Keywords

1 Introduction

The shortcomings such as poor durability and stability of the fiber nets used in inshore netting aquaculture industry under the action of long wave currents have seriously affected the marine environment and the living space of fish, resulting in the reduction of fish quantity and quality. The deep-water metal mesh box has become a popular mode of aquaculture development with the advantages of wave current resistance, high stability, smooth and durable, and low pollution. Metal netting is an important part of deep-water netting and one of the most complex and major components under stress, which is directly related to the safety and energy saving of fishery production and quality improvement, and is an important branch of aquatic science.

More research has been conducted by scholars in various countries on the hydrodynamic characteristics of net coats, and Wang Yintao et al. [1] studied the hydrodynamic characteristics of nets through experiments, and calculated the wave force of nets and nets frames. Cao Xuerui et al. [2] used the “nine-point coordinate method” to calculate and analyze the effects of flow velocity and counterweight on the preparation of netting. Chen, Cheng et al. [3] investigated the interaction of the mesh coat with regular and focused waves using porous medium theory. Wang, Wen et al. [4] investigated the water resistance characteristics of metal rhombic mesh coat under the action of water flow by model experiments. Huke et al. [5] based on the finite element principle, a computational model that can be used to calculate the hydrodynamic force of the mesh coat under the action of water flow was prepared by combining the empirical equations of the mesh plane. Shi Xinghua [6] Based on a new mesh grouping method, numerical simulation is used to analyze the deformation and force of the mesh coat. Huang Xiaohua et al. [7, 8] numerical simulation of mesh based on concentrated mass method to analyze the effect of counterweight on the force, deformation and motion characteristics of mesh under the action of water flow. Lader et al. [9] assumed the mesh coat as a flexible body composed of micro-element mesh connected by nonlinear springs, and studied the force and deformation of the circular mesh coat under the action of water flow by numerical methods. Although many scholars have studied various aspects of the hydrodynamic properties of mesh coats, most of them are analyzed for fixed-size mesh coats, and the analysis of the hydrodynamic laws of mesh coats with different height and width ratios is rare.

Metal diamond chain link mesh is a small-scale porous elastic mesh structure, and its connection method is more special compared with traditional fiber-based flexible mesh clothing. In this paper, we adopt the finite unit method [10] ABAQUS software is used to numerically calculate the hydrodynamic properties of a zinc-aluminum alloy rhombic metal mesh [3, 4]. The hydrodynamic characteristics of a zinc-aluminum alloy rhombic metal mesh under the action of water flow are numerically calculated, and the relationship between the maximum deformation and axial stress of the mesh and the height/width ratio of the mesh is analyzed on the basis of the results of good fit with the previous experimental results, changing the preparation direction and height/width ratio of the mesh, and the relationship between the overall mesh, the water resistance of the long and short sides and the force transfer on the fixed side of the mesh, as well as the maximum deformation of the mesh. The results of the study will provide design basis for the optimization design of the mesh jacket and the maximization of energy saving benefits.

2 Numerical Model

2.1 Geometric Model of the Mesh Coat

A three-dimensional wire model is used to model the metal rhombic mesh coat, and the vertical single mesh wire is regarded as a component, for which operations such as vertical array are performed to simulate the transversely woven metal mesh coat. The contact is simulated by adding a connection unit at the intersection of the two wires, and the relative degrees of freedom in the three displacement directions at the contact are constrained during the calculation, and the relative degrees of freedom of rotation are not constrained [5]. The relative rotational degrees of freedom are not constrained. Figure 1 shows the model diagram of a metal diamond-shaped chain link mesh with mesh size m = 45 mm, wire diameter 3.2 mm, horizontal side x and vertical side y.

Fig. 1.
figure 1

Model diagram of metal diamond-shaped chain link network

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2.2 Numerical Methods

Force Analysis

Gravity and Buoyancy

Because the whole net coat is submerged below the water surface, the gravity and buoyancy are considered at the same time and the circular section rod [11] of gravity and buoyancy are calculated as follows:

$$ P_z = \rho_f gV - \rho_w gV = (\rho_f - \rho_w )g\frac{\pi D^2 }{4}l $$
(1)

where: Pz is the combined force of gravity and buoyancy on the circular rod; ρf and ρw are the densities of the metal mesh and water, respectively; D is the cross-sectional diameter of the circular rod; l is the length of the rod; V is the volume of the rod.

Water Flow Force

The water flow can be approximated as a steady plane flow, so the interaction of the water flow with a circular bar [12] can be expressed by the equation of planar flow and lead cylindrical load.

$$ F_c = \frac{1}{2}\rho_w C_d Dv_{c\max }^2 $$
(2)

where: Fc is the water flow load per unit length of the circular rod; Cd is the drag coefficient; v2cmax is the maximum possible velocity of the fluid.

Calculation Method

The mesh coat is simulated using a two-node beam unit. Each node has three displacement degrees of freedom in three dimensions, and its discretized equation of motion [4]:

$$ M\ddot{u} + C\dot{u} + Ku = Q $$
(3)

where: M, C, K and Q are the mass matrix, damping matrix, stiffness matrix and nodal load vector of the system nodes, respectively; \(\ddot{u}\) and \(\dot{u}\) and \(u\) are the acceleration vector, velocity vector and displacement of the system nodes, respectively.

$$ \begin{array}{*{20}c} {M = \sum\limits_e {M^e } \quad M^e = \int_{V_e } {\rho N^T NdV} } \\ {C = \sum\limits_e {C^e } \quad C^e = \int_{V_e } {\eta N^T NdV} } \\ {K = \sum\limits_e {K^e } \quad K^e = \int_{V_e } {B^T DBdV} } \\ {Q = \sum\limits_e {Q^e } \quad Q^e = \int_{V_e } {N^T fdV + \int_{S_e } {N^T Tds} } } \\ \end{array} $$
(4)

where: Me, Ce, Ke, and Qe are the mass matrix, damping matrix, stiffness matrix, and load vector of the unit nodes, respectively; N is the interpolation function matrix; B is the strain matrix; D is the elasticity matrix; f is the nodal load matrix composed of the unit volume forces; T is the nodal load matrix composed of the unit surface forces; Ve is the unit volume; Se is the unit area; ρ is the mass density; and η is the damping coefficient. The discretized equations of motion are solved using the implicit algorithm in the ABAQUS/Standard direct integration method.

3 Results and Discussion

3.1 Total Resistance to Water Flow of the Mesh Coat

In this paper, the material parameters of zinc-aluminum alloy, mesh size 45 mm and wire diameter 3.2 mm are used in the validated literature. Keeping the total area of the mesh coat the same, the aspect ratio is varied to Ly/Lx = 1/2.3, 1/2, 1/1.7, 1/1.4, 1, 1.4, 1.7, 2, 2.3, and calculated at 0.2 m/s, 0.4 m/s, 0.6 m/s, 0.8 m/s and 1.0 m/s different flow velocity conditions of the net clothing water resistance and the relationship between the height and width ratio.

Figure 2 shows the comparison of the water resistance of the mesh coat under the above conditions.

From Fig. 2, it can be seen that the water resistance of the mesh coat is independent of the height to width ratio. This is due to the fact that under the premise of identical environmental conditions, the magnitude of the force on the mesh is related to the projected area of the mesh in the direction of the water flow. In this paper, the total area of the mesh, mesh size, mesh diameter and the direction of incoming flow are determined to be unchanged, and the weave direction and height/width ratio of the mesh are changed to calculate the constant force on the mesh.

Fig. 2.
figure 2

Variation of water resistance of netting with height to width ratio at different flow rates

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3.2 The Force Transmission Law of the Fixed Edge of the Net Clothing

Figure 3 shows the relationship between the ratio of the force on the x(y) side of the mesh and the total force on the mesh for different aspect ratios of 0.2 m/s, 0.4 m/s, 0.6 m/s, 0.8 m/s, and 1 m/s flow velocity λA,x or λA,y and the aspect ratio Ly /Lx, respectively.

Fig. 3.
figure 3

Relationship between the reaction force distribution coefficient on the x(y) side of the mesh and the aspect ratio Ly /Lx at different flow rates

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From Fig. 3, the ratio λA,x of the horizontal side of the mesh to the total force decreases as the aspect ratio Ly /Lx increases; the ratio λA,y of the vertical side to the total force increases as the aspect ratio Ly/Lx increases. This reflects that under the effect of uniform incoming flow, the forces on the mesh are mainly transmitted along the short side.

The maximum value of the difference between the distribution coefficients of horizontal and vertical side forces all appear in the Ly/Lx = 1/2.3 working condition; when the aspect ratio is less than 1, the flow velocity has little effect on the force transfer of different aspect ratios of net clothing; when the aspect ratio is greater than 1, the two curves gradually approach with the increase of flow velocity, and the changes are more obvious; the maximum values of λA,y are 19%, 21%, 26%, 32% and 36% under different flow velocity conditions from low to high.

3.3 Relationship Between Mesh Deformation and Mesh Height/Width Ratio

Figure 4 shows the comparison of the maximum deformation produced by the mesh coat under the above working conditions.

Fig. 4.
figure 4

Variation of the maximum deformation of the mesh with the aspect ratio at different flow rates

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Figure 5 shows the deformation diagram of the mesh coat with different aspect ratios under the flow velocity of 1 m/s at 100 times magnification.

Fig. 5.
figure 5

Deformation of mesh coat with different aspect ratios at flow velocity 1 m/s with 100 times magnification

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As can be seen from Fig. 4, the maximum deformation produced by the mesh coat is positively correlated with the mesh coat height to width ratio. This is because the intertwined mesh knots at the connection of the diamond-shaped metal mesh make the transverse and longitudinal bending stiffness of the mesh differ, and the larger the aspect ratio is, the more hinges the mesh can rotate longitudinally, and the more bending moments are transmitted transversely at the same flow rate, and the larger the displacement of the mesh can produce. As can be seen from Fig. 5, the middle of the mesh is the largest deformation, and the deformation gradually decreases when it spreads around, and the mesh is deformed in a mesh pocket inside the mesh.

4 Conclusion

Based on the basic principle of finite element, this paper investigates the overall mesh, force transfer law and mesh deformation under different aspect ratios under the action of water flow through numerical simulation. The force on one side is related to the aspect ratio of the mesh, and the force on the vertical side increases gradually with the increase of aspect ratio, while the force on the horizontal side decreases gradually with the increase of aspect ratio; the force on the mesh is mainly transmitted along the short side in the uniform incoming flow. The maximum deformation produced by the mesh coat is positively related to the mesh coat height to width ratio. Therefore, in the production of the physical mesh box, attention should be paid to the reinforcement on the longer fixed edges of the mesh, and the optimal aspect ratio should be determined according to the incoming flow velocity to make the mesh have better safety and stability.