Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 3.7.2 - Improved Eulerian Model for Liquid Films
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 Material Information
Title: 3.7.2 - Improved Eulerian Model for Liquid Films Interfacial Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Hagemeier, T.
Hartmann, M.
Thévenin, D.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: liquid film model
drop-wall interaction
film break-up
 Notes
Abstract: Different models have been proposed in the literature in order to simulate by Computational Fluid Dynamics (CFD) liquid films generated by spray impingement on vehicle surfaces. Generally, the discrete phase film model introduced by O’Rourke and Amsden (1996) and adapted by Kruse and Chen (2007) or the continuous phase film model as proposed by Anderson and Coughlan (2006) are applied when simulating vehicle soiling by CFD. Although several specific adaptations have been reported to increase model relevance and generality, it is still very difficult to capture all physical details of film flow dynamics, especially concerning the film break-up physics and the occurrence of splashing. The continuous phase film model approach of Anderson and Coughlan (2006), which is in the focus of the present paper, has been therefore improved with both objectives in mind. The modified model accounts for splashing of impacting droplets based on experimental results of Mundo, Sommerfeld and Tropea (1995), as well as for film break-up based on an adapted Weber number criterion. Test simulations have been performed on a simplified wind shield geometry. CFD predictions are compared with results from experimental investigations relying on Phase Doppler Anemometry (PDA) and Shadowgraphy measurements in a two-phase wind tunnel.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Volume ID: VID00095
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 372-Hagemeier-ICMF2010.pdf

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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Improved Eulerian Model for Liquid Films


Thomas Hagemeier *, Michael Hartmann i and Dominique Th6venin*



University of Magdeburg "Otto von Guericke", Institute of Fluid Dynamics and Thermodynamics (LSS), Germany
t Volkswagen AG, Wolfsburg, Germany
Corresponding author: Thomas.Hagemeier@ovgu.de
Keywords: liquid film model, drop-wall interaction, film break-up




Abstract

Different models have been proposed in the literature in order to simulate by Computational Fluid Dynamics (CFD)
liquid films generated by spray impingement on vehicle surfaces. Generally, the discrete phase film model introduced
by O'Rourke and Amsden (1996) and adapted by Kruse and Chen (2007) or the continuous phase film model as
proposed by Anderson and Coughlan (2006) are applied when simulating vehicle soiling by CFD. Although several
specific adaptations have been reported to increase model relevance and generality, it is still very difficult to capture
all physical details of film flow dynamics, especially concerning the film break-up physics and the occurrence of
splashing.
The continuous phase film model approach of Anderson and Coughlan (2006), which is in the focus of the present
paper, has been therefore improved with both objectives in mind. The modified model accounts for splashing of
impacting droplets based on experimental results of Mundo, Sommerfeld and Tropea (1995), as well as for film
break-up based on an adapted Weber number criterion. Test simulations have been performed on a simplified wind
shield geometry. CFD predictions are compared with results from experimental investigations relying on Phase
Doppler Anemometry (PDA) and Shadowgraphy measurements in a two-phase wind tunnel.


Nomenclature

Roman symbols
Oh Ohnesorge number (-)
Re Reynolds number (-)
We Weber number (-)
g gravitational constant (m.s 1)
h film thickness (m)
K splashing parameter (-)
m mass (kg)
p pressure (Pa)
S film mass source (kg.s 1)
u velocity (m.s 1)
Greek symbols
6 dimensionless film thickness (-)
P/ viscosity (kg.m 1.s 1)
p density (kg.m 3)
a surface tension (N.m 1)
T shear stress (Pa)
Subscripts
crit critical K value


deposition
film
momentum-induced film velocity
direction component
incoming
outgoing
primary
secondary
tangential velocity of primary droplets
wall


Introduction

Calculating film flow dynamics is an important step
when designing new automobiles. In this manner, sur-
face wetting and vehicle soiling resulting from rain im-
pingement can be predicted. Safety aspects as well as
passengers' comfort are the motivation for this effort.
Experimental investigations in wind tunnel facilities are
often combined with numerical fluid dynamics to esti-







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


mate the contamination of the vehicle surface, mostly
in a qualitative manner. A broad range of experimen-
tal techniques are applied to quantify the soiling behav-
ior. In particular, Phase Doppler Anemometry (PDA)
is applied for characterization of the dispersed liquid
phase (droplets), while fluorescence imaging is used for
the continuous phase (liquid film). Concerning numer-
ical tools, different film modeling approaches are avail-
able. Either Eulerian or Lagrangian models are used, or
Volume of Fluid (VOF) approaches are applied. Most
present film models rely on research work associated
with fuel injection, later adapted for application in vehi-
cle soiling. In particular, the contributions of O'Rourke
and Amsden (1996) concerning a Lagrangian film model
and of Bai and Gosman (1996) and Stanton and Rut-
land (1998) associated with Eulerian film models are the
background of further developments.
A discrete film model was first used for vehicle soil-
ing simulation by Borg and Vevang (2006) and later im-
proved by Kruse and Chen (2007). It calculates the film
flow dynamics in terms of a modified equation of mo-
tion for wall-bound droplets, which constitute the film.
It also accounts for droplet separation from the film by
entraining droplets into the bulk gas phase at sharp cor-
ners. Due to the fact that all injected droplets are active
and tracked until they exit the computational domain,
the associated requirements in terms of computing time
and memory are considerable. Concerning Eulerian ap-
proaches, Anderson and Coughlan (2006) adapted the
film model of Bai and Gosman (1996) for application in
vehicle soiling simulation. Since the present paper will
focus on the latter, it is described in more detail after a
brief introduction concerning vehicle soiling simulation
practice.
As mentioned previously, simulation of vehicle soil-
ing is part of the aerodynamic investigation during the
development of new car designs. Different working
steps are run through, until finally the soiling behavior
of new geometries can be classified.
In general, vehicle soiling can be attributed to two rea-
sons: 1. foreign contamination due to wind-driven rain
or raised liquid from other road users and 2. self-soiling
owing to raised mist or solid dirt particles from wheel
rotation.
Usually, soiling simulations are performed in a three-
step algorithm, such as described by Karbon and Long-
man (1998) and Foucart and Blain (2005). As a first step
the flow field around the whole car geometry is calcu-
lated, in order to account for all parameters influencing
the film flow in the later steps. Subsequently, the results
for the flow field are mapped to the regions of interest,
which in case of soiling due to rain are the wind shield,
A-pillar with rear view mirror and the side window. In
the third step the tracking of the droplets and the calcula-


Figure 1: Model wind shield geometry installed within
the wind tunnel test section.


tion of the film flow are performed. No back coupling of
the droplets or liquid film onto the gas phase is consid-
ered, so that the flow field is frozen during the mapping
step.
In case of contamination due to rain impingement,
wind tunnel experiments are carried out to validate
the simulation results. Atomization systems generating
droplet size distributions close to those of realistic rain,
as described by Bouchet, Delpech and Palier (2004),
are installed within the facility. Fluorescent agents are
added to the water to enable the visualization of the
film flow along the vehicle surface by UV illumination
and video cameras, as described for instance in Campos,
Mendonca, Weston and Islam (2006). In this manner, a
qualitative comparison between experiments and numer-
ical simulations is possible. Regions of intense contam-
ination can be identified and solutions can be found.

Film modeling

The film model introduced by Anderson and Coughlan
(2006) is implemented as a two-dimensional model of
liquid films on three-dimensional surfaces. Modifying
the continuity equation for this purpose, the mass is con-
served in terms of the film thickness h .


Ohf (., .. ) Sin Sout
at dxi pfA


The mass source for the liquid film, Sin is the deposited
mass of impinging droplets, which is defined in the
model of Anderson and Coughlan (2006) as pure de-
position, keeping the total droplet mass. Also included
as (negative) source term is the re-entrained mass from
droplets leaving the film due to break-up, Sout in equa-
tion (1). The film break-up is captured by using a film












I6.24e-04



4.34e-04

3.52e-04

2.71e-04

1...89e-04

8.07e-05


Figure 2: Particle tracks of primary and secondary
droplets, colored by the size of the diameter
in meter.


Weber number Wef and prescribing in this manner a sta-
bility criterion for the film:


Here us is the film surface velocity induced by shear
stress from the air flow. If the local Wef number ex-
ceeds a fixed threshold value, droplets are released from
the film, with a diameter equal to the local film thick-
ness. From first tests a threshold value of Wef 10
should give qualitatively good results, as reported by
Anderson and Coughlan (2006). However, varying this
critical value, which is not based on any physical moti-
vation, significantly influences the flow dynamics of the
film, as will be shown in this paper.
The conservation of momentum is not described by
the Navier-Stokes equations in this model. The mass
(film thickness) is transported instead with the mean film
velocity, which is governed by gravity and shear stress,
as induced by the surrounding air flow. The resulting
film velocity is estimated in an analytical manner, yield-
ing a parabolic velocity profile (for the influence of grav-
ity) and an additional linear velocity profile (resulting
from shear stress):

= [2hf (pgi), + 3ri] (3)

Both velocities are then simply superposed to give the
local mean film velocity ui, which is then used in the
continuity equation.
Contrary to Lagrangian and VOF models, which need
a large number of discrete film particles to reach sta-
tistical independence or have to resolve the film height


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


with grid elements, the model of Anderson and Cough-
lan (2006) is a promising alternative with much lower
computational requirements.
From the governing equations it is however obvious,
that some essential physical aspects are not included in
the formulation of Anderson and Coughlan (2006). In
particular the droplet-wall interaction is reduced to sim-
ple deposition, not accounting for realistic impingement
behavior.
The original model has been first implemented in the
industrial CFD software ANSYS-Fluent via User De-
fined Functions (UDF). After that, it has been improved
to account for droplet-wall interaction, in particular to
describe splashing of primary droplets and momentum
transfer of the impinging droplets toward the film.
The modification of the film model relies on empiri-
cal and semi-empirical correlations published in the lit-
erature. In particular, Mundo, Sommerfeld and Tro-
pea (1995) published experimental results for droplet-
dry wall interaction. They investigated the effect of sev-
eral parameters on the outcome of droplet impingement
onto dry walls and introduced the dimensionless number
K as parameter for discrimination between deposition
and splashing.
K = Oh Re125 (4)

A threshold for the transition from deposition to splash-
ing was found at a critical value of K > 57.7, a value im-
plemented in existing film models (O'Rourke and Ams-
den (2000); Kruse and Chen (2007)). Based on the value
of K the post-impingement characteristics, in particular
number, size and velocity of secondary droplets can be
calculated with the splashing model of Mundo, Som-
merfeld and Tropea (1995) for droplet-dry wall inter-
action. O'Rourke and Amsden (2000) not only used,
but adapted this model for the purpose of wetted walls,
based on the results of Yarin and Weiss (1995). For this
purpose they included the film thickness as additional
parameter within the dimensionless number K, which is
now used in square for correlating the post-impingement
characteristics mentioned before:

K2 P2d in (6, 1) + (5)


The correlations given by Mundo, Sommerfeld and Tro-
pea (1995) and O'Rourke and Amsden (2000) are imple-
mented within the model UDF by adapting the boundary
conditions for the dispersed liquid phase. The former
"trap" boundary condition, which kept all droplets com-
ing in contact with the wall from being tracked any fur-
ther, switches now between "trap" and "reflect", depend-
ing on the impingement conditions. In case of reflection,
the numerical parcel is not simply reflected, but essen-
tial properties are modified, in particular the represen-













700
E600
S500
E
w 400
0
S300
0
- 200
S100


700

600
8 500
E
a 400
300
200
E 100
0

700

S600

S500
E
.1 400
-o
S300

200
E 100


* .
-


* 10 mm distance to wal
* 20 mm distance to wall
30 mm distance to wall


0 50 100 150
plate length in flow direction [mm]


200 250


0 S


50 100 150
plate length in flow direction [mm]





U I
S N q ~


0 50 100 150
plate length in flow direction [mm]

Figure 3: Spatial evolution of mean diame
plate at 15, 20 and 25 [m/s] (froi
tom).



tative diameter and mass flow rate, implici
the number of splashed droplets.
In case of droplet-dry wall interaction
impingement characteristics are calculated

n, 1.676 x 105 K2.539 n

for number of secondary droplets,

d, = min (8.72 exp (-0.0281 K),

for mean diameter of secondary droplets an


m 1 n!, l")
m, d, /


20C


250


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


(2000) are applied. Here the splashed mass fraction is
calculated according to


nP 1.8 x 10 KKcrit

as long as Kit < K < 7500, while for K2 > 7500
the splashed mass fraction is assumed to be constant and
takes the form
ms
S0.75. (10)
Tnp
The secondary droplet size is not given in terms of
mean diameter, but as maximum radius of a Nukiyama-
Tanasawa distribution function.


r" = max t 64 0.06) (11)
rp K2 -We'

Then, the number of secondary droplets can be esti-
mated from

n 16 ( 12)
3 P max


Post-impingement characteristics also imply secondary
velocities. Here, reflection properties are applied, which
means that the normal impingement velocity is inverted,
while the tangential impingement velocity is kept con-
stant for secondary droplet velocities. This approach is
not perfectly correct for ambient air at rest, as shown
recently by Muehlbauer (2009). For practical configura-
tions the high ambient air velocity and the fast response
of the secondary droplets, which are rather small com-
pared to the primary ones, justify this first assumption.
Observe the change in droplet properties after wall
contact from Figure 2, where droplet diameter is shown.
ter along the In this test case the primary droplets are injected mono-
m top to bot- disperse with a diameter of 624 pm. According to the
splashing correlation, the diameter, number and flow
rate of the incoming parcels are changed. They are not
trapped anymore, but active until they escape the com-
tly including putational domain. Comparing the trajectories of non-
impinging primary particles with those of secondary
n the post- droplets, the major differences resulting from the im-
according to proved model and associated with different sizes are
clearly visible.
p (6) Beside the generation of secondary droplets, the mo-
mentum transfer from impinging droplets to the film has
also been systematically neglected in previous models.
1) dp (7) This point has been taken into account in the present
formulation, so that tangential momentum is now con-
id served. Since not the momentum, but the local film ve-
locity is of interest, a momentum-induced film velocity
(8) is calculated from balancing the film momentum with
the momentum transferred by impacting droplets:


for deposited mass fraction. When the wall is covered
with a liquid film, correlations of O'Rourke and Amsden


mdep
nf





















-mplB Jan [-1s


Figure 4: Interpolated results of mean droplet diame-
ter [pm] at the top and mean droplet velocity
[m/s] at the bottom, for 15, 20 and 25 [m/s]
air flow velocity (from left to right).



Table 1: Working conditions for experiments

Parameter Value

atomization pressure 0.3 [bar]
water volume flow rate 5.4 [1/min]
air flow velocity 15, 20 and 25 [m/s]



The given ratio of deposited mass mdep and film mass
mf (including the deposited mass) is multiplied by the
original tangential velocity of the impinging droplet uto,
to derive the momentum-induced film velocity .,.
This velocity can then be combined with the two pre-
viously described velocity fields, caused by gravity and
shear stress, to give the new film velocity.


Wind tunnel experiments

To validate these model improvements, experiments are
carried out in a two-phase wind tunnel using a simplified
wind-shield geometry as target plate for the droplets. In
the following section the experimental facility will be
described briefly, before discussing the results for later
comparison with numerical simulation.
The wind tunnel at our Laboratory, a closed-loop wind
tunnel, features a flexible water atomization system, in-
cluding water recirculation and variable nozzle types.
For experimental soiling simulation a flat cone pressure
atomizer is applied to generate droplets with a mean di-
ameter in the range of 400-700 /m.
The nozzle is directed co-current to the air flow and
located at the center line, in front of the wind tunnel test
section. The measurement section allows optical mea-


ohl~~~lo,,lca

'"
i a




---
om~slu,~~~lmirl


j r
-i I j


:


D-MEmlO~~)I~ml
4ii'"""


D-Mean (D^) Im|


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


surement techniques through three large windows, one
at each side and one at the top. Additionally, the bot-
tom plate, which is mainly used to fix the wind shield
geometry, is also equipped with a small window, giving
access to the inside of the (hollow) geometry. Work-
ing parameters during the experiments for the atomizer
and air flow are listed in Table 1. The boundary condi-
tions measured for the droplets are shown in Figure 4.
Here, the real measurement locations are indicated by
the grid, shown only in the left image. From interpolat-
ing these results, a 2-D contour plot was obtained. At
each measurement location 10000 samples have been
acquired, since first tests have demonstrated that this is
needed to yield reliable statistics. As can be seen (atom-
ization conditions being kept constant), the mean droplet
diameter decreases with increasing air flow velocity. Si-
multaneously, the mean droplet velocity increases with
increasing air velocity. In order to quantify the occur-
rence of splashing, PDA measurements have been also
carried out in the middle of the test section and along its
center line.
As mentioned before, the geometry is a simplified
wind shield configuration, a glass plate with an incli-
nation of 28.5 towards the horizontal plane. It is fixed
between aluminum side walls, having a radius similar
to A-pillar curvature of real vehicles, in order to avoid
vortices affecting film development onto the plate.
Laser Doppler Anemometry (LDA) and PDA are em-
ployed to measure the inlet boundary conditions for the
air flow as well as for the dispersed droplets in front of
the geometry. Film thickness measurements with high
spatial and temporal resolution are still very challeng-
ing and are the subject of present work. As a conse-
quence, the comparison of numerical and experimental
results can only take place in an indirect manner up to
now.


Numerical simulation

The computational domain is discretized with approxi-
mately 2.1 million grid cells using a structured grid.
The numerical simulation of the film flow was car-
ried out using the algorithm described previously. The
first step consists in calculating the flow field around the
obstacle. For this purpose a steady, isothermal RANS
approach is applied. Flow turbulence is modeled with
the SST k-cw model, which is more accurate for flows
where wall deposition of droplets is of interest, as was
shown by Langrish and Kota (2007). The inlet condi-
tions for the air flow, obtained by LDA, have been pro-
cessed to take the format of a Fluent profile, with infor-
mation concerning main flow velocity and turbulent ki-
netic energy at the inlet boundary. In that way the exper-
imental results can be used directly within the numerical







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


LW nealreen.t C .l imlation










. . I .


0.25
0.2
0.15
0.1
0.05

-0.05
-0.1
-0.15
-0.2
-0.25
0.3


0.1 0.2 0.3


Figure 5: Computed velocity vectors along the middle
plane of the wind tunnel.



simulation. The results of flow field simulation, as well
as the validation by further LDA measurements will be
presented in the next section.
Since the mapping of numerical results to relevant
regions was not required here, the Lagrangian particle
tracking and film flow simulation can directly be car-
ried out in a second step. It is assumed that there is
only one-way coupling between the liquid phases and
the gas phase. Therefore, the flow field was frozen af-
ter the first step. The initial conditions for the dispersed
phase were obtained from the PDA measurements (as
described in the previous section), which have been used
to define the initial position, velocity, diameter and flow
rate of the dispersed phase. Since PDA measurements
were only performed at a finite number of measurement
points within the spray cone, a random fluctuation of the
initial positions has been used to simulate the wetting
from the complete spray cone. The variation of initial
position was set equal to the step size between the mea-
surement positions, 2.5 cm.
For film modeling only the plate was defined as target
for the droplets to build up the surface film. Initially,
there was no film on the plate. Since the build-up of the
film is a transient process, we use variable time steps for
the unsteady simulation, with a maximum time step of
0.05 s, based on Courant (CFL) criterion. The break-
up of the film was investigated using three different We
number threshold values (10, 1 and 0.1). In this manner,
the impact of this parameter on the film flow dynamics
can be quantified in detail.
To check the changes induced by the model modifica-
tions, simulations have been repeated twice with identi-
cal conditions, first using the original model of Ander-
son and Coughlan (2006) and then the modified version
of the model, including splashing and momentum trans-


Figure 6: Mean axial flow velocity behind the geometry.


Results and Comparison

In the present section the results from experimental and
numerical investigations are presented, discussed and
compared. From wind tunnel experiments a broad range
of data are available, concerning the properties of the gas
phase and the dispersed liquid phase.
As the results for initial droplet conditions have been
discussed in the experimental section, we put the fo-
cus here on the spray-wall interaction, in particular the
occurrence of secondary droplets generated by splash-
ing. The effect of splashing on the mean diameter is
clearly visible from Figure 3. When traveling along
the inclined plate surface, the mean diameter decreases
due to a higher amount of secondary droplets within the
samples. At the same time a decreasing number of sec-
ondary droplets is detected for higher distances between
the measuring location and the wall. Additionally, the
effect of increased velocity of the ambient air flow on
the spray structure can be observed. When the veloc-
ity is increased the mean diameter decreases due to the
higher impact velocity, causing smaller and more sec-
ondary droplets. Higher impact velocity also results in
higher secondary velocity, leading to more secondary
droplets also in higher distances from the wall. This in-
formation is visible in the spreading of the curves, which
decreases with increasing air velocity.
As mentioned previously, the results for the air flow
obtained by experiments and simulation are compared.
Figure 6 shows the contour of the axial velocity behind
the geometry, comparing experiment with simulation,
where the simulation result was mirrored along the cen-
ter line for a better view. The computed velocity shows
a good agreement in comparison with the experimental


-02 -0.1








7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


7 25 rns
-2-20 mis
6 -b-15 rms
5


3
2


0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
dimensionless plate length in flow direction


09 10


Figure 7: Shear stress along the plate for 15, 20 and 25
m/s.



results. Differences in the center of the contour plot, in
particular the concave structure towards the symmetry
line is owed to limited spatial resolution of the measure-
ment. Additional information, which are important for
later film simulations, can be obtained from the veloc-
ity vectors shown in Figure 5. Note that Figures 6 and
5 employ identical color levels for the velocity in order
to facilitate comparison. In Figure 5, the maximum ve-
locity is observed at the end of the inclined plate, at the
transition point toward the short horizontal plate close
to the end of the model. This point is interesting for the
later film simulation, since the highest shear stresses are
observed here (Figure 7). On the contrary, a minimum
of shear stress can be observed at the leading edge. Fig-
ure 7 shows the shear stress for the 3 different air flow
velocities 15, 20 and 25 m/s, particularly relevant for
vehicle soiling simulation. The point of maximum shear
stress visible in Figure 7 is particularly important since,
locally combined with high values for the film thickness,
the film tends to break up first at this particular location.
The film flow dynamics are affected by incoming liq-
uid mass, so that film build-up is a function of time, as
can be seen in Figure 8. Here, the film thickness along
the center line of the plate is shown for increasing flow
times (given in ms in the legend). Beside the increase
of film thickness with time, the accumulation of liquid
mass at certain points of the wind shield geometry is
visible. The maximum film thickness is observed at the
location of minimum shear stress, at the bend along the
leading edge of the plate. Liquid is transported follow-
ing the main flow direction towards this point and then
flows sidewise, to the edges of the geometry. Another
location where liquid accumulates is the rear edge of
the wind shield geometry. This is a typical phenomenon
associated with liquid films at edges, well documented


0 45 t=44.14
E 0 -t=463.85
E 40 t=750.25
0,35 1 i"t=969.49
0 30 4
030

0 10

S025
0,00,i._ A-- A__IW

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
dimensionless plate length in flow direction


Figure 8: Computed film thickness along the center line
of the plate for air flow velocity of 15 m/s.


1,20

- 1,00

S0,80
'C
M 0,60
E
S0,40

O 0,20
E
i 0,00
0,


4- t=44.14
*" t=463.85
% t=750.25
* -t=969.49


0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1.0
dimensionless plate length in flow direction


Figure 9: Computed film velocity magnitude.


in the literature. The accumulation holds on until the
threshold for film break-up is exceeded and a droplet is
released.
In addition to the film thickness, the film velocity is
a second important aspect of film flow dynamics. As
shown in Figure 9, the evolution of film velocity magni-
tude follows closely that of the wall shear stresses shown
in Figure 7. Comparing the original model of Ander-
son and Coughlan (2006) with the modified one, the dif-
ferences are quite obvious. The splashing of impinging
droplets leads to a smaller amount of liquid mass de-
posited on the plate to build up the film. At identical
flow times the film thickness values are therefore lower
than those predicted by the original model, see Figure
10 (top).
The momentum transfer from impinging droplets to
the film is taken into account in the modified model.
Comparing the film velocity predicted by the original
and the modified model (Figure 10 middle) the results












Film depth


0,50


E

(A
E
U,
0
Co
e-<

E
;=


0,45 *o rig.
0,40 t=761.14
0,35 r' *modif.
0,3 ,, r ^ A t=750.25
0,30
0,25


0,20
0,15



0,0 0,1 0,2 0.3 0,4 0,5 0,6 0,7 08 0,9 1
dimensionless plate length in flow direction


0 Film velocity
2 0,60
.E orig.
S0,50 t=761.14
0- modif.
S0,40 t=750.25
E o0,30

0,20

a? 0 10 >
E 0 i

S 0,0 0,1 0,2 03 0,4 0,5 0,6 07 0,8 0,9 1,0
dimensionless plate length in flow direction
Film breakup
6E 006


S5E-006

S4E006

) 3E-006

2E-006

, 1E-006

OE000
0,


"- orig.
t=761.14
- modif.
t=750.25


0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0 8 09 1,0
dimensionless plate length in flow direction


Figure 10: Comparison of the original model Ander-
son and Coughlan (2006) and the modified
model.



first seem surprising, since the velocity coming from the
modified model shows in general lower values. How-
ever, it must be kept in mind that the film velocity is cal-
culated analytically from Equation (3), where the film
thickness is directly included. Since the modification
also accounts for splashing, with mass being partially re-
flected from the wall, the film thickness is also different
using the modified model. As a consequence both model
modifications interact directly with each other, leading
to non-intuitive modifications of the results. In order
to validate directly the model improvements, measure-
ments of film thickness would be very valuable and are
p1I'c'ml carried out. The film break up has also been
investigated in more details (Figure 10 bottom). For this
purpose the area-weighted average value of the mass re-
lease rate has been computed along the plate for different


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010



Table 2: Computed film break-up at flow time 750.25
ms

We number threshold value mass release rate

10 0 [kg/s]
1 1.26 x 10-9 [kg/s]
0.1 7.2 x 10-8 [kg/s]



We-number threshold values. As can be seen from Table
2 the mass release increases with decreasing threshold
value. For the highest threshold value chosen here, no
mass is release at all. Since this is in clear contradic-
tion with the already available experimental results, the
original suggestion of Anderson and Coughlan (2006)
(threshold value of Wef 10) can not be employed in
the present case. Also interesting in association with the
results for the flow field is, that most release spots are lo-
cated towards the rear edge of the geometry (Figure 10
bottom), due to the reasons mentioned previously.



Conclusions


Experimental and numerical investigations of vehicle
soiling have been performed in order to develop an im-
proved soiling simulation model for CFD. An existing
Eulerian model has been extended, in particular to ac-
count for splashing and momentum transfer to the film.
Identical simulations relying on the original and on the
improved model show differences in film build-up time,
with more reasonable results obtained using the ex-
tended model. The influence of the critical Weber num-
ber used as a threshold for film break-up has also been
quantified. With decreasing critical Weber number the
film tends to break-up faster. The critical value proposed
originally by Anderson and Coughlan (2006) is not suit-
able for the present configuration. As a whole, it ap-
pears that a different break-up criterion should be iden-
tified, based on more physical considerations. Quanti-
tative comparisons between simulations and measure-
ments of film thickness with high spatial and temporal
resolution are the subject of future work.



Acknowledgements


The financial support of Volkswagen AG Wolfsburg is
gratefully acknowledged. We also acknowledge the co-
operation with ISM Braunschweig under the direction of
Prof. R. Radespiel concerning film thickness measure-
ments.











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