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By Peter Strakey, National Energy Technology Laboratory, Morgantown, WV and Douglas Talley, Air Force Research Laboratory, Edwards Air Force Base, CA
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Liquid surface colored by velocity magnitude for the gas-centered swirl coaxial injector
using a k- ε (top), and an LES (bottom) turbulence model and the VOF model, after a
statistically steady-state condition has been reached
The U.S. Air Force Research Laboratory, Space and
Missile Propulsion Division, Aerophysics Branch
(AFRL/PRSA) has been conducting simulations of liquid
film and droplet breakup with FLUENT 6.1. Several simulations
have been completed for a variety of gas-centered
swirl coaxial rocket injectors, similar to the injector styles
used in some large booster engines. This type of rocket
injector involves a high-velocity oxidizer gas flowing down
the core of the injector and a liquid propellant film injected
through several tangential inlets just downstream of a
sudden expansion.
Initial simulations using the volume of fluid (VOF) interface
tracking method with a k-ε turbulence model revealed
that the Reynolds averaging turbulence approach overly
damped the fine scales of atomization, showing only the
larger waves and surface fluctuations. Grid refinement
resulted in very little improvement and the overall agreement
with experimental data was poor. A similar approach
using large eddy simulation (LES) coupled with the VOF
model showed a dramatic increase in the prevalence of
small scale atomization and better qualitative agreement
with the experimental observations.
A transient simulation of water droplet breakup with a time between frames of 1.5 µs
A more fundamental study is currently underway to
understand the basic physics of turbulent atomization using
a combined modeling and experimental approach. This
study involves the observation of the breakup of a confined,
thin liquid film flowing along a wall in a pressurized channel.
The liquid is introduced through a laminar velocity inlet
adjacent to the wall. A gas inlet is located above the liquid
inlet, and also has a prescribed laminar velocity. The gas and
liquid velocities are in the ratio of 10:1. A turbulence trip,
located along the bottom wall of the gas channel, upstream
of the liquid injection point, is included in both the model
and experiment to provide a gas flow field with turbulence
levels characteristic of rocket injectors at the point of liquid
injection. The front and back edges of the 3D square channel
are modeled using periodic conditions.
Using the VOF and LES models, the interface shows
widespread film breakup after a statistically steady-state
condition is achieved. Both the experiment and numerical
results show large perturbations of the gas-liquid interface
with a wavelength similar in size to the scale of the large,
energy containing eddies. This is in contrast to the very small Kelvin-Helmholtz wavelength usually associated with
the breakup at high velocity gas-liquid interfaces. Plots of
the vorticity magnitude on the central plane indicate that
there is a large amplification of the turbulence intensity in
the region of the interface. The numerical results for film
thickness are in good qualitative agreement with the experimentally
measured values.
An iso-surface of density, showing the liquid surface for the flat-film injector
simulation
Secondary atomization at high pressure is also being
studied at AFRL using the VOF model in conjunction with
LES. The simple case of a droplet breaking up in a highspeed
gas flow has been used to study the behavior. The
problem domain is set up as a 3D rectangular space with a
velocity inlet at one end, a pressure outlet at the other, and
symmetry boundaries on the sides. Gaseous nitrogen
enters through the inlet with a speed of 50 m/s. At time
t=0, a 100 µm water droplet is “placed” in the computational
domain near the entrance of the duct and the resulting
gas and liquid flow field is calculated. Using a grid of
approximately 4 million cells, with cell sizes of about 1.5
µm, the initial droplet diameter is represented by about 67
cells (160,000 cells by volume). This is believed to be somewhat
under-resolved, based on a secondary droplet size
approximately 1/10th the parent droplet size, and a need
for approximately 10 grid cells across the diameter of the
secondary droplets for sufficient numerical accuracy. This
case corresponds to a Weber number (ratio of inertial force
to surface tension) of 347, which means that the drop is
likely to break up rapidly. Each frame in the series shown
above represents an advancement in time of 1.5 µs, using
a timestep of 0.005 µs. Requiring 2.7 minutes per time step
on 8 CPUs, the entire simulation required 81 hours with a
parallel efficiency of about 80%. Also note that much of the
droplet impinged upon the duct (symmetry) walls, indicating
that the computational domain was too small to sufficiently
encompass the breakup of the droplet.
A center-plane slice of density contours for the wall film breakup case; the
inset shows experimental results under the same conditions
A center-plane slice showing vorticity magnitude contours (log scale)
The waves evident on the surface of the droplet after
1.5 µs of this simulation are interesting. A quick analysis
reveals that the predicted wavelength, based on Raleigh-
Taylor type instabilities, is around 20 µm or 1/5th of the initial
droplet diameter, which is reasonably close to the
observed wavelength in the simulations. Grid refinement
studies are currently being conducted to determine the
effect of grid resolution on the resulting breakup characteristics.
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