Hydrocyclone flow field simulation method based on self-adaptive smoothed particle method

Abstract

The invention discloses a hydrocyclone flow field simulation method based on an adaptive smoothed particle method, and the simulation method comprises the following steps: (1) determining structural parameters of a hydrocyclone, and constructing a geometric model of the hydrocyclone; (2) establishing a basic control equation, and discretizing the basic control equation into an adaptive smoothed particle normal equation; (3) setting boundary conditions and initial calculation parameters on the basis of the geometric model of the hydrocyclone, and then importing the boundary conditions and the initial calculation parameters into a fluid simulation scene for simulation; and (4) respectively monitoring the particle flow at the outlet of the underflow pipe of the hydrocyclone and the flow at the outlet of the overflow pipe, and stopping calculation after the flows at the two outlets are stable, thereby completing simulation. The flow field behavior in the hydrocyclone is simulated through the adaptive resolution smoothed particle method, the change and breakage of the interface in the hydrocyclone can be accurately captured, it is guaranteed that the change at the gas-liquid interface is clear and visible, the track of particles in the hydrocyclone is traceable, and the calculation amount and the calculation time are reduced through the adaptive resolution.

Description

Technical Field

[0001] The present invention relates to the technical field of flow field simulation of a hydrocyclone, and in particular to a method for simulating the flow field of a hydrocyclone based on an adaptive smooth particle method. Background Art

[0002] Hydrocyclone is a device that uses the principle of centrifugal sedimentation to achieve separation and classification. At present, hydrocyclone is widely used in various industries such as food processing, environmental protection engineering and mineral processing. Its working principle is to inject a multiphase fluid mixture with a certain density difference at a certain pressure at the inlet, and the fluid rotates and flows at a high speed under the restriction of the tube wall. Due to the existence of the wall, the fluid close to the wall rotates and moves downward, and the movement trajectory is a spiral downward flow, forming an external vortex; when the fluid moves to the cone section, due to the low central pressure and the cone section provides an oblique upward support force, the internal fluid no longer flows downward, but rotates upward to form an external vortex. The forces on solid particles are centrifugal force, centripetal buoyancy and flow resistance. Centrifugal force forces particles to move radially, which plays an important role in separation efficiency; centripetal buoyancy is the pressure on particles caused by the pressure difference caused by different fluid velocities in the radial direction; fluid resistance is the drag force of the fluid on particles when particles and fluid move relative to each other. Since larger particles have a higher density, they move downward along the wall under the action of these three forces and are discharged from the bottom flow port. Water and smaller particles move upward in the internal vortex and are discharged from the overflow port, thus separating particles from the fluid and achieving the effect of graded separation. It is most widely used in the field of mineral sorting.

[0003] Among the existing simulation and analysis methods for flow field phenomena in hydrocyclones, the most widely used are the finite volume method (FDM) and finite difference method (FVM) based on grids. Numerical simulation methods in engineering applications generally use grid methods, but for complex transient flows in hydrocyclones with the generation of air columns, traditional grid methods cannot accurately capture the changes and fragmentation of interfaces.

[0004] At present, we have found patents on flow field simulation of hydrocyclones: Application number: 202110319537.4. Name of the invention: A numerical simulation method for optimizing the separation performance of a liquid-solid hydrocyclone, comprising the following steps: determining the geometric parameters of the liquid-solid hydrocyclone; determining the physical parameters and operating parameters of the liquid-solid hydrocyclone; constructing a three-dimensional model of the liquid-solid hydrocyclone based on the geometric parameters, physical parameters and operating parameters; meshing the three-dimensional model of the liquid-solid hydrocyclone and importing the mesh obtained by the meshing into the CFD software; determining the flow characteristics of the gas-liquid two-phase flow and the air column characteristics; determining the solid phase flow characteristics; and performing numerical simulation of the three-dimensional model of the liquid-solid hydrocyclone through CFD software. This invention provides a reference for the optimization of the separation performance of the hydrocyclone, and achieves the improvement of the separation performance of the liquid-solid hydrocyclone in a simple, economical and efficient way. This simulation method is still the grid-based method mentioned above. Its disadvantage is that it uses the commercial software Fluent, which is restricted by copyright. Secondly, the grid-based method has a large error when simulating the gas-liquid interface in the cyclone and cannot guarantee conservation. Summary of the invention

[0005] The purpose of the present invention is to solve the above technical problems and provide a hydrocyclone flow field simulation method based on an adaptive smooth particle method, which has clear changes in the gas-liquid interface and can reduce the calculation time.

[0006] To achieve the above-mentioned purpose, the technical solution of the present invention is:

[0007] A hydrocyclone flow field simulation method based on an adaptive smooth particle method, the simulation method comprising the following steps:

[0008] (1) Determine the structural parameters of the hydrocyclone and construct a geometric model of the hydrocyclone;

[0009] (2) Establish the basic control equation and discretize it into the adaptive smooth particle normal equation;

[0010] (3) Based on the geometric model of the hydrocyclone, boundary conditions and initial calculation parameters are set, and then imported into the fluid simulation scene for simulation;

[0011] (4) Monitor the particle flow rate at the outlet of the underflow pipe of the hydrocyclone and the flow rate at the outlet of the overflow pipe respectively. Stop the calculation after the flow rates at the two outlets are stable, and complete the simulation.

[0012] As a further technical solution, the structural parameters of the hydrocyclone described above include: inlet height h1 and width b, column diameter d1, overflow pipe diameter d2, overflow pipe insertion depth h2, overflow pipe wall thickness δ, cone angle θ, underflow pipe diameter d3.

[0013] As a further technical solution, the basic control equations described above are:

[0014]

[0015] The adaptive smooth particle normal equation is:

[0016]

[0017] Where ρ is the fluid density, t is the time, u is the fluid velocity, g is the gravitational acceleration, p is the pressure, μ is the dynamic viscosity, and F s is the surface tension; the subscripts i and j represent the particle number, W is the smooth kernel function, ∏ is the artificial viscosity value, r ij is the distance between particles i and j, η is the relaxation coefficient;

[0018] At this time, the computational domains of particles, water bodies, and gases are discretized into a specific number of particles with different physical properties;

[0019] The physical and mechanical parameters of particles, the physical and mechanical parameters of water bodies and the physical and mechanical parameters of gases are assigned to the physical and mechanical parameters corresponding to each physical particle.

[0020] As a further technical solution, the calculation areas of the above particles, water bodies and gases are discretized into a specific number of particles with different physical properties, including:

[0021] The fluid region enclosed by the boundary of the gas and water bodies in the geometric model is internally discretized, and water particles and granular particles are uniformly inserted according to the material concentration;

[0022] The gas region enclosed by the gas boundary in the geometric model is internally discretized, and gas particles are uniformly inserted.

[0023] As a further technical solution, the above-mentioned physical and mechanical parameters of particles include density, gravitational acceleration and diameter of particles; the physical and mechanical parameters of water body include particle density, gravitational acceleration and viscosity of water particles; the physical and mechanical parameters of gas include particle density and gravitational acceleration of gas particles.

[0024] As a further technical solution, the above-mentioned boundary conditions include conditions of model boundary, wall boundary, inlet boundary and outlet boundary.

[0025] As a further technical solution, the model boundary described above adopts dynamic boundary conditions, the wall boundary is three layers of fixed virtual particles distributed on the wall, the inlet boundary is a given inlet velocity or pressure, and the outlet boundary is a free boundary, that is, the fluid can flow out freely.

[0026] As a further technical solution, the initial calculation parameters mentioned above include kernel function, variable smoothing length, reference particle spacing, particle splitting and merging technology.

[0027] As a further technical solution, the kernel function described above is a cubic spline function and a hyperbolic kernel function, and the cubic spline function is expressed as:

[0028]

[0029] The hyperbolic kernel function is expressed as:

[0030]

[0031] In the formula, s = r / h, r represents the distance between two particles, h represents the smooth length, and d represents the degree of spatial dimension. In two-dimensional and three-dimensional space, α d They are 5 / (14πh 2 ) and 1 / (4πh 3 );

[0032] The variable smooth length is expressed as:

[0033]

[0034] Where n is the time step, is the smoothing length of particle i at time step n+1, is the smoothing length determined by the number of adjacent particles i, is the average smooth length of adjacent particles i, is the smoothing length of particle i at time step n, N r is a given constant number of particles, is the number of neighboring particles i at time step n, is the smoothing length of particle j at time step n;

[0035] The reference particle spacing is expressed as:

[0036] Δs k+1 =C r Δs k ,

[0037] Where ΔS is the reference particle spacing, k is the particle band index, which increases with the distance from the interface, and C r is an adaptive number, which indicates the ratio of the reference particle spacing between two adjacent particle bands and controls the size of the refinement area. 1≤C r ≤1.2; when C r = 1, the particle spacing is uniform and the resolution no longer changes adaptively; when C rWhen the value increases, the particle spacing increases as the distance to the interface increases;

[0038] The particle splitting and merging technique uses a reference particle mass, which is expressed as:

[0039] m r =ρ r Δs d ,

[0040] In the formula, ρ r is the reference density, d is the spatial dimension; when the mass of particle i is m i With its reference particle mass m r The ratio is greater than γ s , then the particle splits into two particles of equal mass, and the distance between the two new particles is γ s It is a parameter that limits the mass of particles to prevent them from being too large, and its range is 1.5≤γ s ≤2.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1. Compared with the grid method, the present invention simulates the flow field behavior in the hydrocyclone through the adaptive resolution smooth particle method, which can accurately capture the changes and fragmentation of the interface in the hydrocyclone, ensure that the changes at the gas-liquid interface are clearly visible and the trajectory of the particles in the hydrocyclone can be tracked, and reduce the amount of calculation and calculation time through adaptive resolution.

[0043] 2. Due to the discontinuity of physical fields such as density and velocity at the phase interface, the SPH multiphase model is more complex and challenging than the single-phase model, which easily leads to problems such as low accuracy, poor stability, and long calculation time. The adaptive SPH multiphase model of the hydrocyclone constructed by the present invention can show its characteristics for different objects by setting different parameters for particles, water bodies and gases, thereby ensuring the accuracy of the calculation results; the present invention also assigns various physical and mechanical parameters to particles according to the physical parameters of the entity to improve the matching of the simulation with the actual flow state in the hydrocyclone; in addition, the present invention makes the simulation more in line with the actual operation situation by subdividing the boundary conditions; a hyperbolic kernel function is used to solve the problem of stress instability, and a variable smoothing length is used to solve the problem of adaptive spatial resolution, uneven particle spacing and time-varying problems, and reference is also made to particle spacing, particle splitting and merging technology, etc., to greatly reduce the amount of calculation and calculation time; ultimately, the advantages of high accuracy, good stability, low amount of calculation, and high calculation efficiency are achieved.

[0044] 3. The present invention can quantitatively determine whether the calculation has reached stability by monitoring the flow rate of the granules and the water flow rate at the two outlets of the hydrocyclone, thereby improving the credibility of the hydrocyclone simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A flowchart of a hydrocyclone flow field simulation method based on an adaptive smooth particle method according to the present invention;

[0046] Figure 2 It is a structural schematic diagram of a simulated hydrocyclone of the present invention;

[0047] Figure 3 This is a particle distribution diagram at the gas-liquid interface of the present invention.

[0048] Reference numerals:

[0049] 1-Overflow pipe, 2-Inlet, 3-Column section, 4-Cone section, 5-Underflow pipe. DETAILED DESCRIPTION

[0050] The present invention is further described in detail below in conjunction with examples, but the implementation mode of the present invention is not limited to the scope represented by the examples.

[0051] Embodiment 1:

[0052] like Figure 1 As shown, a hydrocyclone flow field simulation method based on an adaptive smooth particle method comprises the following steps:

[0053] (1) Figure 2 As shown, the structural parameters of the hydrocyclone are determined, and the structural parameters of the hydrocyclone include: inlet height h1 = 50mm and width b = 20mm, column diameter d1 = 150mm, overflow pipe diameter d2 = 50mm, overflow pipe insertion depth h2 = 60mm, overflow pipe wall thickness δ = 10mm, cone angle θ = 20°, underflow pipe diameter d3 = 25mm;

[0054] (2) Establish the basic control equation and discretize it into the adaptive smoothed particle normal equation (SPH particle equation);

[0055] The basic governing equation is:

[0056]

[0057]

[0058] The adaptive smooth particle normal equation is:

[0059]

[0060] Where ρ is the fluid density, t is the time, u is the fluid velocity, g is the gravitational acceleration, p is the pressure, μ is the dynamic viscosity, and F sis the surface tension; the subscripts i and j represent the particle number, W is the smooth kernel function, ∏ is the artificial viscosity value, r ij is the distance between particles i and j, η is the relaxation coefficient;

[0061] At this time, the calculation areas of particles, water bodies and gases are discretized into a specific number of particles with different physical properties; including: internally discretizing the fluid area enclosed by the gas-water body boundary in the geometric model, and uniformly inserting water particles and particle particles according to the material concentration; internally discretizing the gas area enclosed by the gas boundary in the geometric model, and uniformly inserting gas particles.

[0062] The physical and mechanical parameters of particles, water and gas are assigned to the physical and mechanical parameters corresponding to each physical particle. The present invention sets different parameters based on particles, water and gas, and can show the characteristics of different objects to ensure the accuracy of the calculation results. At the same time, the physical and mechanical parameters of particles are assigned according to the physical parameters of the entity to improve the matching of the simulation with the real flow state in the hydrocyclone. In this embodiment, the density of the particle is 固 =2680kg / m 3 , diameter d 固 =0.000028m; water particle density ρ 水 =998.3kg / m 3 , viscosity μ 水 =0.001003Ns / m 2 ; Density of gas particles ρ 气 =1.29kg / m 3 ; Gravitational acceleration g = 9.8 m / s 2 , the physical parameters of boundary particles are not set;

[0063] (3) Based on the geometric model of the hydrocyclone, boundary conditions and initial calculation parameters are set, and then the fluid simulation scene is imported for simulation; the boundary conditions include the setting of model boundaries, wall boundaries, inlet boundaries and outlet boundaries. By subdividing the boundary conditions, it can be more in line with the actual operation conditions.

[0064] In this embodiment, the inlet velocity u 入 =2.23m / s, the mass of particles in the inlet material accounts for 30%; the outlet boundary is a free boundary; the wall boundary condition is set to three layers of fixed virtual particles, which can be penetrated by wall particles; the model boundary adopts dynamic boundary conditions.

[0065] Initial computational parameters, including kernel function, variable smoothing length, reference particle spacing, and particle splitting and merging techniques.

[0066] The kernel function is a cubic spline function and a hyperbolic kernel function. The cubic spline function is expressed as:

[0067]

[0068] The hyperbolic kernel function is expressed as:

[0069]

[0070] In the formula, s = r / h, r represents the distance between two particles, h represents the smooth length, and d represents the degree of spatial dimension. In two-dimensional and three-dimensional space, α d They are 5 / (14πh 2 ) and 1 / (4πh 3 ), the hyperbolic kernel function is proposed to avoid the problem of stress instability;

[0071] For adaptive spatial resolution, the particle spacing is not uniform and changes over time. Therefore, the present invention uses a variable smoothing length, which is expressed as:

[0072]

[0073] Where n is the time step, is the smoothing length of particle i at time step n+1, is the smoothing length determined by the number of adjacent particles i, is the average smooth length of adjacent particles i, is the smoothing length of particle i at time step n, N r is a given constant number of particles, is the number of neighboring particles i at time step n, d represents the degree of spatial dimension, is the smoothing length of particle j at time step n;

[0074] For adaptive spatial resolution, all particles are divided into a series of particle bands parallel to the interface, and particles in the same particle band have the same reference particle spacing. The reference particle spacing is related to the distance from the interface, and the formula is expressed as:

[0075] Δs k+1 =C r Δs k ,

[0076] Where ΔS is the reference particle spacing, k is the particle band index, which increases with the distance from the interface, and C r (1≤C r ≤1.2) is an adaptive number, which indicates the ratio of the reference particle spacing between two adjacent particle bands and controls the size of the refinement area. r = 1, the particle spacing is uniform and the resolution no longer changes adaptively; when Cr When the value increases, the particle spacing increases as the distance to the interface increases;

[0077] For adaptive spatial resolution, the particle splitting and merging techniques require the use of a reference particle mass, expressed as:

[0078] m r =ρ r Δs d ,

[0079] Where ρ r is the reference density, d is the spatial dimension; when the mass of particle i is m i With its reference particle mass m r The ratio is greater than γ s , then the particle splits into two particles of equal mass, and the distance between the two new particles is γ s It is a parameter that limits the mass of particles to prevent them from being too large, and its range is 1.5≤γ s ≤2.

[0080] (4) Monitor the particle flow rate at the outlet of the hydrocyclone underflow pipe and the water flow rate at the outlet of the overflow pipe respectively, stop the calculation after the flow rates at the two outlets are stable, complete the simulation, and obtain stable numerical simulation results of hydrocyclone separation. By monitoring the flow rate of the particle particles at the outlet, it is possible to quantitatively determine whether the calculation has reached stability, thereby improving the credibility of the hydrocyclone simulation results. Through the simulation method of the present invention, the calculation results and data comparison shown in Table 1 are obtained:

[0081] Table 1

[0082]

[0083] As can be seen from Table 1, the comparative example uses the traditional smooth particle method to simulate the hydrocyclone, which has a large amount of calculation and a long calculation time; while the calculation amount and calculation time of the present invention are reduced by about 40 times.

[0084] like Figure 3 As shown, the blue particles are gas particles and the red particles are liquid particles. The changes at the gas-liquid interface are clearly visible in the figure, which can ensure that the trajectory of the particles in the hydrocyclone can be tracked.

[0085] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "front", "rear", "left", "right", "head", "tail", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the scope of protection of the present invention. It should also be noted that, unless otherwise clearly specified and limited, the terms "connected" and "connected" should be understood in a broad sense, for example, it can be a fixed connection; it can be a detachable connection; it can also be a point connection; it can be a direct connection; it can be an indirect connection through an intermediate medium, so that the internals of the two elements can be connected. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances. The device connection methods not fully described in the present invention are all understood as conventional connection methods in the field.

[0086] The above embodiments are only specific examples for further describing the purpose, technical solutions and beneficial effects of the present invention, and the present invention is not limited thereto. Any modification, equivalent replacement, improvement, etc. made within the scope disclosed by the present invention are included in the protection scope of the present invention.

Claims

1. A hydrocyclone flow field simulation method based on an adaptive smooth particle method, characterized in that: The simulation method includes the following steps: (1) Determine the structural parameters of the hydrocyclone and construct a geometric model of the hydrocyclone; (2) Establish the basic control equation and discretize it into the adaptive smooth particle normal equation; (3) Based on the geometric model of the hydrocyclone, boundary conditions and initial calculation parameters are set, and then imported into the fluid simulation scene for simulation; (4) Monitor the particle flow rate at the outlet of the underflow pipe of the hydrocyclone and the flow rate at the outlet of the overflow pipe respectively. Stop the calculation after the flow rates at the two outlets are stable, and complete the simulation.

2. The method for simulating the flow field of a hydrocyclone based on the adaptive smooth particle method according to claim 1, characterized in that: The structural parameters of the hydrocyclone include: inlet height h1 and width b, column diameter d1, overflow pipe diameter d2, overflow pipe insertion depth h2, overflow pipe wall thickness δ, cone angle θ, and underflow pipe diameter d3.

3. The method for simulating the flow field of a hydrocyclone based on the adaptive smooth particle method according to claim 1, characterized in that: The basic governing equation is: The adaptive smooth particle normal equation is: Where ρ is the fluid density, t is the time, u is the fluid velocity, g is the gravitational acceleration, p is the pressure, μ is the dynamic viscosity, and F s is the surface tension; the subscripts i and j represent the particle number, W is the smooth kernel function, ∏ is the artificial viscosity value, r ij is the distance between particles i and j, η is the relaxation coefficient; At this time, the computational domains of particles, water bodies, and gases are discretized into a specific number of particles with different physical properties; The physical and mechanical parameters of particles, the physical and mechanical parameters of water bodies and the physical and mechanical parameters of gases are assigned to the physical and mechanical parameters corresponding to each physical particle.

4. The method for simulating the flow field of a hydrocyclone based on the adaptive smooth particle method according to claim 3, characterized in that: The computational domain of the particles, water and gas is discretized into a specific number of particles with different physical properties, including: The fluid region enclosed by the boundary of the gas and water bodies in the geometric model is internally discretized, and water particles and granular particles are uniformly inserted according to the material concentration; The gas region enclosed by the gas boundary in the geometric model is internally discretized, and gas particles are uniformly inserted.

5. The method for simulating the flow field of a hydrocyclone based on the adaptive smooth particle method according to claim 3, characterized in that: The physical and mechanical parameters of the particles include density, gravitational acceleration and diameter of the particles; the physical and mechanical parameters of the water body include particle density, gravitational acceleration and viscosity of water particles; and the physical and mechanical parameters of the gas include particle density and gravitational acceleration of gas particles.

6. The method for simulating the flow field of a hydrocyclone based on the adaptive smooth particle method according to claim 1, characterized in that: The boundary conditions include model boundary, wall boundary, inlet boundary and outlet boundary conditions.

7. The method for simulating the flow field of a hydrocyclone based on the adaptive smooth particle method according to claim 6, characterized in that: The model boundary adopts dynamic boundary conditions, the wall boundary is three layers of fixed virtual particles distributed on the wall, the inlet boundary is a given inlet velocity or pressure, and the outlet boundary is a free boundary.

8. The method for simulating the flow field of a hydrocyclone based on the adaptive smooth particle method according to claim 1, characterized in that: The initial calculation parameters include kernel function, variable smoothing length, reference particle spacing, particle splitting and merging technology.

9. The method for simulating the flow field of a hydrocyclone based on the adaptive smooth particle method according to claim 8, characterized in that: The kernel function is a cubic spline function and a hyperbolic kernel function. The cubic spline function is expressed as: The hyperbolic kernel function is expressed as: In the formula, s = r / h, r represents the distance between two particles, h represents the smooth length, and d represents the degree of spatial dimension. In two-dimensional and three-dimensional space, α d They are 5 / (14πh 2 ) and 1 / (4πh 3 ); The variable smooth length is expressed as: Where n is the time step, is the smoothing length of particle i at time step n+1, is the smoothing length determined by the number of adjacent particles i, is the average smooth length of adjacent particles i, is the smoothing length of particle i at time step n, N r is a given constant number of particles, is the number of neighboring particles i at time step n, is the smoothing length of particle j at time step n; The reference particle spacing is expressed as: Δs k+1 =C r Δs k , Where ΔS is the reference particle spacing, k is the particle band index, which increases with the distance from the interface, and C r is an adaptive number, which indicates the ratio of the reference particle spacing between two adjacent particle bands and controls the size of the refinement area. 1≤C r ≤1.2; when C r = 1, the particle spacing is uniform and the resolution no longer changes adaptively; when C r When the value increases, the particle spacing increases as the distance to the interface increases; The particle splitting and merging technique uses a reference particle mass, which is expressed as: m r =ρ r Δs d , In the formula, ρ r is the reference density, d is the spatial dimension; when the mass of particle i is m i With its reference particle mass m r The ratio is greater than γ s , then the particle splits into two particles of equal mass, and the distance between the two new particles is γ s It is a parameter that limits the mass of particles to prevent them from being too large, and its range is 1.5≤γ s ≤2.

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