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Twenty-Second Symposium on Naval Hydrodynamics Development of an Alternating Color Image Anemometry Method and Its Application in Ship Flow Measurements S.-Y.Jaw, Y.-Z.Kehr (National Taiwan Ocean University, Taiwan, China) ABSTRACT In this study, the alternating color image anemometry (ACIA) method is proposed. Alternating color, multi-exposure particle image was recorded by a three-chip color CCD camera. Knowing that the red, blue, and green CCD chip of a 3-CCD camera has different sensitivity to the color of scattering light, the alternating color, multi-exposure particle image can be separated into sequential images by performing appropriate band processes. With sequential images available, the magnitude and direction of the velocity vectors can be determined from the digital correlation method. The ACIA method thus preserves the merits of both PIV and DPIV methods by analyzing a multi-exposure particle image using the digital correlation method of sequential images. The proposed ACIA method was first calibrated by measuring a constant speed rotating disk and an empty channel flow, and then applied to measure the turbulent wake behind a flat plate and a ship hull. Satisfactory results were obtained. I. INTRODUCTION In studying fluid mechanics, flow visualization is a useful technique to observe flow patterns. The classical methods of flow visualization, using dye tracers, hydrogen bubble, or smoke, provide valuable information about the behavior of the whole flow field. However, these methods can only provide qualitative, but not quantitative, velocity distribution. Recent advancement in optics, electronics and imaging techniques allow one to capture the instantaneous Eulerian velocity images for a flow field and thus make quantitative flow visualization possible. The quantitative flow visualization methods have attracted many investigations because of its characteristics that fluid motion was measured frame by frame. This is convenient as compared with traditional point-by-point measurement such as using hot-wire, or Laser Doppler anemometry, especially when the measurement of an unsteady flow field is required. As the velocity distribution is available, one may further take advantage of the digital data processing techniques to derive additional information, such as Reynolds stresses, streamlines, or vorticity distributions, etc.. Overview of quantitative flow visualization methods can be found from several literatures (Hesselink 1988, Adrian 1991, etc.). Recent development of quantitative flow visualization methods is briefly summarized in the following. Their advantages, and also limitations, are clearly explained. 1. Particle Streak Velocimetry (PSV) Method: Among the quantitative flow imaging techniques, the particle streak velocimetry method has been the most popular one since the PSV method is conceptually simple. In the PSV method, the light scattered from the particles that were seeded in the moving fluid was imaged by the recording medium such as film or CCD (Charge Coupled Device). The recorded image was streaks tracing the motion of the particle during the exposure time. By measuring the distance between the end points of the streak and knowing the exposure time, the velocity vectors are obtained at a discrete number of points. The directional ambiguity can be resolved by coding the image of the streaks asymmetrically with a light chopper (Khalighi 1989, Walter and Chen 1989) or using the color coding technique (Wung 1992). The advantage of the PSV method is that it is relatively simple. The drawback of the method is that the flow image is difficult to analyze when particles were densely seeded because the streaks thus obtained may overlap during the exposure time. In addition, the PSV method is inappropriate to measure highly transient or fluctuating flows since the finite streak length required to measure the velocity may not be available in the highly transient flows. 2. Particle Image Velocimetry (PIV) or Laser Speckle Velocimetry (LSV) Method: Unlike the PSV method, the particle image velocimetry method or the laser speckle velocimetry method analyzes the multiple exposure image recorded on a single frame by the Young’s fringe principle. Recently, the PIV method is given a broader definition to include the LSV method. The PIV method, which allows much denser seeding particles, was devised to overcome the limitations of
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Twenty-Second Symposium on Naval Hydrodynamics seeding concentration in the PSV method. In the PIV method, particles moving within the light sheet may be recorded photographically as pairs of particle image. The local fluid velocity was determined statistically from a small interrogating window on the developed photograph by sequentially measuring the displacement of the particle images within each window. The particle displacement within an interrogating window can be found by a variety of methods such as the Young’s fringe method (Meynart 1980 & 1982, Reynolds, et. al. 1985) or the 2-D auto-correlation analysis (He et. al. 1984, Vogel and Lauterborn 1988). One of the difficulties in implementing the PIV method is that there exists no characteristic to distinguish first image from second image on the double-exposure PIV photograph. As a result, measurement of the particle image displacement can not determine the direction of the fluid velocity, and the velocity was ambiguous in direction. To resolve the directional ambiguity, imaging shift (Adrian 1986 & 1988), and thus an introduced velocity, of a certain amount can be applied during the time interval between successive exposures. Subtracting the introduced velocity from the measured fluid velocity, flow direction can be determined from the sign, positive or negative, of the velocity vector. However, this technique tends to complicate the experimental setup and the subsequent analysis. In addition, the multi-exposure particle image should not overlap imposes restrictions on the spatial resolution and the dynamic range of the velocity measurement. 3. Digital Particle Image Velocimetry (DPIV) Method: In order to eliminate the limitations of the PIV method, another technique, called the digital particle image velocimetry method, was proposed in various manners since the late 1980s. Instead of taking multi-exposure images, the DPIV method analyzed a series of time sequential images captured either from a high-speed camera or from a video camera, with each frame containing a single-exposure image. The captured digital images were stored directly to computer memory through A/D converter without conventional picture taking and film development. The major advantage of DPIV method is that both the magnitude and direction of the velocity vector can be determined from the cross-correlation analysis as a series of single-exposure images were available (Willert and Gharib 1991). The cross correlation analysis of two sequential images is also better than the multi-exposure, auto-correlation analysis of the PIV method. The cross-correlation, i.e. the convolution of two sequential images, set restrictions on the particle paring from image one to two, which reduces the opportunity of miscalculating the magnitude and direction of particle displacement. A major disadvantage of the DPIV method is that the time interval between sequential images are limited by the frame speed, usually 30 frames per second, of the recording device. Since velocity is determined from dividing the particle moving displacement with the time interval of sequential images, the dynamic range of the velocity measurement is thus limited to tens of centimeter per second for typical applications. Higher speed recording device is available at the present time, which moderately increases the dynamic range of velocity measurement at the expense of high cost and sacrificing image resolution. Light chopper was also devised (Dabiri and Gharib 1996) to control the time interval between sequential images, which complicates the operation of image capturing, however. From the descriptions stated above, it is found that each flow visualization method has its advantages and also drawbacks. What’s interesting is that the advantages of one method happen to be the limitations of other methods. For instances, by analyzing multi-exposure particle image, the dynamic range of the velocity measurement of the PIV method is highly increased while the determination of flow direction is ambiguous and requires additional equipment such as the image shifting devices. The DPIV method determines the flow direction easily from a series of sequential images, allows denser seeding particles, but the dynamic range of velocity measurement is limited by the frame speed of the recording device. One way to preserve the advantages of both the PIV and DPIV methods is to analyze the flow field from a multi-exposure particle image using sequential image files. This is accomplished in the proposed alternating color image anemometry (ACIA) method by separating a multi-exposure particle image into sequential images of different color. II. THE PROPOSED ALTERNATING COLOR IMAGE ANEMOMETRY METHOD In the proposed ACIA method, the flow image was recorded by a three-chip, color CCD camera. The blue laser and green laser, deflected alternately from a 4 watt, Argon-Ion laser, were adopted as the light source. The laser beam was guided to a multi-facet, rotating mirror to generate alternating color, blue and green laser sheets. The particles seeded in the fluid was then illuminated by the two different, alternating color laser sheets. A single frame, even times exposure, alternating color particle image was then recorded by the red, blue, and green CCD-chip of a 3-CCD camera. Knowing that different color CCD chip has different sensitivity to the color of the incoming
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Twenty-Second Symposium on Naval Hydrodynamics light, the recorded multi-exposure, alternating color particle image can be separated into different color, sequential images by applying appropriate band process. For instance, if the seeding particles were illuminated by the blue laser, the particle image intensity recorded by the blue CCD-chip was much higher than those recorded by the red and green CCD chips, as shown in Fig. 1(a). Similarly, as the seeding particles were illuminated by the green laser, the image intensity recorded by the green CCD chip was much higher than those recorded by the red and blue CCD chips, as shown in Fig. 1(b). To separate the single frame, multi-exposure, alternating color particle image into two sequential images, certain particle image intensity must be specified as the threshold to distinguish signal from noise. If the image intensity is lower than the threshold, it is considered as noise and its value is reset to zero, otherwise it is considered as a signal and its value is reserved. Comparing the image intensity of every pixel in the blue and green images with the threshold respectively, two sequential particle image files, one illuminated by blue laser and the other illuminated by green laser, can be obtained. Figure 2(a) shows a four times exposure, alternating color particle image of a rotating disk. Figures 2 (b), (c) show the separated, blue and green laser exposure sequential images of Fig. 2(a). With two sequential images available, the flow direction and velocity magnitude can be determined by analyzing the flow image using the spatial cross-correlation method, as those adopted in the DPIV method. It should be emphasized that the time interval between the two separated sequential images is not limited by the frame speed of CCD camera but is determined from the frequency of the generated, alternating color laser sheet. Therefore the dynamic range of the velocity measurement of the ACIA method is much higher than that of the DPIV method. More importantly, each CCD chip of a 3-CCD camera has a resolution of 640*480 pixels, hence the image resolution of each color will not be deteriorated as the alternating color particle image were separated into sequential images of different color. Therefore, the ACIA method does not sacrifice the image resolution to increase the dynamic range of velocity measurement, which is generally the status as using a higher speed CCD camera in the DPIV method. The experimental setup of the proposed ACIA method is shown in Figure 3. The test section is where the fluid motion was visualized and studied. Guiding an all line Argon Ion laser through a PCAOM (Poly-Chromatic Acousto-Optic Modulator), the monochromatic blue or green laser will be deflected from the PCAOM. Pulsed laser sheet was generated by directing the laser beam to a multi-facets rotating mirror (Rockwell et al. 1993). A fiber optic was placed at the upstream of the laser sheet. If a laser beam is detected by the fiber optic, a voltage signal was sent to the driver of the PCAOM to alter the output wavelength of the monochromatic laser. An alternating color, pulsed laser sheet can thus be generated by such an optical system. The frequency of the generated alternating color laser sheet is equal to the product of the number of mirror facets and the angular velocity of the rotating mirror. For the present setup, a twenty-facet polygon mirror rotates 30 to 500 revolution per second is used. The frequency of the generated alternating color laser sheet thus varies from 30 Hz (one-facet mirror by 30 rev/s) to 10,000 Hz (twenty-facet mirror by 500 rev/s), and the corresponding dynamic range of velocity measurement varies from several centimeters per second to more than three-hundred-fold of it. III. Flow Image Analysis Since it is difficult to trace the movement of individual particle between two sequential images, the displacement of a group of particles within a sampled subregion is determined. To find the displacement function s(m,n) in a sampled subregion, one may utilize a statistical technique that applies a spatial correlation method. The method involves the computation of auto-correlation, of the spatial input signals, f(m,n), and the cross-correlation, of the spatial input and output signals, g(m,n). Because the input function f(m,n) correlates with itself in the maximum of the auto-correlation function is always located at the origin of the correlation domain. The origin thus is the initial position of all particles within the sampled subregion. Cross-correlation is obtained by performing a convolution on the auto-correlation function with the shift function s(m,n). This operation moves the peak of auto-correlation away from its origin by the average spatial displacement of particles in the sampled region, as shown in Fig. 4. Once the maximum value of within the sub-region is determined, one finds the shift function s(m,n) by measuring the distance between the origin and the location of the maximum value of . Knowing the time interval between two sequential images, the magnitude
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Twenty-Second Symposium on Naval Hydrodynamics of the velocity vectors at the sampled sub-region can then be determined by dividing the shifted distance with the given time interval. And clearly the flow direction is pointed from the first image to the second. Physically the cross-correlation function reveals the degree of matching among particles of initial and shifted images in the sampled subregion with a domain of m by n pixels. The location of the maximum of cross-correlation function represents the most probable displacement of the particles within the sampled area. To obtain the locally averaged displacement of particles, one may divide the digital image into hundreds, or thousands, of small interrogation windows. If the interrogation window is small enough, the averaged displacement of particles may be approximated as the most probable fluid movement at the corresponding area. To determine the full-field velocity distribution, these procedures are repeated on each interrogation window and over the entire flow image. If the highest peak of the cross correlation function is selected to determine the representative velocity of the interrogating window, the accuracy of the velocity vector is limited to the size of pixel. That is, the velocity measurements can have differences only as small as the physical dimension of a pixel. To overcome this limitation, one remedy is to construct the centroid of the cross-correlation function using a weighted interpolation scheme (Chen et al. 1992, Lourenco et al. 1995). The weighted interpolation is performed once the peak location of cross-correlation is found, using the cross-correlation values of its surrounding pixels, Here i and j is the indices of the correlation peak, X, Y represent the interpolated coordinates on the cross-correlation domain, and B(i,j)’s are the value of cross-correlation determined for the peak and its surrounding pixels. The size of the square region m was varied in proportion to the size of the interrogation spot for the resolution under consideration. Figure 5 illustrates the velocity measured before (pixel accuracy), and after (sub-pixel accuracy), the weighted interpolation. Although Lourenco et. al. (1995) pointed out from an analysis of a multi-exposure particle image using auto-correlation function that for small particle displacements, the determination of centroid will be contaminated by the auto-correlation peak at the origin and hence deteriorates the measurement accuracy. However, such a situation will not happen as analyzing two sequential images using cross-correlation function since there is no cross-correlation peak at the origin. Prasad, et. al. (1992) also pointed out that alternative peak location methods such as parabolic or Gaussian curve fits may yield smaller rms errors than the centroiding technique, nevertheless, that trend is true only for flows wherein the velocity gradient is negligible. When velocity gradients are comparable to those found in real flows the centroid method is actually superior to curve fit techniques. In this study, we found that the interpolation scheme indeed improves the velocity measurement, especially in determining the direction of velocity vectors. For a steady flow, a series of flow images can be captured at distinct time. Any pair of sequential images can be used to perform the correlation analysis. Theoretically, one needs to process only one pair of two sequential images to measure the velocity. However, in practice different image pairs will often produce different velocities on the same location of the flow field due to the noise of disappearance or addition of particles on the selected image pair. To examine whether a measurement is consistent or not, one needs to define certain criteria to verify the measurements. The magnitude and the angle of the velocity vectors are the indices used for verification of consistency. For two sequential image pairs, if the difference of the velocity magnitude is less than 5% and the difference of the angle is less than 15 degrees (approximately 4% error compared with 360 degrees of allowance), the measured velocity was confirmed as a consistent data. If either one of the above criteria is not satisfied, the process is continued to the next image pairs. Similar processes were repeated for all image pairs until consistent data were found. If no consistent data were found after all image pairs had been examined, the measurement at the sampled area failed to produce meaningful data and no magnitude of the velocity at that location was assigned. The examination then moves to the next sample area. If the velocity data were crucial at a location, one may take new images with different time interval to process and make sure that the velocity is measured at the desired location.
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Twenty-Second Symposium on Naval Hydrodynamics IV Measurement of a rotating disc The proposed ACIA method was first calibrated by measuring a rotating disk with known angular velocity. Particles were distributed randomly on a disk, with diameter 10 cm and rotating six revolutions per second. For such a case, the tangential velocity at the edge of the disk is about 2 m/s, far beyond the dynamic range can be measured by the DPIV method. The advantages of high dynamic range of velocity measurement of the proposed ACIA method over the DPIV method will thus be clearly manifested. The multi-exposure particle image was recorded by the Sony DXC-9000, three-chip progressive scan color CCD camera. Each CCD chip has a resolution of 640×480 pixels. Hence the separated, blue and green images will have the same image resolution as the alternating color image, i.e. the image resolution will not be deteriorated as the alternating color image was separated into sequential images. The CCD was triggered externally as the blue laser was detected by the fiber optic placed at the upstream of the laser sheet. The total exposure times of the alternating color particle image was determined from the frequency of the pulsed laser sheet and controlled by the shutter speed of the CCD camera. Figures 6 (a), (b), (c) present a six times exposure, alternating color particle image and its separated, blue and green particle images respectively. The shutter speed was set to be 1/250 second and the frequency of the pulsed laser sheet is 1500 Hz. The physical dimension of the image is 88 mm horizontally and 66 mm vertically, covering more than one-quarter of the disk. The pixel size is 137.5 μm. Particles adopted were polymer spheres with diameters around 200 μm such that the particle to pixel ratio is about 2. According to Prasad et al. (1992), such a particle to pixel ration will minimize the total error of the velocity measurements. The separated, sequential images were used to calculate the velocity vectors by the digital correlation method with interrogation windows of size 64×64 pixels. For larger particles occupying more than one pixel, the centroid of the particles was found using their image intensity and coordinates on each pixel. Then the larger particles were represented by a pixel located at their centroid with unity intensity. It is found that using the particle centroid to perform the digital correlation analysis really improves the measurement accuracy. The velocity vector, magnitude and direction, of the clockwise rotating disk are clearly determined from the separated sequential images without any difficulty. To obtain a smoother velocity distribution, the interrogation window shifts only 10 pixels as calculating neighboring velocity vectors, allowing most of the interrogating windows overlapped. The particle number within each interrogating window was kept around one hundred to reduce the measurement uncertainty. Figure 7(a) shows the measured velocity vector of the rotating disk. The linear velocity distribution along the radius of the disk is shown in Figs. 7 (b), (c). Figure 7(b) shows the measured tangential velocity without performing sub-pixel accuracy analysis. For a pixel-accuracy calculation, the neighboring velocity can either has no difference or has a whole pixel difference, hence the velocity distribution is like a step-function. Figure 7(c) shows the ensemble averaged velocity distribution of 10 images using the centroiding sub-pixel accuracy analysis. Obviously, the measured velocity distribution is much better than the one shown in Fig. 7(b). For a linear velocity distribution, the centroid method indeed improves the measurement accuracy. Relative error of each data point was evaluated as follows: where Va is the velocity measured from ACIA method and Vt is the theoretical velocity of the solid body rotation at the point of measurement. Figure 8 shows the distribution of the relative errors of data points along the radius. The maximum error is less than 3%, which is smaller than the magnitude criterion set in the flow image analysis. It is thus concluded that the proposed ACIA method can successfully, and satisfactorily measure the velocity field of a rotating disk. V. Measurements of a two-dimensional channel flow The image of solid-body rotation does not contain some of the defects that occur in a real flow image, such as the pairing loss from one exposure to the next, or the strong velocity gradients near a solid boundary. All these imply that the sequential images may lose some of their correlation with each other. To further verify the applicability of the proposed ACIA method in conducting the quantitative, whole field flow measurement, an empty channel with known uniform velocity is selected as the second test case. Two imaging techniques, namely the proposed ACIA method and the aforementioned DPIV method, were adopted to measure an empty channel and experimental
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Twenty-Second Symposium on Naval Hydrodynamics results were compared with each other. In the DPIV method, a black and white CCD camera with a transfer rate of 30 frames per second is used. In the ACIA method, the alternating color laser sheet is generated by a single facet mirror rotating at a speed of 30 revolutions per second. The shutter speed of the color CCD was set to be 1/15 second. This way, a double exposure, alternating color image can be separated into two sequential images with 1/30-second time difference, comparable to the images taken from 30 frames per second black and white CCD camera. The image resolution is 640*480 pixels for both the black & white and the color CCD cameras. The experiments were conducted in a circulation water tunnel with a test section 110 cm in length and 25 cm by 25 cm in cross section. The test fluid, water, was seeded with polymer spheres that has a specific weight 1.05, index of reflection 1.59, and 53 μm to 88 μm in diameter, so that the seeded particles will move with the fluid and scatter light as they were exposed to the laser sheet. In general, the adopted polymer spheres meet the primary requirements for the sizing of tracer particles. That is, they must be nearly equal in density to that of the working fluid for neutral buoyancy, the particles must not themselves disturb the flow field, and the particles must be detectable by the recording medium. Figures 9 present the alternating color and its separated flow images of the two-dimensional channel flow acquired from a color CCD camera. Limited by the frame transfer rate of the black & white CCD camera, the velocity measured using the DPIV method can not be high. Hence a channel flow with uniform velocity 3.28 cm/s was measured. The physical dimension measured is 10 cm in height and 14 cm in length. To increase the image resolution, the domain measured is divided into the near-wall and outer regions. For each domain, the pixel size is kept about 50 μm. To ensure that most of the particles were remained in the interrogating window and a clear cross-correlation peak exists between two sequential images, the maximum particle displacement was kept around 5 pixels only. Since the dimension of the measured physical domain is small, the size of interrogation window is set to be 32*32 pixels. Near the wall, where larger velocity gradients exist, the size of interrogation window is reduced to 32*20 pixels to obtain a better resolution of the near-wall flow. The particle number within each interrogation window was kept more than fifty to reduce the measurement uncertainty. The velocity vectors obtained from the DPIV method is presented in Fig. 10. Velocity distributions obtained from the ACIA and DPIV imaging techniques are compared in Fig. 11 at five different locations. The uniform velocity measured from ACIA method is 3.32 cm/s, and from the DPIV method it is 3.34 cm/s, both are very close to the channel velocity, 3.28 cm/s. Again, the experimental results demonstrate that the proposed ACIA method can successfully measure the flow field. VI. Turbulent wake flow measurements As the proposed ACIA method has been successfully calibrated, it is then applied to measure the more complicate turbulent wake flows. A two-dimensional turbulent wake behind a flat plate is measured first. A flat-plate 20 cm long, 25 cm wide, and 0.8 cm thick is placed parallel to the flow in the circulation water tunnel. To reduce the disturbance to the flow, the leading and trailing edges of the plate is sharpen to a wedge shape with a tip angle of 60 degree. The uniform velocity of the incoming flow is 7 cm/s. The corresponding Reynolds number at the trailing edge of the flat plate is 1.4×104, far beyond the critical Reynolds number of a wake flow. The physical dimension measured is 3.35 cm by 2.5 cm. The image resolution is 640 by 480 pixels, hence the pixel size is about 53 μm. The 500 Hz laser sheet was generated using 10-facet polygon mirror rotating at 50 revolution. The shutter speed of the CCD was set to 1/125 second such that a four-time exposure alternating color particle image can be acquired, as shown in Fig. 12. The measured velocity vector and velocity profiles at different locations are presented in Fig. 13 and 14 respectively. The final flow field measured is the turbulent wake behind a container ship. A 1:550 scale double model of the “TOYAMA” container ship, 55 cm long, 5.5 cm wide, and 4.5 cm high, as shown in Fig. 15, was placed in the water tunnel. The inflow velocity was set to be 60 cm/s. The corresponding Reynolds number, based on the length of the container ship, is 3.3×105. The flow around the ship was measured frame by frame from the ship bow to stern. Each frame has a physical dimension of 4.26 cm by 3.2 cm with resolution 640 by 480 pixels. The pixel size is 67 μm. Most of the flow images analyzed were four-time exposure, acquired using a 1000 Hz laser sheet generated from a 20-facet polygon mirror rotating at 50 revolution per second, with the shutter speed 1/250 second. Except in the separation zone right after the ship stern where the flow velocity is low, the flow
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Twenty-Second Symposium on Naval Hydrodynamics image analyzed is six-time exposure, acquired using a 750 Hz laser sheet with shutter speed 1/125 second. Some of the flow images and the measured velocity vectors are presented in Figs. 16. All these experimental results clearly manifest that the proposed ACIA method can successfully measure either a steady or unsteady flow field, from low to high dynamic range and without directional ambiguity. VII. CONCLUSION In this study, a new flow visualization technique, the alternating color image anemometry method, is proposed. It is realized from paper review that, to increase the dynamic range of velocity measurement, analyzing a multi-exposure particle image is necessary, while to eliminate the directional ambiguity of a flow, determining its velocity vectors from sequential images is preferred. The proposed ACIA method successfully preserves these advantages by separating a multi-exposure particle image into sequential images and analyzing them using the digital correlation method. Alternating color, blue and green, multi-exposure particle image was acquired from a three-chip color CCD camera. By performing an appropriate band process, the multi-exposure particle image can be separated into two sequential images. Each separated image has the same resolution as the original alternating color image, and the time interval between them is equal to the frequency of the alternating color, pulsed laser sheet. With two sequential images available, the flow direction and velocity distribution can be determined by digital correlation method. The proposed ACIA method was first calibrated by measuring a constant speed rotating disk and an empty channel flow, and then applied to measure the turbulent wakes behind a flat plate and a container ship. The tangential velocity of the rotating disk, several meters per second, is far beyond the dynamic range that can be measured by the DPIV method, hence only the ACIA measurement was performed. It is demonstrated that high-speed velocity measurement and its direction determination is not a problem for the proposed ACIA method. Limited by the frame transfer rate, generally 30 frames per second, of the CCD camera, the velocity measured using the DPIV method can not be high. An empty channel flow with uniform velocity 3.28 cm/s was measured using both the ACIA and DPIV methods. Experimental results show that the velocity measurements from both methods are almost identical and very close to the velocity setting of the channel. Applications of the proposed ACIA method in turbulent wake flows measurement further manifest that the proposed ACIA method can successfully measure either a steady or unsteady flow field, from low to high dynamic range and without directional ambiguity. REFERENCES 1. Adrian, R.J., “Image Shifting Technique to Resolve Directional Ambiguity in Double-Pulsed Velocimetry,” Applied Optics, Vol. 25, No. 21, 1986, pp. 3855–3858. 2. Adrian, R.J., “Electrooptical Image Shifting for Particle Image Velocimetry,” Applied Optics, Vol. 27, No. 20, 1988, pp. 4216–4220. 3. Adrian, R.J., “Particle Imaging Techniques for Experimental Fluid Mechanics,” Annual Review of Fluid Mechanics, Vol. 23, 1991, pp. 261–304. 4. Dabiri, D. and Gharib, M., “Generation mechanisms and sources of vorticity within a spilling breaking wave,” Twenty-First Symposium on Naval Hydrodynamics, Trondheim, Norway, June 24–28, 1996, pp. 520–533. 5. He, Z.H., Sutton, Μ.Α., Ranson, W.F., and Peters, W.H., “Two Dimensional Velocity Measurements by Use of Digital-Speckle Correlation Techniques,” Experimental Mechanics, June, 1984, pp. 117–121. 6. Hesselink, L., “Digital Image Processing in Flow Visualization,” Annual Review of Fluid Mechanics, Vol. 20, 1988, pp. 421–485. 7. Khalighi, B., “Quantitative Fluid Velocity Measurements by Automatic Analysis of Flow Visualization Images,” Experiments in Fluids, Vol. 7, No. 2, 1989, pp. 142–144. 8. Chen, C.J., Chen, L.J., and Kim, Y.G., “Quantitative flow visualization of three-dimensional flows,” Proceedings of the Sixth International Symposium on Flow Visualization,” Yokohama, Japan, Oct. 1992, 5–9, pp. 3–11. 9. Lourenco, L. and Krothapalli, A., “On the accuracy of velocity and vorticity measurements with PIV,” Experiments in Fluids, Vol. 18, 1995, pp. 421–428. 10. Meynart, R., “Equal Velocity Fringes in a Rayleigh-Benard Flow by a Speckle Method,” Applied Optics, Vol. 19, No. 9, 1980, pp. 1385–1386. 11. Meynart, R., “Convective Flow Field Measurement by Speckle Velocimetry,” Revue De Physique Appliquee, Vol. 17, 1982, pp. 301–
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Twenty-Second Symposium on Naval Hydrodynamics 305. 12. Prasad, A.K., Adrian, R.J., Landreth, C.C., and Offutt, P.W., “Effect of resolution on the speed and accuracy of particle image velocimetry interrogation,” Experiments in Fluids, Vol. 13, 1992, pp. 105–116. 13. Reynolds, G.A., Short, M., and Whiffen, M.C., “Automated Reduction of Instantaneous Flow Field Images,” Optical Engineering, Vol. 24, No. 3, 1985, pp. 475–479. 13. Rockwell, D., Magness, C., Towfighi, J., Akin, O., and Corcoran, T., “High image-density particle image velocimetry using laser scanning techniques,” Experiments in Fluids, Vol. 14, 1993, pp. 181–192. 14. Vogel, A. and Lauterborn, W., “Time Resolved Particle Velocimetry Used in the Investigation of Cavitation Bubble Dynamics,” Applied Optics, Vol. 27, 1988, pp. 1869–1876. 15. Walter, J.A. and Chen, C.J., “Flow Visualization of Particle Streaks in Offset Channel Flow by a Direct CCD Imaging Process,” The Winter Annual Meeting of ASME, San Francisco, CA., FED-85, 1989, 115–120. 16. Willert, C.E. and Gharib, M., “Digital Particle Image Velocimetry,” Experiments in Fluids, Vol. 10, 1991, pp. 181–193. 17. Wung, T.S. and Tseng, F.G., “A Color-Coded Particle Tracking Velocimeter with Application to Natural Convection,” Experiments in Fluids, Vol. 13, 1992, pp. 217–223. Figure 1 Alternating color image intensity distribution of a 3-CCD camera. Figure 2 Four-time exposure, alternating color particle image of a rotating disk.
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Twenty-Second Symposium on Naval Hydrodynamics Figure 3 The system setup of the ACIA method. Figure 4 Cross-correlation map of two sequential images. Figure 5 Sub-pixel analysis of the weighted interpolation, centroiding scheme. Figure 6 Multi-exposure particle image of a rotating disk.
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Twenty-Second Symposium on Naval Hydrodynamics Figure 7 Velocity distribution of a rotating disk. Figure 8 Error distribution along the radius of the rotating disk. Figure 9 Alternating color and its separated images of a channel flow. Figure 10 Velocity vectors of a two-dimensional channel flow.
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Twenty-Second Symposium on Naval Hydrodynamics Figure 11 Velocity profiles at five different locations of a channel flow. Figure 12 Particle image of the turbulent wake behind a fat plate. Figure 13 Velocity vector distribution. Figure 14 Velocity profiles at different locations.
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Twenty-Second Symposium on Naval Hydrodynamics A New Tracer Technique for Turbulent Flow J.Hoyt (San Diego State University, USA), R.Sellin (University of Bristol, United Kingdom) ABSTRACT A new tracer formulation is described which resists breakup in turbulent and complex separated flows. The capability of the technique is demonstrated using examples of flow around smooth and rough cylinders, as well as in visualizing the large structures in the turbulent boundary layer. INTRODUCTION A dye-streak tracer is under development as an inexpensive alternate to laser-based diagnostic tools used in water-flow studies. The tracer is effective in strongly eddying and turbulent-flow situations encountered in water flow around objects and in the turbulent boundary layer. Flow visualization has provided information useful in all facets of fluid dynamics, since some method of actually seeing the flow events taking place appears to be an optimal way to make progress in understanding the details of fluid motion. One can then arrange more quantitative instrumentation, or simply gather insight regarding the flow. Visualization of turbulent water flow around objects and in the boundary layer, however, has resisted simple methods, and up to now only very complicated instrumentation has been available to study such flows. A new dye-streak formulation under development offers a return to simplicity in visualizing flows of this kind. It is interesting that the concept of the tracer evolved from years of effort on additive drag reduction, especially on the idea that coherent “threads” of some kind of additive might reduce the friction by interference with large structures in the flow. This concept eventually proved groundless, but it was noticed that threads formed from certain compounds followed closely the eddies and vortices encountered in turbulent flow. From these observations, shear-thickening and high-extensional viscosity solutions were selected for the tracer. The tracer is formulated with a colorant of white pigment, which contrasts well with flat-black surfaces in the flow channel. The streamers, dispensed from hypodermic tubing singly or from rakes of tubes, thus show up well against the black background. The tracer resists immediate break-up so as to display streaklines of interest, then dissipates into the overall flow. Still photos and home-type video with ordinary lighting can be used to record the tracer paths. The videos can then be transferred to a computer and printed frame-by frame to document streaklines. The ease of video recording during tracer experiments and later frame-by-frame capture can provide detailed information helpful in the analysis of fluctuating or non-steady flows. The technique can be adapted to provide three-dimensional flow information by providing a mirror inclined at 45° over the flow channel. Thus, using the side view through transparent channel walls, and a mirror giving the plan view, 3-D streakline information is readily available on a single film or video clip. There is a slight mismatch in the views due to different optical paths, but no ambiguity. Flows studied using the new tracer which are of special interest in Naval hydrodynamics include the wakes of smooth and rough cylinders, intersections of cylinders and plates, multiple cylinders, and observation of coherent structures in the turbulent boundary layer. The use of the tracer has lead to new information on all of these flows, and these results will be summarized in this paper. Offsetting the advantages of the tracer is the inability to provide vorticity information. Hence the tracer is qualitative, not quantitative. Additionally, the components of the tracer are drag-reducing, thus requiring sparing use, a large reservoir for tracer breakdown, or change of water before making resistance measurements. As will be explained, the drag-reducing aspects are unimportant when examining the large-scale eddy and vortex flow
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Twenty-Second Symposium on Naval Hydrodynamics structures, since these are relatively unaffected by the presence of polymers. We have compared results from a detailed particle-image-velocimetery (PIV) study of flow around shallow-immersion cylinders with a similar experiment using the tracer, and find that the streaklines of the tracer technique offer a virtually identical impression of the principal flow characteristics when compared with the PIV velocity vectors. TRACER COMPOSITION The tracer is a mixture of a surfactant, cetyltrimethylammonium salicylate (C16TASal) and a high extensional-viscosity polymer, poly(ethylene oxide) (PEO). Solutions of C16TASal increase in viscosity by factors of 10 or more when subjected to small shear or strain forces. The C16TASal and PEO components are made up in water solutions, and further diluted after mixing. A small amount of white water-based emulsion wall paint is added as a coloring agent. The paint also adds to the stability of the tracer streamers. A more detailed explanation of the method of preparation is given in the Appendix. A typical formula used in the work described here was: 2% C16TASal 500 ml 1/2% PEO 250 ml Tap water 1000 ml White paint 5–10 ml The experimenter can select, to some extent, the turbulence scales to be visualized, by varying the dilution and composition of the tracer mix. Weak solutions of the tracer show the smaller turbulence scales, while strongly eddying situations can be visualized with a more concentrated tracer mix. The more dilute the tracer, the greater the detail, until all is swept away as with a traditional dye streak. A more concentrated mix survives extensive turbulent excursions, and is more useful for initial flow explorations. Since the tracer is composed of a surfactant (i.e. a detergent) and a polymer used in water-treatment, the mixture appears to be environmentally benign, and seems to biodegrade when dispersed in our laboratory water-storage reservoirs. Both components of the tracer are drag-reducing in sufficient concentration, and this aspect of the tracer use must be kept in mind. At Bristol, the large reservoirs in the laboratory system and high-speed recirculating pumps allowed every-day operation without any effects of contamination from the tracer, as judged from frequent checks to assure Newtonian properties of the test water. Rakes of one or more hypodermic-tubing ejectors can be used to dispense the tracer in front of or in the flow around the object whose wake is to be visualized. A small variable-displacement pump is employed to emit the tracer into the flow at approximately the same velocity as the surrounding stream. Figure 1 shows the tracer being dispensed in front of a circular cylinder. In common with other high-concentration non-Newtonian fluids, the tracer flow first expands as it leaves the ejection tubing (the die-swell effect), then relaxes to form a relatively constant-diameter stream. A surface-tension difference exists between the tracer and the surrounding water; the strands thus become perfectly cylindrical until distorted by turbulence. Figure 1. Method of ejecting tracer in front of cylinder. The vertical bar is outside the flow channel. It should be emphasized that this type of tracer is not suitable for low-speed flows; it relies on a small amount of shear or strain to form coherent strands useful in identifying streaklines. EXPERIMENTAL FACILITY All the work described here was performed in a small water channel at the University of Bristol. The channel is 102 mm wide and 300 mm deep. A constant-head tank located 24 m above the working section provides gravity feed to a header tank, from which flow enters the channel through a convergent section equipped with honeycomb straighteners and screens. Flow velocities were measured with a calibrated velocity meter, as well as occasional checks with a volume-measuring tank. Most of the tests were made at flow velocities around 0.25 m/sec. Much of the work was done with experimental cylinders tested in cross-flow. Each cylinder was fitted with a spring-wedge arrangement so that it could be mounted in place at any location spanning the channel. In addition to single and multiple smooth cylinders, configurations consisting of cylinders having “macro” roughness formed from dimples (like a golf ball), gear-type axial grooves,
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Twenty-Second Symposium on Naval Hydrodynamics Figure 2. Sketch showing mirror arrangement for simultaneous three-dimensional viewing. and circumferential grooves were examined using the tracer. Reynolds numbers of up to 30,000, based on the cylinder diameter, could be obtained while maintaining a smooth free surface on the water channel. For tests involving the turbulent boundary layer, a 10 mm thick, 2 m long brass plate was mounted with its top surface 50 mm above the channel floor. The channel inflow geometry was modified to provide a horizontal ramp, the height of which was 1 mm below the height of the brass plate. A 2 mm gap between the ramp and the plate (the under surface of which was cut away at an angle) allowed the ramp boundary-layer to be sucked away. Thus the turbulent boundary layer on the plate began at a 1/2 mm wide slot (acting as a trip) just behind its leading edge. The entrance conditions were adjusted very carefully using dye streaks to assure smooth entrance to the plate, and that the turbulent boundary layer began at the trip. The plate was smooth to the touch, before being spray-painted matt black. Three-dimensional viewing was obtained for several test configurations by mounting a mirror at 45° above the channel. For the boundary-layer visualizations, an auxiliary mirror was provided to give a view aligned with the flow. Hence, as shown in Figure 2, there were three images available for simultaneous viewing. White stripes on the plate and the adjacent side wall of the channel were used to establish the local Reynolds number and to coordinate the images. In addition to 35 mm camera records of the flow (taken at 1/250 sec exposure on ISO 1600 film), video on VHS tape using a home-type camera was used to document the visualizations. Ordinary flood-lighting proved satisfactory. Where necessary, frame-by-frame video analysis was used to provide a time base. Video capture was accomplished using a miro DC-20 card with Adobe Premier LE processing on a Pentium-based PC. EXPERIMENTAL RESULTS We turn first to visualization of flow around smooth cylinders, one of the oldest problems in fluid mechanics, but one for which as yet there is no adequate understanding for the full range of Reynolds numbers (VD/ν) found in practice. Here V is the free-stream velocity, D the cylinder diameter, and ν the kinematic viscosity. While flow visualization using traditional techniques has been effective up to Reynolds numbers of a few thousand, flow patterns at higher Reynolds numbers are generally not obtainable except with the most sophisticated and expensive equipment. Smooth Cylinder Studies The literature on flow around cylinders is enormous, but information on the wake at Reynolds numbers above 2000 is quite limited. Using the tracer, we now have much more detailed knowledge of how the wake is formed, and how the greatly increased wake size as the Reynolds number is raised from, say, 2–3000 to 20,000 or more reflects the 20% increase in drag coefficient in this range (from CD=1.0 to CD=1.2).
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Twenty-Second Symposium on Naval Hydrodynamics Focusing on the question of how the high Reynolds number wake is formed, the literature is rather sparse. Bloor (1) building on earlier work, used hot-wire anemometry to study the transition from laminar to turbulent flow near the surface of the cylinder. She found that as the Reynolds number was increased to 20,000 or so, the separated flow became turbulent in the region “less than one radius downstream of the cylinder center”. She defined a “formation region” as the location between the separation point on the body and the first appearance of the periodic vortex street. Later, Gerrard (2) studied the high Reynolds number “formation region” in detail. His intuitive sketch (Figure 3) shows the formation region to be the area from the separation point to the location where the upward fluid (in this case) just crosses the horizontal centerline of the cylinder. In the sketch, the arrows representing different fluid paths originate at the end of the formation region. The sketch is remarkable in that only hot-wire data were available as a basis. Using the tracer, we can confirm Gerrard’s ideas as shown in Figure 4. Figure 3. Gerrarďs sketch of the “formation region”. Figure 4. The formation region illustrated with the tracer. An 89 mm dia cylinder at Reynolds number of 22,300. (Video frame.) Figure 4 shows that the formation region of the Kármán vortices extends about 1.5 diameters downstream from the cylinder centerline, as suggested by Gerrard in 1966. The major vortices are seen to form on the horizontal centerline behind the cylinder. The turbulent boundary layer does not seem to trigger the large Kármán vortices, and only occasionally enters into the vortex formation region. The cylinder wake becomes very large as the Reynolds number is increased from 1800 to much higher values, a possible reason for the drag coefficient to increase by 20% (from approximately 1.0 to 1.2). Figure 5 is a comparison of the cylinder wakes at two different Reynolds numbers. Figure 5. Comparison of cylinder wakes at 1800 and 22,300 Reynolds numbers. 10 mm dia cylinder above, and 89 mm dia below. The drag coefficient is estimated at 1.0 for the upper video frame, and 1.2 for the lower. Cylinders with Macro Roughness Cylindrical shapes used in engineering applications often differ significantly from the very smooth cylinders discussed above. Protrusions and depressions on the cylinder surface may result from manufacturing or other considerations. However, the remarkable thing about roughened bluff bodies is that they often show, at higher flow velocities, a distinctly lower drag or resistance than the corresponding perfectly smooth shape. An everyday example is the “dimpled” golf ball, which has a much lower drag than the same size smooth sphere, over a substantial range of high Reynolds numbers. Macro or large-scale roughness on cylinders also leads to lower resistance at relatively low Reynolds numbers.
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Twenty-Second Symposium on Naval Hydrodynamics As early as 1930, Page and Warsap (3) found that by wrapping a smooth cylinder with sandpaper, transition to the lower drag region (sometimes called “critical flow”) could be obtained at Reynolds numbers as low as 30–40,000, or about 1/10 the Reynolds number of a smooth cylinder. Many other workers over the years have confirmed these results for uniform roughness. More recently, the effect of macro, or large-scale roughness has been the subject of considerable study. Very tiny circumferential grooves, axial grooves resembling a fine-toothed gear, and dimples on the cylinder surface all have been shown to give noticeable drag reduction at Reynolds numbers of 15,000 or less. In spite of the considerable literature on roughened cylinders, analysis has been hindered by lack of any way to view the flow around the cylinder and in the wake. The new flow tracer has been used to visualize some of the low-drag configurations mentioned in the literature. In general it was found that the cylinders with macro roughness, all having reported low drag at Reynolds numbers of 30,000 or less, show characteristic changes in the wake pattern as that Reynolds number is approached. Apparently, a high-pressure zone is created, preventing the tracer from entering the region behind the cylinder. Thus the drag is lowered. All the “rough” cylinders studied here had a nominal diameter of 68 mm. Turning first to the gear-type configuration, a cylinder was fabricated having 100 axial grooves with 90° “V” shape, thus resembling a very fine-tooth gear, as shown in Figure 6. The ratio of the groove depth to the outer diameter was 15.6×10−3, geometrically scaled to match earlier drag measurements of Suzuki & Iijima (4) with similar configuration. Figure 6. Cylinder with gear-type roughness. The wake from this cylinder changed from a Kármán-vortex trail to a completely separated appearance as the Reynolds number was increased to 27,300, as shown in Figure 7. Figure 7. Wake photos from the gear-type cylinder. Above, Reynolds number=8,800; below, Re=27,400. A hint of vortex formation is seen at least three diameters downstream from the gear-type cylinder. At a slightly lower Reynolds number, 26,100, the Kármán trail begins around two diameters downstream Suzuki & Iijima (4) show that the drag coefficient is decreasing steeply in this Reynolds number region: from 0.9 at Re=26,000 to 0.6 at Re =27,400. The Strouhal number for the 26,100 Re case was estimated from video records to be 0.32, in good agreement with observations of Roshko (5), Bearman (6) and others for smooth cylinders in the critical-flow regime. Introducing dye into the behind-cylinder region for the high Reynolds number flow shown in Figure 7 indicated that no organized activity exists in the near wake; it seems to be a high-pressure area accounting for the low drag. Similar flow patterns appear for the other low-drag configurations tested. It is amusing to speculate that this type of roughness has evolved in nature for certain cactus species. The saguaro grows only in the Sonoran desert in the U.S. as a very tall cylinder (some attaining 10 m or more height) with a more coarse vertical gear-type roughness than the cylinder tested here. The cactus grows extremely slowly (5–10 cm/year) and has tiny, shallow roots. Yet they withstand desert storms during their very long lifetime with wind velocities of up to 80 km/hr. Perhaps their drag is greatly reduced, for in addition
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Twenty-Second Symposium on Naval Hydrodynamics to axial grooves, many “needles” or spines exist, growing from the tips of the projections. These may also aid in producing a low aerodynamic resistance. Figure 8. Cylinder having “dimples” scaled from a golf ball. The dimples shown on the cylinder in Figure 8 were approximately 6.0 mm dia at the outer surface; the depth of the dimple was 0.635 mm, giving a depth-to-diameter ratio of 9.4×10−3. The dimple density is that of a standard golf ball. Earlier tests with a cylinder having only half the dimple density (similar to the cylinder tested by Bearman & Harvey (7)) led to inconclusive results. The fully dimpled cylinder gave evidence of a changed wake at the lowest Reynolds number tested, 14,600. Figure 9 shows how the vortices in the wake tend to form two diameters or more downstream from the cylinder centerline, rather than immediately behind as with a smooth cylinder. In this photo, a mirror has been installed above the flow channel to show the three-dimensionality of the wake. As vortices begin to roll up, a noticeable expansion in the direction normal to the flow can be seen in the mirror. Figure 9. Wake from fully-dimpled cylinder at Reynolds number 14,600. A plan view of the flow is shown in the mirror above. At a higher Reynolds number, 24,600, the flow appears completely separated, as shown in Figure 10, suggesting that the drag is greatly reduced. Figure 10. Wake of fully-dimpled cylinder at 24,600 Reynolds number. By far the most spectacular change in wake appearance was found with a circumferentially grooved cylinder, the grooves extending only around the leading region. Leung, Ko & Tang (8) found that cylinders of this type can show reduced drag coefficients at Reynolds numbers of 20,00 or less. The geometry is quite complex; in the configuration used here, the leading ±75° of the cylinder was prepared by machining tiny sharp-edged circumferential grooves having a 15° included angle. The grooves were 1.22 mm deep, spaced 0.32 mm apart. The remainder of the cylinder surface was machined smooth, at the root diameter of the grooves. Figure 11 depicts a view of the completed cylinder. Figure 11. Partially circumferentially grooved cylinder. The flow around this cylinder configuration is amazing. At a Reynolds number of 5,000, the wake shows signs of Kármán vortex formation, but these vortices begin much further behind the cylinder compared with the smooth cylinder wake. At 15,000 Reynolds number, the flow appears completely detached from the cylinder, as shown in Figure 12.
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Twenty-Second Symposium on Naval Hydrodynamics Figure 12. Flow around the partially-grooved cylinder at Reynolds number of 15,000. The experiments with macro roughened cylinders suggest that flow at speeds beyond the “critical” Reynolds number is much different from the usual textbook explanation. The lack of activity in the separated wake, as suggested by the photos of Figures 7, 10 and 12 was noticed as early as 1961 by Roshko (5), who found that a splitter plate attached to the rear of a smooth cylinder was ineffective in the post “critical” flow. Thus these photos may lead to greater understanding of very high Reynolds number flows. Intersecting Cylinders Crossed circular cylinders are common components of engineering structures such as bridges and offshore platform supports. The complicated wake arising from flow around these structures often leads to unforseen vibrations and instabilities. The study of flow through screens and grids (another example of crossed cylinders) is also of technical interest, due to the use of these devices in turbulence management schemes for wind and water tunnels. Progress in understanding these flows has been impeded by lack of a suitable method of flow visualization. Background information on various aspects of crossed-cylinder flows has been summarized by Fox (9). The tracer has been used to study several configurations of crossed cylinders, of which only a sample can be displayed here. Since these are complex, three-dimensional flows, the mirror arrangement discussed above was utilized to capture details. The cylinders were stainless steel, 18.7 mm diameter (D) and the crossed-cylinder center-to-center spacing (L) was varied to give L/D ratios from 0 to 10. Figure 13 shows the tracer result for L/D=3. It can be seen that the Kármán vortex wake developing from the horizontal cylinder (seen in the side view) is captured by the vertical cylinder, with the resulting vortex wake dominating the flow. Figure 13. Crossed cylinders with L/D=3. Plan view above; side view below. Note how the vortices from the horizontal cylinder are transformed by the vertical cylinder into a new wake path. The flow at the intersection of a circular cylinder and a flat plate is of very great interest in connection with the problem of bridge-pier “scour”, in which the material surrounding the base of the pier is removed, possibly to a dangerous degree, by action of flowing water. A portion of this type of flow was modeled by mounting a vertical cylinder on a flat plate. The result, depicted in Figure 14, shows (in three dimensions) strong up-flow movements occurring behind the vertical cylinder. Hence sediment, originally eroded by high shear stress at the front of the pier, may be lifted and carried further downstream by the extremely active vortex wake. Figure 14. Flow at the intersection of a vertical cylinder and a flat plate. The tracer is embedded in a turbulent boundary layer as it encounters the cylinder. The cylinder is 18.7 mm dia.; the vertical white line at the right of the side view is 50 mm high, and at that point, the undisturbed boundary-layer thickness is 24 mm. The plan view is shown above.
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Twenty-Second Symposium on Naval Hydrodynamics Multiple Cylinders The tracer has been used to demonstrate flow in multiple cylinder arrangements such as those found in boilers or heat exchangers. The three types of flow oscillations deduced from frequency measurements by Hetz, Dhaubhadel & Telionis (10) can be seen in the tracer photos. The usual nomenclature is adopted with D, the tube diameter (18.7 mm), L the axial distance between centers, and T the transverse spacing of either staggered or in-line rows of tubes. Figure 15 illustrates the “cavity flow’ regime, where pairs of vortices simply rotate in the cavity between two in-line cylinders. Figure 15. Cavity flow with staggered tube arrangement. L/D=1.61; T/D=3.21; Re=5,800. With larger axial spacing (L/D=3.21), “gap shedding” occurs, where vortices formed between the cylinders extend out beyond the in-line region, as shown in Figure 16. Figure 16. “Gap shedding” at Re=5,600 and L/D=T/D=3.21. Finally, Figure 17 shows the “bluff-body” regime, where all the cylinders act as a single body, casting a large vortex wake. It is particularly interesting that the many shear layers (often of alternate signs) contributing to the wake in a multiple-body flow can organize into a single oscillating wake, such as that shown in the Figure. Figure 17. Bluff-body shedding at Re=9,800. L/D=3.21 and T/D=1.61. Flow visualization thus plays a useful role in revealing the characteristics of complicated flows such as these examples of multiple-cylinder arrangements. The tracer is especially valuable here, since other methods of visualization seem awkward. Laser-sheet illumination, for example, casts shadows from cylinders or other objects; the shadow region thus is opaque, possibly obscuring details necessary for interpretation of the flow. Comparison with PIV Recently, an opportunity has arisen to evaluate the usefulness of the tracer information by comparison with a more accepted flow visualization technique. Sheridan, Lin & Rockwell (11) have published results obtained with Particle-Image-Velocimetry for flow past a cylinder close to a free water surface at various immersion depths. We have repeated several of the flow geometries studied by Sheridan, et al. and find that the streaklines of the tracer provide a virtually identical impression of the principal flow characteristics when compared with the PIV velocity vectors. If anything, the tracer provides a clearer guide to interpretation of the flow situation than does the PIV result. Figure 18 compares the PIV result (from Sheridan, et al.) with video scenes from a similar tracer experiment. Here the top of the cylinder is set at a depth, h, (with reference to an upstream free-surface location) divided by diameter (D)=0.3. This ratio is defined as h* by Sheridan, et al.
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Twenty-Second Symposium on Naval Hydrodynamics Figure 18. Video frames of tracer flow at h*=0.30. At left, flow from the upper surface of the cylinder has induced a vortex rotating clockwise (to observer). Flow from the lower surface induces a counterclockwise vortex, which enters the same space and forms a Coanda-like effect around the base of the cylinder, as shown at the right, 54 frames (2.16 sec) later. Flow angles at specific locations have been compared, and both the tracer and PIV give comparable results. This favorable comparison suggests that concerns occasionally expressed, based on computer exercises, regarding adequacy of flow visualization in unsteady flow situations (i.e. Gursell, et al. (12)) disappear in real flows. Apparently, the quasi-steady features of the flow are those detected by the flow tracer. Coherent Structures—Turbulent Boundary Layer A final area where the tracer has provided results of great interest is in visualizing large structures in the turbulent boundary layer on a flat plate. By dispensing a single filament into the lower region of the boundary layer, coherent larger-scale motions are revealed These structures have been a subject of great interest in fluid mechanics for many years, following the insight provided by the sketches of Theodorsen (13) and others. When the tracer is dispensed in the boundary-layer flow, horseshoe-type vortices can be readily visualized, as shown in Figure 19. The tracer is picked up by the structures and transported downstream, giving a visual record of the boundary-layer activity. Figure 19. Horseshoe vortices shown by video frames (0.08 sec apart) of the tracer, compared with the famous sketch of Theodorsen (13).
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Twenty-Second Symposium on Naval Hydrodynamics Figure 20. Tracer visualization of horseshoe vortex structure compared with computer simulation of line vortex in a shear layer, from Smith et al. (14). Figure 21. Three views of boundary-layer activity using mirror arrangement shown in Figure 2. Note the large spanwise excursion of the tracer in the upper right view. An oblique view of the tracer stream revealing horseshoe-type structures is given in Figure 20. Simultaneous side and plan views of the structures revealed by the tracer can be obtained using mirrors, as shown in Figure 21. The ability of the tracer to show these large structures is certain to increase our knowledge of the role they play in the turbulent boundary layer. SUMMARY The development of a new flow tracer technique has made the visualization of both boundary layer and wake flows a simple procedure. We look forward to many new discoveries utilizing this new technique. ACKNOWLEDGEMENT The support of the Benjamin Meaker Visiting Professor Fund at the University of Bristol and the U.S. National Science Foundation is very greatly appreciated. We especially wish to acknowledge the confidence in this work expressed by Dr. Michael Roco of the NSF through Grants CTS-9411980, CTS-9508409, and CTS-9713857. We also wish to thank Mr. Philip Leonard (University of Bristol Hydraulics Laboratory) for his skill in fabricating the experimental equipment and assisting with the tests. REFERENCES 1. Bloor, M.S., “The Transition to Turbulence in the Wake of a Circular Cylinder,”Journal of Fluid Mechanics, Vol. 19, 1964, pp. 290– 304. 2. Gerrard, J.H., “The Mechanics of the Formation Region of Vortices Behind Bluff Bodies,” Journal of Fluid Mechanics, Vol. 25, 1966, pp. 401–413. 3. Page, A. and Warsap, J.H., “The Effects of Turbulence and Surface Roughness on the Drag of a Circular Cylinder,” British ARC Reports and Memoranda No. 1283, 1930. 4. Suzuki, Y. and Iijima, T., “Profile Drag of Circular Cylinders with Surface Roughness of Straight Knurls,” Proceedings FLUCOME ’94, Vol. 2, 1994, pp. 805–810. 5. Roshko, A. “Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Number,” Journal of Fluid Mechanics, Vol. 10, 1961, pp. 345–356. 6. Bearman, P.W., “On Vortex Shedding from a Circular Cylinder in the Critical Reynolds Number Regime,” Journal of Fluid Mechanics, Vol. 37, 1969, pp. 577–585. 7. Bearman, P.W. and Harvey, J.K., “Control of Circular Cylinder Flow by the Use of Dimples,” AIAA Journal, Vol. 31, 1993, pp. 1753–1756. 8. Leung, Y.C., Ko, N.W.M., and Tang, K.M., “Flow Past Circular Cylinder with Different Surface Configurations,” Journal of Fluids Engineering, Vol. 114, 1992, pp. 170–177. 9. Fox, T. A, “Wake Characteristics of Two Circular Cylinders Arranged Perpendicular to Each Other,” Journal of Fluids Engineering, Vol. 113, 1991, pp. 45–50. 10. Hetz, A.A., Dhaubhadel, M.N., and Telionis, D.P., “Vortex Shedding Over Five In-Line Cylinders,” Journal of Fluids and Structures, Vol. 5, 1991, pp. 243–257. 11. Sheridan, J., Lin, J-C., and Rockwell, D., “Flow Past a Cylinder Close to a Free Surface,” Journal of Fluid Mechanics, Vol. 330, 1997, pp. 1–30. 12. Gursul, I., Lusseyran, D., and Rockwell, D., “On Interpretation of Flow Visualization of Unsteady Flows,” Experiments in Fluids, Vol. 9, 1990, pp. 257–266.
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Twenty-Second Symposium on Naval Hydrodynamics DISCUSSION D.Fruman Ecole Navale, France I would like to congratulate the authors for their fine work and the beauty of the visualizations. I have a question concerning the behavior of the visualizing fluid. Because of its properties (visoelastic) the fluid will be reusable to the deformation intensity, that is to say to a time scale proportional to the length scale (L) divided by the velocity scale (V), i.e. L/V. Therefore, the visualization of different length scale models operating at equal Reynolds (v VL) numbers will (or may) be quite different. What is your opinion about this? AUTHORS’ REPLY We appreciate the comments and concerns from a very distinguished scholar in the field of viscoelastic flows. All experiments in which we have had an opportunity to compare our flow visualization results with those of other workers, show very similar visualization patterns. Hence we think the tracer is responding to the length scales in the main body of the flowing liquid (water) rather than scales determined by the tracer itself. In studies of flow around circular cylinders (Hoyt and Sellin (15)), various size cylinders gave very similar Kármán vortex patterns at the same Reynolds numbers (even though the vortex shedding frequency changed substantially as the cylinder size was changed). In preparing the reply to discussion of our paper, we discovered that we had omitted references in the text to our previous papers on the topic, and take this opportunity to add a few of the more recent. References 15. Hoyt, J.W. and Sellin, R.H.J. “A Flow Visualization Study of Separated Flow over Circular, Elliptical and Square Cylinders” in M.V.Otugen, et al., eds. Separated and Complex Flows—1995, ASME FED-Vol. 217, 1995, pp. 115–120. 16. Hoyt, J.W. and Sellin, R.H.J. “Flow Over Tube Banks—A Visualization Study,” Journal of Fluids Engineering, Vol. 119, 1997, pp. 480–483. 17. Hoyt, J.W. and Sellin, R.H.J. “3-D Visualization of Flow Past Intersecting Cylinders,” Proc. ASME Fluids Engineering Division, Summer Meeting 1998 (on disc), Washington, D.C. Paper No. FEDSM-5269, 1998. 18. Hoyt, J.W. and Sellin, R.H.J. “A Mirror and Tracer Method of 3-D Flow Visualization,” Proc. 8th International Symposium on Flow Visualization (1998) (on disc), Sorrento, Italy. Paper No. 2, pp. 2.1–2.6, 1998.
Representative terms from entire chapter: