Deep-sea mining numerical simulation method based on pseudo-fluid model and related equipment

Abstract

The invention discloses a deep-sea mining numerical simulation method based on a pseudo-fluid model and related equipment. The method comprises the following steps: firstly, setting an initial velocity field, an initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline; defining boundary conditions of an inlet and an outlet of the deep-sea mining pipeline; finally, numerical simulation is conducted on the deep-sea mining pipeline through the pseudo-fluid model, a deep-sea mining numerical simulation result is obtained, and the deep-sea mining numerical simulation result comprises pressure distribution, a velocity field, particle concentration distribution, effective density and effective viscosity. In the process, the solid particles are simplified into the pseudo fluid by utilizing the pseudo fluid model, so that the effective density and the effective viscosity are introduced, numerical simulation can be performed on the deep-sea mining pipeline by utilizing the effective density and the effective viscosity, and compared with traditional algorithm calculation, the calculation complexity is simplified, and the numerical simulation efficiency is also improved.

Description

Technical Field

[0001] The present application relates to the field of numerical simulation technology, and in particular to a deep-sea mining numerical simulation method based on a pseudo-fluid model and related equipment. Background Art

[0002] Deep-sea mining is a technology that extracts minerals from the seabed and transports them to the surface. In the technical field of deep-sea mining, numerical simulation of solid-liquid two-phase flow is required to explore suitable flow field schemes for ore collection heads. However, due to the complex conditions of the deep-sea environment, numerical simulation of solid-liquid two-phase flow becomes very complicated.

[0003] Although the methods used in the prior art can provide detailed information on particle movement, they are obviously insufficient in terms of computational efficiency and computing resource consumption due to problems with algorithm calculation. Summary of the invention

[0004] The present application provides a deep-sea mining numerical simulation method and related equipment based on a pseudo-fluid model. The pseudo-fluid model is used to simplify solid particles into pseudo-fluids, thereby avoiding detailed tracking of collisions and movements between particles, reducing the complexity of calculations, and thus improving the efficiency of numerical simulation.

[0005] In a first aspect, the present application provides a deep-sea mining numerical simulation method based on a pseudo-fluid model, the method comprising:

[0006] Set the initial velocity field, initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline;

[0007] Define boundary conditions for the entry and exit of deep-sea mining pipelines;

[0008] A pseudo fluid model is used to perform numerical simulation on a deep-sea mining pipeline to obtain a deep-sea mining numerical simulation result, which includes pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity.

[0009] Optionally, the process of constructing the pseudo fluid model includes:

[0010] The density of solid particles and the density of liquid are weighted averaged according to the particle volume fraction to obtain the effective density;

[0011] Based on the particle volume fraction and the viscosity of the base fluid, the effective viscosity is obtained;

[0012] The Navier-Stokes equation in the pseudo fluid model is determined according to the effective density and the effective viscosity:

[0013]

[0014] Among them, ρeff represents the effective density, u represents the velocity field; It is used to describe the divergence or contraction of the vector field in space; t represents time, that is, represents the rate of change of velocity field over time; p represents pressure field; μ eff represents effective density; g represents gravity; F vib Represents the effect of external vibration force applied in the fluid on the velocity field;

[0015] According to the particle volume fraction, the convection-diffusion equation is constructed, where the convection-diffusion equation is:

[0016]

[0017] in, represents the rate of change of the scalar field φ over time; u represents the velocity field; ▽ represents the divergence operator; D φ represents the diffusion coefficient, which describes the diffusion rate of the scalar field φ; φ represents the scalar field;

[0018] A beam-pipe vibration model is constructed, where the vibration displacement equation of the beam in the beam-pipe vibration model is:

[0019]

[0020] Where, E represents the elastic modulus, I represents the section moment of inertia; EI represents the bending stiffness of the beam; Indicates the variation of beam deflection with beam length; ρ A Indicates line density; represents the second-order derivative of the deflection with time, that is, the acceleration of the beam; F vib (z, t) represents the distributed load along the length of the pipeline; F Cor F stands for Coriolis force; Cen Represents centrifugal force.

[0021] Optionally, a pseudo fluid model is used to perform numerical simulation on the deep-sea mining pipeline to obtain a deep-sea mining numerical simulation result, including:

[0022] Discretize the Navier-Stokes equations, convection-diffusion equations and beam vibration control equations and convert them into discrete equations;

[0023] The discrete equations are solved using a high-precision iterative method to obtain the numerical simulation results of deep-sea mining.

[0024] Optionally, a high-precision iterative method is used to solve the discrete equations to obtain the numerical simulation results of deep-sea mining, including:

[0025] According to the discrete equation, effective density, effective viscosity and velocity field formula, the predicted velocity field is obtained. The velocity field formula is as follows:

[0026]

[0027] Among them, u represents the velocity field; u n represents the value of the velocity field in the previous time step; Δt represents the time step; represents the convection term of the velocity field; ρ eff represents the effective density; represents the pressure gradient term; μ eff It represents the effective viscosity; represents the viscous force term; F vib Represents the effect of external vibration force applied in the fluid on the velocity field;

[0028] Substituting the predicted velocity field into the continuity equation, we get the pressure correction equation, which is as follows:

[0029] A p p′=b

[0030] Among them, A p is the pressure correction coefficient matrix; p′ represents the pressure correction value; b is the source term vector;

[0031] Update the velocity field, pressure field and beam vibration displacement according to the pressure correction equation;

[0032] Update the effective density and effective viscosity according to the updated velocity field and particle concentration distribution at different time steps;

[0033] The above operations from obtaining the predicted velocity field to updating the effective density and effective viscosity are executed cyclically until the changes in the velocity field and the pressure field meet the convergence criterion, and the deep-sea mining numerical simulation results are obtained.

[0034] Optionally, update the effective density and effective viscosity based on the updated velocity field and the particle concentration distribution at different time steps, including:

[0035] The density and viscosity of the solid-liquid mixture are measured by an experimental device to determine the standard effective density and standard effective viscosity;

[0036] Compare the standard effective density and standard effective viscosity with the effective density and effective viscosity respectively, and calculate the error;

[0037] If the error is greater than a preset value, an operation of updating the effective density and the effective viscosity is performed according to the updated velocity field and the particle concentration distribution at different time steps.

[0038] Optionally, define boundary conditions for the inlet and outlet of the deep-sea mining pipeline, including:

[0039] Define fixed flow rates and particle concentrations at the inlet of a deep-sea mining pipeline;

[0040] Define a fixed pressure at the outlet of a deep sea mining pipeline.

[0041] In a second aspect, the present application provides a deep-sea mining numerical simulation device based on a pseudo-fluid model, the device comprising:

[0042] A setting unit is used to set the initial velocity field, initial pressure field and initial particle concentration distribution in the pipeline;

[0043] Define units to define the boundary conditions of the pipeline inlet and outlet;

[0044] The numerical simulation unit is used to perform numerical simulation on the deep-sea mining pipeline using a pseudo-fluid model to obtain the deep-sea mining numerical simulation results, wherein the deep-sea mining numerical simulation results include pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity.

[0045] Optionally, the device further comprises:

[0046] An obtaining unit is used to perform weighted average of the density of solid particles and the density of liquid according to the particle volume fraction to obtain an effective density;

[0047] The obtaining unit is also used to obtain the effective viscosity according to the particle volume fraction and the viscosity of the base fluid;

[0048] Determine the unit used to determine the effective density and effective viscosity in the Navier-Stokes equations in the pseudo-fluid model as:

[0049]

[0050] Among them, ρ eff represents the effective density, u represents the velocity field; It is used to describe the divergence or contraction of the vector field in space; t represents time, that is, represents the rate of change of velocity field over time; p represents pressure field; μ eff represents effective density; g represents gravity; F vib Represents the effect of external vibration force applied in the fluid on the velocity field;

[0051] The building unit is used to construct the convection-diffusion equation according to the particle volume fraction, where the convection-diffusion equation is:

[0052]

[0053] in, represents the rate of change of the scalar field φ over time; u represents the velocity field; ▽ represents the divergence operator; D φ represents the diffusion coefficient, which describes the diffusion rate of the scalar field φ; φ represents the scalar field;

[0054] The construction unit is also used to construct a pipeline vibration model of the beam, wherein the vibration displacement equation of the beam in the pipeline vibration model of the beam is:

[0055]

[0056] Where, E represents the elastic modulus, I represents the section moment of inertia; EI represents the bending stiffness of the beam; Indicates the variation of beam deflection with beam length; ρ A Indicates line density; represents the second-order derivative of the deflection with time, that is, the acceleration of the beam; F vib (z, t) represents the distributed load along the length of the pipeline; F Cor F stands for Coriolis force; Cen Represents centrifugal force.

[0057] Optionally, the numerical simulation unit specifically includes:

[0058] A conversion subunit is used to discretize the Navier-Stokes equation, the convection-diffusion equation and the vibration control equation of the beam and convert them into discrete equations;

[0059] The solving subunit is used to solve the discrete equations using a high-precision iterative method to obtain the numerical simulation results of deep-sea mining.

[0060] Optionally, the solving subunit is specifically used for:

[0061] According to the discrete equation, effective density, effective viscosity and velocity field formula, the predicted velocity field is obtained, and the velocity field formula is as follows:

[0062]

[0063] Among them, u represents the velocity field; u n represents the value of the velocity field in the previous time step; Δt represents the time step; represents the convection term of the velocity field; ρ eff represents the effective density; represents the pressure gradient term; μ eff It represents the effective viscosity; represents the viscous force term; F vib Represents the effect of external vibration force applied in the fluid on the velocity field;

[0064] Substituting the predicted velocity field into the continuity equation, the pressure correction equation is obtained, which is as follows:

[0065] A p p′=b

[0066] Among them, A p is the pressure correction coefficient matrix; p′ represents the pressure correction value; b is the source term vector;

[0067] Update the velocity field, pressure field and beam vibration displacement according to the pressure correction equation;

[0068] Update the effective density and effective viscosity according to the updated velocity field and particle concentration distribution at different time steps;

[0069] The above operations from obtaining the predicted velocity field to updating the effective density and effective viscosity are executed cyclically until the changes in the velocity field and the pressure field meet the convergence criterion, and the deep-sea mining numerical simulation results are obtained.

[0070] Optionally, the solver subunit is used to update the effective density and effective viscosity based on the updated velocity field and the particle concentration distribution at different time steps, specifically for:

[0071] The density and viscosity of the solid-liquid mixture are measured by an experimental device to determine the standard effective density and standard effective viscosity;

[0072] Compare the standard effective density and standard effective viscosity with the effective density and effective viscosity respectively, and calculate the error;

[0073] If the error is greater than a preset value, the effective density and effective viscosity are updated according to the updated velocity field and the particle concentration distribution at different time steps.

[0074] Optionally, the definition unit is specifically used to:

[0075] Define fixed flow rates and particle concentrations at the inlet of a deep-sea mining pipeline;

[0076] Define a fixed pressure at the outlet of a deep sea mining pipeline.

[0077] In a third aspect, the present application provides an electronic device, the electronic device comprising a memory and a processor:

[0078] The memory is used to store computer programs;

[0079] The processor is used to execute the method provided by the first aspect according to the computer program.

[0080] In a fourth aspect, the present application further provides a computer-readable storage medium, which is used to store a computer program, and the computer program is used to execute the method provided in the first aspect above.

[0081] It can be seen that this application has the following beneficial effects:

[0082] The present application provides a method for numerical simulation of deep-sea mining based on a pseudo-fluid model. First, the initial velocity field, initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline are set; then the boundary conditions of the inlet and outlet of the deep-sea mining pipeline are defined; finally, the deep-sea mining pipeline is numerically simulated using the pseudo-fluid model to obtain the numerical simulation results of deep-sea mining, which include pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity. In this process, the solid particles are simplified into pseudo-fluids using the pseudo-fluid model, thereby introducing effective density and effective viscosity. The deep-sea mining pipeline can be numerically simulated using the effective density and effective viscosity. Compared with the traditional algorithm calculation, it not only simplifies the calculation complexity, but also improves the efficiency of numerical simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present application. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0084] Figure 1 A schematic flow chart of an embodiment of a method for numerical simulation of deep-sea mining based on a pseudo-fluid model provided in an embodiment of the present application;

[0085] Figure 2 A schematic flow chart of another embodiment of a deep-sea mining numerical simulation method based on a pseudo-fluid model provided in an embodiment of the present application;

[0086] Figure 3 A schematic diagram of a pseudo fluid model provided in an embodiment of the present application;

[0087] Figure 4 A schematic diagram of a pipeline vibration model provided in an embodiment of the present application;

[0088] Figure 5 A schematic structural diagram of a deep-sea mining numerical simulation device based on a pseudo-fluid model provided in an embodiment of the present application;

[0089] Figure 6 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0090] The following will be combined with the 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 without creative work are within the scope of protection of the present invention.

[0091] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant laws, regulations and standards of relevant countries and regions.

[0092] At present, due to the complex conditions of high pressure, low temperature and strong current in the deep sea environment, the numerical simulation of solid-liquid two-phase flow becomes extremely complicated. Although existing technologies such as discrete element method (DEM) and Euler-Lagrangian method can provide detailed particle motion information, when these algorithms are actually used for numerical simulation, not only the calculation efficiency is low, but also the consumption of computing resources is high.

[0093] In the embodiments of the present application, by adopting a pseudo-fluid model and simplifying solid particles into pseudo-fluids, and by treating solid particles as pseudo-fluids with effective density and effective viscosity, detailed tracking of collisions and movements between particles is avoided, the complexity of calculations can be reduced, and the efficiency of numerical simulation is improved.

[0094] In specific implementation, the method may, for example, include: first setting the initial velocity field, initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline; then defining the boundary conditions of the inlet and outlet of the deep-sea mining pipeline; finally, using a pseudo-fluid model to perform numerical simulation on the deep-sea mining pipeline to obtain deep-sea mining numerical simulation results, wherein the deep-sea mining numerical simulation results include pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity.

[0095] It can be seen that the method provided by the implementation of the present application uses a pseudo-fluid model to simplify solid particles into a pseudo-fluid, thereby introducing effective density and effective viscosity. The effective density and effective viscosity can be used to perform numerical simulation of deep-sea mining pipelines. Compared with traditional algorithm calculations, it not only simplifies the calculation complexity, but also improves the efficiency of numerical simulation.

[0096] To facilitate understanding of the specific implementation of the deep-sea mining numerical simulation method based on the pseudo fluid model provided in the embodiment of the present application, it will be described below with reference to the accompanying drawings.

[0097] It should be noted that the subject implementing the deep-sea mining numerical simulation method based on the pseudo-fluid model can be the deep-sea mining numerical simulation device based on the pseudo-fluid model provided in the embodiment of the present application, and the deep-sea mining numerical simulation device based on the pseudo-fluid model can be carried in an electronic device or a functional module of an electronic device. The electronic device in the embodiment of the present application can be any device capable of implementing the deep-sea mining numerical simulation method based on the pseudo-fluid model in the embodiment of the present application, for example, it can be an Internet of Things (IoT) device.

[0098] Figure 1 A flow chart of a method for numerical simulation of deep-sea mining based on a pseudo-fluid model provided in an embodiment of the present application is provided. The method can be applied to a numerical simulation device for deep-sea mining based on a pseudo-fluid model, which can be, for example, Figure 5 The deep-sea mining numerical simulation device 500 based on the pseudo-fluid model shown in FIG. 1 may also be integrated with a Figure 6 Functional modules in the electronic device 600 are shown.

[0099] like Figure 1 As shown, the method includes the following S101 to S103:

[0100] S101: Setting the initial velocity field, initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline.

[0101] In order to obtain the numerical simulation results of deep-sea mining, the initial velocity field, initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline are first set in the embodiment of the present application, and then the boundary conditions of the inlet and outlet of the deep-sea mining pipeline are defined. Finally, the deep-sea mining pipeline is numerically simulated using a pseudo-fluid model to obtain the numerical simulation results of deep-sea mining, which include pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity. In the embodiment of the present application, S101 is used to make preliminary preparations for the subsequent numerical simulation.

[0102] In this process, in order to perform numerical simulation operations, it is first necessary to set the initial conditions, that is, to set the initial velocity field, initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline, so as to ensure the convergence of the simulation and compliance with physical laws when performing the numerical model later. If the initial conditions are not set properly, it may cause divergence in the simulation process, that is, the calculation results are unstable or unable to converge. For example, in fluid dynamics simulation, if the initial velocity field is not set reasonably, it may cause numerical oscillation or calculation failure in the calculation process. Therefore, reasonable initial conditions can reduce the number of iterations in the calculation process and improve calculation efficiency.

[0103] S102: Define boundary conditions for the inlet and outlet of deep-sea mining pipelines.

[0104] Boundary conditions are an integral part of numerical simulations, and they define the law of variation of variables or their derivatives on the boundaries of the solution region. In the numerical simulation settings of the embodiments of the present application, the setting of boundary conditions at the inlet and outlet of the deep-sea mining pipeline depends on the specific simulation requirements and physical phenomena. According to the description, there are two typical settings:

[0105] (1) Set the flow rate, pressure and particle concentration for the inlet and outlet respectively:

[0106] In this case, the inlet and outlet of a deep-sea mining pipeline have their own set values ​​for flow rate, pressure, and particle concentration. This setting is often used to control the detailed state of the entire flow system, allowing the modeler to accurately control the entire process from the flow entering the system to the flow leaving it. This method is often used in situations where it is necessary to study the complex interactions or reactions between the inlet and outlet of the fluid.

[0107] (2) Only set a fixed flow rate and particle concentration at the inlet and a fixed pressure at the outlet:

[0108] In this case, the flow rate and particle concentration at the inlet of the deep-sea mining pipeline are set to fixed values, while the pressure at the outlet is set to a fixed value. This is a more common boundary condition setting that is suitable for many fluid dynamics simulations, especially in industrial applications such as pipeline flow, chemical processes, etc. This boundary condition simplifies the complexity of the simulation, making it possible to focus more on studying the behavior of the fluid inside the pipeline or equipment rather than the detailed state at the outlet.

[0109] As an example, the present application selects the second setting, that is, S102 may include: defining a fixed flow rate and particle concentration at the inlet of the deep-sea mining pipeline; and defining a fixed pressure at the outlet of the deep-sea mining pipeline.

[0110] S103: numerically simulate the deep-sea mining pipeline using a pseudo-fluid model to obtain a deep-sea mining numerical simulation result, wherein the deep-sea mining numerical simulation result includes pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity.

[0111] In the embodiments of the present application, a pseudo-fluid model is used to simulate the particle effect in solid-liquid mixed flow, ignoring the impact of particle collision. The model normalizes solid particles and fluids and regards them as pseudo-fluids with effective density and effective viscosity, thereby simplifying the calculation process.

[0112] Among them, effective density: In the simulation of solid-liquid mixed flow, effective density is an important parameter because it determines the inertial characteristics of the fluid. It is obtained by weighted average of the density of solid particles and fluid and the volume fraction of particles in the fluid. The effective density affects the inertial term in the fluid dynamics equation, and therefore directly affects the calculation of the velocity field and pressure field. Effective viscosity: The effective viscosity describes the internal friction characteristics of the fluid, especially in fluids containing suspended particles. It takes into account the influence of solid particles and thus adjusts the viscous response of the fluid. In numerical simulations, the effective viscosity affects the viscous dissipation term in the Navier-Stokes equation, which is crucial to the damping effect of the fluid velocity gradient.

[0113] As an example, the process of constructing a pseudo fluid model in the embodiment of the present application includes:

[0114] (1) The density of solid particles and the density of liquid are weighted averaged according to the particle volume fraction to obtain the effective density. The specific calculation formula is as follows:

[0115] ρ eff =φρ s +(1-φ)ρ f

[0116] Among them, ρ eff represents the effective density; φ represents the particle volume fraction; ρ s Represents the density of solid particles; ρ f Indicates the density of the liquid.

[0117] (2) According to the particle volume fraction and the viscosity of the base fluid, the effective viscosity is obtained, where the effective viscosity represents the overall viscosity of the solid-liquid mixture and can be preliminarily estimated using the Einstein formula. The specific preliminary estimation formula is as follows:

[0118] μ eff =μ f (1+2.5φ)

[0119] Among them, μ eff represents effective viscosity; φ represents particle volume fraction; μ f Indicates the viscosity of the base fluid.

[0120] For higher concentrations of solid particles, the effective viscosity can be determined using modified empirical formulas or experimental data, such as the Krieger-Dougherty equation:

[0121]

[0122] Among them, μ eff Indicates effective viscosity; μ frepresents the viscosity of the base fluid; φ represents the particle volume fraction; φ m Represents the maximum volume fraction of solid particles.

[0123] The above Krieger-Dougherty equation often appears in studies related to suspension fluids or particle-enhanced fluids and represents the calculation of effective viscosity.

[0124] (3) According to the effective density and effective viscosity, the Navier-Stokes equation in the pseudo-fluid model is determined as:

[0125]

[0126] Among them, ρ eff represents the effective density, u represents the velocity field; It is used to describe how a vector field (such as a velocity field) diverges or contracts in space, and represents the net outflow rate of a substance (such as a fluid) near a certain point; t represents time, that is, represents the rate of change of velocity field over time; p represents pressure field; μ eff represents effective density; g represents gravity; F vib Represents the effect of external vibration forces applied in the fluid on the velocity field.

[0127] In the embodiment of the present application, Hamilton's virtual work principle is used to derive the momentum equation of the system, that is, kinetic energy, potential energy and external work (pressure, viscous force and pipeline vibration force) are substituted into Hamilton's virtual work principle, and the variational calculus is performed to obtain the momentum equation as the above-mentioned Navier-Stokes equation.

[0128] (4) In order to describe the movement of particles, the convection-diffusion equation can be constructed according to the particle volume fraction, where the convection-diffusion equation is:

[0129]

[0130] in, represents the rate of change of the scalar field φ (such as concentration or other physical quantities) over time; u represents the velocity field; represents the divergence operator, describing the diffusion phenomenon; D φ It represents the diffusion coefficient, which describes the diffusivity or diffusion capacity of the scalar field φ; φ represents the scalar field (such as the concentration of a substance, the phase field, etc.).

[0131] In addition, in order to more accurately simulate the interaction between solid particles and fluids, the solid-liquid sliding model can also be used to construct the velocity relationship between solid particles and internal flow. The solid-liquid sliding model assumes that solid particles slide in the fluid, and there is a linear relationship between the velocity and the fluid velocity as shown below:

[0132] u s =αu f

[0133] Among them, u s is the velocity of the solid particle, u f is the velocity of the fluid and α is the slip coefficient.

[0134] (5) The control equations of single-phase flow and pipeline nonlinear coupling vibration based on Euler-Bernoulli beam are derived by considering uniform flow velocity and constant density as fluid parameters according to the axial and radial dynamic balance principles and Hamilton virtual work principle, respectively.

[0135] Assuming that the pipeline is a slender elastic beam, the vibration behavior of the pipeline can be described by the vibration control equation of the beam, that is, a beam-pipe vibration model is constructed, where the vibration displacement equation of the beam in the beam-pipe vibration model is:

[0136]

[0137] Where, E represents the elastic modulus, I represents the section moment of inertia; EI represents the bending stiffness of the beam; represents the variation of beam deflection (w) with beam length (z); ρ A Indicates line density; represents the second-order derivative of the deflection (w) with time (t), that is, the acceleration of the beam; F vib (z, t) represents the distributed load along the length of the pipeline; F Cor Coriolis force, the inertial force generated by rotational motion; F Cen It represents centrifugal force, which is the centrifugal effect on an object in a rotating reference frame.

[0138] The Coriolis force and centrifugal force mentioned above are calculated by a unified unit composed of a linear superposition of fluid units and particle units. The movement of fluids and particles will cause vibration and instability of the pipeline, which can be expressed as:

[0139] F Cor =-2m(Ω×v)

[0140] F Cen =mΩ×(Ω×r)

[0141] Among them, F Cor F stands for Coriolis force; Cen represents centrifugal force; m represents mass; Ω represents angular velocity of rotation, and v represents speed.

[0142] Assuming that the forced vibration is a simple harmonic vibration, the distributed load along the length of the pipeline can be expressed as:

[0143]

[0144] Among them, F vib (z, t) represents the distributed load along the length of the pipeline; A represents the cross-sectional area of ​​the pipeline; ω represents the vibration frequency; t represents time; z represents the pipeline length coordinate; and L represents the total length of the pipeline.

[0145] The present application also describes the upper and lower boundary conditions of the pipeline, and the upper and lower boundaries are supported by rotation and horizontal elastic support respectively. Specifically, the upper and lower boundary conditions can be expressed as:

[0146] When the upper boundary z = 0, the deflection w(0,t) = 0 (horizontal elastic support); represents the acceleration of the beam (no rotation);

[0147] When the lower boundary z=L, w(L,t)=0 (horizontal elastic support) for deflection; w(L,t)=0 (horizontal elastic support) for beam acceleration (No rotation).

[0148] In this process, a pseudo-fluid model is constructed to replace the detailed tracking of particle motion with effective density and effective viscosity. Compared with previous algorithms, the amount of calculation can be simplified, thereby improving computational efficiency.

[0149] S103: numerically simulate the deep-sea mining pipeline using a pseudo-fluid model to obtain a deep-sea mining numerical simulation result, wherein the deep-sea mining numerical simulation result includes pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity.

[0150] As an example, S103 may include: S1031, discretizing the Navier-Stokes equation, the convection-diffusion equation and the vibration control equation of the beam and converting them into discrete equations; S1032, solving the discrete equations using a high-precision iterative method to obtain numerical simulation results of deep-sea mining.

[0151] Among them, most physical phenomena are mathematically described by continuous partial differential equations (PDEs), such as the Navier-Stokes equations in fluid dynamics. Computers cannot directly process such continuous equations, so they need to be converted into discrete forms before they can be numerically solved. The advantages of discretization may include: (1) Computational feasibility: By dividing the continuous problem domain (such as time and space) into finite discrete units or points, we can use limited computing resources to approximately solve the problem. This method allows the computer to use an algorithm to gradually solve the state of each discrete unit, thereby approximately simulating the behavior of the entire physical system. (2) Algorithm implementation: Discretization makes it possible to apply various mature numerical algorithms to solve the problem, such as the finite difference method (FDM), the finite volume method (FVM), and the finite element method (FEM). These algorithms can effectively process the system of equations obtained by discretization and calculate the numerical solution. (3) Accuracy and stability: In the process of discretization, it is necessary to select appropriate discrete steps and algorithms to ensure the accuracy of the calculation and the stability of the numerical solution. Improper discretization may cause the numerical solution to deviate from the true solution or be numerically unstable. (4) Model verification and adjustment: The discretized numerical model can be compared and verified with experimental data, and the model parameters can be adjusted according to experimental or field data to improve the accuracy and applicability of the model.

[0152] The process of discretizing the Navier-Stokes equation, the convection-diffusion equation, and the vibration control equation of the beam in S1031 and converting them into discrete equations may include:

[0153] Discretize the Navier-Stokes equations using the finite difference method (FDM) or finite volume method (FVM), including:

[0154] (1) Discretization of time derivative:

[0155]

[0156] in, Indicates the rate of change of velocity field over time; u n+1 Indicates the value of the velocity field at the next time step (n+1 moment); u n It represents the known value of the velocity field at the current time step (n); Δt represents the step size of time discretization, or the time interval from the current time step (n) to the next time step (n+1).

[0157] In numerical simulation, discretization of time derivative terms is the process of converting continuous time variables into discrete steps in order to be able to simulate and solve them on a computer. This is a key step in solving dynamic (time-dependent) problems, especially when solving partial differential equations (such as the Navier-Stokes equations in fluid dynamics).

[0158] (2) Discretization of convection terms

[0159]

[0160] Among them, u represents the velocity field; u n represents the known value of the velocity field at the current time step (time n); ▽u represents the gradient of the velocity field, describing the rate of change of velocity in space; Indicates the velocity field value of the adjacent points before and after the current point in the x direction; Indicates the velocity field value of the adjacent points before and after the current point in the y direction; It represents the velocity field value of the adjacent points before and after the current point in the z direction; Δx, Δy, Δz represent the discrete spacing of the grid in the x, y, and z directions.

[0161] In numerical simulation, discretization of convection terms is the process of converting the continuous form of the convection equation (representing the transport process of matter, energy, etc.) in numerical simulation into a discrete form so that it can be solved on a computer.

[0162] (3) Discretization of viscosity term

[0163]

[0164] in, Represents the divergence of a vector field at a certain point, acting on the viscous stress term; μ eff It represents the effective viscosity; represents the velocity gradient, that is, the rate of change of the velocity field in all directions; represents the spatial derivative in the i direction; Represents the j-th dimension component of the velocity field.

[0165] In numerical simulations, discretization of viscous terms involves converting the terms describing viscous effects in the fluid dynamics equations (such as the viscous dissipation terms in the Navier-Stokes equations) into a discrete format that can be processed by computers.

[0166] (4) Discretization of the beam vibration equation

[0167]

[0168] Where, E represents the elastic modulus, I represents the section moment of inertia; EI represents the bending stiffness of the beam; represents the variation of beam deflection (w) with beam length (z); ρ A Indicates line density; It represents the second-order derivative of the deflection (w) with time (t), that is, the acceleration of the beam; A represents the cross-sectional area of ​​the pipe; ω represents the vibration frequency; t represents time; z represents the length coordinate of the pipe; and L represents the total length of the pipe.

[0169] Above The central difference method can be used for discretization:

[0170]

[0171] in, represents the fourth-order derivative of w with respect to z, that is, the rate of change of curvature; w i The variable w at the i-th grid point is the deflection (displacement) of the beam at that point; Δz represents the spatial step length of the grid in the z direction, that is, the distance between adjacent grid points.

[0172] The above S1032 uses a high-precision iterative method to solve the discrete equations to obtain the numerical simulation results of deep-sea mining, including:

[0173] (1) According to the discrete equation, effective density, effective viscosity and velocity field formula, the predicted velocity field is obtained. The velocity field formula is as follows:

[0174]

[0175] Among them, u represents the velocity field; u n It represents the value of the velocity field at the previous time step (i.e., time n); Δt represents the time step; represents the convection term of the velocity field, that is, the change of the velocity of the fluid with space during the movement; ρ eff represents the effective density; represents the pressure gradient term; μ eff It represents the effective viscosity; represents the viscous force term; F vib Represents the effect of external vibration or other external forces on the velocity field in the fluid.

[0176] (2) Substituting the predicted velocity field into the continuity equation, the pressure correction equation is obtained. The pressure correction equation is as follows:

[0177] A p p′=b

[0178] Among them, A p is the pressure correction coefficient matrix; p′ represents the pressure correction value; b is the source term vector.

[0179] (3) Update the velocity field, pressure field and vibration displacement of the beam according to the pressure correction equation.

[0180] First update the corrected velocity field u n+1 :

[0181]

[0182] Among them, u n+1 represents the velocity field of the next time step (n+1), that is, the updated fluid velocity; u * represents the predicted velocity field, which is usually the intermediate velocity field calculated by the velocity equation without considering the pressure term; Δt represents the time step; ρ eff represents the effective density; Represents the pressure gradient at the next time step, that is, the change of pressure with spatial position.

[0183] Update the pressure field p n+1 :

[0184] p n+1 =p n +α p p′

[0185] Among them, p n+1 represents the pressure field at the next time step (n+1); p n represents the pressure field at the current time step (n); α p represents the relaxation factor; p′ represents the pressure correction value.

[0186] Finally, the vibration displacement w of the beam is updated n+1 :

[0187]

[0188] Among them, ρ A Indicates line density; represents the acceleration of the beam at the next time step (n+1); EI represents the bending stiffness of the beam; It represents the change of the beam deflection (w) with the beam length (z) at the next time step (n+1); A represents the cross-sectional area of ​​the pipeline; ω represents the vibration frequency; t represents time; z represents the pipeline length coordinate; and L represents the total length of the pipeline.

[0189] (4) Update the effective density and effective viscosity based on the updated velocity field and the particle concentration distribution at different time steps.

[0190] The specific update formula is as follows:

[0191]

[0192] ρ eff =φρ s +(1-φ)ρ f

[0193] Among them, μ effIndicates effective viscosity; μ f represents the viscosity of the base fluid; φ represents the particle volume fraction; φ m represents the maximum volume fraction of solid particles; ρ eff represents the effective density; ρ s Represents the density of solid particles; ρ f Indicates the density of the liquid.

[0194] It should be noted that in numerical simulations, especially those involving solid-liquid two-phase flow such as pseudo-fluid models, effective density and effective viscosity are core parameters because they are used to describe the overall fluid dynamics behavior of the mixture. These parameters do have an important impact on other variables in the simulation, such as velocity field, pressure field, and structural response (such as the vibration displacement of a beam).

[0195] In this regard, the optimization parameters in the embodiment of the present application need to update the effective density and effective viscosity, that is, they need to be judged based on experimental data. The specific process may include: measuring the density and viscosity of the solid-liquid mixture through an experimental device to determine the standard effective density and standard effective viscosity; comparing the standard effective density and standard effective viscosity with the effective density and the effective viscosity, respectively, and calculating the error; if the error is greater than a preset value, then executing the operation of updating the effective density and effective viscosity according to the updated velocity field and the particle concentration distribution under different time steps. That is, through preliminary numerical simulation, the effective density and effective viscosity parameters are adjusted to make the simulation results consistent with the experimental data, thereby calibrating the effective parameters.

[0196] That is, the embodiments of the present application can accurately determine the effective parameters of the pseudo-fluid through a method combining experiments and numerical simulations, and ensure the accuracy and reliability of the model parameters through experimental measurements and simulation calibration.

[0197] (5) The above operations from obtaining the predicted velocity field to updating the effective density and the effective viscosity are executed repeatedly until the changes in the velocity field and the pressure field meet the convergence criteria, thereby obtaining the numerical simulation results of deep-sea mining.

[0198] The specific formula is as follows:

[0199] ||u n+1 -u n ||<∈

[0200] ||p n+1 -p n ||<∈

[0201] Among them, u n+1 represents the velocity field of the next time step (n+1); u n represents the velocity field at the current time step (n); p n+1 represents the pressure field at the next time step (n+1); p nrepresents the pressure field at the current time step (n); ∈ is the convergence error.

[0202] In this process, the calculation time of the pseudo-fluid model is significantly lower than that of the traditional method, making it suitable for large-scale and long-term simulations. By comparing the calculation efficiency, the actual value of the pseudo-fluid model in engineering applications is demonstrated.

[0203] In addition, the embodiments of the present application can also optimize the operating parameters, specifically including:

[0204] (1) Pressure drop calculation:

[0205] By simulating the pressure drop under different operating conditions, the optimal lifting speed and particle concentration are determined. Assuming different flow rates u at the inlet of the deep-sea mining pipeline in and particle concentration at the inlet of different deep-sea mining pipelines φ in The pressure drop under the load is Δp, and the operating condition with the minimum pressure drop can be selected.

[0206] The following details the relationship between flow rate, particle concentration and pressure drop:

[0207] The higher the flow rate, the greater the resistance to flow through the pipe or system, which may result in a higher pressure drop. At high flow rates, the movement of particles is also affected, there may be stronger convection, and particles may not have enough time to settle.

[0208] The higher the particle concentration, the higher the viscosity and density of the fluid, and the greater the resistance to flow. Especially when the particle concentration is high, the interaction between particles and the fluid and between particles will lead to a greater pressure drop. High particle concentration may cause blockage or increase friction, thus affecting fluidity and pressure distribution.

[0209] Pressure drop is the pressure loss caused by friction, flow resistance, etc. during the flow of a fluid. The higher the flow rate and the greater the particle concentration, the greater the pressure drop. During the simulation, the pressure drop under different operating conditions can be used to evaluate the energy efficiency of the system and the fluid transport capacity. The optimal operating condition is usually to find the point where the pressure drop is minimized while ensuring that the particle concentration is reasonable and the flow rate meets the requirements.

[0210] (2) Flow stability analysis:

[0211] Analyze the impact of external factors such as ocean currents and waves on flow stability in lifting pipelines and optimize pipeline design. Simulate flow conditions under different ocean current speeds and wave conditions to ensure the stability of the system under various external interferences.

[0212] After obtaining the deep-sea mining numerical simulation results in the embodiment of the present application, the deep-sea mining numerical simulation results can be analyzed, and the specific process may include:

[0213] (1) Pressure distribution:

[0214] Display the pressure distribution diagram in the riser pipe and analyze the pressure drop under different operating conditions. Determine the optimal operating parameters by comparing the pressure distribution under different flow rates and particle concentrations.

[0215] (2) Velocity field:

[0216] Display velocity field distribution diagram to analyze the movement behavior of particles in the lifting pipe. Through the visualization of velocity field, potential flow instability areas can be identified.

[0217] Specifically, it can include: Display and analysis of velocity field: By simulating and generating velocity field distribution diagrams, the flow behavior of particles and fluids in the lifting pipeline can be clearly seen. This visualization method helps researchers intuitively analyze the movement trajectory of fluids and particles in the pipeline.

[0218] Identification of unstable areas: In the velocity field diagram, unstable areas are usually manifested as sudden changes in velocity or irregular flow phenomena. These unstable areas may show obvious flow separation, vortices or backflow, and streamline diagrams and velocity vector diagrams can help identify these areas.

[0219] Potential areas of flow instability: By visualizing the velocity field, researchers can identify areas where flow instability may exist. Typically, these areas are where the flow velocity changes dramatically, such as at corners, variable diameter sections, or areas affected by external factors.

[0220] (3) Particle concentration distribution:

[0221] Displays particle concentration distribution to identify potential blockage areas. Optimize pipeline design and operating parameters to avoid blockages by analyzing particle concentration distribution.

[0222] Specific examples include: Analyzing particle concentration distribution: By displaying and analyzing the particle concentration distribution, potential areas of particle accumulation in the flow system can be identified. These areas may cause pipe blockage, increase system resistance or pressure drop.

[0223] Relationship with pipeline design and operating parameters: Particle concentration distribution is closely related to pipeline design (such as pipe diameter, flow channel structure) and operating parameters (such as flow rate, pressure). Uneven particle concentration distribution may be caused by unreasonable pipeline design (such as local sharp diameter change) or improper operating parameter settings (such as too low or too high flow rate).

[0224] Optimization goals: By analyzing the particle concentration distribution, researchers can optimize pipeline design and operating parameters to reduce particle accumulation and avoid blockage. Specific optimization measures may include: adjusting flow rate or pressure to avoid particle deposition. Modifying pipeline structure or materials so that particles can be more evenly distributed in the fluid. Introducing special mixing devices or designs to maintain uniform flow of particles.

[0225] It can be seen that the embodiment of the present application simplifies the calculation of multiphase flow by treating solid particles as pseudo-fluids, that is, by introducing effective density and effective viscosity, it reduces the tracking of particle motion details and improves the computational efficiency of the entire deep-sea mining numerical simulation.

[0226] In order to make the method provided in the embodiment of the present application clearer and easier to understand, Figure 2 A specific example of this method is described.

[0227] like Figure 2 As shown, the implementation may include:

[0228] S201: Construct a pseudo fluid model.

[0229] The present application reduces the tracking of particle motion details by treating solid particles as pseudo-fluids, that is, by introducing effective density and effective viscosity into the pseudo-fluid model, thereby improving the computational efficiency of the entire deep-sea mining numerical simulation.

[0230] In this regard Figure 3 The pseudo-fluid model schematic diagram shown explains the pseudo-fluid model, in which solid particles (Particles): Figure 3 It is represented by small dots and is evenly distributed throughout the fluid. The density of the particles is ρ s , the particle volume fraction is φ. Wherein the liquid (Fluid): Figure 3 The background color is used to represent the liquid filling the entire pipe. The density of the liquid is ρ f The pseudo-fluid characterizes the overall properties of the mixture through effective density and effective viscosity. The specific formulas of effective density and effective viscosity can be as shown in the above embodiment, which will not be described in detail here.

[0231] In the embodiment of the present application, constructing a pseudo-fluid model may include: (1) obtaining an effective density; (2) obtaining an effective viscosity; (3) determining the Navier-Stokes equation in the pseudo-fluid model based on the effective density and the effective viscosity; (4) constructing a convection-diffusion equation based on the particle volume fraction; (5) constructing a vibration control equation for the beam.

[0232] The specific formula for constructing the pseudo fluid model can be known from the above embodiments and will not be described in detail here.

[0233] The vibration control equation of the beam is a pipeline vibration model based on the Euler-Bernoulli beam, which is specifically: Figure 4 As shown, it includes pipeline, vibration displacement and boundary conditions. L in the figure is the pipeline length, and F is the distributed load, which is represented by arrows, showing the distributed load along the length of the pipeline.

[0234] S202: Setting the initial velocity field, initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline.

[0235] In the embodiment of the present application, in order to ensure the convergence and compliance with physical laws of the simulation when the numerical model is subsequently performed, it is necessary to pre-set the initial velocity field, initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline, specifically: Initial velocity field (InitialVelocityField): set to u0; Initial pressure field (Initial Pressure Field): set to p0; Initial particle concentration (Initial Particle Concentration): set to φ0.

[0236] S203: Define boundary conditions for the inlet and outlet of deep-sea mining pipelines.

[0237] In order to define the variation law of the variables or their derivatives on the boundary of the solution area in the embodiment of the present application, it is necessary to define the boundary conditions of the inlet and outlet of the deep-sea mining pipeline. Specifically, the inlet velocity (Inlet Velocity) of the deep-sea mining pipeline can be set to a fixed velocity u in ; Outlet Pressure of deep sea mining pipeline: set to fixed pressure p out ; and the inlet particle concentration at the deep sea mining pipeline: set to φ in .

[0238] S204: discretize the Navier-Stokes equation, the convection-diffusion equation, and the vibration control equation of the beam in the pseudo-fluid model and convert them into discrete equations.

[0239] Since computers cannot directly process such continuous equations, they need to be converted into discrete forms before numerical solutions can be obtained. The specific discretization process includes: (1) discretization of time derivative terms; (2) discretization of convection terms; (3) discretization of viscosity terms; (4) discretization of the vibration equation of the beam. The specific discretization process is shown in the above embodiment and will not be described in detail here.

[0240] S205: Obtain a predicted velocity field according to the discrete equation, the effective density, the effective viscosity and the velocity field formula.

[0241] After obtaining the discrete equation, a high-precision iterative method can be used to solve the discrete equation to obtain the numerical simulation results of deep-sea mining. First, the predicted velocity field is obtained based on the discrete equation, effective density, effective viscosity and velocity field formula. The specific process of obtaining the predicted velocity field is shown in the above embodiment and will not be repeated here.

[0242] S206: Substitute the predicted velocity field into the continuity equation to obtain the pressure correction equation.

[0243] In order to subsequently update and correct the velocity field, pressure field and vibration displacement of the beam, it is necessary to obtain a pressure correction equation before that. The specific process of obtaining the pressure correction equation is as shown in the above embodiment and will not be described in detail here.

[0244] S207: Update the velocity field, pressure field and vibration displacement of the beam according to the pressure correction equation.

[0245] First update the corrected velocity field u n+1 , and then update the pressure field p n+1 , and finally the vibration displacement of the beam w n+1 .

[0246] S208: Update the effective density and effective viscosity according to the updated velocity field and the particle concentration distribution at different time steps.

[0247] In numerical simulation, especially involving solid-liquid two-phase flow such as pseudo-fluid model, effective density and effective viscosity are core parameters because they are used to describe the overall fluid dynamics behavior of the mixture. These parameters do have an important influence on other variables in the simulation such as velocity field, pressure field and structural response (such as vibration displacement of beam). Therefore, it is necessary to optimize the two parameters of effective density and effective viscosity, that is, it is necessary to update the effective density and effective viscosity. The specific update is to accurately determine the effective parameters of the pseudo-fluid according to the method combining experiments and numerical simulations. Through experimental measurement and simulation calibration, the accuracy and reliability of the model parameters are ensured. The specific judgment process is shown in the above embodiment and will not be repeated here.

[0248] S209: Determine whether the changes in the velocity field and the pressure field meet the convergence criterion.

[0249] When performing the numerical simulation of deep-sea mining at last, it is necessary to determine whether the changes in the velocity field and the pressure field meet the convergence criteria. If the convergence criteria are met, it means that the current numerical simulation results meet the requirements, and the numerical simulation process can be ended, that is, S210 is executed; if the convergence criteria are not met, it means that the current numerical simulation results do not meet the requirements, and it is necessary to return to execute the numerical simulation process, that is, return to execute S205.

[0250] S210: If satisfied, a deep-sea mining numerical simulation result is obtained, wherein the deep-sea mining numerical simulation result includes pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity.

[0251] This embodiment provides a method for numerical simulation of deep-sea mining based on a pseudo-fluid model. By applying the pseudo-fluid model in the numerical simulation of deep-sea mining, the calculation process is significantly simplified, the simulation efficiency is improved, and key problems such as pressure drop calculation, particle distribution and flow stability are solved. And by optimizing operating parameters such as lifting speed and particle concentration, the stable operation of the system under various working conditions is ensured. By optimizing operating parameters, the equipment maintenance cost is reduced and the economic benefit is improved. By reducing pressure drop and energy consumption, the operating cost is reduced and the economic benefit is improved.

[0252] See also Figure 5 The embodiment of the present application provides a deep-sea mining numerical simulation device 500 based on a pseudo-fluid model, the device comprising:

[0253] A setting unit 501 is used to set the initial velocity field, initial pressure field and initial particle concentration distribution in the pipeline;

[0254] A definition unit 502 is used to define the boundary conditions of the pipeline inlet and outlet;

[0255] The numerical simulation unit 503 is used to perform numerical simulation on the deep-sea mining pipeline using a pseudo fluid model to obtain a deep-sea mining numerical simulation result, wherein the deep-sea mining numerical simulation result includes pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity.

[0256] Optionally, the device 500 further includes:

[0257] An obtaining unit is used to perform weighted average of the density of solid particles and the density of liquid according to the particle volume fraction to obtain an effective density;

[0258] The obtaining unit is also used to obtain the effective viscosity according to the particle volume fraction and the viscosity of the base fluid;

[0259] Determine the unit used to determine the effective density and effective viscosity in the Navier-Stokes equations in the pseudo-fluid model as:

[0260]

[0261] Among them, ρ eff represents the effective density, u represents the velocity field; It is used to describe the divergence or contraction of the vector field in space; t represents time, that is, represents the rate of change of velocity field over time; p represents pressure field; μ effrepresents effective density; g represents gravity; F vib Represents the effect of external vibration force applied in the fluid on the velocity field;

[0262] The building unit is used to construct the convection-diffusion equation according to the particle volume fraction, where the convection-diffusion equation is:

[0263]

[0264] in, represents the rate of change of the scalar field φ in time; u represents the velocity field; represents the divergence operator; D φ represents the diffusion coefficient, which describes the diffusion rate of the scalar field φ; φ represents the scalar field;

[0265] The construction unit is also used to construct a pipeline vibration model of the beam, wherein the vibration displacement equation of the beam in the pipeline vibration model of the beam is:

[0266]

[0267] Where, E represents the elastic modulus, I represents the section moment of inertia; EI represents the bending stiffness of the beam; Indicates the variation of beam deflection with beam length; ρ A Indicates line density; represents the second-order derivative of the deflection with time, that is, the acceleration of the beam; F vib (z, t) represents the distributed load along the length of the pipeline; F Cor F stands for Coriolis force; Cen Represents centrifugal force.

[0268] Optionally, the numerical simulation unit 503 specifically includes:

[0269] A conversion subunit is used to discretize the Navier-Stokes equation, the convection-diffusion equation and the vibration control equation of the beam and convert them into discrete equations;

[0270] The solving subunit is used to solve the discrete equations using a high-precision iterative method to obtain the numerical simulation results of deep-sea mining.

[0271] Optionally, the solving subunit is specifically used for:

[0272] According to the discrete equation, effective density, effective viscosity and velocity field formula, the predicted velocity field is obtained, and the velocity field formula is as follows:

[0273]

[0274] Among them, u represents the velocity field; u nrepresents the value of the velocity field in the previous time step; Δt represents the time step; represents the convection term of the velocity field; ρ eff represents the effective density; represents the pressure gradient term; μ eff It represents the effective viscosity; represents the viscous force term; F vib Represents the effect of external vibration force applied in the fluid on the velocity field;

[0275] Substituting the predicted velocity field into the continuity equation, the pressure correction equation is obtained, which is as follows:

[0276] A p p′=b

[0277] Among them, A p is the pressure correction coefficient matrix; p′ represents the pressure correction value; b is the source term vector;

[0278] Update the velocity field, pressure field and beam vibration displacement according to the pressure correction equation;

[0279] Update the effective density and effective viscosity according to the updated velocity field and particle concentration distribution at different time steps;

[0280] The above operations from obtaining the predicted velocity field to updating the effective density and effective viscosity are executed cyclically until the changes in the velocity field and the pressure field meet the convergence criterion, and the deep-sea mining numerical simulation results are obtained.

[0281] Optionally, the solver subunit is used to update the effective density and effective viscosity based on the updated velocity field and the particle concentration distribution at different time steps, specifically for:

[0282] The density and viscosity of the solid-liquid mixture are measured by an experimental device to determine the standard effective density and standard effective viscosity;

[0283] Compare the standard effective density and standard effective viscosity with the effective density and effective viscosity respectively, and calculate the error;

[0284] If the error is greater than a preset value, the effective density and effective viscosity are updated according to the updated velocity field and the particle concentration distribution at different time steps.

[0285] Optionally, the definition unit 502 is specifically configured to:

[0286] Define fixed flow rates and particle concentrations at the inlet of a deep-sea mining pipeline;

[0287] Define a fixed pressure at the outlet of a deep sea mining pipeline.

[0288] It should be noted that the specific implementation method and effect of the deep-sea mining numerical simulation device 500 based on the pseudo-fluid model can be found in the above Figure 1 or Figure 2 The relevant descriptions in the provided methods will not be repeated here.

[0289] The present application embodiment also provides an electronic device 600, such as Figure 6 As shown, the device 600 includes a memory 601 and a processor 602:

[0290] The memory 601 is used to store computer programs;

[0291] The processor 602 is used to execute the above Figure 1 or Figure 2 The method provided.

[0292] In addition, the present application also provides a computer-readable storage medium, the computer-readable storage medium is used to store a computer program, and the computer program is used to execute Figure 1 or Figure 2 The method provided.

[0293] Through the description of the above implementation methods, it can be known that those skilled in the art can clearly understand that all or part of the steps in the above-mentioned embodiment method can be implemented by means of software plus a general hardware platform. Based on such an understanding, the technical solution of the present application can be embodied in the form of a software product, which can be stored in a storage medium, such as a read-only memory (ROM) / RAM, a magnetic disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network communication device such as a router) to execute the methods described in each embodiment of the present application or some parts of the embodiments.

[0294] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The device embodiment described above is only schematic, in which the modules described as separate components may or may not be physically separated, and the components displayed as modules may or may not be physical modules, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the goals of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative work.

[0295] The above description is merely an exemplary embodiment of the present application and is not intended to limit the protection scope of the present application.

Claims

1. A numerical simulation method for deep sea mining based on a pseudo fluid model, characterized in that: The method comprises: Set the initial velocity field, initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline; Define boundary conditions for the entry and exit of deep-sea mining pipelines; A pseudo fluid model is used to perform numerical simulation on a deep-sea mining pipeline to obtain a deep-sea mining numerical simulation result, which includes pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity.

2. The method according to claim 1, characterized in that The process of constructing the pseudo fluid model includes: The density of solid particles and the density of liquid are weighted averaged according to the particle volume fraction to obtain the effective density; Obtaining effective viscosity according to the particle volume fraction and the viscosity of the base fluid; The Navier-Stokes equation in the pseudo fluid model is determined according to the effective density and the effective viscosity: Among them, ρ eff represents effective density, u represents velocity field; ▽ represents the divergence or contraction of vector field in space; t represents time, i.e. represents the rate of change of velocity field over time; p represents pressure field; μ eff represents effective density; g represents gravity; F vib Represents the effect of external vibration force applied in the fluid on the velocity field; According to the particle volume fraction, a convection-diffusion equation is constructed, wherein the convection-diffusion equation is: in, represents the rate of change of the scalar field φ over time; u represents the velocity field; ▽ represents the divergence operator; D φ represents the diffusion coefficient, which describes the diffusion rate of the scalar field φ; φ represents the scalar field; A beam pipeline vibration model is constructed, wherein the vibration displacement equation of the beam in the beam pipeline vibration model is: Where, E represents the elastic modulus, I represents the section moment of inertia; EI represents the bending stiffness of the beam; Indicates the variation of beam deflection with beam length; ρ A Indicates line density; represents the second-order derivative of the deflection with time, that is, the acceleration of the beam; F vib (z, t) represents the distributed load along the length of the pipeline; F Cor F stands for Coriolis force; Cen Represents centrifugal force.

3. The method according to claim 2, characterized in that The method of using a pseudo fluid model to numerically simulate a deep-sea mining pipeline to obtain a deep-sea mining numerical simulation result includes: Discretizing the Navier-Stokes equation, the convection-diffusion equation, and the vibration control equation of the beam and converting them into discrete equations; The discrete equation is solved by a high-precision iterative method to obtain the numerical simulation result of deep-sea mining.

4. The method according to claim 3, characterized in that The method of solving the discrete equation by a high-precision iteration method to obtain the deep-sea mining numerical simulation result includes: According to the discrete equation, the effective density, the effective viscosity and the velocity field formula, the predicted velocity field is obtained, and the velocity field formula is as follows: Among them, u represents the velocity field; u n represents the value of the velocity field in the previous time step; Δt represents the time step; u n ·▽u n represents the convection term of the velocity field; ρ eff represents the effective density; ▽p n represents the pressure gradient term; μ eff represents effective viscosity; ▽·[μ eff (▽u n +(▽u n ) T )] represents the viscous force term; F vib Represents the effect of external vibration force applied in the fluid on the velocity field; Substituting the predicted velocity field into the continuity equation, the pressure correction equation is obtained, which is as follows: A p p′=b Among them, A p is the pressure correction coefficient matrix; p′ represents the pressure correction value; b is the source term vector; updating the velocity field, the pressure field and the vibration displacement of the beam according to the pressure correction equation; updating the effective density and the effective viscosity according to the updated velocity field and the particle concentration distribution at different time steps; The operations of obtaining the predicted velocity field to updating the effective density and the effective viscosity are cyclically performed until the changes in the velocity field and the pressure field meet the convergence criterion, thereby obtaining the deep-sea mining numerical simulation result.

5. The method according to claim 4, characterized in that The updating of the effective density and the effective viscosity according to the updated velocity field and the particle concentration distribution at different time steps includes: The density and viscosity of the solid-liquid mixture are measured by an experimental device to determine the standard effective density and standard effective viscosity; Respectively comparing the standard effective density and the standard effective viscosity with the effective density and the effective viscosity to calculate the error; If the error is greater than a preset value, the operation of updating the effective density and the effective viscosity according to the updated velocity field and the particle concentration distribution at different time steps is performed.

6. The method according to claim 1, characterized in that The boundary conditions for defining the inlet and outlet of the deep-sea mining pipeline include: defining a fixed flow rate and particle concentration at an inlet of said deep sea mining pipeline; A fixed pressure is defined at the outlet of the deep sea mining pipeline.

7. A deep-sea mining numerical simulation device based on a pseudo-fluid model, characterized in that: The device comprises: A setting unit is used to set the initial velocity field, initial pressure field and initial particle concentration distribution in the pipeline; Define units to define the boundary conditions of the pipeline inlet and outlet; The numerical simulation unit is used to perform numerical simulation on the deep-sea mining pipeline using a pseudo-fluid model to obtain the deep-sea mining numerical simulation results, wherein the deep-sea mining numerical simulation results include pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity.

8. The device according to claim 7, characterized in that The device also includes: An obtaining unit is used to perform weighted average of the density of solid particles and the density of liquid according to the particle volume fraction to obtain an effective density; The obtaining unit is further used to obtain the effective viscosity according to the particle volume fraction and the viscosity of the base fluid; A determination unit is used to determine the Navier-Stokes equation in the pseudo fluid model by using the effective density and the effective viscosity as: Among them, ρ eff represents effective density, u represents velocity field; ▽ represents the divergence or contraction of vector field in space; t represents time, i.e. represents the rate of change of velocity field over time; p represents pressure field; μ eff represents effective density; g represents gravity; F vib Represents the effect of external vibration force applied in the fluid on the velocity field; A construction unit is used to construct a convection-diffusion equation according to the particle volume fraction, wherein the convection-diffusion equation is: in, represents the rate of change of the scalar field φ over time; u represents the velocity field; ▽ represents the divergence operator; D φ represents the diffusion coefficient, which describes the diffusion rate of the scalar field φ; φ represents the scalar field; The construction unit is also used to construct a pipeline vibration model of the beam, wherein the vibration displacement equation of the beam in the pipeline vibration model of the beam is: Where, E represents the elastic modulus, I represents the section moment of inertia; EI represents the bending stiffness of the beam; Indicates the variation of beam deflection with beam length; ρ A Indicates line density; represents the second-order derivative of the deflection with time, that is, the acceleration of the beam; F vib (z, t) represents the distributed load along the length of the pipeline; F Cor F stands for Coriolis force; Cen Represents centrifugal force.

9. An electronic device, characterized in that: The device includes a memory and a processor, and the electronic device is used to execute a program stored in the memory to run the method according to any one of claims 1 to 6.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium is used to store a computer program, and the computer program is used to execute the method according to any one of claims 1 to 6.

Images