Vibration Induced Droplet Ejection

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24 Οκτ 2013 (πριν από 3 χρόνια και 8 μήνες)

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Fluid Mechanics Research Laboratory

Vibration Induced Droplet Ejection

Ashley James

Department of Aerospace Engineering and Mechanics

University of Minnesota


Marc K. Smith

George W. Woodruff School of Mechanical Engineering

Georgia Institute of Technology


Supported by NASA Microgravity Research Division

and Hoechst Celanese Corp.


Fluid Mechanics Research Laboratory

Outline


Problem definition


Project overview


Transducer
-
drop interaction


Numerical simulations


Conclusions and future work

Fluid Mechanics Research Laboratory


Vertical vibration induces the
formation of capillary waves on
the free surface.


When the forcing amplitude is
large enough secondary droplets
are ejected from the wave crests.

Ejection Schematic

Fluid Mechanics Research Laboratory

Literature


Faraday (1831)
-

wave formation due to vibration


Benjamin & Ursell (1954)
-

stability analysis


Sorokin (1957)
-

vibration induced droplet ejection


Woods & Lin (1995)
-

stability on an incline, ejection


Lundgren & Mansour (1988)
-

vibration of an unattached
drop


Wilkes & Basaran (1997,1999)
-

vibration of an attached drop


Goodridge et al. (1996, 1997)
-

vibration induced droplet
ejection

Fluid Mechanics Research Laboratory

Applications


Fuel atomization and injection for engine combustors


Thermal management and control


Electronic cooling


Mixing processes


Material processing


Encapsulation


Emulsification

Fluid Mechanics Research Laboratory

Heat Transfer Cell

for high power electronic cooling (100 W/cm
2
)

Printed Circuit Board

Integrated Circuit

Condensation

Surface

Fins

Resonance Atomizer

Fluid Mechanics Research Laboratory

Low Frequency Forcing


Axisymmetric motion


Single drop ejected from center


0 to 100 Hz


Driver is a rigid piston


Experiments performed to determine ejection behavior


Focus of simulations

Photographs courtesy of Kai Range

Fluid Mechanics Research Laboratory

High Frequency Forcing


Chaotic motion


Multiple droplet ejection across drop surface


~ 1 kHz


Driver is a flexible diaphragm


Coupling between driver and ejection dynamics


Experimental investigation of spray characteristics

unforced

ejection

atomization

Fluid Mechanics Research Laboratory

Close
-
up of High Frequency Ejection


A crater forms on the
drop surface.


As the crater collapses an
upward jet is created.


One or more secondary
droplets are ejected from
the end of the jet.

crater

Photographs courtesy of Bojan Vukasinovic

Fluid Mechanics Research Laboratory

Transducer
-
Drop Interaction Model

Fluid Mechanics Research Laboratory

Amplitude Response

Unloaded Transducer

0.16 V

1.85 V

4.06 V

Fluid Mechanics Research Laboratory

Effect of Drop Size on Response

0
m
L

100
m
L

200
m
L

Driving Voltage:

0.74 V

Fluid Mechanics Research Laboratory

Response of System to f = 0.99 Forcing

5.91 V

6.20 V

6.50 V

a

f

Fluid Mechanics Research Laboratory

Response of System to f = 1.04 Forcing

5.91 V

6.20 V

6.50 V

6.79 V

f

a

Fluid Mechanics Research Laboratory

Comparison of Model to Experiment

5.91 V

6.20 V

6.50 V

6.79 V

f

a

Model

Experiment

Fluid Mechanics Research Laboratory

Response Behavior

0
m
L

100
m
L

200
m
L

f < f
r

f > f
r

Fluid Mechanics Research Laboratory

Computational Method


Transient, axisymmetric, incompressible governing equations.


Forcing is an oscillating body force in inertial reference frame.


Finite volume discretization on a uniform, staggered grid.


Explicit projection method for Navier Stokes solver.


Incomplete
-
Cholesky conjugate gradient method for solution
of pressure
-
Poisson equation.

Fluid Mechanics Research Laboratory

Volume of Fluid Method


The position of the interface is tracked via a volume
fraction,
F
.


The evolution of the volume fraction is governed by a
convection equation.




The interface is approximated by a straight line in each cell.


To prevent false smearing of the interface the volume
fraction flux is computed from the straight line
approximation.

Fluid Mechanics Research Laboratory

Continuum Surface Force


The surface tension forces are incorporated as a source
term in the momentum equation.



Surface cells and interior cells are treated the same.


The source term is nonzero only near the interface.


The surface tension is distributed over a small region near
the computed interface.


The curvature is calculated directly from the volume
fraction.

Fluid Mechanics Research Laboratory


Continuity:



Radial momentum:





Vertical momentum:





Volume fraction:

Governing Equations

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Verification


Translation of a fluid region.


Exact solution of Poisson equation.


Poiseuille flow.


Transient Couette flow in an annular region.


Stability of a drop in equilibrium.

Fluid Mechanics Research Laboratory

Parameters


Range






0
-

500


Viscous effects







0
-

100


Forcing amplitude







0
-

5


Forcing frequency







0
-

5


Gravity effects

Ejection Simulations

Fluid Mechanics Research Laboratory

Initial and Boundary Conditions

Symmetry

line

Outlet

No
-
slip

walls

80 cells

30 cells

Fluid Mechanics Research Laboratory

Video Cases

Re = 475




Re = 10



Re = 10



Re = 10



Re = 10

A = 8.7




A = 18




A = 20




A = 25




A = 30



= 1.2






= 1






= 1






= 1






= 1

Bo = 1.3




Bo = 0




Bo = 0




Bo = 0




Bo = 0

Fluid Mechanics Research Laboratory

Comparison of Simulation and Experiment


Re = 475, A = 8.7,


= 1.2, Bo = 1.3

Scale:

1 cm

Forcing stepped on

Forcing slowly ramped up

Fluid Mechanics Research Laboratory

Ejection Simulation
-

Case 2

Re = 10, A = 18,


= 1 , Bo = 0

t = 2.8

t = 3

t = 3.2

t = 3.4

t = 3.6

t = 3.8

t = 4

Fluid Mechanics Research Laboratory

Ejection Simulation
-

Case 3

Re = 10, A = 20,


= 1 , Bo = 0

t = 1.8

t = 2

t = 2.2

t = 2.4

t = 2.6

t = 2.8

t = 3

Fluid Mechanics Research Laboratory

Ejection Simulation
-

Case 4

Re = 10, A = 25,


= 1 , Bo = 0

t = 0.6

t = 0.8

t = 1

t = 1.2

t = 1.4

t = 1.6

t = 1.8

Fluid Mechanics Research Laboratory

Ejection Simulation
-

Case 5

Re = 10, A = 30,


= 1 , Bo = 0

t = 0.8

t = 1

t = 1.2

t = 1.4

t = 1.6

t = 1.8

Fluid Mechanics Research Laboratory

Effect of Forcing Amplitude on Ejection

Bo = 0, Re = 10,


= 1

Fluid Mechanics Research Laboratory

Effect of Bond Number on Ejection

Re = 10, A = 25,


= 1

Fluid Mechanics Research Laboratory

Effect of Reynolds Number on Ejection

Bo = 0, A = 25,


= 1

Fluid Mechanics Research Laboratory

Effect of Forcing Frequency on Ejection

Re = 10,

Bo = 0, A = 25

Fluid Mechanics Research Laboratory

Ejection Threshold

Ejection

No ejection

Simulations

Range et al.

Goodridge et al.

low viscosity

Goodridge et al.

high viscosity

Fluid Mechanics Research Laboratory

Conclusions


Although the forcing frequency has a dramatic effect on the
response, ejection may occur when a crater collapses to
form a spike in both the low and high frequency regimes.


The bursting behavior is explained by the coupling of the
diaphragm vibration with the changing drop mass.


The single degree
-
of
-
freedom model with linear droplet
ejection is sufficient to describe the system dynamics.


Low
-
frequency ejection is promoted by increasing A,
decreasing Bo, increasing Re, or decreasing

.


The simulated drop behavior and the ejection threshold
compare well with experiments.

Fluid Mechanics Research Laboratory

Future Work


Extend simulations to three dimensions.


Improve computational methodology.


Investigate the formation of satellite drops.


Determine effect of contact line condition.


Simulate the vibration of a liquid layer.


Improve understanding of high
-
frequency
atomization.


Design systems involving high
-
frequency
spray formation.