Analysis of Hydrodynamic Behavior of the Floating Tapered Trash Intercepting Net in Currents

Abstract

Ensuring the structural reliability and interception efficiency of trash-intercepting nets (TINs) is crucial for the security of the water withdrawal engineering of the nuclear power station (NPS). The numerical model of a flexible TIN using the lumped mass method was developed, and its high accuracy in simulating the tension distribution of the net and its deformation was validated through physical model tests. A systematic analysis was performed to investigate the effect of key parameters (i.e., water depth, intercepting rate, and diameter of longitudinal/transversal ropes) on the structural response, including the total anchor force, the main cable tension, the rope tension, and the netting tension. The results show that the tension forces acting on the transversal ropes are dramatically larger than those acting on the longitudinal ropes, and the net experiences the smallest tension force when the diameter of transversal ropes is the same as the diameter of the longitudinal ropes. This study is useful for the safety design of the TIN of the NPS.

1. Introduction

The TIN is an extremely important component of the seawater withdrawal system of the NPS. Its main function is to intercept floating objects in seawater (such as jellyfish, algae, and plastics) to prevent them from blocking the seawater withdrawal system of the NPS. The optimal design of the TIN is beneficial for the safety operation of the seawater withdrawal system for the NPS. Therefore, studies on the hydrodynamic behavior of flexible nets in waves and current have attracted much attention from many researchers.

To begin with, numerical simulations and experimental tests were employed to analyze the distribution of hydrodynamic forces on the nets. Swift et al. [1] indicated that the drag coefficient of nets increased due to the biofouling with increases varying from 6% to 240%. The maximum drag coefficient for the most heavily bio-fouled net panel was 0.599. Liu et al. [2] analyzed the hydrodynamic behavior of the net oscillating in the water through a combination of experimental and numerical approaches, analyzing the forces acting on the net under various conditions and determining the relevant hydrodynamic coefficients. Xu et al. [3] found that the force on the netting is closely related to the solidity of the netting. The amplitude of the force increases greatly with the increasing solidity. Experimental results indicated that for net panels with the solidity varying from 0.190 to 0.640, the amplitude of the force increased markedly as the solidity increased. Shimizu et al. [4] performed the experimental test of the drag force of the fine-mesh netting in currents. The study focused on analyzing the drag properties of the fine-mesh net through towing experiments in a water tank and explored the key factors influencing the drag force of the net. Chen et al. [5] proposed a drag coefficient prediction formula for the severely hard-fouled aquaculture netting. Dong et al. [6] analyzed the effects of wave forces on marine aquaculture cage netting panels, including the knotless polyethylene (PE) net and the chain-link wire net. They analyzed the hydrodynamic behavior of these net panels using both experimental and numerical simulation methods. Balash et al. [7] investigated the hydrodynamic characteristics of nets in both steady and oscillatory flows. The results indicated that the drag coefficient of the netting is closely associated with the net solidity and the Reynolds number. Specifically, the drag coefficient decreases with the increasing Reynolds number and is positively correlated with the net solidity. Wan et al. [8] analyzed the hydrodynamic behavior of set-nets in various current conditions, thereby providing a holistic assessment of their performance. Bi et al. [9] investigated the effect of the biofouling on the net drag and flow-through properties.

Additionally, the flow field surrounding the nets has been investigated by several researchers. The study by Bi et al. [10] focused on analyzing the fluid flow and drag characteristics of cruciform structures in net panels using computational fluid dynamics models, particularly examining the impact of two different orientations of the cruciform structures on drag. Wang et al. [11] adopted large eddy simulations for investigating the flow field characteristics around the netting made of smooth and twisted materials, analyzing the effects of the inflow velocity, the net twine diameter, and the twine length on the surrounding turbulent flow. Wang et al. [12] proposed a screen force model to assess the hydrodynamic load on knotless nets. They examined how the inclination angles of these nets influence the flow fields and the drag coefficients. Wang et al. [13] proposed an SPH-net model coupling SPH and screen models to study fixed net structures in currents and waves, and validated its accuracy and reliability.

Moreover, some researchers have also explored the hydrodynamic behavior of the TINs used in the NPS. Wu et al. [14] proposed an efficient, reliable, and automated seawater filtration system for the NPS cooling water sources, which optimizes the layout of water intake projects, effectively addresses threats from marine organisms, and reduces maintenance costs and manual intervention risks. Wang et al. [13] demonstrated that the CFD model can effectively predict the wave forces on the TIN under regular wave conditions and identified that the hydrodynamic responses of the netting are greatly influenced by the wave parameters, the net solidity, and the net shape. Jiang et al. [15] performed a numerical simulation and experimental validation to investigate the hydrodynamic behavior of TINs in the seawater withdrawal engineering for the NPS. They focused on the tension forces and deformation characteristics of the nets under current conditions, as well as the effects of various parameters such as the net width, the hanging ratio, the water depth, and the biofouling on the performance of the nets. Sun et al. [16] conducted physical model tests on a novel tapered TIN system, revealing that its hydrodynamic responses are significantly influenced by the coupled effects of the wave height, the wave period, and the current velocity. The study demonstrated that the nonlinear characteristics are closely related to the system’s overall configuration, providing critical insights for the engineering optimization. Xie et al. [17] showed that the mooring characteristics of the TIN are influenced by the significant coupling of the waves, currents and intercepting rates, and its nonlinear response and tension concentration effects need to be considered in the design.

While previous studies have examined the hydrodynamic behavior of TINs, the focus has primarily been on planar nets. However, the research on the hydrodynamic loads acting on novel floating tapered TINs is limited, particularly regarding the tension forces and deformation of these tapered nets in currents. The longitudinal and transversal ropes are critical for the design of TINs, and it is essential to analyze the effect of the longitudinal and transversal ropes on the tension distribution of TINs and mooring system. A numerical model for the floating tapered TIN in currents is developed and validated through a series of experimental tests here. This research is valuable for the optimal design of TINs for the NPS.

This research is structured as follows: Section 2 presents the numerical model arrangement for the TIN. Section 3 describes the numerical method of TIN in detail. The experimental configuration is elaborated in Section 4. Section 5 shows some important results, and Section 6 gives the concluding remarks.

2. Numerical Model

A TIN in current is analyzed in this study. Figure 1 presents the TIN configuration, the overall length of the TIN is 35 m, comprising a 27.0 m guiding net and an 8.0 m collection pocket. The TIN has a total height of 17 m. The opening features a trapezoidal cross-section, with the upper width measuring 17.4 m and the lower width 16.6 m. The mesh size of the netting is 3.0 mm, and the twine diameter of the netting is 0.6 mm. The diameters of both the longitudinal and transversal ropes are 8.0 mm. The top of the net is connected to the main cable, which is directly anchored to the side caisson structures. The sides are secured by artificial anchor points spaced at 1.0 m intervals, and the bottom rope is fixed with anchor points every 0.5 m.

Table 1. Parameters of the numerical model for the TIN.

Parameters	Value	Unit
Mesh size	3 × 3	mm
Twine diameter	0.6	mm
Diameter of longitudinal/transversal ropes	8.0	mm
Upper width of opening	17.4	m
Lower width of opening	16.6	m
Height	19.0	m
Length	35.0	m
Elastic modulus	1.0	GPa
Density	930.0	kg/m3

presents the parameters of the numerical model for the TIN.

3. Numerical Method

In this study, the lumped mass method (Jiang et al. [15]) is adopted for simulating the TINs in currents.

3.1. Motion Equations of the Netting

The netting is discretized as numerous of lumped mass points, as shown in Figure 2. The massless springs are adopted to connect the lumped mass points. To enhance the computational efficiency, the mesh grouping method is used in this study The motion equations of the net structure are given as follows:

$$m\dot{U}=F_D+F_I+F_T+B+W$$

(1)

where U represents the velocity of the node, m is the mass of node. Furthermore, F_D and F_I correspond to the drag force and the inertia force on the netting, respectively, F_T is the tension on the netting, B is the buoyancy force on the netting, and W is the gravity force of the netting. The Runge–Kutta sixth-order method has been adopted to solve Equation (1) based on the self-developed code.

The tension force on the netting can be calculated by

$$F_T=d^2{C}_1{\epsilon }^{C_2},\hspace{1em}\epsilon ={\displaystyle \frac{l-l_0}{l_0}}$$

(2)

where $F_T$ is the tension force on the netting; $l_0$ is the original length of the net twine; $l$ is the length of the net twine after elongation; $d$ is the nominal diameter of the net twine; $C_1$ and $C_2$ are the elastic constants of the netting, referring to Gerhard [18]. For polyethylene (PE), C₁ = 345.37 × 10⁶, and C₂ = 1.0121.

3.2. Hydrodynamic Loads on Nets

When calculating the hydrodynamic forces acting on the net twine, the net twine is treated as a slender circular cylinder. Figure 3 shows that a local coordinate system O-τηε is established on the net twine to account for the direction of the hydrodynamic forces. The origin of the coordinate system is located at the middle point of the net twine. The η-axis lies in the plane formed by the τ-axis and the water velocity vector V.

The hydrodynamic forces on the netting are calculated by the Morison equation. The hydrodynamic forces are then evenly dispersed to the lumped mass points connected to the net twine.

$$F_{D\tau }={\displaystyle \frac{1}{2}}\rho C_{D\tau }dl\left|V_{\tau }-U_{\tau }\right|(V_{\tau }-U_{\tau })$$

(3)

where C_D is the drag coefficient; l is the length of the net twine; U_τ is the velocity of the lumped mass point along the τ direction, V_τ is the velocity of the water particle along the τ direction.

According to Choo and Casarella [19], the hydrodynamic coefficients can be obtained with the following expressions:

$$C_n=\left\{\begin{array}{c}8\pi \left(1-0.87s^{-2}\right)/\left({\mathrm{Re}}_{n}s\right) \left(0<{\mathrm{Re}}_n\le 1\right)\\ 1.45+8.55{\mathrm{Re}}_n^{-0.90} \left(1<{\mathrm{Re}}_n\le 30\right)\\ 1.1+4{\mathrm{Re}}_n^{-0.50} \left(30<{\mathrm{Re}}_n\le {10}^5\right)\end{array}\right.$$

(4)

$$C_{\tau }=\pi \mu (0.55{\mathrm{Re}}_n^{1/2}+0.084{\mathrm{Re}}_n^{2/3})$$

(5)

where ${\mathrm{Re}}_n=\rho V_{Rn}D/\mu$; $s=-0.077215665+\ln (8/{\mathrm{Re}}_n)$; $\mu$ is the water dynamic viscosity; $C_n$ and $C_{\tau }$ are the normal coefficient and tangential coefficient of the node, respectively; $V_{Rn}$ is the relative velocity between the lumped mass point and the fluid; and $\rho$ is the water density.

4. Experimental Validation

To validate the accuracy of the numerical model, the experimental tests were conducted in the water flume at the Tianjin Research Institute for Water Transport Engineering. The water flume is 80.0 m in length, 4.0 m in width, and had a maximum water depth of 1.5 m. The water circulation system can generate various flow velocities up to 1.0 m/s.

To verify the numerical model of the present TIN, numerous experimental tests were performed in a water flume, as shown in Figure 4. Only the tension force on the center set of nets is measured in this study. The specific dimensions of the water flume are presented in Figure 5. The length of the TIN is 2.0 m, with a guide pocket length of 1.47 m and a collect pocket length of 0.53 m. The numerical model was developed according to the physical model of the TIN, and the specific mooring arrangement for the TIN is shown in Figure 6. The 200 N load sensors with ±0.5% F.S. accuracy are adopted to measure the mooring force. The two-scale similitude criterion (referring to the research of Li [20]) is adopted to simulate the TIN in this study.

The discrepancy between the experimental measurements and numerical simulations was given by analyzing the total mooring force on the anchors. Figure 7 indicates the comparison of the total mooring force from the physical model test and the numerical simulation. The results indicate that the numerical model of the TIN in currents can accurately simulate the mooring force of the TIN.

5. Results and Discussion

The tension forces on the main cable, transversal ropes, longitudinal ropes, nets and anchors are analyzed, and the effects of the water depth, intercepting rate, and longitudinal and transversal ropes are discussed. In addition, the deformation of the bottom part of the guiding net can affect the probability of the floating object entering into the collection pocket, which is important for the design of the TIN. Therefore, the deformation of the TIN is also discussed here.

5.1. Effect of the Water Depth

Four kinds of water depths (15 m, 16 m, 17 m, and 19 m) are considered in this part, and the water velocity is 0.475 m/s. Figure 8 shows the tension distribution and deformation of the TIN in currents. It indicates that the ropes close to the opening of the TIN experience larger tensions. The tension force on the transversal ropes is significantly higher than that on the longitudinal ropes. It means the hydrodynamic loads on the netting are firstly transferred to the main cable by the transversal ropes. Figure 9 shows the deformation of the top part and the bottom part of the TIN. It indicates that when the water depth is smaller than 19.0 m, the effect of the water depth on the deformation of the bottom part of the TIN is small. When all of the TIN is submerged into waters (i.e., water depth is 19.0 m), the shape of the TIN is significantly different from other water depths.

Table 2. Tension force on the TIN considering different water depths.

No.	Water Depth (m)	MC (kN)	TAF (kN)	TRF (kN)	LRF (kN)	Net (N)
1	15	3.59	5.09	7.50	6.67	35.87
2	16	4.74	6.29	9.85	8.87	41.29
3	17	5.83	7.43	12.77	11.41	59.65
4	19	7.19	8.40	19.59	14.98	72.72

Notes: MC: main cable; TAF: total anchor force; TRF: transversal rope force; LRF: longitudinal rope force.

shows the tension force on the TIN for different water depths. It indicates that the tension force on the TIN is significantly increased with the increasing water depth because the hydrodynamic force on the TIN is determined by the projected area of the TIN along the direction of currents. The influence of the water depth on the transversal rope force (TRF) is larger than that on the longitudinal rope force (LRF).

5.2. Effect of the Intercepting Rate of TINs

The intercepting rate of TINs can be significantly increased when numerous floating objects in the sea are attached at the TIN. The intercepting rate (R) is the percentage coverage of the mesh opening of the TIN. R = 2d_e/(a − 2d_e), d_e is the equivalent twine diameter of the netting. In this study, the effects of the biofouling on the hydrodynamic loads on TINs is investigated by increasing the equivalent twine diameter of the netting. Five kinds of intercepting rates (0, 20%, 40%, 60%, and 80%) are considered in this study. Figure 10 shows the tension distribution and deformation of TINs for different intercepting rates. It shows that the tension force on most of transversal ropes of the side part of the TIN is significantly increased with the increasing intercepting rate of the TIN. The tension force on the upstream transversal ropes is higher than that on the downstream transversal ropes. For the top part of the TIN, the netting above the water surface experiences larger loads.

Table 3. Tension force on the TIN for different intercepting rates.

No.	Intercepting Rate (%)	MC (kN)	TAF (kN)	TRF (kN)	LRF (kN)	Net (N)
1	0	4.74	6.29	9.85	8.87	41.29
2	20	5.88	7.34	12.27	10.91	58.67
3	40	9.66	12.05	20.16	17.92	133.66
4	60	13.27	17.40	29.76	26.80	167.92
5	80	18.94	23.63	39.53	35.15	188.90

shows the tension force on the TIN for different intercepting rates. It indicates that the tension forces on the main cable, transversal ropes, longitudinal ropes, total anchors, and nets are increased by 299.6%, 301.3%, 296.3%, 275.7%, and 357.5%, respectively, when the intercepting rate of the TIN is increased from 0 to 80%. The increase in rate of the tension force is almost the same for the main cable, transversal ropes, longitudinal ropes.

5.3. Effect of Longitudinal and Transversal Ropes

The longitudinal and transversal ropes are critical for the design of the TIN. Therefore, the effect of longitudinal and transversal ropes on the tension distribution of the TIN is investigated. Figure 11 shows the tension distribution of the TIN for different longitudinal and transversal ropes.

Table 4. Tension force on the TIN for different rope diameters.

No.	Transverse Ropes Diameter (mm)	Longitudinal Ropes Diameter (mm)	MC (kN)	TAF (kN)	TRF (kN)	LRF (kN)	Net (N)
1	8	8	4.74	6.29	9.85	8.87	41.29
2	8	10	4.91	6.88	9.24	9.97	43.43
3	10	8	4.85	6.81	10.41	8.18	44.43
4	-	8	4.59	7.23	-	14.94	45.34
5	8	-	4.41	7.88	15.24	-	46.24

presents the maximum tension force on the TIN for different rope diameters. The following conclusions can be obtained. (1) The tension force on longitudinal ropes is increased by 12.4%, and the tension force on transversal ropes is decreased by 6.2%, as the diameter of longitudinal ropes is increased from 8.0 mm to 10.0 mm. (2) The tension force on longitudinal ropes is decreased by 7.8%, and the tension force on transversal ropes is increased by 5.7%, as the diameter of transversal ropes is increased from 8.0 mm to 10.0 mm. (3) The longitudinal rope force can be significantly increased when there are no transversal ropes. (4) The transversal rope force can be significantly increased when there are no longitudinal ropes. (5) The tension force on nets is smallest when the D_l = 8.0 mm, D_t = 8.0 mm. The net experiences the smallest tension force when the diameter of transversal ropes is same as the diameter of longitudinal ropes.

6. Conclusions

A numerical model of the TIN in currents is developed for analyzing the effect of the water depth, intercepting rate, and longitudinal and transversal ropes on the tension force acting on the TIN. A series of physical model tests indicate that the numerical model can predict the tension force on the TIN accurately. The numerical results also indicate that the tension force on the transversal ropes is significantly larger than that on the longitudinal ropes. When the water depth is smaller than 19.0 m, the effect of the water depth on the shape of the bottom part of the TIN is small. When the intercepting rate of the TIN is increased from 0 to 80%, the increasing rate of the tension force is almost the same for the main cable, transversal ropes, and longitudinal ropes. The net experiences the smallest tension force when the diameter of transversal ropes is same as the diameter of longitudinal ropes.