Contents - Università degli Studi di Bergamo

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Introduction
Experimental studies Numerical simulations Perspectives
Le gocce fanno spread, boing e splash:
esperimenti, fenomeni e sfide
Marengo Marco
University of Bergamo, Italy
Introduction
INDEX
Contents
• Introduction
• The main parameters
Experimental studies
• Isothermal drop impacts
• Onto solid surfaces
• Roughness effects
• Wettability effects
• Inclined surfaces
• ...on small targets
• Onto liquid layers
• in a deep pool
• on very thin film
• on liquid film
• Drop impact on hot surfaces
• Boiling regimes
• Secondary drop generation
• Multiple droplet impacts
Numerical simulations
• Available methods (VOF, Level Set, BEM, etc)
• Isothermal simulations
• Energy equation and phase transition
Perspectives
Introduction
Industrial applications
Spray Impingement in Internal Combustion Engines
G. Popiołek, H. Boye, J. Schmidt,
2005
Institute of Fluid Dynamics and
Thermodynamics
Otto-von-Guericke-University
Magdeburg, Germany
Mitsubishi Web-site
mulda.Avi
Introduction
Spray cooling and quenching
Typical hydrodynamic parameters
(Choi and Yao, 1987)
G = 0.3 – 20 kg/m2 s
U = 3-5 m/s
d10 ≈ 0.5 mm
Maximum heat transfer: 2·106 W/m2
Metallurgical
failures
For G = 80 kg/m2s, dT/dt = 103 K/s
Introduction
Agricultural sprays
Decrease the overspray and avoid
the aerosol
Cosmetic sprays
Small injection
energy, small
droplets, low
velocities
Introduction
Spray in humidifiers and
dryers
High efficiency microspray
Airplane icing
solidification
Cryogenic cooling
evaporation
Introduction
Fire suppression
Spray painting
Progress in Energy and Combustion Science 26 (2000) 79-130
Fire suppression by water sprays
G.Grant, J.Brenton , D.Drysdale
Non-newtonian fluids !!!
Evaporative cooling tower
Cleaner and sanitizers
Introduction
Etc....
Impact parameters
Impact dynamical parameters
U, D, α, ρ , σ, µ, g, t, h, Ra, θ, λ, E ...
Weber number
We =
ρ DU 2
σ
Ohnesorge number
Oh =
We
=
Re
Ca =
µ
ρσD
La =
U
σ /µ
D
µ
2
ρσ
Strouhal number
Dimensionless film
thickness
δ = h D
St = fD U
Dimensionless
roughness
amplitude
R nd = R a D
τ conv ≈
U
t
D
Introduction
Impact parameters
Impact thermal parameters
Saturation temperature
∆ T = Tw − T sat
Eckert number
Ec =
Jakob number
Ja =
ε =
Effusivity
U2
c p ∆T
c p ∆T
h fg
kρc p
Nukijama temperature - CHF
Leidenfrost temperature
Introduction
Isothermal drop impacts
Isothermal drop impact
Introduction
Drop impact onto solid dry surfaces
Isothermal drop impact
time scales
D ≈ 1-4 mm
Drop impact onto solid dry “cold” surfaces
Introduction
Drop impact evolution
Drop spreading on dry surfaces
Introduction
Rioboo R., C. Tropea, M. Marengo, "Outcome from a drop impact on solid
surfaces", Atomization and Sprays Journal, Vol. 4, 2000
Introduction
Roughness influence
Roughness effects
Ra = 3µm
Ra = 120µm
Silicon oil (µ=20 cSt; σ=0.0206 N/m); Vimp=3.16 m/s; D= 2.24 mm
Introduction
Wettability effects
Wettability influence on drop impact
t = 0 ms
t = 0.45 ms
t = 1.31 ms
t = 2.27 ms
t = 6.02 ms
t = 8.21 ms
wax
(D = 2.75 mm)
t = 25.6 ms
t = 34.2 ms
t = 62.4 ms
t = 72.2 ms
t = 20.5 ms
t = 14.0 ms
t = 10.3 ms
θrec =95°
t = 82.8 ms
Vi = 1.18 m/s
Glass
θrec =6°
t = 0 ms
t = 0.45 ms
t = 8.23 ms
Introduction
(D = 3.04 mm)
t = 2.27 ms
t = 6.04 ms
t = 20.5 ms
t = 62.4 ms
t = 1.31 ms
t = 14.0 ms
t = 10.3 ms
Initial shock wave
t ≈ 10ns
Bowden, Lesser, Field, 1985-1988
Drop
Shock wave
Huygens principle of wave propagation
Ve = U/tanβ
Tri-supersonic point
(a)
Drop
Shock wave
z
Liquid
hap
Cs sin β = U
(b)
Drop
Shock wave
r
Liquid
Shock separation
Cs
Jetting flow
β
re
V
Vjetting
x
(c)
Jetting
Cavitation
Introduction
Shock wave formation in droplet impact on a rigid
surface: lateral liquid motion and multiple wave
structure in the contact line region
HALLER, K. K. ; POULIKAKOS, D. ;
VENTIKOS, Y. ; MONKEWITZ, P.
Journal of Fluid Mechanics (2003) vol. 490, no. 1,
pg. 1-14
Time between impact
and shock detachment
Cs = 1481 m/s
Mai D
tsd ≈
2 2Cs
U = 5 m/s
D = 3 mm
tsd = 2 ns
Introduction
Edge propagation: kinetic phase
z = R − R − r
From the geometry 
z = Ut
2
re = DUt − U 2 t 2
if t << D/U
U = 5 m/s
D = 3 mm
Dimensionless form
z
2
t → 0 re ∝ t1/ 2
t << 600 µs
~
re = τ − τ 2
U
R
re
r
Introduction
Edge propagation: kinetic phase
Impact of a water drop on smooth PVC
We = 88
50
Experimental data
Fitting edge propagation V = atb
40
Velocity [m/s]
Fitting cinematic phase V = a exp(bt)
∆t = 60 µs ; t < 250 µs
30
re ≈ DUt = 0.06t 0.5
20
10
Consider a water drop: D = 2.7 mm; U = 1.55 m/s
0
There is a first phase where the impact is driven by the
“geometrical” edge propagation
0
50
100
150
200
250
time [µs]
A detailed study of the kinematic phase
Introduction
Drop impact onto liquid layers
Splash on a dry and wetted surface
Splash of a isopropanol drop
(a) a dry glass surface
We = 1020; Re = 3225; D = 3.26 mm
(b) on a PVC surface covered by
a liquid film of 0.1 mm thickness
(c) on a PVC surface covered by
a liquid film of 0.8 mm thickness.
Introduction
Drop impact onto very thin films
Liquid
[σ (N/m); µ (Pa s); ρ (kg/m3 )]
Range
V (m/s)
D (mm)
H*
We
Oh
Glycerol-water
[0.067; 0.00513; 1100]
min.
max.
min.
max.
min.
max.
min.
max.
1.11
2.59
0.65
2.76
0.44
2.72
0.86
3.14
2.67
2.71
2.22
3.81
1.42
3.06
1.54
2.08
0.018
0.117
0.017
0.189
0.007
0.093
0.004
0.132
55
300
41
741
28
707
54
890
0.0114
0.0115
0.0159
0.0121
0.0195
0.0286
0.0474
0.0548
Hexadecane
[0.0271; 0.00334; 730]
PDMS5
[0.0197; 0.00459; 918]
PDMS10
[0.0201; 0.00935; 930]
3500
splash
2500
K ( We.Oh
-0.4
)
3000
C-S limit
(a)
(c)
2000
(b)
1500
crown
1000
D-C limit
500
Dry
0
0,00
Liquid film
0,02
0,04
0,06
0,08
0,10
0,12
0,14
H* ( h/D )
Rioboo et al. (2003)
Introduction
Drop impact on liquid film
We = 560; Oh = 2.e-3
K = 6730; t = 8.3 ms
δ = 0.1
Perturbations
Jet formation
Secondary droplet formation
Cossali G.E., A. Coghe, M. Marengo „The impact of a sinlge
drop on a wetted solid surface“, Experiments in Fluids, Vol.
22, pp. 463-472, 1997
Introduction
Wetted surfaces
Crown evolution
Important theoretical contributions from Prof. Ilia Roisman
Introduction
Wetted surfaces
Crown height evolution
ηC =
H
Do
ηC ,max = A1 Wen
τ max = A2 Wen
n = 0.65 ÷ 0.75
Introduction
Splash and jetting on a deep pool
We > 60
We~1
with water only...
Oh~1
We > 84
Cascade of
coalescences
Introduction
Rein (1993)
Splash and jetting on a deep pool
Fr = U2/(gD)
Hsiao et al. (1989)
Introduction
Drop impact onto inclined surfaces
Impact on inclined surfaces
Impact of a glycerin droplet (We=51, D=2.45)
Examples of splashing
b
a
isotropic splash
(water droplet D=2.7,
We=390 on rough
glass, α=45°
splash in the forward
direction (isopropanol
droplet D=3.3,
We=544 on smooth
glass, α=45°)
∆t=3 ms
a
b
c
d
a) with rebound from
smooth glass (t1=0.0 ms,
α=8°)
b) t1=7.32 ms,
α=8 c) partial rebound (α=9°)
d) with deposition on
wax (α=5°)
Introduction
Influence of the impact angle
Water on wax
We = 90
Re = 4212
t = 3.67 - 3.99 ms
Dry inclined surfaces
Introduction
Dry inclined surfaces
Sticking and slipping
α = 5°
We=390, Re=8875, d=2.7 mm
contact
contact
t = 4.81 ms
t = 4.81 ms
t = 10.38 ms
t = 10.38 ms
Glass surface
Introduction
Wax surface
Small targets
Impacts onto
small targets
Radial flow
Wetting – Friction
No Wetting – No friction
Dynamics of a liquid lamella resulting from the impact of a water drop on a small target, Rozhkov, A., Prunet-Foch, B.,
Vignes-Adler, M., Proc. Mathematical, Physical, Engineering Sciences (2004), 460, 2049, pp 2681-2704
Introduction
Small targets
Camera 1
Top view
Camera 2
By courtesy M. Vignes-Adler
Introduction
Side view
Small targets
Camera 1
By courtesy M. Vignes-Adler
Camera 2
Introduction
The splashing/deposition limit
SPLASH/DEPOSITION THRESHOLD
Introduction
Influence of air pressure / drag
Ethanol drop
V = 3.74 m/s
P
4
Repeat the experiment with other liquids and with a film
Xu (2005)
Introduction
Crown splash
High values of We, Rnd and with wetted
surfaces. With dry surfaces the crown has a
lower angle respect to the solid surface
Very high number of secondary droplets
dsec = 0.05 - 0.7 D
u = 0.1 - 0.9 V
Introduction
Conical jet breakbreak-up
High and middle values of We, low wettable
or wetted surfaces
Low number of secondary droplets (<3)
dsec = 0.5 - 0.8 D
u < 0.6 V
Recoiling film breakbreakup
Rebound
Very low wettable surface
High value of Weber and low
wettable surfaces, small impact
angle (?), hot surfaces
dsec (?)
u=0
dsec = D (?)
u (?)
Introduction
b)
a)
Prompt splash
Prompt splash
High values of We, Rnd and
with wetted surfaces. Low
liquid viscosity.
Very high number
secondary droplets
of
dsec < 0.2 D
u = (?)
Water drop impact ( D = 2.7 mm) on a glass surface
a) Deterministic roughness Ra = 6 µm, λ = 1mm
b) Ra = 3.5 µm, λ = 100 µm
Introduction
Crown splash threshold
Number K
K = We Oh−0.4
Critical K number
Depending on the impacting drop parameters
Depending on impacted surface parameters
K > Kcr
Secondary droplets formation
K < Kcr
Deposition
Generally
Kcr = fn(Rnd, θ, T, λnd, δ)
n = splash type
Introduction
Dry high wettable surfaces
Kcr = 649 + 3.76/Rnd0.63
Mundo et al. (1995)
Stow and Hadfield (1981)
Coghe et al. (1995)
3500
K = We Oh −0.4
3000
2500
2000
1500
1000
500
Splash limit
Kcr = 657
0
10-5
10-4
10-3
10-2
10-1
100
Dimensionless Surface Roughness R
nd
Introduction
Wetted surfaces (δ < 1)
Splash limit
Kcr = 2100 +5880 δ1.44
Prompt splash limit
Kcr = 2100 + 760 δ0.23
Introduction
Influence of the wettability
Critical Weber number as a function of the dimensionless
surface roughness
° Aluminium; . Glas; * Plexiglas; + 3M Film (Range 1995)
Introduction
Droplet array impact (Ts = 80°)
z
z
x
y
Front and side view
Drop Array Impacts
Introduction
NUMERICAL SIMULATIONS
Introduction
Numerical methods
Volume of fluid interface
(VOF)
C.W. Hirt and B.D. Nichols, “Volume of Fluid (VOF)
Method for the Dynamics of Free Boundaries,” J. Comp.
Phys., 39, 201-225,1981
LEVEL SET METHODS
S. Osher and J. Sethian, Fronts propagating with curvature
dependent speed: Algorithms based on Hamilton-Jacobi
formulations, J. Comput. Phys., 79 (1988), pp. 1249
BOUNDARY ELEMENT
METHODS
Introduction
Cij = Volume of
« fluid » in cell ij
Definition of the VOF Method
In a volume-of fluid method the motion of the interface
itself is not tracked, but rather the volume of each material
in each cell is evolved in time and the interface at the new
time is reconstructed from the values of the volumes at
this new time. For this reason VOF methods are
sometimes referred to as volume tracking methods
Second-order accurate volume-of-fluid algorithms for tracking material interfaces
James Edward Pilliod, Jr. and Elbridge Gerry Puckett
Journal of Computational Physics, Volume 199, Issue 2 , 20 September 2004, Pages 465-502
Introduction
where
and
∆x = ∆y = h
Advection equation
If the fluid is
incompressible
Conservation law for the
volume fraction function
Introduction
Interface
reconstruction
(c) is a first-order method of simple line interface calculation (SLIC) type
(d) is a second-order method of piecewise .... (PLIC) type
Introduction
There are other
methods, like Marker
and Cell (MAC),
Lagrangian Tracking,
Integral Tracking and
so on...
Introduction
LEVEL-SET
Introduction
by courtesy of Daniele Di Pietro
Introduction
Introduction
LEVEL-SET
3-D modeling of the dynamics and heat transfer
characteristics of subcooled droplet impact on a surface
with film boiling
Yang Ge, L.-S. Fan
Int. J. Heat and Mass Transfer 49 (2006) 4231-4249
Introduction
Boundary
element
methods
Introduction
VOF simulations and time accuracy
Contact angle problem
Numerical and experimental drop impact on solid dry surfaces
W.I.Geldorp, R.Rioboo, SJ. A. Jakirlić, S. Muzaferija, C.Tropea,
VIII Int. Conf. on Liquid Atomization and Spray Systems,
Pasadena, USA, 2000
Introduction
Re = 1000, We = 8000
D = 6mm
U = 6m/s
MOVIE
400 grid point in D
1 grid point = 15 microns
by courtesy of Stephane Zaleski
Introduction
Select a numerically « nice » case:
Not too viscous (no splashing)
Not too large Re (too unstable)
A glycerine , 4 mm droplet falling at 2 m/s
256² Simulation ( 128 grid points/diameter )
Repeat at 128² : same result

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