The goal of the protocol is to enable visualization of the detailed flow fields and determination of the near-boundary shear and normal stresses within an equilibrium scour hole induced by a vibrating pipeline.
An experimental method is presented in this paper to facilitate visualization of the detailed flow fields and determination of the near-boundary shear and normal stresses within an equilibrium scour hole induced by a vibrating pipeline. This method involves the implementation of a pipeline vibration system in a straight flume, a time-resolved particle image velocimetry (PIV) system for pipeline displacement tracking and flow fields measurements. The displacement time-series of the vibrating pipeline are obtained by using the cross-correlation algorithms. The steps for processing raw particle laden images obtained by using the time-resolved PIV are described. The detailed instantaneous flow fields around the vibrating pipeline at different vibrating phases are calculated by using a multiple-time-interval cross-correlation algorithm to avoid displacement bias error in the flow regions with a large velocity gradient. By applying the wavelet transform technique, the captured images that have the same vibrating phase are accurately cataloged before the phase-averaged velocity fields are obtained. The key advantages of the flow measurement technique described in this paper are that it has a very high temporal and spatial resolution and can be simultaneously used to obtain the pipeline dynamics, flow fields, and near-boundary flow stresses. By using this technique, more in-depth studies of the 2-dimensional flow field in a complex environment, such as that around a vibrating pipeline, can be conducted to better understand the associated sophisticated scour mechanism.
Subsea pipelines are widely used in offshore environments for the purpose of fluid or hydro-carbon products conveyance. When a pipeline is placed on an erodible seabed, a scour hole around the pipeline is likely to form because of the waves, currents or dynamic motions of the pipeline itself (forced-vibration or vortex-induced-vibration)1,2. To improve the understanding of the scour mechanism around a subsea pipeline, measurements of the turbulent flow fields and estimations of the bed shear and normal stresses within the pipeline-fluid-seabed interaction region are essential in addition to measurements of the scour hole dimension1,2,3,4,5,6,7. In an environment where the bed shear and normal stresses are extremely difficult to be determined because the flow field is unsteady and the bottom boundary is rough, measured instantaneous near-boundary stresses (at approximately 2 mm above the boundary) could be used as their surrogate8,9. In the past few decades, scour around a vibrating pipeline has been studied and published without quantitatively presenting the values of the sophisticated flow fields around the pipeline within the scour hole3,4,5,10,11,12,13,14,15,16,17,18. Therefore, the goal of this method paper is to provide a novel experimental protocol for visualizing the detailed flow fields and to determine the near-boundary shear and normal stresses within an equilibrium scour hole induced by a forced vibrating pipeline. It should be noted that the pipeline-fluid-seabed interaction process in this study is in a quiescent water environment rather than those with unidirectional currents and waves.
This experimental method consists of two important components, namely, (1) simulation of pipeline (forced) vibrations; and (2) measurements of the flow fields around the pipeline. In the first component, the vibrating pipeline was simulated in an experimental flume by using a vibrating system, which has a servo motor, two connecting springs, and pipeline supporting frames. Different vibration frequencies and amplitudes can be simulated by adjusting the motor speed and location of the connecting springs. In the second component, the time-resolved particle image velocimetry (PIV) and wavelet transform techniques were adopted to obtain high temporal and spatial resolution flow field data at different pipeline vibration phases. The time-resolved PIV system consists of a continuous wave laser, a high-speed camera, seeding particles, and cross-correlation algorithms. Although PIV techniques have been widely used in obtaining steady turbulent flow fields19,20,21,22,23,24,25, applications in complex unsteady flow field conditions, such as cases of pipeline-fluids-seabed interaction, are relatively limited8,9,26,27. The reason probably is because traditional single-time-interval cross-correlation algorithm of PIV techniques is unable to accurately capture the flow features in unsteady flow fields where a relatively high velocity gradient is present9,20. The method described in this paper can solve this problem by using the multiple-time-interval cross-correlation algorithm9,28.
1. Laboratory safety check
2. Flume and seabed model setup
3. Pipeline model and vibration system setup
4. PIV setup
5. Experimental setup optimization and calibration
6. Running the experiment and data collection
7. Data processing
An example of the comparison between the raw image and processed image of the pipeline displacements tracking and instantaneous velocity calculation is shown in Figure 3. As shown in Figure 3b, the seeding particles and noise in the raw image are filtered out and the shining pipeline edge is retained to obtain the displacement time series. As shown in Figures 3c, light scatters/reflections around the seeding particles, pipeline edge and seabed surface are filtered out by the Laplacian filter. An example of the displacement time-series of the vibrating pipeline is shown in Figure 4. The vibration of the pipeline is almost sinusoidal, and the vibrating frequency and amplitude are 0.3 Hz and ~50 mm, respectively.
Figure 6 shows an example of the image of the quasi-equilibrium scour profile and vibrating pipeline at t = 1440 min, in which the origin of the coordinate (x–O–y) of this study is set at the intersection point of the original seabed surface and the pipeline vertical centerline. As shown in Figure 6, in addition to the seeding particles, very few suspended sediment particles can be observed in the flow; therefore, the raw image quality was not compromised. This also indicates that a quasi-equilibrium stage was reached for the pipeline scour process.
Examples of the visualized phase-averaged velocity field and vorticity dynamics are shown in Figure 7. It should be noted that because of the shadow of the pipeline during the PIV measurements, the region on the left side of the pipeline has no data (see subplots in Figure 7). As seen in Figure 7, nine discrete phases of the flow field within one cycle of vibration are presented. During the pipeline falling phases (0 ≤ t0/T < 0.5, where T is the vibration period and t0 is the time varies from 0 to T), a pair of vortices with symmetrical patterns is generated from the shear layers on both sides of the vibrating pipeline. Immediately after the pipeline has reached the scour trench bottom (t0/T = 4/8), the counter-clockwise vortex is distorted and sucked into the scour trench as the pipeline rises from the seabed. For the period of the pipeline ascending phases (0.5 ≤ t0/T < 1), another pair of vortices with opposite rotating directions to those in the descending phase is symmetrically generated around the top edge of the pipeline. For a better observation of the flow dynamics in Figure 7, a corresponding video (Video 1) made of 72 phases (frames) of flow fields for one cycle of pipeline vibration is provided.
An example of the near-boundary shear stresses, Ts and normal stresses, Tn evolution along the scour profile within one vibrating cycle is presented in Figure 8. Since the flow field is symmetrical about the y axis, the near-boundary shear stresses and normal stresses presented in this study are confined to the right half of the scour profile (0 < x < 5). As shown in Figure 8, these two stresses are normalized by the value of the critical bed shear stress, Tc (obtained from Shields' curve as 0.243 Pa) of the sand particles on a plane bed condition. The absolute values of Ts and Tn within the scour trench and beneath the vibrating pipeline increase significantly when the pipeline is falling to the bed or ascending from the bed. The regions where Ts and Tn exhibit the maximum and minimum values are consistent with the evolution of flow fields between the vibrating pipeline and scour boundary as shown in Figure 7.
Figure 1: Schematic of the experimental flume. Please click here to view a larger version of this figure.
Figure 2: Schematic of the pipeline model and vibration system set-up. (a) Section view, (b) Side view. This figure has been modified from8. Please click here to view a larger version of this figure.
Figure 3: Example of the comparison between raw and processed images. (a) the raw image, (b) the processed image for pipeline displacements tracking, and (c) the processed image for instantaneous velocity calculation. Please click here to view a larger version of this figure.
Figure 4: Example of the displacement time-series of vibrating pipeline at t = 1440 min. Please click here to view a larger version of this figure.
Figure 5: Comparison between single-time and multi-time interval cross-correlation algorithm. This figure is reproduced from9. Please click here to view a larger version of this figure.
Figure 6: Example image of the quasi-equilibrium scour profile at t = 1440 min. Please click here to view a larger version of this figure.
Figure 7: Examples of visualized phase-averaged velocity field and vorticity dynamics. This figure is reproduced from8. Please click here to view a larger version of this figure.
Figure 8: Example of evolutions of ts and tn along the scour profile within one vibrating cycle. The touchdown and liftoff times refer to the times when the bottom of the pipeline just touches and rises from the scour hole boundary, respectively. This figure is reproduced from8. Please click here to view a larger version of this figure.
Video 1: Flow field evolution around the vibrating pipeline within the equilibrium scour hole. The video is made from 72 phases (frames) of flow fields for one cycle of pipeline vibration. This video is reproduced from8. Please click here to view this video. (Right-click to download.)
The protocol presented in this paper describes a method for visualization of the two-dimensional flow fields and determination of the near-boundary flow stress fields around a forced vibrating pipeline in an equilibrium scour hole by using the PIV techniques. Since the designed pipeline motion is one-dimensional along the y direction, preparing and adjusting the pipeline model and vibration system to fulfill this objective are critical prerequisites for a successful outcome. Any undesirable motions of the pipeline along the x direction may induce asymmetrical flow fields and scour hole formation around the vibrating pipeline. Besides the apparatus effects, the selection of vibration frequency and amplitude of the pipeline for the experiments is also important for inducing a symmetrical flow field around the pipeline. In fact, in a quiescent water condition, Lin et al.31 showed that the structure of flow recirculation behind an impulsively started circular cylinder can maintain its symmetry when the non-dimensional time TD = tDUD/D < 5, where tD = cylinder moving time; and UD = cylinder speed. For the condition when TD > 5, the oblique vortex shedding may occur around the cylinder. In this study, the maximum pipeline speed can be estimated as 2π ƒ • A0, and the cylinder moving time can be taken as 1/2 ƒ, thus the maximum non-dimensional time TD = π A0/D = 4.48.
During the PIV setup stage, the laser sheet and camera adjustments and the seeding particle selection are the critical protocol steps for obtaining high quality flow field data. The camera shooting direction must be perpendicular to the laser sheet, otherwise, perspective distortions will be shown in the captured images. As this method aims to obtain the near-boundary flow stresses in an unsteady flow field, the intensity of the laser and the position of the field-of-view should be properly set to avoid strong light reflection of the boundary. The chosen seeding particles need to effectively scatter the illuminating laser sheet and be able to follow the flow streamlines without excessive settlement20. Based on this consideration, the seeding particles used in this study were aluminum powders, whose settling velocity was estimated to be 92.6 μm/s using Stoke's law. This settling velocity is negligible compared to the flow velocities (0.1-0.2 m/s) near the vibrating pipeline. To optimize the experimental setup, verifying the focus of the camera and determining the camera sampling rate are also crucial steps for reliable measurements.
For the data process stage, there are two challenges for obtaining high quality phase-averaged flow fields and near-boundary flow stresses: (1) accurately calculate the instantaneous flow fields and avoid the displacement bias error in the flow regions with a large velocity gradient; and (2) accurately catalogue the captured images that have the same vibrating phase. For calculating the instantaneous flow fields, the traditional PIV cross-correlation method 19 determines the velocity vector between two consecutive images with a fixed time interval Δt (See Figure 5a). This traditional method may not be suitable for this study because the calculated flow field may have significant displacement bias errors near the vibrating pipeline and seabed boundaries. To overcome this problem, a multi-time-interval algorithm is adopted in this study (See Figure 5b). By using this method, image interrogations are executed reiteratively on different image pairs for different selected intervals. The velocity vector at each grid point is determined based on the estimations of suitable time interval9,27,28. It should be noted that when using this method, the raw image datasets should be acquired by a time resolved PIV with a high sampling rate camera and continuous wave laser. To overcome the second challenge, this paper provides a wavelet transform technique. By applying the wavelet transform function to the displacement time-series of the pipeline, the instantaneous phase of each captured image can be accurately calculated. This method can also be applied to investigate vortex induced vibration processes, such as pipeline vibration induced by asymmetry vortex shedding15,27,32.
The key advantages of the flow measurement technique described in this paper are high temporal and spatial resolution and the capacity to simultaneously obtain the pipeline dynamics, flow fields, and near-boundary flow stresses. By using this technique, more in-depth studies on pipeline scour in complex environments can be carried out and the complex mechanism of scour around the vibrating pipeline could be better understood.
The authors have nothing to disclose.
This work was supported by the Young Scientists Fund of the National Natural Science Foundation of China (51709082) and the Fundamental Research Funds for the Central Universities (2018B13014).
Camera control software | Vision Research | Phantom PCC 2.6 | Camera control, image data acquisition and processing |
Camera lens | Nikon Chiyoda | Nikor 60mm, f=2.8 prime lens | |
Continuous wave laser | Beijing Laserwave optoelectronics technology co. ltd. | PIV Laser source; Nd:YAG laser, 532 nm; air-cooling | |
High-speed camera | Vision Research | Phantom Miro 120 | Image data recording |
Laser sheet forming optics | Thorlabs Inc | Transform the point laser to a thin laser sheet | |
Pipeline model | ZONCEPZ SOLUTIONS | Acrylic cylinder with a diameter of 35 mm | |
Pipeline vibration system | ZONCEPZ SOLUTIONS | Consists of a sever motor, two connecting springs and pipeline supporting frames. | |
PIV calcuation software | AXESEA Engineering Technology Limited Co. | PISIOU | Image data processing for obtaining flow fields and pipeline displacements |
PIV seeding materials | Shimakyu | Aluminum powder with a diameter of 10um | |
Recirculating flume | SZU ENGINEERING PTE LTD | Glass-sided, 11 m long, 0.6 m wide, and 0.6 m deep | |
Tri-pod | MANFROTTO | SKU MT190GOC4US 410 | Camara supporting |