Numerical investigation of flow field around T-shaped spur dyke in a reverse-meandering channel

The flow in a river bend or meandering channel is highly turbulent and stormy due to continuous change in the curvature of banks and high topography irregularities (Pu et al. 2020, 2021). The flow pattern in a curved channel consists of spiral flow between the river bed and water surface, transverse rotational flow generated by the centrifugal force in bend, secondary flow, and so on (Pandey et al. 2018a, 2018b, Singh et al. 2019). It causes heavy bank erosion resulting in its lateral migration. Rozovski (1957) studied and discussed the flow characteristics and boundary shear-stress distribution in a curved channel. Yen (1967) experimented with flow pattern and bed configuration in a meandering channel under subcritical flow conditions. Naji et al. (2010) worked on the flow pattern in a 90-degree channel bend and observed that the flow in the bend is highly influenced by secondary flow and centrifugal force. They further observed that the flow near the channel orients towards the inner bank shifts to the outer bank near the water surface. Vaghefi et al. (2016a, 2016b) conducted experiments in a 180-degree channel bend and analyzed the effect of flow characteristics on bed shear-stress distribution.

To prevent bank erosion in the curved channel, spur dykes are constructed across the channel width extending from the outer bank into the river. Spur dyke restricts the water flow and hence ensures deepening of the main channel. This can be used for navigation purposes, uniform discharge into an irrigation channel, and rehabilitation of flood plain. Despite its significant use, the study on spur dyke present in channel bend is still limited (Fazli et al. 2008; Vaghefi et al. 2019). The majority of studies in this field have been carried out in a straight channel such as Kothyari & Ranga Raju (2001), Jennifer et al. (2011), Jiao et al. (2017), Kuhnle & Alonso (2013), Pandey et al. (2018a, 2019, 2020, 2021), Pourshahbaz et al. (2020), Singh et al. (2020), Xiufang et al. (2012) and so on. The flow past a spur dyke present at the channel bend or meander is highly turbulent, leading to the formation of local scour, which further increases with increasing scour depth. Therefore, it becomes essential to evaluate the flow behavior around the spur dyke. In general, the flow regime is divided into two zones, wake-up and mixing zones around a spur. The flow characteristics around spur dyke include the formation of secondary flow, vortices, down flow, flow, turbulence, and so on (Zhang & Nakagawa 2008; Pandey et al. 2018a, 2021). The current experimental and numerical studies conducted on spur dyke present in a channel bend (mainly 90-degree and 180-degree) or a meander to evaluate the inference of several important parameters on local scour. These parameters include upstream Froude number, submergence ratio, and geometry of channel spur dyke, bed configuration, etc.

Giri et al. (2004) developed the 2D numerical model using a cubic-interpolated pseudoparticle (CIP) numerical technique to study the flow field and turbulence around spur dykes located in a rigid bed meandering channel. Sharma & Mohapatra (2012) experimented with a rigid bed sinusoidal meandering channel with trapezoidal cross-section and fined the dimensions of separation zone (length and width). This is highly influenced by the position of structure in the channel that varies from 4.0 to 22.8 times the spur dyke length; however, it remains nearly unchanged under varying discharge. The same results were also reported in a spur dyke positioned in a straight channel (Yazdi et al. 2010).

Fazli et al. (2008) discuss as the spur dyke shift far from the entry of the bend, the depth of scour and the intensity of the flow increased in a 90-degree channel bend. The separation zone of the vortex expands with an increase in the wing length of the spur dyke, and the vortex with the anti-clock direction was formed both upstream and downstream of the spur dyke Ghodsian & Vaghefi (2009). In addition, a vortex with a clockwise direction is also formed between wings of spur dyke in the channel walls downstream. For a single T-shaped spur dyke located at an angle of 75-degrees (from the entry) in a 90-degree bend, the strength of secondary flow and vorticity gradually increases from the beginning of the bend to maximum value at section 74-degrees. It then decreases until the exit of the bend (Vaghefi et al. 2017). Therefore, it says that these vortices might be formed due to interaction between the longitudinal velocity component of flow and secondary flow. Salamatian et al. (2016) at a 90-degree channel bend with three spur dykes placed in 5-degree consecutive angular spacing along the bend. The position of the first spur dyke (from the entry of bend) was kept at 30-degrees, 45-degrees, and 60-degrees. This study shows that shifting the spur dykes downstream decreases the length of the separation zone while the width remains constant, increasing the bed-shear-stress.

Naji et al. (2010) prove with their experiment that SSIIM (Sediment Simulation in Intakes with Multiblock option) model can be used to simulate the flow pattern accurately in a 90-degree bend (without any structure). Olsen (2018) investigated the variation of flow velocity, which implements model to solve Navier-Stokes's equations in a non-orthogonal grid. Acharya & Duan (2011) implemented the FLOW-3D model to simulate the flow field around a series of three spur dykes using several turbulence models such as renormalization group (RNG) model, standard two-equation model, mixing length model, and large eddy simulation (LES) model. They noticed that none of the models is accurately able to predict the turbulence properties. However, the RNG model can predict the mean velocities and hence recommend the same. Kafle (2013) uses a 2D numerical model with CIP techniques to simulate flow field in spur dyke present at 90-degree channel bend. The turbulence models such as model, zero equation models, and constant eddy viscosity model were implemented and compared. Vaghefi et al. (2014) studied RNG turbulence numerical model FLOW-3D to investigate how the change in Fr number influences flow pattern past a T-shaped spur dyke at a bend angle of 45-degrees (measured from the entry) in a 90-degree bend and estimate as the Froude number increases from 0.2 to 0.6, vertical velocity component of flow increases by about two times, and the distance between return flow and web wing of spur dyke increases by 10 times. Radan & Vaghefi's (2016) study with SSIIM model simulates the submergence on flow and scour pattern around a spur dyke at 45-degrees (from the entry) and 90-degree bend, proposed that with an increase in submergence of the spur dyke, the distance of vortices with a horizontal axis from the structure decreases.

On the other hand, the distance of vortices with the vertical axis from the spur dyke decreases upstream remains unchanged downstream.Similar work done with the same numerical model but only at 90-degree, discussing the secondary flow strength and flow separation around attractive, vertical, and repelling T-shaped spur dykes seems that the secondary flow is higher for attractive than repelling. The separation zone increases with a rise in water elevation Vaghefi et al. (2019).

From the literature survey, most researches have been conducted in a 90-degree channel bend; researches including other curved channels such as 180-degree bend and meandering channel have been either neglected or limited. In hydraulic engineering, soft computing and numerical methods have been widely used and successfully simulated hydraulic parameters (Samadi et al. 2015, 2021). Therefore, this paper investigates the flow pattern numerically in a reverse meandering channel near the spur dyke with a rigid bed under subcritical conditions. It also includes the effect of the Froude number on the flow pattern. The results are then compared with that under the condition when no structure is located in the channel. A numerical investigation was carried out using ANSYS fluent software. The results include streamlines, velocity distribution, flow separation, and bed-shear-stress distribution.

Here, represents the production of turbulence kinetic energy given by ⁠, ⁠, = modulus of the mean rate of strain tensor; and are the turbulent Prandtl numbers; and ⁠, ⁠, ⁠, ⁠, and are constants. The value of constants in the RNG model is listed in Table 1.

The RNG model was developed using the RNG method to normalize the Navier-Stokes equation to account for even small scales of fluid motion. Therefore, it makes RNG model a suitable choice to model turbulence flow around the spur dyke. In this paper, ANSYS fluent software (ANSYS 2018) was used to simulate the flow around the spur dyke located in a reverse-meandering channel.

In this study, the reverse-meandering channel consists of two consecutive bends in reverse order. These bends were connected with the straight inlet and outlet channels, each of length 4.0 m. The channel's cross-section was kept prismatic with a uniform width of 1.0 m and depth of 0.2 m. The central radius of bends was designed as 1.0 m. Since the relative curvature was 1.0, such a bend is categorized as a sharp bend. The central angle of the bend was kept at 180 degrees for the maximum deflection of flow and hence, to generate full development of secondary circulation. Here, two cases were considered: (1) when no spur dyke was located in the bend; and (2) when a T-shaped spur dyke was located at the outer bank of the first bend. For case 2, the spur dyke had a thickness of 0.01 m (or 10 mm) and height of 0.20 m and was placed at an angle of 75-degrees (measured from entry to the first bend). The spur dyke length and wing length were kept at 0.2 m (i.e., 20% of channel width). A schematic diagram for case 2 is shown in Figure 1. The CAD model for both cases was prepared in Solid Works, which were imported in ANSYS fluent for further processing.

By default, unstructured meshing is available in ANSYS fluent (ANSYS 2018), and the same was used in the present research of the complex geometry near the spur dyke. The flow simulation was iterated for several mesh configurations of progressive fine sizes to obtain the most accurate results under identical flow conditions. A mesh system was then considered, which had a negligible effect on computational results while reducing the simulation (model run) time. For case 1, uniform mesh sizes of 20 and 40 mm were used to discretize bends and inlet, and straight outlet reaches, respectively, and for case 2, a uniform mesh size of 20 mm was used in general, while a denser mesh size of 10 mm was used near the spur dyke. Some of the common parameters of volume meshing are listed in Table 2. The volume meshing for both cases is shown in Figure 2.

The flow velocity inlet and pressure outlet were introduced at the entry and exit of the computational domain, respectively. The banks of the channel were defined as a wall with no-slip and standard wall roughness conditions. The empirical standard wall function (Spalding 1974) was used to estimate the effect of the wall on the flow field. The channel bed was rigid, and hence, treated as a wall. At the same time, the water surface exposed to the environment above was assumed to be symmetrical, which enforces zero normal flow velocity and shear-stress. The boundary conditions for computation are shown in Figure 1 (marked in rectangular box).

To solve the numerical model, a pressure-velocity coupling-based SIMPLE scheme was implemented. SIMPLE scheme stands for semi-implicit method for pressure linked equations, which uses the relationship between pressure and velocity corrections to obtain pressure field and to enforce the law of conservation of mass (ANSYS 2018). A steady-state simulation was performed for each case with five different approaching flow conditions, i.e., Froude number equal to 0.29, 0.43, 0.57, 0.71, and 0.86 (subcritical flow condition).

Figures 3 and 4 show the velocity contour at 25% and 75% water depth for case 1 (i.e., when no spur dyke is located in the bend), at Froude numbers equal to 0.29 and 0.86, respectively. From the figures, it is clear that the velocity distribution shows a similar trend for all Froude numbers; only intensity and magnitude increase with increasing Froude number. In general, the flow velocity increases as one gradually moves from the concave side (outer bank) to the convex side (inner bank). The local maximum velocity occurs at the convex tips in both bends. Due to secondary flow formation, the lateral velocity component (across channel width) contributes significantly to the maximum velocity. However, secondary flow strength is relatively higher in the second bend due to a change in curvature of bank and flow direction as the flow enters the second bend. Hence, the maximum velocity at the convex tip of the second bend is greater than that of the first bend, as seen from the velocity streamline in Figure 5. In the vertical direction, the velocity increases from channel bed to water surface.

In the presence of spur dyke (case 2), the velocity distribution shows significant changes, which become more prominent with increasing Froude number. Similar to case 1, the flow velocity increases from the inner bank to the outer bank in both the bends, as shown in Figures 6 and 7. The obstruction to flow caused by the spur dyke increases the mean flow velocity, extending downstream from its location due to channel width contraction. Similar to case 1, the local maximum velocity is found near the convex tip (inner bank) in each bend. However, the global maximum flow velocity shifts to the convex tip of the first bend.

In the absence of the spur dyke (case 1), a low or zero velocity zone forms at the junction of two bends. The zone gets well-defined as one moves from channel bed to water surface. At a high Froude number, it becomes localized (or shrinks or converges) at the junction. Near the channel, it extends downstream along the outer bank of the second bend. It is marked with a circle in Figures 3 and 4. It occurs due to the convolution of flow reflected from the outer bank (secondary flow) and flows separate at the inner bank of the first bend (see Figure 5).

In the presence of the spur dyke (case 2), there is the formation of two such low or zero velocity zones, one near the junction of two bends and the other at the outer bank of the second bend (see Figures 6 and 7). Similar to the previous case, these zones become well-defined near the water surface and at a higher Froude number.

The 3D flow characteristics around the spur dyke (case 2) include upflow, downflow, vortices, and so on, as shown in Figures 8 and 9. At location of 50% of spur dyke length from the outer bank of the first bend, a total of three vortices having a horizontal axis of rotation are formed around the spur dyke. Two vortices with anti-clockwise direction formed close to the spur dyke, upstream and downstream, and another vortex with clockwise direction formed relatively far away from spur dyke downstream. With the increase in Froude number, these vortices shift downward and show an increase in their strength as well (see Figures 8(a) and 9(a)). At the location, 100% of spur dyke length from the outer bank of the first bend (or along the wing length of spur dyke), a vortex with anti-clockwise direction is observed at the upstream end of the spur dyke, while several vortices are observed at its downstream end. At downstream of the spur dyke, a vortex with clockwise direction is formed at the mid-water depth, which eventually dies off at higher Froude number; however, a vortex with anti-clockwise direction is observed near the channel bed, which shifts towards the spur dyke at higher Froude number, probably caused due to strong a returning flow (see Figures 8(b), and 9(b)).

At the upstream, the flow streamline starts to get separated from the boundary (i.e. channel bank) as it approaches the spur dyke. This zone is called the separation zone. The flow streamline then reattaches to the channel bank at the downstream, causing the formation of reattachment zone. A schematic diagram of flow separation is shown in Figure 10. In the figure, separation zone and reattachment zone lengths are represented by ‘’ and ‘’, respectively.

In case 1 (absence of spur dyke), flow separation starts from the begnining of the straight outlet channel (or end of second bend), and stretches downstream, as can be seen in Figures 3–5. In this case, the flow separation zone length is represented by ‘’. Figure 11 shows the variation of at various water depth and inflow Froude number. From Figure 11(a), it can be seen that for all values of inflow Froude number, the value of increases as one moves towards the water surface. The value of is observed maximum at ⁠, while it remains nearly unaffected at higher Froude number, as can be seen from Figure 11(b). At higher inflow Froude number, the strong secondary flow from the outer bank interacts with longitudinal flow streamlines at the downstream causing reduction in flow separation zone length.

In case 2, the flow separation in straight outlet reach becomes negligible due to reduced velocity caused by the presence of the spur dyke. Table 3 shows the separation zone and reattachment zone length around the spur dyke at two water depth levels. From the table, it is clear that the separation zone length, ⁠, remains unaffected by inflow Froude number, while the reattachment zone length, shows slight variation with inflow Froude number. On comparing the values of and at two water depth levels, it is discovered that the remains nearly constant at all water depths, while increases as one moves from channel bed to water surface. A similar observation is made by Vaghefi et al. (2019).

Even though a rigid bed is assumed in this paper, bed-shear-stress distribution can provide a qualitative understanding of scour and sediment transportation in the channel with mobile bed (or live bed condition). In general, the initiation of sediment transport at the channel bed is evaluated using a critical shear-stress threshold (Ouillon & Le Guennec 1996). The shear-stress distribution at the channel bed gives the potential location of sediment erosion and deposition along the channel length. The location characterized by high bed-shear-stress has the potential of bed erosion (or scour) or vice versa.

In case 1, the bed-shear-stress distribution shows a general trend for all flow conditions. In the absence of a spur dyke, the bed-shear-stress increases as one move from the concave side (outer bank) to the convex side (inner bank). A similar observation was also made by Vaghefi et al. (2016a, 2016b) for 180-degree channel bend. It becomes clear from Figure 12 that the bed-shear-stress at the convex tips could potentially result in significant scour in these regions. It occurs due to high flow velocity in these regions, as shown in Figures 12 and 13. However, the maximum bed-shear-stress occurs at the convex tip of the second bend. Due to the formation of high secondary flow in the second bend caused by a reverse flow direction and change in curvature as water enters from bends first to second. The maximum value of bed-shear-stress at these two locations is listed in Table 4. Interestingly, the ratio of shear-stress at the two locations remains nearly constant (equal to 1.38). Further, at the downstream of the second bend (i.e., the straight outlet channel), a high value of bed-shear-stress is observed outside the flow separation zone, which increases drastically with an increase in Froude number, as shown in Figure 13.

In case 2, the bed-shear-stress distribution changes drastically due to a spur dyke in the bend, as shown in Figure 13. However, the general trend of bed-shear remains similar to that in case 1. Due to the presence of the spur dyke, the shear-stress increases in both the bends. However, the location of maximum shear-stress shifts from the convex tip of the second bend to that of the first bend. In this case, the shear-stress ratio at the two locations is equal to 0.89 (a constant). The bed-shear-stress in the separation zone (or recirculation zone) reduces, resulting in a deposition. The same is observed at the concave side (outer bank) of the second bend.

Further, the shear-stress value downstream of the second bend also decreases compared to that in case 1 (see Figures 12 and 13). Near the tip of the spur dyke, the bed-shear-stress increases, resulting in bed erosion. In both cases, the shear-stress increases with an increase in Froude number.

For a particular numerical model to be verified, we compare the variation in the parameter of with and without spur dyke in meandering channel bend at 180-degree with the result of another experimental model under the same condition with other research paper. Present simulations are performed with five different approaching flows under the subcritical condition.

Figures 3 and 4 represent the velocity contour at 25% and 75% depth of water having Froude numbers 0.29 and 0.86 with no structure present in the meander. This velocity shows similar trends with the Froude number.

Figures 7 and 8 show the velocity contour with spur dyke in a meander having water depth of 75% and 0.29 Froude number, and it is clearly shown that from the initial bend to the wings of spur dyke the velocity attended same direction and amount. It is seen that the longitudinal velocity increases at the inner wall but closer to the external bend and vertical velocity found in the middle of the meander. The direction of velocity gets changed with the inference of spur dyke. This numerical modeling data is very similar to Vaghefi et al. (2014). Based on this verification, numerical modeling can be achieved.

Since no experimental investigation was carried out to study the flow pattern around a T-shaped spur dike located in a reverse meandering channel, the experimental results from Vaghefi et al. (2014) were used to validate the numerical model. Vaghefi et al. (2014) studied the effect of inflow Froude number on flow pattern around the spur dike located at 45-degrees in a 90-degree channel bend using RNG model and volume of fluid (VOF). Figure 14 shows the comparison between experimental and numerical velocity results at a longitudinal section located at 58% of channel width, and inflow Froude number equal to 0.34. From the figure, it is clear that there is satisfactory agreement between experimental and numerical data. Hence, it validates the numerical model used in this study.

The numerical simulation presented in this paper considering the parameters with and without the spur dyke in the meandering channel has evaluated and analyzed the velocity distribution, streamline, the strength of the secondary flow, bed-shear-stress distribution, and effect Froude number on flow. The results show that the streamline drawn in cross-section persists the two vortices in anti-clock direction and closer to the spur dyke, and these vortices shifted downwards as the strength of the stream gets increased. Since longitudinal pressure is more significant at bend surface and in the absence of spur dyke, this becomes very low. Without the spur dyke in the channel, there is no formation of flow zones, but in contrast with the spur dyke, there is a formation of two velocity zones at the junction of the two bends. Due to the spur dyke, there is the formation of secondary flows, which is maximum at the first bend of the channel; along with it, the maximum bed-shear-stress is formed outside the flow separation zone at the convex tip of the spur dyke. The meander with spur dyke becomes more complicit to protect the heavy flow in the field and helps in damaging the river less. In hydraulics, performing field experiments is very costly and almost impossible to deal with all parameters accurately within the same time. The numerical models are the best way to analyze all parameters, so we hope this numerical investigation helps in the future findings of hydraulics parameters.

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