CN111062132B - Construction of slender flexible filamentous particle model and numerical simulation method thereof - Google Patents
Construction of slender flexible filamentous particle model and numerical simulation method thereof Download PDFInfo
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Abstract
The invention constructs an elongated flexible filament particle model according to the physical characteristics of an elongated flexible filament biomass, and couples with OpenFoam software of an open source to realize numerical simulation of the elongated flexible filament particle in the fluidization processing process, the numerical simulation result can be used for holographically simulating the motion characteristics of the elongated flexible filament particle in the fluidization processing process, the fluidization morphology and the mass and heat transfer efficiency of the elongated flexible filament particle under different working conditions can be vividly represented, and the simulation result and the field experimental data of the method are basically consistent through verification, so that the reliability is high, the interaction mechanism of the elongated flexible filament particle in the fluidization process is conveniently, efficiently captured and reproduced, the relatively real and objective reflection is obtained, and an effective solving way is provided for improving and optimizing the fluidization processing equipment of the elongated flexible filament particle, and the method has important theoretical significance and practical value.
Description
Technical Field
The invention belongs to the technical field of computer numerical simulation, and particularly relates to construction of an elongated flexible filamentous particle model and a numerical simulation method thereof.
Background
Elongate, flexible, threadlike particles are widely available in the fields of tobacco, food processing, agriculture, biomass combustion, medicine, environmental protection, etc., where fluidization technology-based machinery is widely involved in the flow of particles in two-phase or multiphase flow during processing of elongate, flexible, threadlike particles. In particular, in the tobacco industry, fluidization processing of cut tobacco is widely performed in operation units such as threshing and redrying, air drying, stem and shred separation, loose cooling, impurity removal and dust removal, material conveying and the like, while the cut tobacco is used as a representative of slender filamentous particles, the motion characteristics of the cut tobacco are more complex than those of spherical particles, and the conditions of the cut tobacco are more complex in two-phase or multiphase flow, and the method relates to multiple aspects such as material mechanics, hydrodynamics, rheology, multi-rigid system, turbulence theory and the like. At present, in tobacco fluidization processing, the overall research on the motion characteristics in the tobacco fluidization processing process is imperfect, and a plurality of fluidization problems are needed to be solved in continuous exploration. For example: the cut tobacco in the air flow drying process is agglomerated, and the cut tobacco in the pneumatic conveying process is crushed. Therefore, the research on the flow characteristics of the tobacco shreds in the fluidization processing process is significant in optimizing the process parameters, reducing the agglomeration, breakage and uneven moisture of the tobacco shreds in the fluidization processing, optimizing the fluidization equipment, further improving the quality of the tobacco shreds and improving the quality stability of cigarettes.
However, the tobacco shreds are soft, easy to deform and complex and changeable in movement, and if the movement characteristics of the tobacco shreds in the fluidization process are explored by a traditional experimental means, the experimental period is long, the acquired data are limited, and the cost is high. In recent years, gas-solid two-phase flow simulation based on computational fluid dynamics has been greatly improved, but for the assumption that the simulation of the slender flexible filament particles represented by cut tobacco is based on spherical particles, the change of geometric structural characteristics on the particle scale is ignored, the fluidization motion state and mutual influence factors of the slender flexible filament particles are greatly simplified, the space motion characteristics of the slender flexible filament particles are also lost in the simulation process, the simulation result cannot well represent the complex motion characteristics of the slender flexible filament particles and the defects of the mass and heat transfer process, the simulation result is far different from the true form of the cut tobacco, and the motion characteristics of the cut tobacco are difficult to be truly displayed. Thereby greatly reducing the simulation accuracy in the numerical simulation process. Therefore, it is necessary to construct an elongated flexible filament model and a numerical simulation method thereof.
Disclosure of Invention
The invention solves the technical problems that: the invention can truly and objectively reflect the interaction mechanism between the slender flexible filament particles and the particles, the motion characteristics of the slender flexible filament particles in fluidization equipment, an effective way is provided for product design and optimization of the slender flexible filament particle fluidization processing equipment, and a foundation is laid for the subsequent numerical simulation research of mass and heat transfer.
The invention adopts the technical scheme that: the construction of the slender flexible filament particle model and the numerical simulation method thereof comprise the following steps of;
1) According to the physical structure characteristics of the slender flexible filament particles, based on a DEM model, constructing a slender flexible filament particle model, adding a constraint force equation of the slender flexible filament particle model, and constructing a motion equation of the slender flexible filament particle model;
2) Drawing a three-dimensional solid model by CAD drawing software, and dividing calculation grid nodes of a simulation area according to the three-dimensional solid model by Pointwise;
3) A basic physical model is built for the grid using OpenFoam: basic control equations, namely a continuity equation, a momentum equation and an energy equation, and establishing a wall collision model;
4) Defining physical properties of the elongate flexible filamentary particles, the physical properties comprising: density ρ, thickness h, width d, length l, rolling friction coefficient μ r;
5) Coupling the constructed flexible filamentous particle model with open-source computational fluid dynamics numerical simulation software OpenFoam to realize parallel simulation calculation of discrete simulation of the flexible filamentous particle model;
6) Defining channel inlet and outlet boundary conditions and wall conditions;
7) Defining initial conditions: the quantity of the flexible filiform particles, the initial position and the initial speed of the flexible filiform particle model, and the initial speed and the density of the gas phase are defined;
8) Discretizing the basic control equation of the step 3), and sealing and solving by adopting the boundary conditions and the initial conditions defined in the step 6) and the step 7);
9) Initializing the whole calculation region, setting a time step and a simulation time length, repeatedly iterating algebraic equation sets in the calculation region until the set simulation time length is met, completing numerical simulation of the fluidization process of the flexible filamentous particles, and storing a calculation result by using a time step storage mechanism;
10 Post-processing analysis and display of the calculations.
In the step 1), the particles are assumed to be rigid bodies in the DEM model, and when the DEM model processes the collision among the particles, the interaction between the particles allows slight overlapping, and the overlapping amount is far smaller than the size of the particles; particles can only act with adjacent particles, and individual particles can be subjected to the action of all particles; the collision acting force of particles in the DEM model is processed and calculated by adopting a spring-damper-sliding friction device model;
the calculation method of the inter-particle acting force by adopting the Hooke model and the calculation method of the single spherical inter-particle acting force have the following motion equation:
The collision acting force consists of a normal force and a tangential force, and assuming that the direction from the center of mass of the particle i to the center of mass of the particle j is a normal direction, the normal force F n and the tangential force F t borne by the particle i are as follows:
Fn＝knδnij-γnvnij (1)
Ft＝ktδtij-γtvtij,max(|Ft|)＝|μFn| (2)
the rigidity coefficient in the k n normal direction, the gamma n normal direction is a damping coefficient, the rigidity coefficient in the k t normal direction, the gamma t tangential direction is a damping coefficient, δn ij is the overlap amount between particles, the displacement of the particles generated by δt ij tangential force, and mu is the rolling friction coefficient of the particles; v nij is the component of the relative velocity of the impinging particles in the normal direction, v tij is the slip velocity between the impinging particles;
In the Hooke model, δt ij is ignored and k n,γn,kt,γt is calculated as follows:
kn＝kt (6)
γn＝γt (7)
these 4 coefficients are calculated from the properties and contact states of two particles that collide with each other:
Wherein R is the radius of the particles, m is the mass of the particles, e is a coefficient, Y is Young's modulus, v is Poisson's ratio;
on the basis of a DEM model, adding an action potential function between grouped particles, binding the particles together by adding the action potential function, and forming flexible filamentous particles; the potential function is as follows:
Ψij(rij)＝k(rij-ro) (19)
Wherein r ij represents the distance between the two particles i and j; psi ij is the opposite potential, r o is the truncated radius, which corresponds to the radius of the hard sphere, and k is the coefficient of action;
The specific binding method comprises the following steps: by adding an action potential function between particles, the action potential function added between particles acts when the adjacent particles exceed a set cutoff radius in the movement process of the particles, acting force is applied to the particles and the particles to bind the particles together, and when the adjacent particles are smaller than the set cutoff radius, the particles exert acting force on the particles on the basis of the stress of the DEM model, and the additional action potential function is also applied to the particles and the particles to repel the particles and restore the particle spacing to the set cutoff radius; finally forming a flexible thread-like cut tobacco particle model by a binding method;
Besides the DEM model and the action potential function among particles, the motion equation of the translational motion and the rotation of the particles follows newton's second law, which is respectively:
Wherein m and I represent the mass and moment of inertia of the particles; v and ω represent the translational and rotational speeds of the particles; t is time; g represents gravitational acceleration; r represents a vector pointing from the particle centroid to the collision contact point, the value of which is the particle radius;
and (3) carrying out iterative updating on the solving process of the particle position and speed equation by adopting a frog-leaping algorithm, wherein the frog-leaping algorithm updates the position and the speed by using the position at the time t and the speed at the time t-delta t/2, and the acting force F (t) obtained by calculating the position at the time t is updated by using the formula as follows:
In the step 2), the calculation area of the three-dimensional solid model is divided by adopting a block hexahedral structured grid.
In the step 3), the slender flexible filament particles basically show turbulent motion in the fluidization process, and the basic control equation is as follows;
1. equation of fluid control
The fluid phase satisfies the mass conservation and momentum conservation equations:
Wherein, Epsilon g is the gas phase volume fraction, v pairIs the average speed of particles in the grid, beta is the coefficient of gas-solid drag force,/>Is the resultant force to which the gas phase is subjected, including contact force, van der Waals force;
2. Particulate phase control equation
Ψp-p＝k(dp-p-rcut) (23)
Wherein,The differential pressure force is F c, the inter-particle interaction force is F d, the drag force of particles is mg, the gravity of particles is, ψ p-p is the inter-particle binding force in a flexible filament particle chain, k is the stress coefficient, d p-p is the inter-particle distance in the flexible filament particle chain, and r cut is the particle center-to-center distance in the flexible filament particle chain.
In the step 5), the elongated flexible filament particle model is coupled with OpenFoam, that is, the particle phase of the elongated flexible filament particle model is interacted with the gas phase solved by OpenFoam, wherein the main interaction of the gas phase and the solid phase coupling is the drag force, the drag force is calculated by adopting the drag force model proposed by Gidaspow,
Gidaspow drag model is as follows:
drag coefficient C o is calculated as follows:
Reynolds number The calculation formula of (2) is as follows:
When epsilon g and u s are calculated statistically, mapping the flexible filamentous particle information of the solid phase into the grid of the gas phase, and adopting a simple regular grid to directly carry out mapping by adopting a center point method, namely calculating the volume fraction occupied in the grid of the gas phase by the position of the particle center; the speed information of the solid-phase flexible filamentous particles is processed and calculated according to a traditional DEM particle processing model, and interaction calculation is carried out by adopting a Gidaspow drag model under the action of gas and solid phases.
In the step 6), the inlet of the channel adopts a speed inlet condition, the initial speed is 5m/s, the particle flow at the inlet is assumed to be in a laminar flow state, and the speed gradient is 0; the outlet is directly communicated with the outside, the flexible filamentous particles can freely flow out from the outlet, the outlet boundary condition free outlet is set, and the pressure gradient is 0; the wall is set to be a slip-free boundary condition, the air inlet speed is 5m/s, and the outlet is a free outflow boundary with a pressure gradient of 0.
In the step 7), the initial conditions are: the simulated pressure was 1.01e5Pa, the inlet wind speed was 5m/s, the particle radius was 0.0005m, the initial particle velocity was 0m/s, the initial feed rate was 0.07kg/s, and the outlet wind speed was 0m/s.
In the step 8), the basic control equation in the step 3) is discretized by adopting a finite volume method, a first-order windward format and a PISO speed-pressure coupling algorithm are adopted in the calculation process, and a STANDARD format is adopted in the pressure interpolation format.
In the step 9), the time step is set to be 1 multiplied by 10 < -5 > s, and the simulation time length is 180s; the time step preservation mechanism is as follows: in order to realize the processing of the numerical simulation result of the fluidization process of the flexible filamentous particles, a data file is automatically saved according to the set n multiplied by the time step as an output condition, and the data information of each calculation grid node is stored in the data file.
Compared with the prior art, the invention has the advantages that:
1. According to the method, the long and thin flexible filamentous particle model is constructed according to the characteristics that the particles of the long and thin flexible filamentous biomass are long and thin, the shape is dominant in the axial direction, the long and thin flexible filamentous biomass is soft, and easy to bend, deform and the like, the constructed flexible filamentous particle model can objectively and well reflect the appearance characteristics and the physical characteristics of the long and thin flexible filamentous biomass particles, and the problem that the long and thin flexible filamentous biomass is approximately simplified into spherical particles with single particle rules by a traditional numerical simulation method is solved.
2. Based on the existing mathematical model of large computational fluid dynamics open source software OpenFoam, the invention realizes a programming module by carrying out mathematical expression on the constructed slender flexible filament particle model and simultaneously couples with open source OpenFoam software, thereby realizing numerical simulation of the slender flexible filament particles in the fluidization processing process, the numerical simulation result can holographic simulate the motion characteristics of the slender flexible filament particles in the fluidization processing process, vividly represent the fluidization form and the mass and heat transfer efficiency of the slender flexible filament particles under different working conditions, and the time step storage mechanism can flexibly finish the aftertreatment of simulation results of different fluidization stages. Through verification, the data simulation result obtained by the method is basically consistent with field experimental data, the reliability is high, compared with the prior art, the interaction mechanism of the slender flexible filament particles in the fluidization process is conveniently and efficiently captured and reproduced, the real and objective reflection is obtained, an effective solving way is provided for improving and optimizing design of fluidization processing equipment of the slender flexible filament particles, and the method has important theoretical significance and practical value.
3. The invention is helpful for production enterprise technicians to learn the flow characteristics of the slender flexible filament particles in the fluidization equipment, and the simulation result can also provide reference for continuous, automatic and optimization of process parameters of the fluidization equipment, reduction of material agglomeration, breakage and uneven moisture in fluidization processing, and improvement of product processing quality stability;
4. The method can save human resources required by the traditional experiment through numerical simulation, reduce the experiment cost, reduce the experiment period, greatly reduce the experiment complexity, and lay a foundation for the comprehensive study of mass and heat transfer of the slender flexible filament particles by technicians in the future.
Drawings
FIG. 1 is a schematic view of a DEM model according to the present invention;
FIG. 2 is a schematic view of a particle binding mode according to the present invention;
FIG. 3 is a schematic view of an elongate flexible filamentous particle model in accordance with the present invention;
FIG. 4 is a schematic diagram of coupling in accordance with the present invention;
FIG. 5 is a flow chart of a gas phase solution in the present invention;
FIG. 6 is a flow chart of a particle phase solution in accordance with the present invention;
FIG. 7 is a diagram of meshing in accordance with the present invention;
FIG. 8 is a schematic representation of the instantaneous fluidization motion profile of the elongate flexible filamentous particles of the present invention;
FIG. 9 is a schematic representation of the instantaneous fluidization motion profile of the elongate, flexible, threadlike particles at various moments in time in the present invention;
Fig. 10 is a schematic view of the orientation distribution of elongate flexible filiform particles in the present invention.
Detailed Description
Embodiments of the present invention are described below with reference to fig. 1-10.
The embodiment is based on the construction of an elongated flexible filament particle model and on the existing mathematical model of large computational fluid dynamics open source software OpenFoam, the constructed elongated flexible filament particle model is coupled with the model, namely, the interaction mode of the elongated flexible filament particle model (the construction form of the elongated flexible filament particle model, the particle motion model of the elongated flexible filament particle model and the inter-particle constraint model thereof) and the time step preservation output mechanism are used for realizing the numerical simulation of the gas-solid flow characteristic and the value and heat transfer of the elongated flexible filament particle in the fluidization processing process, and the method comprises the following specific steps:
1) According to the physical structure characteristics of the slender flexible filament particles, based on a DEM model, constructing a slender flexible filament particle model, adding a constraint force equation of the slender flexible filament particle model, and constructing a motion equation of the slender flexible filament particle model;
An elongated flexible filament-like particle model construction based on a DEM model in which particles are assumed to be rigid, deformation of the particles being achieved by springs, damping etc. assumed at the points of contact. The particle-to-particle interactions allow for overlapping to occur, typically by an amount much less than the particle size, as shown in fig. 1. Furthermore, particles can only act with adjacent particles, and individual particles can be subjected to the addition of their effects by all particles. At present, models for calculating inter-particle acting forces include a bilinear model, a Hertz contact model, a Winker model and a Hooke model. The method adopts a Hooke model, and a calculation method motion equation and motion of acting force among particles are introduced on the basis.
The collision acting force consists of a normal force and a tangential force, and the direction from the center of mass of the particle i to the center of mass of the particle j is assumed to be the normal direction. The normal force F n and tangential force F t to which particle i is subjected are:
Fn＝knδnij-γnvnij (1)
Ft＝ktδtij-γtvtij,max(|Ft|)＝|μFn| (2)
the rigidity coefficient in the k n normal direction, the gamma n normal direction is a damping coefficient, the rigidity coefficient in the k t normal direction, the gamma t tangential direction is a damping coefficient, δn ij is the overlap amount between particles, the displacement of the particles generated by δt ij tangential force, and mu is the rolling friction coefficient of the particles; v nij is the component of the relative velocity of the impinging particles in the normal direction and v tij is the slip velocity between the impinging particles.
The calculation method for δt ij varies among different models, here a Hooke model is used that ignores historic effects, δt ij being ignored. The calculation of k n,γn,kt,γt is as follows:
kn＝kt (6)
γn＝γt (7)
these 4 coefficients are calculated from the properties and contact states of two particles that collide with each other:
wherein R is the radius of the particles, m is the mass of the particles, e is the coefficient, Y is the Young's modulus, and v is the Poisson's ratio.
On the basis of the DEM model, the particles can be bound together by adding an action potential function between the grouped particles and the action potential function is added, so that the particles form flexible filamentous particles. The potential function is as follows:
Ψij(rij)＝k(rij-ro) (19)
Wherein r ij represents the distance between the two particles i and j; psi ij is the opposite potential, r o is the radius of truncation, here equivalent to the radius of the hard sphere, and k is the coefficient of action.
The specific binding method is as follows: as shown in figure 2, by adding an action potential function to the particles in the groups 1-2, 1-3, 1-4, 1-5, 1-6, 2-3, 2-4 and the like in figure 2, when the adjacent particles exceed a set cut-off radius in the movement process of the particles, the action potential function added between the particles acts to bind the particles together, and when the adjacent particles are smaller than the set cut-off radius, the particles exert the action force on the particles on the basis of the stress of the DEM model, and the additional action potential function is additionally added to repel the particles from the particles, so that the distance between the particles is restored to the set cut-off radius. Binding constraint parameters between particles are shown in table 1.
TABLE 1 elongate flexible filiform particle model control parameters
By binding through the method, the flexible thread-like tobacco particle model shown in fig. 3 is finally formed.
Besides the DEM model and the action potential function among particles, the motion equation of the translational motion and the rotation of the particles follows newton's second law, which is respectively:
Wherein m and I represent the mass and moment of inertia of the particles; v and ω represent the translational and rotational speeds of the particles; t is time; g represents gravitational acceleration; r represents a vector pointing from the particle centroid to the collision contact point, the value of which is the particle radius.
In the solving process of the particle position and speed equation, the frog-leaping algorithm is adopted to carry out iterative updating, the frog-leaping algorithm uses the position at the time t and the speed at the time t-delta t/2, the acting force F (t) obtained by calculating the updated position and speed by using the position at the time t is updated, and the formula is as follows:
2) And drawing a three-dimensional solid model by CAD drawing software, and dividing calculation grid nodes of a simulation area according to the three-dimensional solid model by Pointwise. And dividing the calculation area of the three-dimensional solid model by adopting a block hexahedral structured grid. The simulation area is set in this embodiment as: length x width x height = 210.0mm x 120.0mm x 3500.0mm, and the calculation region is meshed with a block structured grid with a grid size of 10mm.
3) A basic physical model is built for the grid using 0 penFoam: basic control equations, namely a continuity equation, a momentum equation and an energy equation, and establishing a wall collision model.
The slender flexible filament particles basically present turbulent motion in the fluidization process, and basic control equations comprise a continuity equation and a momentum equation.
1. Equation of fluid control
The fluid phase satisfies the mass conservation and momentum conservation equations:
Wherein, Epsilon g is the gas phase volume fraction, v pairIs the average speed of particles in the grid, beta is the coefficient of gas-solid drag force,/>Is the resultant force to which the gas phase is subjected, including contact force, van der Waals force.
2. Particulate phase control equation
Ψp-p＝k(dp-p-rcut) (23)
Wherein,The differential pressure force is F c, the inter-particle interaction force is F d, the drag force of particles is mg, the gravity of particles is, ψ p-p is the inter-particle binding force in a flexible filament particle chain, k is the stress coefficient, d p-p is the inter-particle distance in the flexible filament particle chain, and r cut is the particle center-to-center distance in the flexible filament particle chain.
4) Defining physical properties of the elongate flexible filamentary particles, the physical properties comprising: density ρ, thickness h, width d, length l, rolling friction coefficient μ r;
the simulation parameters of the slender flexible filament particles are set, and the specific parameter settings are shown in Table 2.
TABLE 2 initialization parameters for simulation of elongate flexible filiform particles
5) And coupling the constructed flexible filamentous particle model with open-source computational fluid dynamics numerical simulation software OpenFoam to realize parallel simulation calculation of discrete simulation of the flexible filamentous particle model.
The constructed elongated flexible filament-like particle model is coupled with OpenFoam, namely the particle phase of the elongated flexible filament-like particle model is interacted with the gas phase solved by OpenFoam, and the coupling flow is shown in figure 4. The solution of the gas phase field mainly adopts a PISO algorithm to solve a discrete control equation under OpenFoam software, the flow chart is shown in fig. 5, the solution of the flexible filament particle motion state equation mainly comprises the steps of calculating particle binding acting force, inter-particle collision force, drag force and acting force of gas phase to particles in a flexible filament particle chain, and finally updating the position and speed information of the flexible filament particle chain through Newton's second law and angular momentum conservation law, and the flow chart is shown in fig. 6.
The constructed flexible filamentous particle model is coupled with open-source computational fluid dynamics numerical simulation software OpenFoam, the main interaction of gas phase and solid phase coupling is drag force, the accuracy of the drag force model is one of important factors of the accuracy of the gas-solid two-phase flow numerical simulation result, and the accuracy of the drag force model is also the key point of the gas-solid two-phase flow theoretical research for many years. In the initial stage of the study, researchers have established various empirical correlations, such as the Wen & Yu correlation, the Ergun correlation, the Gibilaro et al correlation, syamlal and the O' Breien model, from a large number of experimental data. The drag model proposed by Gidaspow is widely used.
Gidaspow drag model is as follows:
drag coefficient C o is calculated as follows:
Reynolds number The calculation formula of (2) is as follows:
when epsilon g and u s are calculated statistically, the flexible filiform grain information of the solid phase is required to be mapped into the grid of the gas phase, the method adopts a simple regular grid, and the mapping is directly carried out by adopting a center point method, namely the volume fraction occupied in the grid of the gas phase is calculated through the position of the center of the grain. The solid-phase flexible filamentous particle velocity information is processed and calculated according to a traditional processing DEM particle model. The interaction between the gas phase and the solid phase is calculated by adopting Gidaspow drag force model.
6) Defining inlet and outlet boundary conditions and wall surface conditions; in the embodiment, a speed inlet condition is adopted for a channel inlet, the initial speed is 5m/s, the particle flow at the inlet is assumed to be in a laminar flow state, and the speed gradient is 0; the outlet is directly communicated with the outside, the flexible filamentous particles can freely flow out from the outlet, the outlet boundary condition free outlet is set, and the pressure gradient is 0; in this embodiment, the wall surface is set to be a slip-free boundary condition; as shown in fig. 7, inlet1 is the inlet, the air inlet velocity is 5m/s, out1 is the outlet boundary, and the outlet is the free outflow boundary with a pressure gradient of 0.
7) Defining initial conditions: the number of flexible filiform particles, the initial position, initial velocity of the flexible filiform particle model, define the initial velocity and density of the gas phase. Specifically, the initial conditions are: the simulated pressure was 1.01e5Pa, the inlet wind speed was 5m/s, the particle radius was 0.0005m, the initial particle velocity was 0m/s, the initial feed rate was 0.07kg/s, and the outlet wind speed was 0m/s.
8) Discretizing the basic control equation of the step 3) by adopting a finite volume method, and sealing and solving by adopting the boundary conditions and the initial conditions defined in the step 6) and the step 7); the calculation process adopts a first-order windward format and a PISO speed-pressure coupling algorithm, and the pressure interpolation format adopts a STANDARD format.
9) Initializing the whole calculation region, setting a time step and a simulation time length, wherein the set time step is 1 multiplied by 10 < -5 > s, and the simulation time length is 180s; and repeatedly iterating the algebraic equation set in the calculation region until the set simulation time is met, completing the numerical simulation of the fluidization process of the flexible filamentous particles, and storing the calculation results of the position, the rotation angular speed, the pressure of the slender flexible filamentous particles, the gas phase flow field data on the calculation nodes and the like by using a time step storage mechanism. The time step storage mechanism is as follows: in order to realize the processing of the numerical simulation result of the fluidization process of the flexible filamentous particles, a data file is automatically saved according to the set n multiplied by the time step as an output condition, and the data information of each calculation grid node is stored in the data file.
10 Post-processing analysis and display of the calculations.
And carrying out post-processing on the calculation results in a cloud image, a vector image, a flow chart, a graph, a three-dimensional data simulation image and the like, wherein the post-processing comprises speed, agglomeration behavior and disturbance deformation of the slender flexible filament particles, axial or radial distribution in a simulation area and orientation distribution of the slender flexible filament particles in the fluidization process.
The post-processing of the calculation results in this embodiment is as shown in fig. 8, 9, 10:
As shown in FIG. 8, in the embodiment, under the working condition that the feeding rate of the elongated flexible filament particles is 0.07kg/s at 5m/s, the elongated flexible filament particles are fluidized and instantaneously move, and the elongated flexible filament particles are subjected to the action of a gas phase field and collide with each other and the wall surface, so that the stress among the flexible filament particles is uneven, and further, the relative movement between the elongated flexible particle chains can occur. Because of the constraint of the potential function added among the long and thin flexible filament particle chains constructed by the method, the long and thin flexible filament particle chains can exhibit rotation, translation and disturbance deformation, and the long and thin flexible filament particle chains are similar to real long and thin flexible filament particle movements. By means of the captured instant fluidization map, the flexible filamentous particles can be found to take on various motion states such as stretching, bending deformation, agglomeration and the like, and basically the motion of the flexible filamentous biomass particles is similar to that of the slender flexible filamentous biomass particles.
As shown in FIG. 9, in the present example, under the working condition that the feeding rate of the elongated flexible filamentous particles is 0.07kg/s at 5m/s, the elongated flexible filamentous particles are fluidized at different moments, the quantity of the particles in the fluidized bed is smaller and the overall distribution of the particles is more uniform in the initial fluidization stage, the particles in the fluidized bed are gradually increased along with the fluidization, the flexible filamentous particles are in a dense state in the bottom of the fluidized bed and other areas, the distribution of the particles is uneven, and the side wall has obvious particle agglomeration phenomenon. This is due to the fact that the particles in the central region are carried at a higher gas velocity and move upwards at a higher velocity, while the particles near the side wall accumulate in the side wall region under the viscous action of the side wall.
As shown in FIG. 10, in the present example, under the condition that the feeding rate of the elongated flexible filament particles is 5m/s and is 0.07kg/s, the simulated value of the orientation distribution of the elongated flexible filament particles is compared with the experimental value, the orientation distribution of the elongated particles during fluidization finally shows a stable distribution along with time, and the tobacco shreds are mainly in the axial direction, so that typical non-spherical flexible elongated particles can perform translational and rotational movement during fluidization, and the orientation is one of important characteristics of the tobacco shreds during fluidization. Verification of the orientation value can reflect the accuracy and feasibility of the constructed flexible filamentous particle model. The analysis of fig. 10 shows that although the measured value and the simulated value of the regionalization distribution of the elongated flexible filament particles are different, the two reflect the general trend of the distribution rule of the orientation, which indicates that the vertical state is dominant (the dominant range is 10-25 degrees) in the fluidization process of the elongated flexible filament particles, and the state is the stable state of the tobacco. In addition, the simulation value is completely consistent with the rule reflected by the actual measurement value, which shows that the constructed flexible filamentous particle model has greater accuracy and feasibility for simulating the motion characteristics of the cut tobacco in the fluidization process.
According to the method, the long and thin flexible filamentous particle model is constructed according to the characteristics that the particles of the long and thin flexible filamentous biomass are long and thin, the shape is dominant in the axial direction, the long and thin flexible filamentous biomass is soft, and easy to bend, deform and the like, the constructed flexible filamentous particle model can objectively and well reflect the appearance characteristics and the physical characteristics of the long and thin flexible filamentous biomass particles, and the problem that the long and thin flexible filamentous biomass is approximately simplified into spherical particles with single particle rules by a traditional numerical simulation method is solved. Based on the existing mathematical model of large computational fluid dynamics open source software OpenFoam, the invention realizes a programming module by carrying out mathematical expression on the constructed slender flexible filament particle model and simultaneously couples with open source OpenFoam software, thereby realizing numerical simulation of the slender flexible filament particles in the fluidization processing process, the numerical simulation result can holographic simulate the motion characteristics of the slender flexible filament particles in the fluidization processing process, vividly represent the fluidization form and the mass and heat transfer efficiency of the slender flexible filament particles under different working conditions, and the time step storage mechanism can flexibly finish the aftertreatment of simulation results of different fluidization stages. Through verification, the data simulation result obtained by the method is basically consistent with field experimental data, the reliability is high, compared with the prior art, the interaction mechanism of the slender flexible filament particles in the fluidization process is conveniently and efficiently captured and reproduced, the real and objective reflection is obtained, an effective solution way is provided for improving and optimizing design of fluidization processing equipment of the slender flexible filament particles, a foundation is laid for the comprehensive research of mass and heat transfer of the slender flexible filament particles by technicians in the future, and important theoretical significance and practical value are provided.
The above embodiments are only preferred embodiments of the present invention and are not intended to limit the scope of the present invention, so that all equivalent modifications made by the appended claims shall be included in the scope of the present invention.
Claims (6)
1. The construction and numerical simulation method of the slender flexible filament particle model is characterized by comprising the following steps of: comprises the following steps of;
1) According to the physical structure characteristics of the slender flexible filament particles, based on a DEM model, constructing a slender flexible filament particle model, adding a constraint force equation of the slender flexible filament particle model, and constructing a motion equation of the slender flexible filament particle model;
2) Drawing a three-dimensional solid model by CAD drawing software, and dividing calculation grid nodes of a simulation area according to the three-dimensional solid model by Pointwise;
3) A basic physical model is built for the grid using OpenFoam: basic control equations, namely a continuity equation, a momentum equation and an energy equation, and establishing a wall collision model;
4) Defining physical properties of the elongate flexible filamentary particles, the physical properties comprising: density ρ, thickness h, width d, length l, rolling friction coefficient μ r;
5) Coupling the constructed flexible filamentous particle model with open-source computational fluid dynamics numerical simulation software OpenFoam to realize parallel simulation calculation of discrete simulation of the flexible filamentous particle model;
6) Defining channel inlet and outlet boundary conditions and wall conditions;
7) Defining initial conditions: the quantity of the flexible filiform particles, the initial position and the initial speed of the flexible filiform particle model, and the initial speed and the density of the gas phase are defined;
8) Discretizing the basic control equation of the step 3), and sealing and solving by adopting the boundary conditions and the initial conditions defined in the step 6) and the step 7);
9) Initializing the whole calculation region, setting a time step and a simulation time length, repeatedly iterating algebraic equation sets in the calculation region until the set simulation time length is met, completing numerical simulation of the fluidization process of the flexible filamentous particles, and storing a calculation result by using a time step storage mechanism;
10 Post-processing analysis and display of the calculation;
in the step 1), the particles are assumed to be rigid bodies in the DEM model, when the DEM model processes collision among the particles, the interaction between the particles allows slight overlapping, the particles can only act with adjacent particles, and the action of a single particle can be added by all the particles; the collision acting force of particles in the DEM model is processed and calculated by adopting a spring-damper-sliding friction device model;
the method for calculating the acting force among particles by adopting the Hooke model comprises the following steps of:
The collision acting force consists of a normal force and a tangential force, and assuming that the direction from the center of mass of the particle i to the center of mass of the particle j is a normal direction, the normal force F n and the tangential force F t borne by the particle i are as follows:
Fn＝knδnij-γnvnij (1)
Ft＝ktδtij-γtvtij,max(|Ft|)＝|μFn| (2)
The rigidity coefficient in the k n normal direction, the gamma n normal direction is a damping coefficient, the rigidity coefficient in the k t normal direction, the gamma t tangential direction is a damping coefficient, δn ij is the overlap amount between particles, the displacement of the particles generated by δt ij tangential force, and mu is the rolling friction coefficient of the particles; v nij is the component of the relative velocity of the impinging particles in the normal direction, v tij is the slip velocity between the impinging particles;
In the Hooke model, δt ij is ignored and k n,γn,kt,γt is calculated as follows:
kn＝kt (6)
γn＝γt (7)
these 4 coefficients are calculated from the properties and contact states of two particles that collide with each other:
Wherein R is the radius of the particles, m is the mass of the particles, e is a coefficient, Y is Young's modulus, v is Poisson's ratio;
On the basis of a DEM model, adding an action potential function between grouped particles, binding the particles together by adding the action potential function, and forming flexible filamentous particles; the potential function is as follows:
Ψij(rij)＝k(rij-ro) (19)
Wherein r ij represents the distance between the two particles i and j; psi ij is the opposite potential, r o is the truncated radius, which corresponds to the radius of the hard sphere, and k is the coefficient of action;
The specific binding method comprises the following steps: by adding an action potential function between particles, the action potential function added between particles acts when the adjacent particles exceed a set cutoff radius in the movement process of the particles, acting force is applied to the particles and the particles to bind the particles together, and when the adjacent particles are smaller than the set cutoff radius, the particles exert acting force on the particles on the basis of the stress of the DEM model, and the additional action potential function is also applied to the particles and the particles to repel the particles and restore the particle spacing to the set cutoff radius; finally forming a flexible thread-like cut tobacco particle model by a binding method;
Besides the DEM model and the action potential function among particles, the motion equation of the translational motion and the rotation of the particles follows newton's second law, which is respectively:
Wherein m and I represent the mass and moment of inertia of the particles; v and ω represent the translational and rotational speeds of the particles; t is time; g represents gravitational acceleration; r represents a vector pointing from the particle centroid to the collision contact point, the value of which is the particle radius;
and (3) carrying out iterative updating on the solving process of the particle position and speed equation by adopting a frog-leaping algorithm, wherein the frog-leaping algorithm updates the position and the speed by using the position at the time t and the speed at the time t-delta t/2, and the acting force F (t) obtained by calculating the position at the time t is updated by using the formula as follows:
In the step 3), the slender flexible filament particles basically show turbulent motion in the fluidization process, and the basic control equation is as follows;
1. equation of fluid control
The fluid phase satisfies the mass conservation and momentum conservation equations:
Wherein, Epsilon g is the gas phase volume fraction, v pairIs the average speed of particles in the grid, beta is the coefficient of gas-solid drag force,/>Is the resultant force to which the gas phase is subjected, including contact force, van der Waals force;
2. Particulate phase control equation
Ψp-p＝k(dp-p-rcut) (23)
Wherein,The differential pressure force is F c, the inter-particle interaction force is F d, the drag force borne by particles, mg is the particle gravity, ψ p-p is the inter-particle binding force in the flexible filamentous particle chain, k is the stress coefficient, d p-p is the inter-particle distance in the flexible filamentous particle chain, and r cut is the particle center-to-center distance in the flexible filamentous particle chain;
In the step 5), the elongated flexible filament-like particle model is coupled with OpenFoam, namely the interaction between the particle phase of the elongated flexible filament-like particle model and the gas phase solved by OpenFoam; wherein the main interaction of the gas phase and the solid phase coupling is the drag force, the drag force calculation adopts a drag force model proposed by Gidaspow,
Gidaspow drag model is as follows:
drag coefficient C o is calculated as follows:
Reynolds number The calculation formula of (2) is as follows:
When epsilon g and u s are calculated statistically, mapping the flexible filamentous particle information of the solid phase into the grid of the gas phase, and adopting a simple regular grid to directly carry out mapping by adopting a center point method, namely calculating the volume fraction occupied in the grid of the gas phase by the position of the particle center; the speed information of the solid-phase flexible filamentous particles is processed and calculated according to a traditional DEM particle processing model, and interaction calculation is carried out by adopting a Gidaspow drag model under the action of gas and solid phases.
2. The method for constructing and numerically simulating an elongated flexible filamentous particle model as set forth in claim 1, wherein: in the step 2), the calculation area of the three-dimensional solid model is divided by adopting a block hexahedral structured grid.
3. The method for constructing and numerically simulating an elongated flexible filamentous particle model as set forth in claim 1, wherein: in the step 6), the inlet of the channel adopts a speed inlet condition, the initial speed is 5m/s, the particle flow at the inlet is assumed to be in a laminar flow state, and the speed gradient is 0; the outlet is directly communicated with the outside, the flexible filamentous particles can freely flow out from the outlet, the outlet boundary condition free outlet is set, and the pressure gradient is 0; the wall is set to be a slip-free boundary condition, the air inlet speed is 5m/s, and the outlet is a free outflow boundary with a pressure gradient of 0.
4. The method for constructing and numerically simulating an elongated flexible filamentous particle model as set forth in claim 1, wherein: in the step 7), the initial conditions are: the simulated pressure was 1.01e5Pa, the inlet wind speed was 5m/s, the particle radius was 0.0005m, the initial particle velocity was 0m/s, the initial feed rate was 0.07kg/s, and the outlet wind speed was 0m/s.
5. The method for constructing and numerically simulating an elongated flexible filamentous particle model as set forth in claim 1, wherein: in the step 8), the basic control equation in the step 3) is discretized by adopting a finite volume method, a first-order windward format and a PISO speed-pressure coupling algorithm are adopted in the calculation process, and a STANDARD format is adopted in the pressure interpolation format.
6. The method for constructing and numerically simulating an elongated flexible filamentous particle model as set forth in claim 1, wherein: in the step 9), the time step is set to be 1 multiplied by 10 < -5 > s, and the simulation time length is 180s; the time step preservation mechanism is as follows: in order to realize the processing of the numerical simulation result of the fluidization process of the flexible filamentous particles, a data file is automatically saved according to the set n multiplied by the time step as an output condition, and the data information of each calculation grid node is stored in the data file.
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