The vertical U-shaped gate holds significant potential for widespread application in flow control within U-shaped channels, as it eliminates the necessity for constructing auxiliary hydraulic structures. The boundary conditions associated with the U-shaped gate are complex, offering distinctive hydraulic features. In this study, the hydraulic characteristics of a vertical U-shaped gate have been investigated by model test and numerical simulation on a U-shaped channel under different flow rates, and the hydraulic evolution process was analyzed. The results show that the minimum relative error of discharges is 0.4%, so the numerical simulation can accurately describe the hydraulic performance of the vertical U-shaped gate. The flow generates a contracted cross-section and presents rhomboid water waves with a ‘hump-like’ convex structure after passing the U-shaped gate, accompanied by large kinetic energy dissipation. The gate opening exerts notable influence on the free surface width. The width of the first contraction section increased by 53.88% as the gate opening ranged from 2.5 to 5.5 cm with a flow rate of 8.24 L/s. The power function relationship of upstream flow Froude number, the width of free surface and energy loss is established. The results are helpful for engineering designing and operation management of a U-shaped gate.

  • Indoor experiments and numerical simulation are used to investigate the hydraulic performance of a U-shaped gate.

  • Water flow presented rhomboid-shaped water wave downstream for U-shaped gates.

  • Diamond-shaped water waves will result in kinetic energy dissipation.

  • The value of free surface width can estimate the kinetic energy loss.

  • The width of the free surface and the energy loss present a power function relationship.

The U-shaped channel features a distinctive cross-sectional design, with a curved bottom and an upper portion consisting of straight segments at a specific inclination. Compared with trapezoidal and rectangular channels, the U-shaped channel exhibits a more uniform flow velocity distribution, enhanced water conveyance capacity, and commendable resistance to seepage and freezing. It is commonly employed as a cross-sectional form in channel water conveyance projects. However, when measuring the flow in such channels, it is typically necessary to construct specialized flow measurement facilities, such as twisted surface and water columns (Bijankhan & Ferro 2019; Kapoor et al. 2019), measuring water tank (Samani & Magallanez 1993, 2000; Xiaoyi et al. 2002; Sun et al. 2021), quantity horizontal plate. The construction of these facilities not only causes secondary head loss in the channel (Wahl 2005; Shayan & Farhoudi 2013; Mohamed & Abdelhaleem 2020), but also require additional construction and maintenance. Among all flow measurement devices, the flat-plate sluice gate stands out for its simplicity and compact structure, eliminating the need for additional structures. This not only reduces construction costs but also renders it widely applicable in small-scale channels. However, compared with other channels, the hydraulic performance of a flat-plate sluice gate in a U-shaped channel exhibits significant distinctions. Therefore, investigating the hydraulic characteristics and kinetic energy loss of a flat-plate sluice gate in a U-shaped channel is of crucial significance for the development of flow rate measurement devices tailored for U-shaped channels.

Presently, the hydraulic performance of open-channel flow measurement devices is commonly investigated through methods such as theoretical analysis, model experiments, and numerical simulations. For example, Ferro (2000) established the relationship between water level and discharge through dimensional analysis and incomplete similarity theory. Some researchers (Clemmens et al. 2003; Habibzadeh et al. 2011; Vaheddoost et al. 2021) derived the flow rate calculation formula of radial gate by simultaneously solving the energy and momentum equations, demonstrating the high accuracy of the modified formula; Akoz et al. (2009) proved that the kε turbulent closure model can simulate the velocity field and free surface profile of upstream and downstream flow of vertical sluice more accurately compared with the kω turbulence model; Kubrak et al. (2020) verified the feasibility of estimating the discharge flow using the gate calculation formula under submerged outflow conditions with experimental methods, and the accuracy of the flow coefficient was about 10%. These studies have provided numerous insights into selecting research methods for assessing the hydraulic performance of gates.

At present, the research on the hydraulic performance of channel flow measurement devices is predominantly focused on rectangular and trapezoidal channels. Omid et al. (2007) investigated the hydraulic jump phenomenon formed in the stilling pool with a gradually expanding cross-section in trapezoidal channels, and an implicit equation was proposed for the sequent depth and the energy loss. Mitchell (2008) proposed a series of algorithms to predict the ratio of conjugate depths for trapezoidal and circular channels, it can be applied to predict energy loss in civil engineering hydraulics design. Nedim (2021) presents an analysis of water flow and flow velocity in the rectangular channel for free flow conditions, and a quadratic function of water velocity and flow depending on the water depth in the channel was proposed; Lamri et al. (2021) proposed two direct solutions for head loss and normal water depth in rectangular and triangular open channels, the explicit equations for the normal depths are developed, the results presented a high accuracy. Daneshfaraz et al. (2020, 2022) studied the energy dissipation of supercritical water flowing through a sudden contraction, which found that the rate of relative depreciation of energy is increased and hysteresis occurs when the supercritical flow is dealing with contraction. The formation of hysteresis increases the relative residual energy of different sections by 49.47–56.18%. Also, the crescent-shaped contraction has a significant effect on energy dissipating for supercritical flow, the energy dissipation is increased with increasing the upstream Froude number of crescent-shaped contraction (Daneshfaraz et al. 2021).

For U-shaped channels, Bushra & Afzal (2006) simplified the three-dimensional flow in the U-shaped channel to two-dimensional flow and analyzed the turbulent structure of hydraulic jump in the channel employing the Reynolds equation. Liu et al. (2014) proposed a water-measuring column with a round head to measure flow based on the cylindrical flow around theory, and a calculation formula for water column flow with a circular head was obtained by regression analysis. Azimi et al. (2017) conducted numerical studies on the three-dimensional morphology of hydraulic jump in the U-shaped channel, the comparison between the computational results and experimental findings indicates that the numerical model exhibits good accuracy. Mingyu et al. (2023) studied the flow capacity of the gate under different working conditions, and a formula to estimating flow rates was derived based on the hydraulic characteristics of the gate and channel, it is helpful for designing U-shaped channels. These researches focus on the hydraulic characteristics of various channels. Nevertheless, the flow pattern behind the vertical U-shaped sluice gate under the condition of free discharge has not been systematically examined, meanwhile, energy dissipation is a critical parameter for the evaluation of a sluice gate in the channel (Kalateh et al. 2024), but little research have been conducted for U-shaped sluice gates.

The U-shaped channel has been widely used in the irrigated area, but the review of previous studies indicates that a thorough investigation into the hydraulic characteristics of U-shaped gates under free discharge conditions is necessary, especially for the changes of flow pattern and energy dissipation. In order to solve these problems, this paper investigates the hydraulic characteristics of a vertical U-shaped gate under varying flow rates and gate openings through model testing cooperating with numerical simulation. The flow pattern behind the gate is observed, and flow parameters such as water depth, free surface width and velocity distribution at different measuring points are recorded, and the energy losses under different working conditions are calculated.

Dimensional analysis

Dimensional analysis is adopted on the basis of the achievements of Rasoul (Daneshfaraz et al. 2020). The relationship of parameters is as follows:
formula
(1)
is the channel width, C is the arc length, e is the gate opening, l is the contraction width, y is the flow depth after the jump, g represents the gravity acceleration; is the density; is the dynamic viscosity; is the specific energy upstream; is the specific energy downstream. On the basis of theorem, the non-dimensional parameters are produced as follows:
formula
(2)
The shape and dimension parameters of the channel are constant during the test, so their changes are ignored; the independent dimensionless parameters are defined as follows:
formula
(3)

Experimental setup

The experiments were carried out in the laboratory of Hydraulics in the School of Water Conservancy and Transportation at Zhengzhou University. The experimental platform is composed of a 12.5 m long U-shaped channel, U-shaped sluice gate, stabilization pond, pumping station, regulating value, circulation pipeline, electromagnetic flow meter, triangular weir and tailgate, the experimental setup is shown in Figure 1. The stability of the output of the pump is controlled by the frequency conversion device, meanwhile, the stabilization pond is installed in the front of the U-shaped channel to mitigate the turbulence. The length and longitudinal slope of the channel are 12.5 m and 0.003, respectively; the top width of the channel is 0.5 m. The U-shaped gate is installed 1.5 m away from the stabilization pond to stabilize the surface wave. The tailgate is installed at the end of the channel to control the downstream depth, and the triangular weir is set up in the return canal section to calibrate the flow rate measured by an electromagnetic flow meter.
Figure 1

Experimental setup.

Figure 1

Experimental setup.

Close modal
The flow rate of the triangular weir can be calculated by the following formula:
formula
(4)
where Q is the flow rate (m3/s), H is the water level above the weir (m).

In this research, five gate openings with five different flow rates were designed to investigate the influence of gate opening and upstream depth on hydraulic characteristics and energy dissipation under free flow. The experimental factors and levels are shown in Table 1, and the total number of experiments and simulations are both 29. The flow rate is controlled by a valve installed in the water supply pipe, the gate opening is measured by the ruler, upstream and downstream flow depths are measured by needle water level gauge, and the width of the water surface is measured by steel tape. The velocity is measured by a velocity meter (HD-LS300-A, propeller-type), and the duration of velocity data collection is about 30 s.

Table 1

Experiment factors and levels

Gate opening (cm)Upstream water level (m)Downstream water level (m)Flow rate (L/s)Experimental group numberTest numberFlow condition
2.5 0.082–0.143 0.052–0.078 5.01–8.05 A11 A12
B11 B12 
Free discharge 
4.0 0.055–0.222 0.050–0.122 5.01–16.88 A21 A22
A23
B21 B22
C11 C12
D11 D12 
Free discharge 
5.5 0.075–0.195 0.068–0.125 8.05–19.44 B31 B32
C21 C22
D21 D22
E11 E12 
Free discharge 
7.5 0.105–0.148 0.081–0.123 14.09–19.44 C31 C32
D31 D32
E21 E22 
Free discharge 
9.5 0.122–0.125 0.099–0.122 19.24–20.60 E31 E32 Free discharge 
Gate opening (cm)Upstream water level (m)Downstream water level (m)Flow rate (L/s)Experimental group numberTest numberFlow condition
2.5 0.082–0.143 0.052–0.078 5.01–8.05 A11 A12
B11 B12 
Free discharge 
4.0 0.055–0.222 0.050–0.122 5.01–16.88 A21 A22
A23
B21 B22
C11 C12
D11 D12 
Free discharge 
5.5 0.075–0.195 0.068–0.125 8.05–19.44 B31 B32
C21 C22
D21 D22
E11 E12 
Free discharge 
7.5 0.105–0.148 0.081–0.123 14.09–19.44 C31 C32
D31 D32
E21 E22 
Free discharge 
9.5 0.122–0.125 0.099–0.122 19.24–20.60 E31 E32 Free discharge 

Numerical simulation

Fluent software (ANSYS FLUENT 21.0.) is used to investigate the hydraulic characteristics of channel with U-shaped plate gate. The continuity and Navier–Stokes equations for fluid flow are adopted to describe the flow state (Temam 2001; Liu et al. 2014), standard k–epsilon model is chosen to solve the unsteady calculation. The continuity and momentum equation was written as follows:

Continuity:
formula
(5)
Momentum:
formula
(6)
formula
(7)
formula
(8)
where (,,) are the body accelerations in (,,) directions; (,,) are the viscous accelerations in (,,) directions; (,,) are the fraction of flowable area in (, y, ) directions. (,,) are velocity components in (, y, ) directions, respectively; p is the pressure; t is the time; is the density of the fluid, and the object of study is water; is the fractional volume open to flow.
To numerically solve the rapidly varying flow pattern, it is important that the free surface be accurately tracked. The Multiphase Volume of Fraction model, renowned for its accuracy in tracking the free surface of open-channel flow, is employed in this research (Savage & Johnson 2001; Kim & Lee 2003; Ashgriz et al. 2004). In this method for calculating the fluid volume component, the following equation is calculated:
formula
(9)

The three-dimensional model is created using SolidWorks software, with the U-shaped gate positioned 1.5 m from the upstream entrance. A tetrahedral mesh is generated for the model using ANSYS ICEM software, with a cell grid size set to 2.5 cm and a total of 681,114 grid cells. The boundary conditions are configured as follows: The channel's water inlet is designated as a pressure inlet, while the water outlet employs a pressure outlet boundary (Figure 8). The inlet and outlet boundary conditions are assigned with values derived from experimental measurements, encompassing water depth and velocities. A pressure inlet is applied at the air inlet boundary atop the channel. The sidewall and the U-shaped gate are defined as no-slip wall boundaries. The SIMPLE algorithm is employed for solving the mass conservation and Navier–Stokes equations. A time step size (t) of 0.01 s is chosen, with a convergence precision of 0.0001 applied to all equations.

Mesh Independence check

Three different grid sizes were selected for meshing the numerical model, resulting in a total of 681,114; 711,358; and 880,506 grid cells, respectively. Under the same boundary conditions, the comparison of the width in contraction and diffusion sections at the same location in the numerical models with three different grid sizes was conducted to test grid independence (Table 2). It was observed that the width at the same location remained essentially unchanged for different numbers of grid cells. Therefore, the mesh size with 681,114 grid cells was selected to save computational resources and reduce simulation time while achieving the desired results.

Validation

To validate the accuracy of the numerical simulation model, the experimental results of the U-shaped channel are compared with the numerical simulation results. Figure 2 shows the flow velocity of the monitoring points in the channel along the flow direction, and the relative error of the monitoring points' velocity is −14.74 to 3.73% in test C11 (Figure 2(a)), while for test E11 (Figure 2(b)), the relative errors ranged from −14.54 to 5.06%. Under different working conditions, the simulated values are close to the test results, and the numerical simulation results are in good agreement with the test results. Therefore, the numerical model used in this study is viable for investigating flow patterns and energy dissipation through sluice gates in U-shaped channels.
Figure 2

The comparison of velocities in test C11 and E11 for simulation and experiment method.

Figure 2

The comparison of velocities in test C11 and E11 for simulation and experiment method.

Close modal

Flow pattern

Figures 3(a) and 3(c) illustrate the flow field distribution at a flow rate of 8.05 L/s, with a gate opening of 2.5 cm and a water head in front of the gate of 14.29 cm. Figures 3(b) and 3(d) depict the flow field distribution at a flow rate of 16.88 L/s, with a gate opening of 7.5 cm and a water head in front of the gate of 13.89 cm. The experimental results show that water flows through the stilling basin into the channel, causing a continuous rise in downstream water levels while upstream water levels gradually stabilize. In proximity to the gate, the resistance imposed by the gate impedes the water flow, resulting in an elevation of upstream water levels. Due to the difference in water levels between the upstream and downstream, the water along the sidewalls of the channel flow inclined downward under the influence of gravity and the supporting force from the channel sidewalls after passing through the U-shaped gate, and then converges with the bottom flow of the channel, leading to a reduction in water surface width to a minimum at the section of confluence (Figure 3(a) and 3(b)). (Lin & Shuaijie 2023) also observed the same phenomenon in the vertical trapezoidal gate experiment, with hump-like water flow behind the gate and the width of the water surface shrinking. Meanwhile, the water depth near the central axis reaches its maximum, and presents a hump-like shape (Figure 3(c) and 3(d)). The water flow behind the gate exhibits significant fluctuations, leading to contracting and expanding water flow alternately after the water impinges on the side wall of the channel, and presents a rhomboid-shaped water wave downstream.
Figure 3

The comparison of flow regime. (a) Top view of test number B11 (b) Top view of test number D32 (c) Side view of test number B11 (d) Side view of test number D32

Figure 3

The comparison of flow regime. (a) Top view of test number B11 (b) Top view of test number D32 (c) Side view of test number B11 (d) Side view of test number D32

Close modal

The numerical simulation results show that the water flow presented a rhomboid flow pattern along the channel, and the central water level of the contraction section was increased, these findings are consistent with the experimental observation results.

  • (1)

    Water surface profile

Figure 4 illustrates the water surface profile distribution at the central section for various gate opening degrees with different flow rates. The measured water level values obtained during the experiment align closely with the simulated values corresponding to the respective operating conditions. Once the flow field stabilizes, the water flow near the gate experiences resistance from the gate, leading to an elevated water level upstream of the gate. The water surface abruptly descends at the gate location. As the water flows through the U-shaped sluice gate, a hump-like shape manifests at the end of the contraction section. The height of the hump generates in the first contraction section is largest, and then sequentially decreases with the increase of the flow process, and the water surface profile tended to be stable. It is observed that the water surface elevation in front of the gate and the amplitude of fluctuations behind the gate decrease with an increase in the gate opening for the same discharge. Additionally, the upstream water depth is inversely proportional to the downstream water depth (Figures 4(a) and 4(b)). In addition, the amplitude of fluctuations behind the gate increases with an increase in flow rate for a constant gate opening (Figures 4(c) and 4(d)).
  • (2)

    The characteristic of rhomboid-shaped water wave

Figure 4

The comparison of simulated and experimental water surface profile distribution in the central section.

Figure 4

The comparison of simulated and experimental water surface profile distribution in the central section.

Close modal
The contraction section, diffusion and hump formed in the channel are important factors to reflect the overflow force characteristics of the U-shaped gate. The contraction width in the first and second sections, the diffusion width in the first section and the height of the hump formed in the first section were measured. Figure 5 shows the comparison of rhomboid-shaped parameters between experimental and simulation methods. The results show that the relative deviation of the width in the first and second contraction sections ranges from −6.8 to 11.04% and −6.92 to 10.98%, respectively (Figure 5(a) and 5(c)). The value in the first diffusion section is −8.59 to 5.13% (Figure 5(b)), and the relative deviation of hump height ranges from −12.98 to 2.16% (Figure 5(d)). The simulated values under different working conditions are in good agreement with the experimental results, it gave further verification that the numerical simulation can be used to evaluate the hydraulic characteristics of the U-shaped sluice gate.
Figure 5

The comparison of hydraulic characteristic of rhomboid-shaped water wave with simulation and experimental method.

Figure 5

The comparison of hydraulic characteristic of rhomboid-shaped water wave with simulation and experimental method.

Close modal

Discharge and velocity

  • (1)

    Discharges

A triangle weir is set in the return canal section to measure the flow rate, and the flow rate can be calculated by Equation (4) as soon as the water head on the weir is obtained. The comparison of flow rates are presented in Table 3. It can be seen that the relative error between the experiments and the simulations ranges from 0.40 to 7.25%, which indicates that the numerical simulation method is accurate in describing the flow rate of the U-shaped sluice gate.

  • (2)

    Velocities

The free surface velocities in the central section of the channel are measured. Figure 6 presents the comparison of velocities under different working conditions. It shows that the flow velocity obtained in the experiments has a high consistency with the simulated value. The flow velocities distribution in the upper reaches of the channel are stable, as water flows through the gate, velocities increase sharply, accompanied by pronounced fluctuations. The reason for the increasing velocity is that the gravitational potential energy of the upstream water transforms into kinetic energy, and the velocity downstream increases proportionally with greater water depth upstream. Diamond flow formed behind the gate has a remarkable influence on the velocity distribution: a converging flow is generated and flows toward the central cross-section after water impacts the sidewall, the water depth diminishes in the diffusion section, causing an increase in velocity, consequently.
Table 2

Mesh independence study of the width in contraction and diffusion section

Numbers of cellsThe width in contraction and diffusion section (cm)
First contraction sectionFirst diffusion sectionSecond contraction section
681,114 19.62 32.30 24.48 
761,358 19.54 31.20 24.40 
880,506 19.55 31.24 24.47 
Numbers of cellsThe width in contraction and diffusion section (cm)
First contraction sectionFirst diffusion sectionSecond contraction section
681,114 19.62 32.30 24.48 
761,358 19.54 31.20 24.40 
880,506 19.55 31.24 24.47 
Table 3

The comparison of flow rate with simulation and experiment method

Flow regimeTest numberDischarge (L/s)
Relative deviation
Experimental valueSimulation data
Free discharge 5.01 5.03 0.40% 
8.05 8.24 2.36% 
14.09 14.75 4.68% 
16.88 18.25 8.12% 
19.44 20.85 7.25% 
Flow regimeTest numberDischarge (L/s)
Relative deviation
Experimental valueSimulation data
Free discharge 5.01 5.03 0.40% 
8.05 8.24 2.36% 
14.09 14.75 4.68% 
16.88 18.25 8.12% 
19.44 20.85 7.25% 
Figure 6

The comparison of velocity distribution at the center section for simulation and experiment method.

Figure 6

The comparison of velocity distribution at the center section for simulation and experiment method.

Close modal

Dissipation of kinetic energy

  • (1)

    Evolution of rhomboid water waves

Diamond-shaped water waves will result in kinetic energy dissipation. In order to quantify the kinetic energy loss caused by the waves, the evolution of rhomboid water waves with different gate opening working conditions was analyzed using simulation data. Figure 7 shows the contour of streamline with a flow rate of 8.24 L/s, it shows that as the water flows through the U-shaped sluice gate, the free flow on both sides of the gate moves toward the central axis of the channel with the constraint of the sidewall of the channel, additionally, the component of flow velocity in spanwise direction is opposite, and resulting in colliding flow as converging with the water passing through the bottom of the gate. Simultaneously, the width of the free surface contracts to its minimum, and is accompanied by a significant amount of energy loss in this junction. With increasing flow distance, colliding flow continues to propagate downstream resulting in rhomboid water waves.
Figure 7

The contour of streamline with a flow rate of 8.24 L/s. (a) e = 2.5 cm (b) e = 4.0 cm (c) ) e = 5.5 cm.

Figure 7

The contour of streamline with a flow rate of 8.24 L/s. (a) e = 2.5 cm (b) e = 4.0 cm (c) ) e = 5.5 cm.

Close modal

Figure 7 also shows that the greater the velocity of the impacting flow, the smaller the contracted cross-sectional width in the first contraction section, and gate opening has a remarkable influence on the width, the width is 16.11 and 24.79 cm as the gate opening increased from 2.5 to 5.5 cm, it indicates that the width of free surface in first contraction section can estimate the kinetic energy loss.

  • (2)

    Kinetic energy loss

For the flow pattern to be stable at section 1 and section 2 (Figure 8) in the channel, the mechanical energy in these two sections was calculated under different working conditions, and kinetic energy losses caused by the gate were analyzed. Figure 9(a) shows the kinetic energy loss variation with upstream flow Froude number. It shows that the energy loss decreases with the increase of upstream Froude numbers, and the descending range decreases for larger Froude numbers as a constant gate opening. The variation character of energy loss against the Froude number is different from that proposed by Daneshfaraz et al. (2020). It may be that the Froude number in this research is smaller than 1, i.e.; the flow pattern of upstream is subcritical flow for all gate opening conditions. Figure 9 also shows that the kinetic energy loss increases as the gate opening increases, proving the reasonableness of the conclusion. Considering the width of the free surface in the first contraction section can estimate the kinetic energy loss, the relationship between the width of the contraction section and the energy loss is revealed (Figure 9(b)). It is evident that, for a constant gate opening, a smaller width of the contraction section corresponds to a greater energy loss. The power function relationship of upstream flow Froude number, the width of free surface and the energy loss is established. Parameters of a power function with different gate openings are presented as Equation (10). It can estimate the kinetic energy loss for a constant gate opening.
formula
(10)
Figure 8

Boundary conditions.

Figure 8

Boundary conditions.

Close modal
Figure 9

The power function fit curve of energy loss with Froude number and e/l. (a) Kinetic energy loss for different Froude number (b) Kinetic energy loss in different e/l

Figure 9

The power function fit curve of energy loss with Froude number and e/l. (a) Kinetic energy loss for different Froude number (b) Kinetic energy loss in different e/l

Close modal

In this research, the hydraulic characteristics of a vertical flat gate were investigated under varying flow rates and gate openings through model testing cooperating with numerical simulation, the main results can be summarized as follows:

  • (1)

    The flow generates a contracted cross-section after passing the U-shaped gate, and a raised structure resembling a camel hump is formed. Meanwhile, the water flow presented rhomboid-shaped water wave downstream; the intensity of the diamond-shaped waves diminishes with the increasing flow distance, leading to a stabilized water surface eventually.

  • (2)

    The flow field distribution obtained by model testing is consistent with the results obtained through numerical simulation; in addition, the disparities between experimental and simulated values, including water depth, velocity, and discharge, are small. The minimum relative error of discharges is 0.4% while the maximum relative error of the width in the first diffusion section is −8.59%, which indicates that the numerical simulation results can be used to describe the hydraulic performance of the vertical U-shaped sluice gate under free flow conditions.

  • (3)

    Gate opening and flow rate have a remarkable influence on free surface width in the first contraction section. The width is 16.11 and 24.79 cm as the gate opening increased from 2.5 to 5.5 cm with a flow rate of 8.24 L/s. The greater the velocity of the impacting flow, the smaller the width, i.e. diamond-shaped water waves lead to kinetic energy dissipation.

  • (4)

    The power function relationship of upstream flow Froude number, the width of free surface and the energy loss is established, which can estimate the kinetic energy loss for a constant gate opening.

I would like to express my deepest gratitude to the editors and reviewers.

This research was supported by The Scientific and Technological Research Program of Henan Province (No. 242102321001), for which the authors are grateful.

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

The authors declare there is no conflict.

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