Pipeline solid-liquid two-phase flow prediction method and device and storage medium

Abstract

The invention provides a pipeline solid-liquid two-phase flow prediction method and device and a storage medium. The method comprises the steps that working conditions of a to-be-tested mineral hydraulic conveying pipeline are collected; a turbulence diffusion term # imgabs0 # # imgabs1 # is introduced to represent turbulence viscosity, subscript T represents a phase state type, when T is equal to L, the subscript T represents a liquid phase, when T is equal to S, the subscript T represents a solid phase, phi T represents a phase local average volume fraction, sigma is a turbulence diffusion coefficient and needs to be calibrated in advance; establishing a solid-liquid two-phase mass conservation equation and a solid-liquid two-phase momentum conservation equation considering the influence of the turbulence diffusion term # imgabs2 # so as to construct a single-parameter double-fluid model; and inputting the collected working conditions of the to-be-measured mineral hydraulic conveying pipeline into the constructed two-fluid model, solving the working conditions, and outputting parameters for predicting pipeline solid-liquid two-phase flow behavior. The method is high in prediction efficiency and precision, only one parameter, namely the turbulence diffusion coefficient, needs to be calibrated, and the calibration of model parameters and the complexity of application are simplified.

Description

Technical Field

[0001] The present invention belongs to the field of hydraulic calculation for pipeline transportation in seabed mining, and in particular relates to a pipeline solid-liquid two-phase flow prediction method, device and storage medium based on the Euler method. Background Art

[0002] Seabed mining is an important area in global resource development. Its special environment and complex working conditions place extremely strict requirements on pipeline transportation. Traditionally, the design and operation management of seabed mining pipelines face multiple challenges, including high pressure, low temperature, multiphase flow in the seabed environment, and corrosion in seawater. Effective pipeline design is not only related to the efficiency of resource extraction, but also directly affects environmental protection and ecological balance. Solid-liquid two-phase flow is one of the core issues in the design of seabed mining pipelines. The transportation behavior of solid particles in the pipeline directly affects the degree of pipeline wear, energy consumption and system stability. Therefore, it is crucial to accurately predict and optimize the solid-liquid two-phase flow performance.

[0003] The prediction technology of solid-liquid two-phase flow performance in seabed mining pipeline transportation currently mainly relies on empirical formulas and simplified models. However, these traditional methods often fail to provide sufficient accuracy and reliability in complex seabed environments. With the advancement of computer technology and numerical simulation methods, computational fluid dynamics (CFD) has become a powerful tool that can simulate and analyze various flow phenomena in complex fluid systems. At present, the numerical methods used to predict pipeline two-phase flow mainly include Lagrangian method and Eulerian method. Considering the computational efficiency, the former is generally applicable to scenarios with a solid particle volume fraction of less than 10%, while the latter highlights its advantages in predicting pipeline transportation of high-concentration minerals. Since the traditional Eulerian two-fluid model is coupled with the complex Kinetic Theory of Granular Flow (KTGF), there are many parameters that need to be calibrated, which makes it difficult to apply and the prediction speed is slow. Therefore, it is urgent to develop an efficient prediction method for pipeline solid-liquid two-phase flow based on the Euler method, which can quickly clarify the solid-liquid two-phase flow characteristics of seabed mining pipeline transportation. Summary of the invention

[0004] The present invention aims to solve the problems of low efficiency, low accuracy and complicated application of existing pipeline solid-liquid two-phase flow prediction methods. The present invention proposes an efficient pipeline solid-liquid two-phase flow prediction method based on the Euler method, and its main innovations include: (1) The prediction method is more theoretical, using the Euler method (two-fluid) to describe the solid-liquid two-phase flow in the pipeline, and by solving the NS equations (Navier-Stokes equations), accurately calculates key parameters such as particle volume fraction, flow velocity, turbulence parameter distribution and hydraulic gradient along the pipeline; (2) The model is relatively simple, with only one parameter that needs to be calibrated - the turbulent diffusion coefficient v, which greatly simplifies the complexity of parameter calibration and application compared with the traditional complex two-phase flow model.

[0005] In order to achieve the above objectives, the present disclosure adopts the following technical solutions:

[0006] A first aspect of the present disclosure provides a pipeline solid-liquid two-phase flow prediction method, comprising:

[0007] Collect the working conditions of the hydraulic pipeline of the mineral to be tested, including pipeline diameter, mixture velocity, mineral in-situ concentration, solid phase density, particle median size, liquid phase density and liquid phase dynamic viscosity;

[0008] Introducing turbulent diffusion terms represents turbulent viscosity, subscript T represents phase type, T=L represents liquid phase, T=S represents solid phase, Φ T represents the local average volume fraction of the phase, σ is the turbulent diffusion coefficient, which needs to be calibrated in advance; establish a turbulent diffusion term The affected solid-liquid two-phase mass conservation equation and solid-liquid two-phase momentum conservation equation are used to construct a single-parameter two-fluid model;

[0009] The collected working conditions of the hydraulic pipeline for the mineral to be tested are input into the dual-fluid model, which is solved to output parameters for predicting the behavior of the solid-liquid two-phase flow in the pipeline, including the velocity distribution of key sections, mineral concentration distribution, turbulence characteristics and hydraulic gradient.

[0010] In some embodiments, the operating conditions of the mineral hydraulic pipeline to be tested are collected based on engineering design data and pipeline operating conditions.

[0011] In some embodiments, the mathematical expression of the solid-liquid two-phase mass conservation equation is:

[0012]

[0013] Where t represents time; ρ T represents phase density; U T represents the phase velocity vector.

[0014] In some embodiments, the mathematical expression of the solid-liquid two-phase momentum conservation equation is:

[0015]

[0016] Where t represents time; ρ T represents phase density; U T represents the phase velocity vector; P L represents the liquid phase pressure; g is the acceleration due to gravity; μ T and denote the phase dynamic viscosity and phase turbulent viscosity, respectively; represents the momentum transfer term, which only considers the drag force between the liquid and solid phases.

[0017] In some embodiments, the mathematical expression of the two-fluid model is:

[0018]

[0019] μ m =Φ L μ L +Φ S μ S (4)

[0020]

[0021] in,

[0022] Formula (1) is the mass conservation equation of the solid-liquid two-phase, formula (2) is the momentum conservation equation of the solid-liquid two-phase, and formulas (3) to (13) are closed equations;

[0023] t represents time; ρ T represents phase density; Φ T ,U T ,P L represent the local average volume fraction of the phase, the phase velocity vector and the liquid phase pressure respectively; μ T and represent the phase dynamic viscosity and phase turbulent viscosity respectively; C in Indicates the in-situ concentration of minerals; μ m represents the viscosity of the mixture; g represents the acceleration due to gravity; represents the momentum transfer term, which only considers the drag force between the liquid and solid phases; C d represents the drag coefficient; d p Indicates the median particle size of solid particles; k L and ε L represent the liquid phase turbulent kinetic energy and its dissipation rate respectively; σ kL , σ εL , C μLis a set of empirical parameters; P kL represents the volumetric generation rate of turbulent kinetic energy; represents the solid wall shear stress; represents the flow velocity of the first layer of grid parallel to the pipe wall; S S represents the solid friction coefficient; δ represents the distance from the inner wall of the pipe to the center of the first layer of grid; κ represents the von Karman constant; E represents the roughness parameter of the pipe; represents the solid wall Reynolds number.

[0024] In some embodiments, σ kL =1.0,σ εL =1.314, C μL =0.09; k=0.4; for hydraulically smooth pipes, E=8.6.

[0025] In some embodiments, the open source platform OpenFOAM is used to construct and solve the two-fluid model of the pipeline to be tested.

[0026] In some embodiments, solving the two-fluid model specifically includes:

[0027] Step S31, according to the actual simulation scenario, use blockMesh to establish the geometric model of the mineral hydraulic pipeline to be tested, divide it into grids, set the boundary conditions, initial conditions and known parameters of the model, and complete the initialization of the geometric model;

[0028] Step S32: Enter the solid-liquid two-phase mass conservation equation cycle to solve the local average volume fraction Φ of the phase T , specifically:

[0029] The solid phase local average volume fraction equation is solved by the MULES algorithm, and implicit under-relaxation is applied to the coefficient matrix of the linear algebraic equations shown in formulas (15) to (16) to obtain the solid phase local average volume fraction Φ S ; Calculate the local average volume fraction of liquid phase Φ L =1-Φ S ; Repeat the above steps until the convergence criterion is met;

[0030] Step S33: Calculate and update the mixture viscosity μ in the solid-liquid two-phase momentum conservation equation using the updated phase local average volume fraction m and the drag coefficient C d ; Calculate and update the dynamic viscosity μ of the solid phase using the updated local average volume fraction of the phase S ; Calculate the friction coefficient S corresponding to the wall shear stress caused by the solid phase S ;

[0031] Step S34: After omitting the pressure term, buoyancy term and explicit drag force term in formula (2), discretization is performed using the finite volume method to obtain the following algebraic expression:

[0032] A L,P U L,P +ΣA L,N U L,N =S L,P (15)

[0033] A S,P U S,P +ΣA S,N U S,N =S S,P (16) Among them, A L,P The coefficient matrix representing the linear algebraic equations for the current control volume from the discretization of the fluid phase momentum conservation equation, A S,P represents the coefficient matrix of the linear algebraic equations of the current control volume from the discretization of the solid phase momentum conservation equation, and the subscripts P and N represent the current control volume and its adjacent volume discretized based on the finite volume method, respectively; S L,P and S S,P They represent the source term from the discretized liquid phase momentum conservation equation and the source term from the discretized solid phase momentum conservation equation respectively;

[0034] Step S35: By solving formula (15) and formula (16), and adding the previously omitted pressure term, buoyancy term, and explicit drag force term, the predicted velocity U of the liquid phase of the discretized current control volume is obtained: L,P and the predicted velocity U of the solid phase S,P and the interface momentum transfer coefficient C LS,P , the calculation formula is as follows:

[0035]

[0036] Among them, HbyA L,P , HbyA S,P Respectively represent the predicted velocity of the liquid phase and the predicted velocity of the solid phase calculated after removing the pressure term, buoyancy term and explicit drag force term; Φ L,P , Φ S,P They represent the local average volume fraction of the liquid phase and the local average volume fraction of the solid phase in the discretized current control volume respectively; P rgh,P represents the pressure term corresponding to the discretized current control volume without hydrostatic pressure; h P Represents the water elevation corresponding to the discretized current control volume;

[0037] Liquid velocity flux on each discretized grid surface Solid phase velocity flux and the interface momentum transfer coefficient CLS,f Then:

[0038]

[0039] Wherein, the subscript f represents the discretized mesh surface based on the finite volume method; A L,f , A S,f HbyA represents the coefficient matrix of the linear algebraic equations on the discretized mesh surface from the liquid phase momentum conservation equation and the solid phase momentum conservation equation respectively; L,f , HbyA S,f They represent the predicted liquid velocity and solid velocity of the discretized mesh surface calculated after removing the pressure term, buoyancy term and explicit drag force term; Φ L,f , Φ S,f represent the local average volume fraction of the liquid phase and the local average volume fraction of the solid phase on the discretized grid surface respectively; P rgh,f represents the pressure term corresponding to the discretized mesh surface excluding the hydrostatic pressure; ρ L,f , S,f Represent the liquid density and solid density of the discretized grid surface respectively; U L,f , U S,f represent the predicted velocity of the liquid phase and the predicted velocity of the solid phase on the discretized grid surface respectively; h f represents the water elevation corresponding to the discretized grid surface, S f is the discretized grid surface area;

[0040] Step S36: Update the interpolation value Φ of the phase volume fraction and the interface momentum transfer coefficient on the grid surface T,f , C LS,f ; Calculate the coefficient matrix A of the linear algebraic equations of the discretized mesh surface by interpolation L,f and A S,f ;

[0041] Step S37, enter the pressure equation loop, and change formula (1) into the following discrete form:

[0042] ∑(Φ L,f U L +Φ S,f U S )·S f =0 (22)

[0043] Step S38: Substitute the phase velocity flux expressed by formulas (20) and (21) into formula (22): and Replace U in formula (22) L and U S , then we get the pressure Poisson equation:

[0044]

[0045] in, and represent the liquid phase velocity and solid phase velocity without considering the pressure correction, respectively;

[0046] Step S39: After correcting the phase velocity flux represented by formulas (20) and (21) by using the new pressure field obtained by solving formulas (23) to (25), the liquid phase velocity at the center of the grid can be obtained by reconstructing the grid surface velocity flux. and solid phase velocity

[0047]

[0048] Thus, all variables corresponding to this time step are obtained, including the phase velocity at the center of the grid, the local average volume fraction of the phase, and the pressure;

[0049] Step S310, solving the turbulence equations represented by formula (8) and formula (9);

[0050] Step S311: adjust the time step, repeat steps S312 to S310, and iterate until the convergence criterion is met or the maximum number of iterations is reached, and output parameters used to describe the behavior of the solid-liquid two-phase flow in the pipeline.

[0051] The second aspect of the present disclosure provides a pipeline solid-liquid two-phase flow prediction device based on the prediction method described in any embodiment of the first aspect of the present disclosure, comprising:

[0052] The first module is used to collect the working conditions of the hydraulic pipeline of the mineral to be tested, including the pipeline diameter, mixture velocity, mineral in-situ concentration, solid phase density, particle median size, liquid phase density and liquid phase dynamic viscosity;

[0053] The second module is used to introduce turbulent diffusion terms represents turbulent viscosity, subscript T represents phase type, T=L represents liquid phase, T=S represents solid phase, Φ T represents the local average volume fraction of the phase, σ is the turbulent diffusion coefficient; the turbulent diffusion term is established The affected solid-liquid two-phase mass conservation equation and solid-liquid two-phase momentum conservation equation are used to construct a single-parameter two-fluid model;

[0054] The third module is used to input the collected operating conditions of the mineral hydraulic transport pipeline to be tested into the constructed dual-fluid model, solve it, and output parameters for predicting the solid-liquid two-phase flow behavior of the pipeline, including flow velocity distribution in key sections, mineral concentration distribution, turbulence characteristics and hydraulic gradient.

[0055] A third aspect of the present disclosure provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the prediction method described in any embodiment of the first aspect of the present disclosure.

[0056] The present disclosure provides a pipeline solid-liquid two-phase flow prediction method, device and storage medium based on the Euler method, which can provide more accurate and reliable tools and methods for the design, operation and management of solid particle hydraulic transmission pipelines, and has the following characteristics and beneficial effects:

[0057] (1) The model itself has only one parameter that needs to be calibrated, and it is easy to use. The prediction accuracy is not lower than that of similar methods, and for some working conditions, the accuracy is improved.

[0058] (2) Apply simple and fast prediction methods to optimize the design of pipelines, reduce energy consumption and maintenance costs, and improve the control ability of solid-liquid two-phase flow, thereby improving production efficiency and safety.

[0059] (3) By efficiently and accurately predicting the solid-liquid two-phase flow in the pipeline, unnecessary resource waste and environmental impact can be reduced, and sustainable development can be promoted.

[0060] (4) Based on the continuously iterative and improved prediction method, we provide advanced technical support for enterprises in the field of seabed mining, enhance their market competitiveness, and promote technological progress and industry development. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is an overall flow chart of a pipeline solid-liquid two-phase flow prediction method provided by an embodiment of the first aspect of the present disclosure;

[0062] Figure 2 (a) is the comparison data between the prediction result obtained by using the prediction method provided by the embodiment of the first aspect of the present disclosure and the measured data; Figure 2 (b) is the comparison data of the prediction results obtained by using the prediction method provided by the embodiment of the first aspect of the present disclosure and the existing method;

[0063] Figure 3 It is a schematic diagram of the structure of an electronic device provided in an embodiment of the third aspect of the present disclosure. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0065] On the contrary, the present application covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present application as defined by the claims. Further, in order to make the public have a better understanding of the present application, some specific details are described in detail in the detailed description of the present application below. Those skilled in the art can fully understand the present application without the description of these details.

[0066] See also Figure 1 The first aspect of the present disclosure provides a pipeline solid-liquid two-phase flow prediction method based on the Euler method, comprising the following steps:

[0067] Step S1: collecting the working conditions of the hydraulic pipeline of the mineral to be tested, including the pipeline diameter, the mixture velocity, the in-situ concentration of the mineral, the solid phase density, the median particle size of the particles, the liquid phase density and the liquid phase dynamic viscosity;

[0068] Step S2: Introducing turbulent diffusion terms represents turbulent viscosity, subscript T represents phase type, T=L represents liquid phase, T=S represents solid phase, Φ T represents the local average volume fraction of the phase, σ is the turbulent diffusion coefficient, and σ is the only parameter that needs to be calibrated in the prediction method provided by the embodiment of the present disclosure; establish a method that takes into account the turbulent diffusion term The affected solid-liquid two-phase mass conservation equation and solid-liquid two-phase momentum conservation equation (i.e., NS equation) are used to construct a two-fluid model with a single parameter (i.e., turbulent diffusion coefficient σ);

[0069] Step S3: Input the operating conditions of the mineral hydraulic pipeline to be tested collected in step S1 into the two-fluid model constructed in step S2, solve it, and output parameters for predicting the solid-liquid two-phase flow behavior of the pipeline, including flow velocity distribution in key sections, mineral concentration distribution, turbulence characteristics and hydraulic gradient, to provide a scientific basis and theoretical reference for the safe and stable operation of the pipeline.

[0070] In some embodiments, in step S1, necessary parameters of the mineral hydraulic transport pipeline are collected according to engineering design data and operating conditions, including pipeline diameter, mixture velocity, mineral in-situ concentration, solid phase density, particle median size, liquid phase density and liquid phase dynamic viscosity.

[0071] In some embodiments, in step S2, in order to predict key information such as velocity field, turbulence field, volume fraction and pressure field of pipeline solid-liquid two-phase flow, it is necessary to construct a single-parameter two-fluid model based on the solid-liquid two-phase mass conservation equation and the solid-liquid two-phase momentum conservation equation and the corresponding closed equation, and divide the grid. The mathematical expression of the two-fluid model is as follows:

[0072]

[0073] μ m =Φ L μ L +Φ S μ S (4)

[0074]

[0075] in:

[0076] Formula (1) is the mass conservation equation of the solid-liquid two-phase, formula (2) is the momentum conservation equation of the solid-liquid two-phase, and formulas (3) to (13) are closed equations;

[0077] The italic t represents time; the subscript T represents the phase type, T=S represents solid phase, T=L represents liquid phase; ρ T is the phase density; Φ T ,U T ,P L represent the local average volume fraction of the phase, the phase velocity vector and the liquid phase pressure, respectively, which are the unsolved items of the two-fluid model constructed in this embodiment; μ T and are phase dynamic viscosity and phase turbulent viscosity respectively; C in is the mineral in-situ concentration; μ m is the viscosity of the mixture; g is the acceleration due to gravity; is the momentum transfer term, where only the drag force between the liquid and solid phases needs to be considered; C d is the drag coefficient; d p is the median particle size of solid particles; k L and ε L are the liquid phase turbulent kinetic energy and its dissipation rate respectively; σ kL , σ εL , C μL is a set of empirical parameters that are usually kept at the same values ​​as recommended for single-phase flow, i.e., σ kL =1.0,σ εL =1.314, C μL =0.09; P kL is the volumetric generation rate of turbulent kinetic energy; is the solid wall shear stress; is the flow velocity of the first layer of grid parallel to the pipe wall; S S is the solid friction coefficient; δ is the distance from the inner wall of the pipe to the center of the first grid layer; κ is the von Karman constant, whose value is 0.4; E is the roughness parameter of the pipe, and its value is 8.6 for a hydraulically smooth pipe; is the solid phase wall Reynolds number; an important feature of the two-fluid model constructed in this embodiment is that the turbulent diffusion term appears in all governing equations, which characterize the turbulent diffusion of particles. The phase diffusion term depends on the coefficient σ, which must be calibrated before application.

[0078] In some embodiments, the open source platform OpenFOAM is used to construct and solve the two-fluid numerical simulation model of the pipeline to be tested, and output parameters for predicting the solid-liquid two-phase flow behavior of the pipeline. Specifically: based on the existing twoPhaseEulerFoam solver of OpenFOAM, the four libraries in the twoPhaseEulerFoam solver folder, namely compressibleTwoPhaseSystem, compressibleEulerianInterfacialModels, phaseCompressibleTurbulenceModels and pUf, are modified respectively in the form of formula (1) to formula (13), and compiled in sequence in the above order. After success, it can be used to predict the flow velocity distribution, mineral concentration distribution, turbulence characteristics and important parameters of engineering concern such as hydraulic gradient in key sections. The specific steps are as follows:

[0079] Step S31: According to the actual simulation scenario, after using blockMesh to establish the pipeline geometry model and divide the grid, set the boundary conditions and initial conditions of the model in the 0 folder, such as the mixture velocity in the pipeline, the volume fraction of solid particles, the liquid phase turbulent kinetic energy and its dissipation rate, the phase turbulent viscosity, and the liquid phase pressure; set the gravitational acceleration g and the phase density ρ in the Constant folder. T , phase dynamic viscosity μ T , particle median diameter, drag force model (Formula (5) to Formula (7)), turbulence model (Formula (8) to Formula (10)) and turbulent diffusion coefficient σ; set the prediction time, output result step size, second-order discrete format and PIMPLE solution method in the System folder to complete the initialization of the two-fluid numerical simulation model of the pipeline to be tested.

[0080] Step S32: Enter the solid-liquid two-phase mass conservation equation (Formula (1)) loop to solve the local average volume fraction Φ of the phase T The solid phase local average volume fraction equation (Formula (14)) is solved by the MULES algorithm, and implicit under-relaxation is applied to the coefficient matrix of the linear algebraic equation system (Formula (15) to Formula (16)) to obtain the solid phase local average volume fraction Φ S ; Calculate the local average volume fraction of liquid phase Φ L =1-Φ S ; Repeat the above steps until the convergence criterion is met.

[0081]

[0082] Step S33: Use the updated phase local average volume fraction to calculate and update the mixture viscosity μ in the solid-liquid two-phase momentum conservation equation m (Formula (3)) and drag coefficient C d (Formula (6)); Use the updated phase local average volume fraction to calculate and update the dynamic viscosity μ of the solid phase S (Formula (4)); Calculate the friction coefficient S corresponding to the wall shear stress caused by the solid phase S (Formula (12)), after this step is completed, the PIMPLE algorithm corresponding to steps S34 to S35 is executed in sequence to calculate all variables corresponding to this time step;

[0083] Step S34: Substitute the pressure term (i.e. ) and the buoyancy term (i.e. Φ T ρ T g) and explicit drag force term After omitting, the finite volume method is used for discretization, and the following algebraic expression is obtained:

[0084] A L,P U L,P +ΣA L,N U L,N =S L,P (15)

[0085] A S,P U S,P +ΣA S,N U S,N =S S,P (16) Among them, A L,P The coefficient matrix representing the linear algebraic equations for the current control volume from the discretization of the fluid phase momentum conservation equation, A S,P represents the coefficient matrix of the linear algebraic equations of the current control volume from the discretization of the solid phase momentum conservation equation. The subscripts P and N respectively represent the current control volume (the solution region is divided into multiple subregions, each subregion corresponds to a control volume) and its adjacent volume based on the finite volume method, the same below; S L,P and S S,P They represent the source term from the discretization of the liquid phase momentum conservation equation and the source term from the discretization of the solid phase momentum conservation equation, respectively.

[0086] Step S35: By solving formula (15) and formula (16) and adding the previously omitted terms (i.e., pressure term, buoyancy term, and explicit drag force term), the predicted velocity U of the liquid phase of the discretized current control volume can be obtained: L,P and the predicted velocity U of the solid phase S,P and the interface momentum transfer coefficient C LS,P , the calculation formula is as follows:

[0087]

[0088] Among them, HbyA L,P Represents the predicted liquid velocity calculated after removing the pressure term, buoyancy term, and explicit drag force term, HbyA S,P represents the solid phase predicted velocity calculated after removing the pressure term, buoyancy term and explicit drag force term; Φ L,P , Φ S,P Respectively with Φ L , Φ S Correspondingly, it represents the local average volume fraction of the liquid phase and the local average volume fraction of the solid phase in the discretized current control volume; P rgh,P represents the pressure term corresponding to the discretized current control volume without hydrostatic pressure; h P Represents the water elevation corresponding to the current discretized control volume.

[0089] Liquid velocity flux on each discretized grid surface Solid phase velocity flux and the interface momentum transfer coefficient C LS,f Then:

[0090]

[0091]

[0092] Wherein, the subscript f represents the discretized mesh surface based on the finite volume method; A L,f The coefficient matrix representing the linear algebraic equations on the mesh surface from the discretization of the fluid phase momentum conservation equation, A S,f The coefficient matrix representing the system of linear algebraic equations on the mesh surface from the discretization of the solid phase momentum conservation equation; HbyA L,f Represents the predicted velocity of the liquid phase on the discretized mesh surface calculated after removing the pressure term, buoyancy term, and explicit drag force term, HbyA S,f represents the solid phase predicted velocity on the discretized mesh surface calculated after removing the pressure term, buoyancy term and explicit drag force term; Φ L,f , Φ S,f Respectively with Φ L , Φ S Correspondingly, it represents the local average volume fraction of the liquid phase and the local average volume fraction of the solid phase on the discretized grid surface; P rgh,f represents the pressure term corresponding to the discretized mesh surface excluding the hydrostatic pressure; ρ L,f , S,f Represent the liquid density and solid density of the discretized grid surface respectively; U L,f , U S,frepresent the predicted velocity of the liquid phase and the predicted velocity of the solid phase on the discretized grid surface respectively; h f represents the water elevation corresponding to the discretized grid surface, S f is the discretized mesh surface area.

[0093] Step S36: Update the interpolation value Φ of the phase volume fraction and the interface momentum transfer coefficient on the mesh surface T,f , C LS,f ; Calculate the coefficient matrix A of the linear algebraic equations of the discretized mesh surface by interpolation L,f and A S,f .

[0094] Step S37: Enter the pressure equation loop and change formula (1) into the following discrete form:

[0095] ∑(Φ L,f U L +Φ S,f U S )·S f =0 (22)

[0096] Step S38: Substitute the phase velocity flux expressed by formulas (20) and (21) into formula (22): and Replace U in formula (22) L and U S , then we get the pressure Poisson equation:

[0097]

[0098] in, and represent the liquid phase velocity and solid phase velocity without considering the pressure correction, respectively.

[0099] Step S39: After correcting the phase velocity fluxes represented by equations (20) and (21) by solving the new pressure field obtained by equations (23) to (25), the liquid phase velocity at the center of the grid can be obtained by reconstructing the grid surface velocity flux. and solid phase velocity

[0100]

[0101] Thus, all variables corresponding to this time step are obtained, including the phase velocity at the center of the grid, the local average volume fraction of the phase, and the pressure;

[0102] Step S310: Solve the turbulence equations represented by formula (8) and formula (9).

[0103] Step S311: Adjust the time step, repeat steps S312 to S310, and iterate until the convergence criterion is met or the maximum number of iterations is reached, and output parameters used to describe the behavior of the solid-liquid two-phase flow in the pipeline, including the predicted flow velocity distribution, mineral concentration distribution, turbulence characteristics and hydraulic gradient in the key section, thereby providing a scientific basis and theoretical reference for the safe and stable operation of the pipeline.

[0104] Validation of the embodiments of the present disclosure:

[0105] By comparing and verifying with experimental data and cases in existing literature (Matousek et al., 2002; Gillies et al., 2004; Kaushal and Tomita, 2017), it is found that the predicted solid volume fraction is in good agreement with the measured data, see Figure 2 (a) The predicted hydraulic gradient is only 15% different from the actual data, see Figure 2 (b) demonstrates the reliability and accuracy of this method in predicting the behavior of solid-liquid two-phase flow in pipelines. Figure 2 In (b), the vertical axis is the result predicted by the method of the embodiment of the present disclosure, the horizontal axis is the experimental observation result, and Own measurements is the experimental data conducted by the applicant.

[0106] A pipeline solid-liquid two-phase flow prediction device provided in an embodiment of the second aspect of the present disclosure includes:

[0107] The first module is used to collect the working conditions of the hydraulic pipeline of the mineral to be tested, including the pipeline diameter, mixture velocity, mineral in-situ concentration, solid phase density, particle median size, liquid phase density and liquid phase dynamic viscosity;

[0108] The second module is used to introduce turbulent diffusion terms represents turbulent viscosity, subscript T represents phase type, T=L represents liquid phase, T=S represents solid phase, Φ T represents the local average volume fraction of the phase, σ is the turbulent diffusion coefficient; the turbulent diffusion term is established The affected solid-liquid two-phase mass conservation equation and solid-liquid two-phase momentum conservation equation are used to construct a single-parameter two-fluid model;

[0109] The third module is used to input the collected operating conditions of the mineral hydraulic transport pipeline to be tested into the constructed dual-fluid model, solve it, and output parameters for predicting the solid-liquid two-phase flow behavior in the pipeline, including flow velocity distribution in key sections, mineral concentration distribution, turbulence characteristics and hydraulic gradient.

[0110] It should be noted that the above-mentioned explanation of the embodiment of a pipeline solid-liquid two-phase flow prediction method is also applicable to a pipeline solid-liquid two-phase flow prediction device of this embodiment, and will not be repeated here.

[0111] In order to implement the above embodiment, the embodiment of the present disclosure further proposes a computer-readable storage medium on which a computer program is stored. The program is executed by a processor to execute the pipeline solid-liquid two-phase flow prediction method of the above embodiment.

[0112] Reference below Figure 3 , which shows a schematic diagram of the structure of an electronic device suitable for implementing the embodiments of the present disclosure. It should be noted that the electronic device in the embodiments of the present disclosure may include but is not limited to mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), vehicle-mounted terminals (such as vehicle-mounted navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, servers, etc. Figure 3 The electronic device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present disclosure.

[0113] like Figure 3 As shown, the electronic device may include a processing device (e.g., a central processing unit, a graphics processor, etc.) 101, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 102 or a program loaded from a storage device 108 to a random access memory (RAM) 103. In the RAM 103, various programs and data required for the operation of the electronic device are also stored. The processing device 101, the ROM 102, and the RAM 103 are connected to each other via a bus 104. An input / output (I / O) interface 105 is also connected to the bus 104.

[0114] Typically, the following devices may be connected to the I / O interface 105: an input device 106 including, for example, a touch screen, a touch pad, a keyboard, a mouse, a camera, a microphone, etc.; an output device 107 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; a storage device 108 including, for example, a magnetic tape, a hard disk, etc.; and a communication device 109. The communication device 109 may allow the electronic device to communicate with other devices wirelessly or by wire to exchange data. Figure 3 An electronic device having various devices is shown, but it should be understood that it is not required to implement or possess all the devices shown. More or fewer devices may be implemented or possessed instead.

[0115] In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, the present embodiment includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program contains program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication device 109, or installed from the storage device 108, or installed from the ROM 102. When the computer program is executed by the processing device 101, the above-mentioned functions defined in the method of the embodiment of the present disclosure are executed.

[0116] It should be noted that the computer-readable medium disclosed above may be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present disclosure, a computer-readable storage medium may be any tangible medium containing or storing a program that may be used by or in combination with an instruction execution system, device or device. In the present disclosure, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, in which a computer-readable program code is carried. This propagated data signal may take a variety of forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. The computer readable signal medium may also be any computer readable medium other than a computer readable storage medium, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. The program code contained on the computer readable medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (radio frequency), etc., or any suitable combination of the above.

[0117] The computer-readable medium may be included in the electronic device, or may exist independently without being installed in the electronic device.

[0118] The computer-readable medium carries one or more programs. When the one or more programs are executed by the electronic device, the electronic device executes the pipeline solid-liquid two-phase flow prediction method.

[0119] Computer program code for performing the operations of the present disclosure may be written in one or more programming languages, or a combination thereof, including object-oriented programming languages, such as Java, Smalltalk, C++, python, and conventional procedural programming languages, such as "C-" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0120] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0121] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0122] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code that includes one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

[0123] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in combination with these instruction execution systems, devices or apparatuses. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in combination with these instruction execution systems, devices or apparatuses. More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk box (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or otherwise processing in a suitable manner if necessary, and then stored in a computer memory.

[0124] It should be understood that the various parts of the present application can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0125] A person of ordinary skill in the art may understand that all or part of the steps carried out in the above-mentioned embodiment method may be completed by instructing the relevant hardware through a program, and the developed program may be stored in a computer-readable storage medium, which, when executed, includes one of the steps of the method embodiment or a combination thereof.

[0126] In addition, each functional unit in each embodiment of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0127] The storage medium mentioned above may be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application. A person of ordinary skill in the art may change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A pipeline solid-liquid two-phase flow prediction method, characterized in that: include: Collect the working conditions of the hydraulic pipeline of the mineral to be tested, including pipeline diameter, mixture velocity, mineral in-situ concentration, solid phase density, particle median size, liquid phase density and liquid phase dynamic viscosity; Introducing turbulent diffusion terms represents turbulent viscosity, subscript T represents phase type, T=L represents liquid phase, T=S represents solid phase, Φ T represents the local average volume fraction of the phase, σ is the turbulent diffusion coefficient, which needs to be calibrated in advance; establish a turbulent diffusion term The affected solid-liquid two-phase mass conservation equation and solid-liquid two-phase momentum conservation equation are used to construct a single-parameter two-fluid model; The collected working conditions of the hydraulic pipeline for the mineral to be tested are input into the dual-fluid model, which is solved to output parameters for predicting the behavior of the solid-liquid two-phase flow in the pipeline, including the velocity distribution of key sections, mineral concentration distribution, turbulence characteristics and hydraulic gradient.

2. The prediction method according to claim 1, characterized in that: The operating conditions of the mineral hydraulic transmission pipeline to be tested are collected based on the engineering design data and pipeline operating conditions.

3. The prediction method according to claim 1, characterized in that: The mathematical expression of the solid-liquid two-phase mass conservation equation is: Where t represents time; ρ T represents phase density; U T represents the phase velocity vector.

4. The prediction method according to claim 1, characterized in that: The mathematical expression of the solid-liquid two-phase momentum conservation equation is: Where t represents time; ρ T represents phase density; U T represents the phase velocity vector; P L represents the liquid phase pressure; g is the acceleration due to gravity; μ T and denote the phase dynamic viscosity and phase turbulent viscosity, respectively; represents the momentum transfer term, which only considers the drag force between the liquid and solid phases.

5. The prediction method according to claim 1, characterized in that: The mathematical expression of the two-fluid model is: m m =φ L m L +φ S m S (4) in, Formula (1) is the mass conservation equation of the solid-liquid two-phase, formula (2) is the momentum conservation equation of the solid-liquid two-phase, and formulas (3) to (13) are closed equations; t represents time; ρ T represents phase density; φ T ,U T ,P L represent the local average volume fraction of the phase, the phase velocity vector and the liquid phase pressure respectively; μ T and represent the phase dynamic viscosity and phase turbulent viscosity respectively; C in Indicates the in-situ concentration of minerals; μ m represents the viscosity of the mixture; g represents the acceleration due to gravity; represents the momentum transfer term, which only considers the drag force between the liquid and solid phases; C d represents the drag coefficient; d p Indicates the median particle size of solid particles; k L and ε L represent the liquid phase turbulent kinetic energy and its dissipation rate respectively; σ kL , σ εL , C μL is a set of empirical parameters; P kL represents the volumetric generation rate of turbulent kinetic energy; represents the solid wall shear stress; represents the flow velocity of the first layer of grid parallel to the pipe wall; S S represents the solid friction coefficient; δ represents the distance from the inner wall of the pipe to the center of the first layer of grid; κ represents the von Karman constant; E represents the roughness parameter of the pipe; represents the solid wall Reynolds number.

6. The prediction method according to claim 5, characterized in that: σ kL =1.0,v εL =1.314, C μL =0.09; κ=0.4; for hydraulically smooth pipes, E=8.

6.

7. The prediction method according to claim 5, characterized in that: The open source platform OpenFOAM is used to construct and solve the two-fluid model of the pipeline to be tested.

8. The prediction method according to claim 5, characterized in that: Solving the two-fluid model specifically includes: Step S31, according to the actual simulation scenario, use blockMesh to establish the geometric model of the mineral hydraulic pipeline to be tested, divide it into grids, set the boundary conditions, initial conditions and known parameters of the model, and complete the initialization of the geometric model; Step S32: Enter the solid-liquid two-phase mass conservation equation cycle to solve the local average volume fraction Φ of the phase T , specifically: The solid phase local average volume fraction equation is solved by the MULES algorithm, and implicit under-relaxation is applied to the coefficient matrix of the linear algebraic equations shown in formulas (15) to (16) to obtain the solid phase local average volume fraction Φ S ; Calculate the local average volume fraction of liquid phase Φ L =1-Φ S ; Repeat the above steps until the convergence criterion is met; Step S33: Calculate and update the mixture viscosity μ in the solid-liquid two-phase momentum conservation equation using the updated phase local average volume fraction m and the drag coefficient C d ; Calculate and update the dynamic viscosity μ of the solid phase using the updated local average volume fraction of the phase S ; Calculate the friction coefficient S corresponding to the wall shear stress caused by the solid phase S ; Step S34: After omitting the pressure term, buoyancy term and explicit drag force term in formula (2), discretization is performed using the finite volume method to obtain the following algebraic expression: A L,P U L,P +∑A L,N U L,N =S L,P (15) A S,P U S,P +∑∑A S,N U S,N =S S,P (16) Among them, A L,P The coefficient matrix representing the linear algebraic equations for the current control volume from the discretization of the fluid phase momentum conservation equation, A S,P represents the coefficient matrix of the linear algebraic equations of the current control volume from the discretization of the solid phase momentum conservation equation, and the subscripts P and N represent the current control volume and its adjacent volume discretized based on the finite volume method, respectively; S L,P and S S,P They represent the source term from the discretized liquid phase momentum conservation equation and the source term from the discretized solid phase momentum conservation equation respectively; Step S35: By solving formula (15) and formula (16), and adding the previously omitted pressure term, buoyancy term, and explicit drag force term, the predicted velocity U of the liquid phase of the discretized current control volume is obtained: L,P and the predicted velocity U of the solid phase S,P and the interface momentum transfer coefficient C LS,P , the calculation formula is as follows: Among them, HbyA L,P , HbyA S,P Respectively represent the predicted velocity of the liquid phase and the predicted velocity of the solid phase calculated after removing the pressure term, buoyancy term and explicit drag force term; Φ L,P , Φ S,P They represent the local average volume fraction of the liquid phase and the local average volume fraction of the solid phase in the discretized current control volume respectively; P rgh,P represents the pressure term corresponding to the discretized current control volume without hydrostatic pressure; h P Represents the water elevation corresponding to the discretized current control volume; Liquid phase velocity flux on each discretized grid surface Solid phase velocity flux and the interface momentum transfer coefficient C LS,f Then: Wherein, the subscript f represents the discretized mesh surface based on the finite volume method; A L,f , A S,f HbyA represents the coefficient matrix of the linear algebraic equations on the discretized mesh surface from the liquid phase momentum conservation equation and the solid phase momentum conservation equation respectively; L,f , HbyA S,f They represent the predicted liquid velocity and solid velocity of the discretized mesh surface calculated after removing the pressure term, buoyancy term and explicit drag force term; Φ L,f , Φ S,f represent the local average volume fraction of the liquid phase and the local average volume fraction of the solid phase on the discretized grid surface respectively; P rgh,f represents the pressure term corresponding to the discretized mesh surface excluding the hydrostatic pressure; ρ L,f , S,f Represent the liquid density and solid density of the discretized grid surface respectively; U L,f , U S,f represent the predicted velocity of the liquid phase and the predicted velocity of the solid phase on the discretized grid surface respectively; h f represents the water elevation corresponding to the discretized grid surface, S f is the discretized mesh surface area; Step S36: Update the interpolation value φ of the phase volume fraction and the interface momentum transfer coefficient on the grid surface T,f , C LS,f ; Calculate the coefficient matrix A of the linear algebraic equations of the discretized mesh surface by interpolation L,f and A S,f ; Step S37, enter the pressure equation loop, and change formula (1) into the following discrete form: ∑(φ L,f IN L +φ S,f IN S )·WITH f =0 (22) Step S38: Substitute the phase velocity flux expressed by formulas (20) and (21) into formula (22): and Replace U in formula (22) L and U S , then we get the pressure Poisson equation: in, and represent the liquid phase velocity and solid phase velocity without considering the pressure correction, respectively; Step S39: After correcting the phase velocity flux represented by formulas (20) and (21) by using the new pressure field obtained by solving formulas (23) to (25), the liquid phase velocity at the center of the grid can be obtained by reconstructing the grid surface velocity flux. and solid phase velocity Thus, all variables corresponding to this time step are obtained, including the phase velocity at the center of the grid, the local average volume fraction of the phase, and the pressure; Step S310, solving the turbulence equations represented by formula (8) and formula (9); Step S311: adjust the time step, repeat steps S312 to S310, and iterate until the convergence criterion is met or the maximum number of iterations is reached, and output parameters used to describe the behavior of the solid-liquid two-phase flow in the pipeline.

9. A pipeline solid-liquid two-phase flow prediction device based on the prediction method according to any one of claims 1 to 8, characterized in that: include: The first module is used to collect the working conditions of the hydraulic pipeline of the mineral to be tested, including the pipeline diameter, mixture velocity, mineral in-situ concentration, solid phase density, particle median size, liquid phase density and liquid phase dynamic viscosity; The second module is used to introduce turbulent diffusion terms represents turbulent viscosity, subscript T represents phase type, T=L represents liquid phase, T=S represents solid phase, Φ T represents the local average volume fraction of the phase, σ is the turbulent diffusion coefficient; the turbulent diffusion term is established The affected solid-liquid two-phase mass conservation equation and solid-liquid two-phase momentum conservation equation are used to construct a single-parameter two-fluid model; The third module is used to input the collected operating conditions of the mineral hydraulic transport pipeline to be tested into the constructed dual-fluid model, solve it, and output parameters for predicting the solid-liquid two-phase flow behavior of the pipeline, including flow velocity distribution in key sections, mineral concentration distribution, turbulence characteristics and hydraulic gradient.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the prediction method according to any one of claims 1 to 8.

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