Spatial configuration bidirectional fluid-solid coupling analysis method for deep-sea mining hose

Abstract

According to the spatial configuration bidirectional fluid-solid coupling analysis method for the deep-sea mining hose, an internal flow coupling equation is constructed based on internal fluid parameters and hose physical property parameters, an external flow coupling equation is constructed based on external fluid parameters and hose physical property parameters, boundary conditions are obtained based on near-wall fluid parameters and hose physical property parameters, and the deep-sea mining hose is obtained. Coupling the external flow coupling equation and the internal flow coupling equation through boundary conditions to construct a bidirectional coupling dynamic equation set; an undamped free vibration equation and a hose balance equation are constructed based on hose physical property parameters, the undamped free vibration equation and the hose balance equation are combined, and an additional fluid mass matrix is introduced to establish a wet modal analysis model; and high-precision simulation and efficient optimization of the deep-sea mining hose spatial configuration are realized.

Description

Technical Field

[0001] The invention relates to the field of deep sea mining, and in particular to a bidirectional fluid-solid coupling analysis method for the spatial configuration of a deep sea mining hose. Background Art

[0002] The deep-sea mining hose is a key transportation channel connecting the surface mining ship and the seabed mining machine. Its spatial configuration is significantly affected by the coupling of complex fluid loads (inflowing slurry, outflowing ocean currents) and structural dynamics. The hose configuration directly affects the hose transportation efficiency and service life. The hose is affected by the seabed ocean currents when transporting slurry, causing displacement of the hose during transportation, affecting the stability of the hose during operation.

[0003] The existing technology has the following limitations in designing the spatial configuration of deep-sea mining hoses: 1. Insufficient one-way coupling analysis: Traditional methods mostly use one-way fluid-solid coupling (only considering the one-way effect of the fluid on the structure), ignoring the feedback effect of hose deformation on the fluid field, resulting in large deviations in the prediction of dynamic responses such as internal flow pressure fluctuations and external flow vortex-induced vibrations. For example, the interaction between the transient impact force in the pipe and the vibration of the pipe wall during slurry transportation is not fully modeled, which can easily cause hose fatigue fracture.

[0004] 2. Modal analysis is divorced from actual working conditions: Existing wet modal analysis often simplifies the fluid into additional mass, without considering the coupling effect of the internal flow velocity gradient and the external flow viscosity effect, resulting in errors in the calculation of natural frequency and vibration mode (such as ignoring the risk of hose configuration instability caused by ocean currents).

[0005] 3. Over-simplification of boundary conditions: The hose-fluid interface conditions (such as velocity continuity and stress balance) are mostly based on empirical assumptions, lacking strict coupling between the NS equations and the solid mechanics equations, making it difficult to capture the boundary layer effects in deep-sea high-pressure environments.

[0006] 4. Configuration optimization lacks quantitative basis: The selection of single-arch / double-arch configurations relies on engineering experience, and lacks joint evaluation methods of bidirectional coupled dynamics and wet modes, making it difficult to balance transportation efficiency and structural reliability.

[0007] The above-mentioned problems all lead to the fact that the existing analysis methods for deep-sea mining hoses are not comprehensive enough. Summary of the invention

[0008] The purpose of the present invention is to provide a bidirectional fluid-solid coupling analysis method for the spatial configuration of a deep-sea mining hose, which realizes high-precision simulation and efficient optimization of the spatial configuration of a deep-sea mining hose through collaborative modeling of bidirectional fluid-solid coupling dynamics and wet modal analysis.

[0009] To achieve the above objectives, the present technical solution provides a bidirectional fluid-solid coupling analysis method for the spatial configuration of a deep-sea mining hose, comprising the following steps: S1: Construct the internal flow coupling equation based on the internal fluid parameters and the physical properties of the hose, construct the external flow coupling equation based on the external fluid parameters and the physical properties of the hose, obtain the boundary conditions based on the near-wall fluid parameters and the physical properties of the hose, and couple the external flow coupling equation and the internal flow coupling equation through the boundary conditions to construct a two-way coupled dynamic equation group; S2: Based on the physical properties of the hose, the undamped free vibration equation and the hose equilibrium equation are constructed. The undamped free vibration equation and the hose equilibrium equation are combined and the additional fluid mass matrix is ​​introduced to establish a wet modal analysis model. S3: Adjust the hose physical parameters of the deep-sea mining hose input into the two-way coupled dynamic equations and the wet modal analysis model, and analyze the spatial configuration of the deep-sea mining hose based on the wet modal index output by the wet modal analysis model and the dynamic index output by the two-way coupled dynamic equations.

[0010] Compared with the prior art, this technical solution has the following characteristics and beneficial effects: 1. Comprehensive coupling analysis capability: By establishing a bidirectional fluid-solid coupling dynamics equation set, this solution realizes the simultaneous analysis of the internal flow (slurry transportation) and external flow (ocean current load) of the deep-sea mining hose. This coupling analysis method can more accurately reflect the interaction between fluid and structure in actual working conditions, overcoming the limitations of traditional one-way coupling analysis.

[0011] 2. Accurate boundary condition processing: This solution innovatively establishes boundary conditions including velocity continuity, stress balance and other physical quantities, ensuring the accuracy of physical quantity transfer at the interface between fluid and structure. This processing method significantly improves the reliability of the calculation results.

[0012] 3. Efficient wet modal analysis: By introducing an additional fluid mass matrix, the wet modal analysis method of this scheme can quickly evaluate the impact of different hose physical parameters on the vibration characteristics. This method incorporates the fluid inertia effect into the modal calculation and provides an effective tool for structural optimization.

[0013] 4. Multi-physics field collaborative simulation: This solution realizes the collaborative simulation of fluid dynamics and structural dynamics, and can simultaneously consider the multi-physics field coupling effects such as internal flow pressure fluctuations, external flow vortex-induced vibrations, and pipe wall deformation, providing a complete solution for hose performance evaluation under complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flow chart of a bidirectional fluid-solid coupling analysis method for the spatial configuration of a deep-sea mining hose provided in this scheme. DETAILED DESCRIPTION

[0015] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field belong to the scope of protection of the present invention.

[0016] Those skilled in the art should understand that, in the disclosure of the present invention, the terms "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the drawings, which are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the above terms should not be understood as limiting the present invention.

[0017] Embodiment 1 like Figure 1 As shown, this scheme provides a bidirectional fluid-solid coupling analysis method for the spatial configuration of a deep-sea mining hose, including the following steps: S1: Construct the internal flow coupling equation based on the internal fluid parameters and the physical properties of the hose, construct the external flow coupling equation based on the external fluid parameters and the physical properties of the hose, obtain the boundary conditions based on the near-wall fluid parameters and the physical properties of the hose, and couple the external flow coupling equation and the internal flow coupling equation through the boundary conditions to construct a two-way coupled dynamic equation group; S2: Based on the physical properties of the hose, the undamped free vibration equation and the hose equilibrium equation are constructed. The undamped free vibration equation and the hose equilibrium equation are combined and the additional fluid mass matrix is ​​introduced to establish a wet modal analysis model. S3: Adjust the hose physical parameters of the deep-sea mining hose input into the two-way coupled dynamic equations and the wet modal analysis model, and analyze the spatial configuration of the deep-sea mining hose based on the wet modal index output by the wet modal analysis model and the dynamic index output by the two-way coupled dynamic equations.

[0018] The bidirectional fluid-solid coupling analysis method for the spatial configuration of deep-sea mining hoses provided in this solution combines bidirectional fluid-solid coupling dynamic modeling and wet modal analysis to achieve the analysis and optimization adjustment of the deep-sea mining hose configuration. When constructing the bidirectional coupling dynamic equation group, the bidirectional fluid-solid coupling analysis method for the spatial configuration of deep-sea mining hoses simultaneously considers the interaction between internal flow (slurry transportation) and external flow (ocean current load), forces the physical quantity to be continuous through boundary conditions, and accurately obtains the dynamic indicators of the hose under the action of the composite fluid; and when constructing the wet modal analysis model, an additional fluid mass matrix is ​​introduced, and the fluid inertia effect is included in the modal calculation, and the influence of different hose physical parameters on the vibration characteristics is quickly evaluated. The bidirectional fluid-solid coupling analysis method for the spatial configuration of deep-sea mining hoses can be used to comprehensively, efficiently and accurately analyze whether the spatial configuration of deep-sea mining hoses meets the actual design requirements, and provide a quantitative decision-making basis for the design of deep-sea mining hoses.

[0019] In step S1, this scheme analyzes the force of the deep-sea mining hose in the deep sea, combines the fluid mass conservation equation and momentum conservation equation, and the solid stress equilibrium equation and displacement equation, and solves the displacement and stress of the hose for the fluid inside and outside the hose respectively, and establishes a two-way coupled dynamic equation group by simultaneous equations.

[0020] About the construction of internal flow coupling equation: The deep-sea mining hose satisfies the laws of conservation of momentum and mass under the action of internal flow, and satisfies the friction coupling equation and Poisson coupling equation during fluid movement. Subsequently, based on the internal flow coupling equation, the internal flow force can be obtained by analyzing the physical properties of the fluid in the deep-sea mining hose and parameters such as the moment of inertia and angle of the pipeline.

[0021] Specifically, in the step of "constructing internal flow coupling equations based on internal fluid parameters and hose physical properties", the internal fluid parameters refer to the slurry properties, and the hose physical properties refer to the structural characteristics of the deep-sea mining hose. The internal flow coupling equations of this scheme include momentum conservation equations, mass conservation equations, pipeline axial stress equations, and geometric physics equations.

[0022] In the embodiment of the present solution, the internal fluid parameters include the internal flow density r f , internal flow velocity V , internal flow viscosity m、 The velocity caused by the internal flow impact pressure C f , average fluid pressure P And the fluid drop height h .

[0023] The indicators of internal fluid parameters are summarized as shown in Table 1 below: Table 1 Internal fluid parameter index table

[0024] In the embodiment of this scheme, the physical parameters of the hose include elastic modulus E , Poisson's ratio n , Material density r t , hose inner diameter D , hose wall thickness δ, hose wall cross-sectional area A t And the moment of inertia I t .

[0025] The indicators of the physical parameters of the hose are summarized as shown in Table 2 below: Table 2 Hose physical property parameter index table .

[0026] The internal flow coupling equation is constructed based on the internal fluid parameters and the physical parameters of the hose as follows: ; Wherein, equation (1) is the momentum conservation equation, equation (2) is the mass conservation equation, equation (3) is the pipeline axial stress equation, and equation (4) is the geometric physics equation.

[0027] Formula (1) describes the transient momentum conservation of the fluid in the tube. V represents the internal flow velocity, t Indicates time, h represents the fluid drop height, f represents the Darcy friction factor, g represents the acceleration due to gravity, z represents the axial coordinate of the pipeline, V r It represents the velocity of the hose wall along the pipe axis. D Indicates the inner diameter of the hose. It should be noted that the velocity of the hose wall along the pipe axis is V r It is calculated according to formula (1), the velocity of the hose wall along the pipeline axis is V r It will affect the internal flow friction loss and dynamic displacement of the hose.

[0028] Formula (2) describes the coupling relationship between the transient motion of the fluid in the tube and the dynamic response of the hose. V represents the internal flow velocity, t Indicates time, g represents the acceleration due to gravity, H It represents the fluid pressure head, which can be calculated by the average fluid pressure P; C fIndicates the velocity caused by the impact pressure of the flow in the hose, E represents the elastic modulus of the hose, v represents the Poisson's ratio of the hose, s z Indicates the axial stress of the hose.

[0029] Formula (3) describes the dynamic equilibrium equation of the hose axial motion. r t Indicates the material density of the hose; r f Indicates the flow density in the hose; A t represents the cross-sectional area of ​​the hose wall, Represents the displacement of the hose along the pipeline axis. t Indicates time, E represents the elastic modulus of the hose, D Indicates the inner diameter of the hose. v represents the Poisson's ratio of the hose, z represents the axial coordinate of the pipeline, P represents the average pressure of the fluid, A f Indicates the cross-sectional area of ​​water flow, which is obtained by the inner diameter of the hose. V r It represents the velocity of the hose wall along the pipe axis. g represents the gravity parameter, c Indicates the pipe inclination angle, f is the Darcy friction factor.

[0030] Equation (4) describes the control equation of the lateral vibration of the hose, where E represents the elastic modulus of the hose, I t represents the moment of inertia, z represents the axial coordinate of the pipeline, r t Indicates the material density of the hose, A t represents the cross-sectional area of ​​the hose wall, r f represents the flow density in the hose, A f represents the cross-sectional area of ​​water flow, It represents the lateral displacement of the hose in the direction perpendicular to the pipeline axis. t Indicates time.

[0031] This scheme uses the internal flow coupling equation to obtain the lateral displacement of the hose in the direction perpendicular to the pipeline axis. and the axial displacement of the hose along the pipe axis As the displacement of the hose under the action of the internal fluid, the axial stress of the hose is calculated by formula (2), that is, the momentum conservation equation (Formula 1) and the mass conservation equation (Formula 2) in the internal flow coupling of this scheme describe the fluid movement, and the pipeline axial stress equation (Formula 3) and the geometric physics equation (Formula 4) describe the deformation of the hose. Then, the internal flow coupling equation can be used to solve the displacement and axial stress of the hose under the action of the internal flow as a dynamic indicator.

[0032] Correspondingly, in the step of "Analysis of spatial configuration of deep-sea mining hose based on dynamic indicators output by bidirectional coupled dynamic equations", the internal flow coupling equation outputs dynamic indicators including displacement, stress and pressure loss of the hose, including the axial displacement of the hose along the pipeline axis. , axial speed , axial acceleration and axial stress , where the axial displacement is the deformation of the hose along the axis, which can be used to reflect the amount of stretching or compression; the axial velocity is the vibration velocity of the hose, which can be used to evaluate the dynamic response; and the axial acceleration is the peak acceleration of the hose when it is subjected to transient impact or vibration.

[0033] About the construction of external flow coupling equation: The fluid motion equations under the action of external flow include the NS equation and the continuity equation. The deep-sea mining hose satisfies the equilibrium equation, so the external flow coupling equation can be constructed by coupling the interface between the outer wall of the hose and the external fluid through the combined force of the external fluid pressure and the external load on the hose.

[0034] Specifically, in the step of "constructing external flow coupling equations based on external fluid parameters and hose physical properties", external fluid parameters refer to the physical properties of the marine environment fluid outside the hose and its dynamic variables affecting the deep-sea mining hose, and hose physical properties refer to the structural characteristics of the deep-sea mining hose. The external flow coupling equations of this scheme include NS equations, continuity equations and dynamic equilibrium equations, among which the NS equations are a group of partial differential equations describing the conservation of momentum of viscous fluids, and the continuity equations are the data expression of the law of conservation of mass.

[0035] In an embodiment of the present invention, the external fluid parameters include the fluid density of the external fluid r w , fluid dynamic viscosity m , average fluid pressure P and the external fluid velocity vector u l In the embodiment of the present solution, the physical property parameters of the hose include a stiffness matrix, a damping matrix and a mass matrix.

[0036] Specifically, the stiffness matrix K in the hose physical parameters is constructed by the material elastic modulus E, hose inner diameter D and wall thickness δ of the deep-sea mining hose based on the Euler-Bernoulli beam theory or the Timoshenko beam theory; the mass matrix M is constructed by the material density r t and the cross-sectional area of ​​the hose wall A t Calculated; the damping matrix C is calculated by the mass matrix M and the stiffness matrix K, and the Rayleigh damping model can be used, C=αM+βK, where α and β are proportional coefficients.

[0037] The external flow coupling equation is obtained based on the external fluid parameters and the hose physical parameters as follows: ; Equation (5) is the NS equation, which is used to describe the conservation of momentum of the external fluid. u l represents the external fluid velocity vector, t Indicates time, ▽ represents the Hamilton operator, r represents the fluid density, f l Represents the volume force per unit mass ,m represents the fluid dynamic viscosity, p l is the fluid pressure, is the Laplace operator.

[0038] Equation (6) is the continuity equation, which is used to describe the mass conservation of the external fluid. u l represents the external fluid velocity vector, ▽ Represents the Hamilton operator.

[0039] Formula (7) is the hose equilibrium equation, which is used to describe the motion law of the hose under the action of external load. F represents the resultant force of the external load on the hose, including the resistance of the external fluid, the buoyancy of the external fluid and the gravity of the hose. M represents the mass matrix of the hose, C represents the damping matrix of the hose, K represents the stiffness matrix of the hose, u g Refers to the hose displacement, ü g Indicates the hose acceleration, Indicates hose speed.

[0040] In the external flow coupling equation of this scheme, the NS equation (Equation 5) and the continuity equation (Equation 6) are used to describe the external flow movement, and the dynamic equilibrium equation (Equation 7) is used to describe the dynamic response of the hose. Then, the displacement and stress of the hose under the action of the external flow can be solved based on the external flow coupling equation.

[0041] Correspondingly, in the step of "analyzing the spatial configuration of the deep-sea mining hose based on the dynamic indicators output by the two-way coupled dynamic equations", the external flow coupling equation can output the motion state of the hose and the resultant force of the external load as dynamic indicators, where the motion state of the hose includes hose displacement, hose acceleration and hose velocity, where the hose displacement can represent the three-dimensional displacement response of the hose node, the hose velocity can reflect the vibration velocity of the hose, and the hose acceleration represents the rate of change of the vibration velocity.

[0042] After obtaining the motion state of the hose, this scheme can further evaluate the hose restoring force, resistance and inertial force of the hose, where the hose restoring force is the value of the hose displacement and the stiffness matrix multiplied, the damping force is the value of the hose velocity and the resistance matrix multiplied, and the inertial force is the value of the maximum hose acceleration and the mass matrix multiplied. When the deep-sea mining hose is transporting slurry, the internal fluid pressure and the external fluid impact interact with the pipe wall deformation to form a strongly coupled system, and the velocity gradient, pressure distribution and shear stress at the junction of the fluid and the pipe wall directly affect the vibration and fatigue life of the hose. The precise establishment of boundary conditions is the core to ensure the reliability of the bidirectional coupling calculation between fluid and structure. Therefore, this scheme also needs to combine the boundary conditions to construct a bidirectional coupling dynamic equation group.

[0043] "Obtain boundary conditions based on near-wall fluid parameters and hose physical properties", boundary conditions include average fluid velocity, average fluid pressure, hose axial velocity and axial stress, where the average fluid velocity indicates that the velocity of the fluid and the hose at the interface is continuous, the average fluid pressure represents the balance between the fluid pressure and the hose stress, the axial velocity of the hose represents the coordination between the hose movement speed and the fluid velocity; the axial stress represents the axial stress of the hose and the transmission of fluid pressure.

[0044] About obtaining the average fluid velocity: The fluid motion equation is constructed based on the continuity equation of fluid flow, and the average fluid velocity is calculated by assuming that the state equation is introduced. The calculation formula is as follows:

[0045] ; Equation (8) is the continuity equation for fluid flow, which describes the mass conservation of the fluid (slurry) in the pipe and is suitable for transient analysis considering radial flow (such as radial motion of the fluid caused by hose vibration). r f represents the internal flow density of the hose,v f It represents the axial velocity of the fluid; v r represents the radial velocity of the fluid; r Indicates the diameter coordinate of the hose; z Indicates the axis direction coordinate of the hose; t Indicates time; r f represents the internal flow density; V f represents the average fluid velocity, P Indicates the average pressure of the fluid.

[0046] About obtaining the average pressure of the fluid: Specifically, the average pressure of the fluid is obtained according to the NS equation and the pipeline axial balance equation. The calculation formula is as follows: ; Equation (10) is a simplified dynamic equation for the axial motion of the hose, which describes the equilibrium relationship between the axial velocity change (acceleration) of the hose and the axial stress gradient. represents the axial movement speed of the hose, t represents time, σ z represents the axial stress of the hose, z represents the axis direction coordinate of the hose, r t Indicates the material density of the hose.

[0047] About obtaining the axial velocity of the hose: Specifically, the stress-displacement relationship of the hose is obtained according to the generalized Hook's law and the axial velocity of the hose is obtained. The calculation formula is as follows: ; ; in Indicates the axial movement speed of the hose. z Represents the axis direction coordinate of the hose, σ z represents the axial stress of the hose, z represents the axis direction coordinate of the hose, E represents the elastic modulus, d is the wall thickness of the hose, u r Indicates the axial velocity of the hose; v represents the Poisson's ratio of the hose, R represents the pipe radius, P represents the average pressure of the fluid, t Indicates time.

[0048] Regarding the acquisition of formula (12), firstly, the stress-displacement relationship of the hose is obtained according to the generalized Hook's law. The formula of the stress-displacement relationship is shown in formula (11): ; Then, we take the derivative of both sides of formula (11) with respect to time t, and regard the inner and outer walls of the tube as having constant velocity, and simplify to obtain formula (12): ; Then, by differentiating both sides of formula (12) with respect to time t and substituting the pipeline radial equilibrium equation and pipeline annular physical equation into the axial geometric physical equation, formula (13) is obtained.

[0049] About obtaining axial stress: Specifically, according to the continuity equation of fluid flow and ignoring the influence of Coriolis acceleration, assuming that the hose is placed horizontally, the state equation is introduced, and the fluid continuity equation is obtained after sorting and integration. The axial stress is solved after introducing boundary conditions: ;

[0050] In formula (14) and formula (15), K f represents the bulk modulus of the fluid, v f represents the axial velocity of the fluid, t Indicates time, R represents the pipe radius, v r represents the radial velocity of the fluid, r represents the diameter coordinate of the hose, represents the fluid density, E represents the elastic modulus, P represents the average pressure of the fluid; σ z represents the axial stress of the hose, z represents the axis direction coordinate of the hose, d is the thickness of the hose, t Indicates time, Represents the Poisson's ratio of the hose.

[0051] Specifically, formula (10) is solved together with formula (9), formula (13) and formula (15) to obtain the average pressure of the fluid: P , the average fluid velocity V f , hose axial stress s z and hose axial speed .

[0052] In the step of "coupling the external flow coupling equation and the internal flow coupling equation through boundary conditions to construct a two-way coupled dynamic equation group", the external flow coupling equation and the internal flow coupling equation are coupled through boundary conditions to form a closed two-way coupled dynamic equation group.

[0053] Specifically, taking the axial stress as the boundary condition as an example, at this time, the axial stress of the hose and the fluid pressure are transmitted, and the axial stress of the hose output in the internal flow coupling equation is the same as the fluid pressure of the external flow coupling equation at the interface; taking the average fluid velocity as the boundary condition as an example, at this time, it means that the velocity of the fluid and the hose at the interface is continuous, and the average fluid velocity output by the internal flow coupling equation is the same as the axial velocity of the hose in the external flow coupling equation; when the boundary condition is the average fluid pressure, at this time, the fluid pressure at the interface is coordinated with the deformation of the hose, and the axial stress of the hose output in the internal flow coupling equation and the fluid pressure output in the external flow coupling return satisfy the stress balance; when the boundary condition is the axial velocity of the hose, at this time, the movement speed of the hose is synchronized with the fluid velocity field, and the axial stress of the hose output by the internal flow coupling equation and the fluid pressure output by the external flow coupling equation satisfy the stress balance condition.

[0054] In step S2, this scheme adopts the wet modal method to calculate and take into account the fluid around the structural system that has an impact on the natural mode. By analyzing the undamped free vibration equation of the fluid-solid system and the hose balance equation, the effect of the additional fluid mass is considered in the fluid-solid coupling, and finally the natural frequency and wet mode under coupling are obtained. According to the matrix equations of each unit obtained, the system composed of the pipe unit can be calculated. The transfer matrix of each unit is connected in series to form the product, and the transfer relationship between the inlet and outlet of the whole system is obtained; then the boundary conditions of the end surfaces of the pipeline are obtained, and the natural frequency and vibration mode of the system are obtained. This method can quickly calculate and obtain the results.

[0055] Specifically, in the step of "constructing an undamped free vibration equation based on the physical properties of the hose", the undamped free vibration equation is expressed as follows: ; in H is the fluid inertia matrix, p is the average fluid pressure, f is the fluid density, B is the coupling matrix, is the acceleration of the hose, is the speed of the hose, u is the structural displacement vector, M is the mass matrix, K is the stiffness matrix.

[0056] It should be noted that when constructing the undamped free vibration equation, this scheme takes into account that the fluid is an incompressible fluid, so the influence of the fluid free surface and the excitation vector are not considered.

[0057] In the step of "Simultaneously establish the undamped free vibration equation and the hose equilibrium equation and introduce the additional fluid mass matrix to establish the wet modal analysis model", the wet modal analysis model is expressed as follows: ; ; ; ; in f is the wet mode; r is the displacement matrix of each node on the fluid-structure interaction surface, r O is the dry node displacement matrix; r I is the displacement matrix of the wet nodes (not in contact with the fluid); q is a generalized coordinate vector.

[0058] Regarding the acquisition of the wet modal analysis model, the undamped free vibration equation and the hose equilibrium equation are combined and the additional fluid mass matrix is ​​introduced to obtain formula (18) as follows: ; in M a is the mass matrix of the additional fluid, M S is the mass matrix, K S is the stiffness matrix, is the acceleration of the hose, is the speed of the hose, u is the structural displacement vector.

[0059] Solving the characteristic equation of formula (18) yields formula (19) as follows: ; In the formula l n is the natural frequency of fluid-structure interaction, let , and then substituted into formula (18) to diagonalize and obtain the wet modal analysis model.

[0060] The wet modal analysis model of this scheme introduces the influence of fluid medium into the vibration analysis. By taking into account the influence of internal and external flows on the natural frequency and vibration mode of the structure, the model can accurately calculate the dynamic response of the hose under actual working conditions.

[0061] Correspondingly, in the step of "analyzing the spatial configuration of the deep-sea mining hose based on the wet modal index output by the wet modal analysis model", the wet modal index includes the wet modal frequency and the wet modal vibration shape.

[0062] In step S3, the hose physical property parameters of the deep-sea mining hose to be analyzed are respectively input into the two-way coupling dynamic equation group and the wet modal analysis model to perform fluid-solid coupling dynamic analysis and hose wet modal method analysis respectively, and the fluid effect of the deep-sea mining hose to be analyzed is judged based on the wet modal index output by the wet modal analysis model and the dynamic index output by the two-way coupling dynamic equation group.

[0063] Specifically, the wet modal method can be used to obtain the influence of internal flow density, internal flow viscosity, hose elastic modulus, hose diameter, etc. on the hose mode through finite element analysis, providing a basis for optimizing pipeline design. The dynamic analysis method using two-way fluid-solid coupling can obtain the stress condition and motion state of the hose during operation. According to the results obtained, the hose operation motion state can be actively adjusted to achieve more efficient hose operation acquisition conditions.

[0064] Further, in the step of “S3: adjusting the hose physical properties of the deep-sea mining hose input into the two-way coupled dynamic equations and the wet modal analysis model”, the hose physical properties that need to be adjusted include hose length, hose elastic modulus, hose inner and outer diameters, hose density, and outflow fluid depth, outflow fluid dynamic viscosity, and outflow fluid density.

[0065] Embodiment 2 In this scheme, the spatial configuration bidirectional fluid-solid coupling analysis method of the deep-sea mining hose is applied to analyze the deep-sea mining hoses with single arch configuration and double arch configuration. The wet modal index output by the wet modal analysis model is used to analyze the influence of different hose physical properties on the vibration frequency and vibration mode characteristics of the two different configurations of deep-sea mining hoses when coupled with internal and external flows. The results show that the first six wet modal frequencies of the deep-sea mining hose with double arch configuration are smaller than those of the deep-sea mining hose with single arch configuration. The elastic modulus and diameter of the hose have a greater influence on the natural frequency of the hose. According to the results obtained, the hose vibration problem can be further optimized.

[0066] In addition, this scheme further calculates the stress of deep-sea mining hoses of different configurations at different internal and external flow velocities based on the two-way coupled dynamic equations, and analyzes the coupling effect of single-arch and double-arch hoses by changing the internal and external flow velocities. It is found that the internal flow velocity of the single-arch configuration has a more gentle change trend. Under the condition of similar internal flow velocity, the displacement in each direction, total displacement, stress and strain values ​​of the single-arch configuration are all smaller than those of the double-arch configuration. According to the results obtained, the hose can be adjusted according to different situations during operation.

[0067] Those skilled in the art should understand that the technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0068] The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A bidirectional fluid-solid coupling analysis method for the spatial configuration of a deep-sea mining hose, characterized in that: The following steps are involved: S1: Construct the internal flow coupling equation based on the internal fluid parameters and the physical properties of the hose, construct the external flow coupling equation based on the external fluid parameters and the physical properties of the hose, obtain the boundary conditions based on the near-wall fluid parameters and the physical properties of the hose, and couple the external flow coupling equation and the internal flow coupling equation through the boundary conditions to construct a two-way coupled dynamic equation group; S2: Based on the physical properties of the hose, the undamped free vibration equation and the hose equilibrium equation are constructed. The undamped free vibration equation and the hose equilibrium equation are combined and the additional fluid mass matrix is ​​introduced to establish a wet modal analysis model. S3: Adjust the hose physical parameters of the deep-sea mining hose input into the two-way coupled dynamic equations and the wet modal analysis model, and analyze the spatial configuration of the deep-sea mining hose based on the wet modal index output by the wet modal analysis model and the dynamic index output by the two-way coupled dynamic equations.

2. The spatial configuration bidirectional fluid-solid coupling analysis method of a deep-sea mining hose according to claim 1 is characterized in that: The internal fluid parameters refer to the slurry characteristics, the hose physical parameters refer to the structural characteristics of the deep-sea mining hose, and the internal flow coupling equations include the momentum conservation equation, the mass conservation equation, the pipeline axial stress equation, and the geometric physics equation.

3. The spatial configuration bidirectional fluid-solid coupling analysis method of a deep-sea mining hose according to claim 2 is characterized in that: The internal flow coupling equation is as follows: ; Wherein, equation (1) is the momentum conservation equation, equation (2) is the mass conservation equation, equation (3) is the pipeline axial stress equation, and equation (4) is the geometric physics equation; in V represents the internal flow velocity, t Indicates time, h represents the fluid drop height, f represents the Darcy friction factor, g represents the acceleration due to gravity, z represents the axial coordinate of the pipeline, V r It represents the velocity of the hose wall along the pipe axis. D Indicates the inner diameter of the hose. H represents the fluid pressure head, C f Indicates the velocity caused by the impact pressure of the flow in the hose, E represents the elastic modulus of the hose, ν represents the Poisson's ratio of the hose, σ z represents the axial stress of the hose, ρ t Indicates the material density of the hose; ρ f Indicates the flow density in the hose; A t represents the cross-sectional area of ​​the hose wall, Represents the displacement of the hose along the pipeline axis. P represents the fluid pressure, A f represents the cross-sectional area of ​​water flow, γ Indicates the pipe inclination angle, I t represents the moment of inertia, ρ f represents the flow density in the hose, A f represents the cross-sectional area of ​​water flow, Indicates the lateral displacement of the hose in the direction perpendicular to the pipeline axis.

4. The spatial configuration bidirectional fluid-solid coupling analysis method of a deep-sea mining hose according to claim 1 is characterized in that: External fluid parameters refer to the physical properties of the marine environment fluid outside the hose and its dynamic variables of its effect on the deep-sea mining hose. Hose physical property parameters refer to the structural characteristics of the deep-sea mining hose. The external flow coupling equations include the NS equation, the continuity equation and the dynamic equilibrium equation.

5. The method for bidirectional fluid-solid coupling analysis of the spatial configuration of a deep-sea mining hose according to claim 4, characterized in that: The external flow coupling equation is as follows: ； in t Indicates time, ▽ represents the Hamilton operator, ρ represents the fluid density, f l Represents the volume force per unit mass , μ represents the fluid dynamic viscosity, p l is the fluid pressure, is the Laplace operator, F represents the resultant force of the external load on the hose, including the resistance of the external fluid, the buoyancy of the external fluid and the gravity of the hose. M represents the mass matrix of the hose, C represents the damping matrix of the hose, K represents the stiffness matrix of the hose, u g Refers to the hose displacement, ü g Indicates the hose acceleration, Indicates hose speed.

6. The method for analyzing the spatial configuration of a deep-sea mining hose according to claim 1, characterized in that: The boundary conditions include average fluid velocity, average fluid pressure, hose axial velocity and axial stress, wherein the average fluid velocity indicates that the velocity of the fluid and the hose at the interface is continuous, wherein the fluid average pressure represents the balance between the fluid pressure and the hose stress, and wherein the hose axial velocity represents the coordination between the hose movement velocity and the fluid velocity; The axial stress characterizes the axial stress of the hose and the fluid pressure transmission.

7. The method for analyzing the spatial configuration of a deep-sea mining hose according to claim 6, characterized in that: Taking the boundary condition as axial stress as an example, the axial stress of the hose output in the internal flow coupling equation is the same as the fluid pressure of the external flow coupling equation at the interface; taking the boundary condition as average fluid velocity as an example, the average fluid velocity output by the internal flow coupling equation is the same as the axial velocity of the hose in the external flow coupling equation; When the boundary condition is the average fluid pressure, the axial stress of the hose output in the internal flow coupling equation and the output fluid pressure in the external flow coupling return plant satisfy the stress balance; When the boundary condition is the hose axial velocity, the hose axial velocity output by the internal flow coupling equation should satisfy the stress balance condition with the fluid pressure output by the external flow coupling equation.

8. The method for bidirectional fluid-solid coupling analysis of the spatial configuration of a deep-sea mining hose according to claim 1, characterized in that: The undamped free vibration equation is expressed as follows: ； in H is the fluid inertia matrix, p is the average fluid pressure, f is the fluid density, B is the coupling matrix, is the acceleration of the hose, is the hose speed, u is the structural displacement vector, M is the mass matrix, K is the stiffness matrix.

9. The method for bidirectional fluid-solid coupling analysis of the spatial configuration of a deep-sea mining hose according to claim 1, characterized in that: The wet modal analysis model is expressed as follows: ； ； ； ； in φ It is the wet mode; r is the displacement matrix of each node on the fluid-structure interaction surface, r O is the dry node displacement matrix; r I is the displacement matrix of the wet node; q is a generalized coordinate vector.

10. The method for bidirectional fluid-solid coupling analysis of spatial configuration of deep-sea mining hose according to claim 1, characterized in that: The internal flow coupling equation outputs the dynamic indicators of the hose, including displacement, stress and pressure loss. The external flow coupling equation outputs the motion state of the hose and the resultant force of the external load as dynamic indicators. The wet modal indicators include wet modal frequency, wet modal vibration shape and additional mass matrix.

Images