SMART IMAGE PROCESSING OF FLOW VISUALIZATION

Transcription

1 SMAR IMAGE PROCESSING OF FLOW VISUALIZAION H Li (A Rinoshika) 1, M akei, M Nakano 1, Y Saito 3 an K Horii 4 1 Department of Mechanical Systems Engineering, Yamagata University, Yamagata , JAPAN Department of Mechanical Engineering, Nihon University, okyo , JAPAN 3 Department of Electrical & Electonic Engineering, Hosei University, okyo , JAPAN 4 Shirayuri College, okyo , JAPAN ABSRAC he purpose of this stuy is to evelop an application of the smart visualize image processing to turbulent flow images an PIV (Particle Image Velocimetry) technique in orer to improve the temporal resolution of images Flow images consist of a set of sequentially iscretize images in time omain he smart visualize image processing can convert the iscretize images into continuous images base on Helmholtz equation In this paper the turbulent wake images an stanar PIV images were use to evaluate the smart visualize information processing Images of a turbulent wake with higher temporal resolution were generate, which were use to analyze the mechanism of wake flow he PIV results obtaine from the generate PIV images agree with the accurate solution One can say that the smart visualize image processing technique is effective in both flow image analysis an PIV system INRODUCION he flow visualization technique, such as image processing [1] an Particle Image Velocimetry (PIV) [], can provie qualitative an quantitative information on flow fiel It has the unique ability to capture instantaneous full-fiel flow an thus to allow the etection of spatial structures in unsteay flows In general, the flow visualization technique flow is ivie into two processes: image recoring an analysis he recore images consist of a set of sequentially iscretize images in time omain, an the evaluation of a flow visualization technique is often characterize by its temporal an spatial resolutions of images Much progress in harware has been mae for improving the spatial an temporal resolutions, however, the temporal resolution is still a problem to be solve since the recoring spee of CCD cameras is limite herefore it is important to evelop software for increasing the temporal resolution of image Recently, Saito [3] evelope a new visualization technique, calle the smart visualize information processing his technique can convert the iscretize images into continuous images by using Helmholtz equation, an has been prove to be effective when it is use in image processing However, few investigations are focuse on its application to the visualization of turbulent flow an PIV analysis he purpose of this paper is first applie the smart visualize information processing to turbulent flow images an PIV image for improving its temporal resolution an generating animation images hen the generate images with the higher temporal resolution are use to visualize turbulent structure an obtain PIV results SMAR VISUALIZED INFORMAION PROCESSING Any image with arbitrary resolution can be generate by solving the following image governing (Helmholtz) equation: V + ε V = ρ t where V, ε an σ are the image scalar potential to be evaluate, meium parameter an image source ensity, respectively In orer to generate the image with any resolution from Eq(1), a finite ifference metho is use he iscrete form of Helmholtz equation can be written as: C V t + D Vt = F () Further, Equation () may be rewritten in the stanar form V = C DV + C F or V = AV + F' Let X 1,X,,X n respectively be the n-th orer characteristic vectors of the characteristic values λ 1, λ,, λ n in the matrix A, then we have [ X X ] Z = 1 X n (4) Z is calle the moal matrix It is well known that any solution vector V of a physical system may be obtaine as linear combinations of the characteristic vector Z: V = ZY (5) Accoring to the linear transformation, Equation (3) can be transforme into the following form or (1) (3) Y = ( Z AZ) Y + Z F (6a) Y = Λ Y + Z F (6b) Physical where Z AZ=Λ physical he formal solution of moal Eq(6) is given by Y = Λ = Y Final ΛPhysicalt ( Y Λ Z F) ΛPhysicalt 1 PhysicalZ F + e Physical + e ( Y Y ) Start Final If U t represents an image between the images U Start an U Final in image system, Equation (7) can be expresse as (7)

2 [ U ] Λt Ut = UFinal + e Start UFinal (8) where If Λ = Λ physical, the state transition matrix A of physical system can be represente in terms of the moal matrix Z: A = ZΛZ (9) where λ1 Λ = λ λ n (1) (a) t = ms herefore any image U i+1 between the images U i an U i+ can be generate by using [ U U ] Λ t Ui+ 1 = Ui+ + ε i i+ (11) he image state transition matrix Λ is obtaine by: 1 Ui+ 1 Ui+ Λ = ln t Ui Ui+ (1) APPLICAION O URBULEN WAKE IMAGES he experiment was carrie out in a water tunnel with a square working section (15m x 15m) of 5 m long wo sie-by-sie acrylic circular cyliners with an ientical iameter of 1 mm were horizontally mounte A wake flow was generate at a Reynols number of 75 A thin laser sheet, which was generate by Argon Ion laser source, provie illumination vertically, an the images were recore with a igital vieo camera with a frame rate of 4 frames/s Figure 1 shows three successive original images of wake flow he flow pattern immeiately behin the cyliners is symmetrical about the flow centerline wo consecutive rolling-up vortices of opposite sign appear on each sie of the wake In orer to improve the temporal resolution of the image an to analyze the wake flow structure, the wake images are analyze by the smart visualize information processing First, the image state transition matrix Λ is etermine base on the three successive images of Fig1 by using Eq (1) hen the solution (8) of image Helmholtz equation (1) can generate any image between the starting (Fig1 (a)) an final (Fig1(c)) images he images generate between the first image (Fig1a) an the secon one (Fig1b) are shown in Fig hese successive images exhibit the flow pattern an the evelopment of vortical structures can be instantaneously observe As shown in Fig, the formation an growth of rolling-up vortices at ifferent instants, marke by arrows, can be clearly visualize, which cannot be foun in original images From the above results, one is can say that the smart visualize image processing technique is effective in flow visualization Further investigation will focus on multi-resolution analysis of vortical structures (b) t = 4 ms (c) t = 84 ms Fig1 Original wake flow images (a) t = 4 ms

3 (b) t = 16 ms APPLICAION O PIV Particle Image Velocimetry (PIV) is a non-intrusive flow visualization technique an is now firmly establishe as a powerful flui ynamics tool to measure flow velocity in the area of flui mechanics Even more important than this remarkably improve performance of the PIV technique, is its unique ability to capture instantaneous full-fiel flow an thus to allow the etection of spatial structures in unsteay flows quantitatively, which is not possible with other experimental techniques Although a cross-correlation CCD array camera can recor pairs of images with a frequency of 1 Hz, it is important to evelop software to improve the temporal resolution Comprehensive reviews on the principles, the historical evelopment an application of PIV were given by Arian (1991) [], an the etails will not be repeate here For typical metho of PIV, instantaneous planar velocity vector is usually etermine by crosscorrelating the interrogation winows (or small image masks) in two successive PIV images separate by a known time interval In typical approaches, the image ata from a winow taken in the first image an that from a winow at the same position in the secon image are cross-correlate he iscrete cross correlation coefficient is efine as (c) t = 1 ms R ( m, n) = f + i j f i j ( i, j) g( i + m, j n) ( i, j) g ( i, j) i j (13) () t = 94 ms (e) t = 378 ms Fig Generate wake images where f ( i, j) an ( i, j) of the interrogation winows at pixel locations (, j) g represent the pixel intensities i in the first an secon images, respectively he function R ( m,n) measures the correlation of the iscrete i, j g i, j when they are relatively functions f ( ) an ( ) shifte by (,n) m pixels he location of the maximum cross-correlation peak gives the mean isplacement of the particles in the interrogation winow within a known time interval he instantaneous velocity vector at location ( i, j) is calculate from this mean isplacement In orer to evaluate the smart visualize information processing, the stanar PIV images of a steay two-imensional wall shear flow, which were evelope by the Visualization Society of Japan, are use in this stuy Figure 3 shows three successive PIV stanar images (56x56 pixels with an 8bit grayscale) with the time interval t = 33s he number of particles is 4 he average particle iameter an stanar eviation are 5 an 14 pixels, respectively he average image velocity is 74 pixels/interval an the maximum image velocity is 15 pixels/interval he average an maximum out-of-plane velocities are respectively 17 an 1 intervals -1 Figure 4 shows the accurate velocity fiel by analyzing two successive stanar PIV images (Fig3 (a) an (b)) using PIV technique

4 (a) t = ms (a) t = 33 ms (a) t = 33 ms (b) t = 66 ms (a) t = 66 ms Fig3 Original stanar PIV images (c) t = 99 ms Fig4 Accurate velocity fiel of PIV stanar images () t = 13 ms

5 (e) t = 165 ms (f) t = 198 ms Fig6 Reconstructe velocity fiel base on generate PIV stanar images In this stuy three successive PIV stanar images (Fig3) are analyze by the smart visualize image processing Figure 5 shows the generate PIV images between the first an secon PIV stanar images hese successive images exhibit clearly the particle flow patterns or streamlines, which cannot be foun in original images of Fig3 he velocity vector fiel that is obtaine from the generate two images of Fig5 (b) an (h) using cross-correlation PIV metho (Eq13) is shown in Fig6 It is evient that the PIV result of generate images agrees with the accurate solution in Fig5 his result verifies that the smart visualize image processing technique can generate the higher temporal resolution of PIV images an is effective in PIV system CONCLUSIONS Although preliminary, this paper emonstrates that the smart visualize image processing is very effective when applie to the flow image processing an PIV technique for generating the higher temporal resolution of images Further investigation will focus on the etail analysis of turbulent structures an evaluating measurements of instantaneous velocity an turbulent statistics in the complex turbulent flows (g) t = 31 ms (h) t = 64 ms Fig5 Generate stanar PIV images ACKNOWLEDGMENS he first author wishes to acknowlege support given to him by Grant-in-Ai for Scientific Research (C) (No ) from Japanese Society for the Promotion of Science REFERENCES 1 H LI, M akei, M Ochi, Y Saito an K Horii, Application of wo-imensional Orthogonal Wavelets to Multiresolution Image Analysis of a urbulent Jet, ransactions of the Japan Society for Aeronautical an Space Sciences 4, 1-17 (1999) R J Arian, Particle-imaging echniques for Experimental Flui Mechanics, Ann Rev Flui Mech 3, (1991) 3 Y Saito, Smart Visualize Information Processing- Key Iea, ool an Application, Proceeings of the 3r Pacific Symposium on Flow Visualization an Image Processing NoF3398, 1-8 (1)