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8/12/2019 3 Breakup Dense
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MCEN 6228
Multiphase Flow
Surface Tension &Secondary Breakup
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MCEN 6228
Multiphase Flow
Surface Tension
Liquid is held together by van der Vaals force
liquid
gas
surface distorted surface
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MCEN 6228
Multiphase Flow
Surface Tension
Definition force Fper unit length, exerted
parallel to the liquid surface
Where is the pressure higher: inside a liquid drop,or inside a soap bubble (or are they equal)?
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MCEN 6228
Multiphase Flow
Surface Tension
Pressure inside a liquid drop
Pressure inside a liquid film bubble
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MCEN 6228
Multiphase Flow
Surface Tension
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MCEN 6228
Multiphase Flow
Surface Tension
Characteristic numbers Weber number
Ohnesorge number
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MCEN 6228
Multiphase Flow
Drop Breakup: Regimes
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MCEN 6228
Multiphase Flow
Drop Breakup: Regimes
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MCEN 6228
Multiphase Flow
Drop Breakup: Regimes
We = 20: bag breakup
We = 272: sheet stripping
We = 952: chaotic breakup
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MCEN 6228
Multiphase Flow
Drop Breakup: Regimes
We = 5000: chaotic breakup (Joseph et al. 98)
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MCEN 6228
Multiphase Flow
Drop Breakup: TAB Model
Treat drop as a mass-spring-damper system
external force
spring
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MCEN 6228
Multiphase Flow
Drop Breakup: TAB Model
damper
breakup criterion
with
consider only fundamental mode (n=2)!
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MCEN 6228
Multiphase Flow
Drop Breakup: TAB Model
Solution
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MCEN 6228
Multiphase Flow
Drop Breakup: TAB Model
Need to determine shock tube experiments
!
!
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MCEN 6228
Multiphase Flow
Drop Breakup: TAB Model
oscillation of an inviscid spherical drop, mode n(Lamb 45)
damped oscillation of viscous spherical drop, mode n(Lamb 45)
!
!
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MCEN 6228
Multiphase Flow
Drop Breakup: TAB Model
postulate breakup occurs if oscillation amplitude is halfthe drop radius
!
!
!
(for initially non-oscillating sphere)
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MCEN 6228
Multiphase Flow
Drop Breakup: TAB Model
Timescales large We !stripping mode
low We ! bag mode
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MCEN 6228
Multiphase Flow
Drop Breakup: TAB Model
What child drops are produced? energy conservation
!
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MCEN 6228
Multiphase Flow
Drop Breakup: TAB Model
from experiments
large We !stripping mode:
low We ! bag mode:
replace parent drop by drops with radius randomlysampled from "2-PDF with R32
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MCEN 6228
Multiphase Flow
Drop Breakup: WAVE model
linear stability analysis of around liquid jet
Mayer 93
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MCEN 6228
Multiphase Flow
WAVE Model: Jet Breakup
growth rate vs wave length, parameter: gas densityMayer 93
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MCEN 6228
Multiphase Flow
WAVE Model: Jet Breakup
growth rate vs wave length, parameter: surface tensionMayer 93
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MCEN 6228
Multiphase Flow
WAVE model: Jet Breakup
optimal wavelength #and growth rate $(Reitz 87)
1: liquid, 2: gas
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MCEN 6228
Multiphase Flow
WAVE model: Jet Breakup
optimal wavelength #and growth rate $(Reitz 87)
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MCEN 6228
Multiphase Flow
Drop Breakup: WAVE Model
Treat drop breakup as liquid jet breakup
low We ! bag mode
large We !stripping mode
TAB:
TAB:
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MCEN 6228
Multiphase Flow
Drop Breakup: WAVE model
What child drops are produced? at t
buadd drop of size
Difference between TAB and WAVE
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MCEN 6228
Multiphase Flow
Drop Breakup: DDB model
Extension of TAB model to non-linear effects Consider center of mass of half-drop Deformation due to extensional flow Equate work done by pressure and
viscous dissipation to internal energy
breakup when
with
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MCEN 6228
Multiphase Flow
Drop Breakup: Alternatives
Rayleigh-Taylorbreakup model (Bellman & Pennington 54) high relative velocity: catastrophic breakup regime
wave length Stochastic model(Apte et al. 03)
(Hwang & Reitz 95)
(Reitz)
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MCEN 6228
Multiphase Flow
Collision &Coalescence
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MCEN 6228
Multiphase Flow
Particle/Wall Interaction
Assumptions (hard sphere model) particles are spheres particle deformation is neglected walls are smooth Coulombs friction law once particle stops sliding, no further sliding
Split interaction into compression phase (1) recovery phase (2)
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MCEN 6228
Multiphase Flow
Particle/Wall Interaction
Solution use impulse equations
(3 translational velocities + 3 angular velocities)
use boundary conditions + friction law (coefficient f) introduce coefficient of restitution e
sliding may stop in compression, recovery phase,or not at all
recovery phase impulse
compression phase impulse
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MCEN 6228
Multiphase Flow
Particle/Wall Interaction
Two cases:
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MCEN 6228
Multiphase Flow
Particle/Wall Interaction
Problem large particles will not stay in suspension (e< 1)
Solution consider non-spherical particles consider roughness of the wall
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MCEN 6228
Multiphase Flow
Particle/Wall Interaction
Non-spherical particles rx introduces wall normal velocity particles characterized by r(&)
on impact choose randomly &!r perform analysis as before
sphere non-sphere
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MCEN 6228
Multiphase Flow
Particle/Wall Interaction
Rough wall model rough wall as series of inclined planes
transform velocities to plane coordinate system &use equations as before
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MCEN 6228
Multiphase Flow
Particle/Wall Interaction
Example near spherical particle in horizontal channel (Shen et al. 89) D = 1.1mm, e = 0.93, f = 0.28
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MCEN 6228
Multiphase Flow
Drop/Wall Interaction
Interaction of a drop with a hot wall: Experiment
(Wachters &
Westerling 66)
elastic rebound
vapor film
prevents wetting
spreading, splashing
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MCEN 6228
Multiphase Flow
Drop/Wall Interaction
Watkins & Wang model (90) use critical Weber number from Wachters & Westerling
&
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MCEN 6228
Multiphase Flow
Drop/Wall Interaction
Park model (94) use fitted data from Wachters & Westerling for We
We(0)
We
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MCEN 6228
Multiphase Flow
Drop/Wall Interaction
Park model (94) use fitted data from Wachters & Westerling for We
= D(0)
= vn(0)
at t = "t*with 1 < "< 1.548
exp.:
exp.:
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MCEN 6228
Multiphase Flow
Drop/Wall Interaction
Park model (94) mass spreading tangentially & rebounding from wall aims to mimic splash
(Rieber & Frohn 99)
(Yarin & Weiss 95)
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MCEN 6228
Multiphase Flow
Drop/Wall Interaction
Numerous other models Grover et al. 2001 ORourke & Amsden 2000 Naber & Reitz 1988 etc.
Mostly using energy conservation, distribution arguments correlations from experiments or DNS like numerical
simulations
Advanced description requires wall film model
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MCEN 6228
Multiphase Flow
Drop/Wall Interaction
5mm glycerin-water drop impacting ethanol layer
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MCEN 6228
Multiphase Flow
Drop/Drop Interaction
Can often be neglected in engine sprays Dominant for rain formation
terminal velocity is function of D drops collide & merge
For coalescence drops must be closer than 100A Statistically hard to model, since joined PDFs of
two drops must be known
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MCEN 6228
Multiphase Flow
Drop/Drop Interaction
Regime diagram
(Qian & Law 97)
hydrocarbon droplets
"U/2
U/2
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MCEN 6228
Multiphase Flow
Drop/Drop Interaction
(Qian & Law 97)
coalescence
bouncing
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MCEN 6228
Multiphase Flow
Drop/Drop Interaction
(Qian & Law 97)
coalescence
coalescence
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MCEN 6228
Multiphase Flow
Drop/Drop Interaction
(Qian & Law 97)
near head-on
separation
near head-on
separation
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MCEN 6228
Multiphase Flow
Drop/Drop Interaction
(Qian & Law 97)
near head-on
separation
near head-on
separation
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MCEN 6228
Multiphase Flow
Drop/Drop Interaction
(Qian & Law 97)
coalescence
off-center
separation
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MCEN 6228
Multiphase Flow
Drop/Drop Interaction
(Qian & Law 97)
off-center
separation
off-centerseparation
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MCEN 6228
Multiphase Flow
Drop/Drop Interaction
Modeling approximate regime diagram on collision detection, determine B and We!collision result from approximated regime diagram
Statistical modeling is very challenging sincejoined PDFs of two drops are needed
Phase interface tracked DNS is challenging,since van der Waals forces must be considered
for correct time of coalescence
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MCEN 6228
Multiphase Flow
Drop/Pool Interaction
Dancing drops