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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 3-dimensional flows where the image processing method and numerical computational method are complementari- ly used; the 3-dimensional 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 time-consuming 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 2-dimensional flows but some are intended to be 3- dimensional flows where the tracers are tracked 3-dimensionally 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 N-S equations are remarkable. However, there are still limitations in the hardwares of computers to have reliable results even by modern computers of high-speed 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 3-dimensional 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 "Three-dimensional 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 higher-version of softwares.

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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 He-Ne 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 . : 3-Dimensional : . 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 ladder-like 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 He-Ne 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

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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 8-bit 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 Ai-Bi. 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 a-a" and a-a"' and within a given distance. At the next time step t3, A3 is identi- fied. Thus all the images are identi- fied as B1-B2-B3, C1-C2-C3, 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

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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 y-components 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

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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 pin-hole 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 3-dimen- 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)

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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 3-dimensional flow In order to confirm the present scheme to reproduce the 3-dimensional 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 for-lows; The Poisson equation (12) is solved by S.O.R., where 1.4 is used as the relaxation factor.

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. 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 3-dimensional 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 y-z plane velocity vector is shown in Fig.9 together with the results calculated analytically. It is seen that the third z-component 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 x-y 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

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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 non-uniformity 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

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5.3 Results of 3-dimensional flow cal- culations For the calculations to reproduce the 3-dimensional flows, 22 plane flows are presumed by the B-spline 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 (x-y plane, z=O.O ); ax/az = 0 ~ = 0 z =0 (13) The 3-dimensional velocity vectors at the section of A.P. is shown in Fig.14 compared with those measured by a 5-hole 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 3-dimensional 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 3-dimensional velocity vectors et the A.P. section

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6. Conclusion In the present paper, a new method to measure the 3-dimensional 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) 3-dimensional 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 Grant-in-Aid 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.81-89 (1987) (in Japanese). 2. Kobayashi,K., Saga,T., Segawa,S. and Tohnosu,S., "An Image Processing Technique for Determining Two-Dimen- sional Flow Fields with Reverse Flow", J. of the Flow Visualization Society of Japan, Vol.5, No.17, pp. 57-64 (1985) (in Japanese). 3. Doi,J. and Miyake,T., "Three-Dimen- sional Flow Measurement by Shape Reconstruction from Multiple Video Images", J. of the Flow Visualiza- tion Society of Japan, Vol.7, No.24, pp.46-52 (1987) (in Japanese). 4. Sata,Y.,Nishino,K. and Kasagi,N., "A New Algorithm of Three-Dimensional Particle Tracking For Whole Field Velocimeter", J. of the Flow Visua- lization Society of Japan, Vol.9, No.34, pp.237-240 (1 989) (in Japanese). 5. Ishikawa,H., "Calculation of Three- Dimensional Wind Flows by Varia- tional Method (WIND04)", JAERI-M 83- 113 (1983) (in Japanese). 490

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DISCUSSION by T. Suzuki This question is about the measurement principle, Fig.2. The laser sheet in Fig.2 shows us a cross section, x-y 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 u-component. 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 u-component 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 y-z plane Fig.Al 491 , additional -- movement Ay=w At · tans

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