Keywords

1 Introduction

Pipelines are usually buried or half-buried in rivers for oil and gas transmission or cable conduits. The flow past the pipelines underwater has long been a subject of study and research due to the complicated interaction between the structure and the hydrodynamics. Numerous papers have been written on this subject (Ahmed and Rajaratnam 1998; Bearman and Trueman 2016; Jensen et al. 1990; Lin et al. 2009; Okajima 1990; Roshko 1960; Tritton 1959; Yang et al. 2021). The flow characteristics, including patterns and turbulent structures around the submerged pipelines, a typical cylindrical structure underwater, have also been extensively investigated. Jensen et al. (1990) studied the flow patterns around a submerged pipeline placed on a flat, erodible bed under current-only conditions. The flow features around the pipeline and the vortex shedding pattern were presented using the two-color flow visualization technique. Zhu et al. (2013) investigated the flow fields around the pipeline on a scoured bed by numerical simulation. The numerical results indicated that the flow field around the pipeline is subjected to the gap between the pipeline and the scoured bed. Guan et al. (2019) investigated the flow field around the vibrating pipeline within a scour hole and presented a visualization method to obtain the detailed flow fields. These studies have revealed a general principle of the flow structure around the pipeline. However, the studies concerning the flow structure around a submerged half-buried pipeline are not available yet.

The purpose of this study is to investigate the flow structure and its features around a submerged half-buried pipeline by physical experiment. Because this study focuses on the flow structure, the scour process is not considered, and the bed is set as fixed and smooth in the experiments. To visualize the vortex development and to manifest the features of the flow structure, Particle Imaging Velocimetry (PIV) technique as a contactless measurement has been adopted in hydrodynamic experiments in recent years (Apsilidis et al. 2015; Jenssen and Manhart 2020; Yang et al. 2021), was used in this study. The experiment results are expected to enhance the knowledge of the flow structure around the submerged half-buried pipelines and facilitate channel improvement and river-crossing pipeline construction design.

2 Methodology

2.1 Experiment Set-up

The experiment set-up comprises three main parts: a semi-cylinder model, a water circulating flume, and a PIV system. As shown in Fig. 1, the flume dimensions were length = 11 m, width = 0.6 m, height = 6 m. An aluminum semi-cylinder model with a length of 0.6 m and a radius of 0.025 m, used as the model of the half-buried pipeline. The model was fixed in the flume at a distance of 5 m away from the outfall, as shown in Fig. 2(a). The PIV system consists of a highspeed camera (Photron FASTCAM Mini WX50) and a laser device. The laser device was mounted on the flume at the position above the pipeline model so that the laser light plane (as shown in Fig. 2(b)) could be cast into the flume. The laser light plane was perpendicular to the lengthwise direction of the pipeline model and parallel to the flow direction in the flume. The highspeed camera was placed at the side of the flume aiming at the laser light plane with the axis view perpendicular to the laser light plane.

Fig. 1.
figure 1

The dimensions of the flume

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Fig. 2.
figure 2

Experiment set-up: (a) Front view; (b) Top view.

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2.2 Experimental Method

Three tests were taken in this study, and the test conditions are shown in Table 1. The water depth was kept constant in the tests at 0.3 m. The mean velocity of the flow was calculated based on the flow discharge in each test.

Table 1. Test conditions.
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The procedure of each test is described below:

  1. (1)

    Running the water pump, and adjusting the flow discharge to the designated value in each test.

  2. (2)

    Turning on the laser device, injecting tracking particles slowly into the water at the inlet of the flume, then taking photos by highspeed camera when the tracking particles pass through the laser light plane.

  3. (3)

    Saving the images taken during the test for flow field calculation, then starting the next run.

A total of 3000 images of each test were used to obtain the time-averaged flow field around the pipeline model by the PIV technique. The details of the PIV technique and the calculation principle can be found in Guan et al. (2019). It is worth noting that, as shown in Fig. 3., the origin of coordinates adopted in this study is located at the center of the semi-cylinder bottom; the X-axis and the Y-axis of the coordinates are parallel to the longitudinal and vertical axis of the flume, respectively. u and v are the horizontal velocity and vertical velocity of the flow, respectively.

Fig. 3.
figure 3

Two-dimensional coordinates

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3 Experimental Results and Discussion

3.1 Characteristics of Time-Averaged Flow Field

The time-averaged flow field around the half-buried pipeline model in three tests was calculated by the PIV technique. The time-averaged flow features of each test, including the distribution of streamlines, the average kinetic energy (AKE), and the vorticities, were presented in Fig. 4.

As shown in Fig. 4(a), three vortices could be observed around the pipeline model. To better distinguish the vortices, these vortices were defined as:

  1. (1)

    Vup: the vortex closed to the upstream side of the pipeline model;

  2. (2)

    Vdp: the vortex closed to the downstream side of the pipeline model;

  3. (3)

    Vwp: the relatively big vortex situated at the wake of the pipeline model, the size of this vortex is much larger than that of the two vortices stated above and is nearly the same as the pipeline model.

By comparing the streamline distributions of the three tests, it can be found that as the Reynolds number increases, Vup gradually disappears, Vdp becomes unstable, but Vwp exists all the time. It can be deduced that with the increase of the approaching flow velocity, the backflow zone in front of the pipeline is compressed, causing the Vup becomes smaller and disappear eventually. In the meantime, the area of the Vdp is contracted to cause a unstable status. Moreover, with the increase of the Reynolds number of the flow, the Vwp exists all the time during the experiment, and its position remains unchanged.

The different distributions of AKE, as shown in Fig. 4(b), indicate that with the increase of Reynolds number of the flow, the wake zone is compressed and becomes smaller, especially in the vertical direction. In the meantime, as the Reynolds number increases, the difference between the AKE of pipeline wake and the AKE of undisturbed flow grows significantly.

The time-averaged vorticities at different flow Reynolds number are shown in Fig. 4(c). The two-dimensional distribution of the vorticities shows that the area with relatively large vorticities mainly appears downstream of the pipeline model near the Vdp and Vwp. The maximum vorticity appears on the top of the pipeline model. With the increase of flow Renolds number, the maximum vorticity increases, and the area with relatively large vorticities extends downstream. It may because that the pipeline’s existence constrains the vertical development of the area of relatively large vorticities above the pipeline, but the horizontal extension of this area receives fewer restrictions. Thus, the area of relatively large vorticities tends to extend significantly downstream in the horizontal direction rather than in the vertical direction.

Fig. 4.
figure 4

Time-averaged flow field around the half-buried pipeline at different Reynolds number. (a) Streamlines distributions; (b) AKE distributions; (c) Vorticities distributions.

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3.2 Characteristics of Wake Turbulence Structure

Figure 5 shows the characteristics of the wake turbulence structure in three tests, including the Reynolds shear stresses, turbulence intensities, and turbulence kinetic energy (TKE).

As shown in Fig. 5(a), the areas with considerable Reynolds shear stress, situated downstream of the half-buried pipeline model, can be classified as the upper region behind the top of the pipeline and the lower region near the bed surface. It is found that the Reynolds shear stress in the upper region is much greater than that in the lower region, which is different from the Reynolds shear stresses of flow around the single-cylinder, where the Reynolds shear stresses of the upper and lower shear layers are almost equal in magnitude. In addition, the comparison of the Reynolds shear stresses at different Reynolds number indicates that as the flow Reynolds number increases, the maximum value of Reynolds shear stress as well as the kinetic energy of the flow increase.

Figure 5(a) and Fig. 5(c) show the turbulence intensity at different Reynolds number in the axis-X direction (TIx) and in the axis-Y direction (TIy), respectively. It can be observed that with the increase of the flow Reynolds number, TIx and TIy in the half-buried pipeline wake increase, and the triangular-shaped region with relatively high TIx and TIy value at the pipeline wake is expanded. TIx and TIy of the area upstream of the pipeline above the bed surface developed as the flow Reynolds number increased. Moreover, similar to the turbulence intensity distribution around submerged weir in the downstream direction and vertical direction (Guan et al. 2014), TIx are more than twice TIy by comparing turbulence intensities of the same point at the same Reynolds number. The triangular-shaped region of relatively high TIx is broader than that of TIy. The main reason is that the flow velocity in the horizontal direction (u) is much higher than that in the vertical direction (v), resulting in a more significant turbulent intensity TIu. Furthermore, the flow above the half-buried pipeline is constrained vertically. u is more affected than v in the wake flow of the pipeline.

The distribution pattern of TKE in the flow field of each test, as shown in Fig. 5(d), is similar to that of TIu. The outline of the high TKE zone and the high TIu zone at the wake of the pipeline are almost the same. Similar to the development rules of TIx and TIy, with the increase of the flow Reynolds number, the maximum TKE increases, and the area of the high TKE region develops. Especially the turbulence intensity at the upstream side of the half-buried pipe near the bed surface increases significantly when the Reynolds number increases. It indicates that the flow structure of the upstream side of the half-buried pipeline becomes turbulent at high flow velocity conditions, which may lead to the potential scour in front of the pipeline, and may eventually result in the suspension of the submerged pipeline above the scoured bed threatening the safety of the pipeline. The scour problem of the submerged half-buried pipeline needs to be further studied in the future.

Fig. 5.
figure 5

Turbulence structure around the half-buried pipeline at different Reynolds number. (a) Reynolds shear stresses distributions; (b) TIx distributions; (c) TIy distributions; (d) TKE distributions.

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4 Conclusion

This experimental study investigated the flow field patterns and the turbulent structures around the half-buried pipelines at different Reynolds number using the PIV technique. The flow structures studied include the streamlines, the average kinetic energy, the vorticities, the Reynolds shear stress, the turbulence intensities, and the turbulence kinetic energy. The main conclusions are summarized as follows:

  1. (1)

    As the approaching flow Reynolds number increases, the vortex at the upstream side of the half-buried pipeline vanishes gradually. In the meantime, the vortex closed to the downstream of the pipeline is compressed and becomes unstable. However, another vortex positioned at the pipeline wake remains unchanged.

  2. (2)

    The increase of the approaching flow Reynolds number results in the increase of AKE, the vorticities, the Reynolds shear stress, and TKE of the flow structure at the half-buried pipeline wake.

  3. (3)

    The turbulence intensity at the wake of the half-buried pipeline develops dramatically with the increase of the approaching flow Reynolds number. Furthermore, the turbulence intensity at the upstream side of the half-buried pipe near the bed surface strengthens significantly under high Reynolds number conditions.