A numerical simulation method for online coupling of discrete and continuous phases at two scales

Abstract

This invention provides a numerical simulation method for online coupling of discrete and continuous phases at two scales. The core of this method considers the significant impact of small-scale flow structures on the accuracy of the coupled calculations of the discrete and continuous phases. It proposes coupling a small-scale continuous phase calculation model during the calculation of the discrete unit and the large-scale continuous phase, analyzing the parameters characterizing the flow structure at the small scale, and transferring these parameters to the coupled calculation process of the discrete and large-scale continuous phases. This establishes a simulation method for online coupled calculation of the discrete and continuous phases at both large and small scales. Based on the motion characteristics of the discrete and continuous phases at different time and spatial scales, this invention proposes corresponding mapping algorithms and stability constraints to improve computational efficiency while ensuring accuracy.

Description

Technical Field

[0001] This invention belongs to the field of multiphase flow and relates to numerical simulation methods for particle-fluid systems, particularly a numerical simulation method that couples discrete and continuous phases online. Background Technology

[0002] Particulate fluid systems are widely present in chemical reaction processes and have important applications in energy, pharmaceuticals, food, and powder materials. Due to the complex interactions between particles and fluids in these systems, mesoscale structures such as agglomerates and bubbles exist during the two-phase evolution, significantly impacting reaction and transport processes. Because experimental research methods have limitations in terms of accuracy, sensitivity, and measurement stability, computational fluid dynamics methods are playing an increasingly important role.

[0003] Based on the characteristics of particle and fluid-scale motion, computational fluid dynamics (CFD) methods can treat particles as discrete unit particles and fluids as a continuous phase, establishing a discrete-continuous phase coupled computational model (CFD-DEM). Newton's second law is used to track the position and velocity of each particle. The calculation of the continuous phase is usually performed by solving the Navier-Stokes equations on an Eulerian grid, with the grid size typically an order of magnitude larger than the particle diameter. An interphase drag model is used to characterize the interaction force between the two. This discrete-continuous coupling method conforms to the particle state and physical laws in nature. However, the interaction force between particles and fluids, as a key variable, is calculated using empirical correlations, resulting in lower computational accuracy.

[0004] The Direct Numerical Simulation (DNS) method analyzes the motion of fluids using Eulerian grids smaller than discrete particles. It can describe the flow characteristics of continuous phases at the microscale and obtain the interaction forces between particles and fluids without any assumptions. It is currently recognized as the most accurate calculation method. Summary of the Invention

[0005] To address the technical problems existing in the prior art, this invention provides a numerical simulation method that couples discrete and continuous phases online at two scales. The numerical simulation method couples a small-scale DNS calculation model (with a calculation grid size much smaller than the particle size) into the CFD-DEM calculation to solve the gas-solid phase interaction forces in real time, which significantly improves the accuracy of the calculation results.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention provides a numerical simulation method for online coupling of discrete and continuous phases at two scales, the method comprising the following steps:

[0008] (1) Obtain discrete phase parameters, continuous phase parameters, and boundary conditions of the device;

[0009] (2) Based on the discrete unit size d in the discrete phase parameters described in step (1), set the small-scale grid size h and the large-scale grid size l of the continuous phase, where h < l; calculate the discrete phase time step Δt based on h and l. d Continuous phase small-scale time step Δt h and the large-scale time step Δt of the continuous phase l ;

[0010] (3) Based on the Δt obtained in step (2) d Δt h and Δt l Set up mappings between discrete phases and continuous phases at small scales, between discrete phases and continuous phases at large scales, and between continuous phases at small scales and continuous phases at large scales.

[0011] (4) Based on the h, l, Δt set in step (2) d Δt h and Δt l Establish a set of equations, and through the mapping set in step (3), establish the logical relationship between the calculation of the discrete phase and the small-scale continuous phase and the large-scale continuous phase, and complete the calculation.

[0012] In this invention, two scales (small and large dual scales h and l for the continuous phase) are set up. A small-scale computational model is used to analyze the local microstructure of the continuous phase, obtain the characteristic variables of the coupling between micro-flow and discrete phase units, and pass them to the computational equations of the larger continuous phase scale. The spatiotemporal evolution progression process is calculated using a coupled model of discrete phase and large-scale continuous phase, balancing computational efficiency and accuracy, and realizing multi-scale simulation of the evolution process of complex systems.

[0013] As a preferred technical solution of the present invention, the discrete phase parameters in step (1) include the particle diameter d. p Particle density ρ p Particle location information X p and particle velocity v p .

[0014] Preferably, the continuous phase parameter includes the fluid density ρ. f Fluid viscosity μ f And the fluid velocity u.

[0015] Preferably, the boundary conditions of the device include the device length L, the device width W, the device height H, and the device diameter D.

[0016] As a preferred technical solution of the present invention, the discrete unit size d in step (2) is the characteristic scale of the unit mass point in discrete simulation.

[0017] Preferably, the small-scale grid size h of the continuous phase is the interface size at the contact edge between the analytical continuous phase and the discrete phase.

[0018] Preferably, the continuous phase large-scale grid size l is a scale containing more than one discrete unit point.

[0019] Preferably, the relationship between the discrete unit size d, the small-scale grid size h of the continuous phase, and the large-scale grid size l of the continuous phase is h < d < l.

[0020] In this invention, the values ​​of h, d, and l are mainly determined by the selection of accuracy and working conditions. In this invention, h = (1 / 5 to 1 / 60)d and l = (3 to 5)d are preferred, but the actual numerical relationship between h, d, and l is not limited to the above relationship.

[0021] As a preferred technical solution of the present invention, the discrete phase time step Δt in step (2) d It is related to the material properties.

[0022] In this invention, preferably, the discrete phase time step Δt in step (2) is... d The elastic modulus and mass of the fluid material are related, and satisfy the following expression:

[0023]

[0024] Where m p and k n These represent the mass and elastic modulus of the particle, respectively.

[0025] However, it is not limited to the aforementioned Δt. d The solution method, other solutions for Δt d The same method applies in this application.

[0026] Preferably, the small-scale time step Δt of the continuous phase h The continuous phase small-scale mesh size h satisfies the following relationship: the continuous phase small-scale movement distance is less than the continuous phase small-scale mesh size h.

[0027]

[0028] Among them, u j '(max) represents the maximum velocity of the continuous phase in a small-scale grid.

[0029] Preferably, the large-scale time step Δtl of the continuous phase and the large-scale grid size l of the continuous phase satisfy the following relationship: that is, the large-scale motion distance of the continuous phase is less than the large-scale grid size l of the continuous phase.

[0030]

[0031] Among them, u i '(max) represents the maximum velocity of the continuous phase on a large-scale grid.

[0032] As a preferred technical solution of the present invention, the mapping in step (3) includes the mass, velocity and mechanical characteristics of the discrete phase and the flowing phase, and satisfies the conservation of energy and momentum.

[0033] As a preferred technical solution of the present invention, the large-scale mapping between the discrete phase and the continuous phase in step (3) satisfies the following relationship:

[0034]

[0035] Where X represents the variable mapped to the continuous phase large grid, M is the characteristic variable of the discrete phase, and the characteristic variable includes mass, volume, velocity and force; for some discrete points on the interface of the continuous phase large-scale grid, w is defined as the weight of the characteristic variable of the discrete element in grid i, V is the volume of the large grid, i is the number of the large grid, and k is the number of the discrete element point in each large grid.

[0036] Preferably, when mapping the large-scale parameters of the continuous phase to the discrete phase, interpolation calculations are performed based on the distances between the center point of the large grid and the grid intersections using the following formula:

[0037]

[0038] Wherein, Y and S are the characteristic parameters required for large-scale coupling calculation of discrete and continuous phases, including continuous phase velocity and pressure, D is the weight of the center point and intersection of the large grid to the discrete phase, the weight is calculated based on the distance between the discrete point and the center point and intersection of the large grid, k is the discrete unit point number in the large grid, and c is the statistical number of the center point and intersection of the large grid.

[0039] As a preferred technical solution of the present invention, the calculation method for the small-scale mapping between the discrete phase and the continuous phase in step (3) includes:

[0040] z is uniformly selected on the surface of each discrete unit. k Lagrange markers are used to calculate the flow field information Ψ* in the absence of a discrete phase. Ψ* includes either velocity U* or pressure P*. The velocity field of each discrete element's surface Lagrange point is calculated based on the velocity and coordinates of the discrete phase. Ψ is obtained by correcting the field information of the small-scale continuous phase according to the no-slip boundary conditions of the discrete and continuous phases, as well as the coupling force f of the Lagrange markers on the continuous phase. k For all f kSumming yields the coupling force F between a single discrete unit and the continuous phase. i , will F i It is added to each discrete unit point to achieve mechanical equilibrium.

[0041] Preferably, the calculation method for the mapping between the small-scale and large-scale continuous phases in step (3) includes:

[0042] The small-scale grid size h and the large-scale grid size l of the continuous phase should satisfy l = Nh, where N is a positive integer, meaning that each large-scale grid contains N... 3 A small-scale grid; the mapping between the small-scale and large-scale continuous phases involves a time scale span, with the time step relationship being Δt. h <Δt l When mapping from a small scale to a large scale of a continuous phase, it is necessary to convert N contained in each large-scale grid. 3 The field variables within a small-scale grid are linearly averaged according to the following relationship:

[0043]

[0044] Among them, Ψ i This refers to large-scale grid information, which includes pressure and velocity fields, Ψ n This represents small-scale grid information, where i is the large-scale grid number.

[0045] As a preferred technical solution of the present invention, step (4) involves setting d, h, l, Δt according to step (2). d Δt h and Δt l The system of equations is established based on the DEM model, containing d and Δt. d The discrete phase particle motion equations, and the establishment of equations containing h and Δt based on DNS. h Small-scale continuity equations and the establishment of equations containing l and Δt based on CFD l The large-scale continuity equations;

[0046] Preferably, the logical relationship of the calculation in step (4) is as follows: map the particle position and velocity information in step (1) to the large-scale continuity equation system, calculate the solid phase volume fraction and solid phase velocity; solve the small-scale continuity equation system to obtain the force F between the fluid phase and each particle; map the F to the discrete phase particle motion equation system to update the particle position and velocity information; map the F to the large-scale continuity equation system according to the updated particle position, calculate the force of the fluid per unit volume on the particles, solve the fluid phase momentum exchange equation and update the fluid velocity and pressure.

[0047] As a preferred technical solution of the present invention, in the calculation process of the continuous phase small-scale calculation model in step (4), it is necessary to obtain stable values ​​and pass them to the discrete phase and continuous phase large-scale calculation equations in the process of cross-time and space scales.

[0048] Preferably, the obtained stable value satisfies the stability constraint condition, which is determined by calculating the interaction force F between the small-scale continuous phase and the discrete phase through at least one iteration. i Characterization.

[0049] Preferably, the average value of all discrete phases in the system And the F of a single particle i The following conditions must be met simultaneously for small-scale continuous phase calculations to reach stability:

[0050]

[0051] Where 0<i≤N, σ and δ are relaxation thresholds, and N is the number of discrete units in the system.

[0052] As a preferred technical solution of the present invention, the above-mentioned numerical simulation method for online coupling of discrete and continuous phases includes the following steps:

[0053] (1) Obtain discrete phase parameters, continuous phase parameters, and boundary conditions of the device;

[0054] The discrete phase parameters include the particle diameter d. p Particle density ρ p Particle location information X p and particle velocity v p The continuous phase parameters include the fluid density ρ. f Fluid viscosity μ f and the fluid velocity u; the boundary conditions of the device include the device length L, device width W, device height H, and device diameter D;

[0055] (2) Based on the discrete unit size d in the discrete phase parameters described in step (1), set the small-scale grid size h and the large-scale grid size l of the continuous phase, where h < l; calculate the discrete phase time step Δt based on h and l. d Continuous phase small-scale time step Δt h and the large-scale time step Δt of the continuous phase l ;

[0056] The discrete phase time step Δt d Related to the material properties of the fluid;

[0057] The small-scale time step Δt of the continuous phase hThe continuous phase small-scale mesh size h satisfies the following relationship: the continuous phase small-scale movement distance is less than the continuous phase small-scale mesh size h.

[0058]

[0059] Among them, u j '(max) represents the maximum velocity of the continuous phase within a small-scale grid;

[0060] The large-scale time step Δtl of the continuous phase and the large-scale grid size l of the continuous phase satisfy the following relationship: the large-scale motion distance of the continuous phase is less than the large-scale grid size l of the continuous phase.

[0061]

[0062] Among them, u i '(max) represents the maximum velocity of the continuous phase on a large-scale grid;

[0063] (3) Based on the Δt obtained in step (2) d Δt h and Δt l Set up mappings between discrete phases and continuous phases at small scales, between discrete phases and continuous phases at large scales, and between continuous phases at small scales and continuous phases at large scales.

[0064] The mapping includes the mass, velocity, and mechanical characteristics of both the discrete and flowing phases, and satisfies energy conservation and momentum conservation.

[0065] The large-scale mapping between the discrete phase and the continuous phase satisfies the following relationship:

[0066]

[0067] Where X represents the variable mapped to the continuous phase large grid, M is the characteristic variable of the discrete phase, and the characteristic variable includes mass, volume, velocity and force; for some discrete points on the interface of the continuous phase large grid, w is defined as the weight of the characteristic variable of the discrete element in grid i, V is the volume of the large grid, i is the number of the large grid, and k is the number of the discrete element point in each large grid.

[0068] When mapping the large-scale parameters of the continuous phase to the discrete phase, interpolation calculations are required based on the distances between the center point of the large grid and the grid intersections using the following relationship:

[0069]

[0070] Wherein, Y and S are the characteristic parameters required for large-scale coupling calculation of discrete and continuous phases, including continuous phase velocity and pressure, D is the weight of the center point and intersection of the large grid to the discrete phase, the weight is calculated based on the distance between the discrete point and the center point and intersection of the large grid, k is the discrete unit point number in the large grid, and c is the statistical number of the center point and intersection of the large grid.

[0071] The calculation method for the small-scale mapping between the discrete phase and the continuous phase in step (3) includes:

[0072] zk Lagrange markers are uniformly selected on the surface of each discrete element. The flow field information Ψ* is calculated in the absence of a discrete phase. Ψ* includes velocity U* or pressure P*. The velocity field of each Lagrange point on the surface of the discrete element is calculated based on the velocity and coordinates of the discrete phase. Based on the no-slip boundary condition of the coupling between the discrete and continuous phases, the field information of the small-scale continuous phase is corrected to obtain Ψ, along with the coupling force f of the Lagrange markers on the continuous phase. k For all f k Summing yields the coupling force F between a single discrete unit and the continuous phase. i , will F i It is added to each discrete unit point to achieve mechanical equilibrium;

[0073] The calculation method for the mapping between the small-scale and large-scale continuous phases includes:

[0074] The small-scale grid size h and the large-scale grid size l of the continuous phase should satisfy l = Nh, where N is a positive integer, meaning that each large-scale grid contains N... 3 A small-scale grid; the mapping between the small-scale and large-scale continuous phases involves a time scale span, with the time step relationship being Δt. h <Δt l When mapping from a small scale to a large scale of a continuous phase, it is necessary to convert N contained in each large-scale grid. 3 The field variables within a small-scale grid are linearly averaged according to the following relationship:

[0075]

[0076] Among them, Ψ i This refers to large-scale grid information, which includes pressure and velocity fields, Ψ n This represents small-scale grid information, where i is the large-scale grid number;

[0077] (4) Based on the h, l, Δt set in step (2) d Δt h and Δt lEstablish a system of equations, and through the mapping set in step (3), establish the logical relationship between the small-scale calculation of the discrete phase and the continuous phase and the large-scale calculation of the continuous phase, and complete the calculation;

[0078] The d, h, l, Δt set according to step (2) d Δt h and Δt l The system of equations is established based on the DEM model, containing d and Δt. d The discrete phase particle motion equations, and the establishment of equations containing h and Δt based on DNS. h Small-scale continuity equations and the establishment of equations containing l and Δt based on CFD l The large-scale continuity equations;

[0079] The logical relationship of the calculation is as follows: map the particle position and velocity information in step (1) to the large-scale continuity equation system, calculate the solid phase volume fraction and solid phase velocity; solve the small-scale continuity equation system to obtain the force F between the fluid phase and each particle; map the F to the discrete phase particle motion equation system to update the particle position and velocity information; map the F to the large-scale continuity equation system according to the updated particle position, calculate the force of the fluid per unit volume on the particles, solve the fluid phase momentum exchange equation and update the fluid velocity and pressure;

[0080] During the calculation process of the continuous phase small-scale computational model, stable values ​​need to be obtained and passed to the discrete phase and continuous phase large-scale computational equations across time and spatial scales. Obtaining stable values ​​means satisfying stability constraints, which are achieved by calculating the interaction force F between the continuous phase small-scale and the discrete phase through at least one iteration. i Characterization; that is, the average value of all discrete phases in the system. And the F of a single particle i The following conditions must be met simultaneously for small-scale continuous phase calculations to reach stability:

[0081]

[0082] Where 0<i≤N, σ and δ are relaxation thresholds, and N is the number of discrete units in the system.

[0083] The steps of the numerical simulation method involving the online coupling of discrete and continuous phases can be further broken down into the following steps:

[0084] Step 11, input particle, fluid, and equipment boundary conditions, including: particle diameter d p Particle density ρ p Particle location information X p Particle velocity vp , the fluid density ρ f , the fluid viscosity μ f , the fluid velocity u, equipment parameters (structural parameters such as length L, width W, height H, equipment diameter D, etc.).

[0085] Step 12, according to the parameter list in Step 11, set the large grid calculation size of the fluid as l and the small scale grid size as h (where h < l); according to the scale size (particle size d and h, l), sequentially set the calculation time steps of the discrete phase and the two continuous phases: discrete phase Δt d , continuous phase large scale Δt l and continuous phase small scale Δt h .

[0086] Step 13, according to the time step and calculation grid size information in Step 12, establish three sets of equations for the two-scale continuous phase and particles as shown in Table 1.

[0087] Table 1

[0088]

[0089] Step 14, transfer the particle position and velocity information to the large grid continuous phase equation, and calculate the solid volume fraction and solid velocity;

[0090] Step 15, use the DNS model to calculate the force F between the fluid phase and each particle in the small scale continuity equations, and transfer F to the discrete phase particle motion equation (DEM) to update the particle velocity and position;

[0091] Step 16, transfer the F received by each particle to the large scale continuity equation (CFD) according to the particle position, calculate the force exerted by the particles on the fluid per unit volume, solve the fluid phase momentum exchange equation and update the fluid velocity and pressure.

[0092] Step 17, set the time interval for updating the drag force between the discrete particles and the large scale fluid phase, and repeat Steps (13) - Step (16) before reaching the end step of the calculation.

[0093] According to Step (15), use DNS calculation to obtain the stable force F between the fluid and the particles. Here, set the stability constraint condition of F as:

[0094] where 0 < i ≤ N

[0095] σ and δ are the relaxation thresholds respectively, and N is the number of discrete units in the system. Iterative calculation is performed before the statistical values of single particle and global particles reach the relaxation threshold.

[0096] According to step (15), when DNS resolves the fluid-particle interaction force F at a small scale in the continuous phase, the DEM and CFD calculations are suspended and waiting. Here, in order to ensure the computational efficiency of the model, the DNS method is only used as a means of resolving F, and the particle and fluid position and velocity update process is calculated by the discrete model (DEM) and the large-scale continuous phase (CFD) equations.

[0097] Compared with existing technical solutions, the present invention has at least the following beneficial effects:

[0098] (1) This invention provides a numerical simulation method for online coupling of discrete and continuous phases at two scales. The numerical simulation method uses the DNS method with high computational accuracy to calculate the interaction force between fluid and particles in real time, which significantly improves the accuracy of the calculation results.

[0099] (2) This invention provides a numerical simulation method for online coupling of discrete phase and continuous phase at two scales. The numerical simulation method can be applied to gas-solid two-phase flow systems such as irregular particles, multi-component particle systems and microscale complex systems (lift pipes). Traditional drag force models are derived based on spherical particles. The numerical simulation method provided by this invention breaks through the limitations of the drag force model and has a wider and more widespread application range.

[0100] (3) The present invention provides a numerical simulation method with online coupling of discrete phase and continuous phase at two scales. The numerical simulation method has a significantly higher computational efficiency than the traditional DNS method and can accurately simulate large-scale fluidized systems. Attached Figure Description

[0101] Figure 1 This is a flowchart illustrating the calculation process of an application example of the present invention;

[0102] Figure 2 This is a flowchart illustrating the calculation process of an application example of the present invention.

[0103] Figure 3 Axial distribution diagrams of solids content were calculated for DNS, CFD-DEM, and application examples of this invention;

[0104] Figure 4 Calculate the axial pressure distribution using DNS, CFD-DEM, and the application examples of this invention;

[0105] Figure 5 A comparison chart of the drag probability density distribution of particles calculated using DNS, CFD-DEM, and the application example of this invention;

[0106] Figure 6 A comparison chart showing the computational efficiency of DNS, CFD-DEM, and the application example of this invention.

[0107] The present invention will now be described in further detail. However, the examples described below are merely simplified examples of the present invention and do not represent or limit the scope of protection of the present invention. The scope of protection of the present invention is determined by the claims. Detailed Implementation

[0108] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0109] To better illustrate the present invention and facilitate understanding of its technical solutions, typical but non-limiting embodiments of the present invention are as follows:

[0110] Example

[0111] This embodiment provides a numerical simulation method for online coupling of discrete and continuous phases at two scales, the method comprising the following steps:

[0112] (1) Obtain discrete phase parameters, continuous phase parameters, and boundary conditions of the device;

[0113] The discrete phase parameters include the particle diameter d. p Particle density ρ p Particle location information X p and particle velocity v p The continuous phase parameters include the fluid density ρ. f Fluid viscosity μ f and the fluid velocity u; the boundary conditions of the device include the device length L, device width W, device height H, and device diameter D;

[0114] (2) Based on the discrete unit size d in the discrete phase parameters described in step (1), set the small-scale grid size h and the large-scale grid size l of the continuous phase, where h < l; calculate the discrete phase time step Δt based on h and l. d Continuous phase small-scale time step Δt h and the large-scale time step Δt of the continuous phase l ;

[0115] The discrete phase time step Δt d Related to the material properties of the fluid;

[0116] The small-scale time step Δt of the continuous phase h The continuous phase small-scale mesh size h satisfies the following relationship: the continuous phase small-scale movement distance is less than the continuous phase small-scale mesh size h.

[0117]

[0118] Among them, u j '(max) represents the maximum velocity of the continuous phase within a small-scale grid;

[0119] The large-scale time step Δt of the continuous phase l The large-scale mesh size l of the continuous phase satisfies the following relationship: the large-scale motion distance of the continuous phase is less than the large-scale mesh size l of the continuous phase.

[0120]

[0121] Among them, u i '(max) represents the maximum velocity of the continuous phase on a large-scale grid;

[0122] (3) Based on the Δt obtained in step (2) d Δt h and Δt l Set up mappings between discrete phases and continuous phases at small scales, between discrete phases and continuous phases at large scales, and between continuous phases at small scales and continuous phases at large scales.

[0123] The mapping includes discrete types and the mass, velocity, and mechanical characteristics of the flowing phase, and satisfies energy conservation and momentum conservation.

[0124] The large-scale mapping between the discrete phase and the continuous phase satisfies the following relationship:

[0125]

[0126] Where X represents the variable mapped to the continuous phase large grid, M is the characteristic variable of the discrete phase, and the characteristic variable includes mass, volume, velocity and force; for some discrete points on the interface of the continuous phase large grid, w is defined as the weight of the characteristic variable of the discrete element in grid i, V is the volume of the large grid, i is the number of the large grid, and k is the number of the discrete element point in each large grid.

[0127] When mapping the large-scale parameters of the continuous phase to the discrete phase, interpolation calculations are required based on the distances between the center point of the large grid and the grid intersections using the following relationship:

[0128]

[0129] Wherein, Y and S are the characteristic parameters required for large-scale coupling calculation of discrete and continuous phases, including continuous phase velocity and pressure, D is the weight of the center point and intersection of the large grid to the discrete phase, the weight is calculated based on the distance between the discrete point and the center point and intersection of the large grid, k is the discrete unit point number in the large grid, and c is the statistical number of the center point and intersection of the large grid.

[0130] The calculation method for the small-scale mapping between the discrete phase and the continuous phase in step (3) includes:

[0131] zk Lagrange markers are uniformly selected on the surface of each discrete element. The flow field information Ψ* is calculated in the absence of a discrete phase. Ψ* includes velocity U* or pressure P*. The velocity field of each Lagrange point on the surface of the discrete element is calculated based on the velocity and coordinates of the discrete phase. Based on the no-slip boundary condition of the coupling between the discrete and continuous phases, the field information of the small-scale continuous phase is corrected to obtain Ψ, along with the coupling force f of the Lagrange markers on the continuous phase. k For all f k Summing yields the coupling force F between a single discrete unit and the continuous phase. i , will F i It is added to each discrete unit point to achieve mechanical equilibrium;

[0132] The calculation method for the mapping between the small-scale and large-scale continuous phases includes:

[0133] The small-scale grid size h and the large-scale grid size l of the continuous phase should satisfy l = Nh, where N is a positive integer, meaning that each large-scale grid contains N... 3 A small-scale grid; the mapping between the small-scale and large-scale continuous phases involves a time scale span, with the time step relationship being Δt. h <Δt l When mapping from a small scale to a large scale of a continuous phase, it is necessary to convert N contained in each large-scale grid. 3 The field variables within a small-scale grid are linearly averaged according to the following relationship:

[0134]

[0135] Among them, Ψ i This refers to large-scale grid information, which includes pressure and velocity fields, Ψ n This represents small-scale grid information, where i is the large-scale grid number;

[0136] (4) Based on the mapping set in step (3), establish the logical relationship between the calculation of discrete phase and continuous phase at small scale and continuous phase at large scale;

[0137] The d, h, l, Δt set according to step (2) d Δt h and Δt l The system of equations is established based on the DEM model, containing d and Δt. d The discrete phase particle motion equations, and the establishment of equations containing h and Δt based on DNS. h Small-scale continuity equations and the establishment of equations containing l and Δt based on CFD l The large-scale continuity equations;

[0138] The logical relationship of the calculation is as follows: map the particle position and velocity information in step (1) to the large-scale continuity equation system, calculate the solid phase volume fraction and solid phase velocity; solve the small-scale continuity equation system to obtain the force F between the fluid phase and each particle; map the F to the discrete phase particle motion equation system to update the particle position and velocity information; map the F to the large-scale continuity equation system according to the updated particle position, calculate the force of the fluid per unit volume on the particles, solve the fluid phase momentum exchange equation and update the fluid velocity and pressure;

[0139] During the calculation process of the continuous phase small-scale computational model, stable values ​​need to be obtained and passed to the discrete phase and continuous phase large-scale computational equations across time and spatial scales. Obtaining stable values ​​means satisfying stability constraints, which are achieved by calculating the interaction force F between the continuous phase small-scale and the discrete phase through at least one iteration. i Characterization; that is, the average value of all discrete phases in the system. And the F of a single particle i The following conditions must be met simultaneously for small-scale continuous phase calculations to reach stability:

[0140]

[0141] Where 0<i≤N, σ and δ are relaxation thresholds, and N is the number of discrete units in the system.

[0142] The applicant declares that the detailed structural features of the present invention are illustrated through the above embodiments, but the present invention is not limited to the above detailed structural features, that is, it does not mean that the present invention must rely on the above detailed structural features to be implemented. Those skilled in the art should understand that any improvements to the present invention, equivalent substitutions for the components selected in the present invention, additions of auxiliary components, selection of specific methods, etc., all fall within the protection scope and disclosure scope of the present invention.

[0143] Application examples

[0144] This application example uses specific numerical values ​​and employs the numerical simulation method provided in the embodiment to perform actual calculations. The calculation process is as follows: Figure 1 As shown, the specific steps include the following:

[0145] Step 11: Read particle, fluid, and equipment structural parameters: including particle diameter d p =1.2mm, particle density ρ p =1000kg / m 3 Fluid density ρ f =1.2kg / m 3 Fluid viscosity μ f=1.8Pa*s, Equipment parameters (W*D*H=12d) p *6d p *45d p The inlet fluid velocity is Ug = 0.9 m / s.

[0146] Step 12: Setting the time step and mesh size for particles and fluid: In this calculation method, a continuous phase dual-scale mesh needs to be generated independently. The large mesh is 3 times the particle diameter, the small mesh is 1 / 12 of the particle diameter, and the large mesh is 36 times the size of the small mesh. This is mainly determined by the different analytical scale and accuracy requirements, as shown in Table 2.

[0147] Table 2

[0148]

[0149] Step 13: Establish three sets of equations for the coupled process of discrete phase and two-scale continuous phase:

[0150] Equation set 1 (CFD):

[0151] Fluid continuity equation:

[0152]

[0153] Momentum exchange equation:

[0154]

[0155] Where, ε f ρ represents the volume fraction of a fluid. f The fluid density is represented by u, the fluid velocity by t, the time by P, and the pressure by S. p τ represents the source term. f denoted by viscous stress, and g represents gravity.

[0156] Equation 2 (DNS): The Immersed Boundary Model (IBM) in DNS calculations is used to calculate the force F between the fluid and each particle. The governing equations are:

[0157]

[0158] During the calculation preparation, the coordinates X of the Lagrange marker points are first generated on the particle surface. p In the above formula, f is the volume force, that is, the force exerted by the particle on the fluid. The specific steps are as follows:

[0159] (i) The DNS Euler velocity field u* is calculated using the pressure Poisson equation in the absence of a source term f;

[0160] (ii) The fluid velocity U near the particle is obtained by interpolating the Euler velocity field u* using the Dirac function. n The Dirac function is calculated using a three-point piecewise format;

[0161] (iii) Based on the Lagrange point velocity V on the particle surface d (V d =v p +ω p (X p -X c ), X c (coordinates of the particle center) and U n Calculate the fluid force F acting on each Lagrange point. n , RHS includes convection, pressure, and viscosity terms (n refers to the number of Lagrange points on the particle surface);

[0162] (iiii) The force F at the Lagrange mark point n Then, by interpolating the Dirac function into the Eulerian field and summing the results, we obtain the force f exerted by the particle on the fluid, i.e., the force F exerted by the fluid on the particle.

[0163] Equation system 3 (DEM):

[0164]

[0165] m p V represents the weight of the particles. p F represents the velocity of a single particle, and F represents the particle-fluid force. c This represents the particle-particle (wall) collision force.

[0166] Step 14: Map the particles to a large grid according to their location information and calculate the solid volume fraction and solid velocity of the large grid:

[0167]

[0168] V p and V cell This represents the volume of particles within the mesh and the mesh itself.

[0169]

[0170] Step 15: Calculate the particle-fluid interaction force F using the above equation set 2.

[0171] Step 16: Transfer F to the continuous phase large grid and the discrete particle motion equations to update particle position and velocity, fluid velocity and pressure.

[0172] Step 17: Set the traction update interval to 10.-4 s.

[0173] like Figure 2 The diagram shows the framework for online coupled computation of discrete and continuous phases at two scales.

[0174] Simulation studies of the above examples were conducted using both the traditional CFD-DEM method and the present invention. The results of the DNS method, which has the best computational accuracy, were used as a reference standard to illustrate the advantages of the present invention through comparison.

[0175] Figure 3 The axial distribution of particle solids content obtained by the three methods shows that the calculation results of the present invention are basically consistent with the DNS calculation results, and the accuracy is significantly improved compared with the CFD-DEM method.

[0176] Figure 4 The probability density distribution of the drag force values ​​of all particles in the bed shows that the calculation results of this invention are in good agreement with the DNS results.

[0177] Figure 5 As can be seen from the axial distribution of the pressure values ​​inside the bed, the pressure drop value of the whole bed calculated by the present invention is basically the same as that of DNS and is significantly greater than the result calculated by the CFD-DEM method.

[0178] Figure 6 For comparison of computational efficiency, it can be found that the computational efficiency of the invention is about 100 times higher than that of the most accurate computational model DNS, while the computational efficiency of the CFD-DEM method is about 50 times higher than that of the invention.

[0179] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.

[0180] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

[0181] Furthermore, various different embodiments of the present invention can be combined in any way, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed by the present invention.

Claims

1. A numerical simulation method for online coupling of discrete and continuous phases at two scales, characterized in that, The method includes the following steps: (1) Obtain discrete phase parameters, continuous phase parameters, and boundary conditions of the device; (2) Based on the discrete unit size d in the discrete phase parameters described in step (1), set the small-scale grid size h and the large-scale grid size l of the continuous phase, where h < l; set the calculation time step Δt of the discrete phase based on h and l. d The computational time step Δt for small-scale continuous phases h And the large-scale computational time step Δt of the continuous phase l ; (3) Based on the d, h, l, Δt set in step (2) d Δt h and Δt l The algorithm sets up a small-scale mapping algorithm between discrete phase and continuous phase, a large-scale mapping algorithm between discrete phase and continuous phase, and a small-scale mapping algorithm between continuous phase and large-scale continuous phase. (4) Based on the h, l, Δt set in step (2) d Δt h and Δt l Establish a system of equations, and through the mapping set in step (3), establish the logical relationship between the small-scale and large-scale calculations of the discrete phase and the continuous phase, and complete the calculations; Step (4) describes the setting of d, h, l, Δt according to step (2). d Δt h and Δt l The system of equations is established based on the DEM model, containing d and Δt. d The discrete phase particle motion equations, and the establishment of equations containing h and Δt based on DNS. h Small-scale continuity equations and the establishment of equations containing l and Δt based on CFD l The large-scale continuity equations; The logical relationship of the calculation in step (4) is as follows: map the particle position and velocity information in step (1) to the large-scale continuity equation system, calculate the solid phase volume fraction and solid phase velocity; solve the small-scale continuity equation system to obtain the force F between the fluid phase and each particle; map the F to the discrete phase particle motion equation system to update the particle position and velocity information; map the F to the large-scale continuity equation system according to the updated particle position, calculate the force of the fluid per unit volume on the particles, solve the fluid phase momentum exchange equation and update the fluid velocity and pressure.

2. The numerical simulation method according to claim 1, characterized in that, The discrete phase parameters in step (1) include the particle diameter d. p Particle density ρ p Particle location information X p and particle velocity v p ; The continuous phase parameters include the fluid density ρ. f Fluid viscosity μ f And the fluid velocity u; The boundary conditions of the device include the device length L, device width W, device height H, and device diameter D.

3. The numerical simulation method according to claim 1, characterized in that, The discrete unit size d mentioned in step (2) is the characteristic scale of the unit mass point in the discrete simulation; The small-scale mesh size h of the continuous phase is the interface size at the contact edge between the analytical continuous phase and the discrete phase; The continuous phase large-scale grid size l is a scale containing more than one discrete unit point; The relationship between the discrete unit size d, the small-scale grid size h of the continuous phase, and the large-scale grid size l of the continuous phase is h < d < l.

4. The numerical simulation method according to claim 1, characterized in that, The discrete phase time step Δt mentioned in step (2) d Related to material properties; The small-scale time step Δt of the continuous phase h The continuous phase small-scale mesh size h satisfies the following relationship: the continuous phase small-scale movement distance is less than the continuous phase small-scale mesh size h. Among them, u j '(max) represents the maximum velocity of the continuous phase within a small-scale grid; The large-scale time step Δtl of the continuous phase and the large-scale grid size l of the continuous phase satisfy the following relationship: the large-scale motion distance of the continuous phase is less than the large-scale grid size l of the continuous phase. Among them, u i '(max) represents the maximum velocity of the continuous phase on a large-scale grid.

5. The numerical simulation method according to claim 1, characterized in that, The mapping in step (3) includes the mass, velocity and mechanical characteristics of the discrete phase and the flowing phase, and satisfies the conservation of energy and momentum.

6. The numerical simulation method according to claim 5, characterized in that, The large-scale mapping between the discrete phase and the continuous phase in step (3) satisfies the following relationship: Where X represents the variable mapped to the continuous phase large grid, M is the characteristic variable of the discrete phase, and the characteristic variable includes mass, volume, velocity and force; for some discrete points on the interface of the continuous phase large grid, w is defined as the weight of the characteristic variable of the discrete element in grid i, V is the volume of the large grid, i is the number of the large grid, and k is the number of the discrete element point in each large grid. When mapping the large-scale parameters of the continuous phase to the discrete phase, interpolation calculations are required based on the distances between the center point of the large grid and the grid intersections using the following formula: Wherein, Y and S are the characteristic parameters required for large-scale coupling calculation of discrete and continuous phases, including continuous phase velocity and pressure, D is the weight of the center point and intersection of the large grid to the discrete phase, the weight is calculated based on the distance between the discrete point and the center point and intersection of the large grid, k is the discrete unit point number in the large grid, and c is the statistical number of the center point and intersection of the large grid.

7. The numerical simulation method according to claim 5, characterized in that, The calculation method for the small-scale mapping between the discrete phase and the continuous phase in step (3) includes: z is uniformly selected on the surface of each discrete unit. k The flow field information Ψ* is calculated for each Lagrange marker point in the absence of a discrete phase. Ψ* includes either velocity U* or pressure P*. The velocity field of each discrete element's surface Lagrange point is calculated based on the velocity and coordinates of the discrete phase. The field information of the small-scale continuous phase is corrected according to the no-slip boundary condition of the coupling between the discrete and continuous phases to obtain Ψ, along with the coupling force f of the Lagrange marker points on the continuous phase. k For all f k Summing yields the coupling force F between a single discrete unit and the continuous phase. i , will F i It is added to each discrete unit point to achieve mechanical equilibrium; The calculation method for the mapping between the small-scale and large-scale continuous phases in step (3) includes: The small-scale grid size h and the large-scale grid size l of the continuous phase should satisfy l = Nh, where N is a positive integer, meaning that each large-scale grid contains N... 3 A small-scale grid; the mapping between the small-scale and large-scale continuous phases involves a time scale span, with the time step relationship being Δt. h <Δt l When mapping from a small scale to a large scale of a continuous phase, it is necessary to convert N contained in each large-scale grid. 3 The field variables within a small-scale grid are linearly averaged according to the following relationship: Among them, Ψ i This refers to large-scale grid information, which includes pressure and velocity fields, Ψ n This represents small-scale grid information, where i is the large-scale grid number.

8. The numerical simulation method according to claim 1, characterized in that, In the calculation process of the continuous phase small-scale calculation model described in step (4), it is necessary to obtain stable values ​​and pass them to the discrete phase and continuous phase large-scale calculation equations during the cross-time and spatial scale process; The obtained stable value satisfies the stability constraint condition, which is calculated by at least one iteration of the interaction force F between the small-scale continuous phase and the discrete phase. i Characterization; The average value of all discrete phases in the system And the F of a single particle i The following conditions must be met simultaneously for small-scale continuous phase calculations to reach stability: Where 0<i≤N, σ and δ are relaxation thresholds, and N is the number of discrete units in the system.

9. The numerical simulation method according to claim 1, characterized in that, The method includes the following steps: (1) Obtain discrete phase parameters, continuous phase parameters, and boundary conditions of the device; The discrete phase parameters include the particle diameter d. p Particle density ρ p Particle location information X p and particle velocity v p The continuous phase parameters include the fluid density ρ. f Fluid viscosity μ f The boundary conditions of the device include the device length L, device width W, device height H, and device diameter D. (2) Based on the discrete element size d in the discrete phase parameters described in step (1), set the small-scale grid size h and the large-scale grid size l of the continuous phase, where h < l; calculate the discrete phase time step Δt based on h and l. d Continuous phase small-scale time step Δt h and the large-scale time step Δt of the continuous phase l ; The discrete phase time step Δt d Related to the material properties of the fluid; The small-scale time step Δt of the continuous phase h The continuous phase small-scale mesh size h satisfies the following relationship: the continuous phase small-scale movement distance is less than the continuous phase small-scale mesh size h. Among them, u j '(max) represents the maximum velocity of the continuous phase within a small-scale grid; The large-scale time step Δtl of the continuous phase and the large-scale grid size l of the continuous phase satisfy the following relationship: the large-scale motion distance of the continuous phase is less than the large-scale grid size l of the continuous phase. Among them, u i '(max) represents the maximum velocity of the continuous phase on a large-scale grid; (3) Based on the Δt obtained in step (2) d Δt h and Δt l Set up mappings between discrete phases and continuous phases at small scales, between discrete phases and continuous phases at large scales, and between continuous phases at small scales and continuous phases at large scales. The mapping includes the mass, velocity, and mechanical characteristics of both the discrete and flowing phases, and satisfies energy conservation and momentum conservation. The large-scale mapping between the discrete phase and the continuous phase satisfies the following relationship: Where X represents the variable mapped to the continuous phase large grid, M is the characteristic variable of the discrete phase, and the characteristic variable includes mass, volume, velocity and force; for some discrete points on the interface of the continuous phase large grid, w is defined as the weight of the characteristic variable of the discrete element in grid i, V is the volume of the large grid, i is the number of the large grid, and k is the number of the discrete element point in each large grid. When mapping the large-scale parameters of the continuous phase to the discrete phase, interpolation calculations are required based on the distances between the center point of the large grid and the grid intersections using the following formula: Wherein, Y and S are the characteristic parameters required for large-scale coupling calculation of discrete and continuous phases, including continuous phase velocity and pressure, D is the weight of the center point and intersection of the large grid to the discrete phase, the weight is calculated based on the distance between the discrete point and the center point and intersection of the large grid, k is the discrete unit point number in the large grid, and c is the statistical number of the center point and intersection of the large grid. The calculation method for the small-scale mapping between the discrete phase and the continuous phase in step (3) includes: zk Lagrange markers are uniformly selected on the surface of each discrete unit. The flow field information Ψ* is calculated without a discrete phase. Ψ* includes either velocity U* or pressure P*. The velocity field of each Lagrange point on the surface of the discrete unit is calculated based on the velocity and coordinates of the discrete phase. Based on the no-slip boundary condition of the coupling between the discrete and continuous phases, the field information of the small-scale continuous phase is corrected to obtain Ψ, along with the coupling force f of the Lagrange markers on the continuous phase. k For all f k Summing yields the coupling force F between a single discrete unit and the continuous phase. i , will F i It is added to each discrete unit point to achieve mechanical equilibrium; The calculation method for the mapping between the small-scale and large-scale continuous phases includes: The small-scale grid size h and the large-scale grid size l of the continuous phase should satisfy l = Nh, where N is a positive integer, meaning that each large-scale grid contains N... 3 A small-scale grid; the mapping between the small-scale and large-scale continuous phases involves a time scale span, with the time step relationship being Δt. h <Δt l When mapping from a small scale to a large scale of a continuous phase, it is necessary to convert N contained in each large-scale grid. 3 The field variables within a small-scale grid are linearly averaged according to the following relationship: Among them, Ψ i This refers to large-scale grid information, which includes pressure and velocity fields, Ψ n This represents small-scale grid information, where i is the large-scale grid number; (4) Based on the h, l, Δt set in step (2) d Δt h and Δt l Establish a system of equations, and through the mapping set in step (3), establish the logical relationship between the small-scale and large-scale calculations of the discrete phase and the continuous phase, and complete the calculations; The d, h, l, Δt set according to step (2) d Δt h and Δt l The system of equations is established based on the DEM model, containing d and Δt. d The discrete phase particle motion equations, and the establishment of equations containing h and Δt based on DNS. h Small-scale continuity equations and the establishment of equations containing l and Δt based on CFD l The large-scale continuity equations; The logical relationship of the calculation is as follows: map the particle position and velocity information in step (1) to the large-scale continuity equation system, calculate the solid phase volume fraction and solid phase velocity; solve the small-scale continuity equation system to obtain the force F between the fluid phase and each particle; map the F to the discrete phase particle motion equation system to update the particle position and velocity information; map the F to the large-scale continuity equation system according to the updated particle position, calculate the force of the fluid per unit volume on the particles, solve the fluid phase momentum exchange equation and update the fluid velocity and pressure; During the calculation process of the continuous phase small-scale computational model, stable values ​​need to be obtained and passed to the discrete phase and continuous phase large-scale computational equations across time and spatial scales. Obtaining stable values ​​means satisfying stability constraints, which are achieved by calculating the interaction force F between the continuous phase small-scale and the discrete phase through at least one iteration. i Characterization; that is, the average value of all discrete phases in the system. And the F of a single particle i The following conditions must be met simultaneously for small-scale continuous phase calculations to reach stability: Where 0<i≤N, σ and δ are relaxation thresholds, and N is the number of discrete units in the system.

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