Numerical simulation method of solid-liquid two-phase in rotating flow channel based on multi-reference system

Abstract

The present invention relates to the field of multiphase numerical simulation, and discloses a numerical simulation method for solid-liquid two-phase in a rotating flow channel based on a multi-reference system. The method first obtains the rotating flow field generated by the multi-reference system method, and extracts the rotating domain information as well as the particle information and the fluid calculation domain grid information in the current time step. Secondly, the particles in the rotating domain and the particles outside the rotating domain are determined according to the rotating domain information and the particle information; the final flow field velocity and reconstructed porosity of the particles in the rotating domain and the particles outside the rotating domain are calculated respectively by combining the particle information and the fluid calculation domain grid information, and then the drag force is calculated according to the final flow field velocity, the reconstructed porosity and the particle information; at the same time, the Coriolis force and centrifugal force are calculated for the particles in the rotating domain according to the particle information and the rotating domain information. Finally, the drag force, Coriolis force and centrifugal force are iteratively calculated to obtain the particle information and grid information of the next time step, thereby realizing the numerical simulation calculation of the particle motion in the rotating flow channel under a fixed grid.

Description

Technical Field

[0001] The present application relates to the field of multiphase numerical simulation, and in particular to a method for numerical simulation of solid-liquid two-phases in a rotating flow channel based on multiple reference frames. Background Art

[0002] In rotating mechanical equipment such as mixing pumps and agitators, solid-liquid two-phase flow is widely present, and the internal flow patterns are complex. The interaction between particles and fluid has an important impact on the operating stability, energy efficiency and wear characteristics of the equipment. In order to deeply understand the motion behavior of particles in rotating flow channels, numerical simulation has become an important means. In the existing technology, the sliding grid method is used to simulate solid-liquid two-phase flow in rotating flow channels. This method requires updating the rotating area grid at each time step. Frequent grid updates lead to large consumption of computing resources. Especially under conditions of high particle concentration or large-scale particle intervention, the computational efficiency is significantly reduced. In addition, when the fluid calculation grid size is smaller than the particle size, the traditional non-analytical method cannot accurately characterize the local interaction between particles and fluid, affecting the accuracy of the simulation results and engineering usability. Summary of the Invention

[0003] To overcome these issues, the present invention provides a multi-reference-frame numerical simulation method for solid-liquid two-phase flow in a rotating flow channel. This method employs a multi-reference-frame approach, introducing a rotating coordinate system for the fluid domain and particles to achieve an equivalent representation of the rotational effect. Fluid-solid coupling calculations are performed on a fixed grid, avoiding the resource consumption associated with frequent grid updates. Furthermore, the drag force model is modified during particle force calculations to more accurately predict the particle trajectory and dynamic response in the rotating flow field, improving the simulation accuracy and stability.

[0004] According to a first aspect of an embodiment of the present application, a method for numerical simulation of solid-liquid two-phase in a rotating flow channel based on multiple reference frames is provided, comprising:

[0005] S1: Obtain the rotating flow field generated by the multi-reference system method;

[0006] S2: determining rotation domain information according to the rotating flow field;

[0007] S3: Get the particle information and fluid calculation domain grid information in the current time step;

[0008] S4: determining particles within the rotation domain and particles outside the rotation domain according to the rotation domain information and the particle information;

[0009] S5: Calculating the final flow field velocity and reconstructed porosity of the particles in the rotating domain and the particles outside the rotating domain respectively according to the particle information and the fluid calculation domain grid information;

[0010] S6: calculating the drag force according to the final flow field velocity, the reconstructed porosity and the particle information;

[0011] S7: Calculating the Coriolis force and the centrifugal force for the particles in the rotation domain according to the particle information and the rotation domain information;

[0012] S8: Iteratively calculating the drag force, Coriolis force, and centrifugal force to obtain particle information for the next time step;

[0013] S9: adding the drag force, Coriolis force and centrifugal force to the momentum equation in the form of source terms to iteratively calculate the motion of the fluid, and obtaining the fluid calculation domain grid information of the next time step;

[0014] S10: Determine whether the current time step is the last time step. If not, return to S3 to continue execution; if so, terminate the operation process and obtain the final particle information and fluid calculation domain grid information.

[0015] The technical solutions provided by the embodiments of the present application may have the following beneficial effects:

[0016] It can be seen from the above embodiments that the present application adopts multi-reference system technology to introduce rotating coordinate systems for fluids and particles respectively, and corrects the local flow field velocity and porosity information during the particle drag calculation process, overcoming the problem of large computing resource consumption caused by the traditional sliding grid method updating the grid at each time step, and the technical difficulty of inaccurate simulation results when the particle size is larger than the grid scale, thereby realizing the simulation of particles in a rotating flow field under a fixed grid.

[0017] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0019] Figure 1 The present invention is a flowchart of a method for numerical simulation of solid-liquid two-phase in a rotating flow channel based on multiple reference frames according to an exemplary embodiment.

[0020] Figure 2 FIG. 1 is a distribution cloud diagram of particles in the impeller area of ​​a mixed flow pump according to an exemplary embodiment.

[0021] Figure 3 3 is a velocity vector cloud diagram of particles in the impeller area of ​​a mixed flow pump according to an exemplary embodiment. DETAILED DESCRIPTION

[0022] Exemplary embodiments will be described in detail herein, with examples illustrated in the accompanying drawings. In the following description, when referring to the drawings, identical numerals in different figures represent identical or similar elements, unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all embodiments consistent with the present application. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present application, as detailed in the appended claims.

[0023] The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. As used in this application and the appended claims, the singular forms "a," "an," "the," and "the" are intended to include the plural forms, unless the context clearly indicates otherwise. It should also be understood that the term "and / or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

[0024] Figure 1 FIG. 1 is a flow chart showing a method for numerical simulation of solid-liquid two-phase in a rotating flow channel based on multiple reference frames according to an exemplary embodiment. Figure 1 As shown, the method may include the following steps:

[0025] S1: Obtain the rotating flow field generated by the multi-reference system method;

[0026] Specifically, the multi-reference frame method includes adding Coriolis force and centrifugal force source terms to the governing equation of the fluid phase of the solid-liquid two-phase solution algorithm.

[0027] In CFDEMcoupling, copy the cfdemSolverPiso folder and replace all file names and contents of cfdemSolverPiso with cfdemSolverPisoMRF;

[0028] (1) Enter the cfdemSolverPisoMRF.C file and add the code “MRF.correctBoundaryVelocity(U);” under “ / / Momentum predictor”. This code means that before the velocity prediction equation, the absolute velocity is subtracted from the circumferential velocity to obtain the relative velocity.

[0029] (2) In the cfdemSolverPisoMRF.C file, add the code “+ MRF.DDt(U)” before the equal sign in fvVectorMatrix Ueqn. This means that the Coriolis force and centrifugal force calculation formulas are added to the velocity prediction equation.

[0030] (3) In the cfdemSolverPisoMRF.C file, add “MRF.makeRelative(phi);” and “adjustPhi(phi, U, p);” in the two lines before “ / / Update the fixedFluxPressure BCsto ensure flux consistency”. Their meanings are respectively to subtract the additional flux of the rotating reference frame relative to the grid surface from the absolute flux to obtain the relative flux; and to correct the flux by adjusting the pressure field and velocity field until convergence and satisfying the continuity equation.

[0031] (4) In the cfdemSolverPisoMRF.C file, comment out #include "fixedFluxPressureHandling.H" and add the following lines:

[0032] if (modelType=="A")

[0033] {

[0034] volScalarField rUsed = rUA*voidfraction;

[0035] constrainPressure(p, U, phi, rUsed, MRF);

[0036] }

[0037] else constrainPressure(p, U, phi, rUA, MRF);

[0038] To adapt to the correction of pressure boundary conditions in multiple reference frames.

[0039] (5) Enter the createField.H file and add #include "createMRF.H" to the bottom line to indicate that the multi-reference frame calculation method is included in the initialization field variables.

[0040] (6) Go to the cfdemSolverPisoMRF folder, open the terminal, and enter wmake to complete the compilation.

[0041] With the introduction of the multi-reference frame feature, the influence of rotational non-inertial forces can be considered in the fluid phase, allowing the use of a fixed grid to simulate rotational flows, significantly reducing computational overhead and facilitating the subsequent calculation of additional rotational forces in the particle phase.

[0042] S2: determining rotation domain information according to the rotating flow field;

[0043] Specifically, the rotational domain information includes the angular velocity, radius, and coordinates of the highest and lowest points in the rotational domain. The rotational flow field information generated in OpenFOAM, including the angular velocity, radius, and coordinates of the highest and lowest points in the rotational domain, is transferred to LIGGGHTS via the CFDEM coupling interface to synchronize information between the particles and the rotating flow field, improving the physical rationality of the mechanical coupling and the simulation accuracy.

[0044] S3: Get the particle information and fluid calculation domain grid information in the current time step;

[0045] Specifically, the particle information includes particle position coordinates, particle size, particle density and particle velocity, and the fluid calculation domain grid information includes grid position coordinates, grid volume, grid porosity and flow field velocity.

[0046] LIGGGHTS first performs dynamic calculations on the particles, solving their equations of motion based on the forces acting on them to obtain particle position coordinates, particle size, density, and velocity. This particle information is then passed to CFDEM coupling, which uses OpenFOAM to extract the fluid computational domain mesh information, including mesh position coordinates, mesh volume, mesh porosity, and flow field velocity. This systematically obtains accurate data on both the particles and the mesh.

[0047] S4: determining particles within the rotation domain and particles outside the rotation domain according to the rotation domain information and the particle information;

[0048] Specifically, the particle position coordinates, particle size and rotation domain information are used to determine whether the particle is in the rotation domain. If so, it is considered as a particle in the rotation domain. The details are as follows: x 、 y 、 z weight, when and z When the particle is located within the coordinate interval corresponding to the highest point and the lowest point of the rotation domain, it is determined to be a particle within the rotation domain; x, y, z are the particle position coordinate components, d p is the particle size, R is the radius of rotation;

[0049] If not, the particle is determined to be an out-of-rotation particle.

[0050] This step selects particles within the rotation domain through geometric relationships, providing a basis for subsequent calculations of particles inside and outside the rotation domain using different methods.

[0051] S5: Calculating the final flow field velocity and reconstructed porosity of the particles in the rotating domain and the particles outside the rotating domain respectively according to the particle information and the fluid calculation domain grid information;

[0052] Specifically, we first search through the grid where the particle center is located, starting from the center grid, and use the neighboring grid search method to determine whether the distance between the center of the adjacent grid and the center of the particle is less than twice the particle diameter. If it is less, the grid is defined as a grid in the extended domain, and the relevant grid index is recorded to avoid subsequent repeated searches. This continues until all grids in the extended domain are searched. The grids in the above extended domain are used as the background flow field grids for the particle, and the flow field velocity of each grid is weighted by the kernel function to obtain the reconstructed flow field velocity. The porosity is obtained by the averaging method to obtain the reconstructed porosity, as follows:

[0053] ;

[0054] ;

[0055] in, To reconstruct the flow field velocity, ε i To reconstruct the porosity, ε j 、V cell,j and U f,j Respectively j The porosity, volume and flow velocity of each grid, H ( r i - r j ) is the kernel function ，r i For the i The particle position coordinates, r j For the j grid position coordinates;

[0056] The final flow field velocity is obtained by subtracting the circumferential velocity from the reconstructed background flow field velocity of the particles in the rotating domain. The calculation formula is as follows:

[0057] ;

[0058] in, is the final flow field velocity, ω is the angular velocity of rotation, r is the radial vector of the particle's spatial position relative to the rotation axis.

[0059] When the particle size is larger than the grid size of its center, traditional non-analytical methods can lead to inaccurate calculations of the background flow velocity and porosity. Therefore, by expanding the particle neighborhood and reconstructing the background flow field and porosity, the accuracy of the flow field effects on the particle can be improved. Furthermore, within the rotating region, the particle must adapt to the rotational characteristics of the flow field. By subtracting the circumferential velocity from the reconstructed flow field, the relative flow velocity can be obtained, which more accurately reflects the actual particle motion.

[0060] S6: calculating the drag force according to the final flow field velocity, the reconstructed porosity and the particle information;

[0061] Specifically, the calculation formula of the drag force is as follows:

[0062] ;

[0063] ;

[0064] in, V p is the particle volume, d p is the particle size, F d is the drag force, β d is the momentum exchange coefficient, ε i To reconstruct the porosity, is the final flow field velocity, U p is the particle velocity; where:

[0065] ;

[0066] ;

[0067] .

[0068] in, ρ f is the fluid density, C d is the drag coefficient, Re p is the particle Reynolds number, μ f is the dynamic viscosity.

[0069] This step introduces the corrected flow field velocity to effectively avoid the particle force error caused by the difference in grid scale.

[0070] S7: Calculating the Coriolis force and the centrifugal force for the particles in the rotation domain according to the particle information and the rotation domain information;

[0071] Specifically, when the particle is in the rotating region, the Coriolis force and the centrifugal force are additionally calculated. The calculation formulas of the Coriolis force and the centrifugal force are as follows:

[0072] ;

[0073] ;

[0074] ;

[0075] in, m p represents the particle mass, ρ p is the particle density, d p is the particle size, F Coriolis represents the Coriolis force, F Centrifugal represents the centrifugal force, ω is the angular velocity of rotation, r is the radial vector of the particle's spatial position relative to the rotation axis, U p is the particle velocity.

[0076] Introducing Coriolis force and centrifugal force in multiple reference frames helps to accurately describe the real motion behavior of particles in the rotating domain, compensates for the influence of non-inertial effects on particle trajectories, improves model accuracy, and provides support for analyzing phenomena such as particle migration and retention.

[0077] S8: Iteratively calculating the drag force, Coriolis force, and centrifugal force to obtain particle information for the next time step;

[0078] Specifically, LIGGGHTS solves the particle's equation of motion based on the forces acting on the particle, simultaneously accounting for inter-particle and wall collision forces, as well as dynamically coupled drag forces, and particle motion to determine the particle's position coordinates and velocity at the next time step. This ensures that the particle's dynamic response evolves synchronously with the fluid state, providing support for high-fidelity CFD-DEM modeling.

[0079] S9: adding the drag force, Coriolis force and centrifugal force to the momentum equation in the form of source terms to iteratively calculate the motion of the fluid, and obtaining the fluid calculation domain grid information of the next time step;

[0080] Specifically, the forces are uniformly converted into source terms and added to the momentum conservation equation in the governing equations. This is coupled with the existing fluid momentum equation to achieve multiphase mechanical linkage. During the numerical calculation process, an iterative solution method is used to solve the updated momentum equation to obtain the flow field velocity at the next time step of the particle interaction. This in turn updates the mesh information of the entire fluid computational domain, providing the flow field foundation for subsequent particle trajectory prediction.

[0081] S10: Determine whether the current time step is the last time step. If not, return to S3 to continue execution; if so, terminate the operation process and obtain the final particle information and fluid calculation domain grid information.

[0082] Specifically, after each calculation cycle, the system accumulates the time steps. If the accumulated time steps are less than the preset total time steps, the system returns to step S3 to continue updating the particle information and the fluid computational domain mesh information and performing the coupled calculation. If the accumulated time steps reach the preset total time steps, the system terminates the cycle and outputs the final particle state information and the fluid computational domain mesh data.

[0083] It can be seen from the above embodiments that the present invention introduces rotating coordinate systems for fluids and particles respectively based on the multi-reference system method, and corrects the local flow field velocity and porosity information during the particle drag calculation process, thereby overcoming the problem of large computing resource consumption caused by the traditional sliding grid method updating the grid at each time step, and the technical difficulty of inaccurate simulation results when the particle size is larger than the grid scale, thereby realizing the computational simulation of particles in a rotating flow field under a fixed grid.

[0084] Figure 2 This is the particle distribution diagram of the mixed flow pump impeller area. It can be clearly seen that the particles are mainly concentrated in the pressure surface area of ​​the blade, and the particle velocity gradually increases with the distance from the impeller center. Figure 3 The particle velocity vector diagram in the impeller area of ​​the mixed flow pump shows the movement direction and velocity change characteristics of the particles in the impeller area.

[0085] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the contents disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present application that follow the general principles of the present application and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered merely as exemplary, and the true scope and spirit of the present application are indicated by the claims.

[0086] It should be understood that the present application is not limited to the exact structures described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. A numerical simulation method for solid-liquid two-phase in a rotating flow channel based on multiple reference frames, characterized in that: include: S1: Obtain the rotating flow field generated by the multi-reference system method; S2: determining rotation domain information according to the rotating flow field; S3: Get the particle information and fluid calculation domain grid information in the current time step; S4: Determine particles within the rotation domain and particles outside the rotation domain according to the rotation domain information and the particle information; S5: Calculating the final flow field velocity and reconstructed porosity of the particles in the rotating domain and the particles outside the rotating domain respectively according to the particle information and the fluid calculation domain grid information; S6: Calculating the drag force according to the final flow field velocity, the reconstructed porosity, and the particle information; S7: Calculating the Coriolis force and the centrifugal force for the particles in the rotation domain according to the particle information and the rotation domain information; S8: Iteratively calculating the drag force, Coriolis force, and centrifugal force to obtain particle information for the next time step; S9: adding the drag force, Coriolis force and centrifugal force to the momentum equation in the form of source terms to iteratively calculate the motion of the fluid, and obtaining the fluid calculation domain grid information of the next time step; S10: Determine whether the current time step is the last time step. If not, return to S3 to continue execution; if so, terminate the operation process and obtain the final particle information and fluid calculation domain grid information.

2. The method for numerical simulation of solid-liquid two-phase in a rotating flow channel based on multiple reference frames according to claim 1, characterized in that: In S1, the multi-reference frame method includes adding Coriolis force and centrifugal force source terms to the governing equations of the fluid phase of the solid-liquid two-phase solution algorithm.

3. The method for numerical simulation of solid-liquid two-phase in a rotating flow channel based on multiple reference frames according to claim 1, characterized in that: In S2, the rotation domain information includes the rotation angular velocity, the rotation radius, and the coordinates corresponding to the highest point and the lowest point of the rotation domain.

4. The method for numerical simulation of solid-liquid two-phase in a rotating flow channel based on multiple reference frames according to claim 3, characterized in that: In S3, the particle information includes particle position coordinates, particle size, particle density and particle velocity, and the fluid calculation domain grid information includes grid position coordinates, grid volume, grid porosity and flow field velocity.

5. The method for numerical simulation of solid-liquid two-phase in a rotating flow channel based on multiple reference frames according to claim 4, characterized in that: In S4, particles within the rotation domain and particles outside the rotation domain are determined, including: The particle position coordinates, particle size and rotation domain information are used to determine whether the particle is in the rotation domain. If so, it is considered as a particle in the rotation domain. The details are as follows: x 、 y 、 z weight, when and z When the particle is located within the coordinate interval corresponding to the highest point and the lowest point of the rotation domain, it is determined to be a particle within the rotation domain; x, y, z are the particle position coordinate components, d p is the particle size, R is the radius of rotation; If not, the particle is determined to be an out-of-rotation particle.

6. The method for numerical simulation of solid-liquid two-phase in a rotating flow channel based on multiple reference frames according to claim 1, characterized in that: In S5, the final flow field velocity and reconstructed porosity of the particles inside and outside the rotating domain are calculated respectively, including: The flow field velocity and porosity of the particles are reconstructed to obtain the reconstructed flow field velocity and reconstructed porosity. The calculation formula is as follows: ； ； in, To reconstruct the flow field velocity, ε i To reconstruct the porosity, ε j 、V cell,j and U f,j Respectively j The porosity, volume and flow velocity of each grid, H ( r i - r j ) is the kernel function ，r i For the i The particle position coordinates, r j For the j grid position coordinates; The final flow field velocity is obtained by subtracting the circumferential velocity from the reconstructed background flow field velocity of the particles in the rotating domain. The calculation formula is as follows: ； in, is the final flow field velocity, ω is the angular velocity of rotation, r is the radial vector of the particle's spatial position relative to the rotation axis.

7. The method for numerical simulation of solid-liquid two-phase in a rotating flow channel based on multiple reference frames according to claim 6, characterized in that: In S6, the drag force is calculated as follows: ； ； in, V p is the particle volume, d p is the particle size, F d is the drag force, β d is the momentum exchange coefficient, ε i To reconstruct the porosity, is the final flow field velocity, U p is the particle velocity.

8. The method for numerical simulation of solid-liquid two-phase in a rotating flow channel based on multiple reference frames according to claim 1, characterized in that: In S7, the calculation formulas for the Coriolis force and the centrifugal force are as follows: ； ； ； in, m p represents the particle mass, ρ p is the particle density, d p is the particle size, F Coriolis represents the Coriolis force, F Centrifugal represents the centrifugal force, ω is the angular velocity of rotation, r is the radial vector of the particle's spatial position relative to the rotation axis, U p is the particle velocity.

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