The effect of collar width ratio on the flow pattern around an oblong pier in a bend

Rivers with a straight path are rarely be found in nature since most rivers follow a sinusoidal path. River bends have always been considered by hydraulic engineers due to the presence of a flow pattern known as spiral flow. The complexity of the flow pattern increases with the placement of a bridge pier in the bend (Moghanloo et al. 2020). Due to variations of velocity along the flow depth, a pressure gradient is generated upstream of the pier from top to bottom and leads to formation of a downflow in front of the pier. The downflow acts as a vertical jet, causing scouring around the pier after encountering the river bed (Zarrati et al. 2004). One of the major reasons for bridge destruction is the occurrence of scour around the bridge piers. Therefore, protection of bridges against scouring is deemed necessary. The scour around bridge piers can be reduced by using collars. These collars are flat plates of low thickness that are installed around the pier. The collars prevent the direct collision of the downflow with the river bed and reduce the flow velocity. As a result, the scour at pier decreases.

Despite a very large amount of research carried out so far, the flow pattern around bridge piers has not yet been fully understood due to its complexity. The flow pattern in a straight channel has been studied by researchers around a single pier (Kirkil & Constantinescu 2010; Kumar et al. 2012; Das et al. 2013a, 2013b) and around a group of piers (Ataie-Ashtiani & Aslani-Kordkandi 2012, 2013; Das & Mazumdar 2015; Beheshti & Ataie-Ashtiani 2016). Also, Gautam et al. (2019) investigated the flow characteristics around single and complex piers with the pile-cap in different Reynolds numbers. The results showed that in a straight channel the flow around a single pier is more complicated than that of complex piers. Also, downstream of the pier, the intensity of vortices is reduced by placing the pile-cap around the pier. Vijayasree et al. (2019) studied the flow and scour pattern around piers with different shapes in different discharges in a straight channel and showed that the greatest reduction in flow velocity occurred near the bed around rectangular, oblong and trapezoidal piers. With an increase in the velocity and discharge of flow, the scouring depth in front of all piers increases. Vijayasree et al. (2020) investigated the flow pattern around oblong and circular piers. They concluded that in a straight channel the turbulence of flow around a circular pier is greater than that of an oblong pier, which under the same flow conditions causes more scouring around the circular pier. Furthermore, other research has investigated this phenomenon in 180 degree bends (Tang & Knight 2014; Vaghefi et al. 2014, 2016; Dey et al. 2017; Abdi Chooplou et al. 2018). Moghanloo et al. (2020) investigated experimentally the flow pattern around the combination of an oblong pier and collar with different thicknesses in a 180-degree sharp bend. The results showed that increasing the thickness of the collar placed at a level 0.4 times the pier width above the initial bed level significantly reduces the kinetic energy at the pier upstream and increases the orientation of the streamlines toward the bed, thus deepening the scour hole. Keshavarz et al. (2021) studied and compared the flow pattern around rectangular and oblong piers accompanied by a collar placed in a 180-degree sharp bend. They installed the collar at a level equal to 0.4 times the pier width below the initial bed and with a thickness equal to 0.12 times the pier width. They indicated that the Reynolds stresses around the oblong pier and collar combination had lower values than those around the rectangular pier and collar combination.

Since collars play an important role in reducing scour around bridge piers, quantitative studies have been conducted on the flow pattern around the collar structure. Therefore, in this research, the flow pattern around an oblong pier located at 90 degrees along with installation of the collar around it with different ratios of collar width to pier width has been investigated. Given the long duration of the flow pattern experiment, only the parameter of the collar width to pier width ratio, an influential parameter in the flow pattern and consequently scouring, was investigated.

Experiments were conducted in a rectangular channel with a 180-degree bend as shown in Figure 1(a). The width and height of the channel were 1 m and 0.7 m, respectively. The curvature radius of the channel bend was 2 m with R_C/B= 2, where R_C is the central radius of the bend and B is the channel width, and according to Leschziner & Rodi (1979), it qualifies as a sharp bend. Sediment particles with a mean diameter of 1.5 mm and a standard deviation of 1.14 were used as the bed material and covered the total length of the channel with a thickness of 0.3 m. The discharge and flow depth at the end of the upstream straight path (y_u) were 0.07 m³/s and 0.178 m for all the experiments, respectively. Following the criteria suggested by Chiew & Melville (1987) and Melville & Sutherland (1988), an oblong pier, made of PVC, with width and length of 0.05 and 0.2 m, respectively, was used (L/b= 4, L is the pier length and b is the pier width). Two experiments (hereafter named as PC2 and PC4) were carried out with the installation of collars having ratios of W/b= 2 (PC2) and W/b= 4 (PC4) around the pier. W is the width of the collar. The collars, made of Plexiglas, with a thickness of 3 mm were placed on the bed with the top level equal to the sediment bed level. The pier and collar were placed at the 90 degrees section of the bend.

Initially, the scouring experiments were carried out under threshold conditions; U/U_C≈ 0.98. U is the average flow velocity and U_C represents the flow velocity at the threshold motion of particles. To create the maximum local scour around the pier and collar combination as well as the maximum bed topography changes in the bend, the U/U_C ratio was selected near one, equal to 0.98. This experiment was conducted for about 15 hrs, during which the equilibrium state was achieved. The bed topography was recorded with a digital point gauge after the water was drained out. The bed was then stabilized by spraying an adhesive over the scour hole. Water was again allowed to flow into the channel and 3D velocity components were obtained by using an Acoustic Doppler Velocimeter. Velocity measurements were taken at different heights from the channel bed (Figure 2(a)). At each section, velocity components were recorded at 5 levels above the original bed level, 4 levels in the scour hole, and 33 points at 3 cm intervals of width (Figure 2(b)). X and Y represent respectively the longitudinal and transverse axes and Z is the level of measurement.

Flow velocity was measured with a Vectrino device with three-receiver tentacles. The three-dimensional flow velocity was measured by using an ultrasonic signal sent by a transmitter and then receiving a reflection wave from the flow with at least three transceivers. Two probes, down-looking and side-looking, were used to measure the flow velocity (Figure 2(c)). In most parts of the network, harvesting was performed by a down-looking probe that measures the flow velocity in all three directions at a point 5 cm below the probe. The side-looking probe was used in the areas near the flow surface, the bed level and the banks. This device is capable of measurement within a velocity range of 0 to 7 m/s. In this study, the measured velocities fell within a range of 0 to 1 m/s, which enjoyed an acceptable accuracy considering the stated correlation coefficients. A frequency of 25 Hz and duration of 60 s were used in these experiments, and at sensitive points, the duration was set to 120 s (Akbari et al. 2021). The device can record up to 1,500 data of flow velocity per minute in three directions. The quality of the velocity signals was investigated using two parameters: Signal-to-Noise Ratio (SNR) and correlation coefficient. The SNR amounts for the mean and instantaneous velocity measurements should be greater than 5 and 15 dB, respectively. The correlation coefficient evaluates the rate of disturbance in velocity signals by calculating the rate of change between consecutive readings of the instantaneous velocity. An average correlation of 71% is suitable for high-quality data. In these experiments, the appropriate ranges for SNR and correlation coefficient were 10 dB and 70%, respectively.

Since the flow pattern experiments were performed under balanced bed conditions, first, the bed topography changes in the bend caused by the installation of collars with W/b ratios of 2 (PC2) and 4 (PC4) around the oblong pier at the bend vertex were provided. Figure 1(b) and 1(c) show the bed topography of the scour pattern after the relative equilibrium time. The sedimentation area adjacent to the inner bank and scour holes around the pier was determined. The maximum scour depth is one of the most effective components of a scour hole. The maximum scour depth in Experiment PC2 was measured to be 13.5 cm and equal to 0.75 times the flow depth at the pier nose. In Experiment PC4, according to Figure 1(c), due to the larger collar dimensions, two scour holes occurred around the pier. The maximum scour depths in the first and second scour holes were measured to be 5.2 and 9.3 cm, respectively, equal to 0.28 and 0.51 times the flow depth along the collar and 7 times the pier width at the pier downstream. In both experiments, sedimentation began adjacent to the inner bank at 30 degrees and continued to 150 degrees. Also, the maximum sedimentations for Experiments PC2 and PC4 were 6 and 7.6 cm, equal to 0.33 and 0.42 times the flow depth at 115 and 136 degrees, respectively.

Figure 3 shows samples of the streamlines at positive and negative levels at the plan section in Experiments PC2 and PC4 at the pier and collar position at 90 degrees. Close-ups of the streamlines around the pier are also given to better illustrate the flow pattern. In these figures, in some areas at positive levels, the streamlines have not been plotted due to the formation of sedimentary stacks and zero velocity. The streamlines crossing through the collar at positive levels and crossing beneath the collar at negative levels are evidently illustrated in the figures. According to Figure 3(a), since the collars have been installed at the initial bed level in both experiments, the only factor affecting the flow near the surface is the placement of the oblong pier at 90 degrees to the bend. Therefore, in both experiments, the streamlines near the flow surface in the first half of the bend orient toward the outer bank. Also, at 1 cm below the flow surface (95% of the flow depth from the bed level), at about 26 times the pier width at the pier upstream for both experiments, return flows are observed to have followed the deviation of the streamlines toward the outer bank. The reason for this is the collision of the flow with the oblong pier, the return to the pier upstream and collision with the mainstream. Also, this deviation causes higher deviation of the streamlines from about 80% of the channel width from the inner bank to the outer bank in the second half of the bend. These return flows are not observed at lower levels. In Experiment PC4, at the distance of 7 times the pier width at the pier downstream, a wave of flow has been formed at the water surface affected by the upward flow generated from the collar, and streamlines are deviated more toward the outer bank than those in Experiment PC2. According to Figure 3(b) and considering the presence of collars at the bed level, as the collar width increases, the tendency of the streamlines toward the inner bank increases in Experiment PC4 after the pier. This causes the formation of a sedimentary stack near the inner bank so that the maximum sedimentation rate in Experiment PC4 occurs at 136 degrees and that in Experiment PC2 at 115 degrees. Due to sedimentation on the inner bank at the second half of the bend, the deviation of the streamlines toward the outer bank in Experiment PC4 is greater. In both experiments and at this level, it is observed that the flows after the sedimentary stacks near the inner bank are slightly deviated toward the inner bank, which is due to the flow drop from the sedimentary stack. Due to the presence of sediments around the scour hole at negative levels, there are no streamlines at any points. Since the collar has been installed at the bed level around the oblong pier, in Experiment PC2, the flow can penetrate beneath the collar and cause a scour hole around the oblong pier. In Figure 3(c), the flow into the scour hole is directed from the outer bank to the inner bank. Therefore, this flow causes the sediments to leave the scour hole and move toward the inner bank. At the level of 50% of the flow depth in the scour hole below the initial bed level in Experiment PC2, the streamlines return to the upstream sections after penetration below the collar and collision with the pier nose. Collision with the plunging flows leads to accumulation and turbulence of the streamlines at the pier upstream, and also the deviation of the flow toward the inner bank. On the other hand, with an increase in the collar width, as shown in the close-up figure, the flow has somehow penetrated the collar. This flow caused a small scouring hole near the collar edge, ranging from 33 to 42% of the inner bank around the pier and the collar.

The streamlines in a 50% longitudinal section of the channel width from the inner bank are shown in Figure 4(a). θ is the position of the velocity harvest along the bend. In both experiments, the flow after collision with the pier, causes a return and a downflow at the pier upstream. These changes have occurred at the middle levels to the flow surface, and the flow continues in downstream direction after passing the pier parallel to the mainstream. In Experiment PC2, after penetration beneath the collar and collision with the pier, the flow is transmitted into the scour hole in the form of downflows and causes scouring at the pier nose. An up flow is also observed along the pier due to wake flows. In Experiment PC4, after collision with the collar, the flow is transmitted downstream and falls into the second scour hole, and at the end of the bend and under the influence of topography changes in the lateral sections, the flow near the bed is directed upward. In Figure 4(b)–4(d), samples of the streamlines in different transverse sections has been plotted for the region around the oblong pier in Experiments PC2 and PC4. The main secondary flow is observed along the channel due to the reduction in the effect of the longitudinal pressure gradient and the dominance of the centrifugal force on the field as a rotary cell. Figure 4(b) indicates that in Experiment PC2, two clockwise vortices have been formed alongside the pier nose, one near the inner bank at mid-depth, and the other approximately at the mid-channel width near the bed level. The vortex formed near the bed level causes the formation of a scour hole in front of the pier nose while, due to the larger collar width in Experiment PC4, the formed clockwork vortex did not fully penetrate the collar. Also, due to the collision between the flows generated by the vortex and the collar, these flows deviate toward the pier downstream side. Figure 4(c) indicates that the pier nose causes the flow to be separated. These isolated flows create clockwise vortices around the pier due to collisions with the pier. As in Experiment PC2, these clockwise vortices penetrate beneath the collar and cause scouring around the pier. Near the inner bank, as a result of the collision of the flows with the collar and the bed level, a small counterclockwise vortex was formed beneath the collar near the pier. However, in Experiment PC4, in addition to deviating vortices toward the pier downstream side, the collar prevents their penetration beneath. Also, the pier in both experiments transformed the secondary flow of the main channel into two secondary flows. According to Figure 4(d), as the flow progresses downstream, the secondary flows on both sides of the pier collide in front of the pier tail. In Experiment PC4, at the collision point of flows, downflows have been formed, and they extend to the downstream side due to collision with the collar and cause scouring downstream. Also, in Experiment PC2, the wake and up flow is more noticeable at the collision point of the flows and causes higher scouring.

Figure 5(a) indicates the return flows at the pier upstream side near the flow surface at 50% of channel width. In both experiments, the tangential velocity is increasing at the pier upstream until mid-depth from the bed level and the flow collides with the pier nose at the same velocity and is then deviated. In Experiment PC2, due to the small size of the collar dimensions and the bed topography, the tangential velocity in the scour hole is increasing and the return flow is observed below the collar near the bed. This occurs as a result of the collision of the flow with the pier and its return toward upstream. However, in Experiment PC4, the tangential velocity has decreased beneath the collar; whereas, it increases after the collar and inside the second scour hole. In both experiments, with progression of the flow along the bend toward the downstream side of the pier, the tangential velocity increases from the proximity of the collar to the flow surface so that the tangential velocity values ​​at the positive levels in both experiments are approximately identical at 1.2 times the pier length toward the pier downstream. Such a difference in the increase and decrease of tangential velocity in the pier placement range is a consequence of the difference in the width of the collar, which causes a difference in the values ​​of this tangential velocity. Figure 5(b) shows the positive direction of radial velocity toward the outer bank and the negative radial velocity toward the inner bank. It is observed at the pier upstream that the radial velocity for both experiments at the negative levels and near the bed level occurs toward the inner bank. Approaching the flow surface, the radial velocity is shifted toward the outer bank. This change in direction in the radial velocity creates a secondary flow through the channel width. However, at the pier downstream at the levels close to the flow surface, the redial velocity is directed toward the inner bank. Moreover, variations and irregularities of the radial velocity are reduced away from the pier region in the downstream direction, but radial velocity values ​​and its changes at the upstream side and at the pier area are higher than those at the pier downstream. The radial velocity value in Experiment PC4 below the collar is negative. The highest positive radial velocity in both experiments occurred at a level of 45% of the flow depth from the bed level in front of the pier nose. In Experiments PC2 and PC4, the highest negative radial velocity was detected in the scour hole around the pier and the second scour hole near the materials, respectively (the levels of −60 and −40% of the flow depth from the bed level, respectively). In Figure 5(c), the performance of the collar with W/b ratio of 4 is clearly observed compared to the collar with W/b ratio of 2. Although the downflow in Experiment PC2 has the greatest velocity in front of the pier nose, the vertical velocity in the same position in Experiment PC4 is very small. This implies the greater impact of collar dimensions on downflows and zero penetration of the flows underneath the collar at the pier nose. The maximum vertical velocity values for Experiments PC2 and PC4 are −14 and −11.8 cm/s, respectively. In Experiment PC2, the vertical velocity at the pier upstream is directed downward, and the negative vertical velocity is increasing at negative levels (within the scour hole) as the flow approaches the pier. This causes scouring at the pier nose, whereas the vertical velocity at the pier downstream is upward, and consequently the wake flows occur after the pier. By doubling the W/b ratio at the pier upstream, the vertical velocity has decreased sharply. Also, the vertical velocity at the downstream side of the pier is downward. These downflows incline toward the second scour hole after collision with the collar. With progression from the negative levels toward the flow surface in both experiments along the bend, the vertical velocity decreases.

In the figures on the transverse sections, B represents the width of the section. Figure 6(a) shows the tangential velocity. In the figure, at the intervals of 10 to 20 and 80 to 90% of the channel width from the inner bank, according to the topography of the bed, the variation of the velocity longitudinal component (tangential velocity) at the collection levels is identical for both experiments so that, at both intervals, the tangential velocity is increasing up to 5 and 45% of the flow depth from the bed level, but after that, the variations in tangential velocity to the flow surface are almost constant. According to the figure, in Experiment PC2, the return flow occurred from 50 to 60% of the channel width from the inner bank near the flow surface, while in Experiment PC4, the return flow occurred with a lower value. In Experiment PC4, at a distance of 40% of the channel width from the inner bank, it is observed that the tangential velocity has penetrated beneath the collar, and the tangential velocity decreased with progress toward the outer bank so that the collar has directed the tangential velocity toward downstream from 60% of the channel width from the inner bank to the outer bank according to the topography of the bed. However, in the region around the pier and collar in Experiment PC2 up to 45% of the flow depth from the bed level, the tangential velocity is positive and increasing. Also, in Experiment PC2, at negative levels close to the bed level, the tangential velocity penetrates beneath the collar, and its value is positive; the tangential velocity becomes negative (return flow) with progression into the scour hole (the level of −60% of the flow depth from the bed level) (area A). This is due to the collision of the mainstream to the pier and its return to the upstream side of the pier. The transverse velocity component (radial velocity) is shown in Figure 6(b). As can be seen, in both experiments, the radial velocity has been negative at the levels close to the bed surface and the negative level (inside the scour hole around the pier), and it becomes positive by approaching the flow surface. This negative value of radial velocity on the channel bed leads to the movement of the outflow sediment from the scour hole toward the inner bank. This means that the flow near and below the bed is directed toward the inner bank and that near the flow surface is directed toward the outer bank. This suggests the presence of a vortex in this position. This vortex is actually the main vortex of the secondary flow. In Experiment PC4, the tangential velocity has penetrated beneath the collar at the distances of 40 and 42% of the channel width from the inner bank, and the highest tangential velocity values have ​​occurred at these distances, whereas from approximately 48% of the channel width from the inner bank to the outer bank affected by the collar, the flow is deviated toward the outer bank. In Experiment PC2, a small clockwise vortex is observed at 10% of the channel width from the inner bank at the level of 45% of the flow depth from the bed level (area B). Also, in area C, a clockwise vortex was formed at 44% of the channel width from the inner bank, which causes scouring in front of the pier nose. The vertical velocity in Figure 6(c) at the levels near the flow surface and at 80 to 100% of the channel width from the internal bank is insignificant in both experiments. In Experiment PC4, the vertical velocity has decreased and approaches zero away from the inner bank up to 80% of the channel width from the inner bank at positive levels. As has previously been stated, the reason for this sharp decrease in vertical velocity at this transverse section is the presence of the collar at the bed level at this section so that it has completely neutralized the impact of the vertical flows on the bed at this section. However, in Experiment PC2, due to the small size of the collar, the highest negative vertical velocity (downflow) has occurred at this section in front of the pier nose. In the figure, in Experiment PC2, in the range of 20 to 42% of the channel width from the inner bank within the scour hole, the vertical velocity has a positive value, and after this interval up to 70% of the channel width from the inner bank, it is negative. This change in the direction of vertical velocity causes irregularity and turbulence of the flow at 42% of the channel width from the inner bank at −40% of the flow depth from the bed level (area D). Also, the vertical velocity in this experiment decreases by moving from negative levels toward the flow surface.

This paper has studied the flow pattern around an oblong pier with installation of a collar at different ratios of collar width to pier width (W/b= 2, 4), located at 90 degrees from a 180 degrees bend. The presence of collars around the oblong pier causes generation of vortices in the opposite direction of the longitudinal flow, further deviations of the streamlines toward the pier downstream, and a decrease in the downflow power in front of the pier nose so that increasing the collar width adds to the deviation of the streamlines near the bed level toward the inner bank and the downstream side of the pier. By installing a collar with W/b= 4 (Experiment PC4), more sedimentation accumulated along the inner bank compared with installation of a collar with W/b= 2 around the oblong pier (Experiment PC2). Also, doubling the collar width decreased the width of the scour hole around the combination of pier and collar by 85%.

The maximum tangential and radial velocities increased by 15 and 10%, respectively after doubling the ratio of the collar width to pier width, whereas the maximum vertical velocity decreased by about 15%, which indicates the effect of increasing the collar width on decreasing the downflows and the consequent reduction of the scour around the pier.

The maximum secondary flow power was observed by installing the collar with W/b= 2 around the oblong pier (Experiment PC2) at 86 degrees of the bend, equal to 17.5%. By doubling the collar width around the oblong pier, the maximum position of the secondary flow was shifted 4 times the pier width toward the pier upstream. Also, the maximum power of the secondary flow decreased by about 10%. The maximum value of vorticity was reduced by 30% after increasing the collar width, and for both experiments, it was observed at 86 degrees of the bend.

Doubling the collar width reduced the maximum values of the Reynolds stresses on yx and zy coordinates by 45 and 60%, respectively, and increased the Reynolds stress on zx by 25%.

With an increase in the collar width around the pier, the maximum and minimum turbulence kinetic energy values increased by approximately 50 and 55%, respectively.

All relevant data are included in the paper or its Supplementary Information.