Department of Aerospace Engineering & Engineering Mechanics Injector Dynamics and Atomization Behaviors of Liquid Monopropellants in Pintle Injectors
Jacob Gamertsfelder & Prashant Khare Department of Aerospace Engineering & Engineering Mechanics University of Cincinnati
Acknowledgements: CEAS, University of Cincinnati, OSGC
1 Gamertsfelder & Khare/UC Outline
Department of Aerospace Engineering & Engineering Mechanics • Background • Current Research and Objectives • Theoretical formulation • Model Validation • Operating conditions and Geometry • Analysis • Conclusions and future work
2 Gamertsfelder & Khare/UC Background/Motivation
Department of Aerospace Engineering & Engineering Mechanics Google images
Mark 48 Torpedo Lunar Excursion Module SpaceX Merlin Rocket Engine
3 Gamertsfelder & Khare/UC Garden Hose, Monopropellant pintle injector SpaceX raptor engine bipropellant pintle injector cold flow test Current Status and Objectives
Department of Aerospace Engineering & Engineering Mechanics 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.
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
4 Gamertsfelder & Khare/UC Multiphase & Multiscale Challenges
Department of Aerospace Engineering & Engineering Mechanics
• Discontinuity of material properties at the interface multiphase • Surface tension singularity force active only at the interface • Frequent topology changes multiscale • Time and length scales vary over several orders of magnitude
2 gUD Weber number, We
gUD Reynolds number, Re g
l Density ratio g
l Viscosity ratio g
4 Gamertsfelder & Khare/UC Governing Equations: Volume- of-Fluid Method (VOF) Department of Aerospace Engineering & Engineering Mechanics
• Incompressible, variable-density, Navier-Stokes equations:
(t u + uu) = −p + (2D)+s n
t + (u) = 0 u = 0 • Volume fraction, two-phase fluid density and viscosity:
(c) c1 + (1− c)2 Gas (c) c1 + (1− c)2 0.8 0.2 0 • Advection for volume fraction:
t c + (cu) = 0 1 0.95 0.3
1 1 0.9 Liquid
6 Gamertsfelder & Khare/UC Adaptive Mesh Refinement (AMR)
Department of Aerospace Engineering & Engineering Mechanics
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
7 Gamertsfelder & Khare/UC Validation Of The Model
Department of Aerospace Engineering & Engineering Mechanics
• Model validation will be based upon the work of Vlad Petrescu • The model validation will be three faceted comparing • Spray Angle • Sauter mean diameter Chamber gas (air Physical Properties Water (1.6psi) • Physical inspection atmospheric) Density, ρ (kg/m3) 1000 1.28 Viscosity, μ (Pa∙s) 9.532x10-4 1.822x10-5 Experimental geometry Surface Tension, σ N/m) 0.07275 Model geometry
Atomized spray properties in pintle injection , Petrescu, Schrijer and Zandbergen 8 Gamertsfelder & Khare/UC Qualitative comparison with experimental measurements Department of Aerospace Engineering & Engineering Mechanics Liquid sheet
Ligaments
Droplet formation 20mm 40mm 55mm 70mm
From the Experiment
Atomized spray properties in pintle injection , Petrescu, Schrijer and Zandbergen 9 Gamertsfelder & Khare/UC Validation: SMD and spray angle comparison with experiment
Department of Aerospace Engineering & Engineering Mechanics
Location SMD from SMD from % error from experiment present injector (µm) calculations (µm)
60 mm 1291.32 1273.74 1.36%
65 mm 1194.56 1242.79 -4.04% 70 mm 1104.14 1101.92 0.20%
Experimental Present % error 60mm 70mm Calculations Spray 31.0 29.7 4.2% angle
Atomized spray properties in pintle injection , Petrescu, Schrijer and Zandbergen 10 Gamertsfelder & Khare/UC Physical Properties and Geometry
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 annulus diameter, d w Surface Tension, σ N/m) 0.03445 r no-slip boundary condition pintle u pintle movement r P10.62= MPa w T 300K= g l g constant l
inflow l
outflow u = 3.34m/s 𝜌 푢2푟 d = 5mm We = 푙 = 500 𝜎
8 Gamertsfelder & Khare/UC Pintle Injector Atomization at We=20 Department of Aerospace Engineering & Engineering Mechanics
3-D VOF
9 Gamertsfelder & Khare/UC Pintle Injector Atomization at We=20 Department of Aerospace Engineering & Engineering Mechanics
10 Gamertsfelder & Khare/UC Detailed Physics: Ligament Formation 3-D
Department of Aerospace Engineering & Engineering Mechanics
Side View Axial view
Side View non-dimensionalized time, t = t*/(d/Uj ) = 0.0 - 0.11 11 Gamertsfelder & Khare/UC Detailed Physics: Ligament Formation 2-D
Department of Aerospace Engineering & Engineering Mechanics
2-D center plane slice
Tracer VOF 1.0
0.5
0.0
non-dimensionalized time, t = t*/(d/Uj ) = 0.0 - 0.11
15 Gamertsfelder & Khare/UC Detailed Physics: First break-up 3-D
Department of Aerospace Engineering & Engineering Mechanics Axial view
3-D View
non-dimensionalized time, t = t*/(d/Uj ) = 0.11- 0.21
16 Gamertsfelder & Khare/UC Detailed Physics: First break-up 2-D
Department of Aerospace Engineering & Engineering Mechanics 2-D center plane slice
Tracer VOF 1.0
0.5
0.0
non-dimensionalized time, t = t*/(d/Uj ) = 0.11- 0.21
17 Gamertsfelder & Khare/UC Detailed Physics: Sheet Sheering and Break-up Department of Aerospace Engineering & Engineering Mechanics 3-D VOF - Outside 3-D VOF -Inside
non-dimensionalized time non-dimensionalized time t = t*/(d/Uj ) = 0.22 - 0.90 t = t*/(d/Uj ) = 0.19
18 Gamertsfelder & Khare/UC Detailed Physics: Appearance of Kelvin- Helmholtz Instabilities Department of Aerospace Engineering & Engineering Mechanics
2-D Center Plane Slice 3-D VOF
non-dimensionalized time, t = t*/(d/Uj ) = 0.50 - 1.00
19 Gamertsfelder & Khare/UC Detailed Physics: Droplet Recirculation Vortex Formation Department of Aerospace Engineering & Engineering Mechanics 2-D Vorticity slice 2-D center slice
non-dimensionalized time t = t*/(d/Uj ) = 1.24 – 1.40
17 Gamertsfelder & Khare/UC Detailed Physics: Clumping and Droplet Coalescence Hinders Atomization Department of Aerospace Engineering & Engineering Mechanics
3-D VOF 2-D Tracer Iso-line
non-dimensionalized time, t = t*/(d/Uj ) = 1.64
21 Gamertsfelder & Khare/UC Droplet Production Changes with Time
Department of Aerospace Engineering & Engineering Mechanics
1722 Gamertsfelder & Khare/UCKhare/UC Droplet Production in terms of Probability
Department of Aerospace Engineering & Engineering Mechanics
23 Gamertsfelder & Khare/UC Sauter Mean Diameter
Department of Aerospace Engineering & Engineering Mechanics
1 Ds = fi i di
21 Gamertsfelder & Khare/UCKhare/UC Droplet production over time
Department of Aerospace Engineering & Engineering Mechanics
25 Gamertsfelder & Khare/UC Conclusion
Department of Aerospace Engineering & Engineering Mechanics • 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
26 Gamertsfelder & Khare/UC Future Investigations
Department of Aerospace Engineering & Engineering Mechanics
• 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
27 Gamertsfelder & Khare/UC Questions?
Department of Aerospace Engineering & Engineering Mechanics
28 Gamertsfelder & Khare/UC Department of Aerospace Engineering & Engineering Mechanics
Back-up
29 Gamertsfelder & Khare/UC Sauter Mean diameter Comparison
Department of Aerospace Engineering & Engineering Mechanics Extrapolated Sauter mean diameter from emperical equation 2500
2000
1500 Experimental Values
Model Values SMD SMD µm in 1000
500
0 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 Distance from the Pintle injector in mm
Atomized spray properties in pintle injection , Petrescu, Schrijer and Zandbergen 30 Gamertsfelder & Khare/UC Spray Angle Comparison
Department of Aerospace Engineering & Engineering Mechanics
Model had a 31 degree half spray angle measured at 10mm
Atomized spray properties in pintle injection , Petrescu, Schrijer and Zandbergen 31 Gamertsfelder & Khare/UC