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OCR for page 481
Development of a New Velocity Measurement System by Using
Computerized Flow Visualization and Numerical Method
K. More and S. Ninom~ya
Hiroshima University
Hiroshima, Japan
Abstract
A hybrid method is developed to
measure 3dimensional flows where the
image processing method and numerical
computational method are complementari
ly used; the 3dimensional flow field
is reproduced by the numerical calcu
lations by making use of several scan
ned plane flows which have been ob
tained by the flow visualization and
image processing.
The combination of the numerical
computation has made the flow visuali
zation system much less sophisticated.
The method is applied to measure the
flow field around the Wigley model to
conclude that the method is promising
although the used system is rather
. . .
prlml lve .
1. Introduction
It is common to measure velocity
fields by traversing an anemometer at
one position after another even in a 3
dimensional domain. Needless to say,
it is timeconsuming and requires much
labor. Even more, there are some
cases where the velocity field cannot
be measured by the conventional method
due to reverse flows, abrupt changes of
the velocity or stagnant flows.
The flow visualization has ever been
a qualitative method which is useful
to understand the flow field globally.
However, owing to the advent of a new
era of image processing techniques, it
can be even quantitative.
There are some pioneering researches
where the velocity field is determined
481
by the image processing techniques [1]
[2]. Most of them are for 2dimensional
flows but some are intended to be 3
dimensional flows where the tracers are
tracked 3dimensionally by making use
of several cameras [3][4]. However,
the instruments for measurements and
the algorithm for analysis are compli
cated.
On the other hand, recent develop
ments in computational fluid dynamics
to simulate flow fields by solving the
NS equations are remarkable. However,
there are still limitations in the
hardwares of computers to have reliable
results even by modern computers of
highspeed and large memory storage;
the computing domain and the grid size
can not be taken enough for required.
The present method is a kind of
hybrid methods of the image processing
and the computational fluid dynamics;
a 3dimensional flow is reproduced by
numerical computations from several
scanned plane flows obtained by the
flow visualization and image pro
cessing. It consists of five stages, as
the block diagram shown in Fig.1; 1)
flow visualization, 2) image process
ing, 3) image analysis, 4) numerical
computation and 5) graphic display.
The method is called "Threedimensional
Anemometer System by complementarily
use of Computational and Optical
Methods" (TASCOM).
Although the method is still under
development and the instruments used
here are rather primitive, the system
may be much improved by an introduction
of more sophisticated machines or
higherversion of softwares.
OCR for page 481
2. Plane Flow Analysis
2.1 Flow visualization
The arrangement for the measurements
is shown in Fig.2. A laser light
sheet is used to scan a plane flow
field which is traversed in z direction
whose velocity component w is presumed
the smallest among the three compo
nents. A 25 mW HeNe laser beam and a
circular cylindrical lens are used to
realize a light sheet in the present
experiment.
Hydrogen bubbles are used as tracers
which are generated by the electrolysis
of water. The reasons for the use of
the hydrogen bubbles are, first, that
they can trace flows without inertia
and both their size and brightness can
be controlled. Secondly, but essen
tially important, they do not pollute
the water. They can be used in towing
tanks also. Of course, they do not
work well for the flows whose velocity
is so small that the buoyant effect is
relatively large.
[FLOW
VISUALIZATION]
ScanningbyLaser
Lig! it Sheet
[IMAGE
PROCESSIN G]
. Picture by 1.
: COD Camera :
. 1 .
: . :
. Acquisition .
: of Images :
: . :
. Binar' r  2
: Processing '
: . I:
. , .
: . ,:
. Thinning .
: Processing :
.' ,,
, .
[IMAGE
ANALYSIS]
....... ,
I
.tIdentiflcation.
.~.
: I :
: . :
: Remove of :
. Poor Data .
: . :
: 1 :
. Velocity of .
. Plane Flow .
. 1 .
~ — — — —  — — — ——— '  — — — 1 —— ——— —— — —  — ——  —
[NUMERICAL
COMPUTATION]
, . ... .. . .
. .
. Velocities at .
: Grid Points :
. .
: :
.'
: :
. Reproduction of .
: 3Dimensional :
. Velocity Field .
. 1 .
. . .
. Computation for .
. Unmeasurable .
: Points :
. 1 !
. Pressure and .
. Force .
. .
8
[GRAPHIC
DISPLAY]
. ....
: :
: :
: Vectorization :
. and Perspective .
: View of :
. Velocity Field .
: :
1 1
Fig.1 Block diagram of the present
measuring system, TASCOM
The electrode is made of platinum
wires which are formed ladderlike as
shown in Figs.2 and 10. They can pro
duce vertical segments of bubbles
which cut the laser light sheet without
fail.
In general, there are some regions
where tracers do not get into; we call
such regions "unmeasurable region"
here. We do not pay special attentions
for such regions and we expect the
velocity there will be supplied by
numerical computations.
2.2 Method of image processing
The process of the present image
processing is shown schematically in
Fig.1. This process consists of the
following three steps.
1) freezing images of tracers:
The path lines of tracers on the
scanned plane are recorded by a CCD
camera (384 x 491 pixels), as shown in
r
!1
1 1
2.5mW HeNe Laser
Lase r L i 8h t Shee t Cy l i nd r i ca l Lens
1 400~(max)
 nc Poise Generator 
lIydroSe') Bubb I es
/ _
P I a t i nu m W i re
\j Laser Light Sheet
~ \ .  _ A
1
Image Process i n8 
 9; t Computer ~ ~
Fig.2 Arrangement of the system
l
482
OCR for page 481
Fig.2. The acquired analogue image
signals are converted to digital data
by making use of a image processing
device (256 x 256 pixels, 8 bit). The
device can freeze successive four
frames at once at the time interval of
50 msec.
2) binary processing:
The 8bit value of brightness of
each pixel are binarized based on dis
criminating level. It is important how
to set the value of the level, for the
optimum value depends much on experi
mental conditions such as brightness of
tracers, velocity and so on. Here it
is set by a trial and error method.
3) thinning processing:
In order to have more reliable data
of the tracers such as the length and
the positions of start and termination,
the thinning process is essential. As
shown in Fig.3, the thinned line Ci is
determined as the centerline of the
segment AiBi.
2.3 Calculation of plane velocity
As shown in Fig.4, the plane velo
AIA
A2
He'd
/ B3
_ ~/~
1—I//
1—4/
B2 BE
~3,—
/
BE
Fig.3 Thinning process of images
t, ~2 _
~ ~ (d ' ' ." <)
_
:_' ' ,,. ~~
appear onto Lo disappear fro~LLS
Fig.4 Calculation of the velocity
483
city (u,v) is evaluated from the two
distances, Q1 and Q2, between the three
images of the same tracer at the three
sequential times, t1, t2 and t3. The
three images have been identified to be
the images of a single tracer. The
plane flow velocity components are
determined from the components of the
distances in their directions.
1) identification of tracers:
The algorithm of identification of
tracers is schematically shown in
Fig.5. A priority is given to the
image to be identified when it lies
within a certain distance and fan
angle; the image A2 on the frame at
time t2 is identified with A1 because
A2 lies within the fan angle of aa"
and aa"' and within a given distance.
At the next time step t3, A3 is identi
fied. Thus all the images are identi
fied as B1B2B3, C1C2C3, and so on.
Through the above processes, if a
tracer could not be identified, the
tracer is assumed "stray" and is neg
lected in the following analysis. The
distance and the fan angle are empiri
cally given here.
2) selection:
There are still some possibilities
to identify wrong images. If the two
distances between the three identified
images, Q1' Q2 in Fig.4, are extremely
/ C,
/
, A,, ;
t,/ ,
,
1 ~
1 1
. .
, .
. .
/
j ~ B3  /
~ C3, /
 _1 .~/
Fig.5 Identification of the images on
three different frames
OCR for page 481
different each other or their average
differs much from the surroundings, the
set of images is assumed wrong and
removed from the stored data.
3) calculation of the velocity compo
nents:
The plane velocity component (ui,
vi) is calculated from the distances
between the identified images on the
three sequential frames by the fol
lowing equations;
. _ Q;x
u,  At
Tim
v i =  
where At is the interval time between
the frames and Six and Qiy are the x
and ycomponents of the length Qi
4) interpolation of the velocity:
It is necessary to have the velocity
on assigned matrix points, which can be
realized by the weighed interpolation
of the original data at arbitrary
points. The velocity vector q(x,y) at
(x,y) is calculated by
q (x, Y)  (~ ri Yi)} /
Am, r; } (2)
where ri is the distance to the data
interpolated, and N is the number of
the possible data for interpolation.
The maximum ri is properly chosen and
if N is less than 3, the velocity at
the point is regarded as "not mea
sured".
3. Accuracy Analysis of
the Measuring System
It is important to estimate the
accuracy of the measuring system. The
nominal accuracy of the image analysis
is given in terms of the density of the
pixels of COD camera and the sampling
interval time.
The resolving power of the image
processing, denoted by d, is given by
d = L_ (3)
where n is the number of pixels and L
is the actual size of the object to be
pictured.
In the present system, the number of
pixels is 256 x 256 and the size of the
picture is about 100 mm x 100 mm. Then
the resolving power d is 0.4 mm/pixel
and the accuracy of positioning may be
~0.2 mm/pixel.
(1) The minimum velocity, which can be
resolved, Umin, is given by
Umin = Act (4)
where At is the sampling interval time.
In the present system 10 frames (pic
tures) are frozen per a second and the
accuracy of the measured velocity is i2
mm/sec. The optimum sampling interval
time should be determined depending on
the uniform flow velocity and the den
sity of pixels.
In practice, the final accuracy must
include the errors which arise during
the image processings due to non
uniformity of image brightness, wrong
identifications and so on.
soo
(Mets)
400 _
lo,
+~
. _
A'
o
a;

=
V)
~ 200
~ . .
300 _
100 /
/ , . , , , ~
0 100 200 300 400 500
(err i age Speed (its)
484
Fig.6 Accuracy analysis of the image
processing
OCR for page 481
200 250 300
Measu red Ye I oc i ty (mm/s)
Fig.7 Histogarm of the measured velo
city for the uniform flow
To confirm the total accuracy of the
present system, two measurements are
carried out in advance. One is to
analyze the velocity of a pinhole
light which moves as a constant speed;
this is realized by fixing the light
onto the towing carriage. The other is
to measure the uniform flow velocity of
water circulating channel.
Fig.6 shows the results of the first
experiment; the abscissa gives the
carriage speed and the coordinate, the
analyzed velocity by the present meth
od. The mean curve seems to be giving a
good correlation and the error of meas
urement is smaller than the resolving
power of the image processing. ~F(u v w, A)
Fig.7 is the results of the second
experiments; the measured velocity of
the uniform flow of circulating water
channel. 367 measured data are shown in
histogram. The nominal velocity of the
uniform flow by the indicator is 300
mm/see and the nominal uniformity of
the flow is about 96%. The total
average of the measured data is 307.1
mm/sec. 64% of the measured data lies
within 300~25 mm/see of the uniform
flow velocity.
4. Reproductionof the 3
Dimensional Flow Field
4.1 Invoked equations and the scheme
The reproduction of the 3dimen
sional flows from the scanned plane
velocity fields is achieved numerically
by a variational method to satisfy the
continuity equation [5]. There the
measured plane flow velocities (u0, v0)
on the scanned planes are used as ini
tial values.
The reason why the variational
method is invoked is that the scheme
must be robust or tough enough even if
the initial values, provided by the
scanned plane flows, are contaminated
by measurement errors. The use of the
variational method is expected to cor
rect the given boundary values to sa
tisfy the continuity equation.
The functional, F. is defined as
F (u, v, w, A)
i: {X,2 (U—Up) 2
+ {X22 ( V—V0 ) 2 +{X32 (W—W0 ) 2
+A [~x + gy + ~~z ]}dV
(a)
where ~ is the Lagrangian multiplier,
and ~1' ~2 and ~3 are weighing con
stants. The problem is to find (u,v,w)
to minimize F in the computing domain
V.
The first variation of F is given by
  [ T2 (X~2 ( U—U0 ) —~ X } ~ U
+ {2~22 (v—v~)— ~pA } Sv
+12~32 (w—w0) — pA}Sw
~u + ~v + ~w ] bA] dV
S485
{ASunx+Advny+Adnz} dE;
(6)
OCR for page 481
where ~ is the first variation, (nx,
ny, nz) are the components of the nor
mal on S which is the computing bound
ary surface of V.
The condition of CF=0 yields a set
of following equations;
l SA
u = us ~ 2~ ~ ~
l SA
v = van + 2a22 pY~~
W = WB + 2a
(7)
[_Su + _8v_ + low ~ = 0 (10)
tASunx+Advny+Adnz}dS = 0
s
(11)
Substituting (7), (8) and (9) into
(10), we have
r ~> ~ ail r ~3] 292A + 32A
La,J X2 ta2J ~y2 oz2
= ~ 2 (X32 ~ 89 UB + ~ VB + _0W0]
(12)
~~) is the Poisson equation by
which ~ can be determined. It is
solved by S.O.R. method under the boun
dary condition of (11). Then the velo
~9
o.o .
Fig.8 Computationaldomainfor3
dimensional reproduction
Domain for analysis
N1 Y
Boundary ~ ~  A = 0.0 °C1 ~ oc2 = 10.0,
Co nd i t i 0 ns
= 0.1
do
486
city vectors (u,v,w) is calculated from
(7),(8) and (9).
Because the velocity component w,
normal to the scanned plane, is impor
tant in the present calculation, the
ratio of ~1/~3 and ~2/~3 should be
properly chosen.
The boundary condition of (11) can
be satisfied by providing a suitable
subsidiary conditions for (6u, Jv,
dw)=0 or X=0 on the boundary S.
4.2 An example of reproduction of
3dimensional flow
In order to confirm the present
scheme to reproduce the 3dimensional
flow, the flow behind a sphere is ana
lyzed.
The coordinates and the analyzed
region is shown in Fig.8. The plane
flows are provided on twenty horizontal
planes by the potential flow calcula
tion. The computation region is di
vided into 20 x 20 x 20 cubic cells.
This grid size may not be sufficient
for enough accuracy, but the use of
too fine grids does not always meet the
experimental condition where the depar
tures between the scanned planes can
not be so small as expected in
computation.
The boundary conditions for ~ and
Gu, Jv and dw are given as
follows:
on x=O, DX/az=O,
Ju, Jv and dw=O,
on the other boundary planes,
N=0,
(13)
The boundary condition (13) satis
fies (11).
The weighing constants ~1, ~2, and
are assumed as forlows;
The Poisson equation (12) is solved
by S.O.R., where 1.4 is used as the
relaxation factor.
OCR for page 481
. by Analytical Hethod
1.00tZ, ~
.90 t
.80
.?9
.60
.N
.10 ,
.30,
.20 ~ r
.10
r
~ f
t t
t
r
t
1
· by
Present Method
O.It I ~ ~ ~ ~ l ~ , ~ ~
t.09 .IQ .20 .3Q .10 .5' .6t .19 .8Q .90 1.00
{Yl
Fig.9 Comparison of reproduced
3dimensional velocity
vectors behind a sphere
with the analytical
/ Wigley Double Hul I
I \ / Mode I
ail/
Laser Li jht Sheet
El ectrode (anode)
The reproduced yz plane velocity
vector is shown in Fig.9 together with
the results calculated analytically.
It is seen that the third zcomponent
of the velocity is well reproduced,
although there can be seen some discre
pancies between them where velocity
gradients are large just behind the
sphere. The use of a finer grid has
improved the results.
We can now conclude that the present
variational method can be applicable to
our analysis.
5. Measurement of the Stern
Flow of Wigley Model
5.1 Arrangements and sampling
To study the applicability of the
present method, a measurement of the
stern flow of the 1.2m Wigley double
hull model is carried out.
The arrangement of the measurement
is shown in Fig.10. The laser light
sheet is installed parallelly to the
uniform flow; the xy plane is scanned.
In the present experiment, the model is
traversed vertically for the plane
flows to be scanned.
Cathode
/ CCD Camera
_
~ r it ~ Fig.10
to the Pulse Generator \\\ Arrangement for the meas
to the Image Processi ng ~ urements of the wake of
Wigley model
Sys ted ~
487
OCR for page 481
try)
F LOW
~ ~1.0 ,
ID
k'igleyll''ll
~
0.1 Measur irlg
~ Re,£;ioll
Fig.11 Measuring region and scanned
planes for the Wigley model
As shown in Fig.11, eight planes are
scanned at 0.02 intervals. Although the
number of scanned planes may not be
enough for the following calculation,
the hardware of our system can not
afford any more. The region for mea
surements, i.e., the scope of the
camera, is determined to have a neces
sary accuracy. The maximum accuracy of
the image processing unit here is +0.2
mm/pixel.
The experiment is carried out in the
circulating water channel whose dimen
sions of the measuring section is as
follows; L x B x d = 2.0m x 1.4m x
0.9m. The uniform flow speed is 100
mm/see and the Reynolds number is about
1.2 x 105.
One measuring plane has 60 pictures
whose sampling time is 100 msec. This
means that the determined velocity
field is the mean velocity for 6
seconds.
5.2 Results of the plane flows
Fig.12 shows one example of tracer
images on z=0 plane, the reflecting
plane; (a) is the original binary pic
Fig.12 Frozen imagesonz=0plane(a)
and the thinned images (b)
ture from which background noises are
removed by smoothing, while (b) is the
thinned picture of (a).
From the picture (a), we can judge
that the present technique of the flow
visualization can stand for the quan
titative analysis of the velocity and
also that the images of the tracers are
well frozen for the following proc
essings. However, the pictures of the
thinned images, (b), suggest that we
have still some ill images when thin
ned due to noises or nonuniformity of
the brightness of tracers. The wrong
images are removed by estimating their
length.
Fig.13 shows the plane velocity
vectors analyzed by the procedure men
tioned in 2.3. They are well measured.
Thus we have 8 plane flow vectors where
u and v are determined but w is assumed
zero.
488
OCR for page 481
5.3 Results of 3dimensional flow cal
culations
For the calculations to reproduce
the 3dimensional flows, 22 plane flows
are presumed by the Bspline interpo
lation of the eight scanned plane velo
city fields. This is because the de
parture between the plane flows of the
present measurements is not small
enough for the numerical calculations.
More plane flows are expected to be
scanned to have more accurate results.
.02
(y)
Fig.13 Plane flow vectors on
( a )
D o8 °° 1 2 3 ~ 5 6
.01 Jew_
.02. ,
.031 W:
°~1 ~ \
·051 , \ \ \
.061 .W \
O?' `: \ ~ \. of
.08 1 ~: ~ \. \.
.094 ,\ ~ ~ ~ ..\"
.IOI \ ~ \,.~"
·~ll  ~ !. 'i
.121 i,.1"
13'
~ ~ a. ~
.14 1 Z)
~ ~ 1 ~

The computing domain is 1.00 < x <
1.10, 0.01 < y < 0.08 and 0.0 < z <
0.14. The boundary conditions are as
follows;
on the reflecting plane (xy plane,
z=O.O );
ax/az = 0
~ = 0
z =0
(13)
The 3dimensional velocity vectors
at the section of A.P. is shown in
Fig.14 compared with those measured by
a 5hole pitot tube. The calculation
can be carried out on the same compu
ters as real time.
Although the results do not always
agree quantitatively with those by
conventional method, the third velocity
components are well reproduced. The
computation was stable and robust as
expected even if the measured plane
flows contain some errors.
We can say through the present
example that the method is applicable
to 3dimensional measurements. It can
be also pointed out that an introduc
tion of more qualified hardwares will
guarantee us to have more accurate
results.
( b ) (Y)
0.00 1O ~ _2t  3'  ~ St It 1 8, 9 .10
.01
.02
.03
.Ol
.05
.06
.01
.08
.09
10
.11
12
.13
.11 z]
~ W\ ~ ~ ~ _ ~ ..
~ \ ~ ~ ~ ~ _ ~
\ ~ \ ~ A,
\~\~\_,.."`
\ ~ "'_ _
\ — /e
~ a\""\ ~ _, '~
\ \ _ ~ ~ Fig. 1 4
, ~ \ (10~/sec)
489
3dimensional
velocity vectors
et the A.P.
section
OCR for page 481
6. Conclusion
In the present paper, a new method
to measure the 3dimensional flow field
by a complimentary use of the flow
visualization and numerical compu
tation, TASCOM, is demonstrated with
some pilot examples. The attractive
feature of the present method are the
simplicity of the experimental appara
tus and technique. The method is po
tentially applicable to the measure
ments in the towing tank also.
Through the present study following
findings are summarized;
1) The use of the hydrogen bubble with
the laser light sheet is practical
and efficient for the image ana
lysis. The vertical segment of the
bubble always cuts the light sheet
and leaves clear images. No pollu
tion remains in the tank after the
measurements.
2) The present algorithm for image
processing, although primitive and
directive, is efficient and accu
rate enough. The use of more sophi
sticated machines will assure more
efficiency and accuracy.
3) 3dimensional flow can be reproduced
from several scanned plane flows to
satisfy the continuity condition.
The variational method is useful for
the reproduction calculation where
the measured plane flow components
are contaminated by errors. This is
because the method is tough enough
through relaxation.
The authors wish to express their
appreciations to Professors Y. Doi and
T. Hotta at Hiroshima University for
their variable discussions and advices.
The present research is partially
supported by the GrantinAid for
Developmental Scientific Research of
The Ministry of Education, Science and
Culture.
References
1. Mori,K., Hotta,T. and Ninomiya,S.
"Development of a Method to Measure
Flow Field by Flow Visualization and
Image Processing Techniques", J. of
the Society of Naval Architects of
Japan, Vol.162, pp.8189 (1987) (in
Japanese).
2. Kobayashi,K., Saga,T., Segawa,S. and
Tohnosu,S., "An Image Processing
Technique for Determining TwoDimen
sional Flow Fields with Reverse
Flow", J. of the Flow Visualization
Society of Japan, Vol.5, No.17, pp.
5764 (1985) (in Japanese).
3. Doi,J. and Miyake,T., "ThreeDimen
sional Flow Measurement by Shape
Reconstruction from Multiple Video
Images", J. of the Flow Visualiza
tion Society of Japan, Vol.7, No.24,
pp.4652 (1987) (in Japanese).
4. Sata,Y.,Nishino,K. and Kasagi,N., "A
New Algorithm of ThreeDimensional
Particle Tracking For Whole Field
Velocimeter", J. of the Flow Visua
lization Society of Japan, Vol.9,
No.34, pp.237240 (1 989) (in
Japanese).
5. Ishikawa,H., "Calculation of Three
Dimensional Wind Flows by Varia
tional Method (WIND04)", JAERIM 83
113 (1983) (in Japanese).
490
OCR for page 481
DISCUSSION
by T. Suzuki
This question is about the measurement
principle, Fig.2. The laser sheet in Fig.2
shows us a cross section, xy plane, of the
hydrogen bubble sheet, so that you can get the
velocity components u and v independently on w
in this paper.
However, the hydrogen bubble sheets are
inclining their vertical plane, even if the
platinum wire is kept vertically, after the
sheet streams down along the streamlines near
the ship stern (see Fig.Al). In this case,
one of the particles in the sheet should go
upward (or downward) along the sheet and
additional horizontal movement should occur.
I think that this movement is not caught in
this paper and it gives the error of v
components.
Could you give me comments on this error
and how it effects the w component?
Author's Reply
Thank you for your instructive discussion.
It is a crucial point of our method. As you
pointed out, if the hydrogen bubble segment
have an inclination, there may be an error by
By/ At in the ucomponent. This error can be
minimized by keeping the bubble segment as
vertical as possible.
In the present measurement, the platinum
wire was moved parallelly to the main flow
direction by every 50 mm step. In this case
the maximum angle of inclination can be
estimated about 9 degrees at most, then the
maximum error in the ucomponent is about 2%
under the assumption that w is 0.lu.
Because the present study is still at the
beginning, we didn't take this error so
serious, but it can be corrected iteratively.
hydrogen bubble cheat
z
tin
A]
\
an,
t=At/
y
~1
yz plane
Fig.Al
491
, additional
 movement
Ay=w At · tans
OCR for page 481