Optimization of Anti-Scour Device Combined with Perforated Baffle and Ring-Wing Plate Based on a Multi-Factor Orthogonal Experiment

Abstract

In this paper, a new anti-scour device combined with a perforated baffle and ring-wing plate is proposed to enhance the traditional method for better protection of bridge piers from local scour. Based on computational fluid dynamics (CFD), the orthogonal experiments investigated the general laws of the influence of the main factors, such as the ratio of baffle perforated, the position of baffle, and the height of ring-wing plate on the anti-scour effect. Under the protection of the combined device, the maximum scour depth reduction rate in front of the pier is between 65.18% and 81.01%, while that at the side of the pier is between 52.63% and 68.42%. Especially when the perforated ratio is 20%, the baffle is 2d (d is diameter of the pier) away from the pier, and the ring-wing plate is located at 1/3 of water depth, the anti-scour effect is the best. Also, the flow field around the pier under the protection of the combined device is further investigated. The results show that the structure blocks the down-flow actively and diverts and dissipates the flow energy to decrease flow below the critical velocity of sediment. Thus, the device combined with perforated baffle and ring-wing plate has a prominent anti-scour effect and provides a basis for further studies and engineering application.

1. Introduction

As vital transportation infrastructure, sea-crossing bridges play a key role in the comprehensive development of coastal regions. Therefore, it is essential to secure the safety of hydraulic structures such as piers. However, numerous cases and theoretical studies show that the complex ocean environment will lead to scouring around the pier [1,2]. Through investigation and research on the existing bridge monitoring systems, as well as the bridge condition rating systems, scholars like Matos [3] and Brighenti [4] have discovered that the existing bridge scour monitoring systems have difficulties in effectively monitoring the scour situation. Thus, Ayoubloo et al. [5], Pang et al. [6], and Jiawang Zhan et al. [7] have proposed modern technology to predict scour depth. Similarly, based on the scour mechanisms [8,9], proposing reasonable measures to reduce local scour is of enormous economic and social significance.

Existing research shows that the anti-scour measures can be divided into active protection and passive protection [10]. The first category is carried out by changing the flow structure around the pier, while passive protection is carried out by improving the anti-scour capacity of the riverbed through riprap countermeasure [11] and so on.

As discussed and concluded by Mohsen et al. [12], Liang and Wang [13], Fouli and Elsebaie [14], Shan Wang et al. [15], and many other scholars, compared with passive protection, active protection is more economical and effective, with better application prospects [16].

Numerous studies have been carried out on flow-altering devices. Zarrati et al. [17] tested the effectiveness of collars on rectangular piers, and a 74% reduction in maximum scour depth was obtained. Ghorbani and Kells [18] observed that the plate diverted the flow from the pier and reduced the strength of horseshoe vortex. Cheng et al. [19] figured out that the plate was most effective when located at 1/3 water depth, and the length of the plate was the same as the radius of the pier. Under clear-water conditions and uniform bed materials, Karami et al. [20] investigated the anti-scour effect of collar on abutment experimentally. Park et al. [21,22] studied the effect of sacrificial piles on scour through experiments and empirical formulas. And Oral Yagci et al. [23] studied scour and deposition patterns around hexagonal arrays of circular cylinders; the results showed that this method reduced 27% scour volume and 22% scour depth compared to a single solid cylinder counterpart. Tsung-chow et al. [16] tested a small detached ring and obtained a 70% reduction in the initial stage of scouring, which was effective for all angles of attack.

However, all of the approaches used to decrease scour have certain shortcomings, it is indeed difficult to choose a device that can counter the scour effectively under all adverse and unpredictable field conditions. Thus, researchers have been studying combinations of these devices so that the combinations are able to reduce the local scour more effectively. Vittal et al. [24] tested a combination of a full-depth pier group with a collar plate; the results showed that the full pier group was seen to be as effective as a solid cylinder with a collar 3.5 times its diameter. And Mashahir et al. [25] examined a combination of continuous collars and a riprap in clear-water scour conditions. Moncada-M et al. [26] found a combination of collar and piercing of a rectangular slot was able to almost entirely eliminate the scour for the considered flow conditions. Considering the advantages of active countermeasures and the above research experience, the current study proposes an new anti-scour device combined with two active protection devices: a perforated baffle and a ring-wing plate. To the best of our knowledge, there is no report on the on the combination of these two devices.

The aim of the present work is two-fold: (1) to explore the best combination of the new device through an orthogonal experiment to achieve the best anti-scour effect; (2) to verify the effectiveness of the combined optimization device and investigate the underlying mechanisms by a detailed description of the flow field on the horizontal and vertical planes, as well as thoroughly analyzing the flow velocity changes around the pier before and after the installation of the combined device with the help of empirical formulas.

Different from the optimal design of a single device, since the overall efficiency of a combined device is not the linear sum of the individual efficiency of each device [12], an orthogonal experiment of multiple factors and two observation indicators can more effectively show the impact of each parameter on scour depth. In addition, the study on the variation of the flow field on the vertical plane and the variation of the sediment starting velocity on the horizontal plane can further verify the effectiveness of the optimal design of the combined device. The results show that the anti-scour effect of the combined device is better than most of the measures, and it is a reasonable choice for an existing pier to reduce local scour. This paper provides a method and theoretical basis for the design and mechanism analysis of similar types of combined anti-scour devices.

2. Numerical Model

2.1. Governing Equations and Turbulence Model

2.1.1. Governing Equations

In this paper, the mixture model, a simplified two-fluid model that assumes local equilibrium at small spatial scales, is used to solve the equations for the continuity, momentum, and energy conservation of the mixed phase and the volume fraction equation for the second phase, slip velocity, and drift velocity formulas.

Considering incompressible and unsteady flow, the Reynolds averaged N-S equations are as follows:

$$\rho {\displaystyle \frac{\partial u_{\mathrm{i}}}{\partial t}}+\rho u_{\mathrm{j}}{\displaystyle \frac{\partial u_{\mathrm{i}}}{\partial x_{\mathrm{j}}}}-{\displaystyle \frac{\partial p}{\partial x_{\mathrm{i}}}}+\mu ∆u_{\mathrm{i}}+\rho {\displaystyle \frac{\partial {\tau }_{\mathrm{i}\mathrm{j}}}{\partial x_{\mathrm{j}}}},\mathrm{i},\mathrm{j}=1,2,3$$

(1)

The continuity equations are as follows:

$${\displaystyle \frac{\partial u_{\mathrm{i}}}{\partial x_{\mathrm{i}}}}=0$$

(2)

in which x_i (i = 1, 2, 3) are three directions in Cartesian coordinates; u_i (i = 1, 2, 3) are corresponding velocity components; ρ is density of fluid; p is pressure; t is flow time; Re(=u₀D₀/v) is Reynolds number, defined by the flow velocity u₀ and the characteristic length D₀; μ is dynamic viscosity; and τ_ij is Reynolds effect force. Boussinesq proposed the eddy viscosity μ_t, which relates the Reynolds stress to the partial derivative of velocity.

$${\mathsf{\tau }}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{{\mu }_{\mathrm{t}}}{\rho }}\left({\displaystyle \frac{\partial u_{\mathrm{i}}}{\partial x_{\mathrm{j}}}}+{\displaystyle \frac{\partial u_{\mathrm{j}}}{\partial x_{\mathrm{i}}}}\right)-{\displaystyle \frac{2}{3}}{\delta }_{\mathrm{i}\mathrm{j}},k,\mathrm{i},\mathrm{j}=1,2,3$$

(3)

in which k is turbulent kinetic energy, and δ_ij is the sign of Kronecker.

2.1.2. Turbulence Model

In view of the fact that the k-ε turbulence model, as a two-equation model based on Reynolds averaging, has the ability to effectively describe the key physical quantities of turbulent flow, by solving the equations of turbulent kinetic energy and turbulent kinetic energy dissipation rate, it can better capture the basic characteristics of turbulence. Especially for the complex flow conditions around bridge piers, including wake regions, boundary layer separation, and vortices, it can reasonably describe the turbulent kinetic energy and its dissipation situation and effectively characterize the turbulent behavior. Moreover, compared with more complex models, such as the Reynolds Stress Model (RSM), the k-ε turbulence model requires less computational resources and time. In addition, the k-ε turbulence model is relatively mature, with stable mathematical expressions and solution methods. The ANSYS-FLUENT used in this paper provides good support for it, and there are relatively complete setting options in terms of boundary condition treatment and discretization format selection. Therefore, in order to obtain relevant simulation results efficiently and accurately, this paper selects the k-ε turbulence model as the finite element calculation model.

This study adopts the standard k-ε turbulence model. The model parameters are shown in

Table 1. Model parameters for the standard k-ε model.

Gu	σk	σε	Gε1	Gε2
0.09	1.0	1.3	1.44	1.92

. And the governing equations are as follows:

$$\rho {\displaystyle \frac{\partial k}{\partial t}}+\rho u_{\mathrm{i}}{\displaystyle \frac{\partial k}{\partial x_{\mathrm{i}}}}={\displaystyle \frac{\partial }{\partial x_{\mathrm{i}}}}\left[\left(\mu +{\displaystyle \frac{{\mu }_{\mathrm{t}}}{{\sigma }_{\mathrm{k}}}}\right){\displaystyle \frac{\partial k}{\partial x_{\mathrm{i}}}}\right]+G_{\mathrm{k}}-\rho \epsilon$$

(4)

$$\rho {\displaystyle \frac{\partial \epsilon }{\partial t}}+\rho u_{\mathrm{i}}{\displaystyle \frac{\partial \epsilon }{\partial x_{\mathrm{i}}}}={\displaystyle \frac{\partial }{\partial x_{\mathrm{i}}}}\left[\left(\mu +{\displaystyle \frac{{\mu }_{\mathrm{t}}}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x_{\mathrm{i}}}}\right]+G_{{\mathsf{\epsilon }}^1}{\displaystyle \frac{\epsilon }{k}}{G}_{\mathrm{k}}-\rho G_{{\mathsf{\epsilon }}^2}{\displaystyle \frac{{\epsilon }^2}{k}}$$

(5)

$${\mu }_{\mathrm{t}}=\rho G_{\mathsf{\mu }}{\displaystyle \frac{k^2}{\epsilon }}$$

(6)

in which G_k = 2μ_tS_ijS_ij is source term of turbulent kinetic energy and S_ij = ½(∂u_j/∂x_i + ∂u_i/∂x_j) is average strain rate. G_u, G_ε1, and G_ε2 are empirical constants; σ_k and σ_ε are Prandtl numbers corresponding to turbulent kinetic energy and dissipation rate, respectively.

It should be pointed out that the particle dispersion motion theory caused by uniform turbulence is used to describe the characteristics of solid phase turbulence. The relevant equations, turbulent kinetic energy, and dispersion coefficient of the particle phase are given by two different time scales. The first is the characteristic example relaxation time scales associated with particle inertial effects.

$${\tau }_{F.sf}={\alpha }_s{\rho }_f{K}_{sf}^{-1}\left({\displaystyle \frac{{\rho }_s}{{\rho }_f}}+C_V\right)$$

(7)

Lagrangian integral time scale computed along particle trajectories:

$${\tau }_{t.sf}={\tau }_{t,f}{\displaystyle \frac{1}{\sqrt{1+C_{\beta }{\xi }^2}}}$$

(8)

in which $C_V$ is the additional quality factor, and the value is 0.5; the turbulent vortex characteristic time scale is ${\tau }_{t,f}={\displaystyle \frac{3}{2}}C\mu {\displaystyle \frac{K_f}{{\epsilon }_f}}$; $\xi ={\displaystyle \frac{\left|V_r\right|}{\left(\frac{2}{3}{k}_f\right)}}$; $V_r$ is the average value of liquid–solid relative velocity; $C_{\beta }=1.8-1.35{cos}^2{\theta }_0$; and θ₀ is the angle between the average particle velocity and the relative velocity of the group.

2.1.3. Sediment Transport Model

Sediment transported by water above the river bed can be divided into suspended load and bed load. suspended load means sediment carried by flow settles down sufficiently slowly without any touching on river bed, If the silt carried by the flow settles down slowly enough without contacting the river bed, it is referred to as suspended load; otherwise, it is referred to as bed load. The sediment transport form depends on the size of sediments and flow velocity, which can be judged by the critical diameter

$$d={\displaystyle \frac{U^2}{360·g}}$$

(9)

where d_c is the critical diameter to distinguish suspended load and bed load, and U is the mean approach flow velocity. The average flow velocity is calculated by Equation (9), and the incipient velocity of sediment with the particle size in this research is U = 0.25 m/s, and the d = 1.77 × 10⁻⁵ m, smaller than the critical diameter d_c = 0.8 × 10⁻⁴ m. Therefore, the sediment will be transported in the form of bed load.

The accuracy of the model calculation largely depends on the accuracy of bed load transport rate, which can be calculated by the following equation:

$$q_{b,i}=q_b^{\prime }{\displaystyle \frac{{\tau }_i}{\left|\tau \right|}}-C{q}_b{\displaystyle \frac{\partial h}{\partial x_i}}$$

(10)

where $q_{b,i}$ is the component of time-averaged volumetric sediment transport rate per unit width; τ_i (i = x, y, z) is the bed shear stress vector; C = 1.5 is an empirical constant; h is the bed elevation; and $q_b^{\prime }$ is the time-averaged volumetric sediment transport rate per unit width on the horizontal bed, which can be calculated by the following equations:

$$q_b^{\prime }=0.053{\left(s-1\right)}^{0.5}{g}^{0.5}{d}_{50}^{1.5}{D}_{\ast }^{-0.3}{T}^{2.1}\left(T<2.5\right)$$

(11)

$$q_b^{\prime }=0.100{\left(s-1\right)}^{0.5}{g}^{0.5}{d}_{50}^{1.5}{D}_{\ast }^{-0.3}{T}_m^{1.5}\left(T\ge 2.5\right)$$

(12)

where s is the relative density of sediment; d₅₀ is the median sediment grain size; $D_{\ast }=d_{50}{\left[\right(s-1)g/v^2]}^{1/3}$ is the dimensionless sediment parameter; and v is the viscosity coefficient. T and T_m can be recovered from the following equations:

$$T=\left(\left|\tau \right|-{\tau }_{b,cr}\right)$$

(13)

$$T_m={\displaystyle \frac{\lambda \left|\tau \right|-{\tau }_{b,cr}}{{\tau }_{b,cr}}}$$

(14)

where τ is the shearing stress of riverbed bottom; ${\tau }_{b,cr}$ is the critical bed shear stress; and λ is the modification factor, which can be obtained through

$$\mathsf{\lambda }=e^{\left(0.45\mathsf{\alpha }+0.2\mathsf{\beta }\right)}$$

(15)

$$\alpha =1-\left(d_{84}/d_{50}+d_{50}/d_{16}\right)/2$$

(16)

$$\beta =d_{50}/d_{90}-d_{10}/d_{50}$$

(17)

where di is the sediment size.

2.2. Computational Domain and Mesh

As shown in Figure 1, the numerical model is a K-epsilon two-phase flow model, adopting the standard wall function. Given that the flow fields near the cylindrical pier and baffle are rather complex, the grids in these parts have been refined locally. In this paper, the grid independence was numerically verified by establishing different grid sizes, and it was found that the result errors were within a controllable range. It is known from the meshing software that the number of grids is approximately 2.5 × 10⁵, and the average quality of grids is above 0.85 (the closer to 1, the better). The maximum skew-ness is 0.84, while the user manual requires that it should not be greater than 0.95.

The numerical model in this paper is established by using ANSYS-FLUENT. The model is 1.2 m long and 0.8 m wide. And the pier diameter is 0.04 m, which locates at the center of the model, 0.6 m away from the water inlet and outlet and 0.4 m away from the two side walls. All the flume properties are the same as Wang’s [27] flume in the laboratory. And Melville and Coleman [28] indicated that the flume width should be at least 10 times greater than the pier diameter to minimize any contraction effects on the scour depth. In this study, the flume width is 0.8 m, and a 0.04 m pier diameter was selected. Therefore, the resultant ratio of the flume width to the pier diameter is 20, and it satisfies this criterion. As indicated in Figure 2, the water depth of the upper layer is 0.1 m, and the sand in the lower layer is 0.15 m. As stated by Melville [29], the ratio of the diameter of the bridge pier (d) to the average size of the sediment particles (d₅₀) should be greater than 25. In this research, the mean grain size was set as d₅₀ = 0.80 mm, so d/d₅₀ = 50 is evaluated.

2.3. Boundary Conditions and Method

In order to apply the boundary conditions, the upstream is set as Specified Velocity (u₀ = 0.25 m/s) and downstream boundary is set as Outflow. The top boundary is set as Symmetry. Also, the Wall boundary condition is defined for left and right walls, pier, and baffle, which act as virtual frictionless walls. Applications of boundary conditions to this model are shown as Figure 2.

The mixture model obtains the flow field information and the concentration distribution of each phase by solving the governing equations of the mixture and the volume fraction and relative velocity of the second phase. And it determines the scour surface by defining the water–sand interface with the sand volume fraction in CFD-Post. Using the SIMPLE algorithm, which iteratively solves the discrete form of the N-S equation, a pressure field is given and corrected, and the next iterative calculation is started with the corrected pressure field and velocity field until convergence. And the residuals of the continuity equation, velocity, turbulent kinetic energy, and other variables are 1 × 10⁻⁶. Standard initialization from the velocity inlet and the time step size is 0.01 s. According to Melville [30], scour mainly occurs in the first 30 min of the test and is almost fully developed; after that, the growing process is not intensive and goes very slow. Therefore, in order to save time and improve efficiency, the model in this paper only calculates the scour in the first 30 min.

3. Test Design Using Orthogonal Method

3.1. Definition of Variables

As shown in Figure 3, for the aim of determining the optimal location and dimension of the combined device to achieve the least scour depth, the variables of the combined device considered are the perforated ratio of the baffle (S), the distance between baffle and pier (L), and the height of ring-wing plate (H).

Based on the outcomes of Cheng et al. [19], the extension length of the ring-wing plate is consistent with the radius of the pier, and three values were considered for H (i.e., H = 1/2, 1/3, 1/6 h; h is the water depth). Huang et al. [31] reported that the optimal parameters of the surface guide panels are an interior angle θ = 60°, L/D = 2–2.5, and P_D/h = 0.7. Similarly, the interior angle of perforated baffle is 60°, and the height is 3/4 h. Furthermore, considering the diversion and permeability of the baffle, three values of S are tested (i.e., S = 10, 20, 30%). And this structure is located at three different spacings from the pier (i.e., L = 2, 3, and 4 d). It should be noted that, first of all, an oblique flow may affect the efficiency of the device, and the device proposed in this study is mainly intended to reduce the down-flow in front of the pier and the flow intensity near the bed surface in front of the pier. In addition, changes in the angle of attack seem to have an unsafe effect on piers as the approach flow cannot pass smoothly around the pier, forming stronger down-flow and a horseshoe vortex [10]. This design is the same as the ideas of Huang et al. [31] and Lauchlan [32] on similar structures, such as surface guide panels and permeable sheet tiles.

3.2. Test Plan

In order to avoid the influence of human factors on laboratory experiments and improve the experimental efficiency, this paper selected ANSYS-FLUENT finite element software to conduct the simulation experiments. The experimental parameters are shown in

Table 2. Factors and levels of orthogonal experiment.

Levels	Variables
	S	L	H
1	10%	2 d	1/2 h
2	20%	3 d	1/3 h
3	30%	4 d	1/6 h

. There are three independent variables, and for each of them, three levels are considered. Moreover, the typical parameters of the three levels are taken out and designed as three grades for test grouping. In this experiment, the interaction among these three variables is ignored, and an orthogonal experimental scheme L9(3⁴) with 3 factors and 3 levels is designed. In addition, the single pier and the single ring-wing plate are set as the control tests. The configurations of all the tests are listed in Table 2. Compared with the full test, only 11 tests have been carried out in this paper, which has greatly improved the work efficiency.

4. Results and Discussion

4.1. Model Verification

4.1.1. Flow Field Verification

Local scour is a complex process in the flow field, so whether the flow field around the pier can be accurately simulated is very important to ensure the calculation accuracy of local scour. Thus, to verify the accuracy of the finite element model in this paper, the simulated results, including the streamlines and scour depth, are fully compared with laboratory experiment. The upper part of Figure 4 shows the simulation results of the streamlines, which are around the pier and 1 mm above the riverbed.

The experimental results of streamlines at the same section are also given in Figure 4 [29,32]. As concluded by Pang et al. [6], a flow constriction occurs at approximately a 45° angle to the pile, showing good correlation between the two results.

Velocity contour and streamlines on the y-axis plane in front of the pier are given in Figure 5. Upstream of the pier, part of the flow becomes down-flow, which impinges on the bed materials and results in the scour around the pier. The simulations show that the standard k-ε turbulence model is capable of capturing the key flow features, down-flow and flow amplification, which are the main driving force for the sediment transport around the pier and the formation of scour hole. This is consistent with the finding of Roulund et al. [33].

4.1.2. Validation of Scour Pit Model

As known, scour hole is the most direct characterization of local scour, and it can be described by scour depth. Taking the nonprotected pier as an example, the numerical simulation results in this paper are compared with the physical experiment. The overall riverbed surface after equilibrium scour is shown in Figure 6. Obviously, the scour patterns on both sides of the pier are symmetrical, and the sand accumulates at back surface of the pier. Figure 7a,b show the local scour around the pier in the numerical simulation test and physical experiment, respectively. It can be observed that the scour holes are approximately circular, and their shapes are basically the same. The maximum scour depth in front of the pier is greater than that on both sides of the pier. The maximum scour depths of the simulated value and physical experiment value are 3.16 cm and 3.1 cm, respectively, with an error of 1.9%.

In terms of flow field verification, the model established in this paper was compared and verified with the streamline diagrams obtained by Pang et al. [6], and it was found that the flow field patterns were similar. Regarding the scouring pit, by establishing a laboratory flume scouring experiment and comparing it with the scouring pit obtained from the numerical model, the error was found to be around 1.9%. The results indicate that the CFD model in this paper has high reliability and accuracy and can be used for subsequent simulations.

4.2. Analysis of Orthogonal Experimental Results

The maximum scour depth can directly reflect the anti-scour effect of the combined device. Therefore, it has a high reliability to be the evaluation index of the orthogonal experiment. The output responses from the orthogonal experimental tests are recorded in

Table 3. Schemes and results of orthogonal experiment.

Test Number	Factors				Scour Depth
	S	L	H	Empty Column	Front End of Pier (cm)	Side End of Pier (cm)
1	-	-	-	-	3.16	1.9
2	-	-	1/3 h	-	1.2	0.8
3	10%	2d	1/2 h	1	0.8	0.9
4	10%	3d	1/3 h	2	0.9	0.7
5	10%	4d	1/6 h	3	1.1	0.8
6	20%	2d	1/6 h	3	0.8	0.8
7	20%	3d	1/2 h	1	0.6	0.7
8	20%	4d	1/3 h	2	0.6	0.8
9	30%	2d	1/3 h	2	0.7	0.6
10	30%	3d	1/6 h	3	0.9	0.9
11	30%	4d	1/2 h	1	0.9	0.6

. In order to show the change rule of the index (scour depth) more clearly when the level of each factor changes, the main-effect plots are depicted.

According to the simulation results in Table 3, Figure 8 shows the reduction rate of maximum scour depth at the front and side end of the pier. It can be seen that under the protection of the combined device, the scour depth is greatly reduced. More specifically, the reduction rate of the maximum scour depth in front of the pier is between 65.18% and 81.01%, while that at side of the pier is between 52.63% and 68.42%.

Referring to

Table 4. Results of range analysis.

Analysis Results	Maximum Scour Depth at Front End of Pier				Maximum Scour Depth at Side End of Pier
	S	L	H	S	L	H
K1	0.933	0.767	0.767	0.833	0.767	0.733
K2	0.667	0.800	0.733	0.767	0.767	0.700
K3	0.833	0.867	0.933	0.700	0.733	0.867
R	0.266	0.100	0.200	0.133	0.034	0.167
Rank	1	3	2	2	3	1
Optimal level	S2	L1	H2	S3	L3	H2

, when the maximum scour depth in front of the pier is used as the evaluation index, the variable ranked first is the ratio of perforated area (S); the sequence of the impact of all other variables on the maximum scour depth at the front end of pier can be expressed as H > L. While when the index is the maximum scour depth at the side of the pier, the significance ranks as H > S > L. Although the results in Table 4 show that the factors are arranged differently, L is in the last rank for reducing the scour depth. In other words, the distance from the perforated baffle to the pier has little effect on the reduction of the scour depth.

Furthermore, as shown in Figure 9, when the indexes are different, the values of RS are very different, while those of RH are very close, indicating that the influence of S on the scour depth at front end and side end of the pier is stronger than that of H. On the whole, the significance of the three factors on the scour depth can be ranked as S > H > L.

Grimaldi et al. [34] reached a scour reduction in front of the pier of about 45% with a best combination of downstream bed-sill and slot. Odgaard and Wang [35] obtained 64% and 45% scour depth reduction by using combinations of submerged vanes and collar or pier plates and collar, respectively. Zarrati et al. [36] examined a combination of continuous collar and riprap, and a 50% and 60% scour depth reduction in the vicinity of the front and rear piers was achieved. Compared with the above conclusions, the combined device proposed in this paper has a good anti-scour effect, especially at the front side of the pier. However, it is necessary to emphasize that there are oscillations in the results of different cases of combined devices versus single plate, such as in tests 3 and 10. In other words, the maximum scour depth reduction (52.63%) of these combinations is lower than that of the single ring-wing plate (57.89%). The reason for this phenomenon is that combining two devices may change their combined behavior for better or worse, and the mechanisms of both devices are not mutually reinforcing, which is consistent with the findings of Garg et al. [37]. In summary, it is necessary to obtain the best combination through range analysis.

4.2.1. Range Analysis for Factors

Range analysis is an important analysis technique in orthogonal experiments. The range of a factor is the difference between its average maximum and lowest values at different levels; the larger the value of the range, the more important this factor is. Thus, the primary and secondary relationship of the factors and the best dimensions can be obtained. The range can be expressed as Equation (7), and the results of range analysis are illustrated in Table 4.

$$R=K_{max}-K_{min}$$

(18)

4.2.2. Influence of Factors on Maximum Scour Depth

In order to obtain the best level of each factor, the influence of different levels of each factor on the maximum scour depth is needed to be further investigated. As indicated in Figure 10, the increase of the perforated ratio will reduce the scour depth at the side of the pier; this is because the larger perforated ratio allows more water to flow through the baffle to the front end of the pier; correspondingly, the scour depth increases. However, there is still a question regarding efficiency when the perforated ratio is lower than 20%. Accordingly, the optimal ratio of the perforated area is 20%.

As shown in Figure 11, the trend of distance between the pier and the perforated baffle shows that, the farther the baffle is, the deeper the scour at front end of the pier is, and the depth at the side of the pier is opposite. It can also be clearly seen from Figure 11 that when the baffle is 2d from the pier, the combined device has the same anti-scour effect on the front and side of the pier. Instead, the longer distance provides the flow with enough space to recover parallel to the incoming flow and becomes down-flow after meeting the pier, and the scour depth in front of the pier is also increased. However, it should be pointed out that increasing the distance between the baffle and the pier has little effect on reducing the scour depth at side of the pier. Accordingly, 2d can be considered as the best installation location for the perforated baffle.

As illustrated in Figure 12, both lines show that the optimal height for the ring-wing plate is 1/3 of the water depth. Increasing H may reduce the effectiveness of this structure. However, there is still a question regarding the efficiency of the ringwing plate when its height is lower than 1/3 of water depth. This finding is consistent with the conclusion of Cheng et al. [19].

Under comprehensive consideration, the best dimensions of a combined device to achieve the maximum reduction of the scour depth are equal to S = 20%, L = 2 d, and H = 1/3 h.

4.2.3. Effect of the Optimal Combined Device on Flow Field

In order to see how the optimized combined device impacts the flow field and reduces the scour depth, the flow field is further studied. Shown in Figure 13 are the streamlines near the bed for the two conditions. And the background of this figure shows the velocity of flow (V_a = (u₂ + v₂)^0.5).

It can be clearly seen from Figure 13a that there is separation and acceleration of the water flow on the sides of the pier; more specifically, the velocity on the pier side is 1.2 times the inlet velocity, which is almost the same as the magnification of 1.3 obtained by Pang et al. [4]. On the contrary, with the protection of a combined device, the velocity at both sides of the pier is 0.22 m/s, as shown in Figure 13b. It is also seen that the velocity around the perforated baffle is smaller than the inlet velocity.

To better illustrate the anti-scour mechanism of the combined device, two empirical equations proposed by Melville [29] and Dou Guoren [38] are used to calculate the critical velocity of the sand, given as Equations (19)–(21).

$${\displaystyle \frac{V_c}{U_{\ast }}}=5.75\log \left(5.53{\displaystyle \frac{y}{d_{50}}}\right)$$

(19)

$$U_{\ast }=0.0115+0.012d_{50}^{0.14}\left(0.1\mathrm{m}\mathrm{m}<d_{50}<1\mathrm{m}\mathrm{m}\right)$$

(20)

$$V_c={\left({\displaystyle \frac{y}{d_{50}}}\right)}^{0.14}{\left(0.000000605{\displaystyle \frac{10+y}{d_{50}^{0.72}}}\right)}^{0.5}$$

(21)

where $V_c$ is the critical velocity of sediment, $U_{\ast }$ is the critical shear velocity, y is the water depth, and d₅₀ is the median particle size of sand. The critical velocity obtained in this paper and calculated by the above equations is equal to 0.34 and 0.31 m/s. According to the results, the flow at both sides of the unprotected pier almost reaches the critical velocity of sediment. As shown in Figure 13b, due to the diversion and shielding effect of the perforated baffle, the velocity of the accelerated region (0.28 m/s) is reduced, and the region is far from the pier. These findings interpret the reduction of local scour at the vicinity of the pier.

Figure 14 shows the streamlines and velocity contour on the vertical plane. As concluded by Aslani-Kordkandi and Beheshti [39] and Keshavarzi et al. [40], Figure 14a shows the streamlines impinging on the sediment, with the maximum V_z = 0.16 m/s. And as expected and shown in Figure 14b, the flow filed upstream of the pier changes significantly after installing the combined device. Although there is still down-flow above the ring-wing plate, due to the shielding effect of the perforated baffle, its vertical velocity is very small, only 0.06 m/s. It is also worth mentioning that the flow under the ring-wing plate is basically parallel to the incoming flow. These changes in the flow field interpret the reduction of local scour at the vicinity of the pier, and together with the other results in this study, very clearly show the anti-scour effect of the combined device.

Based on the above conclusions, it can be deduced that the optimized combined device is able to change the vortex systems, including down-flow and the horseshoe vortex upstream of the pier, and it is considered a very effective countermeasure against scour around the pier. The combined device can be applied for both new and existing bridge piers, especially when the direction of flow is perpendicular to the arrangement of the bridge piers. It should be pointed out that the above conclusions apply exclusively for the flow and sand conditions considered in the present research.

5. Conclusions

This study proposed a new anti-scour device combined with perforated baffle and ring-wing plate. By using ANSYS-FLUENT, with the maximum scour depth at the front and side ends of the pier as evaluation indices, the effect of the ratio of baffle perforated, relative position of baffle, and height of ring-wing plate on local scour was analyzed. The best dimensions of the combined device were recommended by orthogonal testing, and the flow filed around pier under the protection of the optimal combined device was further studied. The results allow us to draw the following conclusions:

(1) The comparisons between the numerical and the experimental results show that the numerical model adopted in this paper is of high accuracy and advantageous for investigating the shape of scour hole and flow field characteristics around the bridge pier.

(2) After installing the combined device, the maximum scour depth reduction rates in front of the pier are between 65.18% and 81.01%, while those at the side of the pier are between 52.63% and 68.42%. However, some combinations (no. 2 and no. 10, with 52.63%) have a low scour reduction, which is less than the scour reduction of the ring-wing plate alone (57.89%). These results indicate that the efficiency of a combined device is not the linear sum of the individual efficiency of each device.

(3) Based on the orthogonal experiments, the significance of the three factors on the scour depth can be ranked as S > H > L. And the best dimensions of a combined device to achieve the maximum reduction of the scour depth are equal to S = 20%, L = 2d, and H = 1/3 h.

(4) The study of the flow field shows that the ring-wing plate blocks most of the down-flow, so the bed is protected from impinging. In addition, on the horizontal plane, the effect of diversion and water energy dissipation provided by the perforated baffle reduce the velocity of the flow below the critical velocity of sediment. With the two protection mechanisms to reinforce each other, the combined device provides excellent performance.

6. Methods

In order to better control the specific parameters of the test and reduce human influence, ANSYS-FLUENT finite element software was mainly used to conduct simulation tests of the device, and laboratory flume tests were used to verify the numerical model to prove its effectiveness. In terms of test parameters, a variety of test parameters were de-signed, and the orthogonal test method was adopted to select the optimal device parameters. Through the finite element software, the protection effect of the device was better presented through the scouring pit morphology and flow field morphology. After obtaining the specific data, the scour reduction rate of the protection device around the bridge pier was calculated and analyzed to evaluate and analyze the scour reduction effect.