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Department of Aerospace Engineering & Engineering Mechanics
Gamertsfelder & Khare/UC 1
Jacob Gamertsfelder & Prashant Khare
Department of Aerospace Engineering & Engineering Mechanics
University of Cincinnati
Injector Dynamics and Atomization Behaviors of Liquid Monopropellants in
Pintle Injectors
Presented at
The Gerris/ Basilisk Users Meeting
18.06.19
Acknowledgements: CEAS, University of Cincinnati
Department of Aerospace Engineering & Engineering Mechanics
Gamertsfelder & Khare/UC 2
Outline
• Background
• Current Research and Objectives
• Theoretical formulation
• Model Validation
• Operating conditions and Geometry
• Analysis
• Conclusions and future work
Department of Aerospace Engineering & Engineering Mechanics
Gamertsfelder & Khare/UC 3
Background/Motivation Google images
Mark 48 Torpedo Lunar Excursion Module SpaceX Merlin Rocket Engine
Garden Hose, Monopropellant pintle injector SpaceX raptor engine bipropellant pintle injector cold flow test
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Current Status and Objectives
Gamertsfelder & Khare/UC 4
Objectives:
• Identify the fundamental mechanisms underlying the injector dynamics and
atomization behaviors of liquid monopropellants in pintle injectors
• Quantitatively investigate the droplet size distributions and their temporal and
spatial evolution
• Conduct parametric studies to investigate these behaviors at a wide range of
Weber numbers and operating pressures
Current Status and unresolved research issues: • Limited research exists on the fundamental mechanisms underlying the
monopropellant pintle injector dynamics and atomization behaviors
• Most research is dedicated to bipropellant engines.
Department of Aerospace Engineering & Engineering Mechanics
Multiphase & Multiscale Challenges
Weber number, We
Reynolds number, Re
Density ratio
Viscosity ratio
2
gU D
g
g
UD
l
g
l
g
Gamertsfelder & Khare/UC 4
• Discontinuity of material properties at the interface
• Surface tension singularity force active only at the interface
• Frequent topology changes
multiphase
multiscale • Time and length scales vary over several orders of magnitude
Department of Aerospace Engineering & Engineering Mechanics
0.2
0.3
0.8
1 1
1
0
0.9
0.95
Gas
Liquid
Gamertsfelder & Khare/UC 6
Governing Equations: Volume-of-Fluid Method (VOF)
• Incompressible, variable-density, Navier-Stokes equations:
• Volume fraction, two-phase fluid density and viscosity:
• Advection for volume fraction:
0
0)(
2((
u
u
nD)u)uus
t
tp
21
21
)1()(
)1()(
ccc
ccc
0)( ucct
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Gamertsfelder & Khare/UC 7
Adaptive Mesh Refinement (AMR)
• Gradient and value based refinement
• Cells without AMR 5.49 × 1012
• Cells with AMR = 28.623 million
• Total reduction = 99.47%
• Min. cell size = 0.305µm
Adaptive Mesh Refinement (AMR)
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Validation Of The Model
• Model validation will be based upon the work of Vlad Petrescu
• The model validation will be three faceted comparing
• Spray Angle
• Sauter mean diameter
• Physical inspection
Gamertsfelder & Khare/UC 8
Physical Properties Water (1.6psi) Chamber gas (air
atmospheric)
Density, ρ (kg/m3) 1000 1.28
Viscosity, μ (Pa∙s) 9.532x10-4 1.822x10-5
Surface Tension, σ N/m) 0.07275
Model geometry
Experimental geometry
Atomized spray properties in pintle injection , Petrescu, Schrijer and Zandbergen
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Qualitative comparison with experimental measurements
Gamertsfelder & Khare/UC 9
20mm 40mm 55mm 70mm
From the Experiment
Liquid sheet
Ligaments
Droplet formation
Atomized spray properties in pintle injection , Petrescu, Schrijer and Zandbergen
Department of Aerospace Engineering & Engineering Mechanics
Validation: SMD and spray angle comparison with experiment
Location
from
injector
SMD from
experiment
(µm)
SMD from
present
calculations
(µm)
% error
60 mm 1291.32 1273.74 1.36%
65 mm 1194.56 1242.79 -4.04%
70 mm 1104.14 1101.92 0.20%
Gamertsfelder & Khare/UC 10
60mm 70mm Experimental Present
Calculations
% error
Spray
angle
31.0 29.7 4.2%
Atomized spray properties in pintle injection , Petrescu, Schrijer and Zandbergen
Department of Aerospace Engineering & Engineering Mechanics
Otto Fuel II Chamber gas
Density, ρ (kg/m3) 1232 123.2
Viscosity, μ (Pa∙s) 0.44 2.0764 x 10-7
Surface Tension, σ N/m) 0.03445
Physical Properties and Geometry
no-slip boundary condition
3.34m/s
5mm
l
l
u
d
constant
inflow
outflow
g
g
g
g
𝜌𝑙𝑢2𝑟
𝜎 We = = 500
P 10.62
T 300K
MPa
annulus
diameter, d
r
r
u
w
l
w
pintle
pintle movement
Gamertsfelder & Khare/UC 8
g
g
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3-D VOF
Pintle Injector Atomization at We=20
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Gamertsfelder & Khare/UC 10
Pintle Injector Atomization at We=20
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Side View
Detailed Physics: Ligament Formation 3-D
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non-dimensionalized time, t = t*/(d/Uj ) = 0.0 - 0.11
Side View Axial view
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2-D center plane slice
Detailed Physics: Ligament Formation 2-D
Tracer VOF
1.0
0.5
0.0
non-dimensionalized time, t = t*/(d/Uj ) = 0.0 - 0.11
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16 Khare/UC
non-dimensionalized time, t = t*/(d/Uj ) = 0.11- 0.21
Detailed Physics: First break-up 3-D
Axial view
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3-D View
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Tracer VOF
1.0
0.5
0.0
Detailed Physics: First break-up 2-D
non-dimensionalized time, t = t*/(d/Uj ) = 0.11- 0.21
2-D center plane slice
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18 Khare/UC
Detailed Physics: Sheet Sheering and Break-up
Gamertsfelder & Khare/UC
non-dimensionalized time
t = t*/(d/Uj ) = 0.22 - 0.90
non-dimensionalized time
t = t*/(d/Uj ) = 0.19
3-D VOF - Outside 3-D VOF -Inside
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19 Khare/UC
non-dimensionalized time, t = t*/(d/Uj ) = 0.50 - 1.00
2-D Center Plane Slice 3-D VOF
Detailed Physics: Appearance of Kelvin-Helmholtz Instabilities
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Khare/UC
2-D
center
slice
2-D Vorticity slice
Detailed Physics: Droplet Recirculation Vortex Formation
Gamertsfelder & Khare/UC 17
non-dimensionalized time t = t*/(d/Uj ) = 1.24 – 1.40
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21 Khare/UC
3-D VOF
non-dimensionalized time,
t = t*/(d/Uj ) = 1.64
Detailed Physics: Clumping and Droplet Coalescence Hinders Atomization
Gamertsfelder & Khare/UC
2-D Tracer Iso-line
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Droplet Production Changes with Time
Khare/UC 17 Gamertsfelder & Khare/UC 22
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Droplet Production in terms of Probability
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Sauter Mean Diameter
Khare/UC 21 Gamertsfelder & Khare/UC
s
1D
i
ii
f
d
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Gamertsfelder & Khare/UC 25
Conclusion
• High-fidelity numerical simulations were conducted to
quantitatively identify the atomization of
monopropellant pintle injectors was investigated
• By the formation of recirculation zones slowing the
flow in the U direction.
• By the ligaments breaking inwards leading to formation
of larger droplets
• Droplet distribution analysis shows that droplet
coalescences increaces the overall sauter mean
diameter
• Droplet distribution analysis also shows an Gaussian
droplet distribution with a slowing production rate due
to droplet coalescence
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Future Investigations
• Investigate and quantify the differences in breakup
and droplet distribution for different Weber numbers
and operating pressures
• Determine the effect of pintle angle and location on
droplet distribution
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Questions?
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Back-up
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Sauter Mean diameter Comparison
Gamertsfelder & Khare/UC 29
0
500
1000
1500
2000
2500
20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115
SMD
in µ
m
Distance from the Pintle injector in mm
Extrapolated Sauter mean diameter from emperical equation
Experimental Values
Model Values
Atomized spray properties in pintle injection , Petrescu, Schrijer and Zandbergen
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Spray Angle Comparison
Gamertsfelder & Khare/UC 30
Model had a 31 degree half spray angle measured at 10mm
Atomized spray properties in pintle injection , Petrescu, Schrijer and Zandbergen