Energy Fuels 2010, 24, 451–455 Published on Web 12/23/2009
: DOI:10.1021/ef900665g
VOF Method for Impinging-Jet Atomizers Du Cong,* Liu Jian-Zhong, Huang Zhen-Yu, Zhou Jun-Hu, and Cen Ke-Fa State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, Zhejiang, China Received July 2, 2009. Revised Manuscript Received October 15, 2009
Impinging jet atomization is an effective method to produce fine sprays for extremely high viscosity fuels such as coal water slurry (CWS). This technique has been used successfully in a number of CWS applications since its inception. The purpose of this study is to analyze the effect of liquid viscosity and jet velocity in an impinging jet atomizer with a combined volume of fluid (VOF) model. It is observed that the film thickness increases with increased liquid viscosity, and the (a) relative velocity between the liquid and gas phase, (b) the gas liquid ratio (GLR), and (c) the atomizing gas pressure all play important roles. Mean droplet size predicted with the VOF model agrees well with experiments.
1. Introduction Atomization of high viscosity liquids is very important for spray and combustion applications. In heavy oil burners for example, the fuel viscosity usually exceeds 0.5 PaS posing a challenge for atomization and therefore efficient combustion. The situation is even worse for coal water slurry (CWS) burners because of the higher viscosity and various rheological properties of the CWS fuel. Because it is essential to obtain rapid and effective atomization in liquid fuel combustion, a type of CWS injector known as a jet-on-surface impinging atomizer or an impinging jet atomizer, was developed. In impinging jet atomizers, liquid fuel is injected to impinge over a circular metal block/rod (which is located at the center of the atomizer-end, inside) and breaks up into small droplets (Figure 1). Two or more stages of assisting gas may be added, surrounding the jet, to accelerate mixing. The main advantage of such an atomizer over other internal-mixing atomizers is that it is capable of producing fine CWS sprays at relatively low GLR and high viscosity, and owing to the fact that the impingement block is made from a hard alloy, nozzle lifetime is substantially prolonged. However, the mechanism of liquid breakup inside the atomizer is not completely understood. It is important to develop predictive models for the jet breakup process so that the resulting droplets size can be determined. Impingement atomization of liquid jet streams have been extensively studied. Dixon et al.1 investigated the liquid film formed by means of rotating disks and measured the velocity and thickness of the film. Ashgriz et al.2 noted that the mean drop diameter increases with an increase in the impingement surface to jet diameter ratio. For industrialized impinging jet atomizers with assisting gas added, previous researchers estimated the influence of internal geometry and fluid loading on spray behavior. Ren3 showed experimentally that droplet size is largely dependent on the shape of the impingement
Figure 1. An impinging jet atomizer.
block and the smallest SMD is obtained when the liquid jet is directly against the flat side of the block. Yu4 dealt with nozzles where mixing chamber has tangential holes. Cao et al.5 made industry tests of impinging jet atomizers in a power plant CWS boiler and investigated the combustion efficiency with different CWS. Results showed that the atomizing gas pressure plays an important role in the atomization-combustion process, and the optimal loading range for impinging jet atomizer is 40-100%, and the unburned carbon content of fly ash declined with the increase of atomizing gas pressure. In this study, a Dombroski-WAVE model is assumed to analyze the breakup process of liquid jet/sheets. The shape, velocity of liquid flow, and resulting droplet diameter is computed from a combined VOF method, and simulation is compared with experimental data. Finally, the objective is to make possible statements about the droplets size of the atomizer for industrial applications. 2. Computational Model 2.1. Modeling Background. As noted above, the atomizer normally consists of a front section and back section. With assisting gas ejected from the orifices or annular passages arranged around the axis of the nozzle, the front section is similar in construction to an air-blast atomizer. By phase interaction, momentum is imparted from gas to liquid. The back section is the key impingement section where the center
*To whom correspondence should be addressed. E-mail: ducong@ zju.edu.cn. (1) Dixon, B. E; Russell, A. W.; Swallow, J. E. Liquid Films Formed by Means of Rotating Disks. Br. J. Appl. Phys. 1952, 3, 115–119. (2) Ashgriz, N.; Washburn, R.; Barbat, T. Segregation of Drop Size and Velocity in Jet Impinging Splash-Plate Atomizers. Int. J. Heat Fluid Flow . 1996, 17, 509–516. (3) Ren Jian-xing. A study on CWS Atomizer; Zhe Jiang University: Hang Zhou, PRC, 1992 r 2009 American Chemical Society
(4) Hai-long, Yu; Chao, Zhang; Jian-zhong, Liu Experimental Study of the Atomizing Performance of a New Type of Nozzle for Coal Water Slurry. Energy Fuels. 2008, 22, 1170–1173. (5) Xin-yu, Cao; Wei-guo, Weng; Zhen-yu, Huang Industry Test for Burning Water-Coal Slurry in 230 t/h boiler of Baiyanhe Power Plant. Chin. Electr. Power. 2001, 7, 16–18.
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Energy Fuels 2010, 24, 451–455
: DOI:10.1021/ef900665g
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A. Impingement of Droplet. Inside a nozzle, the impact of a droplet on a wetted surface may cause the droplet to bounce, adhere, or splash, depending on We and La(=FσDd/μ2) of the droplet. According to the study of Bai and Gosman,10 bouncing rarely occurs unless We < 5 and the drop can be treated as a solid particle; in other conditions droplets adhere or splash(We > 1320 La-0.18). Droplet splash is one of the most complex multiphase flow phenomena and attracts much interest,11 but a detailed description is not necessary in this discussion. Based on statistical methods, results showed that the mean splash mass ratio is between 0.6 and 0.7, which means that 30-40% of the impact droplet mass is absorbed by the liquid film on the impingement surface. B. Impingement of Center Liquid Jet and VOF Method. A substantial amount of liquid in the form of a steady stream impinges on the block, and a film structure of a certain thickness is formed, which then ejects from the edge of the block and breaks up into rings, lines, and droplets. According to stability analysis, the diameter of the liquid line, Dl, and the resulting droplet diameter, Dd, are given by6 0:5 2 λb δb Dl ¼ ð4Þ π 0:5 2 λb δb ð5Þ Dd ¼ 1:89Dl ¼ 1:89 π This model is suited for low-Weber-number liquid sheets. For high-Weber-number liquid sheets, WAVE model is more applicable. And according to the study of Dombrowski12 on attenuating sheets produced by flat fan nozzles, the break thickness of the liquid sheet, δb, is expressed as !1=3 Dr δr 2=3 F2 U 2 k -σk2 ð6Þ δb ¼ 2H F1 U 2
liquid stream impinges upon the block and disintegrates into pieces and droplets. The droplets then continue exchanging momentum and kinetic energy with the gas phase. 2.1.1. Twin-Fluid Atomization Mechanism. One of the most well-known twin-fluid atomization mechanisms is the instability theory introduced by Rayleigh and developed by Taylor et al.6,7. Theoretically, the basic breakup process is controlled by the growth of unstable waves on the surface of the liquid jet/bulk. These processes may be classified as surface tension dominated (Rayleigh’s model), aerodynamically dominated (Taylor’s model), or a combination of both (R-T model, WAVE model), depending on the growth mode of the surface wave. Based on Kelvin-Helmholtz (K-H) instability analysis, for low velocity and low gas/liquid density ratio Q (=F2/F1), pneumatic force is relatively smaller and the breakup process is controlled by surface tension force (Rayleigh’s model), but for high velocity (high Weber number) and high density ratio, the breakup process is controlled by pneumatic force, therefore the jet/bulk is more inclined to break according to Taylor’s model. The WAVE model of Reize is suited for moderate ejection pressure/ velocity. Assuming that the time of breakup and the resulting droplet size are related to the fastest-growing KelvinHelmholtz instability, and by curve fits of numerical solutions to the dispersion equations, the maximum growth rate, Ω, and the corresponding wavelength, λ0, are given by Reize8 as below: λ0 ð1 þ 0:45Oh0:5 Þð1 þ 0:4T 0:7 Þ ¼ 9:02 a ð1þ0:87We2 1:67 Þ0:6 !0:5 F a3 0:34 þ 0:38We2 1:5 ¼ Ω 1 σ ð1 þ OhÞð1 þ 1:4T 0:6 Þ We1 ¼
ð1Þ ð2Þ
F1 U 2 a Ua F U2a We1 0:5 , We2 ¼ 2 , , Re1 ¼ , Oh ¼ Re1 σ ν1 σ T ¼ OhWe2 0:5
Where k* is the wavenumber of the most unstable wave. The impingement of two cylindrical liquid jets has been widely investigated.13 But the boundary conditions of the impinging jet atomizer is crucially different from the jet-on-jet atomizer, as the shear stress the wall offers to the flow cannot be neglected, especially for high-viscosity liquid films. The accurate location of the interface between the two phases is of special importance and interest for multiphase flow. However, the nature of the phase interface is different from inside. Furthermore, it is difficult to measure the internal interface parameters (sheet velocity, thickness, etc) directly because of the special construction of the atomizer. Numerical approaches must instead be introduced. At present, interface computing models include the ALE (Arbitrary Lagrangian-Eulerian) method and the VOF method. In the past three decades the VOF method has developed popularity and is now widely used in interface tracking techniques. Combined with different flow models of inside of phases, the VOF model is applicable for a large range of Reynolds numbers, especially for different kinds of complex boundary conditions, e.g., bubbling flows in fluidized bed, hydraulic jump in rivers and lakes, etc.14,15
a is the radius of liquid jet or bulk .The influence of secondary breakup is also considered in this model. 2.1.2. Liquid Impingement Mechanism. Knowledge of the mechanism by which atomization occurs is still unsatisfactory, especially for high velocity jets atomization. Numerous phenomenological breakup models are proposed by means of experiment. In the case of an impinging jet atomizer, in the front section, the liquid jet is exposed to high velocity gas streams and the breakup length (Xb) can be calculated according to the result of Lasheras:9 Xb 1 ¼ ð3Þ 0:5 D γM j 2 F U2 M ¼ 2 2 , is the momentum flux ratio per unit volume. F 1 U1 The resulting length is significantly longer than the overall length of the atomizer. It follows that if the nozzle end with the impingement block is removed from the nozzle, the liquid jet (which has not totally disintegrated) will eject out of the nozzle for some distance downstream. Experiments have confirmed this calculation. In fact, however, in impinging jet atomizers, before the impingement occurs, droplets are flaking off from the center liquid column by the disturbing effect of the gas stream and the column becomes thinner. Thus the impingement process must be described in two parts: (A) impingement of droplet; (B) impingement of center liquid jet.
(10) Bai C. ;Cosman A. D. A Phenomenological of Diesel Spray Atomization. Proceedings International Conference on Multiphase Flows., Tsukuba, Japan, 1991. (11) Naber, J. D.; Reitz, R. D. Modeling Engine Spray/Wall Impingement, SAE 880107, SAE: Warrendale, PA, 1988. (12) Dombrowski, N.; Johns, W. R. the Aerodynamic Instability and Disintegration of Viscous Liquid Sheets. Chem. Eng. Sci. 1972, 18, 467– 478. (13) Ibrahim, E. A. Impinging Jets Atomization. Phys. Fluids. 1991, A 3, 2981–2987. (14) Sanyal, J.; Vasquez, S.; Roy, S.; Dudukovic, M. P. Numerical Simulation of Gas-liquid Dynamics in Cylindrical Bubble Column Reactors. Chem. Eng. Sci. 1999, 54, 5071–5083. (15) Cook, M; Behnia, M. Bubble motion during inclined intermittent flow. Int. J. Heat Fluid Flow. 2001, 22, 543–551.
(6) Rayleigh, L. on the Instability of Jets. Proc. Lond. Math. Soc. 1879, 10, 4–13. (7) Taylor, G. I. the Dynamics of Thin Sheets of Fluid. III Disintegration of Fluid Sheets. Proc. R. Soc. Lond. 1959, A 253, 313–321. (8) Reitz, R. D. Mechanisms of Atomization Processes in HighPressure Vaporizing Sprays. Atomization Spray Technol. 1987, 3, 309– 337. (9) Lasheras, J. C.; Villermaux, E.; Hopfinger, E. J. Break-up and Atomization of a Round Water Jet by a High-Velocity Annular Air Jet. J. Fluid Mech. 1998, 357, 351–379.
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: DOI:10.1021/ef900665g
Du et al. Table 1. Turbulence Model Function Γj
Sj
u
νþνta
y-momentum
v
νþνt
0 0 D Du D Dv DP ðν þ νt Þ þ ðν þ νt Þ Dx Dx Dy Dx Dx D Du D Dv DP ðν þ νt Þ þ ðν þ νt Þ Dx Dy Dy Dy Dy
turbulence kinetic energy
k
(νþνt)/σk
Gb-ε
dissipation rate
ε
(νþνt)/σε
ε ε2 Cε1 G -Cε2 k k
a
Function
j
volume fraction mass continuity
F 1
x-momentum
0 0
" 2 2 # Du Dv 2 Du Du þ :νt=Cμk /ε :G=νt þ2 þ2 Dy Dx Dx Dy 2
b
Figure 2. Film shape (low viscosity).
Figure 4. Velocity vector field.
than the overall length of the nozzle, therefore the effect of the surface wave of the liquid jet can also be negated. Simulation is carried out for different liquid physical properties thus the state of the liquid film at different viscosities and jet velocities can be obtained.
3. Simulation Results 3.1. Effect of Liquid Viscosity on Film Thickness and Velocity. The resulting shape of the liquid film is shown in Figures 2 and 3. The jet enters the domain from the left side, impinges upon the solid wall and the liquid film is formed. Figure 2 is the final shape of a low-viscosity liquid flow, which forms instantly after impingement. Figure 3 is the computed shape of liquid flow formed by a high viscosity liquid jet a short period of time after impingement, just before the film ejects from the surface of block. Figure 4 is the velocity vector field formed by a lowviscosity liquid flow. A comparison of the surface profile with the results of laser Doppler velocimetry (LDV) experiment of Stevens and Webb17 is shown in Figure 5. The model results are in reasonably good agreements with experimental data. Results of the simulation confirmed that the viscosity of the liquid strongly affects the thickness and mean velocity of the film at the rim of the block (rim velocity). As illustrated in Figure 6, at a jet velocity of 15 m/s, while the liquid viscosity increases from 0.01 PaS to 1.03 PaS, the dimensionless thickness of the film at the rim increases from 1 to 4.1
Figure 3. Film shape (high viscosity).
2.2. Boundary Conditions and Flow Model. A geometric reconstruction scheme is utilized to track the movement of liquid flow in the VOF model. The internal flow of each phase is computed by the standard k-ε model. The governing equations of momentum, volume fraction, mass continuity, and turbulence kinetic energy are expressed below:16 Dφ DðuφÞ DðvφÞ D Dφ D Dφ ð7Þ þ þ ¼ Γφ þ Γφ þ Sφ Dt Dx Dy Dx Dx Dy Dy The corresponding functions are given in Table 1. Constant Cμ = 0.09, Cε1 = 1.44, Cε2 = 1.92, σε = 1.3, σk = 1.0.The computational domain is the cylinder space above the impingement surface. A two-dimensional axis-symmetric grid mesh with the smallest cell distance of 0.1 mm is used. To simplify computation, the effect of droplet impact is neglected. As mentioned above, the theoretical breakup length is longer
(17) Stevens, J.; Webb, B. W. Measurements of Flow Structure in the Radial Layer of Impinging Free-Surface Liquid Jet. Int. J. Heat Mass Transfer 1993, 36, 3751–3758.
(16) Chen C. J.; Jaw S .Y. Fundamentals of Turbulence Modeling; Taylor & Francis: Washington DC, 1998.
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: DOI:10.1021/ef900665g
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Figure 7. Effect of viscosity on velocity. Figure 5. Comparison of surface profile with experimental data.
Figure 8. Effect of jet velocity.
Figure 6. Effect of viscosity on thickness.
(Dimensionless thickness δþ is defined as δþ = δ/δ*, δ is the actual rim thickness of the liquid film, δ* is the film thickness formed by an ideal, inviscid liquid jet, δ* = Dj2/4Dr). Further investigations show that the increase in liquid viscosity raises the thickness of the boundary layer of the flow, reducing the mean velocity of the film, and consequently increasing the film thickness. 3.2. Effect of Jet Velocity on Film Behavior. Results show that film behavior varies with the increase in jet velocity from 10 to 18 m/s. As illustrated in Figures 8 and 9, an increase in jet velocity causes the rim velocity to rise, and the boundary layer thickness and liquid film thickness to decline. Further, the higher the viscosity of the liquid, the faster the film thickness decreases. For low-viscosity liquids, a variation of jet velocity has a smaller effect on film thickness because of a relatively thinner boundary layer.
Figure 9. Effect of jet velocity.
Our experiment has been conducted with the same diagnostic system described in the previous work of Yu.4 The performance of a ZD-type impinging jet atomizer with a load capacity of 1.67 kg/s of CWS fuel has been examined. Likewise, we use industrial glue as a substitute for CWS to avoid degradation of our laboratory apparatus. The viscosity of industrial glue used in this experiment is 8.45 mPaS (1/100 s). Although the macroscopic viscosity of CWS is large (0.5-1 PaS), the microscopic viscosity is similar to industrial glue. Compressed air was utilized as the atomizing gas, and the rotation velocity of a screw-pump controlled the liquid mass flow rate. The SMD was measured by a laser diffraction particle sizing instrument (LDS). Comparison between simulation and experiment is shown in Figures 10 and 11. Based on the simulation results of film thickness and rim velocity, the spray droplet diameter can be
4. Experiment and Comparison with Simulation Several experimental investigations on impinging jet atomizers are available where the effect of liquid viscosity on atomization efficiency has been studied. These results show that droplet size is affected by the liquid viscosity substantially while other parameters remain unchanged, and the increase of SMD can be observed when liquid viscosity increases.3 Based on the simulation results showed above, it is reasonable to conclude that an increase in viscosity causes the thickness of liquid film to increase and the atomization efficiency decline. 454
Energy Fuels 2010, 24, 451–455
: DOI:10.1021/ef900665g
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5. Conclusion The VOF method has been used to compute film thickness and rim velocity in a gas-assisted impinging jet atomizer. Droplet size has been calculated according to DombrowskiWAVE and Rayleigh models. Simulation results show that the rim velocity increase and film thickness decrease with an increase in jet velocity. As for the effect of liquid viscosity, rim velocity is reduced and film thickness increases when the liquid viscosity increases. The agreement between the predicted and experimental results reasonable. The methods presented here make it possible to quantitatively analyze and predict the droplet size produced by internal-mixing atomizers. However, the impingement of droplets and vibration on film surfaces may affect the behavior of liquid sheet, consequently affecting the droplet size and thus a diameter distribution is formed in reality.
Figure 10. GLR and SMD (0.8 MPa).
Acknowledgment. We gratefully acknowledge Dr. Damian Carrieri from Princeton University for the help on this paper, and the support of the Special Funds for Major State Basic Research Projects of China (2010CB227001).
Nomenclature a = radius C = constant D = diameter F = volume fraction G = model function H = model constant La = Laplace number k = wave number; kinetic energy(in turbulence model) M = momentum flux ratio P = pressure Q = dense ratio Oh = Ohnesorge number Re = Reynolds number T = model parameter U = velocity u,v = x-, y- velocity in turbulence model We = Weber number X = length of jet γ = velocity ratio ε = dissipation rate δ = sheet thickness F = density λ = wavelength ν = viscosity σ = surface tension j, Γ, S = turbulence model function
Figure 11. GLR and SMD (0.9-1.1 MPa).
computed with a Rayleigh’s model (low Weber number) or a WAVE model (high Weber number). Experimentally, an increase in GLR could be obtained either by decreasing the liquid flow rate or increasing the gas flow rate. Figure 10 is the resulting SMD for different GLR at the given atomizing gas pressure of 0.8 MPa. At a given atomizing gas pressure, the gas velocity (higher than liquid velocity) remains almost constant, and it is observed that SMD decreases with liquid flow rate. The reason is that a decrease in liquid flow rate leads to a decrease in rim velocity, and as the gas velocity remains constant, the relative velocity of the two phases increases. Based on the twin-fluid atomization mechanism, the interaction between phases is enhanced and atomization improves. And, though the sheet thickness increases slightly when the liquid flow rate decreases, results show that the influence of thickness on SMD is not as important as that of phase interaction. Experiments show that atomization efficiency is improved by increasing the atomizing gas pressure for the same GLR, as illustrated in Figure 11. Although at the same liquid flow rate, the film thickness and the rim velocity remain nearly constant when atomizing gas pressure increases, the calculated results (based on Dombroski-WAVE model) of the wavelength of the maximum growth rate decrease, thus a smaller droplet size is achieved. Simulations and experiments agree well in most conditions, but for low GLR, the SMD in simulation is relatively smaller than what is measured experimentally. This may be due to omission of droplet impingement in the model, and the simulation could be improved if this effect is considered.
Subscripts 1 = liquid phase 2 = gas phase b = breakup d = droplet j = jet l = line r = rim t = turbulence
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