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Measurement of rivulet movement on inclined cables during rain–wind induced vibration
Accepted Manuscript Title: Measurement of rivulet movement on inclined cables during rain-wind induced vibration Author: Yongle Li Haiquan Jing Yong Xia Youlin Xu Huoyue Xiang PII: DOI: Reference:
S0924-4247(15)00163-6 http://dx.doi.org/doi:10.1016/j.sna.2015.03.040 SNA 9138
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
22-8-2014 27-3-2015 27-3-2015
Please cite this article as: Y. Li, H. Jing, Y. Xia, Y. Xu, H. Xiang, Measurement of rivulet movement on inclined cables during rain-wind induced vibration, Sensors and Actuators: A Physical (2015), http://dx.doi.org/10.1016/j.sna.2015.03.040 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Measurement of rivulet movement on inclined cables during rain-wind induced vibration
Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China
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Department of Bridge Engineering Southwest Jiaotong University, Chengdu, China
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Yongle Li1, Haiquan Jing2, Yong Xia2,, Youlin Xu2 and Huoyue Xiang1
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Abstract
The large amplitude vibration of stay cables has been observed in several cable-stayed bridges under
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the simultaneous occurrence of rain and wind, which is called rain-wind induced vibration (RWIV).
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During RWIV, the upper rivulet oscillating circumferentially on the inclined cable surface is widely
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considered to have an important role in this phenomenon. However, the small size of rivulets and
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high sensitivity to wind flow make the measurement of the rivulet movement challenging. This study proposes a digital image processing method to measure the rivulet movement in wind tunnel tests. RWIV of a cable model was excited during the test and a digital video camera was used to record the video clips of the rivulets, from which the time history of the rivulet movement along the entire cable is identified through image processing. The oscillation amplitude, equilibrium position, and dominant frequency of the upper rivulet are investigated. Results demonstrated that the proposed non-contact, non-intrusive measurement method is cost-effective and has good resolution in
Corresponding author. E-mail address: [email protected]; Tel: +852-27666066. 1
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measuring the rivulet vibration. Finally the rivulet vibration characteristics were also studied when the cable was fixed. Comparison demonstrates the relation between the upper rivulet and cable
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vibration.
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Key words: Cable; water rivulets; Rain-wind induced vibration; Image processing.
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1 Introduction
Stay cables may experience large vibration under support movements [1, 2] or rain and wind
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loadings [3]. Vibration of stay cables in some cable-stayed bridges have been observed under the
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simultaneous occurrence of rain and wind, which is referred to as rain-wind induced vibration
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(RWIV). Such a large amplitude vibration may cause severe damage, such as the reduction of the
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cable’s life, destruction of the connections, breakdown of the protection [3], and damage of the dampers [4]. Extensive research have been conducted to reveal the excitation mechanisms of RWIV through field measurements [5–8], wind tunnel tests [3, 9–15], and numerical analysis [16–21]. Most of researchers believe that the upper rivulet located on inclined cable surface plays the most important role in this kind of phenomenon. However, the excitation mechanisms of RWIV are still not fully understood given the limited information of the rivulet. The rivulet has become a crucial factor in understanding the RWIV of cables. Several researchers have investigated the rivulet on cables theoretically and numerically during past
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decades. For the first time, Lemaitre et al. [22, 23] proposed a lubrication theory-based numerical model to simulate the evolution of a water film around a cylinder under the action of wind. Taylor
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and Robertson [24, 25] developed a computational approach combining the discrete vortex method
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and lubrication theory to calculate the evolution and growth of rivulets on the cable surface when the cable with water film on surface is blown by wind. Bi et al. [26] derived 2D coupled equations of
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water film evolution, for the first time, by combining the lubrication theory and single-mode system
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vibration theory. The water film evolution, lift force and cable vibration were numerically investigated by solving the coupled equations.
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However, directly measuring the rivulet in field or laboratory is very difficult and challenging
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because the rivulet is small, thin, and sensitive to wind flow. To date, no measurement of rivulet has
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been conducted on-site and only few have been reported in wind tunnel tests. For example,
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Coesentino et al. [12, 13] measured the thickness of the upper rivulet ranging from 0.2 to 0.5 mm by using eight pairs of wires. Li et al. [14] employed an ultrasonic technique to investigate the shape, thickness, position, and movement of rivulets on an inclined cable model in a wind tunnel test. The thickness and mean width of the water rivulet were measured as approximately 0.5 mm and 7.96 mm, respectively. The lower rivulet was more or less fixed, whereas the upper rivulet oscillated around the circumferential direction of the cable at the same frequency of the cable model. In the study of Coesentino et al. [12], however, the wires on the surface could affect the formation and movement of the upper rivulet. As such, non-intrusive measurement technique could
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provide more reliable information. In the study of Li et al. [14], the material of the surface of the cable model differed from that of the real stay cable. Therefore the measured rivulets might differ
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from that formed on real cables as rivulets are very sensitive to the cable surface. In addition, the
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above two experiments measured the rivulet at a fixed section of the cable only. Distribution of the rivulet along the entire cable was not available.
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Under the circumstance, the non-contact digital image processing technique has potential to
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avoid the aforementioned disadvantages. The technique has advantages of the non-intrusion, non-destruction, multi–point measurement, high resolution, and cost-effectiveness. For these reasons,
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it has been applied to displacement measurement of civil structures. For example, Lee and Shinozuka
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[27] developed the method to measure the dynamic displacement of a flexible bridge. Pankanin et al.
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[28] applied it to quantitatively determine the geometric parameters of the Karman vortex street.
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Zhou et al. [29] used it to measure the cable vibration of a real cable-stayed bridge. Choi et al. [30] demonstrated the precision and cost-effectiveness of the digital image processing method in measuring structural dynamic displacement. In this paper, the digital image processing method is developed and applied to measure the position of the rivulet on real cable models. The large RWIV of the model was reproduced in a wind tunnel. Water rivulets were simulated by colored water. The movement of the upper rivulet on the cable model was recorded using a digital video camera. Through digital image processing, the time history of the upper rivulet vibration along the entire cable was obtained. During this test, the
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movement of the rivulet was not disturbed. Finally, the characteristics of the rivulet movement during RWIV were investigated. The results will help elucidate the excitation mechanism of RWIV
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of cables.
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2 Methodologies
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In this study, RWIVs are simulated in a wind tunnel. The water rivulets were simulated by real water, colored either in red or blue. Black marks were drawn on the cable surface as reference. These enable
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the rivulet more distinguishable from the cable. During the test, a digital video camera was installed
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at one end of the cable model and moved together with the cable (see Figure 8b). When the RWIV of
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the cable occurred, the rivulet moved in the circumferential direction relative to the cable, which was
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recorded by the camera. The video clips will then be processed via three steps, namely, image pre-processing, rivulet identification, and rivulet locating, to obtain the rivulet movement on the cable.
2.1 Image pre-processing
The recorded video clip is first converted into a series of images. The video camera used in this test captures 25 frames per second and each frame has 720 (height) × 1280 (width) pixels. The frames of
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the video clip are converted into a series of RGB images. RGB refers to the three hues of light (red, green, and blue) of each pixel, which arrange from 0 to 255 and can form any color by mixing
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together. For example, three intensities of 255 create the white color and three zeros present the black.
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The k-th image can be represented as a three-dimensional matrix I k with the size of 720×1280×3, which corresponds to the three RGB intensities of each pixel. These images are named as raw
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images.
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The raw images contain a big region irrelevant to the cable (see Figure 1). They are then cropped such that only the key area including the cable with rivulet remains. Consequently, the
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computational region in each image is reduced. To make sure the cable model located at the same
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position in all cropped images, one particular crossing point on the cable surface is chosen as the
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reference point in all images (see Figure 1). Its position in image k (or I k ) is set as (rk , ck ) , where
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rk and ck denote row and column numbers of the reference point, respectively. The reference point is identified by examining the neighborhood of the point, which is a 51×51 pixels square in this study (see Figure 1). In the first original image, the position of the reference point (r1 , c1 ) is defined by the user. The neighborhood is determined such that its center is located at (r1, c1 ) . The RGB of the neighborhood, denoted as R1 , is a three-dimensional matrix of 51×51×3. In the subsequent image, for example I k , a 51×51 pixels square marching R1 best is found and its center (rk , ck ) is the reference point of I k . That is,
(rk , ck ) (r , c) min R k R1
(1)
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where (2)
R k I k (r , c)51513
(3)
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R1 I 1 (r1 , c1 )51513
R1 is the RGB matrix of the neighborhood of the reference point in I 1 with the central point at
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( r1 , c1 ), and R k is the RGB matrix of a 51×51 pixels square in I k with the central point at (r , c) .
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When R k R1 reaches the minimum, the central point of R k (rk , ck ) will be identified as the
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reference point of I k .
After the reference point is identified, the identical computational region is determined in all
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images. In this study, the computational region is a 170 (height) × 650 (width) pixels rectangle. The
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upper-left corner of the image.
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reference points in all cropped images are located at (150, 50). The origin (1, 1) is located at the
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Subsequently, the contrast of the cropped images is enhanced with the histogram equalization method to make the rivulet more distinguishable. Finally, the cropped and enhanced RGB images are converted into a grayscale image, as shown in Figure 2. The three intensities (R, G and B) of each pixel in the RGB image are translated to one gray intensity in the grayscale image (gray intensity = 0.2989×R + 0.5870×G + 0.1140×B). The grayscale image, hereinafter, is referred to as the objective image, which is denoted by a two-dimensional matrix with the size of 170 (row) × 650 (column). Each item in the matrix represents the gray intensity of the pixel.
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2.2 Identifying rivulets in the images
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The objective image, a collection of 170×650 discrete pixels, is smoothed by the two-dimensional
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(2D) Gaussian filter. A Gaussian filter is a filter whose impulse response is a Gaussian function and thus efficient to filter out the noise with Gaussian distribution. Figure 3 shows a 2-D 5×5 discrete
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Gaussian kernel used in this study. The 170×650 matrix is convolved with the 5×5 Gaussian kernel,
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k k resulting in a new 170×650 matrix ( A0 ). A0 represents the gray intensity of the filtered image and
used to identify the position of the upper rivulet.
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The background of upper rivulet is slightly different in different objective images. To eliminate this effect, the background is removed by deducting the averaged values of the adjacent images as (4)
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Ak A0k avg ( A0k 10 , , A0k 10 )
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The background of 21 adjacent images (about one period of rivulet vibration) is averaged. Ak is the matrix after the background is removed and the items can be positive, negative, or zero. Given that the rivulets in the wind tunnel test have been colored in red or blue, the rivulet appear darker than others in the grayscale image (see Figure 2). Consequently, the corresponding items in matrixes Ak have smaller intensity. More water indicates smaller intensity. As the rivulet oscillates on the cable, the intensity of the rivulet in the present image ( Ak ) should be smaller than those of the same location in the previous ( Ak 1 ) and succeeding image ( Ak 1 ). Consequently, the rivulet location can be identified by the following two means under the ideal conditions: 1) to determine the determining minimal intensity in matrix Ak and 2) to find the maximal reduction of Ak from Ak 1 . However, 8
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we have observed that both are significantly affected by noise in practice. In this paper, we integrate the two approaches as the following steps:
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1) Calculate intensity change as Ak Ak Ak 1 ; k k 2) For each column j, the intensity is Aj and intensity change is Aj ;
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k 3) Obtain the local minimums of Aj ;
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4) If the local minimum has the large reduction from the previous image, the point is
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determined as the rivulet and the row number is the position of the rivulet; k 5) Otherwise, the global minimum of Aj is determined as the rivulet;
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6) Let j=j+1, until all columns are identified. The rivulet location at j-column of k-th image
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is denoted as RL(k , j ) .
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Figure 4 shows an example of a rivulet located in one column. Here, only rows 10 to 130 are
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illustrated because the rivulets are observed within this range in all images.
2.3 Locating rivulets on the cable surface
The rivulet position RL(k , j ) obtained in Step 2 is converted to the position on the cable surface. As shown in Figure 5, a virtual reference mesh is established on the cable surface. The distance of the reference mesh is 1 cm and 10 cm in the circumferential and longitudinal directions, respectively.
RL(k , j ) is the pixel number and converted to the physical position in this mesh. It is then
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converted to angle defined in Figure 6. The conversion is based on the relationship between the circumferential angle and reference mesh. In this regard, is the upper rivulet position measured
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from the top of the cable, and positive anti-clockwise.
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3 Wind tunnel test
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The proposed method is applied to a real cable in a wind tunnel test. A series of tests were conducted when the wind speed varied from 5 to 14 m/s, which aimed to ensure that RWIV can be realized.
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Large amplitude RWIV was successfully excited at wind speed of 11 m/s. During the experiment, the
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rivulet was recorded using a digital camera (JVC HD30AC) with 720 (height) × 1280 (width) pixels
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and 25 frames per second. The cable displacement was measured by two laser sensors with the
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resolution of 100μm and the sample frequency of 512 Hz.
3.1 Wind tunnel
The wind tunnel test was conducted at Southwest Jiaotong University, Sichuan Province, China. The wind tunnel is an open-jet wind tunnel with the outlet of 1.34 m wide and 1.54 m high (Figure 7). The cable model was suspended by especially designed springs at both ends, as shown in Figure 8(a). The design allows the model to freely oscillate in the cross-wind and along-wind directions. Previous 10
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studies show that RWIV is prone to occur when the inclination angle and yaw angle range from 20° to 50° and from 20° to 60°, respectively [31]. In this study, the cable model was installed with an
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inclination angle of 32° and yaw angle of 35°. RWIVs under similar configurations have been
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successfully reproduced in wind tunnel tests [3, 31] and observed in field measurement [6, 7]. The
is defined as
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sin1 (sin cos )
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definition of inclination angle α and yaw angle β are shown in Figure 8(b). The relative yaw angle β*
(6)
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3.2 Cable model
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which is calculated as 29.1°. It represents the angle between the wind direction and the cable axis.
The cable model shown in Figure 9(a) is made of steel tube coated by polyethylene tube, which is the same as the real stay cables. The cutaway view is shown in Figure 9(b). The cable model is 160 mm in diameter and 2.7 m in length. The test segment is the middle 2-meter segment and was placed in the flow field during the test. The transition segments of the two ends were placed at the edge of the wind field. The mass of the entire cable model is 66.0 kg and the fundamental frequency is measured as 1.27 Hz. The damping ratio is 0.24%, resulting in the corresponding Scruton number
Sc
m =4.26. D2
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3.3 Simulation of water rivulets
In the wind tunnel test, two small flexible plastic pipes were installed at the top transition segment of
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the model to guide two colored water-lines—one at the upper surface and the other at the lower
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(Figure 10(a)). These two water-lines can run from the top end to the bottom by the action of gravity,
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inertia, and wind pressure, simulating the upper and lower water rivulets, respectively. Figure 10(b) shows an upper water rivulet simulated with the approach. The effectiveness of this simulation has
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been verified to be the same as spraying water on the cable surface directly [31]. That test was
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conducted at the same wind tunnel with the cable model of almost the same configuration (D=160
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mm, α=30°, and β=35°). In the previous and present tests, the upper rivulet was observed similarly
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oscillating in the circumferential direction while the lower rivulet was always static during RWIV, as reported by other researchers [3, 5, 14].
3.4. Digital video camera setup
A digital video camera was installed at the bottom end of the cable model (see Figure 8(b)). It was 1.2 m above the cable model approximately and moved with the cable together during RWIV. Given that the digital camera is out of the flow field and the distance between the camera and cable is far 12
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enough, the equipment has no effect on the formation and movement of the upper rivulet. The recorded rivulet is thus considered as undisturbed. The lower rivulet was observed to be static and its
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effect on the cable vibration can be ignored. Consequently, only the upper rivulet was recorded in the
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4 Movement of the upper rivulet during RWIV
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test.
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Two laser sensors were installed at one end of the cable model to measure the cross-wind (perpendicular to cable axis) and along-wind (horizontal) displacement of the cable. As no horizontal
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movement has been observed, only the cross-wind displacement is presented in this paper and downward is set to be positive. Figure 11 shows the time history of the cable displacement under the
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wind speed of 11 m/s. The cable vibrated at the amplitude of 50 mm with a frequency of 1.27 Hz, equal to the fundamental frequency of the model. The movement of the upper rivulet is obtained using the proposed image processing method during the large RWIV (a video clip can be downloaded from the supplementary material in the Web). Figure 12 shows examples of the captured upper rivulet at several time instants. The cable is divided into 15 segments (S1 to S15) in the longitudinal direction, each 5 cm long. It shows that the upper rivulet distribution along the cable is not uniform. The maximum difference between different sections at the same instant can be as large as 20°. 13
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Figure 13 shows the time history and power spectral density (PSD) of the upper rivulet position at segment 2 (S2). Similarly, Figure 14 shows those results at S9. The five time instants (t1 to t5) in
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figures 13 and 14 correspond to the five instants in Figure 12. The upper rivulet periodically
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oscillates between 15° and 40° with the frequency of 1.27 Hz, same as the cable fundamental frequency. Therefore, the oscillation of the upper rivulet on the cable is regular, and the amplitude is
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large and stable. Nevertheless, the rivulets on the two segments are different in phase, which is
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evidenced from Figure 12.
To better understand the rivulet movement during RWIV, the position of the rivulet along the
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entire cable is averaged over 15 segments and shown in Figure 15. The averaged rivulet position
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oscillates between 18° and 36°, with the equilibrium position at 27°. It is smoother and closer to a
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sinusoid as compared with those on one segment. Again, the dominant frequency of the averaged
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rivulet position is equal to the cable fundamental frequency, which is consistent with previous researches [12, 14] but with different vibration amplitude. For example, Coesentino et al. [12] measured the upper rivulet oscillating between 13° and 25°. Li et al. [14] reported that the upper rivulet oscillated around the equilibrium position of 35.7° (using this angle definition) with the standard deviation of 7°. The discrepancies are probably caused by the different configuration of the cable model used and different wind speed in the wind tunnels. Comparison between Figures 15(b) and 11(b) reveals that the upper rivulet oscillation is almost in-phase with the cable vibration, whereas the former is noisier than that the latter. Similar results have been observed when the wind
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speed is 10 m/s to 14 m/s. Figure 16 shows the time history of the cable displacement under the wind speed of 14 m/s and Figure 17 the coinstantaneous time history of the averaged upper rivulet. In that
between 17° and 38°, both at the frequency of 1.27 Hz.
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5 Movement of the upper rivulet when the cable is static
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case, the cable oscillated at the amplitude of 45 mm approximately and the upper rivulet vibrated
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For comparison purpose, the stationary cable with two ends fixed was also tested in the wind tunnel.
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The movement of the upper rivulet was recorded and identified similarly. Figures 17 and 18 show the
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upper rivulet vibration on segments 2 (S2) and 9 (S9), respectively, when the wind speed was 11 m/s.
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In the two figures, the upper rivulet vibration is not periodic. There is no dominant frequency in the PSDs. The time history and PSD of the averaged rivulet position are shown in Figure 19. The averaged rivulet position moves between 22° and 32° non-periodically, with the equilibrium position at 27.4°. The PSD shows that the rivulet vibration is like a wide band random process, which differs from the harmonic vibration when the RWIV of cable is excited.
This observation demonstrates that the RWIV and the upper rivulet movement are closely associated with each other. The large RWIV of the cable may assist the formation and stable vibration of the upper rivulet along the cable, and vice versa. When the upper rivulet is
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homogeneously and stably oscillating on the cable surface, the rivulet generates harmonic loads along the cable in-phase, causing a strong resultant force on the cable. As a consequence, large cable
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vibration can be excited. In turn, the large cable vibration gives a harmonic inertia force on the
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upper rivulet exhibits disorganized and out-of-phase movement.
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rivulet. When the cable is fixed, no harmonic inertia force is applied on the upper rivulet and the
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6 Conclusions
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In this study, an image processing method has been developed to measure the movement of the upper
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rivulet on cable surface during RWIV. A wind tunnel test was conducted to demonstrate the
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effectiveness of the proposed method. The following conclusions can be drawn:
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(1) For the first time, this study measured the rivulet movement along the entire cable. The distribution of the upper rivulet is found to be non-uniform even when the cable is suffering from large amplitude oscillation. The amplitude of rivulet oscillation is approximately similar along the cable.
(2) Under large RWIV, the oscillation of the upper rivulet is stable and the amplitude is relatively large (greater than 10° from the equilibrium position). The oscillation frequency is exactly the same as the fundamental frequency of the cable. The averaged upper rivulet oscillates almost in-phase with the cable vibration.
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(3) Because the digital video camera was installed away from the cable and rivulet, the non-contact, non-intrusive method has no disturbance on the formation and movement of the
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rivulet.
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(4) The quality of the image significantly affects the accuracy of the identified rivulet position. A high-speed and high-definition video camera is suggested during the test to obtain better
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results.
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Acknowledgements
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The study has been supported by the Research Grants Council of Hong Kong (No. PolyU 5298/11E).
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The experiment was conducted at Southwest Jiaotong University of China. The authors are grateful
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to Professor Hui Li of Harbin Institute of Technology for her valuable comments and suggestions.
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[25] I.J. Taylor, A.C. Robertson, Numerical simulation of the airflow- rivulet interaction associated with the rain-wind induced vibration phenomenon. J. Wind Eng. Ind. Aerodyn. 99 (2011) 931–944.
[26] J.H. Bi, J. Wang, Q. Shao, P. Lu, J. Guan, Q.B. Li, 2D numerical analysis on evolution of water film and cable vibration response subject to wind an drain, J. Wind Eng. Ind. Aerodyn. 121 (2013) 49–59. [27] J.J. Lee, M. Shinozuka, Real-time displacement measurement of a flexible bridge using digital image processing techniques, Exp. Mech. 46 (2006) 105–114.
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[28] G.L. Pankanin, A. Kulinczak, J. Berlinski, Investigations of karman vortex street using flow visualization and image processing, Sens. Actuators A 138 (2007) 366–375.
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[29] X.Q. Zhou, Y. Xia, Z.L. Wei, Q.X. Wu, A videogrammetric technique for measuring the
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vibration displacement of stay cables, Geo-spatial Information Science 15 (2012) 135-141.
[30] H.S. Choi, J.H. Cheung, S.H. Kim, J.H. Ahn, Structural dynamic displacement vision system
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using digital image processing, NDT & E Int. 44 (2011) 597–608.
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[31] Y.L. Li, W. Lu, Q.Y. Tao, W.B Xiong, Study on rain-wind induced vibration of cables in
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cable-stayed bridges by wind tunnel test, J. Exp. Fluid Mech. 21 (2007) 36–44. (in Chinese)
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Figure List Figure 1. An original image from the video clip
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Figure 2. The computational region of the image
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Figure 3. Discrete two-dimensional Gaussian function
Figure 5. Reference mesh established in images
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Figure 6. Definition of the upper rivulet position on cable
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Figure 4. An example of the algorithm
Figure 7. Open-jet wind tunnel
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Figure 8. The cable model in wind tunnel and definition of yaw angle
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Figure 10. Simulation of water rivulet
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Figure 9. Cable model
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Figure 11. Time history of the displacement of cable model (U=11 m/s) Figure 12. The upper rivulet position at different time when RWIV of the cable occurs Figure 13. Time history and PSD of identified upper rivulet position at S2 during RWIV (U=11 m/s) Figure 14. Time history and PSD of identified upper rivulet position at S9 during RWIV (U=11 m/s) Figure 15. Time history and PSD of the averaged upper rivulet position during RWIV (U=11 m/s) Figure 16. Time history of the displacement of cable model (U=14 m/s) Figure 17. Time history of the averaged upper rivulet position during RWIV (U=14 m/s)
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Figure 18. Time history and PSD of the upper rivulet position at S2 when cable is static Figure 19. Time history and PSD of the upper rivulet position at S9 when cable is static
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Figure 20. Time history and PSD of the averaged upper rivulet position when cable is static
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Neighborhood of reference point
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a0 =150 b0 =50
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Figure 6. Definition of the upper rivulet position on cable
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Figure 7. The open-jet wind tunnel
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Ca bl em
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Figure 8. The cable model in wind tunnel and definition of yaw angle
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80 mm
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Upper pipe
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0o S9
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Figure 14. Time history and PSD of identified upper rivulet position at S9 during RWIV (U=11 m/s)
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Yongle Li obtained his Bachelor of Engineering, Master of Philosophy and Doctor of Philosophy in Bridge Engineering from Southwest Jiaotong University in 1995, 1998 and 2003, respectively. He
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then worked at Southwest Jiaotong University. He has been a Professor in the Department of Bridge
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Engineering since 2007. His research areas include bridge aerodynamic, vehicle-bridge coupling
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vibration, and cable dynamics.
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Haiquan Jing graduated from Harbin Institute of Technology in 2012 with a Master degree in Engineering. He joined Department of Civil and Environmental Engineering at The Hong Kong
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Polytechnic University in 2012 as a Ph.D. research student. He is working on rain-wind induced
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cable vibration with numerical analysis and wind-tunnel experiments.
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Yong Xia obtained a Ph.D. in Engineering in 2002 from Nanyang Technological University. He then worked at the The University of Tokyo and The University of Western Australia. He joined Department of Civil and Environmental Engineering at The Hong Kong Polytechnic University in 2006 as an Assistant Professor and currently an Associate Professor. His research interests include structural dynamics and structural health monitoring.
You-Lin Xu received a Ph.D. in Engineering in 1992 from The University of Sydney, Australia. He joined Department of Civil and Environmental Engineering at The Hong Kong Polytechnic
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University in 1995 and was promoted to Chair Professor in Structural Engineering in 2003. His research areas include wind engineering, earthquake engineering, structural health monitoring,
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structural vibration control and smart structures. He is currently Dean of Faculty of Construction and
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Environment.
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Huoyue Xiang obtained a Ph.D. in Engineering in 2013 from Southwest Jiaotong University. He
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bridge wind engineering and vehicle aerodynamics.
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worked at the Southwest Jiaotong University in 2014 as lecturer. His research interests include
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Highlights: We developed an image processing method to measure the position of rivulets during RWIV. This method has no effect on the rivulet formation and wind flow field.
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For the first time, the rivulet along the entire cable is measured, and the distribution of the upper rivulet is found to be non-uniform.
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The averaged upper rivulet position is found oscillating almost in-phase with the cable vibration.
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S0924-4247(15)00163-6 http://dx.doi.org/doi:10.1016/j.sna.2015.03.040 SNA 9138
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
22-8-2014 27-3-2015 27-3-2015
Please cite this article as: Y. Li, H. Jing, Y. Xia, Y. Xu, H. Xiang, Measurement of rivulet movement on inclined cables during rain-wind induced vibration, Sensors and Actuators: A Physical (2015), http://dx.doi.org/10.1016/j.sna.2015.03.040 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Measurement of rivulet movement on inclined cables during rain-wind induced vibration
Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China
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Department of Bridge Engineering Southwest Jiaotong University, Chengdu, China
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Yongle Li1, Haiquan Jing2, Yong Xia2,, Youlin Xu2 and Huoyue Xiang1
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Abstract
The large amplitude vibration of stay cables has been observed in several cable-stayed bridges under
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the simultaneous occurrence of rain and wind, which is called rain-wind induced vibration (RWIV).
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During RWIV, the upper rivulet oscillating circumferentially on the inclined cable surface is widely
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considered to have an important role in this phenomenon. However, the small size of rivulets and
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high sensitivity to wind flow make the measurement of the rivulet movement challenging. This study proposes a digital image processing method to measure the rivulet movement in wind tunnel tests. RWIV of a cable model was excited during the test and a digital video camera was used to record the video clips of the rivulets, from which the time history of the rivulet movement along the entire cable is identified through image processing. The oscillation amplitude, equilibrium position, and dominant frequency of the upper rivulet are investigated. Results demonstrated that the proposed non-contact, non-intrusive measurement method is cost-effective and has good resolution in
Corresponding author. E-mail address: [email protected]; Tel: +852-27666066. 1
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measuring the rivulet vibration. Finally the rivulet vibration characteristics were also studied when the cable was fixed. Comparison demonstrates the relation between the upper rivulet and cable
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vibration.
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Key words: Cable; water rivulets; Rain-wind induced vibration; Image processing.
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1 Introduction
Stay cables may experience large vibration under support movements [1, 2] or rain and wind
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loadings [3]. Vibration of stay cables in some cable-stayed bridges have been observed under the
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simultaneous occurrence of rain and wind, which is referred to as rain-wind induced vibration
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(RWIV). Such a large amplitude vibration may cause severe damage, such as the reduction of the
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cable’s life, destruction of the connections, breakdown of the protection [3], and damage of the dampers [4]. Extensive research have been conducted to reveal the excitation mechanisms of RWIV through field measurements [5–8], wind tunnel tests [3, 9–15], and numerical analysis [16–21]. Most of researchers believe that the upper rivulet located on inclined cable surface plays the most important role in this kind of phenomenon. However, the excitation mechanisms of RWIV are still not fully understood given the limited information of the rivulet. The rivulet has become a crucial factor in understanding the RWIV of cables. Several researchers have investigated the rivulet on cables theoretically and numerically during past
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decades. For the first time, Lemaitre et al. [22, 23] proposed a lubrication theory-based numerical model to simulate the evolution of a water film around a cylinder under the action of wind. Taylor
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and Robertson [24, 25] developed a computational approach combining the discrete vortex method
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and lubrication theory to calculate the evolution and growth of rivulets on the cable surface when the cable with water film on surface is blown by wind. Bi et al. [26] derived 2D coupled equations of
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water film evolution, for the first time, by combining the lubrication theory and single-mode system
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vibration theory. The water film evolution, lift force and cable vibration were numerically investigated by solving the coupled equations.
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However, directly measuring the rivulet in field or laboratory is very difficult and challenging
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because the rivulet is small, thin, and sensitive to wind flow. To date, no measurement of rivulet has
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been conducted on-site and only few have been reported in wind tunnel tests. For example,
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Coesentino et al. [12, 13] measured the thickness of the upper rivulet ranging from 0.2 to 0.5 mm by using eight pairs of wires. Li et al. [14] employed an ultrasonic technique to investigate the shape, thickness, position, and movement of rivulets on an inclined cable model in a wind tunnel test. The thickness and mean width of the water rivulet were measured as approximately 0.5 mm and 7.96 mm, respectively. The lower rivulet was more or less fixed, whereas the upper rivulet oscillated around the circumferential direction of the cable at the same frequency of the cable model. In the study of Coesentino et al. [12], however, the wires on the surface could affect the formation and movement of the upper rivulet. As such, non-intrusive measurement technique could
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provide more reliable information. In the study of Li et al. [14], the material of the surface of the cable model differed from that of the real stay cable. Therefore the measured rivulets might differ
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from that formed on real cables as rivulets are very sensitive to the cable surface. In addition, the
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above two experiments measured the rivulet at a fixed section of the cable only. Distribution of the rivulet along the entire cable was not available.
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Under the circumstance, the non-contact digital image processing technique has potential to
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avoid the aforementioned disadvantages. The technique has advantages of the non-intrusion, non-destruction, multi–point measurement, high resolution, and cost-effectiveness. For these reasons,
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it has been applied to displacement measurement of civil structures. For example, Lee and Shinozuka
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[27] developed the method to measure the dynamic displacement of a flexible bridge. Pankanin et al.
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[28] applied it to quantitatively determine the geometric parameters of the Karman vortex street.
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Zhou et al. [29] used it to measure the cable vibration of a real cable-stayed bridge. Choi et al. [30] demonstrated the precision and cost-effectiveness of the digital image processing method in measuring structural dynamic displacement. In this paper, the digital image processing method is developed and applied to measure the position of the rivulet on real cable models. The large RWIV of the model was reproduced in a wind tunnel. Water rivulets were simulated by colored water. The movement of the upper rivulet on the cable model was recorded using a digital video camera. Through digital image processing, the time history of the upper rivulet vibration along the entire cable was obtained. During this test, the
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movement of the rivulet was not disturbed. Finally, the characteristics of the rivulet movement during RWIV were investigated. The results will help elucidate the excitation mechanism of RWIV
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of cables.
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2 Methodologies
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In this study, RWIVs are simulated in a wind tunnel. The water rivulets were simulated by real water, colored either in red or blue. Black marks were drawn on the cable surface as reference. These enable
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the rivulet more distinguishable from the cable. During the test, a digital video camera was installed
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at one end of the cable model and moved together with the cable (see Figure 8b). When the RWIV of
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the cable occurred, the rivulet moved in the circumferential direction relative to the cable, which was
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recorded by the camera. The video clips will then be processed via three steps, namely, image pre-processing, rivulet identification, and rivulet locating, to obtain the rivulet movement on the cable.
2.1 Image pre-processing
The recorded video clip is first converted into a series of images. The video camera used in this test captures 25 frames per second and each frame has 720 (height) × 1280 (width) pixels. The frames of
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the video clip are converted into a series of RGB images. RGB refers to the three hues of light (red, green, and blue) of each pixel, which arrange from 0 to 255 and can form any color by mixing
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together. For example, three intensities of 255 create the white color and three zeros present the black.
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The k-th image can be represented as a three-dimensional matrix I k with the size of 720×1280×3, which corresponds to the three RGB intensities of each pixel. These images are named as raw
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images.
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The raw images contain a big region irrelevant to the cable (see Figure 1). They are then cropped such that only the key area including the cable with rivulet remains. Consequently, the
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computational region in each image is reduced. To make sure the cable model located at the same
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position in all cropped images, one particular crossing point on the cable surface is chosen as the
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reference point in all images (see Figure 1). Its position in image k (or I k ) is set as (rk , ck ) , where
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rk and ck denote row and column numbers of the reference point, respectively. The reference point is identified by examining the neighborhood of the point, which is a 51×51 pixels square in this study (see Figure 1). In the first original image, the position of the reference point (r1 , c1 ) is defined by the user. The neighborhood is determined such that its center is located at (r1, c1 ) . The RGB of the neighborhood, denoted as R1 , is a three-dimensional matrix of 51×51×3. In the subsequent image, for example I k , a 51×51 pixels square marching R1 best is found and its center (rk , ck ) is the reference point of I k . That is,
(rk , ck ) (r , c) min R k R1
(1)
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where (2)
R k I k (r , c)51513
(3)
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R1 I 1 (r1 , c1 )51513
R1 is the RGB matrix of the neighborhood of the reference point in I 1 with the central point at
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( r1 , c1 ), and R k is the RGB matrix of a 51×51 pixels square in I k with the central point at (r , c) .
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When R k R1 reaches the minimum, the central point of R k (rk , ck ) will be identified as the
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reference point of I k .
After the reference point is identified, the identical computational region is determined in all
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images. In this study, the computational region is a 170 (height) × 650 (width) pixels rectangle. The
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upper-left corner of the image.
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reference points in all cropped images are located at (150, 50). The origin (1, 1) is located at the
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Subsequently, the contrast of the cropped images is enhanced with the histogram equalization method to make the rivulet more distinguishable. Finally, the cropped and enhanced RGB images are converted into a grayscale image, as shown in Figure 2. The three intensities (R, G and B) of each pixel in the RGB image are translated to one gray intensity in the grayscale image (gray intensity = 0.2989×R + 0.5870×G + 0.1140×B). The grayscale image, hereinafter, is referred to as the objective image, which is denoted by a two-dimensional matrix with the size of 170 (row) × 650 (column). Each item in the matrix represents the gray intensity of the pixel.
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2.2 Identifying rivulets in the images
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The objective image, a collection of 170×650 discrete pixels, is smoothed by the two-dimensional
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(2D) Gaussian filter. A Gaussian filter is a filter whose impulse response is a Gaussian function and thus efficient to filter out the noise with Gaussian distribution. Figure 3 shows a 2-D 5×5 discrete
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Gaussian kernel used in this study. The 170×650 matrix is convolved with the 5×5 Gaussian kernel,
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k k resulting in a new 170×650 matrix ( A0 ). A0 represents the gray intensity of the filtered image and
used to identify the position of the upper rivulet.
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The background of upper rivulet is slightly different in different objective images. To eliminate this effect, the background is removed by deducting the averaged values of the adjacent images as (4)
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Ak A0k avg ( A0k 10 , , A0k 10 )
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The background of 21 adjacent images (about one period of rivulet vibration) is averaged. Ak is the matrix after the background is removed and the items can be positive, negative, or zero. Given that the rivulets in the wind tunnel test have been colored in red or blue, the rivulet appear darker than others in the grayscale image (see Figure 2). Consequently, the corresponding items in matrixes Ak have smaller intensity. More water indicates smaller intensity. As the rivulet oscillates on the cable, the intensity of the rivulet in the present image ( Ak ) should be smaller than those of the same location in the previous ( Ak 1 ) and succeeding image ( Ak 1 ). Consequently, the rivulet location can be identified by the following two means under the ideal conditions: 1) to determine the determining minimal intensity in matrix Ak and 2) to find the maximal reduction of Ak from Ak 1 . However, 8
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we have observed that both are significantly affected by noise in practice. In this paper, we integrate the two approaches as the following steps:
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1) Calculate intensity change as Ak Ak Ak 1 ; k k 2) For each column j, the intensity is Aj and intensity change is Aj ;
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k 3) Obtain the local minimums of Aj ;
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4) If the local minimum has the large reduction from the previous image, the point is
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determined as the rivulet and the row number is the position of the rivulet; k 5) Otherwise, the global minimum of Aj is determined as the rivulet;
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6) Let j=j+1, until all columns are identified. The rivulet location at j-column of k-th image
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is denoted as RL(k , j ) .
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Figure 4 shows an example of a rivulet located in one column. Here, only rows 10 to 130 are
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illustrated because the rivulets are observed within this range in all images.
2.3 Locating rivulets on the cable surface
The rivulet position RL(k , j ) obtained in Step 2 is converted to the position on the cable surface. As shown in Figure 5, a virtual reference mesh is established on the cable surface. The distance of the reference mesh is 1 cm and 10 cm in the circumferential and longitudinal directions, respectively.
RL(k , j ) is the pixel number and converted to the physical position in this mesh. It is then
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converted to angle defined in Figure 6. The conversion is based on the relationship between the circumferential angle and reference mesh. In this regard, is the upper rivulet position measured
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from the top of the cable, and positive anti-clockwise.
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3 Wind tunnel test
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The proposed method is applied to a real cable in a wind tunnel test. A series of tests were conducted when the wind speed varied from 5 to 14 m/s, which aimed to ensure that RWIV can be realized.
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Large amplitude RWIV was successfully excited at wind speed of 11 m/s. During the experiment, the
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rivulet was recorded using a digital camera (JVC HD30AC) with 720 (height) × 1280 (width) pixels
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and 25 frames per second. The cable displacement was measured by two laser sensors with the
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resolution of 100μm and the sample frequency of 512 Hz.
3.1 Wind tunnel
The wind tunnel test was conducted at Southwest Jiaotong University, Sichuan Province, China. The wind tunnel is an open-jet wind tunnel with the outlet of 1.34 m wide and 1.54 m high (Figure 7). The cable model was suspended by especially designed springs at both ends, as shown in Figure 8(a). The design allows the model to freely oscillate in the cross-wind and along-wind directions. Previous 10
Page 10 of 46
studies show that RWIV is prone to occur when the inclination angle and yaw angle range from 20° to 50° and from 20° to 60°, respectively [31]. In this study, the cable model was installed with an
ip t
inclination angle of 32° and yaw angle of 35°. RWIVs under similar configurations have been
cr
successfully reproduced in wind tunnel tests [3, 31] and observed in field measurement [6, 7]. The
is defined as
an
sin1 (sin cos )
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definition of inclination angle α and yaw angle β are shown in Figure 8(b). The relative yaw angle β*
(6)
Ac ce p
te
3.2 Cable model
d
M
which is calculated as 29.1°. It represents the angle between the wind direction and the cable axis.
The cable model shown in Figure 9(a) is made of steel tube coated by polyethylene tube, which is the same as the real stay cables. The cutaway view is shown in Figure 9(b). The cable model is 160 mm in diameter and 2.7 m in length. The test segment is the middle 2-meter segment and was placed in the flow field during the test. The transition segments of the two ends were placed at the edge of the wind field. The mass of the entire cable model is 66.0 kg and the fundamental frequency is measured as 1.27 Hz. The damping ratio is 0.24%, resulting in the corresponding Scruton number
Sc
m =4.26. D2
11
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ip t
3.3 Simulation of water rivulets
In the wind tunnel test, two small flexible plastic pipes were installed at the top transition segment of
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the model to guide two colored water-lines—one at the upper surface and the other at the lower
us
(Figure 10(a)). These two water-lines can run from the top end to the bottom by the action of gravity,
an
inertia, and wind pressure, simulating the upper and lower water rivulets, respectively. Figure 10(b) shows an upper water rivulet simulated with the approach. The effectiveness of this simulation has
M
been verified to be the same as spraying water on the cable surface directly [31]. That test was
d
conducted at the same wind tunnel with the cable model of almost the same configuration (D=160
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mm, α=30°, and β=35°). In the previous and present tests, the upper rivulet was observed similarly
Ac ce p
oscillating in the circumferential direction while the lower rivulet was always static during RWIV, as reported by other researchers [3, 5, 14].
3.4. Digital video camera setup
A digital video camera was installed at the bottom end of the cable model (see Figure 8(b)). It was 1.2 m above the cable model approximately and moved with the cable together during RWIV. Given that the digital camera is out of the flow field and the distance between the camera and cable is far 12
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enough, the equipment has no effect on the formation and movement of the upper rivulet. The recorded rivulet is thus considered as undisturbed. The lower rivulet was observed to be static and its
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effect on the cable vibration can be ignored. Consequently, only the upper rivulet was recorded in the
an
4 Movement of the upper rivulet during RWIV
us
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test.
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Two laser sensors were installed at one end of the cable model to measure the cross-wind (perpendicular to cable axis) and along-wind (horizontal) displacement of the cable. As no horizontal
te
d
movement has been observed, only the cross-wind displacement is presented in this paper and downward is set to be positive. Figure 11 shows the time history of the cable displacement under the
Ac ce p
wind speed of 11 m/s. The cable vibrated at the amplitude of 50 mm with a frequency of 1.27 Hz, equal to the fundamental frequency of the model. The movement of the upper rivulet is obtained using the proposed image processing method during the large RWIV (a video clip can be downloaded from the supplementary material in the Web). Figure 12 shows examples of the captured upper rivulet at several time instants. The cable is divided into 15 segments (S1 to S15) in the longitudinal direction, each 5 cm long. It shows that the upper rivulet distribution along the cable is not uniform. The maximum difference between different sections at the same instant can be as large as 20°. 13
Page 13 of 46
Figure 13 shows the time history and power spectral density (PSD) of the upper rivulet position at segment 2 (S2). Similarly, Figure 14 shows those results at S9. The five time instants (t1 to t5) in
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figures 13 and 14 correspond to the five instants in Figure 12. The upper rivulet periodically
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oscillates between 15° and 40° with the frequency of 1.27 Hz, same as the cable fundamental frequency. Therefore, the oscillation of the upper rivulet on the cable is regular, and the amplitude is
us
large and stable. Nevertheless, the rivulets on the two segments are different in phase, which is
an
evidenced from Figure 12.
To better understand the rivulet movement during RWIV, the position of the rivulet along the
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entire cable is averaged over 15 segments and shown in Figure 15. The averaged rivulet position
d
oscillates between 18° and 36°, with the equilibrium position at 27°. It is smoother and closer to a
te
sinusoid as compared with those on one segment. Again, the dominant frequency of the averaged
Ac ce p
rivulet position is equal to the cable fundamental frequency, which is consistent with previous researches [12, 14] but with different vibration amplitude. For example, Coesentino et al. [12] measured the upper rivulet oscillating between 13° and 25°. Li et al. [14] reported that the upper rivulet oscillated around the equilibrium position of 35.7° (using this angle definition) with the standard deviation of 7°. The discrepancies are probably caused by the different configuration of the cable model used and different wind speed in the wind tunnels. Comparison between Figures 15(b) and 11(b) reveals that the upper rivulet oscillation is almost in-phase with the cable vibration, whereas the former is noisier than that the latter. Similar results have been observed when the wind
14
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speed is 10 m/s to 14 m/s. Figure 16 shows the time history of the cable displacement under the wind speed of 14 m/s and Figure 17 the coinstantaneous time history of the averaged upper rivulet. In that
between 17° and 38°, both at the frequency of 1.27 Hz.
an
us
5 Movement of the upper rivulet when the cable is static
cr
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case, the cable oscillated at the amplitude of 45 mm approximately and the upper rivulet vibrated
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For comparison purpose, the stationary cable with two ends fixed was also tested in the wind tunnel.
d
The movement of the upper rivulet was recorded and identified similarly. Figures 17 and 18 show the
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upper rivulet vibration on segments 2 (S2) and 9 (S9), respectively, when the wind speed was 11 m/s.
Ac ce p
In the two figures, the upper rivulet vibration is not periodic. There is no dominant frequency in the PSDs. The time history and PSD of the averaged rivulet position are shown in Figure 19. The averaged rivulet position moves between 22° and 32° non-periodically, with the equilibrium position at 27.4°. The PSD shows that the rivulet vibration is like a wide band random process, which differs from the harmonic vibration when the RWIV of cable is excited.
This observation demonstrates that the RWIV and the upper rivulet movement are closely associated with each other. The large RWIV of the cable may assist the formation and stable vibration of the upper rivulet along the cable, and vice versa. When the upper rivulet is
15
Page 15 of 46
homogeneously and stably oscillating on the cable surface, the rivulet generates harmonic loads along the cable in-phase, causing a strong resultant force on the cable. As a consequence, large cable
ip t
vibration can be excited. In turn, the large cable vibration gives a harmonic inertia force on the
us
upper rivulet exhibits disorganized and out-of-phase movement.
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rivulet. When the cable is fixed, no harmonic inertia force is applied on the upper rivulet and the
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6 Conclusions
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In this study, an image processing method has been developed to measure the movement of the upper
d
rivulet on cable surface during RWIV. A wind tunnel test was conducted to demonstrate the
te
effectiveness of the proposed method. The following conclusions can be drawn:
Ac ce p
(1) For the first time, this study measured the rivulet movement along the entire cable. The distribution of the upper rivulet is found to be non-uniform even when the cable is suffering from large amplitude oscillation. The amplitude of rivulet oscillation is approximately similar along the cable.
(2) Under large RWIV, the oscillation of the upper rivulet is stable and the amplitude is relatively large (greater than 10° from the equilibrium position). The oscillation frequency is exactly the same as the fundamental frequency of the cable. The averaged upper rivulet oscillates almost in-phase with the cable vibration.
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(3) Because the digital video camera was installed away from the cable and rivulet, the non-contact, non-intrusive method has no disturbance on the formation and movement of the
ip t
rivulet.
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(4) The quality of the image significantly affects the accuracy of the identified rivulet position. A high-speed and high-definition video camera is suggested during the test to obtain better
an
us
results.
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Acknowledgements
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The study has been supported by the Research Grants Council of Hong Kong (No. PolyU 5298/11E).
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The experiment was conducted at Southwest Jiaotong University of China. The authors are grateful
Ac ce p
to Professor Hui Li of Harbin Institute of Technology for her valuable comments and suggestions.
References
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cable-stayed bridges and its mitigation, J. Wind Eng. Ind. Aerodyn. 93 (2005) 79–95. [4] M. Matsumoto, H. Shirato, T. Yagi, M. Goto, S. Sakai, J. Ohya, Field observation of the
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full-scale wind-induced cable vibration, J. Wind Eng. Ind. Aerodyn. 91 (2003) 13–26.
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[5] Y. Hikami, N. Shiraishi, Rain-wind induced vibrations of cables stayed bridges, J. Wind Eng. Ind. Aerodyn. 29 (1988), 408–418.
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[6] J.A. Main, N.P. Jones, H. Yamaguchi, Characterization of rain-wind induced stay-cable
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[7] Y.Q. Ni, X.Y. Wang, Z.Q. Chen, J.M. Ko, Field observations of rain-wind-induced cable
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vibration in cable-stayed Dongting Lake Bridge, J. Wind Eng. Ind. Aerodyn. 95 (2007)
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[8] D. Zuo, N.P. Jones, J.A. Main, Field observation of vortex- and rain-wind-induced stay-cable vibrations in a three-dimensional environment, J. Wind Eng. Ind. Aerodyn. 96 (2008) 1124–1133.
[9] M. Matsumoto, N. Shiraishi,H. Shirato, Rain-wind induced vibration of cables of cable-stayed bridges, J. Wind Eng. Ind. Aerodyn. 43 (1992) 2011–2022. [10] M. Matsumoto, T. Saitoh, M. Kitazawa, H. Shirato, T. Nishizaki, Response characteristics of rain-wind induced vibration of stay-cables of cable-stayed bridges, J. Wind Eng. Ind. Aerodyn. 57 (1995) 323–333.
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[11] M. Gu, On wind–rain induced vibration of cables of cable-stayed bridges based on quasi-steady assumption, J. Wind Eng. Ind. Aerodyn. 97 (2009) 381–391.
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[12] N. Cosentino, O. Flamand, C. Ceccoli, Rain-wind induced vibration of inclined stay cables, Part
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I: experimental investigation and physical explanation, Wind and Structures 6 (2003), 471–484. [13] N. Cosentino, O. Flamand, C. Ceccoli, Rain–wind induced vibration of inclined stay cables, part
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[14] F.C. Li, W.L. Chen, H. Li, R. Zhang, An ultrasonic transmission thickness measurement system
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for study of water rivulets characteristics of stay cables suffering from wind-rain-induced
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vibration, Sens. Actuators A 159 (2010) 12–23.
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[15] W.L. Chen, S.R. Tang, H. Li, H. Hu, Influence of dynamic properties and position of rivulet on
Ac ce p
rain-wind-induced vibration of stay cables, J. Bridge Eng., 18 (2013), 1021–1031. [16] H. Yamaguchi, Analytical study on growth mechanism of rain vibration of cables, J. Wind Eng. Ind. Aerodyn. 33 (1990) 73–80.
[17] K. Wilde, W. Witkowski, Simple model of rain–wind-induced vibrations of stayed cables, J. Wind Eng. Ind. Aerodyn. 91 (2003) 873–891. [18] D.Q. Cao, R.W. Tucker, C.Wang, A stochastic approach to cable dynamics with moving rivulets. J. Sound Vib. 268 (2003) 291–304. [19] U. Peil, N. Nahrath, Modeling of rain-wind induced vibrations, Wind Struct. 6 (2003) 41–52.
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[20] Y.L. Xu, L.Y. Wang, Analytical study of wind–rain-induced cable vibration, J. Wind Eng. Ind. Aerodyn. 91 (2003) 27–40.
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[21] L.Y. Wang, Y.L. Xu, Analytical study of wind-rain-induced cable vibration : 2DOF model, Wind
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Struct. 6 (2003) 291–306.
[22] C. Lemaitre, P. Hémon, E. de Langre, Thin water film around a cable subject to wind, J. Wind
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Eng. Ind. Aerodyn. 95 (2007) 1259–1271.
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[23] C. Lemaitre, E. de Langre, P. Hémon, Rainwater rivulets running on a stay cable subject to wind. Eur. J. Mech. B 29 (2010) 251–258.
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[24] A.C. Robertson, I.J. Taylor, S.K. Wilson, B.R. Duffy, J.M. Sullivan, Numerical simulation of
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rivulet evolution on a horizontal cable subject to an external aerodynamic field, J. Fluid Struct.
Ac ce p
[25] I.J. Taylor, A.C. Robertson, Numerical simulation of the airflow- rivulet interaction associated with the rain-wind induced vibration phenomenon. J. Wind Eng. Ind. Aerodyn. 99 (2011) 931–944.
[26] J.H. Bi, J. Wang, Q. Shao, P. Lu, J. Guan, Q.B. Li, 2D numerical analysis on evolution of water film and cable vibration response subject to wind an drain, J. Wind Eng. Ind. Aerodyn. 121 (2013) 49–59. [27] J.J. Lee, M. Shinozuka, Real-time displacement measurement of a flexible bridge using digital image processing techniques, Exp. Mech. 46 (2006) 105–114.
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[28] G.L. Pankanin, A. Kulinczak, J. Berlinski, Investigations of karman vortex street using flow visualization and image processing, Sens. Actuators A 138 (2007) 366–375.
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[29] X.Q. Zhou, Y. Xia, Z.L. Wei, Q.X. Wu, A videogrammetric technique for measuring the
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vibration displacement of stay cables, Geo-spatial Information Science 15 (2012) 135-141.
[30] H.S. Choi, J.H. Cheung, S.H. Kim, J.H. Ahn, Structural dynamic displacement vision system
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using digital image processing, NDT & E Int. 44 (2011) 597–608.
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[31] Y.L. Li, W. Lu, Q.Y. Tao, W.B Xiong, Study on rain-wind induced vibration of cables in
Ac ce p
te
d
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cable-stayed bridges by wind tunnel test, J. Exp. Fluid Mech. 21 (2007) 36–44. (in Chinese)
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Figure List Figure 1. An original image from the video clip
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Figure 2. The computational region of the image
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Figure 3. Discrete two-dimensional Gaussian function
Figure 5. Reference mesh established in images
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Figure 6. Definition of the upper rivulet position on cable
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Figure 4. An example of the algorithm
Figure 7. Open-jet wind tunnel
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Figure 8. The cable model in wind tunnel and definition of yaw angle
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Figure 10. Simulation of water rivulet
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Figure 9. Cable model
Ac ce p
Figure 11. Time history of the displacement of cable model (U=11 m/s) Figure 12. The upper rivulet position at different time when RWIV of the cable occurs Figure 13. Time history and PSD of identified upper rivulet position at S2 during RWIV (U=11 m/s) Figure 14. Time history and PSD of identified upper rivulet position at S9 during RWIV (U=11 m/s) Figure 15. Time history and PSD of the averaged upper rivulet position during RWIV (U=11 m/s) Figure 16. Time history of the displacement of cable model (U=14 m/s) Figure 17. Time history of the averaged upper rivulet position during RWIV (U=14 m/s)
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Figure 18. Time history and PSD of the upper rivulet position at S2 when cable is static Figure 19. Time history and PSD of the upper rivulet position at S9 when cable is static
Ac ce p
te
d
M
an
us
cr
ip t
Figure 20. Time history and PSD of the averaged upper rivulet position when cable is static
23
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ip t
Neighborhood of reference point
us
cr
Reference point
Rivulet
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Computational region
Ac ce p
te
d
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Figure 1. An original image from the video clip
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ip t
a0 =150 b0 =50
b1 =600
Rivulet
a1 =20
cr
Reference point
Ac ce p
te
d
M
an
us
Figure 2. The computational region of the image
25
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4
1
4
20 33 20
4
7
33 55 33
7
4
20 33 20
4
1
4
1
7
4
ip t
7
us
331
4
cr
1
1
Ac ce p
te
d
M
an
Figure 3. Discrete two-dimensional Gaussian function
26
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20
40
20
40
us
-20 60 80 100 Row number
120
an
0 -20 -40
ip t cr
0
-40 20
Rivulet location
lmin
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Rivulet location
20
60 80 100 Row number
120
Ac ce p
te
d
Figure 4. An example of the algorithm
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ip t cr
Ac ce p
te
d
M
an
us
Figure 5. Reference mesh established in images
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ip t
Rivulet
us
cr
Wind flow
an
Cable
Ac ce p
te
d
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Figure 6. Definition of the upper rivulet position on cable
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ip t cr us
Ac ce p
te
d
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an
Figure 7. The open-jet wind tunnel
30
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Ca bl em
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*
od el
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Wind flow
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b)
an
a)
Ac ce p
te
d
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Figure 8. The cable model in wind tunnel and definition of yaw angle
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ip t
80 mm
PE coat
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cr
68 mm
Steel tube
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(a) Cross-section view 350 mm
350 mm
Test segment
Transition segment
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Transition segment
2000 mm
d
(b) Cutaway view
Ac ce p
te
Figure 9. Cable model
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ip t
Upper pipe
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Wind flow
an
us
Lower pipe
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(a)
Upper rivulet
(b)
Ac ce p
te
d
Figure 10. Simulation of water rivulet
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us
cr
ip t 20 30 Time (s)
an
10
) 50 m m ( t ne 0 m ec a pl -50 si D 24
40
24.5
25 25.5 Time (s)
26
26.5
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) 50 m m ( t ne 0 m ec a pl -50 si D 0
Ac ce p
te
d
Figure 11. Time history of the displacement of cable model (U=11 m/s)
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0o S9
S3
(a) At 24.88s (t1)
us
43o
S15
cr
S2
S1
ip t
43o
S2
S1
S9
S15
S9
S15
S9
S15
S9
S15
an
0o S3
M
(b) At 25.08s (t2) 43o
0o S2
S3
d
S1
Ac ce p
43o
te
(c) At 25.28s (t3)
0o
S1
S2
S3
(d) At 25.48s (t4)
43o
0o
S1
S2
S3
(e) At 25.68s (t5) Figure 12. The upper rivulet position at different time when RWIV of the cable occurs
35
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30 20 10
20 Time (s)
30
40
ip t
25 25.5 Time (s)
26
26.5
(b) Detailed time history
400
200
d
f=1.27 Hz 300
te
PSD-Rivulet position
24.5
M
(a) Time history
t4
t3
10 24
an
10 0
t2
30 20
t5
t1
40
cr
40
50
us
50
Rivulet location (Deg)
) g e D ( n oi act ol etl u vi R
Ac ce p
100
0 0
2
4 6 8 Frequency (Hz)
10
12
(c) PSD
Figure 13. Time history and PSD of identified upper rivulet position at S2 during RWIV (U=11 m/s)
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20 10 0
10
20 Time (s)
30
40
t3
20 10 24
t4
24.5
25 25.5 Time (s)
26
26.5
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f=1.27 Hz
300
d
200
te
PSD-Rivulet position
t2
30
(b) Detailed time history
400
100
t5
an
(a) Time history
ip t
30
t1
40
cr
40
50
us
50
Rivulet location (Deg)
) g e D ( n oi act ol etl u vi R
Ac ce p
0 0
2
4 6 8 Frequency (Hz)
10
12
(c) PSD
Figure 14. Time history and PSD of identified upper rivulet position at S9 during RWIV (U=11 m/s)
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20 Time (s)
30
40
ip t cr 25 25.5 Time (s)
26
26.5
(b) Detailed time history
250
f=1.27 Hz
d
200
te
PSD-rivulet position
24.5
M
(a) Time history
150
us
10
40 ) g e D ( 30 n oi t si o p 20 etl u vi R 1024
an
40 ) g e D ( 30 n oi t si o p 20 etl u vi R 100
100
Ac ce p
50
0 0
2
4 6 8 Frequency (Hz)
10
12
(c) PSD
Figure 15. Time history and PSD of the averaged upper rivulet position during RWIV (U=11 m/s)
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) m m ( t ne m ec a pl si D
0
-50 10
20 Time (s)
30
40
0
-50 20
20.5
21 21.5 Time (s)
22
22.5
us
0
50
ip t
50
cr
) m m ( t ne m ec a pl si D
Ac ce p
te
d
M
an
Figure 16. Time history of the displacement of cable model (U=14 m/s)
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30
20
10 0
10
20 Time (s)
30
40
35 30 25
cr
) g e D ( n oi act ol etl u vi R
20 15 20
us
) g e D ( n oi act ol etl u vi R
ip t
40
40
20.5
21 21.5 Time (s)
22
22.5
Ac ce p
te
d
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an
Figure 17. Time history of the averaged upper rivulet position during RWIV (U=14 m/s)
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30
20
10 0
10
20 Time (s)
30
10
5
0 0
40
cr
n oi act ol etl u vi RD S P
us
) g e D ( n oi t si o p etl u vi R
ip t
15
40
2
4 6 8 Frequency (Hz)
10
12
Ac ce p
te
d
M
an
Figure 18. Time history and PSD of the upper rivulet position at S2 when cable is static
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30
20
10 0
10
20 Time (s)
30
10
5
0 0
40
cr
n oi act ol etl u vi RD S P
us
) g e D ( n oi t si o p etl u vi R
ip t
15
40
2
4 6 8 Frequency (Hz)
10
12
Ac ce p
te
d
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an
Figure 19. Time history and PSD of the upper rivulet position at S9 when cable is static
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30
20
10 0
10
20 Time (s)
30
2
1
0 0
40
cr
n oi act ol etl u vi RD S P
us
) g e D ( n oi t si o p etl u vi R
ip t
3
40
2
4 6 8 Frequency (Hz)
10
12
Ac ce p
te
d
M
an
Figure 20. Time history and PSD of the upper rivulet average position when cable is static
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Yongle Li obtained his Bachelor of Engineering, Master of Philosophy and Doctor of Philosophy in Bridge Engineering from Southwest Jiaotong University in 1995, 1998 and 2003, respectively. He
ip t
then worked at Southwest Jiaotong University. He has been a Professor in the Department of Bridge
cr
Engineering since 2007. His research areas include bridge aerodynamic, vehicle-bridge coupling
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vibration, and cable dynamics.
an
Haiquan Jing graduated from Harbin Institute of Technology in 2012 with a Master degree in Engineering. He joined Department of Civil and Environmental Engineering at The Hong Kong
M
Polytechnic University in 2012 as a Ph.D. research student. He is working on rain-wind induced
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d
cable vibration with numerical analysis and wind-tunnel experiments.
Ac ce p
Yong Xia obtained a Ph.D. in Engineering in 2002 from Nanyang Technological University. He then worked at the The University of Tokyo and The University of Western Australia. He joined Department of Civil and Environmental Engineering at The Hong Kong Polytechnic University in 2006 as an Assistant Professor and currently an Associate Professor. His research interests include structural dynamics and structural health monitoring.
You-Lin Xu received a Ph.D. in Engineering in 1992 from The University of Sydney, Australia. He joined Department of Civil and Environmental Engineering at The Hong Kong Polytechnic
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University in 1995 and was promoted to Chair Professor in Structural Engineering in 2003. His research areas include wind engineering, earthquake engineering, structural health monitoring,
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structural vibration control and smart structures. He is currently Dean of Faculty of Construction and
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Environment.
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Huoyue Xiang obtained a Ph.D. in Engineering in 2013 from Southwest Jiaotong University. He
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te
d
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bridge wind engineering and vehicle aerodynamics.
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worked at the Southwest Jiaotong University in 2014 as lecturer. His research interests include
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Highlights: We developed an image processing method to measure the position of rivulets during RWIV. This method has no effect on the rivulet formation and wind flow field.
ip t
For the first time, the rivulet along the entire cable is measured, and the distribution of the upper rivulet is found to be non-uniform.
Ac ce p
te
d
M
an
us
cr
The averaged upper rivulet position is found oscillating almost in-phase with the cable vibration.
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