A multi-scale fluid-structure interaction coarse-grained simulation method

Abstract

The application provides a multi-scale fluid-structure coupling coarse-grained simulation method, which is applied to CFD-DEM numerical calculation of a particle-fluid system. The coarse-grained simulation method not only equivalently regards fine particles in the particle-fluid system as coarse particle agglomerates, reduces the number of calculated particles and improves the calculation efficiency, but also provides quantitative coupling relations among fine particles, coarse particle agglomerates and fluid grids of three scales in order to characterize the non-uniform distribution characteristics of the internal particles of the coarse particle agglomerates and the flow field, and adopts a kernel function to establish mapping relations and momentum exchange models of physical quantities such as mass, velocity and force between the coarse particle agglomerates and the fine particles, and between the coarse particles and the fluid grids. Therefore, the coarse-grained simulation method provided by the application not only improves the calculation efficiency, but also guarantees the numerical calculation accuracy of CFD-DEM in the particle-fluid system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of multiphase flow, and relates to a numerical calculation method of a particle-fluid system, in particular to a multi-scale fluid-solid coupling coarse graining simulation method. BACKGROUND

[0002] The particle-fluid system widely exists in chemical reaction processes in the fields of energy, pharmaceuticals, products and powder materials. The particle-fluid system has typical multi-scale characteristics, and the particles and non-uniform structures such as bubbles in the system have a significant influence on the reaction process and the transfer process. Since experimental research means has certain limitations in measurement accuracy and measurement stability, the numerical simulation method plays an increasingly important role in the research of the particle-fluid system.

[0003] The CFD-DEM simulation method processes the particles in the particle-fluid system as discrete unit particles, and processes the fluid as a continuous phase; then the position and velocity of each fine particle are tracked by using Newton's second law, the continuous phase is solved by constructing Euler grid and solving Navier-Stokes equation, and then an interphase drag force model is used to represent the interaction between the two. Therefore, the discrete-continuous coupling method of CFD-DEM conforms to the physical characteristics of the particle motion in nature, and has high accuracy.

[0004] CN 112597712A discloses a method for analyzing the transmission process in a spouted bed of non-spherical particles based on a CFD-DEM model, which comprises the following steps: establishing a fluid phase control equation group in the heat transfer process of the spouted bed, the fluid phase control equation group comprising a continuity equation, a momentum equation and an energy equation; establishing a solid phase control equation, the solid phase control equation comprising a particle motion control equation and a particle interheat equation; performing CFD-DEM coupling simulation and obtaining the temperature of the solid phase particles; selecting several groups of particles with different shapes, and performing simulation calculation under the same conditions of jet velocity, gas temperature and other parameters; and analyzing and comparing the temperature field changes of the particles with different shapes to obtain the influence law of the particle shape on the temperature field of the particles in the fluidized bed.

[0005] CN 113221474A discloses a method for simulating seepage erosion damage by CFD-DEM considering particle shape, comprising: determining the particle shape parameters of the sample in the DEM module, and calculating the particle size of the non-spherical particles by the equivalent spherical diameter method; configuring at least two preset spaces in the DEM module, and generating the sample in the preset space by the hierarchical compaction method; wherein a solid plate is used between the adjacent two preset spaces; a fluid model is established in the CFD module; the coupling module in the DEM module and the CFD module are bidirectionally coupled, and the solid plates at both ends of the sample are replaced with pore plates, and the process of simulating seepage erosion damage is calculated by coupling. It establishes a sample of non-spherical particles by discrete element, and performs bidirectional coupling calculation with the CFD module, thereby studying the mechanism of the interaction between particles and fluid from the macro and micro perspectives.

[0006] However, the above methods all have the same drawbacks. CFD-DEM calculation needs to track the movement process of each particle, which greatly reduces the calculation efficiency. In order to improve the calculation speed of CFD-DEM, a coarse-grained simulation method is usually used, that is, a larger coarse particle is used to replace a group of small particles in the system, and the calculation efficiency is improved by reducing the number of calculation particles.

[0007] For example, CN 112131633A discloses a fluid-structure coupling simulation method and system based on coarse-grained calculation theory. The method uses large particles to replace small real particles in the simulation calculation process by applying coarse-grained theory, reduces the number of discrete element particles in fluid-structure coupling calculation, and realizes the calculation of engineering scale fluid-structure coupling problems. However, this operation of simply reducing the number of particles inevitably reduces the simulation accuracy, and the main reason is that the coupling model of the fluid and the particles after coarse-graining is not improved and optimized.

[0008] Therefore, in order to improve the calculation efficiency while ensuring the accuracy of CFD-DEM simulation calculation, a coarse-grained simulation method for multi-scale fluid-structure coupling after improving and optimizing the coupling model is needed. SUMMARY

[0009] The purpose of the present application is to provide a coarse-grained simulation method for multi-scale fluid-structure coupling, especially a coarse-grained simulation method for multi-scale fluid-structure coupling suitable for CFD-DEM numerical calculation in a particle-fluid system. The coarse-grained simulation method for multi-scale fluid-structure coupling provides a coupling method for the interaction between fine particles, coarse particle aggregates and fluid, and provides a quantitative coupling relationship between fine particles, coarse particle aggregates and fluid grids of three scales, so as to characterize the non-uniform distribution characteristics of the internal flow field of the coarse particle aggregate and the coarse particle aggregate, and improve the calculation accuracy of the coarse-grained simulation.

[0010] To achieve the object of the present application, the present application adopts the following technical solutions:

[0011] The present application provides a multi-scale fluid-structure coupling coarse-grained simulation method, which comprises the following steps:

[0012] (1) determining the parameters of fine particles and fluid;

[0013] (2) setting the parameters of coarse particle agglomerates and the fluid grid size l according to the values obtained in step (1);

[0014] (3) constructing the motion equation set of coarse particle agglomerates and fluid;

[0015] (4) selecting a kernel function ξ for the mapping of coarse particle agglomerates and fluid grids, setting a scope range δ, and establishing the mapping relationship between coarse particle agglomerates and fluid grids according to the kernel function ξ and the scope range δ;

[0016] (5) calculating the volume force F v exerted on each fluid grid by fine particles, wherein the volume force F v meets the stability constraint condition, and the volume force F v is brought into the motion equation of fluid to update the velocity and position of fluid;

[0017] (6) calculating the fluid action force F dc exerted on coarse particle agglomerates, bringing the fluid action force F dc into the motion equation of coarse particle agglomerates to update the position and velocity of coarse particle agglomerates, and iteratively calculating with the fluid grid to complete the coarse-grained simulation method.

[0018] The coarse-grained simulation method not only equivalently treats fine particles in the particle-fluid system as coarse particle agglomerates, but also reduces the number of particles to be calculated and improves the calculation efficiency; further, the coarse-grained simulation method provides a quantitative coupling relationship between the coupling among fine particles, coarse particle agglomerates and fluid grids at three scales, and establishes the mapping relationship and momentum exchange model of mass, velocity and force between coarse particle agglomerates and fine particles, coarse particles and fluid grids by using a kernel function, so that the coarse-grained simulation method not only improves the calculation efficiency, but also ensures the numerical calculation accuracy of CFD-DEM in the particle-fluid system.

[0019] Optionally, when determining the parameters of fine particles and fluid in step (1), the coarse-grained simulation method can also determine device parameters, which include but are not limited to structural parameters such as length, width, height or diameter.

[0020] Preferably, the fine particle parameters in step (1) include fine particle diameter d p , fine particle density ρp , number of fine particles N p , and fine particle packing porosity.

[0021] Preferably, the fluid parameters in step (1) include fluid density p f , and fluid viscosity m f .

[0022] Preferably, the parameters of the coarse particle agglomerate in step (2) include coarse particle agglomerate diameter d c , coarse particle agglomerate volume V c , coarse particle agglomerate porosity e c , coarse particle ratio k, and the number of fine particles in each coarse particle agglomerate; the coarse particle ratio k = d c / d p ; the number of fine particles in each coarse particle agglomerate is k 3 (1-e c ).

[0023] Among the parameters of the coarse particle agglomerate, the coarse particle agglomerate porosity is equal to the fine particle packing porosity.

[0024] Preferably, the coarse particle ratio k is 5-50, for example, it can be 5, 10, 20, 30, 40 or 50, but is not limited to the listed values, and other unlisted values within the value range are also applicable. Within this value range, the calculation accuracy and efficiency of the coarse particle simulation method can be balanced.

[0025] Preferably, the fine particle diameter d p < fluid grid size l < coarse particle agglomerate diameter d c .

[0026] The present application is advantageous in describing the flow field inside the coarse particle agglomerate and the non-uniform distribution characteristics of the coarse particle agglomerate by setting the fine particle diameter d p < fluid grid size l < coarse particle agglomerate diameter d c .

[0027] Further preferably, when setting the fluid grid size l, the calculation time step At f of the fluid grid and the calculation time step At p of the coarse particle agglomerate also need to be set according to the values determined in step (1) and step (2).

[0028] wherein At p is related to material properties, such as the elastic coefficient k n of the material, so that

[0029]

[0030] △t f satisfy where u i (max) is the maximum velocity of the fluid grid, i is the number of the fluid grid, 0 < i ≤ N, N is the total number of the fluid grid.

[0031] Preferably, △t f <△t p .

[0032] Preferably, the motion equation of the coarse particle aggregate is:

[0033]

[0034] m p is the mass of the coarse particle aggregate, v p is the velocity of the single coarse particle aggregate, F dc is the fluid force acting on the coarse particle aggregate, F c is the collision force between the coarse particle aggregates.

[0035] Preferably, the motion equation of the fluid includes a fluid motion equation and a momentum exchange equation.

[0036] The fluid motion equation is:

[0037]

[0038] The momentum exchange equation is:

[0039]

[0040] where, ε f is the fluid volume fraction in the grid, U f is the center point velocity of the fluid grid, P is the center point pressure of the grid, τ f is the fluid pressure tensor.

[0041] Preferably, the kernel function ξ in step (4) includes a Gaussian function or a normal distribution function.

[0042] The present application can construct a stable mapping relationship between the coarse particle aggregate and the fluid grid through the kernel function ξ.

[0043] The kernel function in the present application is ξ(x), and the independent variable of the kernel function represents the distance between the coarse particle aggregate and the fluid grid within the scope.

[0044] Preferably, the scope δ in step (4) is the diameter d c2-5 times, for example, can be 2 times, 2.5 times, 3 times, 3.5 times, 4 times, 4.5 times or 5 times, but not limited to the listed values, other values not listed in the range are also applicable.

[0045] Preferably, step (4) includes: according to the kernel function and the scope of the range, the mapping relationship between the coarse particle agglomerates and the fluid grid is established, including: according to the coarse particle agglomerate center coordinate X p and the fluid grid center point coordinate X c , the kernel function weight ξ(|X p -X c |) is calculated, and then the weight of the volume and velocity of all coarse particle agglomerates is mapped to the fluid grid.

[0046] The solid volume fraction of the fluid grid is:

[0047]

[0048] The coarse particle agglomerate velocity in the fluid grid is:

[0049] <U s > i =∑v p ×ξ(|X p -X c |)

[0050] Wherein, i is the number of the fluid grid, 0 cell is the total number of the fluid grid; V v is the volume of the fluid grid.

[0051] Preferably, the kernel weight of a single coarse particle agglomerate in the scope of the range is normalized after being added up, and the weight addition is 1.

[0052] Preferably, the volume force of each fluid grid in step (5) is: i = N v F di / V cell .

[0053] Wherein, the N i is the number of fine particles in each fluid grid,

[0054] The F di is the fluid force F di (Re, <ε s ) i ) calculated by using the uniform drag force model, Re is the Reynolds number of the fine particle.

[0055] Preferably, the uniform drag force model includes the Gidaspow drag force model.

[0056] Preferably, the Reynolds number of the fine particles i is the number of the fluid grid, 0 < i ≤ N, N is the total number of the fluid grids.

[0057] Preferably, the stability constraint condition in step (5) is that the average value of the volume force of the fine particles on the fluid grid and the volume force (F v ) i satisfies the following conditions simultaneously:

[0058] and |((F v ) i ) t -((F v ) i ) t-1 |≤λ

[0059] wherein i is the number of the fluid grid, 0 < i ≤ N, N is the total number of the fluid grids; t is the calculation time step of the fluid grid, and σ and λ are relaxation calculation thresholds.

[0060] Preferably, the calculation of the fluid force F dc exerted on the coarse particle agglomerate in step (6) is as follows:

[0061] <F dc > j =∑F di *ξ(|X p -X c |×k 3 (1-ε c ))

[0062] wherein j is the number of the coarse particle agglomerate.

[0063] As a preferred technical scheme of the coarse-grained simulation method, the coarse-grained simulation method comprises the following steps:

[0064] (1) determining fine particle parameters and fluid parameters; the fine particle parameters include fine particle diameter d p , fine particle density ρ p , fine particle number N p , and fine particle packing porosity; the fluid parameters include fluid density ρ f and fluid viscosity μ f ;

[0065] (2) setting parameters of coarse particle agglomerates and fluid grid size l according to the values obtained in step (1); the parameters of the coarse particle agglomerates include coarse particle agglomerate diameter d c , coarse particle agglomerate volume Vc , porosity of coarse-grained aggregates ε c , coarse-grained ratio k and the number of fine particles in each coarse-grained aggregate; fine particle diameter d p <Fluid grid size l < Coarse-grained aggregate diameter d c ;

[0066] (3) Construct the motion equation of coarse-grained aggregates and fluid, and then establish the position and velocity mapping of coarse-grained aggregates and fluid grid;

[0067] (4) Select the kernel function ξ of coarse-grained aggregates and fluid grid mapping, and set the scope range δ, which is 2-5 times the coarse-grained aggregate diameter d c ; According to the kernel function ξ and the scope range δ, the mapping relationship between coarse-grained aggregates and fluid grid is established: According to the center coordinates X p of coarse-grained aggregates and the center point coordinates X c of fluid grid, the kernel function weight ξ(|X p -X c |) is calculated, and then the volume and velocity weights of all coarse-grained aggregates are mapped to fluid grid;

[0068] (5) Calculate the volume force F v of each fluid grid received by fine particles, which meets the stability constraint condition, and bring the volume force F v into the motion equation of fluid to update the velocity and position of fluid; The stability constraint condition is that the average value of the volume force F v of the fluid grid received by fine particles and the volume force (F v ) i of each fluid grid meet:

[0069] and |((F v ) i ) t -((F v ) i ) t-1 |≤λ

[0070] Where i is the number of fluid grid, 0 < i ≤ N, N is the total number of fluid grid; t is the calculation time step of fluid grid, and σ and λ are relaxation calculation thresholds, respectively;

[0071] (6) Calculate the fluid action force F dc received by coarse-grained aggregates, bring the fluid action force F dc into the motion equation of coarse-grained aggregates to update the position and velocity of coarse-grained aggregates, and iterate with fluid grid to complete the coarse-grained simulation method.​

[0072] Compared with the prior art, the present application has the following beneficial effects:

[0073] The coarse-grained simulation method provided by the present application can be widely applied to a particle-fluid system, characterizes the non-uniform distribution characteristics of the internal coarse particles and the particle and flow field in the system, establishes a strong coupling correlation model of velocity, force and other physical quantities in three scales of fine particle-agglomerate-coarse particle-fluid grid, improves the calculation efficiency and accuracy of the CFD-DEM simulation method, and can be embedded and applied in various open source and commercial CFD software. BRIEF DESCRIPTION OF DRAWINGS

[0074] Figure 1 A flow chart of the multi-scale fluid-structure coupling coarse-grained simulation method of the present application;

[0075] Figure 2 A schematic diagram of the multi-scale fluid-structure coupling coarse-grained simulation method of the present application;

[0076] Figure 3 A comparison chart of the results of Example 1 and Comparative Example 1 of the present application.

[0077] Figure 4 A comparison chart of the results of Example 2 and Example 3 of the present application. DETAILED DESCRIPTION

[0078] The technical solutions of the present application will be further described below through specific embodiments. Those skilled in the art should understand that the embodiments are only to help understand the present application and should not be regarded as specific limitations on the present application.

[0079] Example 1

[0080] This embodiment provides a multi-scale fluid-structure coupling coarse-grained simulation method as shown in Figure 1 , 2 The coarse-grained simulation method comprises the following steps:

[0081] (1) determining fine particle parameters, fluid parameters and device size; the fine particle parameters include fine particle diameter d p = 0.275 mm, fine particle density p p = 2500 kg / m 3 , fine particle number N p = 1.54 x 10 8 and fine particle packing porosity = 0.4; the fluid parameters include fluid density p f = 1.2 kg / m 3 and fluid viscosity m f= 0.000018 Pa-s; the equipment size includes length L = 0.28 m, width W = 0.025 m and height H = 1 m; the operation parameter includes inlet upward flow rate of 0.46 m / s (the data source of this embodiment is "Taghipour et al, Experimental and computational study of gas-solid fluidized bed hydrodynamics [J], Chemical Engineering Science, 2005 (60): 6857-6867").

[0082] (2) setting the parameters of the coarse particle agglomerate and the fluid grid size l = 2.5 mm according to the numerical value obtained in step (1); the parameters of the coarse particle agglomerate include coarse particle agglomerate diameter d c = 5.5 mm, coarse particle agglomerate volume coarse particle agglomerate porosity ε c = 0.4, coarse particle agglomerate ratio k = d c / d p = 20 and the number of fine particles in each coarse particle agglomerate k 3 (1-ε c ) = 4800; the calculation time step △t f of the fluid = 5 × 10 -5 s, the calculation time step △t p of the coarse particle agglomerate = 1 × 10 -4 s;

[0083] (3) constructing the motion equation set of the coarse particle agglomerate and the fluid, and then establishing the position and velocity mapping of the coarse particle agglomerate and the fluid grid;

[0084] The motion equation set of the coarse particle agglomerate is:

[0085]

[0086] m p is the mass of the coarse particle agglomerate (m p = V c × ρ p = 1.3 × 10 -4 kg), v p is the velocity of a single coarse particle agglomerate, F dc is the fluid acting force on the coarse particle agglomerate, F c is the collision force between the coarse particle agglomerates;

[0087] The motion equation set of the fluid includes the fluid motion equation and the momentum exchange equation;

[0088] The fluid motion equation is:

[0089]

[0090] The momentum exchange equation is:

[0091]

[0092] Wherein, ε f is the fluid volume fraction in the grid, U f is the center point velocity of the fluid grid, P is the center point pressure of the grid, τ f is the fluid pressure tensor;

[0093] (4) Select the core function ξ(X p ) = (1-X p 2 ) 4 of the coarse particle agglomerate and the fluid grid mapping, and set the scope range δ = 2.5d c = 13.75mm (d c is the diameter of the coarse particle agglomerate); According to the core function ξ and the scope range δ, the mapping relationship between the coarse particle agglomerate and the fluid grid is established: According to the center coordinates X p of the coarse particle agglomerate and the center point coordinates X c of the fluid grid, the core function weight ξ(|X p -X c |) is calculated, and then the weight of the volume and velocity of all coarse particle agglomerates is mapped to the fluid grid;

[0094] The solid volume fraction of the fluid grid is:

[0095]

[0096] The coarse particle agglomerate velocity in the fluid grid is:

[0097] <U s > i =∑v p ×ξ(|X p -X c |)

[0098] Wherein, i is the number of the fluid grid, 0 < i ≤ N, N is the total number of the fluid grid: N = 448000; V cell is the volume of the fluid grid: V cell = 2.5 3 mm 3 = 15.625mm 3 ;

[0099] (5) Calculate the volume force F v, the volume force F v , the volume force F v is brought into the motion equation of the fluid to update the velocity and position of the fluid;

[0100] F v = N i F di / V cell , the F di is the fluid force F di acting on the fluid grid calculated by using the Gidaspow drag force model s (Re, <ε i ), Re is the Reynolds number of the fine particles; the Reynolds number of the fine particles i is the number of the fluid grid, 0 < i ≤ N, N is the total number of the fluid grids; the N i is the number of the fine particles in each fluid grid,

[0101] The stability constraint condition is that the average value of the volume force F of the fluid grid and the volume force (F v ) of each fluid grid i satisfy the following conditions simultaneously:

[0102] and | ((F v ) i ) t - ((F v ) i ) t-1 | ≤ λ

[0103] Wherein, i is the number of the fluid grid, 0 < i ≤ N, N is the total number of the fluid grids; t is the calculation time step of the fluid grid, σ and λ are the relaxation calculation thresholds, respectively 0.05G and 0.1G (G is the gravity of the coarse particle agglomerate, in this embodiment, 1.3 × 10 -4 × 9.81 = 1.2 × 10 -3 N);

[0104] (6) calculating the fluid force F dc , the fluid force F dc is brought into the motion equation of the coarse particle agglomerate to update the position and velocity of the coarse particle agglomerate, and the fluid grid is iterated to complete the coarse graining simulation method;

[0105] The calculation of the fluid force F dc acted on the coarse particle agglomerate is:

[0106] <Fdc > j =∑F di ×ξ(|X p -X c |×k 3 (1-ε c ))

[0107] where j is the number of coarse particle aggregates.

[0108] The final calculation results of this example are shown in Table 1. Figure 3

[0109] Example 2

[0110] This example provides a multi-scale fluid-structure coupling coarse-grained simulation method as shown in Table 2, which comprises the following steps: Figure 1

[0111] (1) Determine the fine particle parameters, fluid parameters and equipment size; the fine particle parameters include fine particle diameter d p = 0.125 mm, fine particle density p p = 2500 kg / m 3 , fine particle number N p = 1.75 x 10 9 and fine particle packing porosity = 0.4; the fluid parameters include fluid density p f = 1.2 kg / m 3 and fluid viscosity m f = 0.000018 Pa·s; the equipment size includes diameter D = 0.138 m and height H = 1 m; the operating parameters include an inlet upward flow rate of 0.26 m / s (the above data is from “Yassir et al, The effect of friction and inter-particle cohesive forces on the hydrodynamics of gas-solid flow: A comparative analysis of theoretical predictions and experiments [J], Powder Technology, 2006 (163): 69-79”).

[0112] (2) Set the parameters of coarse particle aggregates and fluid grid size l = 1.0 mm according to the numerical values obtained in step (1); the parameters of coarse particle aggregates include coarse particle aggregate diameter d c = 1.25 mm, coarse particle aggregate volume coarse-grained aggregate porosity e c ​​= 0.4, coarse-grained ratio k = d c / d p = 10 and the number of fine particles within each coarse particle aggregate k 3 (1-ε c ) = 600; the calculation time step of the fluid △t f = 1 x 10 -6 s, the calculation time step of the coarse particle aggregate △t p = 1 x 10 -5 s;

[0113] (3) constructing the motion equation set of the coarse particle aggregate and the fluid, and then establishing the position and velocity mapping of the coarse particle aggregate and the fluid grid;

[0114] The motion equation set of the coarse particle aggregate is:

[0115]

[0116] m p is the mass of the coarse particle aggregate (m p = V c x p p = 1.53 x 10 -6 kg), v p is the velocity of a single coarse particle aggregate, F dc is the fluid acting force on the coarse particle aggregate, F c is the collision force between the coarse particle aggregates;

[0117] The motion equation set of the fluid includes the fluid motion equation and the momentum exchange equation;

[0118] The fluid motion equation is:

[0119]

[0120] The momentum exchange equation is:

[0121]

[0122] wherein, ε f is the fluid volume fraction in the grid, U f is the center point velocity of the fluid grid, P is the center point pressure of the grid, τ f is the fluid pressure tensor;

[0123] (4) selecting the kernel function ξ(X p ) = (1-X p 2 ) 4 of the coarse particle aggregate and the fluid grid mapping, and setting the scope range δ = 2.5d c= 3.125 mm (d c According to the kernel function ξ and the scope range δ, the mapping relationship between the coarse particle agglomerate and the fluid grid is established: according to the coarse particle agglomerate center coordinate X p and the fluid grid center point coordinate X c The kernel function weight ξ (|X p -X c |) is calculated, and then the weight of the volume and velocity of all coarse particle agglomerates is mapped to the fluid grid;

[0124] The solid volume fraction of the fluid grid is:

[0125]

[0126] The coarse particle agglomerate velocity in the fluid grid is:

[0127] <U s > i =∑v p ×ξ(|X p -X c |)

[0128] Wherein, i is the number of the fluid grid, 0 < i ≤ N, N is the total number of the fluid grid: N = 7200000; V cell is the volume of the fluid grid, since the reactor in the embodiment is a cylinder, the volumes of different grids may not be the same, the average volume V cell of the grid = 2.07 × 10 -9 mm 3 ;

[0129] (5) The volume force F v of the fine particles on each fluid grid is calculated, the volume force F v meets the stability constraint condition, and the volume force F v is brought into the motion equation of the fluid to update the velocity and position of the fluid;

[0130] F v = N i F di / V cell , F di is the fluid action force F di (Re, <ε s ) i ) in the fluid grid calculated by using the Gidaspow drag force model, Re is the Reynolds number of the fine particles; the Reynolds number of the fine particles i is the number of the fluid grid, 0 < i ≤ N, N is the total number of the fluid grid; N i is the number of fine particles in each fluid grid,

[0131] The stability constraint condition is that the average value of the volume force of the fluid grid is subjected to fine particles And the volume force (F v ) i Meanwhile, the following conditions are met:

[0132] And |((F v ) i ) t -((F v ) i ) t-1 |≤λ

[0133] Wherein, i is the number of the fluid grid, 0 < i ≤ N, N is the total number of the fluid grid; t is the calculation time step of the fluid grid, σ and λ are relaxation calculation thresholds, the values are 0.05G and 0.1G respectively (G is the gravity of the coarse particle agglomerate, in this embodiment, it is 1.53×10 -6 ×9.81 = 1.5×10 -5 N);

[0134] (6) Calculate the fluid action force F dc on the coarse particle agglomerate, and bring the fluid action force F dc into the motion equation of the coarse particle agglomerate, update the position and speed of the coarse particle agglomerate, and iterate with the fluid grid to complete the coarse graining simulation method;

[0135] The calculation of the fluid action force F dc on the coarse particle agglomerate is as follows:

[0136] <F dc > j =∑F di ×ξ(|X p -X c |×k 3 (1-ε c ))

[0137] Wherein, j is the number of the coarse particle agglomerate.

[0138] The final calculation result of this embodiment is shown in Figure 4 .

[0139] Embodiment 3

[0140] This embodiment provides a multi-scale fluid-structure coupling coarse graining simulation method as shown in Figure 1 , which comprises the following steps:

[0141] (1) determining fine particle parameters, fluid parameters, and equipment size; the fine particle parameters include fine particle diameter d p = 0.125 mm, fine particle density p p = 2500 kg / m 3 , fine particle number N p = 1.75 x 10 9 , and fine particle packing porosity = 0.4; the fluid parameters include fluid density p f = 1.2 kg / m 3 and fluid viscosity m f = 0.000018 Pa-s; the equipment size includes diameter D = 0.138 m and height H = 1 m; and the operating parameters include an inlet upward flow velocity of 0.26 m / s (the above data is from “Yassir et al, The effect of friction and inter-particle cohesive forces on the hydrodynamics of gas-solid flow: A comparative analysis of theoretical predictions and experiments [J], Powder Technology, 2006 (163): 69-79”).

[0142] (2) setting coarse particle agglomerate parameters and fluid grid size l = 2.5 mm according to the values obtained in step (1); the coarse particle agglomerate parameters include coarse particle agglomerate diameter d c = 5 mm, coarse particle agglomerate volume coarse particle agglomerate porosity e c = 0.4, coarse particle ratio k = d c / d p = 40, and the number of fine particles in each coarse particle agglomerate k 3 (1-e c ) = 38400; the calculation time step of the fluid At f = 1 x 10 -6 s, and the calculation time step of the coarse particle agglomerate At p = 5 x 10 -5 s;

[0143] (3) constructing the motion equation set of the coarse particle agglomerate and the fluid, and then establishing the position and velocity mapping of the coarse particle agglomerate and the fluid grid;

[0144] The motion equation set of the coarse particle agglomerate is:

[0145]

[0146] m p The mass of coarse particle aggregates (m p =V c ×ρ p =9.82×10 -5 kg), v p For the velocity of a single coarse particle agglomerate, F dc F represents the fluid force acting on the coarse particle agglomerates. c The collision force between coarse particle aggregates;

[0147] The set of equations of motion for the fluid includes the fluid motion equations and the momentum exchange equations;

[0148] The fluid motion equation is:

[0149]

[0150] The momentum exchange equation is:

[0151]

[0152] Where, ε f U represents the fluid volume fraction in the grid. f Let τ be the velocity at the center point of the fluid mesh, P be the pressure at the center point of the mesh, and τ be the pressure at the center point of the mesh. f For fluid pressure tensor;

[0153] (4) Select the kernel function ξ(X) for mapping coarse-grained agglomerates to the fluid mesh. p )=(1-X p 2 ) 4 And set the scope range δ = 2.5d c =12.5mm(d) c (where ξ is the diameter of the coarse particle agglomerate); establish the mapping relationship between the coarse particle agglomerate and the fluid mesh based on the kernel function ξ and the domain range δ: based on the center coordinates X of the coarse particle agglomerate... p and the center point coordinates X of the fluid grid c Calculate the kernel function weights ξ(|X) p -X c |), and then the volume and velocity weights of all coarse particle agglomerates are mapped to the fluid mesh;

[0154] The solid volume fraction of the fluid mesh is:

[0155]

[0156] The velocity of coarse-particle aggregates in the fluid mesh is:

[0157] s >​i =∑v p ×ξ(|X p -X c |)

[0158] where i is the number of fluid grid, 0 < i ≤ N, N is the total number of fluid grids: N = 608000; V cell is the volume of fluid grid, since the reactor in this embodiment is a cylinder, the volume of different grids can not be the same, the average volume of the grid V cell = 2.46 × 10 -8 mm 3 ;

[0159] (5) Calculate the volume force F v exerted on each fluid grid by fine particles, the volume force F v meets the stability constraint condition, and the volume force F v is brought into the motion equation of the fluid to update the velocity and position of the fluid;

[0160] F v = N i F di / V cell , F di is the fluid force F di (Re, <ε s > i ) in the fluid grid calculated by using the Gidaspow drag force model, Re is the Reynolds number of fine particles; the Reynolds number of fine particles i is the number of fluid grid, 0 < i ≤ N, N is the total number of fluid grids; N i is the number of fine particles in each fluid grid,

[0161] The stability constraint condition is that the average value of the volume force F v exerted on the fluid grid by fine particles and the volume force (F i ) of each fluid grid satisfy:

[0162] and |((F v ) i ) t -((F v ) i ) t-1 |≤λ

[0163] Among them, i is the number of fluid grids, where 0 < i ≤ N, and N is the total number of fluid grids; t is the computational time step of the fluid grid, and σ and λ are the relaxation calculation thresholds, with values of 0.05G and 0.1G respectively (G is the gravity of coarse particle aggregates, which is 9.82×10 -5 ×9.81 = 9.63×10 -4 N);

[0164] (6) Calculate the fluid force F dc acting on the coarse particle aggregates, substitute the fluid force F dc into the motion equation of the coarse particle aggregates, update the position and velocity of the coarse particle aggregates, and perform iterative calculations with the fluid grids to complete the coarse-graining simulation method; the calculation results finally obtained in this embodiment are as shown in Figure 3 ;

[0165] The calculation of the fluid force F dc acting on the coarse particle aggregates is as follows:

[0166] <F dc > j = ∑F di ×ξ(|X p - X c |×k 3 (1 - ε c ))

[0167] Among them, j is the number of the coarse particle aggregates.

[0168] The calculation results finally obtained in this embodiment are as shown in Figure 4 ;

[0169] Comparative Example ①

[0170] This comparative example provides a traditional fluid-structure interaction method, which is carried out according to the method disclosed in the paper "Liqiang Lu et al, EMMS-based discrete particle method (EMMS–DPM) for simulation of gas–solid flows [J]. Chemical Engineering Science, 2014(120): 67 - 87", and the obtained results are as shown in Figure 3 ;

[0171] Figure 3 For the comparison of the result data obtained in Example ① and the result data obtained in Comparative Example ①, it can be seen from Figure 3 that the calculation results of the coarse-graining simulation method provided by the present invention are more accurate.

[0172] Figure 4For comparison of the data obtained in Examples 2 and 3 with the data obtained in experiments and simulations reported in the publication Yassir et al, The effect of friction and inter-particle cohesive forces on the hydrodynamics of gas-solid flow: A comparative analysis of theoretical predictions and experiments [J], Powder Technology, 2006 (163): 69-79, it is known that the calculation results of the coarse-grained simulation method provided by the present application are more accurate. Figure 4 The coarse-grained simulation method provided by the present application is more accurate.

[0173] In summary, the coarse-grained simulation method provided by the present application can be widely applied to particle-fluid systems, characterizes the non-uniform distribution characteristics of the internal coarse particles and the particles and flow field in the system, establishes a strong coupling correlation model of physical quantities such as velocity and force from the three scales of fine particle-agglomerate-coarse particle-fluid grid, improves the calculation efficiency and accuracy of the CFD-DEM simulation method, and can be embedded and applied in various open source and commercial CFD software.

[0174] The applicant declares that the above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto. It should be understood by those skilled in the art that any changes or replacements within the technical scope disclosed by the present application can be easily thought of by any person skilled in the art, and all fall within the protection scope and disclosure scope of the present application.

Claims

1. A coarse-grained simulation method for multi-scale fluid-structure interaction, characterized in that, The coarse-grained simulation method includes the following steps: (1) Determine the fine particle parameters and fluid parameters; the fine particle parameters include the fine particle diameter d. p Fine particle density ρ p Number of fine particles N p With fine particle packing porosity; the fluid parameters include fluid density ρ f With fluid viscosity μ f ; (2) Set the parameters of the coarse particle agglomerates and the fluid grid size l according to the values ​​obtained in step (1); the parameters of the coarse particle agglomerates include the diameter d of the coarse particle agglomerates. c Volume V of coarse particle aggregates c coarse-grained agglomerates porosity ε c The coarsening ratio k and the number of fine particles within each coarse particle agglomerate; the diameter d of the fine particles. p <Fluid mesh size l < coarse particle agglomerate diameter d c ; (3) Construct the equations of motion for coarse particle aggregates and fluids; (4) Select the kernel function ξ for mapping the coarse particle agglomerates to the fluid mesh, and set the scope range δ, where the scope range δ is the diameter d of the coarse particle agglomerates. c 2-5 times; Establish the mapping relationship between coarse-grained agglomerates and the fluid mesh based on the kernel function ξ and the domain range δ: based on the center coordinates X of the coarse-grained agglomerates p and the center point coordinates X of the fluid grid c Calculate the kernel function weights ξ(|X) p -X c |), and then the volume and velocity weights of all coarse particle agglomerates are mapped to the fluid mesh; (5) Calculate the volume force F exerted on each fluid mesh by the fine particles. v The volume force F v The stability constraint condition is met, and the volume force F is... v The velocity and position of the fluid are updated by substituting them into the fluid's equations of motion; the stability constraint is the average volume force exerted on the fluid mesh by the fine particles. and the volume force of each fluid grid Simultaneously satisfy: ,and where i is the number of fluid grids, 0 < i ≤ N, and N is the total number of fluid grids; t is the computational time step of the fluid grid, and σ and are the relaxation calculation thresholds, respectively; (6) Calculate the fluid force F acting on the coarse particle agglomerate. dc The fluid force F dc The motion equations of the coarse-grained agglomerates are substituted into the equations of motion to update the position and velocity of the agglomerates, and the calculation is iteratively performed with the fluid mesh to complete the coarsening simulation method; the fluid force F acting on the coarse-grained agglomerates is calculated. dc for: Where j is the number of the coarse particle agglomerate.

2. The coarse-grained simulation method according to claim 1, characterized in that, The coarsening ratio k=d in step (2) c / d p The number of fine particles within each coarse aggregate is k. 3 (1-ε c ).

3. The coarse-grained simulation method according to claim 2, characterized in that, The coarsening ratio k is 5-50.

4. The coarse-grained simulation method according to claim 1, characterized in that, The equations of motion for the coarse particle agglomerates are as follows: m p v represents the mass of coarse particle aggregates. p For the velocity of a single coarse particle agglomerate, F dc F represents the fluid force acting on the coarse particle agglomerates. c It represents the collision force between coarse particle aggregates.

5. The coarse-grained simulation method according to claim 1, characterized in that, The set of equations of motion for the fluid includes the fluid motion equations and the momentum exchange equations; The fluid motion equation is: The momentum exchange equation is: Where, ε f U represents the fluid volume fraction in the grid. f Let τ be the velocity at the center point of the fluid mesh, P be the pressure at the center point of the mesh, and τ be the pressure at the center point of the mesh. f It is the fluid pressure tensor.

6. The coarse-grained simulation method according to claim 1, characterized in that, The kernel function ξ in step (4) includes a Gaussian function or a normal distribution function; The solid volume fraction of the fluid mesh is: The velocity of the coarse particle aggregates in the fluid grid is: where i is the number of the fluid grid, 0 < i ≤ N, and N is the total number of fluid grids; V cell is the volume of the fluid grid.

7. The coarse-grained simulation method according to claim 4, characterized in that, The weights of individual coarse particle aggregates within the scope of the action are summed and then normalized, with the sum of weights being 1.

8. The coarse-grained simulation method according to claim 6, characterized in that, In step (5), the volume force exerted on each fluid mesh by the fine particles is: F v =N i F di / V cell ; Wherein, the N i The number of fine particles within each fluid grid. ; The F di The fluid force F acting within the fluid grid, calculated using a uniform drag model. di (Re,<ε s > i ), where Re is the Reynolds number of the fine particles.

9. The coarse-grained simulation method according to claim 8, characterized in that, The uniform drag model includes the Gidaspow drag model.

10. The coarse-grained simulation method according to claim 8, characterized in that, The Reynolds number of the fine particles , where i is the number of the fluid grid, 0 < i ≤ N, and N is the total number of fluid grids.

Images