Numerical simulation method for solid phase and liquid phase in rotating flow channel based on multiple reference systems

Abstract

The invention relates to the field of multiphase numerical simulation, and discloses a numerical simulation method for solid and liquid phases in a rotating flow channel based on multiple reference systems, which comprises the following steps of: firstly, acquiring a rotating flow field generated by a multiple reference system method, and extracting rotating domain information as well as particle information and fluid computational domain grid information in a current time step; secondly, particles in a rotation domain and particles outside the rotation domain are determined according to the rotation domain information and the particle information; in combination with the particle information and the fluid calculation domain grid information, the final flow field speed and the reconstructed porosity of the particles in the rotation domain and the particles outside the rotation domain are calculated respectively, and then the drag force is calculated according to the final flow field speed, the reconstructed porosity and the particle information; meanwhile, according to the particle information and the rotation domain information, the Korotkoff force and the centrifugal force of the particles in the rotation domain are calculated. Finally, drag force, Korotkoff force and centrifugal force are calculated through iteration, particle information and grid information of the next time step are obtained, and therefore numerical simulation calculation of particle motion in the rotating flow channel under the fixed grid is achieved.

Description

Technical Field

[0001] This application relates to the field of multiphase numerical simulation, and particularly to a numerical simulation method for solid-liquid two-phase flow in a rotating flow channel based on a multi-reference frame. Background Art

[0002] In rotating mechanical equipment such as mixed transport pumps and agitators, solid-liquid two-phase flow widely exists. Its internal flow pattern is complex, and the interaction between particles and fluid has an important impact on the operation stability, energy efficiency, and wear characteristics of the equipment. In order to deeply understand the motion behavior of particles in a rotating flow channel, numerical simulation has become an important means. In the prior art, the sliding mesh method is used to simulate the solid-liquid two-phase flow in a rotating flow channel. This method requires updating the mesh of the rotating region at each time step, and the frequent mesh update leads to large consumption of computing resources. Especially in the working conditions of high particle concentration or large-scale particle intervention, the calculation efficiency is significantly reduced. In addition, when the fluid calculation mesh size is smaller than the particle diameter, the traditional non-analytical method cannot accurately characterize the local interaction between particles and fluid, affecting the accuracy and engineering usability of the simulation results. Summary of the Invention

[0003] To overcome the above problems, the embodiments of this application provide a numerical simulation method for solid-liquid two-phase flow in a rotating flow channel based on a multi-reference frame. The present invention adopts the multi-reference frame method, and realizes the equivalent expression of the rotation effect by introducing a rotating coordinate system for the fluid domain and particles, and completes the fluid-structure interaction calculation under a fixed mesh, avoiding the resource consumption caused by frequent mesh update. At the same time, the drag force model is corrected in the calculation of the particle force to more accurately predict the motion trajectory and dynamic response of the particles in the rotating flow field, improving the accuracy and stability of the simulation.

[0004] According to the first aspect of the embodiments of this application, a numerical simulation method for solid-liquid two-phase flow in a rotating flow channel based on a multi-reference frame is provided, including: S1: Obtain a rotating flow field generated by the multi-reference frame method; S2: Determine the rotating domain information according to the rotating flow field; S3: Obtain the particle information and the mesh information of the fluid calculation domain at the current time step; S4: Determine the particles inside the rotating domain and the particles outside the rotating domain according to the rotating domain information and the particle information; S5: Calculate the final flow field velocity and the reconstructed porosity of the particles inside the rotating domain and the particles outside the rotating domain respectively according to the particle information and the mesh information of the fluid calculation domain; S6: Calculate the drag force according to the final flow field velocity, the reconstructed porosity, and the particle information; S7: Calculate the Coriolis force and the centrifugal force for the particles inside the rotating domain according to the particle information and the rotating domain information; S8: Obtain the particle information at the next time step through iterative calculation of the drag force, Coriolis force, and centrifugal force; S9: Add the drag force, Coriolis force, and centrifugal force to the momentum equation in the form of source terms for iterative calculation of the fluid motion, and obtain the grid information of the fluid computational domain at the next time step; S10: Determine whether the current time step is the last time step. If not, return to S3 and continue to execute; if so, terminate the operation process to obtain the final particle information and the grid information of the fluid computational domain.

[0005] The technical solutions provided by the embodiments of the present application may include the following beneficial effects: As can be seen from the above embodiments, the present application uses the multi-reference frame technology to introduce rotating coordinate systems for the fluid and particles respectively, and corrects the local flow field velocity and porosity information during the calculation of the particle drag force, overcoming the problems of large consumption of computing resources caused by updating the grid at each time step in the traditional sliding grid method, and the technical problem of inaccurate simulation results under the condition that the particle size is greater than the grid scale. Furthermore, the simulation of particles in a rotating flow field under a fixed grid is realized.

[0006] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the present application, and are used together with the specification to explain the principles of the present application.

[0008] Figure 1 is a flowchart of a numerical simulation method for solid-liquid two-phase flow in a rotating flow channel based on a multi-reference frame shown according to an exemplary embodiment.

[0009] Figure 2 is a distribution cloud map of particles in the impeller region of a hybrid pump shown according to an exemplary embodiment.

[0010] Figure 3 is a velocity vector cloud map of particles in the impeller region of a hybrid pump shown according to an exemplary embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0011] Here, the exemplary embodiments will be described in detail, and the examples are shown in the accompanying drawings. When the following description refers to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. On the contrary, they are only examples of devices and methods consistent with some aspects of the present application as detailed in the appended claims.

[0012] The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. The singular forms "a", "the", and "said" used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

[0013] Figure 1 is a flowchart of a numerical simulation method for solid-liquid two-phase flow in a multi-reference-frame rotating channel shown according to an exemplary embodiment, as Figure 1 shown, the method may include the following steps: S1: Obtain the rotating flow field generated by the multi-reference-frame method; Specifically, the multi-reference-frame method includes adding Coriolis force and centrifugal force source terms to the control equation of the fluid phase in the solid-liquid two-phase solution algorithm.

[0014] In CFDEMcoupling, copy out the cfdemSolverPiso folder and replace all file names and the content "cfdemSolverPiso" within the files with "cfdemSolverPisoMRF"; (1) Enter the cfdemSolverPisoMRF.C file and add the code "MRF.correctBoundaryVelocity(U); " on the line next to " / / Momentum predictor". The meaning of this code is that before the velocity prediction equation, subtract the circumferential velocity from the absolute velocity to obtain the relative velocity.

[0015] (2) In the cfdemSolverPisoMRF.C file, add the code "+ MRF.DDt(U) " before the equal sign in fvVectorMatrix Ueqn. Its meaning is to add the calculation formulas of Coriolis force and centrifugal force to the velocity prediction equation.

[0016] (3) In the cfdemSolverPisoMRF.C file, add "MRF.makeRelative(phi);" and "adjustPhi(phi, U, p); " in sequence two lines before " / / Update the fixedFluxPressure BCs to 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 through the adjustment of the pressure field and velocity field until convergence to satisfy the continuity equation.

[0017] (4)In the cfdemSolverPisoMRF.C file, comment out #include "fixedFluxPressureHandling.H" and add the following lines: if (modelType == "A") { volScalarField rUsed = rUA * voidfraction; constrainPressure(p, U, phi, rUsed, MRF); } else constrainPressure(p, U, phi, rUA, MRF); To adapt to the correction of the pressure boundary condition under the multiple reference frames.

[0018] (5)Enter the createField.H file and add #include "createMRF.H" at the bottom line to include the multiple reference frame calculation method in the initialization of the field variables.

[0019] (6)Enter the cfdemSolverPisoMRF folder, open the terminal, and input wmake to complete the compilation.

[0020] After introducing the multiple reference frame function, the influence of the rotational non-inertial force can be considered in the fluid phase, so as to use the fixed grid to realize the simulation of rotational flow, significantly reducing the computational cost and facilitating the calculation of the rotational additional force in the subsequent particle phase.

[0021] S2: Determine the rotational domain information according to the rotational flow field; Specifically, the rotational domain information includes the rotational angular velocity, the rotational radius, and the coordinates corresponding to the highest and lowest points of the rotational domain. The rotational flow field information generated in OpenFOAM, including the rotational angular velocity, the rotational radius, and the coordinates corresponding to the highest and lowest points of the rotational domain, is transmitted to LIGGGHTS through the CFDEM coupling interface to achieve the information synchronization between the particles and the rotational flow field, improving the physical rationality and simulation accuracy of the mechanical coupling.

[0022] S3: Obtain the particle information and the fluid computational domain grid information at the current time step; Specifically, the particle information includes the particle position coordinates, the particle diameter, the particle density, and the particle velocity, and the fluid computational domain grid information includes the grid position coordinates, the grid volume, the grid porosity, and the flow field velocity.

[0023] LIGGGHTS first performs kinetic calculations on the particles, solves their motion equations based on the forces acting on the particles, and obtains the particle position coordinates, particle size, particle density, and particle velocity. Subsequently, the above particle information is transmitted to CFDEMcoupling, and the OpenFOAM function is called to extract the grid information of the fluid calculation domain, including the grid position coordinates, grid volume, grid porosity, and flow field velocity, so as to systematically obtain the accurate data of particle information and grid information.

[0024] S4: Determine the particles within the rotating domain and the particles outside the rotating domain according to the rotating domain information and particle information; Specifically, it is determined whether the particle is within the rotating domain through the particle position coordinates, particle size, and rotating domain information. If so, it is regarded as a particle within the rotating domain, as follows: According to the particle position coordinates, its x , y , z components are obtained. When and z is within the coordinate range corresponding to the highest and lowest points of the rotating domain, the particle is determined to be a particle within the rotating domain; where x, y, z are the particle position coordinate components respectively, d p is the particle size, R is the rotation radius; If not, the particle is determined to be a particle outside the rotating domain.

[0025] This step screens out the particles within the rotating domain through geometric relationships, providing a basis for subsequent calculations of particles within and outside the rotating domain using different methods.

[0026] S5: Calculate the final flow field velocity and reconstructed porosity of the particles within the rotating domain and the particles outside the rotating domain respectively according to the particle information and the grid information of the fluid calculation domain; Specifically, first, through the grid where the particle center is located, starting from the center grid, the distance between the center of the adjacent grid and the particle center is judged one by one by the adjacent grid search method. If it is less than twice the particle size, the grid is defined as the grid within the extended domain, and the relevant grid index is recorded to avoid subsequent repeated searches. This is done until all grids within the extended domain are searched. The grids within the above extended domain are used as the background flow field grids of the particle, and the flow field velocity of each grid is weighted and calculated through a kernel function to obtain the reconstructed flow field velocity, and the porosity is obtained through the averaging method to obtain the reconstructed porosity, as follows: ; ; Where is the reconstructed flow field velocity, ε iTo reconstruct the porosity, ε j 、V cell,j and U f,j are the porosity, volume, and flow field velocity of the j th grid respectively, H ( r i - r j ) is the kernel function ，r i is the position coordinate of the i th particle, r j is the position coordinate of the j th grid; Subtract the circumferential velocity from the reconstructed background flow field velocity of the particles in the rotating domain to obtain the final flow field velocity. The calculation formula is as follows: ; where, is the final flow field velocity, ω is the angular velocity of rotation, r is the radial vector of the spatial position of the particle relative to the axis of rotation.

[0027] When the particle diameter is larger than the scale of the grid where its center is located, the traditional non-analytical method may lead to inaccurate calculation of the background flow field velocity and porosity. Therefore, by expanding the particle neighborhood and reconstructing the background flow field and porosity, the calculation accuracy of the flow field action on the particles can be improved. And in the rotating region, the particles need to adapt to the rotational characteristics of the flow field. By subtracting the circumferential velocity from the reconstructed flow field, the relative flow field velocity can be obtained, thus more accurately reflecting the actual motion state of the particles.

[0028] S6: Calculate the drag force according to the final flow field velocity, reconstructed porosity, and particle information; Specifically, the calculation formula of the drag force is as follows: ; ; where, V p is the particle volume, d p is the particle diameter, F d is the drag force, β d is the momentum exchange coefficient, ε i is the reconstructed porosity, is the final flow field velocity, U pis the particle velocity; where: ; ; .

[0029] Among them, 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.

[0030] This step introduces the corrected flow field velocity, effectively avoiding the particle force error caused by the grid scale difference.

[0031] S7: Calculate the Coriolis force and centrifugal force on the particles in the rotating domain according to the particle information and the rotating domain information; Specifically, when the particle is in the rotating region, the Coriolis force and centrifugal force are additionally calculated. The calculation formulas for the Coriolis force and centrifugal force are as follows: ; ; ; Among them, m p represents the particle mass, ρ p is the particle density, d p is the particle diameter, 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 spatial position of the particle relative to the axis of rotation, U p is the particle velocity.

[0032] Introducing the Coriolis force and centrifugal force in the multi-reference frame helps to accurately describe the real motion behavior of the particles in the rotating domain, can compensate for the influence of non-inertial effects on the particle trajectory, improve the model accuracy, and provide support for analyzing phenomena such as particle migration and retention.

[0033] S8: Obtain the particle information at the next time step through iterative calculation of the drag force, Coriolis force and centrifugal force; Specifically, LIGGGHTS is used to solve the motion equation of particles according to the forces acting on the particles. At the same time, the collision forces between particles and between particles and the wall are considered, and the forces such as the drag force are dynamically coupled with the motion of the particles to obtain the particle position coordinates and particle velocities at the next time step. This ensures the synchronous evolution of the particle dynamic response and the fluid state, providing support for high-fidelity CFD-DEM modeling.

[0034] S9: Add the drag force, Coriolis force, and centrifugal force to the momentum equation in the form of source terms for iterative calculation of the fluid motion to obtain the grid information of the fluid calculation domain at the next time step; Specifically, the forces are uniformly transformed into the form of source terms and added to the momentum conservation equation in the control equation. Through coupling with the existing fluid momentum equation, the mechanical linkage between multiple phases is realized. During the numerical calculation process, the updated momentum equation is solved using an iterative solution method to obtain the flow field velocity at the next time step under the action of the particles, and then the grid information of the entire fluid calculation domain is updated, providing a flow field basis for subsequent prediction of the particle motion trajectory.

[0035] S10: Determine whether the current time step is the last time step. If not, return to S3 and continue to execute; if so, terminate the operation process to obtain the final particle information and the grid information of the fluid calculation domain.

[0036] Specifically, after each loop calculation is completed, the system will accumulate the time step once. When the accumulated number of time steps is less than the preset total number of time steps, return to step S3 and continue to execute the update and coupling calculation of the particle information and the grid information of the fluid calculation domain; if the accumulated number of time steps reaches the preset total number of time steps, terminate the loop and output the final particle state information and the grid data of the fluid calculation domain.

[0037] As can be seen from the above embodiments, the present invention introduces a rotating coordinate system for the fluid and particles respectively based on the multi-reference frame method, and corrects the local flow field velocity and porosity information during the calculation of the particle drag force, overcoming the problems of large consumption of computing resources caused by updating the grid at each time step in the traditional sliding grid method and the technical problem of inaccurate simulation results under the condition that the particle size is larger than the grid scale. Furthermore, the calculation simulation of particles in a rotating flow field under a fixed grid is realized.

[0038] Figure 2 It is the particle distribution diagram in the impeller region of the hybrid pump. It can be clearly seen from it that the particles are mainly concentrated in the pressure surface region of the blade, and as the distance from the center of the impeller increases, the velocity of the particles gradually increases. Figure 3 It is the particle velocity vector diagram in the impeller region of the hybrid pump, showing the motion direction and velocity change characteristics of the particles in the impeller region.

[0039] Other embodiments of the present application will be readily apparent to those skilled in the art upon consideration of the specification and practice of the disclosure herein. The present 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 known common general knowledge or conventional technical means in the technical field not disclosed in the present application. The specification and examples are only to be considered as exemplary, and the true scope and spirit of the present application are pointed out by the claims.

[0040] It should be understood that the present application is not limited to the exact structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present application is only limited by the appended claims.

Claims

1. A numerical simulation method for solid-liquid two-phase flow in a multi-reference-frame rotating flow channel, characterized in that, Including: S1: Obtain the rotating flow field generated by the multi-reference frame method; S2: Determine the rotating domain information according to the rotating flow field; S3: Obtain the particle information and the fluid computational domain grid information at the current time step; S4: Determine the particles within the rotating domain and the particles outside the rotating domain according to the rotating domain information and the particle information; S5: Calculate the final flow field velocity and the reconstructed porosity of the particles within the rotating domain and the particles outside the rotating domain respectively according to the particle information and the fluid computational domain grid information; S6: Calculate the drag force according to the final flow field velocity, the reconstructed porosity and the particle information; S7: Calculate the Coriolis force and the centrifugal force for the particles within the rotating domain according to the particle information and the rotating domain information; S8: Obtain the particle information at the next time step through iterative calculation of the drag force, the Coriolis force and the centrifugal force; S9: Add the drag force, the Coriolis force and the centrifugal force to the momentum equation in the form of source terms to perform iterative calculation of the motion of the fluid, and obtain the fluid computational domain grid information at the next time step; S10: Judge whether the current time step is the last time step. If not, return to S3 and continue to execute; if so, terminate the operation process to obtain the final particle information and the fluid computational domain grid information.

2. A numerical simulation method for solid-liquid two-phase flow in a multi-reference frame rotating flow channel according to claim 1, characterized in that In S1, the multi-reference frame method includes adding the Coriolis force and the centrifugal force source terms to the control equation of the fluid phase in the solid-liquid two-phase solution algorithm.

3. A numerical simulation method for solid-liquid two-phase flow in a multi-reference frame rotating flow channel according to claim 1, characterized in that In S2, the rotating domain information includes the angular velocity of rotation, the radius of rotation, and the coordinates corresponding to the highest and lowest points of the rotating domain.

4. A numerical simulation method for solid-liquid two-phase flow in a multi-reference frame rotating flow channel according to claim 3, characterized in that In S3, the particle information includes the particle position coordinates, the particle diameter, the particle density, and the particle velocity, and the fluid computational domain grid information includes the grid position coordinates, the grid volume, the grid porosity, and the flow field velocity.

5. A numerical simulation method for solid-liquid two-phase flow in a multi-reference frame rotating flow channel according to claim 4, characterized in that In S4, determining the particles within the rotating domain and the particles outside the rotating domain includes: Determine whether the particle is within the rotation domain based on the particle position coordinates, particle size, and rotation domain information. If so, it is regarded as a particle within the rotation domain, as follows: Obtain its x , y , z components. When and z is within the coordinate range corresponding to the highest and lowest points of the rotation domain, determine that the particle is a particle within the rotation domain; where x, y, z are the particle position coordinate components respectively, d p is the particle size, R is the rotation radius. If not, determine that the particle is a particle outside the rotating domain.

6. A numerical simulation method for solid-liquid two-phase flow in a multi-reference frame rotating flow channel according to claim 1, characterized in that In S5, calculating the final flow field velocity and the reconstructed porosity of the particles within the rotating domain and the particles outside the rotating domain respectively includes: Reconstruct the flow field velocity and the porosity of the particles to obtain the reconstructed flow field velocity and the reconstructed porosity. The calculation formula is as follows: ； ； wherein, is the reconstructed flow field velocity, ε i is the reconstructed porosity, ε j 、V cell,j and U f,j are the porosity, volume and flow field velocity of the j th grid respectively, H ( r i - r j ) is the kernel function ，r i is the position coordinate of the i th particle, r j is the position coordinate of the j th grid; Subtract the circumferential velocity from the reconstructed background flow field velocity of the particles within the rotating domain to obtain the final flow field velocity. The calculation formula is as follows: ； wherein, is the final flow field velocity, ω is the rotational angular velocity, r is the radial vector of the spatial position of the particle relative to the rotation axis.

7. A numerical simulation method for solid-liquid two-phase flow in a multi-reference frame rotating flow channel according to claim 6, characterized in that, In S6, the calculation formula of the drag force is as follows: ； ； Among them, V p is the particle volume, d p is the particle diameter, F d is the drag force, β d is the momentum exchange coefficient, ε i is the reconstructed porosity, is the final flow field velocity, U p is the particle velocity.

8. A numerical simulation method for solid-liquid two-phase flow in a multi-reference frame rotating flow channel according to claim 1, characterized in that In S7, the calculation formulas of the Coriolis force and the centrifugal force are as follows: ； ； ； Among them, 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 rotational angular velocity, r is the radial vector of the spatial position of the particle relative to the rotation axis, U p is the particle velocity.

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