VALIDATION OF Σ−YLIQ ATOMIZATION MODEL IN PRESSURE SWIRL ATOMIZER Sherry K. Amedorme 1, NR.N. Roselina 2 1 Department
of Mechanical and Automotive Technology, Akenten
Appiah-Menka University of Skills Training and
Entrepreneurial Development, Kumasi-Ghana 2 Faculty
of Mechanical Engineering, Universiti Teknologi MARA, 40450 Shah Alam
Selangor Malaysia
1. INTRODUCTION Pressure swirl atomizer also known as simplex
atomizers are of different types ranging from plain orifice to dual orifice
atomizers. The fundamental principle of this atomizer is that liquid is induced
in the tangential ports and the combination of the swirling and the translation
motion of the liquid result in the liquid leaving the exit orifice as a hollow
cone sheet with the formation of air core in the centre. The hollow cone sheet
disintegrates into ligaments and then forms droplets Lefebvre et al. (2017), Rashad et al. (2016), Cui et al. (2017). Liu et al. (2019) and Malý et al. (2018) studied the
motion of liquid in the pressure swirl atomizer and indicate that the flow
mechanism inside and outside the atomizer is complex and not well understood.
Amongst several causes, factors such as the operating condition, design, and
size of the atomizer tested, complex atomization process, as well as
limitations of drop measurement instrument and techniques are very key
considerations. In terms of design, the pressure atomizer has inlet ports,
swirl chamber, and an outlet orifice.
The tangential inlet ports are of several channels and designs and
introduce liquid fuel to the swirl chamber which imparts swirl energy to the
liquid fuel and also contains air-core vortex. In this
chamber, a portion of the swirl motion of the liquid is converted to axial
velocity for the liquid to emerge as a hollow cone spray. The outlet orifice
has contraction or convergence and contains holes for the liquid to be
discharged Dafsari et al. (2017), Liu et
al. (2017). In these parts of the pressure swirl atomizer, the
pressure exerted on the wall by the liquid, the tangential and the axial
components of the velocity, and air-core characteristics are some of the
important parameters analysed. These parameters significantly affect the
discharge coefficient at the exit orifice, mean droplet sizes and distribution,
spray cone angle, velocity distributions, and the liquid film thickness of the
spray emanating from the atomizer. Several researchers including, Hu et al. (2019) and Wu et al. (2020), Shin et al. (2019), Ortman and Lefebvre (1985), and Zhang et al. (2017) and Dafsari et al. (2019) studied the
influence of injection pressure on spray cone angle. The results obtained show
that within a given range of injection pressures, the equivalent spray angle is
inversely related to the change in pressure. Ortman
and Lefebvre also show that starting from atmospheric pressure, the spray cone
angle first widens and then contracts with increases in the liquid pressure.
The most common research on a pressure-swirl atomizer is the influence of
pressure on the mean drop size. Several researchers including Lefebvre and Wang (1987), Belhadef et al. (2012), and Emekwuru and Watkins (2010) did extensive work
in this regard. They show that the mean drop sizes emanating from the
pressure-swirl atomizer decrease with increasing pressure. It is also observed
that within the swirl chamber the pressure is constant but decreases sharply in
both the convergence zone and the outlet orifice. The liquid velocity which has
axial, tangential, and longitudinal components also depend mainly on the
injection pressure and affect the degree of atomization Khani et al. (2020). The internal
characteristics and the nozzle dimensions are not the only factors that govern
atomization performance. Other factors relating to the liquid and ambient gas
properties also affect greatly the mean droplet size and distribution. The
instabilities and break-up of the liquid sheet are promoted by the gas density
due to aerodynamic interaction but prevented by the liquid properties such as
surface tension and viscosity. The ambient gas varies widely in pressure and
temperature and influences strongly the mean droplet
sizes and the spray angle. it is indicated that the ambient gas increases with
decreasing spray angle until a maximum spray value is reached which does not
affect the spray angle. Due to the higher inertia of the liquid phase, liquid density
also alters the performance of the atomizer and the atomization characteristics,
and it has been shown that its effect on the mean droplet size is quite minimal
Lefebvre and McDonell (2017). In many studies,
the liquid viscosity is the most important liquid property analysed in this
atomizer. As indicated by Lefebvre although its influence on atomization is not
that significant as the surface tension, however, its relevance is because it
does not only influence the mean drop size and distribution but flow rate and
the spray formation as well. A key
effect of increase in liquid viscosity is its reduction influence on the
Reynolds number and the prevention of liquid sheet natural instability and
break up. The overall effect is that it delays the disintegration of the liquid
jet or sheet and increases the droplet sizes in the spray. However, in a pressure swirl atomizer, a slight
rise in the viscosity maximizes the flow rate which is achieved by increasing
the liquid film thickness in the discharge orifice which in turn makes the
effective flow area to be raised. But beyond the optimal liquid viscosity, this
trend changes and the flow rate reduce with increase in liquid. The liquid flow
rate does not only depend on the liquid properties but also on the geometrical
sizes and the pressure difference across the atomizer Wimmer and Brenn
(2012). Beheshti et al. (2007) assessed Ʃ
−Y model in an air-assisted atomizer and predicted the effects of liquid
properties and injection regimes on the atomization quality It was shown that
the model predictions and experimental data have a good agreement for a wide
range of variations of density and surface tension of the liquid as well as the
injection regimes for liquid and gas jet exit velocities. They noted however
that the model is limited in the fact that it only attempts to resolve the
Sauter mean diameter (SMD) and as such is unable to resolve effects caused by a
wide distribution of droplet size in polydispersed
sprays such as ballistic drop spreading. They concluded that this is acceptable
in the current application because existing experimental data for gaseous and
aerosol jets show a lower spreading rate for an increasingly heavy central jet
suggesting that variable density effects are more dominant than ballistic
spreading Gharbi et al. (1996), Trask (2010), Beheshti et al. (2007). In modelling two-phase flow in pressure swirl
atomizers using computational fluid dynamics (CFD) two approaches are commonly
used. The Eulerian approach where the spray is treated as a continuum within
the computational flow domain and the Lagrangian
technique tracked the droplets in the flow domain. Lin et al. (2009) and Xiong et al. (2009) carried out a study
on non-swirling effervescent atomization spray using a combination of a
Eulerian k-ɛ turbulence model to capture the droplets and gas-phase
interaction in the secondary break-up and use the Lagrangian
approach to model the disperse droplet phase. In this study, the droplet
velocity is calculated in a far-field using a single-phase approach developed
for high-density variation. In using the Eulerian method to solve two-phase
problems the state equations of each phase are solved and the interaction
between the two phases must be accounted for. This requires complex modelling
and a high number of equations as each fluid is transported Bishop (1975), Drew (1983), Mirjalili et al. (2017). This work focuses
on the entirely one-fluid Eulerian model which potentially brings the advantage
to compute only the transport of one single fluid with a high-density variation
Belhadef et al. (2012). This novel and
general mathematical model developed and presented by Vallet et al. (2001) for an entirely
Eulerian model called the Ʃ-Y atomization model has the potential for all
the basic necessary capabilities. It describes atomization from the first
principle. However, its validation in pressure swirl atomizer is insufficient
and has not been demonstrated well enough at the time being and therefore needs
further research and improvement. 2. MATERIALS AND METHODS The experiment was performed using the Malvern Spraytec drop measuring instrument as shown in Figure 1. Liquid water in 0.4l container was pumped to
the mainline with the aid of a 240V power source. The speed of the pump was
controlled by a 300W triple source which enables the supply voltage to be
varied. In measuring the mean droplet sizes at the various flow rate, the
voltage supplied to the pump was varied since the flow rate could not be
measured directly. The voltages of 0.5, 1, 1.5, 2 and 2.5 were used. The pressure transducer was used to measure
pressure drop across the apparatus and the pressure in the system is detected
by a pressure sensor which converts it to an analogue signal to be read by the
digital multimeter which then changes back to
pressure. The circuit set up for the pressure measurement apparatus was in the
range of 4-20mA containing a 500Ω resistor. The designed atomizer was
clamped to a vertical stand to allow easy changing, and the liquid was sprayed
downwards into the laser beam. The stand was built to accommodate variations in
all directions above the laser beam. To prevent the deflection and splashback
of the liquid absorbent tissue paper was put in the container. Figure 1
The PFS 1392B1 atomizer used
was produced by PNR Ltd which is a nozzle manufacturing company based in the
UK. The specifications of the atomizer are inlet and exit diameters of 3.7 and
3.5mm respectively with a rated spray angle of 70 degrees and 3.90 per minute
as flow rate at 3.0 bar gauge pressure as shown in Table 1. Liquid water was used for the experiment
with density, viscosity property values as 1000 kg/m3, 0.001kg/ms, and 0.072 kg/s2 respectively Crowley et al. (1990) Emekwuru and Watkins (2010). The
parameters of the Malvern instrument are shown in Table 2. Table 1
Table 2
3. RESULTS AND DISCUSSIONS Figure 2 shows the graph of turbulent intensity decays along the axial position by comparing the standard k-epsilon and RNG k-epsilon turbulence models. It can be observed that the standard k-epsilon model predicted a higher decay in the average turbulent intensity as compared to RNG k-epsilon. In comparing the two turbulence models, the inlet turbulent intensity was kept constant. In theory, turbulence is affected by swirl in the mean flow. Since the RNG model accounts for this rotational motion appropriately by modifying the turbulent viscosity, larger decay could be counted for and therefore the turbulence in the flow gets uniformly distributed in the swirl chamber and the computational domain as compared to the standard model. In Figure 3, it can be seen that 10% of turbulent intensity is nearer to the experimental data points and the standard k-epsilon model utilize in this atomization is the best because it tends to produce the smallest SMD and the best match and configurations with the experimental results when compared to the RNG and Realizable K-epsilon turbulence models (Figure 4). It is observed that the turbulent intensity is greater in the periphery of the spray than the center spread of the nozzle, and this conforms to the observation made by Yoon et al. (2011). This is due to the droplet which decreases momentum in the outside spray making an enormous impact by the inflow of surrounding air. Towards the downstream of the spray, the turbulent intensity gets smaller because the momentum of relative velocity is sharply reduced and there are less actions of air current for droplet which is related with the highly small amount of air brought by its surroundings. However, there were no significant changes in the droplet velocity when the three turbulent models were compared as shown in Figure 5. Figure 2
Figure 3
Figure 5
Figure 6 shows the
comparison of the model with measurements for droplet Sauter Mean Diameter
(SMD) at y=60, 80, 100 and 120 mm. The agreement between the model and
experimental radial profiles at 60 mm downstream of the nozzle is good. The
trend shows that the Sauter mean diameter SMD increases with increasing radial
distances which is qualitatively correct, but the rate of change is small with
the mean diameter of the large droplets found on the periphery of the spray
under-predicted and the small mean drop size at the vicinity of the spray
centreline perfectly predicted. At the axial position of 80 mm from the exit of
the nozzle, the agreement between the atomisation model and experimental
radial droplet mean diameter distributions is satisfactory with good prediction
of the droplet size at the spray periphery but higher than the value predicted
at position 60 mm axial distance from the nozzle exit. The rate of increase of
droplet size with radial distance is correct and the size of the largest
droplet at the spray periphery is well predicted. There is also a good
agreement between the radial positions at 100 mm downstream of the nozzle for
the model and the measurement with the droplet SMD having a slight
under-prediction of less than an average of 3%. The result at this axial
position also shows that most of the predicted SMDs near the inner region of
the spray are below the experimental values. In addition, the SMD increases at
similar rates with radial distances for both results at this axial position.
The radial profiles for the mean droplet sizes (SMDs) between the calculations
and the experiments at the axial position 120 mm from the exit of the nozzle
are closer with the SMD being small near the centreline of the spray and SMD
reasonably predicted. The trend of increasing droplet size with radial distance
is observed and agrees with the work of many researchers in predicting the mean
drop sizes from a pressure swirl atomizer Lefebvre and Wang (1987), Emekwuru and Watkins (2010). The mean drop
diameter of the experimental results of the largest droplet at the periphery of
the spray is higher than its predicted values. However, the SMD at a radial
distance near the spray centreline is closely predicted in relation to the
measurements. The more uniform and continuously increasing Sauter mean diameter
with radial distance may be attributed to the farthest axial distance from
which the drop sizes were measured and may also be due to the coalescence of
smaller droplets and this has been accounted for in the model. The small drop
sizes observed around the spray symmetry axis may be attributed to collisions
between the liquid droplets and aerodynamic drag interactions with the
entrained air as a result of the hollow cone spray
pattern emanating from the nozzle Lefebvre and Wang (1987). The
collisions result in unstable interactions between the drops and in turn lead
to the breaking down of droplets smaller than their original sizes. This is
also supported by the observation made by Yoon et al. (2011) that the
separation of small droplets near the centreline arises due to the complex
interaction between fluctuating turbulent length scales and air entrainment.
This causes the mean gas motion to drive the smaller droplets towards the
centreline of the spray. Larger droplets follow more ballistic trajectories
subject to initial velocity vectors resulting from the liquid sheet breakup
process and turbulent dispersion since they are not affected much by the air
entrainment. However, in the downward part of the spray, the inward entrainment
velocities are decreased to the point where smaller droplets are significantly
dispersed from the centre line. Overall, the computational predictions of SMD
for atomisation model shows a very
good agreement with most of the experimental measurements in the radial
positions when standard k-ɛ turbulence was used. However, more
divergence was observed between the
predictions and the experimental measurements when the RNG k-ɛ turbulence
model and Realizable k-ɛ turbulence model were used in the predictions as shown
in Figure 7 and Figure 8. Figure 6
Figure 7
Figure 8
Figure 9 illustrates
the validation of the model with the experimental results on the spray
centreline. It can be observed that the model has good agreement with the
measurements with a percentage error of less than an average of 5% between the
model and the experiments at axial distances of 60 mm and 120mm. Better
predictions are observed at axial distances 80mm and 100mm. Figure 10 shows more
clearly how sensitive SMD is to the pressure differentials. This is because as
pressure increases the faster maximum growth rate of the liquid film occurs and
will lead to the linear stability of the surface wave of the thread film
getting worse. So, the interaction between the liquid phase and the gas phase
becomes stronger and the film can break up more easily. This will make the
droplet SMD get smaller as pressure increases. Figure 9
Figure 10
4. CONCLUSIONS A validation of mean drop sizes at both centreline and radial positions was performed using laser-diffraction-based drop size measurement and atomization model. It is shown that the model predictions have good agreement with the experimental measurements when standard k-ɛ turbulence was used. The experimental results are also consistent with the model predictions when the effect of pressure differential on the SMD was analysed. In all, it can be concluded that the computational predictions of SMD for the atomization model shows good validation with the experimental measurements.
CONFLICT OF INTERESTS None. ACKNOWLEDGMENTS None. REFERENCES Beheshti, N., Burluka, A. A., and Fairweather, M. (2007). Assessment of Σ− Y liq Model Predictions for Air-Assisted Atomisation. Theoretical and Computational Fluid Dynamics, 21, 381-397. https://doi.org/10.1007/s00162-007-0052-3. Belhadef, A., Vallet, A., Amielh, M., and Anselmet, F. (2012). Pressure-Swirl Atomization : Modeling and Experimental Approaches. International Journal of Multiphase Flow, 39, 13-20. https://doi.org/10.1016/j.ijmultiphaseflow.2011.09.009. Bishop, R. (1975). Thermo-Fluid Dynamic Theory of Two-Phase Flow. IOP Publishing. https://doi.org/10.1088/0031-9112/26/12/034. Crowley, J. M., Wright, G. S., and Chato, J. C. (1990). Selecting a Working Fluid to Increase the Efficiency and Flow Rate of an EHD Pump. IEEE Transactions on Industry Applications, 26(1), 42-49. https://doi.org/10.1109/28.52672. Cui, J., Lai, H., Li, J., and Ma, Y. (2017). Visualization of Internal Flow and the Effect of Orifice Geometry on the Characteristics of Spray and Flow Field in Pressure-Swirl Atomizers. Applied Thermal Engineering, 127, 812-822. https://doi.org/10.1016/j.applthermaleng.2017.08.103. Dafsari, R. A., Lee, H. J., Han, J., Park, D. C., and Lee, J. (2019). Viscosity Effect on the Pressure Swirl Atomization of an Alternative Aviation Fuel. Fuel, 240, 179-191. https://doi.org/10.1016/j.fuel.2018.11.132. Dafsari, R. A., Vashahi, F., and Lee, J. (2017). Effect of Swirl Chamber Length on the Atomization Characteristics of a Pressure-Swirl Nozzle. Atomization and Sprays, 27(10), 859-874. https://doi.org/10.1615/AtomizSpr.2017024777. Drew, D. A. (1983). Mathematical Modeling of Two-Phase Flow. Annual Review of Fluid Mechanics, 15, 261-291. https://doi.org/10.1146/annurev.fl.15.010183.001401. Emekwuru, N., and Watkins, A. P. (2010). Analysis of a Two-Fluid Sprayer and its Use to Develop the Number Size Distribution Moments Spray Model, Part II :Computational Analysis. Atomization and Sprays, 20(6), 467-484. https://doi.org/10.1615/AtomizSpr.v20.i6.10. Gharbi, A., Ruffin, A., Anselmet, F., and Schiestel, R. (1996). Numerical Modelling of Variable Density Turbulent Jets. International Journal of Heat and Mass Transfer, 39(9), 1865-1882. https://doi.org/10.1016/0017-9310(95)00290-1. Hu, J., Liu, B., Zhang, C., Gao, H., Zhao, Z., Zhang, F., Wang, Y. (2019). Experimental Study on the Spray Characteristics of an Air-Assisted Fuel Injection System Using Kerosene and Gasoline. Fuel, 235, 782-794. https://doi.org/10.1016/j.fuel.2018.08.083. Khani Aminjan, K., Kundu, B., and Ganji, D. (2020). Study of Pressure Swirl Atomizer with Tangential Input at Design Point and Outside of Design Point. Physics of Fluids, 32(12), 127113. https://doi.org/10.1063/5.0032174. Lefebvre, A. H., and McDonell, V. G. (2017). Atomization and Sprays. CRC press. https://doi.org/10.1201/9781315120911. Lefebvre, A., and Wang, X. (1987). Mean Drop Sizes from Pressure-Swirl Nozzles. Journal of Propulsion and Power. 3(1), 11-18. https://doi.org/10.2514/3.22946. Lin, J., Qian, L., Xiong, H., and Chan, T. L. (2009). Effects of Operating Conditions on Droplet Deposition onto Surface of Atomization Impinging Spray. Surface and Coatings Technology, 203(12), 1733-174. https://doi.org/10.1016/j.surfcoat.2009.01.009. Liu, C., Liu, F., Yang, J., Mu, Y., Hu, C., and Xu, G. (2019). Experimental Investigations of Spray Generated by a Pressure Swirl Atomizer. Journal of the Energy Institute, 92(2), 210-221. https://doi.org/10.1016/j.joei.2018.01.014. Liu, Z., Huang, Y., and Sun, L. (2017). Studies on Air Core Size in A Simplex Pressure-Swirl Atomizer. International Journal of Hydrogen Energy, 42, 18649-18657. https://doi.org/10.1016/j.ijhydene.2017.04.188. Malvern-Instruments (2007). Spraytec User Manual MAN0368. Issue. Malý, M., Sapík, M., Jedelský, J., Janáčková, L., Jícha, M., Sláma, J., Wigley, G. (2018). Internal Flow Characteristics in Scaled Pressure-Swirl Atomizer. EPJ Web of Conferences. 02059. https://doi.org/10.1051/epjconf/201818002059. Mirjalili, S., Jain, S. S., and Dodd, M. (2017). Interface-Capturing Methods for Two-Phase Flows : An Overview and Recent Developments. Center for Turbulence Research Annual Research Briefs, 117-135. Ortman, J., and Lefebvre, A. (1985). Fuel Distributions from Pressure-Swirl Atomizers. AIAA Journal of Propulsion and Power, 1(1), 11-15. https://doi.org/10.2514/3.22752. Rashad, M., Yong, H., and Zekun, Z. (2016). Effect of Geometric Parameters on Spray Characteristics of Pressure Swirl Atomizers. International Journal of Hydrogen Energy, 41(35), 15790-15799. https://doi.org/10.1016/j.ijhydene.2016.04.037. Shin, D., Bokhart, A. J., Rodrigues, N. S., Sojka, P., Gore, J. P., and Lucht, R. P. (2019). Experimental Study of Spray Characteristics at Cold Start and Elevated Ambient Pressure Using Hybrid Airblast Pressure-Swirl Atomizer. AIAA Scitech 2019 Forum, 1737. https://doi.org/10.2514/6.2019-1737. Trask, N. A. (2010). Implementation of an Eulerian Atomization Model to Characterize Primary Spray Formation. Masters Theses, 434. Vallet, A., Burluka, A.A., and Borghi, R. (2001). Development of a Eulerian Model for the "Atomization" of a Liquid Jet. Atomization and Sprays, 11(6). https://doi.org/10.1615/AtomizSpr.v11.i6.20. Wimmer, E., and Brenn, G. (2012). Viscous Effects on Flows Through Pressure-Swirl Atomizers. In Proceedings of the 12th Triennial International Conference on Liquid Atomization and Spray Systems (ICLASS 2012), Heidelberg, Germany. 2-6. Wu, S., Gandhi, A., Li, H., and Meinhart, M. (2020). Experimental and Numerical Study of the Effects of Nozzle Taper Angle on Spray Characteristics of Gdi Multi-Hole Injectors at Cold Condition. Fuel, 275, 17888. https://doi.org/10.1016/j.fuel.2020.117888. Xiong, H. B., Lin, J. Z., and Zhu, Z. F. (2009). Three-Dimensional Simulation of Effervescent Atomization Spray. Atomization and Sprays, 19(1), 75-90. https://doi.org/10.1615/AtomizSpr.v19.i1.50. Yoon, S. H., Kim, D. K., and Kim, B. H. (2011). Effect of Nozzle Geometry for Swirl Type Twin-Fluid Water Mist Nozzle on the Spray Characteristic. Journal of Mechanical Science and Technology, 25, 1761. https://doi.org/10.1007/s12206-011-0506-9. Zhang, T., Dong, B., Chen, X., Qiu, Z., Jiang, R. and Li, W. (2017). Spray Characteristics of Pressure-Swirl Nozzles at Different Nozzle Diameters. Applied Thermal Engineering, 121, 984-991. https://doi.org/10.1016/j.applthermaleng.2017.04.089.
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