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Advanced Scientific Computing
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ITAPS:
Atomization and Spray
Z. Xu, J. Glimm, X. Li, R. Samulyak, and C. Tzanos
In the past year, we have studied mechanisms leading to jet breakup and
spray formation for a high-speed diesel jet injected through a circular
nozzle using first principles simulations. The simulations are conducted
using the Front Tracking method within a 2D axis-symmetric geometry. Our
goal is to model the spray at a microphysical level, with the creation of
individual droplets. Through our study, we have found that the formation of
cavitation vapor bubbles is the key phenomenon contributing to the breakup.
During the inception stage of the cavitation, the flow is characterized by
traveling bubbles. The bubbles grow intensively and coalesce into big
bubbles. These bubbles create an atomizing spray.
We have developed a heterogeneous EOS model consisting of explicitly tracked
cavitation vapor bubbles within the liquid diesel to describe the mixed
phase (diesel vapor/liquid) regime. Motivated by homogeneous nucleation
theory, we have formulated a dynamic bubble insertion algorithm to simulate
the incipient creation of cavitation bubbles.
The interface that separates the liquid and the vapor is modeled as a phase
boundary. A new phase transition model to calculate the solutions for the
dynamic phase transitions has also been developed. In this model, viscosity
and the surface tension on the phase boundary are neglected, because the
thermal effects are normally dominant over the viscous effects in phase
transitions. We use the kinetic theory of evaporation to give the
evaporation rate with a coefficient α determined experimentally. The net
mass flux of evaporation then is
On the phase boundary, the temperature is continuous, while the vapor
pressure is allowed to have a deviation from the Clausius-Clapeyron
equation. Thus the interface motion depends on the phase change under
nonequilibrium thermodynamic conditions along with hydrodynamic conditions.
Three active scales enter into this simulation. The smallest (nm) is a
thermal layer at the edge of the vapor bubble to mediate the phase
transition rate. This scale is modeled, not resolved. The next two scales
are the bubble diameter (mm) and the nozzle/combustion chamber (cm), both
resolved numerically.
In the simulations, we used n-heptane as a replacement for No. 2 diesel fuel
because the thermal data of No. 2 diesel fuel is not available, and N-heptane
is the major component of No. 2 diesel fuel. We have compared our simulation
results with the experimental data [1-4]. These experimental data present
mass vs. time in a 0.55 mm wide observation window that is centered 1 mm
from the nozzle exit. Like the experiments, the simulations also predicted a
peak mass. After the peak, the predicted mass exhibits a small variability
(Figure 1). The opening angle of the jet (Figure 2), which varies as a
function of time, is about 15 to 30 degrees and is in agreement with its
experimental value. Figure 3 shows a comparison of jet tip velocity computed
from simulations [5,6] with experimental data. Although the value computed
from simulation predictions exhibits a wide variability, on the average, it
is in agreement with the value computed from the experiment. It should be
noted that the experimental data has been averaged over 100 injection cycles
to remove fluctuations.
The current work is focused mainly on the simulation of the two-phase
mixture resulting from cavitation; the influence of other parameters on
spray formation is a subject of further research.
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| Figure 1. The vorticity
(above) vs. density (below). The dark spots are the diesel vapor
bubbles. The bubbles appear and disappear as rarefaction waves
progress up and down the nozzle. The large blue region in the
lower frame is a vapor region. |
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Figure 2.
The plot of mass at 1mm from the nozzle exit. |
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Figure 3.
Comparison of jet tip velocity computed from simulations with
experimental data. |
References
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[1] MacPhee, A.G., Tate, M.W., and Powell, C.F. X-ray imaging of shock
waves generated by high pressure fuel sprays. Science 295: 1261-1263
(2002).
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[2] Poola, R.B. et al. Development of a quantitative measurement of a
diesel spray core by using synchrotron X-rays. Eighth International
Conference on Liquid Atomization and Spray Systems, Pasadena, CA, July
16-20, 2000.
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[3] Powel, C.F., Yue, Y., Poola, R., and Wang, J. Time resolved
measurements of supersonic fuel sprays using synchrotron x-rays. J.
Synchrotron Rad. 7: 356-360 (2000).
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[4] Powel, C.F., Yue, Y., Poola, R., Wang, J., Lai, M., and Schaller, J.
Quantitative x-ray measurements of a diesel spray core. In Proc. 14th
Annual Conference on Liquid Atomization and Spray Systems (ILASS),
Dearborn, MI, 2001.
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[5] Glimm, J., Kim, M.-N., Li, X.-L., Samulyak, R., and Xu, Z.-L. Jet
simulation in a diesel engine. Proc. Third MIT Conference on
Computational Fluid and Solid Mechanics, 2004, Computational Fluid and
Solid Mechanics 2005, ISBN: 0-08-044476-8.
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[6] Xu, Z., Kim, M.-N., Oh, W., Glimm, J., Samulyak, R., Li, X., and
Tzanos, C. Atomization of a high speed jet. J. Multiscale Comp. Eng.
Accepted, 2006.
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Last Modified: January 31, 2008
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