Numerical prediction method, storage medium and equipment for dynamic response of flexible pipe of full-scale floating tunnel under vertical-inclined combined anchor mooring

Abstract

The invention relates to a numerical prediction method, storage medium and equipment for the dynamic response of a flexible pipe body of a real-scale suspended tunnel under vertical-inclined combined anchor mooring, which belongs to the technical field of flexible pipe bodies of suspended tunnels. In order to solve the problem that the current model based on the freedom of both ends of the suspended tunnel ignores the significant influence of the end constraints on the mechanical behavior of the tunnel in actual engineering, and the relevant research is carried out on small-scale experimental models. The present invention first establishes a numerical environment model of wave-current coupling excitation and performs meshing, and then establishes a CFD numerical analysis model of the flexible pipe body of the suspended tunnel. The wave force is used as an external excitation. By solving the NS equation, the wave pressure and shear force distribution on the surface of the pipe body are calculated, which triggers the displacement change of the pipe body, thereby affecting the tensile state of the anchor cable and triggering the dynamic adjustment of the anchor cable tension. A dynamic connection is formed between the vibration of the pipe body and the anchor cable tension, and the anchor cable tension is updated in real time according to the relative displacement and velocity change of the pipe body, and the response numerical prediction is completed.

Description

Technical Field

[0001] The present invention belongs to the technical field of flexible pipes for floating tunnels, and in particular relates to a numerical prediction method, storage medium and equipment for dynamic response of flexible pipes for floating tunnels. Background Art

[0002] In recent years, with the rapid development of economy and culture, people's demand for cross-sea interconnection has been further strengthened. However, the construction of traditional cross-sea bridges and submarine tunnels in the face of the vast sea surface and deep seabed requires enormous manpower, material and financial resources, and the construction process is extremely challenging. The new mode of transportation, the Submerged Floating Tunnel (SFT), can overcome the many difficulties encountered by traditional cross-sea transportation buildings when constructed in special sea areas. Compared with traditional structures, SFT avoids the complex construction of piers and large-scale excavation through its floating design, significantly reducing construction costs and construction time. Its superior structural flexibility gives it a clear technical advantage in certain special sea areas (especially fjord areas).

[0003] Anchored floating tunnels are one of the most promising types of floating tunnels. Anchor cables connect the floating tunnel body to the seabed and provide mooring force for the floating tunnel. Regarding anchor mooring constraints, a single vertical anchor cable provides strong vertical stiffness, but lacks horizontal stiffness, resulting in significant horizontal motion of the tunnel body under the influence of waves and currents. While a single inclined anchor cable provides some horizontal stiffness, it lacks vertical stiffness and introduces torsional stiffness. To improve the vertical, horizontal, and torsional stability of the floating tunnel body, researchers (e.g., Kanie, 2010; Faggiano et al., 2016) have proposed a combined vertical-inclined anchor mooring structure. However, limited research has examined the dynamic response and stability characteristics of the floating tunnel body under combined anchor mooring constraints, necessitating further investigation.

[0004] Due to their long-span, flexible structures, suspended tunnels are susceptible to significant vibration responses under environmental loads such as waves and currents, threatening their stability and safety during normal operation. Accurately predicting the structural dynamic response of suspended tunnels constrained by vertical-inclined combined anchor cables under combined wave and current excitation, and optimizing their design based on these vibration responses to improve their stability and safety, are key prerequisites for ensuring the safe and normal operation of suspended tunnels.

[0005] There are currently three main approaches for studying the dynamic response of flexible suspended tunnels under combined wave and flow excitation: theoretical analysis, model experiments, and numerical simulation. While theoretical analysis is computationally inexpensive, it introduces empirical formulas and underlying assumptions, hindering a thorough understanding of the dynamic response mechanisms of flexible tubes under complex wave and flow loading. While model experiments provide intuitive results, they struggle to fully reveal the complex vibration response characteristics of full-scale suspended tunnels due to the scale effect. Furthermore, experimental research is costly. Compared to theoretical analysis and model experiments, numerical simulation offers unique advantages. CFD, in particular, has seen rapid development in recent years. These methods not only efficiently and cost-effectively implement fluid-structure and multi-physics coupling, but also accurately analyze the three-dimensional dynamic response characteristics of suspended tunnels under wave and flow excitation. Using CFD, researchers can deeply explore the dynamic behavior of suspended tunnels under varying environmental loads, providing more reliable theoretical support for structural design, optimization, and safety assessment. Summary of the Invention

[0006] In order to solve the problem that the current model based on the freedom of both ends of the suspended tunnel ignores the significant influence of the end constraints on the mechanical behavior of the tunnel in actual engineering, and the relevant research is carried out on small-scale experimental models, so there is a problem that it cannot be directly extended to the full-scale structural model under real constraint conditions.

[0007] A numerical prediction method for the dynamic response of a flexible pipe in a full-scale floating tunnel moored with vertical-inclined combined anchor cables includes:

[0008] Step 1: Establish a numerical environment model of wave-current coupling excitation based on the VOF method and force wave elimination technology;

[0009] Step 2: Mesh the suspended tunnel body and the surrounding environment, including the following steps:

[0010] Step 201: First, create the component geometric components, including the background watershed component, the wave propagation area component, the overlapping area component that can cover the pipe body movement range, the floating tunnel pipe body component, the internal flow field area component, and the densified area component;

[0011] Step 202: Allocate the background watershed component, the overlapping area component, the suspended tunnel body component, and the internal flow field area component to four different areas;

[0012] Step 203: Expand the geometry and manipulate the nodes; then select a cut volume mesh for the background flow domain, a polyhedral mesh for the overlap region, an oriented mesh for the suspended tunnel body, and an oriented mesh for the internal flow field region.

[0013] Step 204: First, add a volume control for the background flow domain. In this process, select Create Volume Control and rename the new node to Wave. Then, input the Wave Propagation Area component. Next, add an Encryption Area mesh, rename it to Encryption, and customize the size.

[0014] Step 205: Add a volume control for the overlapping area. In this process, select New Volume Control, rename the new node to block, then import the block component, select the Cut Volume Mesher node and customize the size.

[0015] Step 206: Generate a directional mesh. In this process, select the directional mesh node and rename the generated node to tube body. Then enter the component and customize the size.

[0016] The same treatment is performed on the internal flow field area;

[0017] Step 207, define overlapping grids; select the background watershed and the overlapping area at the same time, select Create Interface and then select Overlap Grid;

[0018] Step 208: Generate all grids;

[0019] Step 3: Establish a CFD numerical analysis model for the flexible pipe of the suspended tunnel:

[0020] The forces acting on the suspended tunnel during operation include anchor cable tension, its own weight, and fluid forces, including wave forces. The suspended tunnel's own weight exerts a downward force, while the upward force generated by the tunnel's buoyancy, along with the tube's weight and buoyancy, form the system's initial mechanical equilibrium. Under static water conditions, the anchor cables are tightened to create pretension.

[0021] The vibration response of a suspended tunnel pipe is determined by the combined effects of fluid forces, anchor cable tension, gravity, and buoyancy. Wave forces act as external excitations, and the NS equations are solved using CFD methods to calculate the wave pressure and shear force distribution on the pipe surface. These wave pressures and shear forces excite vibrations and induce displacement changes. These displacement changes affect the tension of the anchor cables, triggering dynamic adjustments to the anchor cable tension. Changes in anchor cable tension are a result of wave-induced pipe vibrations. At the same time, anchor cable tension limits the amplitude of pipe vibrations through reaction forces. The anchor cable-pipe coupled vibration equation establishes a dynamic link between pipe vibration and anchor cable tension. Anchor cable tension is updated in real time based on the relative displacement and velocity of the pipe. The anchor cable tension, gravity, buoyancy, and wave forces maintain the dynamic equilibrium of the suspended tunnel pipe. In STAR-CCM+, based on a combined anchor cable suspended tunnel model, wave forces induce pipe vibrations, and anchor cable tension provides real-time feedback on the pipe's displacement and vibrations. Gravity and buoyancy contribute to maintaining the system's mechanical equilibrium. Wave forces, anchor cable tension, and pipe displacement interact in a continuously iterative process, forming an integrated numerical model of the suspended tunnel's vibration response.

[0022] Finally, based on the flow field conditions of the wave-current coupled excitation numerical environment model set previously, the entire flow field is initialized, and the appropriate calculation step size is selected according to the calculation requirements to start the numerical simulation.

[0023] Furthermore, in the process of calculating the wave pressure and shear force distribution on the pipe surface, the wave pressure in, is the pressure exerted by the wave at position x and depth z, where x is the horizontal position, z is the coordinate perpendicular to the sea surface, and t is time; ρ is the fluid density, g is the acceleration due to gravity, A is the amplitude of the wave; h is the water depth; k is the wave number, and ω is the angular frequency of the wave.

[0024] Furthermore, the wave number k=2π / λ, where λ is the wavelength.

[0025] Furthermore, the anchor cable-tube coupling vibration equation is as follows:

[0026]

[0027] Where ρ is the density of the fluid; C L is the lift coefficient; v is the flow velocity; θ is the inclination angle of the anchor cable; ω v is the vortex discharge frequency; L is the length of the anchor cable; D t is the diameter of the anchor cable; is the sum of the mass of the anchor cable per unit length and the mass of the additional water; D n Symbols introduced for the convenience of calculation, y is the lateral displacement of the anchor cable, and They represent the lateral velocity and acceleration of the anchor cable respectively; n is the order; c is the viscous damping coefficient of the anchor cable; A1 is the cross-sectional area of ​​the anchor cable; E eq is the equivalent elastic modulus; Z is the vibration displacement of the tube body, and are the vibration velocity and acceleration respectively; ω1 is the natural frequency of the anchor cable; ω2 is the natural frequency of the pipe body; ξ2 is the damping ratio of the pipe body; and M is the mass of the suspended tunnel.

[0028] Furthermore, the construction process of the combined anchor cable suspended tunnel model includes:

[0029] (1)Import file:

[0030] Open the STAR CCM+ software and import the mesh file obtained in step 2;

[0031] (2)Selection Physical Model:

[0032] First, create a fluid physics continuum, i.e., physics continuum 1, and select the following models in order: 3D, implicit unsteady, multiphase, multiphase interaction, fluid volume, turbulence model, SST K-Omega model, gradient, separated flow, multiphase equation of state. At the same time, check gravity, VOF wave, and adaptive time step in the optional models, and finally click OK; then create a solid physics continuum, i.e., physics continuum 2, and select 3D, implicit unsteady, solid, solid stress, Rayleigh damping, flexible DFBI motion, and gravity model, and finally click OK;

[0033] (3)Define the flexibleDFBI movement:

[0034] Click Tools > Motion Node, right-click the Motion node, and then select New > DFBI Deformation. A new node named DFBI Deformation is added to the Motion Manager; the ">" indicates the next step.

[0035] (4)Edit 6-DOF volume parameters:

[0036] Select Region > Overlap Region > Physical Value > Motion Assignment and set the motion to DFBI Deformation. Then right-click the DFBI > 6 DOF Body node and select New Body > 3D > Continuum. Rename the newly created node to Tube. Then right-click Tube > Create Body Motion and create a new node named Tube-motion under the Motion node. Create a solid displacement in the Tube-motion node and save it for later use.

[0037] (5)Model parameter setting:

[0038] Select DFBI > 6 DOF Body > Tube and add the moving parts and the mass of the floating tunnel. In the Free Motion node, select the motion properties for X-axis movement, Z-axis movement, and Y-axis rotation. In the Initial Value node, customize the moment of inertia and center of mass of the floating tunnel.

[0039] (6)Define the motion of the SubmergedFloating Tunnel:

[0040] Select Region > Suspension Tunnel Body > Physical Conditions > Flexible DFBI Motion Options and set the Flexible DFBI Motion Option to DFBI-Partially deformable. In the Suspension Tunnel Body > Physical Values ​​> Motion Assignment node, set the motion to Body-motion-Solid Displacement. Then, in the Suspension Tunnel Solid > Segment node, set both end faces to Fixed Constraints.

[0041] (7)Define the internal flow field regional motion:

[0042] Select Region > Internal Flow Region > Physical Values ​​> Motion Assignment node and set the motion to DFBI deformation;

[0043] (8)Create interface:

[0044] Set the surface where the outer wall of the tube contacts the flow field and the surface where the inner wall of the tube contacts the air flow field as the phase-contact interface respectively; the operation method is similar to the method of creating overlapping grids;

[0045] (9)Add the anchor cable to the body coupling module:

[0046] Right-click DFBI > Body Coupling node and add the required anchor cables, including spring-damper, catenary and other contact forms;

[0047] (10)Solver setup:

[0048] Click Solver > Implicit Unsteady State and set the desired time step. Next, click the 6 DOF Mesh Deformation node and check Zero Deformation, Recalculate Interfaces, Boundary Layer Deformation, and Keep Temporary Storage to meet the required deformation requirements.

[0049] (11)Stop criterion setting:

[0050] Click the Stop Criteria node and uncheck the Displacement Criterion, Force Criterion, Maximum Steps, and Stop File functions. Then set the number of iterations in the Maximum Inner Iterations node and the runtime in the Maximum Physical Time node.

[0051] (12)Initialize Solution andRun Calculation:

[0052] First click the Initialize Solution button with the mouse, then click the Run button to start the simulation calculation.

[0053] Furthermore, the multiphase in step (2) is a gas-liquid two-phase flow.

[0054] Furthermore, in the step (2), in the process of selecting the fluid volume, wave load is introduced, and flow is added on this basis to reflect the influence of wave and flow on the vibration of the pipe body;

[0055] The wave loads are as follows:

[0056] Horizontal velocity of the wave:

[0057] u(x,t)=Aωcosh(k(z+h))cos(kx-ωt)

[0058] Where A is the amplitude of the wave; ω is the angular frequency of the wave; k is the number of waves; h is the water depth; z is the coordinate perpendicular to the sea surface; t is time; x is the horizontal position;

[0059] Surface wave pressure:

[0060]

[0061] in, is the pressure exerted by the wave; g is the acceleration due to gravity; η is the deformation of the wave surface; is the rate of change of the water surface over time;

[0062] Wave pressure inside the fluid:

[0063]

[0064] in, is the pressure exerted by the wave at position x and depth z, where x is the horizontal position, z is the coordinate perpendicular to the sea surface, and t is time; ρ is the fluid density, g is the acceleration due to gravity, A is the amplitude of the wave; h is the water depth; k is the wave number, and ω is the angular frequency of the wave.

[0065] Furthermore, in the step (9), during the process of adding the required anchor cables, an anchor cable-tube coupling effect is introduced; the anchor cable-tube coupling effect is realized by an anchor cable-tube coupling vibration equation;

[0066] The anchor cable-tube coupling vibration equation is as follows:

[0067]

[0068] Where ρ is the density of the fluid; C L is the lift coefficient; v is the flow velocity; θ is the inclination angle of the anchor cable; ω v is the vortex discharge frequency; L is the length of the anchor cable; D t is the diameter of the anchor cable; is the sum of the mass of the anchor cable per unit length and the mass of the additional water; D n Symbols introduced to facilitate calculations, CD =0.7 is the drag coefficient, z is the integral variable; y is the lateral displacement of the anchor cable, and They represent the lateral velocity and acceleration of the anchor cable respectively; n is the order; c is the viscous damping coefficient of the anchor cable; A1 is the cross-sectional area of ​​the anchor cable; E eq is the equivalent elastic modulus; Z is the vibration displacement of the tube body, and are the vibration velocity and acceleration respectively; ω1 is the natural frequency of the anchor cable; ω2 is the natural frequency of the pipe body; ξ2 is the damping ratio of the pipe body; and M is the mass of the suspended tunnel.

[0069] A computer storage medium stores a computer program, which is loaded and executed by a processor to implement a numerical prediction method for the dynamic response of a flexible pipe body of a full-scale floating tunnel under a vertical-inclined combined anchor mooring system.

[0070] A device for numerically predicting the dynamic response of a flexible pipe body in a full-scale floating tunnel moored with a vertical-inclined combined anchor cable is disclosed. The device includes a processor and a memory. The memory stores a computer program that is loaded and executed by the processor to implement a method for numerically predicting the dynamic response of a flexible pipe body in a full-scale floating tunnel moored with a vertical-inclined combined anchor cable.

[0071] Beneficial effects:

[0072] This paper proposes a novel numerical prediction method for the dynamic response of a flexible pipe in a long-span floating tunnel moored with vertically-inclined combined anchor cables under combined wave and current excitation. This method can more reliably simulate the complex vibration response characteristics of a full-scale floating tunnel flexible pipe under combined wave and current excitation. Compared with existing technologies, this technical solution has the following advantages:

[0073] 1. In order to simplify the analysis, traditional studies often assume that both ends of the suspended tunnel are free. Although this reduces the complexity of the model, it ignores the significant impact of end constraints on the mechanical behavior of the tunnel in actual engineering. In addition, most of the relevant research is carried out on small-scale experimental models. This simplification of boundary constraints and the reduction of scale models result in the conclusions obtained based on traditional research being unable to be directly extended to full-scale structural models under real constraint conditions. To this end, the present invention provides a new research perspective and research framework for the study of the dynamic response characteristics of full-scale suspended tunnel flexible tubes under complex environmental loads by introducing real end constraints and full-scale suspended tunnel flexible tubes.

[0074] 2. Most current studies simplify the mooring constraints of suspended tunnels into a single vertical or inclined mooring anchor model. Although this improves computational efficiency, it cannot reflect complex mooring constraints. The hybrid anchor layout combines the structural characteristics of vertical and inclined anchors, resulting in better stability characteristics both vertically and horizontally compared to single mooring anchor constraints. However, there are few studies on hybrid anchor layouts, especially the dynamic response mechanism of this layout structure under the combined excitation of waves and currents is still unclear. To this end, the present invention innovatively proposes a numerical prediction method that can reliably analyze the dynamic response characteristics of the flexible pipe body of a suspended tunnel under the mooring constraints of a vertical-inclined combined anchor. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 This is the flow chart of numerical simulation of wave-current combined excitation;

[0076] Figure 2 Schematic diagram of the grid of each component;

[0077] Figure 3 Schematic diagram of the numerical model of the suspended tunnel under wave-current combined excitation (front view);

[0078] Figure 4 Schematic diagram of the numerical model of the suspended tunnel under wave-current combined excitation (side view);

[0079] Figure 5 It is the time history curve of the wave surface at 0m;

[0080] Figure 6 This is the time history curve of the wave surface at -100m;

[0081] Figure 7 This is the time history curve of the wave surface at 100m;

[0082] Figure 8 It is a wave-current coupled numerical environment model;

[0083] Figure 9 is the sway time history curve at y = 1 / 4L;

[0084] Figure 10 It is the heave time history curve at y = 1 / 4L;

[0085] Figure 11 is the sway history curve at y = 1 / 2L;

[0086] Figure 12 is the heave time history curve at y=1 / 2L;

[0087] Figure 13 is the sway history curve at y = 3 / 4L;

[0088] Figure 14It is the heave time history curve at y=3 / 4L;

[0089] Figure 15 This is the anchor chain force curve with back sea tilt;

[0090] Figure 16 The anchor chain force curve is tilted into the sea;

[0091] Figure 17 is the vertical anchor chain force curve under back waves;

[0092] Figure 18 is the vertical anchor chain force curve facing the wave. DETAILED DESCRIPTION

[0093] In view of the problems existing in the background technology, the present invention innovatively proposes a numerical prediction method for the dynamic response of the flexible pipe body of a large-span floating tunnel under the combined excitation of waves and currents under the constraints of a vertical-inclined combined anchor mooring. This numerical method can more accurately simulate the dynamic behavior characteristics of the flexible pipe body of a floating tunnel under loads in a complex environment, providing a reliable theoretical basis and technical support for the design and optimization of floating tunnels. Specific implementation method one:

[0095] This embodiment is a method for numerically predicting the dynamic response of a flexible pipe body in a full-scale floating tunnel under vertical-inclined combined anchor mooring, comprising the following steps:

[0096] Step 1: Establish a numerical environment model for wave-current coupling excitation:

[0097] Establishing an accurate numerical environment model for this wave-current coupling excitation is crucial for numerically studying the dynamic response of suspended tunnels under combined wave and current excitation. This paper constructs a numerical environment model for this wave-current coupling excitation, combining the VOF method with force-wave cancellation technology. This model accurately simulates the interaction between waves and fluids and their impact on suspended tunnels.

[0098] The VOF method is used to simulate the changes in the two-phase flow surface to achieve wave simulation, thereby constructing a numerical water pool. Based on the theory of viscous flow, the NS equations are solved to obtain the velocity field, pressure field, and other flow characteristics of the wave and fluid, and thus the vibration response characteristics of the suspended tunnel. This process can be applied using existing technology and will not be further explained in detail in this invention.

[0099] At the boundary of the numerical water pool, in order to reduce the influence of boundary reflection waves, the present invention introduces a wave-breaking zone. Taking into account the accuracy and computational efficiency of wave numerical simulation, we chose the force wave breaking method. This method can eliminate the reflection waves by setting boundary resistance, and it can also effectively reduce the computational domain, thereby reducing the demand for computing resources. Compared with traditional damping wave breaking, force wave breaking has stronger wave elimination capabilities and can maintain a relatively stable computing effect during wave propagation. The computational domain size and mesh division of the wave-flow numerical environment are crucial to the accuracy of the simulation results. According to the theoretical predictions of different wave front lift heights, the present invention adjusts the size of the computational domain and performs preliminary mesh division on the numerical water pool to ensure the accuracy of the wave simulation. On this basis, by comparing the simulated wave front with the theoretical wave front, the mesh division scheme is optimized to ensure that the wave propagation characteristics and structural responses during the simulation process are accurately reflected, providing an effective numerical tool for the dynamic response analysis of suspended tunnels under wave-flow excitation. The detailed research plan is as follows. Figure 1 shown.

[0100] Step 2: Divide the grid into overlapping grids, directional grids and other components:

[0101] First, a series of parameters are determined, including the style and size of the suspended tunnel body, the elastic modulus E of the anchor cable, and the c , Anchor cable length L c , submergence depth H s , flow velocity U, water depth H w , wave height H and wave period T, etc., and then grid division is performed.

[0102] The meshing process is as follows:

[0103] In this invention, a variety of mesh types, including cut-body meshes, polyhedron meshes, and directional meshes, are used to mesh the dynamic response of a long-span suspended tunnel under combined wave and current excitation. To accurately simulate and capture the motion and deformation of the suspended tunnel, an overlapping mesh method is selected for subsequent simulations. Cut-body meshes are used in the wave-current action region to accurately capture wave propagation and free surface changes. For the dynamic region of the suspended tunnel, i.e., the moving portion of the tube under the influence of waves and currents, an overlapping mesh technique is employed, employing a polyhedron mesh type. This technique effectively captures the tunnel's motion and deformation, particularly when dealing with the interaction between the tunnel surface and the fluid, ensuring higher computational accuracy. Directed meshes are used for the solid portion of the tunnel and the internal air flow field, ensuring accurate simulation of structural details. The uniformity of the directed mesh ensures mesh consistency across each cross-section, thereby improving computational efficiency and accuracy. This optimized combination of meshing techniques enables a more effective response to complex flows and structural dynamic responses under combined wave and current excitation.

[0104] Taking the classic circular cross-section suspended tunnel body as an example, the grid division method of each component to be used in the present invention is as follows: Figure 2 shown.

[0105] Using the powerful meshing function of STAR CCM+ software, the meshing steps for each component are as follows:

[0106] 1. First, create the component geometric components, including the background basin component, the wave propagation area component, the overlapping area component that can cover the movement range of the pipe body, the floating tunnel pipe body component, the internal flow field area component, and the densification area component to ensure that the model meets the analysis requirements.

[0107] It should be noted that, in order to more closely approximate the actual operating environment of a suspended tunnel, the present invention numerically predicts the dynamic response of a flexible pipe. In this case, the overlapping area is the portion where the motion range of the suspended tunnel pipe overlaps with the background area. This area can be larger or smaller, but must at least cover the motion range of the pipe. It should also be noted that, precisely because the present invention numerically predicts the dynamic response of a flexible pipe in a suspended tunnel, although CFD software / toolkit is used, CFD-based modeling and fluid dynamics calculations must be performed based on actual fluid dynamics factors. Therefore, how the modeling is performed, how it is set up, and how the numerical analysis is performed will seriously affect the results of the fluid dynamics calculations, thereby seriously affecting the numerical prediction results of the pipe's dynamic response.

[0108] 2. Assign the background watershed components, overlapping area components, suspended tunnel body components, and internal flow field area components to four different areas.

[0109] 3. Expand the Geometry > Operations node. The “>” indicates the next operation. Then, perform the following operations: select a cut volume mesh for the background flow domain; select a polyhedral mesh for the overlap region; select an oriented mesh for the floating tunnel body; and select an oriented mesh for the internal flow region.

[0110] 4. Add volume control for the background flow domain. Right-click Geometry > Operations > Background Flow Domain > Custom Control, then select New > Volume Control, rename the new node to Wave, then enter the wave propagation area component, select Wave > Control > Cut Volume Mesh Generator Node > Custom Anisotropic Size. Then customize the relative size (X), relative size (Y), and relative size (Z). The relative size (X) and relative size (Y) are generally set to 1 / 80-1 / 100 of the wavelength, and the relative size (Z) is generally set to 1 / 10-1 / 20 of the wave height. Then add a mesh for the reinforcement area, rename it to Reinforcement, select Reinforcement > Control > Cut Volume Mesh Generator Node > Custom Isotropic Size, and then customize the size. If there are multiple reinforcement areas, repeat this step.

[0111] 5. Add a volume control for the overlapping region. Right-click Geometry > Operations > Overlap Region > Custom Control, then select New > Volume Control. Rename the new node to block, then import the block component. Select block > Control > Cut Volume Mesher Node > Custom Isotropic Size, and then customize the size. If you are performing surface meshing, simply select the surface control. The remaining steps are the same as for the volume control.

[0112] 6. Generate a directional mesh. Right-click > Mesh > Directed Mesh node and rename the generated node to Body. Enter the component, customize the dimensions, and then select Body > Mesh Distribution > Layers to define the desired number of mesh layers for the body. Follow the same steps for the directional mesh required for the internal flow region.

[0113] 7. Define the Overlap Grid. Select both the background watershed and the overlap area, right-click, and select Create Interface > Overlap Grid.

[0114] 8. Generate all meshes. Right-click the operation node and select Execute All Operations.

[0115] Step 3: Establish a CFD numerical analysis model for the flexible pipe of the suspended tunnel:

[0116] During operation, the suspended tunnel body is subject to multiple forces, primarily anchor cable tension, its own gravity, and fluid forces. First, the suspended tunnel's own gravity causes it to act downward, while the upward force generated by the tunnel's buoyancy counteracts its gravity. Under static water conditions, the tunnel is anchored to the bottom of the water by anchor cables, which are tightened to generate pretension. This pretension is equal to the difference between the buoyancy and gravity of the tunnel section and is a crucial factor in ensuring tunnel stability. Furthermore, fluid forces (including waves and ocean currents) exert dynamic forces on the tunnel. In particular, under the excitation of waves and currents, the tunnel experiences varying vibration responses, and these dynamic forces may affect the tunnel's stability and operational safety. Therefore, the design and analysis of suspended tunnels must consider the combined effects of these various forces. In particular, the anchor cable tension must be maintained at all times to ensure that the tunnel does not float or become unstable.

[0117] 1. Navier-Stokes (NS) equations:

[0118] Mass conservation equation: (continuity equation)

[0119] ▽·u=0(for incompressible fluid) (1) Momentum conservation equation:

[0120]

[0121] Where u is the fluid velocity; p is the pressure; ρ is the fluid density; μ is the fluid viscosity coefficient; and f is the external force (such as gravity).

[0122] 2. Wave load:

[0123] According to linear wave theory, wave loads are expressed using parameters such as wave amplitude, wavelength, and period. If a sinusoidal wave is considered, the horizontal velocity and pressure of the wave can be expressed as:

[0124] Horizontal velocity of the wave:

[0125] u(x,t)=Aωcosh(k(z+h))cos(kx-ωt) (3)

[0126] Where A is the amplitude of the wave; ω is the angular frequency of the wave; k is the wave number, k = 2π / λ (where λ is the wavelength); h is the water depth; z is the coordinate perpendicular to the sea surface (the positive direction points upward); t is time; and x is the horizontal position.

[0127] Wave pressure is the pressure caused by the surface undulation of water waves. Surface wave pressure is estimated using the linear theory of waves:

[0128]

[0129] in, is the pressure exerted by the wave; g is the acceleration due to gravity; η is the wave surface deformation (i.e., the height of the water surface); is the rate of change of the water surface with time.

[0130] Pressure exerted by waves considering water depth (deep water area):

[0131]

[0132] in, is the pressure exerted by the wave at position x and depth z, and its variations are related to the water depth and the propagation of the wave.

[0133] 3. Anchor cable-pipe coupling:

[0134] The coupled vibration equation of anchor cable and pipe body can be expressed as follows:

[0135]

[0136] Where, ρ = 1028 kg / m 3 ; C L is the lift coefficient, take C L =0.6; v is the flow velocity; θ is the inclination angle of the anchor cable; ω v is the vortex discharge frequency; L is the length of the anchor cable; D t is the diameter of the anchor cable; is the sum of the mass of the anchor cable per unit length and the mass of the additional water; D n Symbols introduced to facilitate calculations, C D =0.7 is the drag coefficient, z is the integral variable; y is the lateral displacement of the anchor cable, and They represent the lateral velocity and acceleration of the anchor cable respectively; n is the order; c is the viscous damping coefficient of the anchor cable; A1 is the cross-sectional area of ​​the anchor cable; E eq is the equivalent elastic modulus; Z is the vibration displacement of the tube body, and are the vibration velocity and acceleration respectively; ω1 is the natural frequency of the anchor cable; ω2 is the natural frequency of the pipe body; ξ2 is the damping ratio of the pipe body; and M is the mass of the suspended tunnel.

[0137] In equations (6) and (7), the vibration of the suspended tunnel causes periodic changes in the anchor cable tension, which in turn affects the anchor cable stiffness and the linear coefficient of y in the vibration equation, causing the anchor cable vibration to be parametrically excited. When the anchor cable's natural frequency approaches half the tunnel vibration frequency, parametric resonance occurs, causing the anchor cable to vibrate laterally with large amplitude. At this point, the system exhibits nonlinear coupled vibration, including linear and nonlinear terms, reflecting the complex relationship between tunnel vibration and the dynamic coupling of the anchor cable. Figure 3-Figure 4 Schematic diagram of the numerical model of a suspended tunnel under combined wave and current excitation.

[0138] The vibration response of the suspended tunnel pipe is determined by the combined effects of fluid force (wave force), anchor cable tension, self-gravity, and buoyancy. These forces form the system's equilibrium mechanism through complex dynamic interactions. Wave force is used as an external excitation, and the Navier-Stokes (NS) equations are solved using the CFD method to calculate the wave pressure (Formula (5)) and shear force distribution on the pipe surface. These wave loads act directly on the pipe, exciting vibration and causing displacement changes. The displacement changes of the pipe further affect the tensile state of the anchor cable, thereby triggering dynamic adjustment of the anchor cable tension. The change in anchor cable tension is not only the result of pipe vibration caused by wave force, but also limits the amplitude of pipe vibration through reaction force and maintains the dynamic balance of the system. Through this anchor cable-pipe coupling (Formulas (6)-(7)) feedback mechanism, a close dynamic connection is formed between pipe vibration and anchor cable tension, in which the anchor cable tension is updated in real time according to the relative displacement and velocity changes of the pipe, providing the necessary constraints and stability for the system.

[0139] Furthermore, the pipe's gravity and buoyancy together form the system's initial mechanical equilibrium. Gravity causes the pipe to sink, while buoyancy provides some upward force. This equilibrium provides the fundamental support for the dynamic effects of anchor cable tension and wave forces. The combined effects of gravity, buoyancy, anchor cable tension, and wave forces determine the system's overall vibration characteristics under the combined excitation of waves and currents.

[0140] In STAR-CCM+, this process is achieved through continuous dynamic interaction. Wave forces induce pipe vibrations, while anchor cable tension provides real-time feedback on the pipe's displacement and vibrations. Gravity and buoyancy contribute to maintaining the system's mechanical equilibrium. These wave forces, anchor cable tension, and pipe displacement interact through continuous iterations, ultimately forming an integrated numerical model of the suspended tunnel's vibration response. This model not only accurately simulates the pipe's dynamic characteristics under combined wave and current excitation but also provides a scientific basis for optimized design and operational stability.

[0141] Construction of combined anchor cable suspended tunnel model:

[0142] First, import the preset grid file into the STAR CCM+ software and create a physical model of the fluid. In the model settings, select the three-dimensional, multiphase, implicit unsteady and adaptive time step options. The turbulence model uses the separated flow and SST (Menter) K-Omega model. The multiphase model of the fluid uses the VOF (Volume of Fluid) method and the gravity acceleration is set to -9.81m / s. 2 In the VOF wave node, define the fifth-order wave as the wave excitation source. The multiphase model of the fluid in the present invention is a gas-liquid two-phase flow.

[0143] Next, create a physical model of the suspended tunnel tube, using an isotropic linear elastic body model. Select the 3D, solid, solid stress, Rayleigh damping, flexible DFBI motion, gravity, and implicit unsteady settings. Then, create a DFBI deformation model using the "Motion" node in the toolbar and configure the relevant parameters in the newly generated DFBI node.

[0144] It is important to note that solid stress, Rayleigh damping, and flexible DFBI motion are key modules in the dynamic analysis of flexible suspended tunnel pipes. Their combination enables realistic simulation of the pipe's dynamic behavior in complex environments. Solid stress describes the stress distribution and deformation characteristics within the pipe. Rayleigh damping effectively suppresses high-frequency vibrations by simulating material energy dissipation. Flexible DFBI motion imparts free deformation to the pipe, enabling dynamic coupling of fluid forces and pipe vibrations, thereby fully reflecting the pipe's complex dynamic response under wave and flow excitation.

[0145] Compared to conventional research that assumes a rigid tube, this invention emphasizes the flexible nature of the tube. Existing studies typically use a rigid DFBI model, which struggles to accurately represent the tube's deformation and actual dynamic response. By combining flexible DFBI motion, solid stress, and Rayleigh damping models, this invention not only simulates tube vibration and deformation under wave and flow excitation, but also captures the impact of flexibility on vibration and energy dissipation. This provides a more realistic and comprehensive analytical approach for studying the dynamics of flexible suspended tunnel tubes in complex environments.

[0146] Finally, based on the flow field conditions of the numerical environment model with wave-current coupling excitation previously set, the entire flow field is initialized, and the appropriate calculation step size is selected according to the calculation requirements to start the numerical simulation.

[0147] The specific steps for constructing the combined anchor cable suspended tunnel model are as follows:

[0148] (1)Import file

[0149] Open the STAR CCM+ software, select the appropriate number of working cores, and import the preset grid file.

[0150] (2)Selection Physical Model

[0151] First, create a fluid physics continuum under Continuum > Physics 1. Select the following models in order: 3D, Implicit Unsteady, Multiphase, Multiphase Interaction (Automatic selection), Volume of Fluid (VOF), Turbulence Model, SST (Menter) K-Omega Model, Gradient (Automatic selection), Separated Flow (Automatic selection), Multiphase Equation of State (Automatic selection). Also, select Gravity, VOF Wave, and Adaptive Time Step in the Optional Models section, and click OK. Then, create a solid physics continuum under Continuum > Physics 2. Select 3D, Implicit Unsteady, Solid, Solid Stress, Rayleigh Damping, Flexible DFBI Motion, and Gravity Model, and click OK.

[0152] Explanation: By using the VOF wave model to simulate the wave propagation process, a foundation is provided for studying the vibration response of the pipe under the combined excitation of waves and currents. In this model, the wave load (Formulas (3)-(5)) is accurately introduced, and the flow is added on this basis to reflect the influence of wave and current on the vibration of the pipe, laying a key foundation for the subsequent vibration characteristics analysis.

[0153] (3)Define the flexibleDFBI movement

[0154] Click Tools > Motion Node, right-click the Motion node, and select New > DFBI Deformation. A new node named DFBI Deformation is added to the Motion Manager.

[0155] (4)Edit 6-DOF volume parameters

[0156] Select Regions > Overlapping Regions > Physical Values ​​> Motion Assignment and set the motion to DFBI Deformation. Next, right-click the DFBI > 6-DOF Body node and select New Body > 3D > Continuum. Rename the newly created node Tube. Next, right-click Tube > Create Body Motion. Under the Motion node, create a new node named Tube-motion. Create a solid displacement in the Tube-motion node and save it for future use.

[0157] (5)Model parameter setting

[0158] Select the DFBI > 6 DOF Body > Tube node and add the moving parts and the mass of the floating tunnel. In the Free Motion node, select the motion properties for X-axis movement, Z-axis movement, and Y-axis rotation. In the Initial Value node, customize the moment of inertia and center of mass of the floating tunnel.

[0159] (6)Define the motion of the SubmergedFloating Tunnel

[0160] Select the Region > Floating Tunnel Body > Physics > Flexible DFBI Motion Options node and set the Flexible DFBI Motion Option to DFBI-Partially deformable. Under the Floating Tunnel Body > Physics > Motion Assignment node, set the motion to Body-motion-Solid Displacement. Then, under the Floating Tunnel Solid > Segment node, set both end faces to Fixed Constraints.

[0161] It should be noted that this invention utilizes a flexible DFBI-partially deformable mode, enabling local deformation of the tube under combined wave and flow excitation while maintaining overall rigidity, thereby accurately simulating its dynamic behavior. The innovative "tube-motion-solid displacement" motion type ensures that the dynamic response conforms to practical laws. Furthermore, the incorporation of fixed constraints at both ends as boundary conditions allows for a realistic reproduction of the fixed state of the suspended tunnel, providing a reliable foundation for simulations that closely resemble actual operating conditions.

[0162] Unlike the rigid-body DFBI translational motion or flexible-body deformation motion setups commonly used in existing research, the "tube-motion-solid-displacement" approach not only simulates the overall motion of the tube but also accurately calculates its local deformation and displacement characteristics. Conventional deformation motion setups struggle to simultaneously meet these two requirements. This approach effectively addresses the shortcomings of existing models, providing a more scientific and comprehensive solution for studying the real-world dynamics of suspended tunnel tubes under combined wave and flow excitation.

[0163] (7)Define the internal flow field regional motion

[0164] Select Region > Interior Flow Region > Physics Value > Motion Assignment node and set the motion to DFBI deformation.

[0165] (8)Create interface

[0166] Set the surface where the outer wall of the tube contacts the flow domain and the surface where the inner wall of the tube contacts the air flow field as mirror contact interfaces. The operation method is similar to the method of creating an overlaid mesh.

[0167] (9)Add the anchor cable to the body coupling module

[0168] Right-click the DFBI > Body Coupling node and add the required anchor cables, including spring-damper, catenary, and other contact types.

[0169] Note: Here, we add anchor cables to the model and introduce the anchor cable-tube coupling effect to simulate the restriction and regulation effect of the anchor cables on the movement of the floating tunnel tube (Formula 6-7), thereby more realistically reflecting its dynamic behavior.

[0170] (10)Solver setup

[0171] Click the Solver > Implicit Unsteady node and set the desired time step. Next, click the 6 DOF Mesh Deformation node and check the boxes for Zero Deformation, Recalculate Interfaces, Boundary Layer Deformation, and Keep Temporary Storage to meet the required deformation requirements.

[0172] (11)Stop criterion setting

[0173] Click the Stop Criteria node and uncheck the Displacement Criterion, Force Criterion, Maximum Steps, and Stop File functions. Then set the number of iterations in the Maximum Inner Iterations node and the runtime in the Maximum Physical Time node.

[0174] (12)Initialize Solution andRun Calculation

[0175] First click the Initialize Solution button with the mouse, then click the Run button to start the simulation calculation.

[0176] Example:

[0177] The above process was used for numerical calculation and analysis. To date, no underwater floating tunnel has been built in the world. This paper uses the conceptual model of the Qiandao Lake floating tunnel as a basis and selects dimensions corresponding to the constructed model for vibration response analysis. The numerical analysis parameters for the floating tunnel are shown in Table 1. The following is a specific implementation path:

[0178] Table 1 Selection of parameters for numerical analysis of suspended tunnel

[0179]

[0180] (1) Construct the corresponding numerical environment model of wave-current coupling excitation:

[0181] Figure 5-Figure 7 Comparing the theoretical and actual values ​​of wave surface lift heights at three locations, namely 0m, -100m, and 100m, it was found that the waves were very stable, in line with expectations, reflecting the reliability of the wave numerical pool.

[0182] (1) Vibration response analysis:

[0183] Referring to the structural parameters of the actual suspended tunnel in Table 1, a wave-current coupled numerical environmental model was established for a 300-m-long, 210-m-wide, and 200-m-high suspended tunnel. Waves with a height of 6 m, a period of 8 s, a wavelength of 105 m, and a velocity of 1 m / s were selected. The wave-current coupled vibration response analysis was performed on a 200-m-long, 15-m-diameter, and 1-m-thick suspended tunnel. Figure 8 It is a wave-current coupled numerical environment model.

[0184] The numerical simulation results of the dynamic response of the combined anchor moored floating tunnel under wave and current excitation are shown below: Figure 9 The horizontal sway time history curve of the suspended tunnel body at y = 1 / 4L, Figure 10Heave time history curve at y=1 / 4L, Figure 11 The horizontal swing history curve at y = 1 / 2L, Figure 12 From the heave history curve at y=1 / 2L, we can see that the lateral and heave vibration response values ​​are different at different cross-sectional locations, reflecting the flexible characteristics of the pipe body, which is in line with expectations. Figure 9 The transverse sway time history curve of the suspended tunnel body at y = 1 / 4L and Figure 13 The horizontal swing history curve at y=3 / 4L, Figure 10 The heave time history curve at y = 1 / 4L and Figure 14 From the heave time history curve at y=3 / 4L, we can see that the vibration response at the symmetrical position of the pipe body is symmetrical, which is consistent with the actual situation. Figure 15 Back wave tilt anchor chain force, Figure 16 Anchor chain force tilting against the waves, Figure 17 Back wave vertical anchor chain force, Figure 18 The vertical anchor chain force against the waves shows that the combined anchor cable mooring has a good restraining effect on the vibration response of the pipe body, and the vibration response of the pipe body shows a certain regularity over time.

[0185] Researchers can use the above method to carry out large-scale numerical simulations by precisely adjusting the key structural parameters of the suspended tunnel, such as the submergence depth, the angle of the inclined anchor cables, etc., and taking into account variable environmental loads such as waves and currents. Through in-depth analysis of the simulation data, the dynamic response characteristics of the long-span suspended tunnel under the combined action of waves and currents under complex constraints can be revealed. This study uses a more detailed wave-current joint excitation simulation, which can more realistically reflect the vibration and deformation behavior of the flexible tunnel structure in the actual environment. The research results provide important theoretical basis and technical support for the design, construction, operation management and safety monitoring of long-span suspended tunnels in complex marine environments, which helps to optimize the structural configuration of the tunnel and improve its anti-interference ability, ensuring the long-term safety and stability of the tunnel. Specific implementation method two:

[0187] This embodiment is a computer storage medium, which stores a computer program. The computer program is loaded and executed by a processor to implement the numerical prediction method for the dynamic response of a flexible pipe body of a full-scale floating tunnel under a vertical-inclined combined anchor mooring.

[0188] It should be understood that the storage medium described in this embodiment includes but is not limited to magnetic storage media and optical storage media; the magnetic storage medium includes but is not limited to RAM, ROM, and other storage media such as hard disks and USB flash drives. Specific implementation method three:

[0190] This embodiment is a numerical prediction device for the dynamic response of a flexible pipe body of a full-scale floating tunnel under a vertical-inclined combined anchor mooring system. The device includes a processor and a memory. The memory stores a computer program. The computer program is loaded and executed by the processor to implement a numerical prediction method for the dynamic response of a flexible pipe body of a full-scale floating tunnel under a vertical-inclined combined anchor mooring system.

[0191] It should be understood that the devices described in this embodiment include, but are not limited to, devices including a processor and memory, and may also include devices corresponding to other units or modules with information collection, information exchange, and control functions. For example, the devices may also include signal acquisition devices. Such devices include, but are not limited to, PCs, workstations, mobile devices, etc.

[0192] The present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A numerical prediction method for the dynamic response of a flexible pipe in a full-scale floating tunnel under vertical-inclined combined anchor mooring, characterized by: include: Step 1: Establish a numerical environment model of wave-current coupling excitation based on the VOF method and force wave elimination technology; Step 2: Mesh the suspended tunnel body and the surrounding environment, including the following steps: Step 201: First, create the component geometric components, including the background watershed component, the wave propagation area component, the overlapping area component that can cover the pipe body movement range, the floating tunnel pipe body component, the internal flow field area component, and the densified area component; Step 202: Allocate the background watershed component, the overlapping area component, the suspended tunnel body component, and the internal flow field area component to four different areas; Step 203: Expand the geometry and manipulate the nodes; then select a cut volume mesh for the background flow domain, a polyhedral mesh for the overlap region, an oriented mesh for the suspended tunnel body, and an oriented mesh for the internal flow field region. Step 204: First, add a volume control for the background flow domain. In this process, select Create Volume Control and rename the new node to Wave. Then, input the Wave Propagation Area component. Next, add an Encryption Area mesh, rename it to Encryption, and customize the size. Step 205: Add a volume control for the overlapping area. In this process, select New Volume Control, rename the new node to block, then import the block component, select the Cut Volume Mesher node and customize the size. Step 206: Generate a directional mesh. In this process, select the directional mesh node and rename the generated node to tube body. Then enter the component and customize the size. The same treatment is performed on the internal flow field area; Step 207, define overlapping grids; select the background watershed and the overlapping area at the same time, select Create Interface and then select Overlap Grid; Step 208: Generate all grids; Step 3: Establish a CFD numerical analysis model for the flexible pipe of the suspended tunnel: The forces acting on the suspended tunnel during operation include anchor cable tension, its own weight, and fluid forces, including wave forces. The suspended tunnel's own weight exerts a downward force, while the upward force generated by the tunnel's buoyancy, along with the tube's weight and buoyancy, form the system's initial mechanical equilibrium. Under static water conditions, the anchor cables are tightened to create pretension. The vibration response of a suspended tunnel pipe is determined by the combined effects of fluid forces, anchor cable tension, gravity, and buoyancy. Wave forces act as external excitations, and the NS equations are solved using CFD methods to calculate the wave pressure and shear force distribution on the pipe surface. These wave pressures and shear forces excite vibrations and induce displacement changes. These displacement changes affect the tension of the anchor cables, triggering dynamic adjustments to the anchor cable tension. Changes in anchor cable tension are a result of wave-induced pipe vibrations. At the same time, anchor cable tension limits the amplitude of pipe vibrations through reaction forces. The anchor cable-pipe coupled vibration equation establishes a dynamic link between pipe vibration and anchor cable tension. Anchor cable tension is updated in real time based on the relative displacement and velocity of the pipe. The anchor cable tension, gravity, buoyancy, and wave forces maintain the dynamic equilibrium of the suspended tunnel pipe. In STAR-CCM+, based on a combined anchor cable suspended tunnel model, wave forces induce pipe vibrations, and anchor cable tension provides real-time feedback on the pipe's displacement and vibrations. Gravity and buoyancy contribute to maintaining the system's mechanical equilibrium. Wave forces, anchor cable tension, and pipe displacement interact in a continuously iterative process, forming an integrated numerical model of the suspended tunnel's vibration response. Finally, based on the flow field conditions of the wave-current coupled excitation numerical environment model set previously, the entire flow field is initialized, and the appropriate calculation step size is selected according to the calculation requirements to start the numerical simulation.

2. The method for numerical prediction of dynamic response of flexible pipes in full-scale floating tunnels under vertical-inclined combined anchor mooring according to claim 1 is characterized in that: In the process of calculating the wave pressure and shear force distribution on the pipe surface, the wave pressure in, is the pressure exerted by the wave at position x and depth z, where x is the horizontal position, z is the coordinate perpendicular to the sea surface, and t is time; ρ is the fluid density, g is the acceleration due to gravity, A is the amplitude of the wave; h is the water depth; k is the wave number, and ω is the angular frequency of the wave.

3. The method for numerical prediction of dynamic response of flexible pipes in full-scale floating tunnels under vertical-inclined combined anchor mooring according to claim 2 is characterized in that: The wave number k=2π / λ, where λ is the wavelength.

4. The method for numerical prediction of dynamic response of flexible pipes in full-scale floating tunnels under vertical-inclined combined anchor mooring according to claim 1 is characterized in that: The anchor cable-tube coupling vibration equation is as follows: Where ρ is the density of the fluid; C L is the lift coefficient; v is the flow velocity; θ is the inclination angle of the anchor cable; ω v is the vortex discharge frequency; L is the length of the anchor cable; D t is the diameter of the anchor cable; is the sum of the mass of the anchor cable per unit length and the mass of the additional water; D n Symbols introduced for the convenience of calculation, y is the lateral displacement of the anchor cable, and They represent the lateral velocity and acceleration of the anchor cable respectively; n is the order; c is the viscous damping coefficient of the anchor cable; A1 is the cross-sectional area of ​​the anchor cable; E eq is the equivalent elastic modulus; Z is the vibration displacement of the tube body, and are the vibration velocity and acceleration respectively; ω1 is the natural frequency of the anchor cable; ω2 is the natural frequency of the tube body; ξ2 is the damping ratio of the tube body; M is the mass of the suspended tunnel; t is time.

5. The method for numerical prediction of dynamic response of flexible pipes in full-scale floating tunnels under vertical-inclined combined anchor mooring according to claim 1 is characterized in that: The construction process of the combined anchor cable suspended tunnel model includes the following steps: (1)Import file: Open the STAR CCM+ software and import the mesh file obtained in step 2; (2)Selection Physical Model: First, create a fluid physics continuum, i.e., physics continuum 1, and select the following models in order: 3D, implicit unsteady, multiphase, multiphase interaction, fluid volume, turbulence model, SST K-Omega model, gradient, separated flow, multiphase equation of state. At the same time, check gravity, VOF wave, and adaptive time step in the optional models, and finally click OK; then create a solid physics continuum, i.e., physics continuum 2, and select 3D, implicit unsteady, solid, solid stress, Rayleigh damping, flexible DFBI motion, and gravity model, and finally click OK; (3)Define the flexibleDFBI movement: Click Tools > Motion Node, right-click the Motion node, and then select New > DFBI Deformation. A new node named DFBI Deformation is added to the Motion Manager; ">" indicates the next step. (4)Edit 6-DOF volume parameters: Select Region > Overlap Region > Physical Value > Motion Assignment and set the motion to DFBI Deformation. Then right-click the DFBI > 6 DOF Body node and select New Body > 3D > Continuum. Rename the newly created node to Tube. Then right-click Tube > Create Body Motion and create a new node named Tube-motion under the Motion node. Create a solid displacement in the Tube-motion node and save it for later use. (5)Model parameter setting: Select DFBI > 6 DOF Body > Tube and add the moving parts and the mass of the floating tunnel. In the Free Motion node, select the motion properties for X-axis movement, Z-axis movement, and Y-axis rotation. In the Initial Value node, customize the moment of inertia and center of mass of the floating tunnel. (6)Define the motion of the SubmergedFloating Tunnel: Select Region > Suspension Tunnel Body > Physical Conditions > Flexible DFBI Motion Options and set the Flexible DFBI Motion Option to DFBI-Partially deformable. In the Suspension Tunnel Body > Physical Values ​​> Motion Assignment node, set the motion to Body-motion-Solid Displacement. Then, in the Suspension Tunnel Solid > Segment node, set both end faces to Fixed Constraints. (7)Define the internal flow field regional motion: Select Region > Internal Flow Region > Physical Values ​​> Motion Assignment node and set the motion to DFBI deformation; (8)Create interface: Set the surface where the outer wall of the tube contacts the flow field and the surface where the inner wall of the tube contacts the air flow field as the phase-contact interface respectively; the operation method is similar to the method of creating overlapping grids; (9)Add the anchor cable to the body coupling module: Right-click DFBI > Body Coupling node and add the required anchor cables, including spring-damper, catenary and other contact forms; (10)Solver setup: Click Solver > Implicit Unsteady State and set the desired time step. Next, click the 6 DOF Mesh Deformation node and check Zero Deformation, Recalculate Interfaces, Boundary Layer Deformation, and Keep Temporary Storage to meet the required deformation requirements. (11)Stop criterion setting: Click the Stop Criteria node and uncheck the Displacement Criterion, Force Criterion, Maximum Steps, and Stop File functions. Then set the number of iterations in the Maximum Inner Iterations node and the runtime in the Maximum Physical Time node. (12)Initialize Solution andRun Calculation: First click the Initialize Solution button with the mouse, then click the Run button to start the simulation calculation.

6. The method for numerical prediction of dynamic response of flexible pipes in full-scale floating tunnels under vertical-inclined combined anchor mooring according to claim 5 is characterized in that: The multiphase in step (2) is a gas-liquid two-phase flow.

7. The method for numerical prediction of dynamic response of flexible pipes in full-scale floating tunnels under vertical-inclined combined anchor mooring according to claim 5 is characterized in that: In the step (2), in the process of selecting the fluid volume, wave load is introduced, and flow is added on this basis to reflect the influence of wave and flow on the vibration of the pipe body; The wave loads are as follows: Horizontal velocity of the wave: u(x,t)=Aωcosh(k(z+h))cos(kx-ωt) Where A is the amplitude of the wave; ω is the angular frequency of the wave; k is the number of waves; h is the water depth; z is the coordinate perpendicular to the sea surface; t is time; x is the horizontal position; Surface wave pressure: in, is the pressure exerted by the wave; g is the acceleration due to gravity; η is the deformation of the wave surface; is the rate of change of water surface with time; Wave pressure inside the fluid: in, is the pressure exerted by the wave at position x and depth z, and ρ is the fluid density.

8. The method for numerical prediction of dynamic response of flexible pipes in full-scale floating tunnels under vertical-inclined combined anchor mooring according to claim 5 is characterized in that: In the step (9), during the process of adding the required anchor cables, an anchor cable-tube coupling effect is introduced; the anchor cable-tube coupling effect is realized by the anchor cable-tube coupling vibration equation; The anchor cable-tube coupling vibration equation is as follows: Where ρ is the density of the fluid; C L is the lift coefficient; v is the flow velocity; θ is the inclination angle of the anchor cable; ω v is the vortex discharge frequency; L is the length of the anchor cable; D t is the diameter of the anchor cable; is the sum of the mass of the anchor cable per unit length and the mass of the additional water; D n Symbols introduced to facilitate calculations, C D =0.7 is the drag coefficient, z is the integral variable; y is the lateral displacement of the anchor cable, and They represent the lateral velocity and acceleration of the anchor cable respectively; n is the order; c is the viscous damping coefficient of the anchor cable; A1 is the cross-sectional area of ​​the anchor cable; E eq is the equivalent elastic modulus; Z is the vibration displacement of the tube body, and are the vibration velocity and acceleration respectively; ω1 is the natural frequency of the anchor cable; ω2 is the natural frequency of the tube body; ξ2 is the damping ratio of the tube body; M is the mass of the suspended tunnel; t is time.

9. A computer storage medium storing a computer program, wherein: The computer program is loaded and executed by a processor to implement the numerical prediction method for dynamic response of a flexible pipe body of a full-scale floating tunnel under vertical-inclined combined anchor mooring as described in any one of claims 1 to 8.

10. A numerical prediction device for the dynamic response of a flexible pipe body in a full-scale floating tunnel under vertical-inclined combined anchor mooring, the device comprising a processor and a memory, characterized in that: The memory stores a computer program, which is loaded and executed by the processor to implement the numerical prediction method for the dynamic response of a flexible pipe body of a full-scale floating tunnel under vertical-inclined combined anchor mooring as described in any one of claims 1 to 8.

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