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WO2004005941A1 - Procede de correlation d'un ensemble a deux points pour des applications de dynamique des fluides - Google Patents

Procede de correlation d'un ensemble a deux points pour des applications de dynamique des fluides Download PDF

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Publication number
WO2004005941A1
WO2004005941A1 PCT/NL2003/000498 NL0300498W WO2004005941A1 WO 2004005941 A1 WO2004005941 A1 WO 2004005941A1 NL 0300498 W NL0300498 W NL 0300498W WO 2004005941 A1 WO2004005941 A1 WO 2004005941A1
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image
correlation
flow
pixel
ensemble
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Jerry Westerweel
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Stichting voor de Technische Wetenschappen STW
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P5/00—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft
    • G01P5/001—Full-field flow measurement, e.g. determining flow velocity and direction in a whole region at the same time, flow visualisation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P5/00—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft
    • G01P5/18—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft by measuring the time taken to traverse a fixed distance
    • G01P5/22—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft by measuring the time taken to traverse a fixed distance using auto-correlation or cross-correlation detection means

Definitions

  • the invention relates to a method for measuring velocity of a plurality of particles in a streaming fluid, comprising: registering at least one image pair successively in time; estimating a two-point correlation for the at least one image pair; deriving from the estimated two-point correlation the velocity of the plurality of particles in the plane of the at least one image pair.
  • the invention further relates to a particle image velocimetry apparatus and the use thereof.
  • PIV particle image velocimetry
  • ⁇ PIV particle image velocimetry
  • the velocity of a streaming fluid is measured indirectly by imaging particles suspended in the fluid.
  • This implementation of PIV has several characteristics that make it different from conventional PIV. For one, the measurement domain in the direction perpendicular the light-sheet plane is limited by the finite depth-of-focus of the imaging optics, as opposed to conventional PIV where it is limited by the finite thickness of the light sheet. Also, for very small tracer particles that are observed at high magnification, the motion of the tracer particles is influenced by the effect of Brownian motion, hi addition, the image density in ⁇ PIV is generally much lower than in conventional PIV.
  • the invention relates to a method as specified in the preamble characterised in that - a plurality of N image pairs is registered successively within a predetermined time period, in which predetermined time period the flow in the streaming fluid is substantially constant; and the two-point correlation is estimated for each image pixel based on all image pairs of the plurality of N image pairs.
  • the ensemble averaging is taken one step further by using an extended ensemble, and applying it to compute the two-point ensemble correlation.
  • the two-point correlation is the theoretical backbone of the PIV method (WESTERWEEL, J. (1993) Particle Image Velocimetry - Theory and Application. Delft University Press (Delft)), but it can not be utilized as the flows under study in conventional PIV are generally not stationary.
  • the two- point correlation is estimated from a spatial correlation over a finite interrogation domain under the assumption that the flow within the interrogation domain is uniform. This also limits the maximal spatial velocity gradient that can be measured reliably.
  • the flow under study is (nearly) stationary, it is possible to record a very large ensemble of image pairs. In that case it would not be necessary to compute a spatial • correlation as an estimate of the two-point correlation, but directly compute the two- point ensemble correlation. For example, instead of computing the spatial correlation over a 32x32-pixel domain, the correlation between two pixels is computed over an ensemble of 1,024 image pairs.
  • figure la shows a spatial correlation in conventional PIV over an NxN-pixel interrogation domain that is computed for a single image pair (top);
  • figure lb shows the ensemble correlation computed over 1 -pixel domains averaged over multiple image pairs (bottom);
  • figure 2a and 2b show examples of a pair of 64x64-pixel synthetic PIV images for the flow near a stagnation point, where the image contains about 80 particle images;
  • figure 2c shows the vector plot of the standard PIV result using 32x32-pixel interrogation windows with 4-pixel spacing (viz., 87.5% overlap), where the dotted line represents the position of the wall, and the circles indicate vectors at 16-pixel spacing;
  • figure 3a, 3b, 3c, 3d, 3e and 3f show a result for the stagnation flow as a function of the number of frames used for the two-point ensemble correlation
  • figure 4 shows the fraction of valid vectors as a function of the number of frames
  • figure 5 a, 5b and 5 c show the measured horizontal displacement (in px) as a function horizontal position (hi px) for the two-point ensemble correlation with 128, 1024 and 8192 frames respectively, where the diagonal lines indicate the reliability level for the measured displacement;
  • figure 6 shows the results for an infinitely thin shear layer: two-point ensemble correlation (fig. 6a), spatial correlation using 32x32-pixel interrogation windows with 4-pixel spacing (fig. 6b), and the profile of the displacement as a function (fig. 6c, O two-point ensemble correlation; • spatial correlation);
  • figure 7a, 7b and 7c show the results for a boundary laminar layer: two-point ensemble correlation (fig. 7a), spatial correlation using 32x32-pixel interrogation windows with 4-pixel spacing (fig. 7b), and the profile of the wall-parallel displacement component as a function of the distance from the wall (fig. 7c, O two-point ensemble correlation; • spatial correlation; — analytical profile);
  • figure 8a and 8b show the results for the flow around a circular cylinder: spatial correlation using 32x32-pixel interrogation windows with 4-pixel spacing (fig. 8a), and two-point ensemble correlation over 1024 frames (fig. 8b) and
  • figure 9 shows a preferred embodiment of a particle image velocimetry apparatus.
  • C is the number density of the tracer particles, ⁇ z 0 the light-sheet thickness, 0 the image magnification, Eo( ⁇ z) the loss-of-correlation due to an out-of-plane displacement z (i.e., the fraction of particles that enter of leave the light sheet during the exposure time delay), F ⁇ s) the particle-image self-correlation, and S D the in-plane particle-image displacement.
  • Eo( ⁇ z) the loss-of-correlation due to an out-of-plane displacement z (i.e., the fraction of particles that enter of leave the light sheet during the exposure time delay)
  • F ⁇ s the particle-image self-correlation
  • S D the in-plane particle-image displacement.
  • N 7 is the number of particle-image pairs in the interrogation domain, or image density
  • A is the characteristic area of the interrogation domain W
  • Fj(s) is the in- plane loss-of-correlation.
  • the bias due to Fj(s) is a known function for a given interrogation domain W.
  • the spatial correlation is a reliable estimate for the ensemble correlation provided that the image field is a homogeneous random field (ROSE ⁇ FELD, A. & KAK, A.C. (1982) Digital Picture Processing (2nd Ed.) Academic, Orlando; KEA ⁇ E, R.D. & ADRIAN, RJ. (1992) 'Theory of cross-correlation analysis of PIV images.' Appl. Sci. Res. A9, 191-215).
  • the principle of interrogation of a single image pair using a spatial-average estimate for the correlation is illustrated in Figure 1.
  • a contemporary PIV system consists of a digital camera with a typical resolution of 1024x1024 pixels, which can record image pairs at a rate of 15 Hz.
  • the success rate for measuring the correct displacement is at least 95%.
  • the measurement precision for the displacement is better than 0.1 px (WiLLERT, C.E. (1996) 'The fully digital evaluation of photographic PIV recordings.' Appl. Sci. Res. 56, 79; WESTERWEEL, J. (2000) 'Theoretical analysis of the measurement precision in particle image velocimetry.' Exp. Fluids 29 (Suppl.), 3-12).
  • the consequence of using a spatial-average estimator for the two-point ensemble correlation is that a camera image that contains more than a million pixels yields (typically) on the order of 10 4 measurements.
  • the image density Nj is generally very low (Ni ⁇ 1), so that it is not possible to obtain reliable estimates of the two-point correlation by means of computing the spatial correlation between two consecutive image pairs.
  • the common procedure to enhance the quality of the spatial-average estimator is to average the spatial correlation of corresponding interrogation domains in successive image pairs. This procedure is generally referred to as ensemble correlation (Dehioij et al. 1999, Meinhart et al. 2000), although in view of the present paper we would prefer to call it: ensemble averaging of the spatial correlation estimate.
  • the effective image density is improved in proportion to the number of image pairs used for the averaging of the spatial-correlation estimate.
  • the amplitude of the displacement-correlation peak is directly proportional to the image density, so that averaging over Np image pairs would yield a displacement-correlation peak with an amplitude Np-Ni.
  • Nj 1
  • N / 20
  • the correlation noise i?'(s) i.e. random correlation peaks defined by: R'(s) s R(s) - (R(s)
  • the flow velocity of the streaming fluid must be substantially constant during the time period in which the N image pairs are captured. No restriction is necessary with regard to the spatial variation of the flow velocity.
  • the tracer particles are fluorescent, and a filter is used to record only the fluorescent light emitted by the tracer particles.
  • the amount of light emitted by the tracer particles would be proportional to the particle surface area or particle volume.
  • the tracer particles are very small (typically 200-300 nm), so that all particle images are diffraction limited, and therefore all particle images have the same diameter.
  • the two-point ensemble correlation was implemented in a Matlab program (version 5.3), running on a PC with a AMD Athlon 900 MHz CPU under Linux (RedHat version 7.2).
  • the time for processing a 1,024-image ensemble is 186 s for computing the two- point ensemble correlation for all 64x64 pixels.
  • the computation of two 32x32-pixel FFTs replicated 61x61 times under Matlab takes 4.1 seconds. (For comparison, our own standard PIV code uses 3.8 s for the processing of a single lkxlk image pair in 61x61 positions using 32x32-pixel interrogation regions.)
  • This velocity biasing is a direct consequence of using the spatial correlation estimator (Adrian 1988; Westerweel 1993), and is absent in the two-point correlation result.
  • the gradient of the result for the two-point ensemble correlation is only about 2 px, whereas the particle-image diameter in the synthetic ⁇ PIV images is 4 px.
  • Our final flow type is the flow around a circular cylinder.
  • This flow type combines aspects of the three earlier flow types, and would be representative of the flow around an object, e.g. a bubble or a blood cell.
  • a 1,024-image ensemble was generated.
  • the results for the two-point ensemble correlation and the standard PIV are shown in Figure 8.
  • the 1 -pixel resolution of the two-point ensemble correlation makes it possible to resolve the detailed flow pattern at any point around the cylinder, whereas the standard-PIV result only represent a rough picture of the flow and has difficulties in resolving the flow near the cylinder wall. Especially the near-wall flow and the front and back stagnation points are not resolved be the spatial correlation.
  • the typical resolution for these high speed cameras is 256x256 pixels; a reduction of the spatial resolution is necessary in order to reach such high framing rates.
  • the ensemble correlation proposed here would enable us to extract a displacement vector for each pixel, so that the number of velocity measurements would also be 256x256, which is still higher than the data resolution for conventional PIV and that would enable us to capture the very steep velocity gradients in near-wall regions (e.g., for the measurement of wall shear stress).
  • This new approach would also create new options for the future. For example, a further reduction of the CCD format, e.g. from 256x256 to 64x64 pixels would make it possible to capture images at a framing rate of 160 kHz (while maintaining the same signal bandwidth). Hence, a set of 1,000 images can be captured in less than 10 milliseconds, and flows with a typical time scale of around 0.01 s could be captured.
  • the particle image velocimetry apparatus 1 comprises processing means 11 and imaging means 12, where the imaging means 12 are arranged to communicate with the processing means 11.
  • the imaging means 12 are arranged to register a plurality of images and to send information about the registered images to the processing means 11.
  • the images can be images of particles in a streaming fluid, such as a channel 1.
  • the processing means 11 are arranged for executing the method as described above.
  • the imaging means 12 can for instance be a sensor array, such as a CCD imaging device or any other known camera known to a person skilled in the art. Such imaging means 12 can for instance be arranged to produce a 64x64 pixel image.
  • the particle image velocimetry apparatus 10 can also comprise integrated optics for maximizing optical performance of the imaging means 12.
  • the imaging means can be also be arranged to register images with a predetermined focus range.
  • the invention makes it possible to produce relatively small PIV- and ⁇ PIV-systems. It will be understood by a person skilled in the art that such small PIV- and ⁇ PIV-systems can, for instance, be used for biological and/or medical applications. Small probes, using e.g. a 0,5x0,5mm CCD array with integrated optics, can be created that can easily, for instance, be placed on the body of an animal, such as a human animal or be inserted in a blood vessel or artery of such an animal, to measure a blood flow.
  • the PIV method has been applied with much success to various fluid mechanical experiments. In a examplary embodiment of the present invention this method is adapted to the measurement of flow phenomena in a compliant biological system that take place on the micrometer scale.
  • the adaptation to microscopic scales involves changes in the optical set-up of the ⁇ PIV-system.
  • the principal limitations are related to fundamental aspects of diffraction limited optics, such as the illumination with a very thin light sheet and the image formation of a very small tracer particle.
  • d f is the diameter of the diffraction spot
  • M magnification
  • f # the numerical aperture
  • ⁇ the wave length of the light
  • f* 1-2.
  • M the diffraction limited spot becomes 28-55 ⁇ m in the image plane and this corresponds to a spatial resolution of 1.4 to 2.3 ⁇ m in the measurement plane and this is sufficient for our purpose. It should be stressed that this is a theoretical upper limit to the spatial resolution and that the real resolution depends on the method of velocity reconstruction as discussed above.
  • the second limitation of known PIV systems in microscopic flows is the thickness of the laser light sheet.
  • standard PIV all particles in the light sheet are illuminated and recorded because all of the illuminated particles are within the focal depth of the imaging optics. In our case we will use microscopes and these have a typical optical depth of a few ⁇ m.
  • Nd:YAG laser in low power configuration for a uniform spatial illumination in backward scattering mode.
  • the use of the Nd:YAG laser is of advantage since the PlV-cameras have to be illuminated with pulsed light. Because the object domain is defined by the focal depth of the optics one will also record out-of- focus particle images. With the proper image processing one can eliminate the influence of these smeared out-of-focus particle images on the measurement.
  • the next problem to be considered is whether particles need to be added to the flow in order for the PIV technique to work.
  • particles need to be added to the flow in order for the PIV technique to work.
  • the blood vessels are transparent for visible light. Therefore we will start with the particles that are already present in the bio fluid. These are for instance the red blood cells, which have a size of 7.5+0.3 ⁇ m. 1
  • the lighting set-up with the Nd:YAG laser may cause too many reflections. In that case we can not work with light scattered from native blood cells.
  • the alternative is to use small fluorescent particles, with a size of about 0.2 ⁇ m, in combination with optical filters.
  • the Nd:YAG laser in combination with a sensitive camera should be sufficient to observe these particles despite their small scattering cross section.
  • dyes, carbon particles and 20-30 nm colloidal gold particles in biological experiments shows that such small particles do not interfere with normal development or function of the organism for at least 20 hours.
  • the invention can also be used to create relatively light PIV- and ⁇ PTV-systems that can cost-effectively be used in space applications, such as scientific experiments in a space station under microgravity.

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  • Engineering & Computer Science (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
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Abstract

La présente invention concerne un procédé de mesure de la vitesse d'une pluralité de particules se trouvant dans un fluide en circulation. Le procédé consiste: à enregistrer au moins une paire d'images de manière successive dans le temps; à estimer une corrélation à deux points pour la ou les paires d'images; à donner, à partir de la corrélation à deux points estimée, la vitesse des multiples particules dans le plan de ladite paire d'images. De surcroît, une pluralité de N paires d'images est enregistrée successivement dans une période de temps prédéterminée pendant laquelle l'écoulement du fluide en circulation est sensiblement constant; et la corrélation à deux points est estimée pour chaque pixel d'image sur la base de toutes les paires d'images faisant partie de la pluralité de N paires d'images.
PCT/NL2003/000498 2002-07-05 2003-07-04 Procede de correlation d'un ensemble a deux points pour des applications de dynamique des fluides Ceased WO2004005941A1 (fr)

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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2011138766A1 (fr) * 2010-05-07 2011-11-10 Telops Inc. Système et procédé permettant de mesurer à distance la carte de vitesse directionnelle d'émissions gazeuses
CN102331510A (zh) * 2011-06-09 2012-01-25 华南理工大学 纸浆两相流piv测量的图像处理方法
DE102010038177B3 (de) * 2010-10-14 2012-04-19 Deutsches Zentrum für Luft- und Raumfahrt e.V. Erfassen eines die Bilder von Punktemustern beeinflussenden Zustands eines Objekts
EP2687829A4 (fr) * 2011-03-15 2014-09-17 Toyota Motor Co Ltd Dispositif de mesure de débit
JP2016099195A (ja) * 2014-11-20 2016-05-30 株式会社ジェイテクト 粒子画像流速測定方法および粒子画像流速測定装置
CN111693729A (zh) * 2020-06-28 2020-09-22 中国科学院力学研究所 基于全局优化的粒子图像测速方法及装置
CN112629679A (zh) * 2020-12-02 2021-04-09 中国人民解放军国防科技大学 一种适应于背景纹影的高精度测量方法、电子设备及介质
CN116012254A (zh) * 2023-02-08 2023-04-25 西北工业大学 一种从两点相关函数实体化预测材料微观组织的方法和系统

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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2011138766A1 (fr) * 2010-05-07 2011-11-10 Telops Inc. Système et procédé permettant de mesurer à distance la carte de vitesse directionnelle d'émissions gazeuses
DE102010038177B3 (de) * 2010-10-14 2012-04-19 Deutsches Zentrum für Luft- und Raumfahrt e.V. Erfassen eines die Bilder von Punktemustern beeinflussenden Zustands eines Objekts
EP2687829A4 (fr) * 2011-03-15 2014-09-17 Toyota Motor Co Ltd Dispositif de mesure de débit
CN102331510A (zh) * 2011-06-09 2012-01-25 华南理工大学 纸浆两相流piv测量的图像处理方法
JP2016099195A (ja) * 2014-11-20 2016-05-30 株式会社ジェイテクト 粒子画像流速測定方法および粒子画像流速測定装置
CN111693729A (zh) * 2020-06-28 2020-09-22 中国科学院力学研究所 基于全局优化的粒子图像测速方法及装置
CN112629679A (zh) * 2020-12-02 2021-04-09 中国人民解放军国防科技大学 一种适应于背景纹影的高精度测量方法、电子设备及介质
CN116012254A (zh) * 2023-02-08 2023-04-25 西北工业大学 一种从两点相关函数实体化预测材料微观组织的方法和系统

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