Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P1.78 - Experimental and numerical study of water transport on a generic mirror
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00468
 Material Information
Title: P1.78 - Experimental and numerical study of water transport on a generic mirror Computational Techniques for Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Tivert, T.
Davidson, L.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: liquid films
break-up relaxation region
 Notes
Abstract: An experimental study of water transport on a generic mirror wa~ carried out. The experimental set-up wa~ a generic mirror that had a total height of 30 cm and a width of 20 cm with 52 holes with a diameter of I mm, see figure I. As the water was introduced, the ambient air formed a rivulet that traveled towards the trailing edge of the mirror. The rivulet breaks up at the trailing edge or just continuously drains on the flat side of the mirror. This rivulet will also break up at the end and form droplets whose size depends on the flow rate and the velocity of the ambient flow. The experiment was done at Volvo Car Corporation using three different water flow rates (0.8, 0.5 and 0.2 IIh) and four ambient velocities (II, 14, 19 and 25 mls). A high-speed camera was used to visualize the water, which contained a fluorescent liquid for easier post processing. Every case was repeated five times in order to obtain reasonably good statistics for the rivulet path and second-order droplets. In this paper we distinguished between moving and non-moving separation of rivulets/films. A moving rivulet is a rivulet that has a velocity when it breaks up, and a non-moving rivulet is one that does not have any velocity when it breaks up. In the latter case it accumulates water at the edge before it breaks up and sheds from the edge. The experiment shows good agreement with previous separation criteria for moving film. The correlation for the non-moving films resulted in a difterent correlation a~ compared to Tivert & Davidson (2010). This discrepancy can be an effect of errors in the local air velocity estimation or have to do with geometry.
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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Bibliographic ID: UF00102023
Volume ID: VID00468
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: P178-Tivert-ICMF2010.pdf

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


Experimental study of water transport on a generic mirror


T. Tivrert* anld L~. D~avidson1*


Dept. of Applied h le Illani,(.Ill~ll.nesl a University of Technology SE-412 96 Gothenburg
[tobias.tivertechalmers.se and ladaechalmers.se]

Keywvords: Liquid films, break-up relaxation region




Abstract

An experimental study of water transport on a generic mirror was carried out. The experimental set-up was a generic
mirror that had a total height of 30 cm and a width of 20 cm with 52 holes with a diameter of 1 mm, see figure 1. As
the water was introduced, the ambient air formed a rivulet that traveled towards the trailing edge of the mirror. The
rivulet breaks up at the trailing edge or just continuously drains on the flat side of the mirror. This rivulet will also
break up at the end and form droplets whose size depends on the flow rate and the velocity of the ambient flow.
The experiment was done at Volvo Car Corporation using three different water flow rates (0.8, 0.5 and 0.2 1/h) and
four ambient velocities (11i, 14, 19 and 25 m/s). A high-speed camera was used to visualize the water, which contained
a fluorescent liquid for easier post processing. Every case was repeated five times in order to obtain reasonably
good statistics for the rivulet path and second-order droplets. In this paper we distinguished between moving and
non-moving separation of rivulets/films. A moving rivulet is a rivulet that has a velocity when it breaks up, and a
non-moving rivulet is one that does not have any velocity when it breaks up. In the latter case it accumulates water at
the edge before it breaks up and sheds from the edge. I lic c'`i per Ilnentl shows good~l lcy a minent 0~ ilil previous separation
criteria for moving film. The correlation for the non-moving films resulted in a different correlation as compared to
1 l~cI s & Davidson (2010). This discrepancy can be an effect of errors in the local air velocity estimation or have to do
with geometry.


Introduction

Liquid films and rivulets play a major role in many pro-
cesses in industry. F~or instance, liquid films are of in-
terest in various kinds of cooling devices in terms of
facilitating separation of liquid and gas in oil industry
and in fuel mixing in engines. Different models avail-
able for simulating a liquid film or a rivulet flow, such
as the classical fourth-order model of Bernis & F~ried-
man (1990) and the boundary layer model. The choice
of model depends on the types of features required.
H-owever, the thin liquid film approach has some
drawbacks that are of great importance, especially the
break-up issue. It does not allow the thin film to break-
up by itself because the models do not include the
physics for break-up. This is a problem because almost
all important flows contain some sort of break-up into
smaller films or droplets. The solution is to use exper-
imental correlations and one can use the correlations in
Friedrich et al. (S il l:,s or 5 u le-lul.i~ et al. (2002) when
the film is moving. If the film is non-moving, the cor-


relation in 1 noII & Davidson (r1 l I r can be used, but it
seems that break-up is dependent on geometry thus re-
quiring further validation work. In the experiment pre-
sented in this paper, both moving film and non-moving
film separation criteria will be validated.


Experimnental set-up and method

The generic side mirror with its dimensions is shown in
figures 2 and 3. The mirror is mounted on a vertical
plate 2.9 m long and 1.6 m wide. The mirror is placed
0.9 m from the leading edge of the plate, as can be seen
in figure 4.
The cameras used in the experiment were a high-
speed camera and two video cameras. The two video
cameras were used when the rivulet was traveling on
the mirror where there was no need of high accuracy.
The resolution and frequency of the video cameras were
much lower than of the high-speed camera. The high-
speed camera was placed so it could captured the separa-
tion of the rivulet. The resolution of the high-speed cam-










































Step 4: Compute a corresponding radius of the closed
area.

Step 5: Compute the distance between a droplet at two
consecutive photos and divide it by the time elapsed
between the two photos, which gives the speed of
the droplet.


o.os

0.04

o.os

0.02

0.01




-0.01
0.26 0.27 0.28 0.29 0.3 0.31

Figure 6: The seek .ign liillirl. the search mesh and a
droplet with its corresponding radius


The following steps were used to get the location and
width of the rivulet:

Step 1: The rivulet was filmed by the video camera. It
was sufficient to use one frame of the entire film be-
cause the rivulet was stationary in each experiment,


7"h International Conference on Multiphase Flow,
ICMF 2010, ~ampa, FL, May 30 -- June 4, 2010






F-~-1
b
3 " r t~
K; 7


'9 ,"
!,
~'.4*
L~ii~
C~ 1 .1111
1'1
~O
:LI :;,11 111111:1111)11111 11::


'I"'' ,-Eq nations used
,,, dv --KRirO-dB R dv


Figure 1: Generic mirror


era was 256 x -'lc.m anl thec I spending f equc,iclcy was 1000
H-z. The camera set-up during the experiment is shown
in figure 5, where A is the location of the video cam-
eras and B is the position of both the video cameras and
high-speed camera, but at different horizontal positions.
The velocity and the size of the released droplets were
obtained by high-speed filming, and L I\ Ilquil was used
to acquire sharper pictures. The measurements were re-
peated at least eight times for each water flow rate and
ambient air flow to obtain good statistics.
Correction has been made for the experiments error
such as blurriness and converting between different for-
mats. Greater detail on the experimental work is given
in Lafuente (r Ir lh
The pictures were analyzed in hL.lblll where the
movement of each droplet was detected. The veloci-
ties of the droplets were obtained from the camera fre-
quency. The ''ccl.'l- l se ':1i lillirl and the approach for find-
ing droplets and calculating the velocities are described
below.

Step 1: Define a very coarse two-dimensional grid
with a cell size of approximately 0.5cm x 0.5cm
(see figure 6) where each cell is checked to see
whether it contains any water.

Step2: If there is any water in a large cell, then an al-
yes iillrl finds the pixels that cover the droplet.

Step 3: If a droplet is in two or more cells, then a new
large cell is defined. It is not a problem if there is
more than one droplet in a cell.











































ILEW. -?-m


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





AB








Figure 5: A and B are the camera positions. I Ilie ..Ilerllc1
air velocity is directed into the paper.


places along the path and was then averaged for the
five experiments.

Step 5: The center line of the rivulet was then mapped
into the millimeter paper.

Exactly the same procedure was used to find the separa-
tion points.

Results

The main object was to gain a good understanding of
the water transport on a mirror-like object. The experi-
ment was also an opportunity to investigate whether the
formulas and correlations in the literature for separation
were fulfilled in this test case. The generic mirror had
52 holes that were drilled, but only ten of them are used
in this experiment. Figure 1 shows which holes are used
and their location. In the first part of the experiment, the
rivulet path was of interest. The path of the rivulet is
shown in figures 7 and 8. The path is strongly depen-
dent on ambient velocity as can be seen in the figure.
As the experimental results showed only a weak depen-
dency on the water flow rate, only one flow rate is pre-
sented here. I lic p.Illi of the rivulet is a mean path of five
experiments. The widths of the rivulets are not shown in
figures 7 and 8 but are listed in table 1.
Figures 9 and 10 show where the rivulets separate
from the generic mirror. A comparison of the separa-
tion points with the rivulet path in figures 7 and 8 shows
that, in many cases, the end of the rivulet is not at the
separation point. The explanation is that the rivulet tray-
els along the lower edg-c of theilc mirror and, in most cases,
the separation would take place close to the lower outer
edge of the half sphere of the mirror, as can be seen in
figures 9 and 10. The reason why there are many sepa-
ration points located in this refion is not yet clear.
Figure 11 shows the present correlation for non-
moving separation, and the equation for separation is:

We =I --96 +- 174Vc


'L


Figure 2: The generic mirror with dimensions
(front view)


Figure 3: The priet 'ic nl~illl n 0
view)

2 m


ill dimensions (side


0.9 m


Figure 4: Dimensions of the experimental set-up


although the rivulet was not in the same place in
different experiments.

Step 2Z: The use of UV liquid in the water made it easy
to obtain an accurate location of the rivulet.

Step 3: Repeat step 2 for the five experiments.

Step 4: The mean path of the rivulet was calculated.
The width was also measured at four different







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


Figure 7: Rivulet path for holes 1-5 with three different
velocities. Red: V, =I 11m/s; white: V, =
19 m/s; blue: V, =I 25 m/s


Figure 9: Separation points for holes 1-5 with three
different velocities. View from downstream.
Red: V, =I 11m/s; white: V, =I 19m/s;
blue: V, =I 25 m/s


Figure 8: Rivulet path for holes 6-10 with three different
velocities. Red: V, =I 11m/s; white: V, =I
19 m/s; blue: V, =I 25 m/s



The formula is only valid inside the interval 11 < V, <
25.
If the rivulet or a film is non-moving at an edge, it will
separate from the surface if the \\c~lies number is above
the curve shown in figure 11. The \\c'lies number is
calculated as follows

PfhfV,
We =

where pf is the density for the liquid in the rivulet or the
film, hf is the height of the rivulcl .I1 thec edge-c just before
it separates, o is the surface tension and I5 is the ambi-
ent air velocity. The height as a function of the \\c'lan
number is shown in figure 12 and, as expected, the criti-
cal height gets smaller when the air velocity increases.
Comparing the correlation and critical height in this
study with In sc t & Davidson (r 1I Irll it is seen that the
critical height is lower in the present experiment. The


Figure l0: Separation points for holes 1-5 with three
different velocities. View from downstream.
Red: V, =I 11m/s; white: V, =I 19m/s;
blue: V, =I 25 m/s



reason for this is probably that the ambient air velocity
is used in the calculation of the \\c~lies number. The lo-
cal air velocity is higher in the present experiment than
in the previous investigation because of the acceleration
caused by the curvature of the front side of the mirror.
Unfortunately there were no measurements of the local
velocity. The use of the ambient velocity in the Hecllerl
number is probably not the best choice; it would have
been much bett-er to use the shear stress.
F~riedrich et al. (r Ir I, proposed a criterion for break-
up when the film is moving over an edge: if the fraction
is Lu yes Ilkinl one, the film/rivulet will separate.


pfu hf
Franio =T







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


x 10-3


1


T0 15 20 25
Velocity, V, [m/s]

Figure 12: Critical hight for different air velocities


* *


Event
Figure 13: F~riedrich F~orce balance. Beginning from the
left with hole I with V, =r 11, then hole 1
V, =r 19 and so on, at right hole 10 with V, =r





are shown in figures 14 and 15 and the averaged quan-
tity is shown in figures 16 and 17. One can clearly see
that the radius decreases the further away the droplets
come from the mirror. This is due to the break-up of
the droplet. The droplet breaks up into smaller droplets
if the diameter is larger than a critical diameter corre-
sponding to the \\c~lies number for the droplet. The ve-
locity of the droplets increases the further downstream
they get. This is caused by the drag increase because of
acceleration of the droplets. It is also due to the break-up
of the droplets, however; when the droplets are smaller
they get a shorter relaxation time and will accelerate to
the ambient velocity more rapidly. In figures 17 and 15
the particle velocity was divided': ic 1. heannierict1 velocity.


Hole Velocity, I (mr/s) flow rate (I/h) Width (mm)
1 11 0.2 2.1
3 11 0.2 1.7
5 11 0.2 2.1
1 14 0.2 2.1
3 14 0.2 2.2
5 14 0.2 2.4
1 19 0.2 2.3
3 19 0.2 1.2
5 19 0.2 1.9
1 25 0.2 2.1
3 25 0.2 1.2
5 25 0.2 1.8

Table 1: The width of the rivulet at different conditions

5000

4500

=r4000

S3500
~3000

S2500
2000

1500 15 20 25
Velocity, V, [m/s]
Figure 1: Dots: experimental \\c~lies number; green
line: the correlation in least square sense



H-ere uf is the velocity of the film. \\ lonl the air ve-
locity was 25 m/s the rivulet did not stop at the edge
and accumulate water (i.e non-moving separation), but
it separated directly (i.e moving separation) or continued
over the upper edge and drained down along the flat side
of the mirror to the lower edge of the mirror, as sees in
figure 7. I liecinee1lc another criterion is needed to judge
whether it would separate or accumulate. If the crite-
rion in Friedrich et al. (r Ir I, were used, there would be
three separations, as can be seen in figure 13, but only
one separation was obtained, namely in the case of 25
m/s and when the water comes from hole two. The rea-
son why the criterion overestimated the number of mov-
ing rivulet separations can be an overprediction of the
rivulet velocity. themlc was no opportunity to measure
the rivulet velocity during the experiment, so the veloc-
ity is an estimation from mass conservation.
Each experiment in which the separation was of in-
terest was run for two seconds and was filmed by the
high-speed camera. The radius and velocity for every
droplet in each picture during the separation experiment








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


X 10-3
--11 m/s
2 ~-13 m/s



19m







0.02 0.04 0.06 0.08 0.10
distance from the edge [m]
Figure 16: Me nll radius for various ambient velocities at
different positions from the mirror


. i : ~'


0.02 0.04 0.06 0.08 0.1 0.12
distance from the edge [m]
Figure 14: The dots are the diameters of the droplets at
different positions from the mirror


i
i' .~. ?:
~'- . ...
;r :.
:
--: .
. . :
; :,
'' ;
. ri~~;
.~ ~~4,
i.d..: ..
nr:. ,~.:; ;':: ~: : C: 1"
? ;;,-.: :~i ~
~+~ ~-
i~~iS~..:t'~~ ,'! ~i~~: ~~n';


0.8


S0.6

0.


O ~~U"Y""UZ~1~~ 5
0.02 0.04 0.06 0.08
distance from the edge [m]
Figure 15: The dots are the velocities (normalized with
V,) of the droplets at different positions from
the mirror



Conclusions

An experimental study of water transport on a generic
mirror was carried out. The generic mirror had 52 drilled
one-mm holes, and ten of them were used to introduce
water in the present study. Four ambient air velocities
and three water flow rates were used in the experiment.
The rivulet path was strongly dependent on the ambient
air velocity but showed almost no dependency on wa-
ter flow rate. A correlation for non-moving rivulet/film
separation is presented, and the experiment also showed
some moving rivulet separations. F~riedrich et al. (r In : ,
criterion was used for moving rivulet/film separations,
and the correlation *iliglul:. overpredicts the number of
separations. H-owever it can be caused by an overestima-
tion of the rivulet velocity in this study. The correlation
in this study has at least one serious drawback: the use of


S0.01 0.03 0.06 0.09
distance from the edge [m]
Figure 17: hlc.ln velocities (normalized with 15) of the
droplet for various ambient velocities



the ambient air velocity in the correlation for the critical
\\ clcl lillr numbe To get a better separation model for non-
moving rivulets/films, it is probably necessary to use the
shear stress instead of the ambient velocity. One way
to obtain the shear stress is to simulate the air flow with
large eddy simulations. The results will be much more
general if the local quantity is used; different geometries
can then more easily be compared and a general model
for non-moving rivulets may finally be achieved.



Acknowledgemnents

This project is financed by Vinnova and the Volvo Car
Corporation. Hec would like to thank the Volvo Car Cor-
poration for support with the wind tunnel and experi-
mental materials.







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


References

J.M.M Lafuente,Experimental studies of water manage-
ment on a flat plate and simplrilled1 Ic.l view mirror,tech-
nical report hl lLcl t I Ile wis 07/15j,Chalmers University
of Technology

M. A. Friedrich, H-. Lan and J. L. \\c-cries and J, A.
Drallmeier, A Separation criterion with experimental
validation for shear-driven films in a separated flows,
Journal of F~luids Engineering, Vol. 130, pp. 051301-1,
2008

T. I 1cl Ie, L. Davidson, \\ iti1-1II IvJen rivulet over an edge
with break-up, internal report, Chalmers University of
Technology, 2010

F. Absle-st~cli~, D. Llory, JF. Le Coz and C. H-abchi, Liq-
uid F~ilm Atomization on \\.III Edges-Separation Crite-
rion and Droplets F~ormation Model,Journal of F~luids
Engineering, Vol. 124, pp.565--575 2002 2

F. Bernis, A. F~riedman, H-igher order nonlinear degen-
erate parabolic equations, J. Differential Equations, Vol.
83, 179-206, 1990




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