Journal of Mechanical Science and Technology 25 (12) (2011) 3047~3052 www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-011-0901-2
An investigation on effect of geometrical parameters on spray cone angle and droplet size distribution of a two-fluid atomizer† Maziar Shafaee*, Sayed Abdolhossein Banitabaei, Vahid Esfahanian and Mehdi Ashjaee School of Mechanical Engineering, Tehran University, Tehran, 11155-4563, Iran (Manuscript Received November 13, 2010; Revised July 12, 2011; Accepted August 16, 2011) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Abstract A visual study is conducted to determine the effect of geometrical parameters of a two-fluid atomizer on its spray cone angle. The liquid (water) jets exit from six peripheral inclined orifices and are introduced to a high speed gas (air) stream in the gravitational direction. Using a high speed imaging system, the spray cone angle has been determined in constant operational conditions, i.e., Reynolds and Weber numbers for different nozzle geometries. Also, the droplet sizes (Sauter mean diameter) and their distributions have been determined using Malvern Master Sizer x. The investigated geometrical parameters are the liquid jet diameter, liquid port angle and the length of the gas-liquid mixing chamber. The results show that among these parameters, the liquid jet diameter has a significant effect on spray cone angle. In addition, an empirical correlation has been obtained to predict the spray cone angle of the present two-fluid atomizer in terms of nozzle geometries. Keywords: Droplet size distribution; Geometrical parameters; Spray cone angle; Visualization ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction Most of the research carried out in recent years in the area of atomization have tended to focus on a method of twin-fluid atomization. The spray cone angle, penetration depth, droplet sizes and their distribution are very important parameters that greatly affect the performance of these types of atomizers. Most of the sprays have a conical shape wherein the cone angle is usually defined as the angle between the tangents to the spray envelope at the atomizer exit. Many practical systems require atomizers that distribute the fuel in the form of a less concentrated and lower penetrating spray. The spray angle of a two-fluid atomizer should be such that it could provide a good mixing between the two fluids which cause the liquid jets to be disintegrated perfectly through the gas stream [1]. The quality of atomization and its effect upon the subsequent evaporation and mixing of chemical reactants occurring within combustion systems is fundamental in determining both the combustion efficiency and the production of emissions for a given system. In particular, the transverse injection of a liquid jet into a high velocity crossflowing gas is common in a variety of fuel injection schemes, such as the fuel injection process for lean premixed prevaporized (LPP) gas turbine †
This paper was recommended for publication in revised form by Associate Editor Gihun Son * Corresponding author. Tel.: +98 912 7034912, Fax.: +98 21 77311565 E-mail address:
[email protected] © KSME & Springer 2011
engines, ramjet and scramjet applications [2]. Varde [3] made a liquid fuel spray injected into a gaseous environment in order to investigate the effects of nozzle orifice size and operating conditions on the spray cone angle. The results showed that the spray cone angle is dependent on the orifice dimensions as well as on the nozzle operating conditions. In addition, he derived a correlation to predict spray cone angle in terms of Reynolds and Weber numbers. Chen et al. [4] measured the spray cone angle of a pressure swirl atomizer for five different values of discharge orifice length/diameter ratio (l0/d0). They found that an increase in l0/d0 always leads to a reduction in spray cone angle. Moreover, in spite of the great effects of the injection pressure on spray cone angle, their results show that the relationship between spray angle and l0/d0 is not markedly affected by the liquid injection pressure. They also found a simple relation to express the effective spray angle of the atomizer versus its geometric parameter (l0/d0). Reitz and Bracco [5] proposed a correlation for estimating the spray cone angle versus nozzle length and nozzle hole diameter. Hiroyasu and Arai [6] established a correlation between the spray cone angle and the nozzle operational conditions and its geometrical parameters. It should be noted that the most investigations on spray cone angle and the nozzle geometry in two-fluid atomizers focused on cross-flow and co-flow types and the transverseflow atomizers are hardly found in the literature. As described
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by Lefebvre [7], the spray angle is influenced by nozzle dimensions, liquid properties and the density of the medium into which the liquid is sprayed. Guildenbecher et al. [8] found that in pressure-swirl atomizers the ambient pressure had a negligible effect on spray cone angle after a value of between 1.5 and 3.5 MPa. Rahman [9] studied the effect of operation conditions and geometrical parameters on the spray cone angle of a gas-liquid coaxial atomizer. He found that the cone angle is invariant with respect to Weber and Reynolds numbers and depends only on the atomizer geometry. Herein, Shafaee et al. [1] investigated the effects of operational conditions, i.e., Reynolds and Weber numbers on spray cone angle of a transverse-flow in a two-fluid atomizer. In each Weber number, Reynolds increasing causes a decrease in spray cone angle followed by approaching to an asymptotic value for higher Reynolds numbers. Similarly, an increase in Weber number in a constant value of Reynolds causes the spray cone angle to decrease with a descending slope. They found that there are ranges of operating conditions in which the Reynolds and Weber numbers have little effect on spray cone angle and it may only depend on the geometrical parameters of the atomizer. Thus, in the present study, the relation between the nozzle geometry and spray angle has been studied in a range of operational conditions in which the cone angle is less dependent on Reynolds and Weber numbers. The spray angle measurement is based on a visual method using a high speed video camera and image processing technique. An empirical correlation has also been obtained to estimate the spray cone angle in terms of the nozzle geometric parameters.
2. Experimental setup and conditions Fig. 1 shows a schematic of the experimental setup used in this study comprising three main parts: the liquid (water) feed line, the compressed gas (air) line and the atomizer, in the presence of a high speed camera system. The liquid feed line consists of five elements including a liquid reservoir with a capacity of 1.1 m3 connected to the main tap water, a stainless steel mesh strainer hampering any possible tiny debris from the liquid flow, a liquid piston pump with a regulating pressure in the range of 0 to 50 bar capable of providing liquid flowrates up to 50 L/min, a needle valve for flowrate adjustment and a rotameter having a measurement range of 0 to 70 L/min with an accuracy of ±1%. The compressed air line is composed of three elements, respectively, including a pre-charged compressed air reservoir having a capacity of 50 L with a maximum allowable pressure of 140 bar and a mesh strainer followed by an air pressure regulator capable of reducing maximum pressure of 230 bar to a range of 0 to 15 bar. The air flowrates have been calculated based on an air anemometry procedure allowing the velocity and mean flowrate calculation for different air pressures. The compressed air pressure in addition to the air regulator is also
Fig. 1. Schematic view of the experimental setup.
(a)
(b)
Fig. 2. The two-fluid atomizer used in this study: (a) 3-D view; (b) a schematic.
monitored at a location in the vicinity of the atomizer inlet in order to ensure no air leakage in the air line. The injector is a two-fluid atomizer connected to the water and compressed air lines using an interface fixture. The fixture is designed to adapt the injector liquid and air entries to the corresponding lines on the setup in addition to mounting the injector in a holder for carrying out subsequent experimental tests. The atomizer and its picture are shown in Fig. 2. The compressed air flows through the middle part of the atomizer while the liquid feeds through an annular passage mounted on the atomizer periphery. The annular passage ends in six inclined holes which are equally arranged on the atomizer periphery with a sector angle of 60°. Each hole is also placed with an angle relative to the atomizer central axis without a swirl angle. The liquid lines simultaneously emerging from the holes are intercepted with the compressed air flow creating the primary atomization zone within the atomizer, which, in turn, results in the production of a spray of drops at the atomizer exit. The geometrical parameters of the investigated atomizers are shown in Table 1. The visualization system employed in this study consists of
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Table 1. Geometrical specifications of the investigated two-fluid atomizers. No
1
2
3
dl (mm)
5
6
7
8
9
10
1.0
a (◦) l (mm)
4
45 6
8
11
12
13
10 12
8
45 6
8
10
40 12
35 8
In the present atomizer, the breakup of liquid jets injected into the air stream somehow would be similar to the breakup process of a liquid jet by a gas cross-flow. But, in this atomizer, the transverse interaction between the gas stream and each of the liquid jets and also the collision of six liquid jets causes a more complicated atomization phenomenon respect to the simple type of the cross-flow. A standard dimensional analysis (Buckingham’s π-theorem) shows that all the parameters affect the spray cone angle can be classified into two main groups which are geometrical parameters and operating conditions (Eqs. (1), (2)).
θ = f ( d g , dl , l , a, u g , ul , ρ g , ρl , µ g , µl , σ ) .
(1)
Applying dimensional analysis results in:
dl
,
ρ gug l , a, , Rel , Weg ) ρl ul dl
in which Rel =
16
17
1.2 40 35 30
3. Results and discussion
dg
15
18
19
20
21
22
23
24
1.6
a high speed digital camera (Mega Speed MS50K) set at a recording rate of 2500 fps with an exposure time of 100 ns capable of recording image files with a resolution of 640×480 pixels. The digital camera simultaneously transmitted the captured files to a dedicated PC as well as providing an online display of the pictures taken. The digital camera is utilized in combination with a halogen lamp with a power of 1000 W to illuminate the spray emanating from the atomizer exit. Accordingly, the spray angle of each atomizer has been measured by applying an image processing method through a frame by frame analysis followed by a manual verification applied on some random selected pictures as shown in Fig. 3.
θ = f(
14
(2)
ρ (u g − ul ) 2 dl ρ ul dl . and Weg = σ µl
Visual investigation shows that increasing the operational parameters, i.e. Reynolds and Weber numbers, in a constant geometry causes the atomizer to pass four different breakup regimes including Rayleigh, first wind induced, second wind induced and atomization mode [1]. The existing regimes and related sizes are shown in Fig. 4. According to the definition presented by Ref. [10], in Rayleigh mode (Fig. 4(a)), the size of droplets is greater than the jet diameter (liquid port diameter), while in first wind induced regime, the droplet sizes are on order of the jet diameter (Fig. 4(b)). Fig. 4(c) shows the second wind induced regime with droplets approximately
30
45 6
8
40 10
θ=59.9° dl=1.0 mm
12
25
26
27
28
40
35
30
1.8 35
30
8
45 6
8
10
θ=77.2° dl=1.6 mm
12
8
θ=50.9° dl=1.8 mm
Fig. 3. Spray cone angle in different liquid port diameters (a=45°, l=6 mm, Rel=90000, Weg=140).
(a) Ug=0 d ≅ 7.8 mm Rayleigh
(b) Weg=1.51 davg ≅ 0.85dl First wind induced
(c) Weg=13 SMD=306 µ Second wind induced
(d) Weg=49.8 SMD=55 µ Atomization
Fig. 4. Different breakup modes based on Weber increment (Rel=1650) [1].
ranging from 100µ to 1450µ. The final mode, atomization, has fine droplets with SMD=55µ (Weg=49.8) and approaches to SMD=34µ as Weber reaches to 150 and varies little with Weber number in higher values of Weg. Since the spray angle investigations are usually carried out in the atomization mode, thus to achieve a full spray in each Reynolds number, the kinetic energy of the employed air stream should be able to atomize the liquid jets completely. Fig. 5 shows the effect of geometrical parameters on the droplet sizes in atomization mode. Decreasing the liquid jet diameter causes the atomizer to generate more fine droplets. The same trend with a less intensity is also observed for mixing length of the atomizer. However, any change in the injection angle of the liquid jets causes a slight effect on the droplet sizes. So, it is clear that the liquid jet diameter has the greatest effect on the droplet sizes in comparison with the other geometrical parameters. Also, the effect of geometrical parameters on SMD is investigated in different Weber numbers. As Fig. 5 shows, in all geometrical parameters, increasing the Weber number causes the SMD to decrease. The curves show that at higher Weber numbers, the effect of Weg on decreasing the droplet sizes becomes less considerable. Fig. 6 shows the cumulative volume fraction of droplets in different liquid jet diameters. The figure verifies the above mentioned result that decreasing the liquid jet diameter causes the generation of more fine droplets. In this figure, to describe
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Table 2. Gas velocities in different liquid port diameters (Weg=727). dl (mm)
Ug (m/s)
1.8
157
1.6
167
1.2
194
Fig. 6. Cumulative volume fraction versus droplet sizes (Weg=727).
Fig. 5. Effect of geometrical parameters on the droplet sizes (Rel=1650).
the difference between dl=1.2 mm and dl=1.6 mm, first the effect of gas velocity on the size of droplets should be explained. As shown in Fig. 7, an increase in the gas velocity for a constant liquid port diameter causes SMD to decrease. The rate of this decrease (slope of curves) is considerable at low gas velocities, whereas for higher values of Ug, the curves lead to an asymptotic value and the size of droplets becomes less dependent on the gas velocity. But in Fig. 6, as dl decreases, the value of Ug should be increased in order to keep the Weg constant. According to Table 2, when the value of dl approaches from 1.8 mm to 1.6 mm, the slight increase in Ug (from 157 m/s to 167 m/s) causes a slight decrease in the size of droplets. More decrease in dl (from 1.6 mm to 1.2 mm) causes a significant increase in Ug (from 167 m/s to 194 m/s), which leads to a considerable decrease in the droplet sizes. According to above-mentioned results from Fig. 7, more increase in gas velocity from Ug=194 m/s has no significant effect on SMD because in higher Weber numbers, the gas velocity is high enough and has a slight effect on droplet sizes. So, in Fig. 6 the curves related to dl=0.8 mm, dl=1.2 mm are close to each other. To verify the above-mentioned points, the results related to
Fig. 7. Effect of gas velocity on droplet sizes (Rel=1650).
Fig. 8. Cumulative volume fraction versus droplet sizes (Weg=2259).
Weg=2259 have been also presented in Fig. 8. Since in all curves the gas velocity is considerably more than the results related to Weg=727, there is no significant difference between any of the existing curves in comparison with Fig. 6.
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Fig. 9. Variations of spray cone angle versus the liquid port diameter for different values of mixing lengths (Rel=90000, Weg=140).
Fig. 10. Correlation accuracy plot.
Also, in Fig. 6 the droplet size distribution is fitted with the famous Rosin-Rammler expression (which may be the most widely used expression for droplet size distribution [7]) using nonlinear least squares for droplets of every generation, which is
angle at various mixing lengths. As the liquid jet diameter increases, the spray cone angle increases with descending slope until it reaches a maximum value. Then with increase of liquid port diameter, the spray angle begins to decrease. In this type of atomizer, the spray cone angle may depend on two main parameters which are the liquid flow rate with an increasing effect on spray cone angle and the gas jet velocity with an opposite effect. As the liquid port diameter is increased for a constant Reynolds and Weber number, the liquid flow rate should be increased and the gas jet velocity should be decreased. As the liquid port diameter is increased, first, the increasing effect of liquid flow rate on spray angle is dominant and then the decreasing effect of gas jet velocity becomes conqueror. From Fig. 9, it is also found that increasing the length of mixing chamber ( l ) causes a little decrease in spray cone angle. Therefore, it can be concluded from Fig. 5 and 9, that the liquid jet diameter has a greater effect on both droplet sizes and spray cone angle respect to the other geometrical parameters. The following empirical correlation has been developed applying a multiple variable least square regression technique on a set of 28 experimental data (atomizers listed in Table 1) in order to predict the spray cone angle as a function of its geometrical parameters (Eq. (5)):
V = 1 − exp(− D / X ) N
(3)
where V is the fraction of total volume of droplets smaller than D, and X and N are constants. The exponent N provides a measure of the spread of droplet sizes. The higher the value of N, the more uniform is the spray. If N is infinite, the droplets in the spray are all the same size. Also, a straight line can be generated by plotting ln(1 –V)-1 vs. droplet diameter on a normal-probability scale. The value of N can be then obtained as the slope of the line, and the value of X equals the value of D corresponding to 1 – V = exp(–1), i.e., V = 0.632. Here, we use SMD as the measure of mean droplets diameter, and N as the measure of the spread of droplet sizes. As mentioned above, Shafaee et al. [1] found that there are ranges of operating conditions in which the spray angle varies little with Reynolds and Weber numbers (Weg >140, Rel >85000). Therefore, in these ranges of operational conditions, the spray cone angle may only depend to the geometrical parameters of the atomizer (Eq. (4)).
θ = 375 + 386dl2 − 261exp(dl ) + 0.8 dg
l , a) θ = f( , dl d l
Rel > 85000,Weg > 140
a l
(5)
(4)
It should be noted that since d g is constant, thus θ is a function of dl , l and a . Accordingly, to investigate the effect of nozzle geometry on spray cone angle, the operational conditions applied in all experiments have been selected as Rel=90000 and Weg=140. To reduce the errors encountered in measurement procedure, the image processing method which is used for spray angle measurement has been repeated five times to assure the repeatability of the results obtained for each geometry. Fig. 9 shows the effect of liquid jet diameter on spray cone
where dl and l are in millimeters and a and θ are in degrees. An error analysis indicates that Eq. (5) is applicable over the entire range which is defined for geometrical parameters with a maximum error of 6%. Spray cone angles which are calculated using the above correlation are plotted against the measured values in Fig. 10. In most cases the correlation is seen to predict the spray cone angle fairly accurately.
4. Conclusions A visualization study is conducted to determine the effect of geometrical parameters of a transverse two-fluid atomizer on
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its spray cone angle. Using a high speed imaging system, the spray cone angle has been measured for constant operational conditions for different nozzle geometries. The results lead to the following conclusions: • There are ranges of operating conditions in which Reynolds and Weber numbers have slight effect on spray cone angle. In these ranges, the spray cone angle may only depend on the geometrical parameters of the atomizer. • For constant Reynolds and Weber numbers, as the liquid port diameter is increased, the increasing effect of liquid flow rate on spray angle is dominant at the beginning, which causes the cone angle to reach a maximum value. Then the decreasing effect of gas jet velocity overcomes and causes the spray angle to decay. • In this type of atomizer, increasing the length of mixing chamber or the liquid port angle causes little variation in spray cone angle. Consequently, it is found that the liquid jet diameter has a more significant effect on droplet size and spray cone angle respect to the other geometrical parameters. • The following empirical correlation has also been presented to predict the spray cone angle of the present two-fluid atomizer as a function of its geometrical parameters:
a l
θ = 375 + 386dl2 − 261exp(dl ) + 0.8 . This equation is applicable over the entire ranges of geometrical parameters defined for the present atomizer with a maximum error of 6%.
Nomenclature-----------------------------------------------------------------------a dg dl l Rel U Urel ul ug SMD Weg
: Angle of liquid ports (◦) : Atomizer exit diameter (mm) : Liquid hole diameter (mm) : Length of gas-liquid mixing chamber (mm) : Reynolds number : Fluid jet velocity (m/s) : Relative velocity of gas and liquid jets (m/s) : Liquid jet velocity (m/s) : Gas jet velocity (m/s) : Sauter mean diameter (µm) : Weber number
Greek symbols θ
: Spray cone angle (◦)
µ ρ σ
: Viscosity (kg/m.s) : Density (kg/m3) : Surface tension (N/m)
Subscripts g l
: Gas : Liquid
References [1] M. Shafaee, S. A. Banitabaei, M. Ashjaee and V. Esfahanian, Effect of flow conditions on spray cone angle of a two-fluid atomizer, J. Mech. Sci. Tech., 24 (7) (2010) 1425-1431. [2] M. A. Linne, M. Paciaroni, J. R. Gord and T. R. Meyers, Ballistic imaging of the liquid core for a steady jet in crossflow, Appl. Opt., 44 (2005) 6627-6634. [3] K. S. Varde, Spray cone angle and its correlation in a high pressure fuel spray, Can. J. Chem. Eng., 63 (1985) 183-187. [4] S. K. Chen, A. H. Lefebvre and J. Rollbuhler, Factors influencing the effective spray cone angle of pressure swirl atomizers, J. Eng. Gas Turbines Power, 114 (1992) 97-103. [5] R. D. Reitz and F. B. Bracco, On the dependence of spray angle and other spray parameters on nozzle design and operating conditions, SAE 790494 (1979). [6] H. Hiroyasu and M. Arai, Fuel spray penetration and spray angle in diesel engines, Trans. JSME, 44 (1980) 3208-3220. [7] A. H. Lefebvre, Atomization and sprays, Hemisphere Publishing Corporation, New York (1989) 281-282. [8] D. R. Guildenbecher, R. R. Rachedi and P. E. Sojka, Pressure-scaling of pressure-swirl atomizer cone angles, J. Eng. Gas Turbines Power, 130 (2008) paper no. 061501. [9] A. Rahman, Primary atomization study of a swirl coaxial liquid propellant rocket injector, The Pennsylvania State University, PhD Thesis (1997) 71-73. [10] S. P. Lin and R. D. Reitz, Drop and spray formation from a liquid jet, Annu. Rev. Fluid Mech., 30 (1998) 85-105.
Maziar Shafaee received his B.S. in Mechanical Engineering from Tabriz University in 2000 and his M.S. from Tehran University in 2002. Mr. Shafaee is currently working on his Ph.D thesis at the Spray and Atomization Lab at the Department of Mechanical Engineering, in Tehran University. His research interests include the numerical and experimental study of spray and atomization systems.
