MEASUREMENT OF VELOCITY FIELD IN THE AERATED REGION OF A HYDRAULIC JUMP USING BUBBLE IMAGE VELOCIMETRY Chang Lin, Shih-Chun Hsieh, Wei-Jung Lin, Kuang-An Chang Department of Civil Engineering, National Chung Hsing University Tauchung 4, Taiwan Department of Civil Engineering, Texas A&M University, College Station, TX 77843-336, U.S.A. ABSTRACT Hydraulic jump has been investigated extensively for several decades. However, a hydraulic jump usually entrains air bubbles in the roller region, making it hard to measure velocity in this region due to many technical difficulties. Many previous studies concentrated on the energy dissipation, jump length, water surface profile, and velocity profile out of the aerated region. The aim of the present study is to provide further insight of the flow in the aerated region of a hydraulic jump at F r = 3.77 by using both PIV and BIV techniques. INTRODUCTION Hydraulic jump is a natural phenomenon usually occurring in rivers or downstream of hydraulic structures (such as sluice gates and spillways) when a supercritical flow transfer into a subcritical flow suddenly. Previous studies on the hydraulic jump concentrated on the measurements of water surface and the length of the hydraulic jump. The general nondimensional water surface profile of a hydraulic jump was demonstrated by Rajaratnam and Subramanya []. In the last decade, non-intrusive measurement techniques were employed in the study of hydraulic jump. Measurements of horizontal and vertical mean velocities, turbulent shear stress and turbulence intensities were studied in Long et al. [] by using LDV. Hornung et al. [3] used control-volume analysis with the flow field measurement by PIV to study the traveling hydraulic jump, indicating that a strong shear layer formed and developed at the toe of the roller. However, all the previous studies have encountered difficulties in the measurement of velocity field of the roller region with large amount of air bubbles, which is the most common phenomenon of hydraulic jump at high Froude numbers. This technical difficulty restricted the study out of the aerated region of the hydraulic jump. Recently, the PIV technique has been successfully used to measure bubble velocity by tracking and correlating each bubble in the recorded images with the shadowgraphy method (Hassan et al. [4]; Nishino et al. [5]; Lindken and Merzkirch [6]). A modified PIV method, called bubble image velocimetry (BIV), was introduced to measure the velocity in the aerated region by using bubbles as the tracer and correlated the texture of the bubble images to measure the bubble velocity. The velocity field in the aerated region of the greenwater and the breaker were successfully measured by Ryu et al. [7]. The aim of the present study is to shed further insight of the flow structure in the aerated region of a hydraulic jump. The velocity field in the aerated region, that is the most interesting and important to the hydraulic engineers, but very difficult to be measured using traditional measuring methods, was obtained using the bubble image velocimetry (BIV) technique in the present study. At Froude number F r = 3.77, the velocity field measured by using both the traditional PIV technique and the new BIV method will be compared and discussed. The sequential velocity fields both in the aerated and non-aerated regions of the hydraulic jump will be demonstrated. EXPERIMENTAL SYSTEM AND SETUP Water Channel Experiments were performed in a recirculating water flume at the Fluid Mechanics Laboratory of the Department of Civil Engineering, National Chung Hsing University, Taiwan. The internal dimensions of the working section were 35. cm long, 5. cm wide by 54. cm deep as shown in Fig.. The working section is enclosed by glass windows on both sides and bottom to allow visual and optical studies throughout the flow domain. Three layers of perforated steel plates (which are installed in the upstream settling plenum cm long), one piece of honeycomb cm in length, four meshes with different grid sizes, and a specially designed 3-D contraction cm in length were arranged to remove any large-scale irregularities and to smooth the inlet flows. By means of such a combination, a turbulence intensity of less than.8 % at 3. cm/s could be achieved at the inlet of the working section. Moreover, the spanwise flow uniformity, defined as the ratio of the uniform flow section outside the side-wall boundary layer to the flume width, was estimated to be 95. %. Fig. Schematic diagrams of the experimental water flume. Setup of BIV System The idea of BIV came from combining the shadowgraphy technique that illuminates the fluid from
behind to reveal the flow pattern, and the PIV technique that correlates the consecutive images to determine the velocity. Since the velocity is calculated through crosscorrelating the images obtained by the shadowgraphy technique with the bubble structure in the images as tracers, the BIV technique requires the light projectors to illuminate the air bubbles in the aerated region. The images were captured by a Phantom high speed camera mounted with a Nikon 5 mm micro focal lens. The camera has a resolution of 4 4 pixels with an -bit dynamic range and a maximum framing rate of fps. As shown in Fig., four regular 6 W light bulbs were used to illuminate the flow. Two lights placed at the back side of the flume was used to illuminate the flow from behind, and a thin sheet of translucent white plastic glass was attached on the back-side glass wall of the flume in order to uniform the back light source. Another two lights were placed at the front side of the flume (at the same side with the high-speed camera but with an angle) to provide sufficient light and to produce the intensity differences in the images. The inverted consecutive images were used to calculate the flow velocity by cross-correlating the air-bubble texture. Since we used the light bulbs instead of the laser light sheet to illuminate the flow, the depth of field (DOF), where we measured bubbles in the cross-tank direction (the spanwise direction) should be carefully defined. The DOF is defined as a distance within which objects captured by the camera is well focused and appear to be sharp. As used in the PIV technique, the DOF can be considered as the laser light sheet thickness. In the BIV technique, the DOF can be calculated by the formulae in Ray [8]. The DOF can be expressed as D = S R. In which R presents the nearest limit as R = Lf /(f + NLC) and S presents the farest limit as S = Lf /(f - NLC), in which f is the camera lens focal length, C the value for circle of confusion (a constant and property of the camera), and N the f- number of the camera aperture. Objects located out of the DOF will appear to be blurring without a clear texture and only the objects located within the DOF will be sharp and clear in the captured image for velocity determination. sliuce gate free flow D hydraulic jump light white plastic glass water tank center of focal plane Setup of PIV System In the non-aerated region, Aluminium powder injected upstream the hydraulic jump was used as the tracking particles for the PIV measurement (as shown in Fig.3). The light source was a 5 W argon-ion laser tube (Coherent Innova 9-4), from which a laser beam was emitted and spread into a fan-shaped light sheet (about.5 mm thick) by a cylindrical lens. The light sheet was used to illuminate the motion of the Aluminium tracer on a vertical plane along the longitudinal direction of the water channel. With the combination of the argon-ion laser light source and Aluminium tracer, we can capture the image with clear particle in the non-aerated region but without strong reflection from the air bubble in aerated region. The images used to calculate the velocity fields were also captured by the Phantom high speed camera. Fig. 3 Experimental Condition Experimental arrangement of PIV. With a sluice gate installed in the front side of the working section in the water flume, the hydraulic jump was easily produced downstream of a sluice gate. The sketch of the experimental section of the hydraulic jump is shown in figure 4. The position at the toe of the roller of the hydraulic jump was denoted as the position where x =, and y = at the bottom of the flume. Due to long-distance development of the nonaerated and aerated areas of the hydraulic jump, seven fields of view (FOV) were used for particle image velocimetry and bubble image velocimetry. With these FOV, the entire length of the desired hydraulic jump could be separately measured. The images in the nonaerated region were captured in FOV through FOV3, on the other hand, the images in the aerated region were captured from FOV4 through FOV7. L light glass side wall high speed camera Fig. Experimental arrangement of BIV for the present study. Fig. 4 Coordinate system and fields of view used in PIV and BIV measurements.
RESULT AND DISCUSSION In the present study, the hydraulic jump conjugate depths and approaching Froude number were measured and compared with the theory. Equation () and equation () were used to confirm the experimental accuracy of Froude number in the supercritical flow region of the jump. As shown in Fig. 4, U presents the incoming flow velocity; y and y present the water depths in the supercritical and sub-critical flow region, respectively. Base on the measurement of the water depths and the velocity field of the incoming flow using point gauge and PIV technique, the depths of y and y equal to. and. (cm) respectively and mean velocity U equals to 69.68 (cm/s). The Froude numbers calculated from Equation () and equation () were 3.77 and 3.74 which were estimated as.7% deviation in the experimental accuracy of Froude number calculation with these two different measurement methods. F r = U gy () have no influence on the calculation of the clear particle image. The corresponding instantaneous velocity fields are shown in Fig. 5(b). Velocity vectors could be measured with the sufficient amount of particles. BIV Measurement Different to the measurement in the non-aerated region with PIV technique, BIV technique was conducted to the measurement in the aerated rolling region of the hydraulic jump. Fig. 6(a) shows the instantaneous flow pattern in the non-aerated region of the roller of hydraulic jump in FOV5. The area outside the DOV was captured as the blurred image and there were no tracer in the water region to be photoed. Clear bubble image was captured by the high speed camera only within the DOV for velocity measurement. The corresponding instantaneous bubble velocity field is shown in Fig. 6(b). y y = + + 8F r () PIV Measurement Fig. 5(a) shows the instant flow pattern in the nonaerated region beneath the roller of hydraulic jump in FOV3. With sufficient Aluminium tracers illuminated by laser light sheet, clear particle images were captured by the high speed camera for velocity measurement. The dim area reflects the aerated region which would (a) aerated region (b) 3 aerated region Fig. 6 Instantaneous flow pattern and velocity field measured in the aerated region of FOV5. Fig. 5 3 4 5 6 Instantaneous flow pattern and velocity field measured in the non-aerated region of FOV3. Mean Velocity Field of the Hydraulic Jump The mean velocity field of the hydraulic jump was calculated and combined with both PIV and BIV techniques. Fig. 7(a) shows the measured regions of these two different techniques in the non-aerated and aerated regions. Fig. 7(b) shows the mean velocity field combined of these two method with two different colors. It could be observed that the velocity near the free surface of the roller of the jump decreased significantly due to the reverse flow in the roller.
(a) 8 6 4 BIV measurd region - PIV measurd region bottom 5 5 5 3 35 4 (b) 8 6 4 - bottom 5 5 5 3 35 4 Fig. 7 Mean velocity measurement (a) measured region for PIV and BIV; (b) velocity field. In the region under the roller, not only water flow but also entrained air bubble exist alternately during the experimental period. Velocity profiles were shown both water and bubbles velocities in this overlap region. Fig. 8 shows the mean velocity profiles of the water flow and bubble flow. The water velocity measured by PIV is a little greater than the bubble velocity. The deviation of bubble velocity from water velocity could be estimated to be 8.7%. The turbulent intensity, defined as I = u u + v v /U, is shown in Fig.9. Large turbulence intensity occurrs in the core region of the roller where the air-entrained bubbles reserved. The maximum turbulent intensity is around.65 in Fig.9 which occurred at about to 5 cm downstream of the toe of the roller. CONCLUSION The measurement of velocity field of the hydraulic jump using the PIV and BIV techniques were presented. While the PIV technique was only capable of obtaining the velocity field outside the aerated region, the BIV method successfully measured the velocity field in the aerated region of the hydraulic jump. With the BIV technique, measurement of velocity field in the aerated region where the PIV technique does not work well or does not work at all can be realized successfully. Fig. 8 Velocity profiles of PIV and BIV measurements at x = 5 cm.
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