A numerical simulation method for deep sea mining based on pseudo fluid model and related equipment

Abstract

The present application discloses a method and related equipment for numerical simulation of deep-sea mining based on a pseudo-fluid model. In the above method, the initial velocity field, initial pressure field and initial particle concentration distribution in the deep-sea mining pipeline are first 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 pseudo-fluid model is used to simplify solid particles into pseudo-fluids, thereby introducing effective density and effective viscosity. The effective density and effective viscosity can be used to perform numerical simulation of the deep-sea mining pipeline. Compared with the traditional algorithm calculation, it not only simplifies the calculation complexity, but also improves the efficiency of numerical simulation.

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 involves extracting minerals from the seafloor and transporting them to the surface. Numerical simulations of solid-liquid two-phase flows are necessary to explore suitable flow field schemes for ore collection. However, the complex conditions of the deep-sea environment make these simulations extremely complex.

[0003] Although the methods used in the prior art can provide detailed information on particle motion, they are obviously insufficient in terms of computational efficiency and computational 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 simulations.

[0005] In a first aspect, the present application provides a method for numerical simulation of deep-sea mining 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 the boundary conditions for the inlet and outlet of deep-sea mining pipelines;

[0008] A pseudo-fluid model is used to perform numerical simulation on a deep-sea mining pipeline to obtain deep-sea mining numerical simulation results, which include 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 effective density is obtained by taking a weighted average of the density of the solid particles and the density of the liquid according to the particle volume fraction;

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

[0012] The Navier-Stokes equation in the pseudo-fluid model is determined based on 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 in time; u represents the velocity field; ▽ represents the divergence operator; D φ represents the diffusion coefficient, which describes the diffusivity 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, and EI represents the bending stiffness of the beam. Indicates the change of beam deflection with beam length; ρ A Indicates linear 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 represents the Coriolis force; F Cen Indicates 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] A high-precision iterative method is used to solve the discrete equations and 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 represents 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 based on 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, based on the updated velocity field and the particle concentration distribution at different time steps, update the effective density and effective viscosity, including:

[0035] Measure the density and viscosity of solid-liquid mixtures using 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 the 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] Setting unit, 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 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 averaging 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 based on 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 construction unit is used to construct the convection-diffusion equation based on the particle volume fraction, where the convection-diffusion equation is:

[0052]

[0053] 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 diffusivity of the scalar field φ; φ represents the scalar field;

[0054] The construction unit is further 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, and EI represents the bending stiffness of the beam. Indicates the change of beam deflection with beam length; ρ A Indicates linear 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 represents the Coriolis force; F Cen Indicates centrifugal force.

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

[0058] The conversion subunit is used to discretize the Navier-Stokes equations, convection-diffusion equations and beam vibration control equations 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] The predicted velocity field is obtained based on the discrete equation, effective density, effective viscosity and velocity field formula, which 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 represents 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, we obtain the pressure correction equation, 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 based on 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 to:

[0071] Measure the density and viscosity of solid-liquid mixtures using 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 the 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 including a memory and a processor:

[0078] Memory is used to store computer programs;

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

[0080] In a fourth aspect, the present application further provides a computer-readable storage medium for storing a computer program for executing the method provided in the first aspect above.

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

[0082] This application provides a method for numerical simulation of deep-sea mining based on a pseudo-fluid model. The method first sets the initial velocity field, initial pressure field, and initial particle concentration distribution within the deep-sea mining pipeline; then defines boundary conditions at the inlet and outlet of the deep-sea mining pipeline; and finally, uses the pseudo-fluid model to numerically simulate the deep-sea mining pipeline, obtaining deep-sea mining numerical simulation results. These deep-sea mining numerical simulation results include pressure distribution, velocity field, particle concentration distribution, effective density, and effective viscosity. In this process, the pseudo-fluid model is used to simplify solid particles into pseudo-fluids, thereby introducing effective density and effective viscosity. Using these effective density and effective viscosity, the deep-sea mining pipeline can be numerically simulated. Compared to traditional algorithm calculations, this method not only simplifies computational complexity but also improves numerical simulation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. 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 flow chart of an embodiment of a numerical simulation method for deep-sea mining based on a pseudo-fluid model provided in an embodiment of the present application;

[0085] Figure 2 A 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 apparatus 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 clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts 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 the relevant laws, regulations and standards of relevant countries and regions.

[0092] Currently, the numerical simulation of solid-liquid two-phase flows is extremely complex due to the complex conditions of deep-sea environments, such as high pressure, low temperature, and strong currents. While existing techniques such as the discrete element method (DEM) and the Euler-Lagrangian method can provide detailed information on particle motion, their practical application to numerical simulations is not only computationally inefficient but also consumes a lot of computing resources.

[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 simulations can be 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; and finally using a pseudo-fluid model to perform numerical simulation of 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 this application uses a pseudo-fluid model to simplify solid particles into a pseudo-fluid, thereby introducing effective density and effective viscosity. Effective density and effective viscosity can be used to perform numerical simulation of deep-sea mining pipelines. Compared with traditional algorithm calculations, this not only simplifies the computational 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 a pseudo-fluid model can be the deep-sea mining numerical simulation device based on a pseudo-fluid model provided in the embodiments of the present application. The deep-sea mining numerical simulation device based on a pseudo-fluid model can be carried in an electronic device or a functional module of an electronic device. The electronic device in the embodiments of the present application can be any device capable of implementing the deep-sea mining numerical simulation method based on a pseudo-fluid model provided in the embodiments of the present application, for example, an Internet of Things (IoT) device.

[0098] Figure 1 This is 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. This method can be applied to a device for numerical simulation of deep-sea mining based on a pseudo-fluid model, such as a device for numerical simulation of deep-sea mining based on a pseudo-fluid model. Figure 5 The deep sea mining numerical simulation device 500 based on the pseudo fluid model shown in FIG. 5 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: Set the initial velocity field, initial pressure field, and initial particle concentration distribution in the deep-sea mining pipeline.

[0101] To obtain deep-sea mining numerical simulation results, the present embodiment first sets the initial velocity field, initial pressure field, and initial particle concentration distribution within the deep-sea mining pipeline. Boundary conditions at the inlet and outlet of the deep-sea mining pipeline are then defined. Finally, a pseudo-fluid model is used to numerically simulate the deep-sea mining pipeline, obtaining deep-sea mining numerical simulation results. These results include pressure distribution, velocity field, particle concentration distribution, effective density, and effective viscosity. In the present embodiment, S101 prepares for subsequent numerical simulations.

[0102] During this process, in order to perform numerical simulation operations, it is first necessary to set initial conditions, that is, to set the initial velocity field, initial pressure field, and initial particle concentration distribution within the deep-sea mining pipeline. This ensures the convergence of the simulation and compliance with physical laws when the numerical model is subsequently performed. If the initial conditions are set improperly, it may cause divergence during the simulation process, that is, the calculation results may be unstable or fail to converge. For example, in fluid dynamics simulations, if the initial velocity field is set improperly, it may cause numerical oscillations or calculation failures during the calculation process. Therefore, reasonable initial conditions can reduce the number of iterations in the calculation process and improve calculation efficiency.

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

[0104] Boundary conditions are an integral part of numerical simulations; they define the behavior of variables or their derivatives at the boundaries of the solution region. In the numerical simulation setup of the present application, the boundary conditions at the inlet and outlet of the deep-sea mining pipeline depend on the specific simulation requirements and physical phenomena. There are two typical setup methods:

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

[0106] In this case, the flow rate, pressure, and particle concentration are set at the inlet and outlet of a deep-sea mining pipeline. This setting is often used to control the detailed state of the entire flow system, allowing the modeler to precisely control the flow from the entry to the exit of the system. This approach is often used when studying 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 a deep-sea mining pipeline are set to fixed values, while the pressure at the outlet is also set to a fixed value. This is a more common boundary condition setting, suitable for many fluid dynamics simulations, especially in industrial applications such as pipeline flow and chemical processes. This boundary condition simplifies the simulation complexity, allowing the focus to be on studying the behavior of the fluid within the pipeline or equipment rather than the detailed conditions 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 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.

[0111] In the examples of this application, a pseudo-fluid model is used to simulate the particle effects in solid-liquid mixed flows, ignoring the effects of particle collisions. This model normalizes the solid particles and the fluid, treating 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 densities of solid particles and fluid and the volume fraction of particles in the fluid. The effective density affects the inertia term in the fluid dynamics equation, and therefore directly affects the calculation of the velocity field and pressure field. Effective viscosity: 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 and 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 Indicates the maximum volume fraction of solid particles.

[0123] The above Krieger-Dougherty equation often appears in studies related to suspended 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 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 slip model can also be used to construct the velocity relationship between solid particles and internal flow. The solid-liquid slip 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 particles, 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 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. 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, and EI represents the bending stiffness of the beam. Indicates the change of beam deflection (w) with beam length (z); ρ A Indicates linear 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 and centrifugal forces mentioned above are calculated using a unified unit consisting of a linear superposition of fluid and particle units. The movement of fluid and particles can cause vibration and instability in the pipeline, which can be expressed as:

[0139] F Cor =-2m(Ω×v)

[0140] F Cen =mΩ×(Ω×r)

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

[0142] Assuming that the forced vibration is 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 length coordinate of the pipeline; and L represents the total length of the pipeline.

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

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

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

[0148] In this process, by constructing a pseudo-fluid model, the detailed tracking of particle motion is replaced by 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 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.

[0150] As an example, S103 may include: S1031, discretizing the Navier-Stokes equations, the convection-diffusion equations, and the vibration control equations 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 algorithms to gradually solve the state of each discrete unit, thereby approximately simulating the behavior of the entire physical system. (2) Algorithm implementation: Discretization allows the application of 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: During the discretization process, 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 become 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 equations, the convection-diffusion equations, and the beam vibration control equations into discrete equations in S1031 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 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 derivatives is the process of converting continuous time variables into discrete steps so that they can be simulated and solved 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 (n); ▽u represents the gradient of the velocity field, which describes 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; Indicates 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.) into a discrete form in numerical simulation so that it can be solved on a computer.

[0162] (3) Discretization of viscosity terms

[0163]

[0164] in, Indicates the divergence of a vector field at a certain point, acting on the viscous stress term; μ eff represents 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 term 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, and EI represents the bending stiffness of the beam. Indicates the change of beam deflection (w) with beam length (z); ρ A Indicates linear density; It represents the second 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 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 fluid velocity with space during movement; ρ eff represents the effective density; represents the pressure gradient term; μ eff represents 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] Then 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 linear density; represents the acceleration of the beam at the next time step (n+1); EI represents the bending stiffness of the beam; Indicates 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 pipe; ω represents the vibration frequency; t represents time; z represents the pipe length coordinate; and L represents the total length of the pipe.

[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's important to note that in numerical simulations, especially those involving solid-liquid two-phase flows such as pseudofluid models, effective density and effective viscosity are core parameters because they describe the overall fluid dynamics of the mixture. These parameters do have a significant impact on other variables in the simulation, such as the velocity field, pressure field, and structural response (e.g., the vibration displacement of a beam).

[0195] In this regard, the optimization parameters in the embodiments of the present application require updating the effective density and effective viscosity, that is, they need to be determined based on experimental data. The specific process may include: measuring the density and viscosity of the solid-liquid mixture using 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 effective viscosity, respectively, and calculating the error; if the error is greater than a preset value, executing the operation of updating the effective density and effective viscosity based on the updated velocity field and the particle concentration distribution at 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 measurement and simulation calibration.

[0197] (5) 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 pressure field meet the convergence criteria, and the deep-sea mining numerical simulation results are obtained.

[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 traditional methods, making it suitable for large-scale and long-term simulations. By comparing the calculation efficiency, the practical value of the pseudo-fluid model in engineering applications is demonstrated.

[0203] In addition, the embodiments of the present application can also optimize 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 deep-sea mining pipeline in and the particle concentration at the inlet of different deep-sea mining pipelines φ in The pressure drop under the condition 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] Higher flow rates generally create more resistance to flow through a pipe or system, which can lead to higher pressure drops. At high flow rates, particle movement is also affected, with stronger convection possible, and particles may not have enough time to settle.

[0208] Higher particle concentrations increase the fluid's viscosity and density, increasing the resistance to flow. Especially at high particle concentrations, particle-fluid interactions and interactions with each other can lead to greater pressure drops. High particle concentrations can cause blockages or increase friction, affecting flow and pressure distribution.

[0209] Pressure drop is the loss of pressure during fluid flow due to friction, flow resistance, and other factors. Pressure drop generally increases with higher flow rates and greater particle concentrations. During simulations, pressure drop under different operating conditions can be used to evaluate the system's energy efficiency and fluid transport capacity. Optimal operating conditions are typically found at the point where pressure drop is minimized while ensuring a reasonable particle concentration and a satisfactory flow rate.

[0210] (2) Flow stability analysis:

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

[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. The specific process may include:

[0213] (1) Pressure distribution:

[0214] Display the pressure distribution 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 diagrams to analyze particle motion in lift pipes. Identify potential flow instability areas through velocity field visualization.

[0217] Specifically, this includes: Velocity field display and analysis: By simulating and generating velocity field distribution maps, the flow behavior of particles and fluids in the lifting pipe can be clearly seen. This visualization method helps researchers intuitively analyze the movement trajectories of fluids and particles in the pipe.

[0218] Identifying Unstable Regions: In velocity field plots, unstable regions often manifest as sudden velocity changes or irregular flow patterns. These unstable regions may exhibit significant flow separation, vortices, or backflow. Streamline plots and velocity vector diagrams can be helpful in identifying these regions.

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

[0220] (3) Particle concentration distribution:

[0221] Displays particle concentration distribution maps to identify potential blockage areas. By analyzing particle concentration distribution, optimize pipeline design and operating parameters to avoid blockage.

[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 to Pipeline Design and Operating Parameters: Particle concentration distribution is closely related to pipeline design (e.g., pipe diameter, flow path structure) and operating parameters (e.g., flow rate, pressure). Uneven particle concentration distribution may be caused by improper pipeline design (e.g., a sharp change in diameter) or improper operating parameter settings (e.g., too low or too high a flow rate).

[0224] Optimization Goal: By analyzing the particle concentration distribution, researchers can optimize pipeline design and operating parameters to reduce particle accumulation and prevent blockage. Specific optimization measures may include adjusting flow rate or pressure to prevent particle deposition, modifying pipeline structure or materials to achieve a more uniform distribution of particles within the fluid, and introducing specialized mixing devices or designs to maintain a uniform particle flow.

[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 below.

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

[0228] S201: Construct a pseudo-fluid model.

[0229] This 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] Regarding this Figure 3 The pseudo-fluid model diagram shown here explains the pseudo-fluid model, in which solid particles (Particles): Figure 3 The particles are represented by small dots and are 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 is characterized by its effective density and effective viscosity to characterize the overall properties of the mixture. The specific formulas for the effective density and effective viscosity can be as shown in the above embodiment and are not 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; and (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, specifically: Figure 4 As shown in the figure, it includes the pipeline, vibration displacement and boundary conditions. In the figure, L is the pipeline length and F is the distributed load, which is represented by arrows and shows 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 of the simulation and compliance with physical laws 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, the initial velocity field (InitialVelocityField) is set to u0; the initial pressure field (InitialPressureField) is set to p0; the initial particle concentration (InitialParticleConcentration) is set to φ0.

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

[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 (Inlet Particle Concentration): set to φ in .

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

[0239] Since computers cannot directly process this continuous equation, it needs to be converted into a discrete form before it can be numerically solved. The specific discretization process includes: (1) discretization of the time derivative term; (2) discretization of the convection term; (3) discretization of the viscosity term; and (4) discretization of the beam vibration equation. The specific discretization process is shown in the above embodiment and will not be repeated 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 this. The specific process of obtaining the pressure correction equation is as shown in the above embodiment and will not be repeated 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 when 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 the vibration displacement of the 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 based on a method combining experiments and numerical simulations. Through experimental measurement and simulation calibration, the accuracy and reliability of the model parameters are guaranteed. The specific judgment process is shown in the above embodiment and will not be described in detail here.

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

[0249] Finally, when performing the deep-sea mining numerical simulation, 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, executing S210; 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 the numerical simulation process, that is, return to execute S205.

[0250] S210: If satisfied, 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.

[0251] This embodiment provides a deep-sea mining numerical simulation method based on a pseudo-fluid model. By applying the pseudo-fluid model to deep-sea mining numerical simulation, the calculation process is significantly simplified, simulation efficiency is improved, and key issues such as pressure drop calculation, particle distribution, and flow stability are addressed. Furthermore, by optimizing operating parameters such as lifting speed and particle concentration, the system ensures stable operation under various operating conditions. By optimizing operating parameters, equipment maintenance costs are reduced and economic benefits are improved. By reducing pressure drop and energy consumption, operating costs are lowered and economic benefits are 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] Definition unit 502, 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 deep-sea mining numerical simulation results, which include pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity.

[0256] Optionally, the apparatus 500 further includes:

[0257] An obtaining unit is used to perform weighted averaging 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 based on 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 construction unit is used to construct the convection-diffusion equation based on 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 diffusivity of the scalar field φ; φ represents the scalar field;

[0265] The construction unit is further 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, and EI represents the bending stiffness of the beam. Indicates the change of beam deflection with beam length; ρ A Indicates linear 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 represents the Coriolis force; F Cen Indicates centrifugal force.

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

[0269] The conversion subunit is used to discretize the Navier-Stokes equations, convection-diffusion equations and beam vibration control equations 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] The predicted velocity field is obtained based on the discrete equation, effective density, effective viscosity and velocity field formula, which 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 represents 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, we obtain the pressure correction equation, 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 based on 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 to:

[0282] Measure the density and viscosity of solid-liquid mixtures using 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 the 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 defining 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 the effect achieved by 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 embodiment of the present application further 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 Provided method.

[0292] In addition, the present application also provides a computer-readable storage medium for storing a computer program for executing Figure 1 or Figure 2 Provided method.

[0293] Through the description of the above embodiments, it can be known that those skilled in the art can clearly understand that all or part of the steps in the above embodiment methods can be implemented by means of software plus a general hardware platform. Based on this 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., and includes a number of instructions for enabling 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 or certain parts of the embodiments of the present application.

[0294] Each embodiment in this specification is described in a progressive manner. The same or similar parts between the embodiments can be referred to each other. 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. For the relevant parts, refer to the partial description of the method embodiment. The device embodiment described above is merely illustrative, in which the modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the goals of the solution of this embodiment. A person of ordinary skill in the art can understand and implement it without expending creative work.

[0295] The above description is merely an exemplary embodiment of the present application and is not intended to limit the scope of protection 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, wherein the deep-sea mining numerical simulation result includes pressure distribution, velocity field, particle concentration distribution, effective density and effective viscosity. The pseudo-fluid model includes a Navier-Stokes equation, a convection-diffusion equation and a vibration displacement equation of a beam. The Navier-Stokes equation is obtained according to the effective density and the effective viscosity. The effective density is obtained by weighted averaging the density of solid particles and the density of liquid according to the particle volume fraction. The effective viscosity is obtained by the particle volume fraction and the viscosity of the base fluid. The convection-diffusion equation is obtained according to the particle volume fraction. The vibration displacement equation of the beam is obtained according to the pipeline vibration model of the beam.

2. The method according to claim 1, characterized in that The process of constructing the pseudo fluid model includes: The Navier-Stokes equation is: 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 viscosity; g represents gravity; F vib Represents the effect of external vibration force applied in the fluid on the velocity field; 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 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.

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; 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; 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; A numerical simulation unit is used to perform numerical simulation on a 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. The pseudo-fluid model includes a Navier-Stokes equation, a convection-diffusion equation and a vibration displacement equation of a beam. The Navier-Stokes equation is obtained according to the effective density and the effective viscosity. The effective density is obtained by weighted averaging the density of solid particles and the density of liquid according to the particle volume fraction. The effective viscosity is obtained by the particle volume fraction and the viscosity of the base fluid. The convection-diffusion equation is obtained according to the particle volume fraction. The vibration displacement equation of the beam is obtained according to the pipeline vibration model of the beam.

8. The device according to claim 7, characterized in that The device also includes: An obtaining unit, configured to perform weighted averaging of the density of the solid particles and the density of the liquid according to the particle volume fraction to obtain the 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 by transforming the effective density and the effective viscosity into: 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 viscosity; 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 the 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 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; The construction unit is further 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.

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