CN117634345B - Numerical forecasting method for dynamic response of suspension tunnel pipe body under wave-current combined excitation - Google Patents

Abstract

A numerical forecasting method for dynamic response of a suspension tunnel pipe body under wave-current combined excitation relates to a numerical forecasting method for dynamic response of the suspension tunnel pipe body. The numerical forecasting method for the dynamic response of the pipe body of the suspension tunnel solves the problem that the numerical forecasting error exists in the influence of fluid on the pipe body caused by vortex release. Firstly, carrying out numerical modeling on a wave field, then constructing a wave flow combined excitation field based on the wave field, and further writing a fluid abscissa direction, an ordinate direction speed and a wave surface change UDF function at a speed inlet; a fourth-order Longgar-Kutta method is used for dispersing a suspension tunnel pipe vibration control equation, and further, a suspension tunnel pipe dynamic response UDF function comprising speeds u and v of a suspension tunnel pipe structure in a transverse oscillation direction and a heave direction and displacements x and y is written; based on the software of Ansys Fluent, a written UDF function is imported, grid division and numerical simulation are carried out, and a pipe body dynamic response is obtained.

Description

Numerical prediction method for dynamic response of suspended tunnel under wave-current combined excitation

Technical Field

The invention belongs to the technical field of underwater suspended tunnels, and in particular relates to a numerical prediction method for dynamic response of a suspended tunnel pipe body.

Background Art

With the development of science and technology, cross-sea bridges, submerged tunnels, submarine tunnels and other cross-sea channels have been built in some important sea areas. The construction of these cross-sea channels has greatly promoted the economic development and cultural exchanges of the areas at both ends of the cross-sea channels. However, when faced with a wide sea surface and a deep seabed, the construction of traditional cross-sea channels such as cross-sea bridges, submerged tunnels and submarine tunnels will consume a lot of manpower, material resources and financial resources, and the construction is extremely challenging. In order to overcome these problems, the concept of underwater floating tunnel came into being. Underwater floating tunnels are referred to as floating tunnels. As a new form of cross-sea transportation, floating tunnels have attracted more and more active research with their unique advantages (such as: the unit length cost is not affected by the distance between the two ends of the cross-sea channel, there is basically no limit on the distance and water depth, it can be free from the influence of bad weather, and it has little impact on the two ends of the cross-sea channel and the marine environment). According to different anchoring methods, floating tunnels can be divided into four types: free type, anchor cable type, buoy type and pressure pier column type. The stability of free-style and pontoon-type suspended tunnels is poor, and the pressure-bearing pier-type suspended tunnel has high requirements for seabed geology. Compared with the other three types, the anchor-cable suspended tunnel is currently recognized as the most promising type of suspended tunnel in the world. Its main body consists of a pipe structure, an underwater foundation, a support system and a connection system. The lower end of the suspended tunnel pipe is connected to the underwater foundation through an anchor support system, and the force balance is achieved under the action of gravity, buoyancy and anchor tension. The pipe is in a complex marine environment. When these complex environmental loads act on the suspended tunnel pipe, the periodic load excitation will cause the structure to vibrate. This vibration will not only affect the comfort and safety of pedestrians and vehicles, but long-term vibration will also cause structural fatigue and may further cause fatigue damage to the pipe. As a large underwater structure, once the structure is damaged, it will cause irreparable casualties and property losses. Therefore, how to ensure that people and vehicles can stably and safely pass through the suspended tunnel pipe under the action of complex environmental loads is one of the key issues in the feasibility study of suspended tunnels.

Among the many marine environmental loads that a suspended tunnel may be subjected to (such as waves, currents, floating ice, earthquakes, etc.), waves and currents have the greatest impact on the dynamic response of the suspended tunnel body and last the longest. Therefore, it is a key research issue to ensure that people and vehicles can pass through the suspended tunnel body safely and stably to establish a stable and reliable numerical prediction method for the dynamic response of the suspended tunnel body under the combined excitation of waves and currents, and to deeply reveal the dynamic response mechanism of the suspended tunnel body under the combined excitation of waves and currents based on this method.

The research on the dynamic response of the suspended tunnel body under the combined excitation of waves and currents can be roughly divided into model experimental research, theoretical calculation research and numerical calculation research according to the research methods. Due to the high research cost of model experimental research, it is impossible to conduct large-scale model experimental research on dynamic response based on the influence of variable parameters. Since theoretical calculation research uses a large number of empirical model coefficients in the calculation process, it is difficult to deeply reveal the dynamic response mechanism of the structure under complex environmental loads. Compared with model experiments and theoretical calculation studies, numerical calculation research based on CFD numerical methods has the advantages of low research cost and few empirical model coefficients used in the research process. It is very suitable for large-scale dynamic response mechanism research based on this method.

Summary of the invention

The present invention aims to solve the problem that the current numerical prediction method of the dynamic response of the suspended tunnel pipe body does not consider the influence of the fluid on the pipe body caused by the vortex release and there is a numerical prediction error.

A numerical prediction method for dynamic response of a suspended tunnel body under wave-current combined excitation comprises the following steps:

Step 1: numerically model the wave field, then construct the wave-current joint excitation field based on the wave field to obtain the velocity of the water particle in the horizontal direction under the wave-current joint excitation Velocity in the vertical direction And the wave surface equation Then write the UDF function of the fluid velocity in the horizontal and vertical directions at the velocity inlet, as well as the UDF function of the wave surface change;

Step 2: Use the fourth-order Runge-Kutta method to discretize the vibration control equation of the suspended tunnel body, obtain the velocities u, v and displacements x, y in the transverse and vertical directions of the suspended tunnel body structure, and the position and velocity conditions of the suspended tunnel section input at the initial moment, and then write a UDF function of the dynamic response of the suspended tunnel body including the position and velocity conditions of the suspended tunnel section input at the initial moment and the velocities u, v and displacements x, y in the transverse and vertical directions of the suspended tunnel body structure;

Step 3: Overlapping grid division and fluid-solid coupling numerical simulation:

Firstly, the parameters of the suspended tunnel body, its size, anchor cable stiffness k _i , engineering damping c _i , submerged depth d , flow velocity U , water depth h , wave amplitude A and wave period T are determined, and then meshing and numerical simulation are performed;

The meshing process includes the following steps:

First, draw the foreground grid. The foreground grid calculation domain is arranged around the suspension tunnel. The height of the first layer of grids and the change of grid height around the surface of the suspension tunnel tube are required to meet the requirements of the turbulence model. Then determine the size of the overall flow field and draw the background grid. At the same time, encrypt some grid calculation areas. First, encrypt the grids occupied by the wave height to meet the requirements of wave simulation. Then encrypt the moving area of the suspension tunnel tube to ensure that its grid size is basically consistent with the size of the foreground grid boundary grid.

The process of performing numerical simulation includes the following steps:

The foreground grid and background grid files are read in through Ansys Fluent software, and the double-precision solver is used. The transient calculation method is selected, the gravity acceleration direction is selected as vertical downward, and the turbulence model is selected as the SST k-omega model; then the multiphase flow model is opened, and water and air are selected as the two calculation phases; then the UDF functions in steps one and two are imported; then the wall of the suspended tunnel and the upper and lower flow field boundaries are set as wall boundary conditions, the outlet is set as the pressure outlet, the inlet is set as the velocity inlet, and the UDF function in step one is assigned, and the foreground grid boundary is set as the overset format; in the dynamic grid setting, the UDF function that controls the dynamic response of the suspended tunnel body is assigned to the suspended tunnel wall, the foreground grid calculation domain, and the foreground grid boundary respectively; the SIMPLE algorithm is selected as the calculation method, and the first-order implicit method is selected as the transient control equation; according to the flow field data determined before the numerical simulation, the entire flow field is initialized, and finally an appropriate calculation time step is selected for calculation, and then the displacement and time relationship curve of the lateral and vertical sway of the suspended tunnel body is obtained, which is the dynamic response.

Furthermore, the velocity of the water particle in the horizontal direction under the combined wave and current excitation in step 1 is Velocity in vertical direction And the wave surface equation as follows:

The velocity in the horizontal direction is:

The velocity in the ordinate direction is:

The wave surface equation is:

Among them, ω is the wave circular frequency, h is the water depth; A is the wave amplitude, x′, y′ are the coordinate positions of the wave water particles, and t is the time; is the wave number of waves under the influence of the oncoming flow, and U is the oncoming flow velocity.

Furthermore, in step 1, the wave field is numerically modeled using Airy linear waves. The numerical model of the wave field established using Airy linear waves is as follows:

The dispersion relation is:

ω ² = gktanh(kh) (1)

The velocity potential is:

The wave surface equation is:

η＝Acos(kx′-ωt) (3)

The velocity in the horizontal direction is:

The velocity in the ordinate direction is:

Where ω is the wave circular frequency, g is the gravitational acceleration, k is the wave number, h is the water depth, A is the wave amplitude, x′ and y′ are the coordinate positions of the wave water particles, φ is the velocity potential, and t is the time.

Furthermore, in the process of constructing the wave-current joint excitation field based on the wave field in step 1, when the water current exists, the dispersion relation is as follows:

In the formula, is the wave number of the wave under the influence of the incoming flow, and U is the incoming flow velocity;

The change of wave number is obtained based on the dispersion relation; and the expression of wave height under the influence of the incoming flow is determined as follows:

Based on equations (6) and (7), the velocity of the water particle in the horizontal direction under the combined wave and current excitation is obtained: Velocity in vertical direction And the wave surface equation

Furthermore, the vibration control equation of the suspended tunnel body described in step 2 is as follows:

The suspended tunnel body is regarded as a rigid body vibration model under wave-current combined excitation. The vibration control equations of the suspended tunnel body in the sway and heave directions are as follows:

Where m is the mass of the suspended tunnel tube structure per unit length, _cx is the sway damping coefficient, _kx is the stiffness coefficient of the structure in the sway direction, _cy is the heave damping coefficient, _ky is the stiffness coefficient of the structure in the heave direction, _Fx (t) is the fluid force on the tube section in the sway direction, _Fy (t) is the fluid force on the tube section in the heave direction, _Fb is the anchor cable pretension distributed on the tube per unit length, x, dx(t)/dt, ^d2x (t)/ ^dt2 represent the displacement, velocity and acceleration in the sway direction, y, dy(t)/dt, ^d2y (t)/ ^dt2 represent the displacement, velocity and acceleration in the heave direction, respectively; further simplified as:

in:

Where _ωx is the natural circular frequency of the structure in the lateral swing direction, _ωy is the natural circular frequency of the structure in the heave swing direction, _ζx is the damping ratio of the structure in the lateral swing direction, and _ζy is the damping ratio of the structure in the heave swing direction.

Furthermore, F _x (t) and F _y (t) in the suspension tunnel pipe vibration control equation are obtained by integrating the suspension tunnel pipe surface pressure and viscous stress based on Ansys Fluent software.

Furthermore, the process of using the fourth-order Runge-Kutta method to discretize the vibration control equation of the suspended tunnel pipe body in step 2, and then writing the UDF function of the dynamic response of the suspended tunnel pipe body including the position and velocity conditions of the suspended tunnel pipe section at the initial moment and the velocities u, v in the lateral and vertical directions of the suspended tunnel pipe body structure and the displacements x, y includes the following steps:

In order to solve the vibration control equation of the suspended tunnel body in the lateral direction, equation (13) is written as:

Based on the classic fourth-order Runge-Kutta method, equation (17) is discretized into:

in:

In order to solve the vibration control equation of the suspended tunnel body in the vertical direction, equation (14) is written as:

Based on the classic fourth-order Runge-Kutta method, equation (23) is discretized into:

in:

Wherein, _K1x , _K2x , K3x _{, K4x} , K1y _{, K2y ,} K3y, K4y, _L1x , _L2x , _L3x , _L4x , _L1y , _L2y , _L3y , _L4y are the transformation equations of the fourth-order Runge-Kutta method, Δt, _tn , tn ₊₁ represent the time step, time _n , and time n+1 respectively, u(t) is the velocity of the structure in the sway direction, and v(t) is the velocity of the structure in the heave direction;

_According to the displacement x( _tn ), y( _tn ) and velocity u( _tn ), v( _tn ) at time tn, the displacement x(tn+1), y( _{tn +1) and velocity u(tn+1} ), v(tn ₊₁ ) at the next time _tn+1 = tn + Δt are calculated by using simultaneous equations ( ₁₇ ) to ( ₂₈ );

The position and velocity conditions of the suspended tunnel section at the initial moment are as follows:

x(t ₀ )＝x ₁ ,y(t ₀ )＝y ₁ (29)

u(t ₀ )＝0,v(t ₀ )＝0 (30)

In the formula, x ₁ and y ₁ represent the center of gravity of the suspended tunnel tube at the initial moment;

First, combine formulas (13) (14) and boundary conditions (29) (30), and then use formulas (17) to (28) to calculate the velocities u, v and displacements x, y in the lateral and vertical directions of the structure; write the UDF function of the dynamic response of the suspended tunnel body according to formulas (17) to (30).

Beneficial effects:

The present invention designs a numerical prediction method for the dynamic response of a suspended tunnel tube under the combined excitation of waves and currents. The method can be used to deeply reveal the dynamic response mechanism of a suspended tunnel tube under the combined excitation of waves and ocean currents, thereby providing technical support for the structural safety design of a suspended tunnel tube. Compared with the prior art, the technical solution of the present invention has the following advantages:

1. In the current theory and numerical calculation, the wave and flow load acting on the suspended tunnel only considers the inertial force and average drag force of the surrounding fluid on the structure based on the Morison equation or diffraction theory, and does not consider the lift and oscillation drag force of the fluid on the tube body caused by vortex release, as well as the interaction between the tube body and the surrounding fluid. Obviously, this current consideration method cannot accurately reveal the coupling response characteristics between the tube structure and the surrounding fluid. In view of this, the numerical prediction model of the dynamic response of the suspended tunnel tube body under wave and flow combined excitation established by the present invention takes into account the coupling effect between the tube body and the surrounding fluid, so the present invention can effectively improve the accuracy of the numerical prediction.

2. In the current model experimental research, due to the limitation of experimental cost, the research on the dynamic response of the suspended tunnel body under the combined excitation of waves and currents is only based on the response characteristics of a small number of structural parameters or environmental parameters. Based on the results obtained from the study of these few parameters, it is difficult to deeply reveal the dynamic response mechanism of the suspended tunnel body. Based on this, the numerical prediction method proposed in the present invention can very conveniently and quickly study the dynamic response of the suspended tunnel under the combined excitation of complex waves and currents. The research cost of this numerical method is low, and it is very suitable for large-scale numerical calculations based on the influence of the pipe body structure and surrounding environmental parameters, and finally achieves the research goal of summarizing the dynamic response mechanism of the suspended tunnel body under the combined excitation of waves and currents based on a large number of numerical calculation results.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic diagram of the numerical prediction process of the dynamic response of the suspended tunnel body under wave and current combined excitation.

Figure 2 is a schematic diagram of the wave-current combined excitation field.

FIG3 is a schematic diagram of an overlapping grid.

FIG4 is a schematic diagram of wave propagation.

Figure 5 is a flow field velocity cloud diagram.

Figure 6 is a vortex discharge cloud map.

FIG. 7 is a graph showing the lateral swing time history of the suspended tunnel body.

FIG8 is a vertical swing history curve diagram of the suspended tunnel body.

FIG. 9 is a graph showing the trajectory of the suspended tunnel tube.

FIG10 is a diagram showing the wave height variation corresponding to the center of the suspended tunnel body.

DETAILED DESCRIPTION

The invention is a numerical prediction method for the dynamic response of a suspended tunnel body under wave-current combined excitation. First, a wave-current combined excitation numerical pool is established based on the velocity boundary wave making method. Then, the vibration control equation of the suspended tunnel body is discretized using the fourth-order Runge-Kutta method. Finally, overlapping grid division and fluid-solid coupling numerical simulation are performed. The method is described in detail below in conjunction with a specific implementation method.

Specific implementation method one:

This embodiment is a numerical prediction method for the dynamic response of a suspended tunnel tube under wave-current combined excitation, as shown in FIG1 , which includes the following steps:

Step 1: Establish a wave-current joint excitation numerical pool based on the velocity boundary wave making method:

This embodiment uses Airy linear waves as an example to illustrate the detailed process of numerically constructing a wave field. However, it is worth noting that the numerical modeling process of the wave field described here is also applicable to high-order nonlinear waves. It is only necessary to modify the wave surface equation and the water particle movement speed through the relevant wave theory, and the obtained wave field is still applicable to the subsequent processing of the present invention. The relevant theoretical formula of Airy linear waves is as follows:

The dispersion relation is:

ω ² = gktanh(kh) (1)

The velocity potential is:

The wave surface equation is:

η＝Acos(kx′-ωt) (3)

The velocity in the horizontal direction is:

The velocity in the ordinate direction is:

Where ω is the wave circular frequency, g is the gravitational acceleration, k is the wave number, h is the water depth; A is the wave amplitude, x′ and y′ are the coordinate positions of the wave water particles, φ is the velocity potential, and t is the time;

The velocity of the fluid at the inlet can be defined by writing a UDF function based on the linear wave theory, and the rear flow field is subjected to wave elimination. The wall boundary condition is used at the rear boundary of the flow field, and the wave field can be obtained when the flow field is stable.

Based on the obtained wave field, a wave-current joint excitation field is further constructed, and the schematic diagram of the wave-current joint excitation field is shown in Figure 2. Since the incoming current interacts with the waves, the wave height and wavelength will change. When the water flow exists, the dispersion relation is different from that of pure waves, which can be expressed as follows:

In the formula, is the wave number of waves under the influence of the oncoming flow, and U is the oncoming flow velocity.

According to theoretical derivation, the wave frequency will not change due to the influence of the incoming flow. Based on the dispersion relation, the change in wave number can be obtained. At the same time, the wave height will also change due to the influence of the current. The expression of the wave height under the influence of the incoming flow is as follows:

Based on equations (6) and (7), the velocity of the water particle in the horizontal direction under the combined wave and current excitation can be obtained: Velocity in the vertical direction And the wave surface equation It is expressed as follows:

The velocity in the horizontal direction is:

The velocity in the ordinate direction is:

The wave surface equation is:

According to formulas (8)-(10), the UDF functions of the fluid velocity in the horizontal and vertical directions at the velocity inlet and the UDF function of the wave surface change can be written.

The purpose of step one is to write a UDF function that defines the velocity inlet boundary conditions. Then, combined with the specific settings of step three, a wave-current joint excitation numerical pool can be established.

Step 2: Use the fourth-order Runge-Kutta method to discretize the vibration control equation of the suspended tunnel body:

The loads on the suspended tunnel can be roughly divided into three categories according to the source of load excitation: the tension load provided by the anchor cables of the suspended tunnel, the gravity load of the tunnel body, and the fluid load acting on the suspended tunnel by the surrounding fluid. The fluid load can be further divided into static load and dynamic load. The static load mainly includes buoyancy and average drag along the flow direction; the dynamic load mainly includes oscillating drag (along the flow direction) and lift (along the transverse direction) caused by vortex release, and additional inertia force caused by structural vibration. The stability of the suspended tunnel requires that the anchor cables used to fix the suspended tunnel always remain in a tensioned state (the anchor cables always have tension). In other words, in any case, the vertical force (i.e., the combined force of gravity, buoyancy and lift) on the suspended tunnel body except the tension of the anchor cables is upward. Based on the stability requirements of the suspended tunnel, the constraint effect provided by the anchor cables of the suspended tunnel can be decomposed along the heave direction and the lateral direction: in the heave direction, it is simplified to a rod that can only withstand tension but not pressure; in the lateral direction, it is simplified to a spring that can withstand both tension and pressure.

The suspended tunnel body is regarded as a rigid body vibration model under wave-current combined excitation. The vibration control equations of the suspended tunnel body in the sway and heave directions are as follows:

In the formula, m is the mass of the suspended tunnel pipe structure per unit length, _cx is the sway damping coefficient, _kx is the stiffness coefficient of the structure in the sway direction, _cy is the heave damping coefficient, _ky is the stiffness coefficient of the structure in the heave direction, _Fx (t) is the fluid force on the pipe section in the sway direction, and _Fy (t) is the fluid force on the pipe section in the heave direction. _Fx (t) and _Fy (t) are obtained by integrating the surface pressure and viscous stress of the suspended tunnel pipe by Ansys Fluent software, _Fb is the anchor cable pretension distributed on the pipe per unit length, x, dx(t)/dt, ^d2x (t)/ ^dt2 represent the displacement, velocity and acceleration in the sway direction, respectively, and y, dy(t)/dt, ^d2y (t)/ ^dt2 represent the displacement, velocity and acceleration in the heave direction, respectively. It can be further simplified as:

in:

Where _ωx is the natural circular frequency of the structure in the lateral swing direction, _ωy is the natural circular frequency of the structure in the heave swing direction, _ζx is the damping ratio of the structure in the lateral swing direction, and _ζy is the damping ratio of the structure in the heave swing direction.

The fourth-order Runge-Kutta method is used to discretely solve the differential equation of the dynamic response of the suspended tunnel body. The movement velocity and displacement of the suspended tunnel body at each time step can be obtained through calculation.

In order to solve the vibration control equation of the suspended tunnel body in the lateral direction, equation (13) is written as:

Based on the classic fourth-order Runge-Kutta method, equation (17) is discretized into:

in:

In order to solve the vibration control equation of the suspended tunnel body in the vertical direction, equation (14) is written as:

Based on the classic fourth-order Runge-Kutta method, equation (23) is discretized into:

in:

In the formula, _K1x , _K2x , K3x, _K4x , _{K1y , K2y} , K3y, _K4y , _{L1x , L2x} , _L3x , _L4x , _L1y , _L2y , _L3y and _L4y are the transformation equations of the fourth-order Runge-Kutta method, Δt, _tn and tn ₊₁ represent the time step, time n and time n+1 respectively, u(t) is the velocity of the structure in the sway direction, and v(t) is the velocity of the structure in the heave direction.

Based on the displacement x( _tn ), y( _tn ) and velocity u( _tn ), v( _tn ) at _time tn, the displacement x(tn+1), y( _{tn +1) and velocity u(tn+1} ), v(tn ₊₁ ) at the next time _tn+1 =tn+Δt can be calculated by using simultaneous equations ( ₁₇ ) to ( ₂₈ ).

The position and velocity conditions of the suspended tunnel section at the initial moment are as follows:

x(t ₀ )＝x ₁ ,y(t ₀ )＝y ₁ (29)

u(t ₀ )＝0,v(t ₀ )＝0 (30)

Where _x1 and _y1 represent the center of gravity of the suspended tunnel tube at the initial moment.

First, combine formulas (13) (14) and boundary conditions (29) (30), and then calculate the velocities u, v and displacements x, y in the lateral and vertical directions of the structure through formulas (17) to (28). The UDF function of the dynamic response of the suspended tunnel body is written according to formulas (17) to (30).

The purpose of step 2 is to write a UDF function to control the dynamic response of the suspended tunnel body, and then combine the specific settings of step 3 to realize the simulation of the dynamic response of the suspended tunnel body.

Step 3: Overlapping grid division and fluid-solid coupling numerical simulation:

Firstly, the parameters such as the suspended tunnel body style and size, anchor cable stiffness k _i , engineering damping c _i , submerged depth d , flow velocity U , water depth h , wave amplitude A and wave period T are determined, and then meshing and numerical simulation are carried out.

Meshing:

Overlapping grids are selected for subsequent numerical simulation. Overlapping grid technology uses interpolation between overlapping areas to achieve data transfer between foreground grids and background grids. There are two reasons for choosing overlapping grids: ① Overlapping grids are one of the dynamic grid numerical simulation methods, which is more suitable for the calculation of the vibration response of suspended tunnels, laying the foundation for the subsequent vibration response of suspended tunnels; ② When changing the calculation conditions of different wave parameters, the foreground grid does not need to be changed, and only the background grid needs to be changed, which is more convenient.

The cross-section of the suspended tunnel body is diverse, among which the circular cross-section is the most widely studied cross-section of the suspended tunnel body, and it is also recognized as one of the cross-sections of the suspended tunnel body with the most application prospects. Taking the classic circular cross-section suspended tunnel body as an example, the overlapping grid division method to be used in the present invention is shown in Figure 3. In the future, based on this grid division method, by modifying the cross-section style, that is, only needing to change the circle to other shapes and re-dividing the foreground grid, the vibration response of the suspended tunnel body with different cross-section forms can be studied.

Draw a suitable grid through ICEM CFD. First, draw the foreground grid. The foreground grid calculation domain is arranged around the suspension tunnel. The height of the first layer of grid and the change of grid height around the surface of the suspension tunnel tube are required to meet the requirements of the turbulence model. Then determine the size of the overall flow field and draw the background grid. The horizontal grid height of the background grid depends on the wavelength and must meet the requirements of wave simulation. At the same time, some grid calculation areas must be encrypted. First, the grid occupied by the wave height must be encrypted to meet the requirements of wave simulation; then the moving area of the suspension tunnel tube must be encrypted to ensure that its grid size is basically consistent with the size of the foreground grid boundary grid.

Numerical simulation:

The foreground grid and background grid files are read in through Ansys Fluent software, and the double-precision solver is used. The transient calculation method is selected, the gravity acceleration direction is selected to be vertically downward with a magnitude of 9.81m/ ^s2 , and the turbulence model is selected as the SST k-omega (2eqn) model. Then the multiphase flow model is opened, and water and air are selected as the two calculation phases. Then the UDF functions in steps one and two are imported. Then the wall of the suspended tunnel and the upper and lower flow field boundaries are set as wall boundary conditions, the outlet is set as the pressure outlet, the inlet is set as the velocity inlet, and the UDF function in step one is assigned, and the foreground grid boundary is set to the overset format. In the dynamic grid setting, the UDF function that controls the dynamic response of the suspended tunnel body is assigned to the suspended tunnel wall, the foreground grid calculation domain, and the foreground grid boundary. The SIMPLE algorithm is selected as the calculation method, and the first-order implicit method is selected for the transient control equation. According to the flow field data determined before the numerical simulation, the entire flow field is initialized, and finally an appropriate calculation time step is selected for calculation, thereby obtaining a wave propagation schematic diagram, a flow field velocity cloud diagram, a vortex discharge cloud diagram, a suspension tunnel tube sway and vertical sway time history curve, and a suspension tunnel tube trajectory curve diagram, etc. Among them, the relationship curve between the displacement and time of the suspension tunnel tube sway and vertical sway is the dynamic response.

The specific steps of numerical simulation are as follows:

(1) Initial settings

Open Ansys Fluent software, select the double precision solver option, read the background mesh file from the File option in the toolbar, then select Append in the Zones toolbar, select Append Case File in Append, and select the foreground mesh file in the submenu.

(2) General settings

Select Transient for Time, check the Gravity option, and fill in the gravity acceleration -9.81m/s ² in the ordinate direction. Leave the other parameters as default.

(3)Viscous settings

Double-click Viscous with the left button of the mouse, select the k-omega(2eqn) model in the pop-up window, select SST in the k-omega(2eqn) model in the pop-up window, leave the other parameters as default, and then click OK.

(4)Materials settings

Select Fluid in the Materials submenu, then click Create/Edit, click Fluent Database in the pop-up menu, select liquid water water-liquid (h2o(l)), then click copy, click Change/create in the pop-up menu, and finally select water-liquid in Materials.

(5)Multiphase setting

Double-click Multiphase in the Models menu, select Volume of Fluid in the Model option in the pop-up menu, select Formulation Implicit in the Volume Fraction Parameters option, check Implicit Body Force in the BodyForce Formulation option, check OpenChannel Flow in the VOF Sub-Models option, and click Apply. Then click Phases on the upper menu bar, change the Name of phase-1 to air, change the Name of phase-2 to water, and finally click Apply.

(6) Import UDF

Select the Define toolbar with the left mouse button, click User-Defined in its drop-down menu, select Functions, select compiled… in its submenu, then click Add in the pop-up window to select the compiled UDF functions, including the UDF functions compiled in step 1 and step 2, and click OK. Then click Build, and finally click Load.

(7)Boundary Conditions Settings

In the zone area of Boundary Conditions, set the wall of the suspended tunnel to wall, set the foreground grid boundary to overset, set the foreground grid and background grid calculation grid area to interior, and set the upper and lower boundaries of the background grid to wall. Set the flow field inlet to velocity inlet, select Components in the Velocity Specification Method in the pop-up window, select the corresponding fluid horizontal and vertical velocity UDF functions (written in step 1) for X-Velocity and Y-Velocity, then click Apply, then select water in the Phase item, select the wave surface change UDF function (written in step 1) in the Volume Fraction item that pops up, and finally click Apply. Set the Outlet to Pressure-outlet, check Open Channel in the Multiphase setting, and enter the corresponding y′ coordinates of the free surface and bottom of the flow field in Free Surface Level and Bottom Level, then click Apply.

(8)Overset Interface Settings

First, click Create, then select the computational grid domains of the foreground grid and the background grid respectively, name the overlapping interface, and click Create.

(9) Dynamic Mesh settings

Check the Dynamic Mesh option, uncheck the option in the Mesh Methods window, click Create in the Dynamic Mesh Zones menu, select the suspended tunnel wall, foreground mesh boundary, and foreground mesh calculation domain in Zone Names, and perform the following operations. Select RigidBody for Type, select the suspended tunnel body dynamic response UDF (written in step 2) for Motion UDF, enter the center of gravity of the suspended tunnel in Center of Gravity Location, and click Create.

(10) Solution Methods settings

The SIMPLE algorithm is used as the basic algorithm, the transient control equation Transient Formulation selects the first order implicit, and the other settings remain unchanged. A coarse particle vertical lifting pipeline vibration experimental device and its comparative prediction method

(11) Solution Controls settings

The relaxation factors used the default parameters.

(12) Report Definitions settings

The monitor can be set to obtain the function of the time-varying parameters such as the lift force, drag force and wave height change at a certain point of the suspended tunnel.

(13) Monitors Residual Settings

Click Monitors with the left mouse button, select Residuals, enter 0.001, 0.001, 0.001, 0.001, 0.001 under Absolute Criteria respectively, and then click OK.

(14)Cell Registers Settings

In the Cell Registers settings window, select the Region option under the New submenu, and enter the y′ coordinates of the free surface and bottom of the liquid phase region of the numerical pool, and the x′ coordinates of the flow field inlet and outlet.

(15) Solution Initialization settings

Click Solution Initialization with the left mouse button, select Standard Initialization in Initialization Methods, select inlet for Computer from, change WaterVolume Fraction to 0, and click Initialize. Then click Patch, select water for Phase, select Volume Fraction for Variable, select 1 for Value, and select the liquid phase region of the numerical water pool created in the previous step in Registers to Patch.

(16) Run Calculation settings

Click Run Calculation with the left mouse button, enter the calculation time step size into Time Step Size, enter the total number of time steps into Number of Time Steps, keep the other parameters unchanged, and click Calculate to start the calculation.

After completing the numerical simulation of the dynamic response of the suspended tunnel body within a time step, Ansys Fluent software will update the specific position of the suspended tunnel body according to the UDF of the dynamic response of the suspended tunnel body. Then the software will update the fluid domain in the entire wave-current joint excitation numerical water pool, and then perform the numerical simulation of the next time step.

Example

The method described in the specific implementation method is used to perform numerical simulation on an example. A classic circular cross-section floating tunnel pipe segment is selected for numerical calculation. The pipe diameter D is 26m, the distance d from the center of the floating tunnel pipe to the water surface is 30m, the unit pipe segment mass m is 298783kg, the stiffness of the tensile rod in the heave direction _ky is 3.4176×10 ⁶ N/m, the spring stiffness in the transverse direction _kx is 2.1267×10 ⁶ N/m, and the heave and transverse damping ratios _ζy and _ζx are both 0.025. The parameters of the wave-current combined excitation field are as follows: the water depth h is 200 m, the parameters of the single wave field are amplitude A of 5.75 m, wavelength λ of 264 m, and period T of 13 s. When coupled with a uniform incoming flow with a velocity U of 2.5 m/s, the theoretical parameters become amplitude A of 5.16 m, wavelength λ of 325.76 m, and period T of 13 s.

The numerical simulation results of the dynamic response of the suspended tunnel body under the combined excitation of waves and currents are as follows: From the wave propagation schematic diagram of Figure 4 and the corresponding wave height change diagram at the center of the suspended tunnel body in Figure 10, it can be seen that the wave motion in the flow field is stable, and the simulation errors of the amplitude and wavelength are small. From the flow field velocity cloud map of Figure 5, it can be seen that the wave-current combined excitation field constructed by the present invention is relatively stable, there is a coupling effect between waves and flows, and the shedding of vortices will also have a certain impact on the velocity field. From the vortex discharge cloud map of Figure 6, it can be seen that when the ocean current flows through the suspended tunnel body, its vortex shedding mode is mainly a "P" type vortex, that is, periodic vortex shedding is generated alternately up and down, and because the suspended tunnel is close to the sea surface, the vortices shedding along the upper surface of the suspended tunnel body will be affected by the wave motion. It can be seen from the lateral swing time history curve of the suspended tunnel tube body in Figure 7, the vertical swing time history curve of the suspended tunnel tube body in Figure 8, and the trajectory curve of the suspended tunnel tube body in Figure 9 that the dynamic response of the suspended tunnel tube body is relatively stable, and it will reciprocate along a similar trajectory, and each movement direction corresponds to two different extreme values; the amplitude of the lateral swing motion of the suspended tunnel tube body in the downstream direction is 0.23m, and the amplitude in the upstream direction is 0.12m; the amplitude of the vertical swing motion in the vertical upward direction is 0.18m, and the amplitude in the vertical downward direction is 0.24m.

Researchers can use the above method to control variables and conduct batch numerical simulation research by adjusting the structural parameters of the suspended tunnel itself, such as the cross-sectional form, cross-sectional size, submergence depth, buoyancy-to-weight ratio, and anchor angle, as well as external environmental load parameters such as waves and currents. On this basis, through the large amount of data extracted from the numerical simulation research, the dynamic response mechanism of the suspended tunnel body under the combined excitation of wave and current loads is deeply revealed, aiming to provide a reliable basis and technical support for improving the design of the suspended tunnel body and improving the stability and safety of the suspended tunnel during operation. Through the present invention, the research progress of my country's underwater suspended tunnel engineering can be further accelerated.

The present invention may also 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 (6)

1. A numerical prediction method for the dynamic response of a suspended tunnel body under wave-current combined excitation, characterized in that it comprises the following steps: Step 1: numerically model the wave field, then construct the wave-current joint excitation field based on the wave field to obtain the horizontal coordinate velocity of the water particle under the wave-current joint excitation Velocity in the vertical direction And the wave surface equation Then write the UDF function of the fluid velocity in the horizontal and vertical directions at the velocity inlet, as well as the UDF function of the wave surface change; Step 2: Use the fourth-order Runge-Kutta method to discretize the vibration control equation of the suspended tunnel body, and obtain the lateral velocity u, vertical velocity v, lateral displacement x, vertical displacement y of the suspended tunnel body structure, and the position and velocity conditions of the suspended tunnel section input at the initial moment, and then write a UDF function of the dynamic response of the suspended tunnel body including the position and velocity conditions of the suspended tunnel section input at the initial moment and the lateral and vertical velocities u, v and displacements x, y of the suspended tunnel body structure; Step 3: Overlapping grid division and fluid-solid coupling numerical simulation: Firstly, the pipe style and size of the floating tunnel, anchor cable stiffness k _i , engineering damping c _i , submerged depth d , flow velocity U , water depth h , wave amplitude A and wave period T parameters are determined, and then meshing and numerical simulation are performed; The meshing process includes the following steps: First, draw the foreground grid. The foreground grid calculation domain is arranged around the suspension tunnel. The height of the first layer of grids and the change of grid height around the surface of the suspension tunnel tube are required to meet the requirements of the turbulence model. Then determine the size of the overall flow field and draw the background grid. At the same time, encrypt some grid calculation areas. First, encrypt the grids occupied by the wave height to meet the requirements of wave simulation. Then encrypt the moving area of the suspension tunnel tube to ensure that its grid size is basically consistent with the size of the foreground grid boundary grid. The process of performing numerical simulation includes the following steps: The foreground grid and background grid files are read in through Ansys Fluent software, and the double-precision solver is used. The transient calculation method is selected, the gravity acceleration direction is selected as vertical downward, and the turbulence model is selected as the SST k-omega model; then the multiphase flow model is opened, and water and air are selected as the two calculation phases; then the UDF functions in steps one and two are imported; then the wall of the suspended tunnel and the upper and lower flow field boundaries are set as wall boundary conditions, the outlet is set as the pressure outlet, the inlet is set as the velocity inlet, and the UDF function in step one is assigned, and the foreground grid boundary is set as the overset format; in the dynamic grid setting, the UDF function that controls the dynamic response of the suspended tunnel body is assigned to the suspended tunnel wall, the foreground grid calculation domain, and the foreground grid boundary respectively; the SIMPLE algorithm is selected as the calculation method, and the first-order implicit method is selected as the transient control equation; according to the flow field data determined before the numerical simulation, the entire flow field is initialized, and finally an appropriate calculation time step is selected for calculation, and then the displacement and time relationship curve of the lateral and vertical sway of the suspended tunnel body is obtained, which is the dynamic response. 2. According to the method for numerical prediction of dynamic response of a suspended tunnel body under wave-current combined excitation according to claim 1, it is characterized in that the velocity of the water particle in the horizontal coordinate direction under the wave-current combined excitation in step 1 is Velocity in vertical direction And the wave surface equation as follows: The velocity in the horizontal direction is: The velocity in the ordinate direction is: The wave surface equation is: Among them, ω is the wave circular frequency, h is the water depth; A is the wave amplitude, x′, y′ are the coordinate positions of the wave water particles, and t is the time; is the wave number of waves under the influence of the oncoming flow, and U is the oncoming flow velocity. 3. According to the method for numerical prediction of dynamic response of a suspended tunnel body under wave-current combined excitation of claim 2, it is characterized in that in step 1, the wave field is numerically modeled using Airy linear waves, and the numerical model of the wave field established using Airy linear waves is as follows: The dispersion relation is: ω ² = gktanh(kh) (1) The velocity potential is: The wave surface equation is: η＝Acos(kx′-ωt) (3) The velocity in the horizontal direction is: The velocity in the ordinate direction is: Where ω is the wave circular frequency, g is the gravitational acceleration, k is the wave number, h is the water depth, A is the wave amplitude, x′ and y′ are the coordinate positions of the wave water particles, φ is the velocity potential, and t is the time. 4. According to the method of numerical prediction of dynamic response of floating tunnel tube under wave-current combined excitation according to claim 3, it is characterized in that in the process of constructing the wave-current combined excitation field based on the wave field in step 1, when the water flow exists, the dispersion relation is as follows: In the formula, is the wave number of the wave under the influence of the incoming flow, and U is the incoming flow velocity; The change of wave number is obtained based on the dispersion relation; and the expression of wave height under the influence of the incoming flow is determined as follows: Based on equations (6) and (7), the velocity of the water particle in the horizontal direction under the combined wave and current excitation is obtained: Velocity in the vertical direction And the wave surface equation 5. According to any one of claims 1 to 4, a numerical prediction method for the dynamic response of a suspended tunnel tube under wave-current combined excitation is characterized in that the vibration control equation of the suspended tunnel tube in step 2 is as follows: The suspended tunnel body is regarded as a rigid body vibration model under wave-current combined excitation. The vibration control equations of the suspended tunnel body in the sway and heave directions are as follows: Where m is the mass of the suspended tunnel tube structure per unit length, _cx is the sway damping coefficient, _kx is the stiffness coefficient of the structure in the sway direction, _cy is the heave damping coefficient, _ky is the stiffness coefficient of the structure in the heave direction, _Fx (t) is the fluid force on the tube section in the sway direction, _Fy (t) is the fluid force on the tube section in the heave direction, _Fb is the anchor cable pretension distributed on the tube per unit length, x, dx(t)/dt, ^d2x (t)/ ^dt2 represent the displacement, velocity and acceleration in the sway direction, y, dy(t)/dt, ^d2y (t)/ ^dt2 represent the displacement, velocity and acceleration in the heave direction, respectively; further simplified as: in: Where _ωx is the natural circular frequency of the structure in the lateral swing direction, _ωy is the natural circular frequency of the structure in the heave swing direction, _ζx is the damping ratio of the structure in the lateral swing direction, and _ζy is the damping ratio of the structure in the heave swing direction. 6. The numerical prediction method for the dynamic response of a suspended tunnel body under wave-current combined excitation according to claim 5 is characterized in that F _x (t) and F _y (t) in the vibration control equation of the suspended tunnel body are obtained by integrating the surface pressure and viscous stress of the suspended tunnel body based on Ansys Fluent software.