centerline, (b) measurements made in the radial direction at Z ¼10 mm, (c) measurements made in the radial direction at Z¼ 63 mm.
It has long been known that the liquid properties relevant to atomization are density, surface tension, and viscosity. Researchers have tried to find a correlation that could predict the droplet diameter based on surface tension and viscosity, these studies have tended to resort to various empirical correlations due to the complex nature of the atomization process. To eliminate these shortcomings, Wang and Lefebvre (1987) proposed an alternate equation from the physical process involved in atomization in pressure-swirl nozzles rather than a mathematical treatment of
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Fig. 17. Experimental results compared to the modified correlation based on water solutions S1, S2, S3, V1 and V2 at the onset of atomization breakup. (a) SMD vs. WeL, (b) SMD predicted vs. SMD measured.
the problem. To summarize their work, they subdivided the two main stages of atomization. According to Semiao et al. (1996) and Wang and Lefebvre (1987), the first stage represents the generation of surface instabilities due to the combined effects of hydrodynamics and aerodynamic forces while the second stage is the conversion of surface protuberances into ligaments and droplets. By following their approach, the SMD can be represented in form of SMD ¼ A
σ 0:5 μl ρ0:5 A ΔP l
!x
σρl y ðt cos θÞ1 1:5x þ B ðt cos θÞ1 y ρA Δ P l
ð9Þ
where A and B are constants determined form the nozzle design and X and Y from the experimental data and t is the film thickness (Suyari and Lefebvre, 1986). To determine constants A and B from the nozzle design Wang and Lefebvre (1987) used the following equations, A ¼ 2:11½ cos 2ðθ 30Þ2:25
0:00034 0:4 d0
B ¼ 0:635½ cos 2ðθ 30Þ2:25
0:00034 d0
ð10Þ
0:2 ð11Þ
where d0 and Ø are the orifice diameter and half spray angle at fully developed conditions, respectively. Since this equation was developed under the assumptions that the atomization occurs in two stages incorporating both the surface instabilities to the development of ligaments and further in to droplets, the comparison was done at the end of primary breakup and the beginning stages of secondary breakup. Since this is an empirical correlation, the values for A, B, X, and Y would normally be iterated to find the best fit. Utilizing Eqs. (10) and (11), constants A and B were determined to be 2.11 and 0.62, respectively. Once these values were calculated, values for X and Y were iterated to determine the best fit, and were found to be 0.5 and 0.1, respectively. This provides the following equation. SMD ¼ 2:11
σ 0:5 μl ρ0:5 A ΔP l
!0:5 ðt cos θÞ0:25 þ 0:62
σρl ρA Δ P l
0:1
4. Conclusion In this experimental study, the effects of surface tension and viscosity on the liquid breakup regimes including droplet coalescence are compared to water. The spray characteristics, droplet diameter, and velocity profiles at different Reynolds number (injection pressure) in the axial and radial direction for different surface tension liquids was observed. From the results presented, it was found that when the surface tension falls below σ ¼48 mN/m, there is no net effect on droplet diameter. It was also found that at low Reynolds number, the driving force for the reduction of the diameter profile is dominated by the surface tension whereas at high Reynolds number this is not the case where the results are similar. The inflexion point of the transition from secondary breakup to coalescence is seen to shift closer to the nozzle for lower surface tension liquids. For majority of the cases, it was seen that the coalescence probability was higher for the lower surface tension solution than water. Similar to the diameter profile at larger Reynolds numbers the coalescence probability became similar to that of water. This suggests that although using a liquid with lower surface tension decreases the overall diameter profile throughout the measurement locations for low Reynolds number, the probability of coalescence increases as two droplets collide. At higher Reynolds number, the inertial force is the dominant mechanism for coalescence. For high viscosity fluids, the spray cone angle is increased with pressure rise. At high injection pressures, an increase in viscosity leads to higher drop sizes in primary and secondary breakup. Similarly the coalescence regime is postponed for viscous cases compared to water, and therefore the transition point from secondary breakup to coalescence shifts towards the nozzle. At low to medium pressures (5–10 bar) the trend and transition points for all liquids seems almost identical. Even though at 5 bar water demonstrates a larger diameter in all axial points. Finally, a correlation was developed based on Wang and Lefebvre (1987)’s work to predict the SMD of the tested nozzle which matched the experimental data reasonably well.
ðt cos θÞ0:9 ð12Þ
The data match the modified correlation reasonably well, suggesting that Wang and Lefebvre’s empirical equation is the best fit for predicting the initial SMD for different hydraulic pressure-swirl nozzles (Fig. 17). It is remarkable that the fit is good for all engineered fluids for different surface tension and viscosity.
Acknowledgements This work was partially supported by AFRL to UCF. The authors would like to thank Parker Hannifin Inc. for providing UCF with their injector nozzles and Pretam Choudhury for his help in the laboratory.
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Lee, J.D., Basu, S., Kumar, R., 2013. Comparison and cross-validation of optical techniques in different swirl spray regimes. Atomization Sprays 23, 697–724. Lefebvre, A.H., 1989. Atomization and Sprays. (Combustion: An International Series). CRC, Boca Raton, Florida. Lin, S.P., Reitz, R.D., 1998. Drop and spray formation from a liquid jet. Ann. Rev. Fluid Mech. 30, 85–105. Lu, J., Corvalan, C.M., 2012. Coalescence of viscous drops with surfactants. Chem. Eng. Sci. 78, 9–13. Park, S.H., Kim, H.J., Suh, H.K., Lee, C.S., 2009. Experimental and numerical analysis of spray-atomization characteristics of biodiesel fuel in various fuel and ambient temperatures conditions. Int. J. Heat Fluid Flow 30, 960–970. Payri, R., Tormos, B., Salvado, F.J., Araneo, L., 2008. Spray droplet velocity characterization for convergent nozzles with three different diameters. Fuel 87, 3176–3182. Qian, J., Law, C.K., 1997. Regimes of coalescence and separation in droplet collision. J. Fluid Mech. 331, 59–80. Rangel, R.H., Sirignano, W.A., 1988. Nonlinear growth of Kelvin–Helmholtz instability: effect of surface tension and density ratio. Phys. Fluids 31, 1845–1855. Saha, A., Lee, J.D., Basu, S., Kumar, R., 2012. Breakup and coalescence characteristics of a hollow cone swirling spray. Phys. Fluids 24, 124103. Schmidt, D.P., Nouar, I., Senecal, P.K., Homan, J., Rutland, C.J., Martin, J., Reitz, R.D., 1999. Pressure-swirl Atomization in the Near Field. SAE Paper 1999-01-0496 . Semiao, V., Andrade, P., Graca Carvalho, M. da, 1996. Spray characterization: numerical prediction of Sauter mean diameter and droplet size distribution. Fuel 75, 1707–1714. Senecal, P.K., Schmidt, D.P., Nouar, I., Rutland, C.J., Reitz, R.D., Corradini, M.L., 1999. Modeling high-speed viscous liquid sheet atomization. Int. J. Multiphase Flow 25, 1073–1097. Shi, H., Kleinstreuer, C., 2007. Simulation and analysis of high-speed droplet spray dynamics. J. Fluids Eng. 129, 621–633. Sirignano, W.A., Mehring, C., 2000. Review of theory of distortion and disintegration of liquid streams. Prog. Energy Combust. Sci. 26, 609–655. Sivakumar, D., Kulkarni, V., 2011. Regimes of spray formation in gas-centered swirl coaxial atomizers. Exp. Fluids 51, 587–596. Suyari, M., Lefebvre, A.H., 1986. Film thickness measurements in a simplex swirl atomizer. J. Propul. Power 2, 528–533. Walzel, P., 2010. Spraying and Atomizing of Liquids, in Ullmann’s Encyclopedia of Industrial Chemistry. Wiley-VCH Verlag GmbH, Weinheim. Wang, X.F., Lefebvre, A.H., 1987. Mean drop sizes from pressure-swirl nozzles. J. Propul. Power 3, 11–18. Yao, S., Zhang, J., Fang, T., 2012. Effect of viscosities on structure and instability of sprays from a swirl atomizer. Exp. Therm. Fluid Sci. 39, 158–166.
Contents lists available at ScienceDirect
Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Effect of viscosity and surface tension on breakup and coalescence of bicomponent sprays Ashkan Davanlou a, Joshua D. Lee a, Saptarshi Basu b, Ranganathan Kumar a,n a b
Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, USA Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
H I G H L I G H T S
G R A P H I C A L
A B S T R A C T
The effects of surface tension and viscosity are studied on spray behavior. Surface tension effect is more dominant at high Reynolds numbers. The spray cone angle increases with increase in pressure. At high pressures, viscous fluids have larger diameters in breakup zones. A correlation was developed to predict the SMD.
art ic l e i nf o
a b s t r a c t
Article history: Received 7 November 2014 Received in revised form 15 March 2015 Accepted 22 March 2015 Available online 14 April 2015
This work deals with an experimental study of the breakup characteristics of liquids with different surface tension and viscosity from a hollow cone hydraulic injector nozzle induced by pressure-swirl. The experiments were conducted at Reynolds numbers Rep ¼ 9500–23,000. The surface tension and viscosity of the surrogate fuels were altered from 72 to 30 mN/m and 1.1 to 1.6 mN s/m2, respectively. High speed photography and Phase Doppler Particle Anemometry were utilized to study the atomization process. Velocity and drop size measurements of the spray using PDPA in both axial and radial directions indicate a dependency on surface tension. However, these effects are dominant only at low Reynolds numbers and are negligible at high Reynolds number. Downstream of the nozzle, coalescence of droplets due to collision was also found to be significant and the diameters were compared for different liquids. For viscous fluids up to 1.6 cP, the independent effects of viscosity and injection pressure are studied. In general, the spray cone angle increases with increase in pressure. At high pressures, an increase in viscosity leads to higher drop sizes following primary and secondary breakup compared to water. This study will extend our understanding of surrogate fuel film breakup and highlight the importance of long and short wavelength instabilities. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Atomization Multiphase flow Pressure-swirl nozzle Coalescence Breakup Phase Doppler Anemometry
1. Introduction The most common atomizer used in the IC and aero-engines is the pressure-swirl nozzle (Simplex nozzle). Simplex nozzle has a swirl chamber that forces the liquid to leave the nozzle as an annular sheet. The sheet subsequently spreads out radially
n
Corresponding author. E-mail address: [email protected] (R. Kumar).
http://dx.doi.org/10.1016/j.ces.2015.03.057 0009-2509/& 2015 Elsevier Ltd. All rights reserved.
through a circular orifice and forms a hollow cone spray of finite film thickness (Lefebvre, 1989). The ejected liquid film undergoes different types of instabilities to disintegrate into ligaments and eventually droplets. In a simplex nozzle, with increase in injection pressure, the spray characteristics evolves through four stages of development; dribble stage, distorted pencil stage, onion stage, and Tulip stage (Lefebvre, 1989), where the last three stages are usually dominated by long wavelength film breakup. Once the spray becomes fully developed, short wavelength film breakup becomes dominant. This was shown analytically (Senecal et al.,
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Fig. 1. Experimental setup.
1999; Schmidt et al., 1999), using a linear instability analysis which allowed for the prediction of film length based on Weber number. Once the Kelvin–Helmholtz instabilities attain the maximum growth, the liquid sheet will shear off to produce liquid ligaments beginning the onset of the breakup process (Saha et al., 2012). Rangel and Sirignano (1988) used vortex-sheet discretization approach to investigate the effect of surface tension and density ratio on nonlinear growth of Kelvin–Helmholtz instability. A few articles have reviewed theories of distortion and disintegration of liquid jets (Senecal et al., 1999; Lin and Reitz, 1998; Sirignano and Mehring, 2000; Lasheras et al., 1998; Lasheras and Hopfinger, 2000; Dumouchel, 2008). The role of surfactants in coalescence of viscous drops is studied by Lu and Corvalan (2012). The breakup process consists of two steps: (a) a primary breakup regime induced by hydrodynamic instabilities and relatively large drag forces that cause the formation of ligaments or other irregular liquid elements and (b) a secondary breakup regime which is caused by aerodynamic instabilities resulting in larger droplets deforming and breaking up into smaller daughter droplets (Saha et al., 2012). The secondary breakup mechanism progresses until the aerodynamic breakup time becomes significantly large (mainly due to small droplet size and lower relative velocity), leading to higher coalescence probability. This increased coalescence change the spray characteristics exhibited by an increase in the average droplet size (Saha et al., 2012). In addition to breakup and coalescence, hollow cone sprays also display non-homogeneity in droplet number distribution in all spatial directions. Normally, dispersion of droplets occurs due to swirl induced centrifuging as well as large scale vortical structures in the surrounding gas flow field. Clark (1988) extended the Taylor’s model for drop breakup in a turbulent flow and suggested that drop size, viscosity and interfacial tension may influence the critical Weber number. Research performed in the last decade has been focused on developing and improving the numerical models which predict
Table 1 Liquid properties. Liquids
Surface tension (mN/m)
Density (kg/m3)
Dynamic viscosity (Ns/m2) 10 3
Water S1 S2 S3 V1 V2
72 60 48 30 71 69
958 962 955 962 955 954
1.11 1.13 1.14 1.15 1.3 1.6
the droplet distribution profiles for liquids. Experimental studies in swirling flows have reported contradictory results over the last few years (Shi and Kleinstreuer, 2007). More fundamental experimental works were conducted using optical diagnostics with water as the main fluid at different pressures (Saha et al., 2012; Davanlou et al., 2013). Ayres et al. (2001) developed a mathematical model to predict the joint distribution for both size and velocity of the droplets in sprays. Belhadef et al. (2012) developed an Eulerian model for liquid sheet atomization at high Weber numbers and Reynolds numbers. They validated their numerical results with Phase Doppler Anemometry (PDA). One of the key reasons for utilizing a simplex nozzle is the uniform distribution of liquid that is generated after primary breakup. This uniform distribution helps increase overall combustion efficiency in IC and aero-engines. Unfortunately, IC and aeroengines use hydrocarbon fuels with wide variations in thermophysical properties like surface tension, density, vapor pressure and viscosity. In fact, new generations of bio-fuels are highly viscous and multicomponent in nature. For this reason, the breakup and coalescence characteristics need to be investigated in more detail with liquids presenting starkly different physical
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Fig. 2. Change of spray angle for liquids S1, S2 and S3 at three pressures of 3, 7 and 14 bar.
Table 2 Comparison between two methods of spray edge detection. P (bar)
Image processing method (1)
Data rate method (2)
Difference between 1 and 2 (in %)
5 10 15 20
49.2217 0.5 65.1117 0.5 70.4717 0.5 75.8517 0.5
47.31 7 1 63.21 7 1 681 7 1 72.91 7 1
3.90 2.93 3.50 3.89
properties like surface tension and viscosity but in simple surrogate fluids first. The literature is limited in the experimental investigation of spray characteristics. Some fundamental research has been done to investigate the effects of various system parameters, i.e. viscosity, density, and surface tension on the distribution of droplet diameters and velocities (Park et al., 2009; Kim et al., 2008; Payri et al., 2008; Yao et al., 2012). For Newtonian liquids, it has been reported that system parameters, such as viscosity, density and nozzle diameter affect the spreading (cone) angle and breakup (Dorfner et al., 1995). Other studies investigated
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the impact of emulsification (Bolszo et al., 2010) or properties on pressure swirl atomization (Fan et al., 2014). Fan et al. (2014) investigated the effect of kinematic viscosity on droplet size distribution in Jetropha oil spray using laser diffraction method. They found five phases for spray cone evolution with viscosity variation, however, other aspects of breakup and coalescence of droplets were not investigated. In summary, even though studies have shown significant effect of liquid thermo-physical properties on the spray, these studies did not fully characterize the spray or provide an understanding of transition from secondary breakup to coalescence when physical properties are changed. Thus, the fundamentals of spray dynamics, such as spray formation, liquid breakup length, and droplet breakup regimes need further investigation. The main objective of this paper is to conduct experiments to understand the individual effects of surface tension and viscosity on the liquid breakup regimes including droplet coalescence compared to the base fluid, water. Droplet diameter and velocity profiles in the axial and radial directions will be characterized at different Reynolds numbers at different injection pressures for different surface tension and viscosity. This study will extend our understanding of surrogate fuel film breakup and highlight the importance of long and short wavelength instabilities for low and high Weber number ranges, respectively. The dependence of liquid breakup characteristics will be validated with experimental data for the first time in the context of high pressure swirling flow. Coalescence probability and swirl induced dispersion will also be studied in conjunction with breakup to provide a holistic view of droplet dynamics in these types of pressure atomizers for low surface tension and high viscosity fluids. Finally, a correlation will be provided for the new data based on the existing correlation given by Wang and Lefebvre (1987).
the Brewster effect on the surface of the liquid droplet for first order refraction angle. For measuring the spray angle and other spray characteristics a high speed Phantom V12.1 camera was used. Images were captured at 28,000 fps at full resolution. More details of the experimental setup can be found in Saha et al. (2012). The data reported in this section is recorded on the vertical plane (Z-axis) which passes through the center of the nozzle. For PDPA to make simultaneous diameter and velocity measurement, the two laser beams were allowed to intersect directly below and in the center of the nozzle exit by moving the nozzle with the traverse system. In order to gather data at different axial or radial distances with respect to the tip, the nozzle was moved using the traverse system without disturbing the optical setup. The autoclave was pressurized with both liquid solutions and air ranging from 0.3 to 2 MPa and was allowed to equilibrate for 20 min. The liquid was then injected into atmospheric conditions (25 1C and 101.325 kPa). Surfactant was added to water at different volumetric percentages to alter the surface tension. Polysorbate 80, 20, and soap were used to engineer three liquids S1, S2, and S3 with customized surface tension. Once the correct volume percentage was added to water, the mixture was placed in a sonicator for an hour to ensure adequate mixing. The solution was then allowed to rest until room temperature was reached before the surface tension was measured using a tensiometer with a 1% measurement uncertainty. Glycerol was used to alter the viscosity with limited change in the surface tension (V1 and V2) so comparisons can be made with available data in water. These values of surface tension and viscosity for the liquids S1–S3 and V1–V2 are so chosen to mimic the properties of real fuels. The properties of the solutions are compiled in Table 1.
2. Experimental setup The schematic diagram of the experimental setup utilized in this study is shown in Fig. 1. The system uses an autoclave (injection pressures up to 7.5 MPa), and a three axis transverse system which precisely controls the placement of the nozzle (25.4 mm increments) with respect to the diagnostic systems. The nozzle used in this study has a Flow number of 0.4 (ratio of the mass flow rate (lbm/h) and the square root of the differential pressure in psi) with orifice diameter 0.3 mm. This work utilizes the non-intrusive laser technique Phase Doppler Particle Anemometry (PDPA) to determine the velocity and diameter distributions. The PDPA setup uses a 632 nm He–Ne laser along with a photo-multiplier tube positioned at a receiving angle of 701 (Saha et al., 2012). The choice of the angle of collection is based on
Fig. 4. Reynolds number effect on spray angle for different surface tension liquids.
Fig. 3. Sample rate variation in the radial direction at Z¼ 10 mm and Z¼63 mm: (a) Liquid S2 compared to water, (b) liquid V1 compared to water.
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measurement volume. For PDPA, this was controlled by having a short fringe distance (Araneo et al., 2006). For the current experimental setup, the fringe spacing was 1.4 mm. The PDPA system had an accuracy of 4% for diameter measurements and 1% for velocity measurements with the spherically validated results corresponding to an aspect ratio range from 0.9 to 1.1. The spray cone angle was obtained using a Phantom V12.1 high speed camera coupled to a high power LED light source used for back lighting. The images were captured at 28,000 fps with 520 480 pixel resolutions. The images were analyzed using an edge detection algorithm in Matlab (Davanlou, 2014; Lee et al., 2013; Saha et al., 2012). The grey scale image was converted to a black and white image by generating the image matrix in binary form. To determine the spray cone angle, the intensity of the image was controlled by the edge detection function “canny” within Matlab with appropriate lower and upper bound limits that would determine how dark the pixel needed to be for it to be counted as 1 on the image matrix. These values were also compared with calculated values from geometric considerations.
3. Results and discussion For droplet velocity and diameter distribution along the axial and radial directions, results are reported in terms of Reynolds number. The Reynolds number can be determined using a velocity scale based on the pressure drop (Walzel, 2010), sffiffiffiffiffiffiffiffiffiffi 2 ΔP U Scale ¼ ð1Þ
ρl
sffiffiffiffiffiffiffiffiffiffi
ρ D 2ΔP Rep ¼ l μl ρl
ð2Þ
To fully characterize the flow and understand the spray dynamics for these liquids (see Table 1), axial and radial measurements were made throughout the spray at various Reynolds numbers (i.e. at different injection pressures). PDPA was the principal optical technique used for measuring droplet diameter and velocity, while high speed photography was used for general spray visualization. Note that the one-dimensional PDPA is capable of making only axial component of velocity measurements. This would have an effect on the velocity values especially towards the outer periphery of the spray where the radial velocity component is stronger than the inner locations. However, the physics that governs the flow can be estimated even with the availability of only axial velocity components. Fig. 5. Comparing the spray angle between water, V1 and V2: (a) Spray angle variation vs. pressure. (b) Spray angle variation vs. viscosity at 5, 10, 15 and 20 bar. (c) Spray angle variation vs. Reynolds number.
2.1. Uncertainty analysis To ensure a statistically significant distribution, a running average was done to determine how many droplets should be recorded to obtain an acceptable mean. It is determined that a minimum of 2000 droplet samples need to be taken in order to capture the true mean. For all PDPA measurement locations, a sample size of 10,000 spherically validated data points was gathered, which is consistent with Kim et al. (2002) and Lee et al. (2013). This data has been compared with data obtained from other techniques at the same location for cross-validation. For each measurement location, great care was taken to ensure accurate results. Since the droplets are small in size, and move at relatively high velocity, it is essential to have a small
3.1. Spray dynamics: Measurements and observations 3.1.1. Spray profile The spray cone angles were determined by high speed photographs (Fig. 2) at different pressures and also by traversing the PDPA probe volume radially. The edge of the spray is determined by the drop in the data rate (Fig. 3) due to the hollow cone swirl effect of the atomizer (Lee et al., 2013). The results of the two optical techniques for S2 fluid are provided in Table 2, and were within 7 4%. It can be clearly seen in Fig. 2 that by reducing the surface tension, the spray cone angle increases significantly. A reduction in the surface tension for pure liquids results in an increase in the growth rate of the most unstable modes, ultimately leading to earlier sheet breakup. The smaller droplet size in low surface tension fluids at the same spatial location leads to significant centrifugal dispersion due to lower inertia causing a wider spray cone angle (Butler Ellis et al., 2001). The spray
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cone angle for the low surface tension liquid (S3) shows almost a two fold increase for lower Reynolds number. At high Reynolds numbers, the difference in spray cone angle reduces for different liquids. Higher viscosity liquids V1 and V2 exhibit much lower Reynolds numbers, but show similar trends as surface tension. This maybe explained as follows. The lower Reynolds number indicates a comparable axial component of the velocity compared to the swirl or tangential velocity component. This leads to a dispersion of the droplets more towards the periphery causing wider cone angle. Figs. 4 and 5 show the spray cone angle variation as a function of Reynolds number for different liquids. Comparing S1–S3 with water shows that the decrease in surface tension results in larger spray angles. As Reynolds number is based on both injection pressure and liquid viscosity, for viscous cases (V1 and V2), the spray angle variation is plotted in terms of injection pressure for various
viscosity fluids (Fig. 5a) and in terms of viscosity for various injection pressures (Fig. 5b). Fig. 5a shows that initially both viscous liquids have greater angles compared to water. However, beyond 15 bar, the spray angle reaches a near-asymptotic value. Fig. 5b illustrates the effect of viscosity on cone angle. Totally, four pressures are compared. Here again, beyond 15 bar, V1 and V2 fluids do not display any noticeable difference in cone angles. Chen et al. (1992) reported that spray angle widens with increase in injection pressure or decrease in liquid viscosity. However, their fluid viscosity ranged from 1 cP to 12 cP, which is significantly greater than that reported here. Similarly, the nozzle orifice i.e., the flow number of atomizers reported by them is about one-twentieth of what is used here. The effect of nozzle geometry, e.g. orifice length, diameter and exit orifice area, are studied by Ballester and Dopazo (1994) for pressure-swirl atomizer.
Fig. 6. Discharge coefficient with respect to (a) pressure and (b) Reynolds number.
Fig. 7. Centerline measurements for the different surface tension liquids using PDPA at Rep 15,000: (a) Diameter, (b) velocity.
Fig. 8. Centerline diameter measurements for two different surface tension liquids using PDPA: (a) Rep 9500 (b) Rep 21,000
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Fig. 6 illustrates the discharge coefficient (CD) of viscous liquids _ compared ffiffiffiffiffiffiffiffiffiffiffiffiffiffi to water. Discharge coefficient is defined as C D ¼ m=A0 : p 2ρl ΔP , where A0 is the exit orifice area. It is seen that the discharge coefficient decreases after pressure increases from 5 bar to 36 bar, however it becomes near asymptotic at high pressures. In general the spray angle decreases with increase in discharge coefficient. Also when liquid viscosity is increased (e.g. V2), discharge coefficient decreases even though the variations are small. 3.1.2. Surface tension effects on diameter profile To determine the effects of surface tension and viscosity on the diameter profiles throughout the spray, several axial and radial locations were considered. Measurements were made at two axial locations, one relatively close to the nozzle at Z ¼10 mm and one far away at Z ¼ 63 mm. In Fig. 7a and b, a clear distinction in diameter and velocity can be seen between the three liquids with different surface tension and water for the axial cases at Rep ¼ 15,000. The diameters are nearly 20% less than that of pure water for solution S1 and nearly 50% less for solutions S2 and S3. However, for surface tension 48 mN/m and 30 mN/m (fluids S2 and S3), the average diameter is nearly the same beyond an axial location of 20 mm. The inflection point which distinguishes secondary breakup to coalescence shifts towards the nozzle for liquids with lower surface tension, indicating a slight relative change in the secondary breakup and coalescence zones. Near the nozzle, a significant decrease in velocity is noted for liquid solutions of lower surface tension (Fig. 7b). The velocity for all three liquid solutions is seen to be very similar, but lower than that for water in all axial locations. Since the diameter profile in the axial direction remains unchanged for S2 and S3, liquid S2 was tested to determine the effects of Reynolds number. The surface tension had little effect on the change in the diameter profile in the axial direction past σ ¼48 mN/m. Results for other Reynolds number are presented in Fig. 8. Fig. 8a and b shows the diameter profiles for Reynolds number Rep 9500 and 21,000, respectively. It can be noticed that at low Reynolds number a decrease in the diameter profile of 25–30% is seen by lowering the surface tension whereas at higher Reynolds number the values are very similar. With this observation it is reasonable to conclude that only at low injection pressures, the diameter of the droplets become affected by the change in the surface tension. This further indicates that at high Reynolds number, surface tension (i.e. We number) does not play a major role.
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affected by surface tension and viscosity. To fully understand its effects, a detailed analysis is done on the liquid film breakup and secondary breakup and coalescence part of the spray for solution S2 and compared to water as presented in our previous paper (Saha et al., 2012). 3.2.1. Theory of breakup and comparison with data The relative velocity between the liquid film and air creates an instability which allows the liquid film to break up into ligaments. The ligaments atomize to create more droplets and further break up into secondary droplets. Senecal et al. (1999) showed that a critical Weber number of 27/16 exists which delineates the long wavelength (WeoWec) and short wavelength (We4Wec) instability. Weber number is defined as We ¼ ρg U 2l t=σ , where ρg is gas phase density, Ul is liquid film velocity, t is half of film thickness (t¼h/2, h: film thickness) and σ is the surface tension of the liquid; t is given by _ μl Þ=ðΔP ρl ÞÞ0:25 where, Sivakumar and Kulkarni (2011) t ¼ 3:66ððmD ρl is liquid density, μl is liquid viscosity, t is half film thickness, ΔP is
3.1.3. Viscosity effects on droplet diameter The high viscosity liquids V1 and V2 were tested at three pressures of 5, 10 and 20 bar and compared with water. At low to medium pressures (5–10 bar), the trend in droplet diameters in the axial direction and transition points for all liquids seems almost identical (Fig. 9a and b) since the spray angles are considerably larger than that for water at these pressures (Fig. 7a and b) and the larger droplets end up on the periphery of the cone. At high injection pressures, increase in viscosity leads to higher drop sizes in primary and secondary breakup compared to water as shown in Fig. 9c. Similarly the coalescence regime is postponed for viscous cases compared to water, therefore the transition point from secondary breakup to coalescence shifts towards the nozzle. Next, these results will be corroborated by plotting the coalescence probability of liquids versus axial locations. 3.2. Breakup and coalescence phenomena All the results presented in Section 3.1.2 indicate that droplet breakup dynamics (primary and secondary) and coalescence are
Fig. 9. Viscosity effects on average droplet diameter profile at (a) P¼ 5 bar, (b) P ¼10 bar, (c) P¼ 20 bar.
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injection pressure and D is nozzle orifice diameter. The velocity of the liquid film is given by Ul ¼ kUscale, where Uscale is the velocity scale defined earlier and k¼0.7 from Senecal et al. (1999) and Saha et al. (2012). According to the film breakup theory, the instability grows very rapidly in a sinusoidal manner. The wavenumber of this instability can be expressed as, ) K s t ¼ We 2 ðfor Long wavelengthÞ ð3Þ K s t ¼ 2We 3 ðfor Short wavelengthÞ Using the relation between wavelength and wave number (Ks ¼2π/λ) one can write: λ ¼ 2π ðfor Long wavelengthÞ We
h
9 =
λ ¼ 3π ðfor Short wavelengthÞ ; 2We
h
ð4Þ
To determine the most unstable wavelength experimentally, shadowgraph technique was used. As shown in the inset of Fig. 10, pixel lengths were measured for each frame to obtain the wavelength for different fluids at different Reynolds numbers and Weber numbers. Most unstable wavelength (λ) denotes the distance from the peak of one wave to another wave just before the breakup of the liquid film. Small scale capillary waves on the surface of the liquid film have not been considered. Fig. 10 shows that the long wavelength for all engineered fluids decreases rapidly along the curve 2π/We up to the transition point of We¼27/16. At higher We in the short wavelength zone, the data for water and other fluids seem to follow the theoretical curve 3π/ (2.We) reasonably well. From the same data sets for all the fluids, the average droplet diameter is plotted in Fig. 11 in terms of dimensional and nondimensional quantities. Once again, in the long wavelength region, the diameter decreases with We up to Wec, and thereafter reaches
Fig. 10. Comparison between experimental results and theory for most unstable wavelengths. Different liquids are compared with water at 0–20 bar.
Fig. 11. Weber number effects on all liquids and Reynolds numbers: (a) average diameter, (b) average diameter non dimensionalized by film thickness.
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an asymptotic value in the short wavelength region. This shows that the initial size of the droplets is dependent on whether the spray is fully developed (short wavelength) or still developing (long wavelength). We noted already in Fig. 8b that the diameter does not change axially for fluids at lower surface tension if the Reynolds number is high enough.
Table 3 Reynolds number and Weber number for tested liquids. Liquid (bar)
Re
We
Water @ Water @ Water @ Water @ S1 @ 10 S1 @15 S1 @ 20 S2 @ 5 S2 @ 10 S2 @ 15 S3 @ 5 S3 @ 10 S3 @ 15 V1 @ 5 V1 @ 10 V1 @ 15 V2 @ 5 V2 @ 10 V2 @ 15
10,541 14,907 18,257 21,082 11,645 14,262 16,469 8,132 11,501 14,086 8,091 11,443 14,014 7,131 10,085 12,352 5,791 8,190 10,031
0.54 0.99 1.41 1.81 1.32 1.88 2.42 0.91 1.67 2.38 1.44 2.65 3.78 0.63 1.16 1.66 0.69 1.26 1.80
5 10 15 20
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In particular, when breakup takes place at high Reynolds number, the instability is in the short wavelength region where the diameter does not change. For these cases, the Weber number is larger than Wec of 27/16. This also suggests that in the short wavelength region, it is inertia and not surface tension that dominates. In the long wave length region, the wavelength decreases from about 0.75t linearly up to the transition of We ¼27/16. Beyond this transition, in the short wavelength region prior to coalescence, the diameter is seen to be constant at 0.4t. This region is dominated more by inertia and less by surface tension. Table 3 tabulates the calculated Reynolds number and Weber number of tested fluids at various injection pressures. 3.2.2. Radial distribution of droplet diameter The radial distribution of diameter at the two axial locations in Fig. 12a show that at Re¼9500, the two liquids display a linear decay in diameter at Z¼10 mm from the axis towards the tip of spray cone. This indicates that secondary breakup is still present and droplet dispersion towards the edge of the spray cone is low due to weak swirl at this low Reynolds number. However, down the axial location at Z¼63 mm, coalescence is dominant at all radial locations. The fact that water has larger average diameter at all radial locations is due to the fact that the diameter is consistently larger for water droplets after primary breakup. At higher Reynolds number (Rep ¼21,000) given in Fig. 12b, the droplet diameter increases at both axial locations near the nozzle and far away from it. At high Reynolds numbers, the swirl intensity
Fig. 12. Radial diameter measurements for liquid S2 compared to water at: (a) Rep ¼ 9500, (b) Rep ¼ 21,000.
Fig. 13. The coalescence probability for water and solution S2 at Rep 9000: (a) Measurements made along the centerline, (b) measurements made in the radial direction.
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Fig. 14. The coalescence probability for water and solution S2 at Rep 21,000: (a) measurements made along the centerline, (b) measurements made in the radial direction.
is high. Therefore, due to the combined effects of coalescence and centrifugal dispersion of larger droplets, the diameter increases even close to the nozzle. However, at Z¼ 63 mm, the increase of the diameter is caused by coalescence only. This can be conjectured from the velocity profile (not shown here) which increases radially at 10 mm, where coalescence does not occur. The presence of centrifugal dispersion of droplets causes the larger droplets to be swept towards the periphery. At Z¼63 mm however, the velocity decreases radially with an increase in diameter (not shown here), suggesting that the droplets coalesce.
coalescence, therefore the current calculations might overestimate the probability as soft merging and bouncing also occur at low Weber numbers. For head-on collision of the same size droplet, the relative velocity (Urel) would be twice that of the droplet velocity. Using PDPA data for 10,000 samples at each measurement location, Wecol and Wecrit were calculated for each individual droplets to evaluate the statistical probability of Wecol oWecrit, at which coalescence occurs (Saha et al., 2012). The coalescence probability is calculated as: Probability of coalescence ¼
Number of droplet with We rWecrit Toal number of droplets ð8Þ
3.3. Property effects on coalescence Secondary breakup consists of several types of breakup depending on the droplet Weber number. In this experimental investigation, Web o11 for all cases and at all locations. Here, the vibration-type secondary breakup mechanism is still dominant. In order to distinguish the end of secondary breakup and the beginning of coalescence, the breakup time and coalescence probability need to be considered. Using the PDPA data which encompassed 10,000 droplets, the breakup time can be calculated from t b =t n ¼ C
ð5Þ n
where C is constant and approximated as 5.0 and t is qffiffiffiffiffiffiffiffiffiffiffiffi do ρl =ρg tn ¼ Uo
ð6Þ
where d0 and U0 represent the droplet diameter and velocity (Hsiang and Faeth, 1992). In the chaotic nature of sprays, droplets are bound to interact with other droplets at all locations of the spray. To determine when the droplets will coalesce or bounce after they come in contact with one another is determined when the critical Weber number is reached. This critical Weber number was found by Qian and Law (1997) which is a function of Ohnesorge number. Wecrit ¼ 30:Ohcol þ 15 ð7Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi where Ohcol ¼ 16μl = ρl σ l do , defined as the collision Ohnesorge number. For coalescence probability calculations, only the head-on collision of same size droplets are considered, which would represent a lower bound. Coalescence will occur if the collision Weber number ðWecol ¼ ðρl U 2rel d0 =σ l ÞÞ is less than the critical Weber number (Eq. (7)). ρl and σl represent the density and surface tension of the liquid; d0 droplet diameter, and Urel the relative velocity between the two colliding droplets. Note that we used a critical Weber number that captures the transition from coalescence to separation after
3.3.1. Coalescence probability of low surface tension fluid S2 Fig. 13 provides the comparison of coalescence probability for water and solution S2 at Rep 9500 and Fig. 14 at Rep ¼21,000. The coalescence probability is low for the low Reynolds number case for the S2 fluid along the axis, and levels off at 50% at Re 21,000. As seen in the radial profiles of droplet diameter (Fig. 12), even though the coalescence probability increases towards the tip of the spray cone, the breakup time is still quite small allowing breakup to dominate. At Z¼ 63 mm, the probability is very high, therefore the increased diameter is predominantly due to coalescence. If coalescence probability is non-zero and the diameter decreases along the cone radius as in the low Reynolds number case, the breakup time needs to be considered to understand the reduction of drop diameter close to the nozzle. At the higher Reynolds number (Figs. 13 and 14), the results in both the axial and radial locations are similar which is in good agreement. At Re¼21,000, the coalescence probability peaked at 50% which is nearly twice as much as for Re 9500 in the axial direction. In the radial direction, similar profiles are seen with the coalescence probability at nearly 100% at Z¼63 mm. However, at Z¼10 mm, the opposite effect is seen where the coalescence probability is higher near the center of the spray than at the spray cone tip. This suggests that the increase in diameter in the radial direction at this particular axial location is due to the centrifugal droplet dispersion characteristics associated with these nozzles and not coalescence., which is also shown later from the breakup time. An interesting feature to note is that at both Reynolds numbers the trends are similar for liquid S2 but not for water. For water at Re 9500, the onion regime was observed and not for liquid S2. This suggests that after the flow has already encountered the pencil and distorted pencil spray regimes (Lefebvre, 1989) and is currently in the later stages of the spray regimes, i.e., onion, Tulip, and fully developed regimes.
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Considering the high Reynolds number case, Fig. 15 illustrates the breakup time using 10,000 droplet samples at different axial locations and radial conditions. At 10 mm, the coalescence probability
Fig. 16. The coalescence probability along the centerline for different viscosity liquids at Rep 15,000.
starts off high in the center of the spray and decreases radially even though the overall diameter is still increasing throughout the periphery. This is corroborated by the breakup time shown in Fig. 15b where at this particular location the breakup time is still very small. Therefore, it is possible to conclude that it is the swirl intensity and not the coalescence probability that increases the droplet diameter. The high swirl causes the majority of the larger droplets to be swept towards the outside of the spray cone. Further downstream in the axial direction in Fig. 15c, the breakup time for all radial locations is high. In addition, the coalescence probability is high throughout the radial direction, suggesting that the sole reason for the increased diameter is coalescence. 3.3.2. Coalescence probability of high viscosity fluids, V1 and V2 By calculating the coalescence probability for high viscosity fluids, V1 and V2, it can be seen from Fig. 16 that these liquids along with water display similar trends in that the percentage is low in the initial stages of breakup then increases before reaching a constant, although the viscous fluids show a high probability of coalescence compared to water. An interesting observation is that it takes liquid V2 longer to reach the asymptotic value than liquid V1. This is associated with the fact that as the viscosity increases, the transition zone gets larger, thus allowing liquid V2 to take a longer axial distance to reach the asymptotic value. Even though the coalescence probability is much higher, the increased diameter is about the same as that of water in the coalescence regime. This suggests that due to the increased injection velocity for the two engineered liquids, breakup could still occur, although not enough to dominate the coalescence process. The coalescence probability only suggests that if two droplets were able to collide in any form or even touch, then the probability of coalescence is higher than bounce-off. Thus, coalescence is the sole reason for the increase in droplet diameter. 3.4. Sauter mean diameter prediction
Fig. 15. PDF for breakup time tb at Rep 21,000, (a) measurements made along the centerline, (b) measurements made in the radial direction at Z ¼10 mm, (c) measurements made in the radial direction at Z¼ 63 mm.
It has long been known that the liquid properties relevant to atomization are density, surface tension, and viscosity. Researchers have tried to find a correlation that could predict the droplet diameter based on surface tension and viscosity, these studies have tended to resort to various empirical correlations due to the complex nature of the atomization process. To eliminate these shortcomings, Wang and Lefebvre (1987) proposed an alternate equation from the physical process involved in atomization in pressure-swirl nozzles rather than a mathematical treatment of
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Fig. 17. Experimental results compared to the modified correlation based on water solutions S1, S2, S3, V1 and V2 at the onset of atomization breakup. (a) SMD vs. WeL, (b) SMD predicted vs. SMD measured.
the problem. To summarize their work, they subdivided the two main stages of atomization. According to Semiao et al. (1996) and Wang and Lefebvre (1987), the first stage represents the generation of surface instabilities due to the combined effects of hydrodynamics and aerodynamic forces while the second stage is the conversion of surface protuberances into ligaments and droplets. By following their approach, the SMD can be represented in form of SMD ¼ A
σ 0:5 μl ρ0:5 A ΔP l
!x
σρl y ðt cos θÞ1 1:5x þ B ðt cos θÞ1 y ρA Δ P l
ð9Þ
where A and B are constants determined form the nozzle design and X and Y from the experimental data and t is the film thickness (Suyari and Lefebvre, 1986). To determine constants A and B from the nozzle design Wang and Lefebvre (1987) used the following equations, A ¼ 2:11½ cos 2ðθ 30Þ2:25
0:00034 0:4 d0
B ¼ 0:635½ cos 2ðθ 30Þ2:25
0:00034 d0
ð10Þ
0:2 ð11Þ
where d0 and Ø are the orifice diameter and half spray angle at fully developed conditions, respectively. Since this equation was developed under the assumptions that the atomization occurs in two stages incorporating both the surface instabilities to the development of ligaments and further in to droplets, the comparison was done at the end of primary breakup and the beginning stages of secondary breakup. Since this is an empirical correlation, the values for A, B, X, and Y would normally be iterated to find the best fit. Utilizing Eqs. (10) and (11), constants A and B were determined to be 2.11 and 0.62, respectively. Once these values were calculated, values for X and Y were iterated to determine the best fit, and were found to be 0.5 and 0.1, respectively. This provides the following equation. SMD ¼ 2:11
σ 0:5 μl ρ0:5 A ΔP l
!0:5 ðt cos θÞ0:25 þ 0:62
σρl ρA Δ P l
0:1
4. Conclusion In this experimental study, the effects of surface tension and viscosity on the liquid breakup regimes including droplet coalescence are compared to water. The spray characteristics, droplet diameter, and velocity profiles at different Reynolds number (injection pressure) in the axial and radial direction for different surface tension liquids was observed. From the results presented, it was found that when the surface tension falls below σ ¼48 mN/m, there is no net effect on droplet diameter. It was also found that at low Reynolds number, the driving force for the reduction of the diameter profile is dominated by the surface tension whereas at high Reynolds number this is not the case where the results are similar. The inflexion point of the transition from secondary breakup to coalescence is seen to shift closer to the nozzle for lower surface tension liquids. For majority of the cases, it was seen that the coalescence probability was higher for the lower surface tension solution than water. Similar to the diameter profile at larger Reynolds numbers the coalescence probability became similar to that of water. This suggests that although using a liquid with lower surface tension decreases the overall diameter profile throughout the measurement locations for low Reynolds number, the probability of coalescence increases as two droplets collide. At higher Reynolds number, the inertial force is the dominant mechanism for coalescence. For high viscosity fluids, the spray cone angle is increased with pressure rise. At high injection pressures, an increase in viscosity leads to higher drop sizes in primary and secondary breakup. Similarly the coalescence regime is postponed for viscous cases compared to water, and therefore the transition point from secondary breakup to coalescence shifts towards the nozzle. At low to medium pressures (5–10 bar) the trend and transition points for all liquids seems almost identical. Even though at 5 bar water demonstrates a larger diameter in all axial points. Finally, a correlation was developed based on Wang and Lefebvre (1987)’s work to predict the SMD of the tested nozzle which matched the experimental data reasonably well.
ðt cos θÞ0:9 ð12Þ
The data match the modified correlation reasonably well, suggesting that Wang and Lefebvre’s empirical equation is the best fit for predicting the initial SMD for different hydraulic pressure-swirl nozzles (Fig. 17). It is remarkable that the fit is good for all engineered fluids for different surface tension and viscosity.
Acknowledgements This work was partially supported by AFRL to UCF. The authors would like to thank Parker Hannifin Inc. for providing UCF with their injector nozzles and Pretam Choudhury for his help in the laboratory.
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