Compact charging bed particle distribution calculation method under plasma jet action based on CFD-DEM

Abstract

The invention discloses a CFD-DEM-based dense charging bed particle distribution calculation method under the action of plasma jet, and the method comprises the steps: employing a zero-dimensional mathematical physical model which comprises pulse circuit discharge, capillary ablation and plasma jet and generates plasma through capillary ablation; obtaining a curve fitting formula of the plasma jet temperature and pressure changing along with time; acquiring initial information of the dense charging bed; establishing a dense charging bed geometric model, setting geometric dimension parameters of the dense charging bed model, performing grid division, and establishing a dense charging bed plasma jet point fire transfer model in a CFD solver; establishing a particle model in a DEM solver; and coupling Fluent and Edem calculation software, carrying out transient calculation solution, and synchronously carrying out numerical calculation on the CFD solver to obtain simulation result data. According to the method, the instantaneous speed distribution of the particles moving in the medicine chamber and the final accumulation condition of the particles in the medicine chamber can be obtained.

Description

Technical Field

[0001] The invention belongs to the technical field of electrothermal chemical emission, in particular to a method for calculating the particle dispersion of a dense charge bed under the action of a plasma jet based on CFD-DEM. Background Art

[0002] Electrothermal chemical gun is a new type of firing technology that uses electrical energy and chemical energy to convert into kinetic energy. Compared with traditional guns, electrothermal chemical guns have better internal ballistic performance, can improve the consistency of gun ignition, and increase the gun firing rate. However, compared with the ignition of traditional guns using ignition powder gas, its initial stage of internal ballistics is more complicated. This is because at the initial moment of gun firing, the propellant particles are concentrated around the fire transfer tube, and the high-temperature and high-pressure plasma jet is ejected from the ignition hole, causing the energetic gunpowder particles to move toward the free space in the chamber. In this process, the energetic particles undergo intense energy and momentum exchange, forming a complex gas-solid flow.

[0003] In the early stages of internal ballistics, it is crucial to understand the gas-particle flow in the chamber, but it is complex to predict. It has been confirmed that the formation of the initial reverse pressure difference will affect the stability of the internal ballistics of the gun and even lead to safety accidents (such as chamber explosion). The main reason is the uneven distribution of propellant particles caused by the compressed propellant bed. Therefore, it is necessary to simulate the gas-particle flow in the chamber of the dense charge bed in detail to optimize the charge, design and ignition procedure. However, the traditional Euler-Euler method ignores the interaction between particles and the collision with the chamber wall, and cannot study the motion and dispersion behavior of particles under the action of airflow from the particle scale. Summary of the invention

[0004] The purpose of the present invention is to provide a method for calculating the particle dispersion of a dense charge bed under the action of a plasma jet based on CFD-DEM, so as to study the movement and dispersion of particles in a cylindrical chamber under the action of a plasma jet, and obtain the instantaneous movement of particles in the dense charge bed and the final stacking morphology when they are stationary.

[0005] The technical solution to achieve the purpose of the present invention is:

[0006] A CFD-DEM-based method for calculating the particle dispersion of a dense charge bed under the action of a plasma jet comprises the following steps:

[0007] Step 1, using a zero-dimensional mathematical physics model of plasma generated by capillary ablation including pulse circuit discharge, capillary ablation, and plasma jet, and obtaining a curve fitting formula of the change of plasma jet temperature and pressure over time by calculation;

[0008] Step 2, obtaining initial information of the dense charge bed, including initial temperature and pressure of the fluid in the chamber, geometric structure and size of the dense charge bed, and plasma jet ignition structure;

[0009] Step 3, using 3D modeling software to establish a dense charge bed geometric model, set the geometric size parameters of the dense charge bed model, use tetrahedral meshes to mesh the dense charge bed geometric model, and establish a dense charge bed plasma jet ignition model in a CFD solver;

[0010] Step 4, establishing a particle model in the DEM solver, including particle simulation calculation parameters, particle contact model, and initial particle generation;

[0011] Step 5, couple the two computing software Fluent and Edem, use the implicit pressure-velocity coupling algorithm to perform transient calculation and solution, based on the set time step and calculation time step, perform numerical calculation on the CFD solver synchronously to obtain the simulation result data.

[0012] Compared with the prior art, the present invention has the following significant advantages:

[0013] The present invention adopts the above technical scheme to realize the study of the movement and dispersion of particles in a cylindrical chamber under the action of a plasma jet, and obtain the instantaneous velocity distribution of the particles moving in the chamber and the final accumulation of the particles in the chamber. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a schematic flow chart of a method for dispersing particles of a dense charge bed under the action of a plasma jet based on CFD-DEM of the present invention;

[0015] Figure 2 is a schematic diagram of an original three-dimensional model of a dense powder bed in an embodiment;

[0016] Figure 3 is a circuit diagram of a pulse discharge system in an embodiment;

[0017] Figure 4 Schematic diagram of the distribution position and structure of the central fire transfer tube in the dense charge bed in the embodiment;

[0018] Figure 5 is the numerical calculation and function fitting curve of plasma jet generated by capillary ablation in the embodiment;

[0019] Figure 6 It is a diagram of the accumulation of particles in a densely packed bed after the particles have come to a standstill in the embodiment;

[0020] Figure 7 It is the instantaneous particle velocity cloud diagram at 6ms in the embodiment. DETAILED DESCRIPTION

[0021] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0022] Combination Figure 1 The present invention provides a method for calculating the particle dispersion of a dense charge bed under the action of a plasma jet based on CFD-DEM, and the specific implementation steps are as follows:

[0023] Step 1, using a zero-dimensional mathematical physics model of plasma generated by capillary ablation including pulse circuit discharge, capillary ablation and plasma jet, and obtaining a curve fitting formula of the change of plasma jet temperature and pressure with time by calculation.

[0024] Step 1-1, the circuit of the pulse discharge system is as follows Figure 2 As shown, it includes a boost device structure composed of an autotransformer, an isolation transformer, and a boost transformer, a capacitor energy storage structure composed of a rectifier stack, a current limiting resistor, and a capacitor bank, and a discharge structure composed of a plasma generator, a discharge switch, and a discharge trigger. The influence of stray inductance and stray capacitance is not considered. The mathematical model of the pulse discharge of the plasma jet generated by capillary ablation is as follows:

[0025]

[0026] P=IU-I 2 R s

[0027] In the above formula, R s is the stray resistance, C is the capacitor bank capacitance, U is the discharge voltage, I is the discharge current, P is the power received by the plasma load, R′ is the plasma mixture equivalent resistance, and t is the time.

[0028] The calculation formula of the plasma mixture equivalent resistance R' is as follows:

[0029]

[0030] lnΛ=a+blnT p -clnn e

[0031] In the above formula, r1 is the capillary radius, l1 is the capillary length, σ p is the conductivity of the plasma, K b is the Boltzmann constant, ε0 is the vacuum dielectric constant, Z is the plasma charge number, e is the electron charge number, T p is the temperature of the plasma, lnΛ is the Coulomb logarithm, a, b, c are constants related to the particle types in the plasma, and n e is the number of free electrons.

[0032] Step 1-2, the capillary ablation mathematical model for generating plasma jet by capillary ablation is as follows:

[0033]

[0034] In the above formula, it is assumed that the plasma generated by capillary ablation is the main body, and the plasma generated in other forms is negligible. The plasma in the capillary is in a state of local thermodynamic equilibrium. The radiation in the capillary is calculated using the "blackbody radiation model". The capillary ablation material is polyethylene material. Its CC bond is destroyed during the ablation process, generating a large number of CH2 free radicals. The number of other free radicals and molecules is very small and negligible. CH2 Indicates the number of CH2 radicals, E CC is the CC bond energy, f is the radiation coefficient, T p is the temperature of the plasma, σ is the Stefan-Boltzmann constant, r1 is the capillary radius, and l1 is the capillary length.

[0035] Steps 1-3, the plasma jet mathematical model of capillary ablation to generate plasma jet is as follows:

[0036]

[0037] m p =(m C +2m H )N CH2

[0038] In the above formula, during the plasma ejection process, the back pressure is greater than the capillary pressure. Assuming that the plasma is a critical flow, m0 is the mass of plasma ejected from the capillary, r0 is the nozzle radius, and γ p is the specific heat ratio of plasma, R p is the plasma gas constant, p p is the plasma jet pressure, m p is the mass of plasma generated by capillary ablation, m1 is the mass of plasma remaining in the capillary, and m C and m H are the masses of carbon and hydrogen atoms respectively.

[0039] Steps 1-4 require supplementing the energy equation and plasma state equation to calculate the data of plasma jet temperature and pressure.

[0040] The energy equation is calculated as follows:

[0041]

[0042] The above formula assumes that the plasma is in a state of thermodynamic equilibrium and the particle energy conforms to the Maxwell distribution. represents the average kinetic energy of plasma, T p represents the plasma temperature and k is the Boltzmann constant.

[0043]

[0044] Where N1 represents the number of plasma, E CH is the C—H bond energy, W i is the electron ionization energy, N0 is the number of plasma ejected, N e is the number of electrons.

[0045] The plasma state equation is as follows:

[0046]

[0047] The above equation is the classical plasma state equation for partial ionization taking into account the Coulomb force, p p ′ is the pressure correction term including the inter-particle forces.

[0048] Step 1-5, take the initial discharge voltage as U=9kv, and calculate Figure 3 The numerical calculation curve of plasma jet generated by capillary ablation is fitted by using the exponential equation, and the fitting formula of the change of plasma jet temperature and pressure with time is obtained as follows:

[0049] p p =f(t)=25×exp -1060.95t +0.1847(MPa)

[0050] T p =g(t)=8000×exp -943.70t +2291.81(K)

[0051] exp in the above formula represents the natural exponential.

[0052] Step 2, obtaining initial information of the dense charge bed, wherein the initial information of the dense charge bed includes initial temperature and pressure of the fluid in the chamber, geometric structure and size of the dense charge bed, and plasma jet ignition structure.

[0053] The schematic diagram of the three-dimensional model of the densely packed drug bed in this embodiment is shown in Figure 4 It is given that the charge bed is a cylindrical structure with L = 490 mm and a diameter of D = 110 mm. The initial temperature of the fluid in the chamber is 300 K and the initial pressure is one atmosphere 101325 Pa.

[0054] In this embodiment, the plasma jet ignition structure is composed of Figure 5The yellow part in the figure is the central fire transfer tube, which is located in the center of the chamber. There are fire transfer holes with a diameter of 6 mm on the tube. The fire transfer holes are symmetrically distributed in four rows, with a total of 14 fire transfer holes. The size structure and position distribution of the central fire transfer tube are given in the figure using x and y coordinates.

[0055] Step 3, using 3D modeling software to establish a dense charge bed geometric model, set the geometric size parameters of the dense charge bed model, use tetrahedral grids to mesh the dense charge bed geometric model, and establish a dense charge bed plasma jet ignition model in a CFD solver.

[0056] Step 3-1, use Ansys meshing to mesh the dense charge bed geometry model, the mesh control size is 12mm, the minimum mesh size at the center flame transfer tube nozzle is 2mm, the center flame transfer tube nozzle is designated as the pressure inlet, the wall adopts a no-slip wall, and the contact type between the wall and the particles is rebound.

[0057] Step 3-2: The turbulence model adopts the Realizable k-ε turbulence model to determine the fluid calculation time step, which is generally 1-100 times the particle phase calculation time step. The calculation time step is 1×10 -6 s, and the total calculation time is 0.7s.

[0058] Step 4: Establish a particle model in the DEM solver, including particle simulation calculation parameters, particle contact model, and initial particle generation.

[0059] Step 4-1, calibrate the simulation parameters of the simulated gunpowder particles according to the known properties of the gunpowder particles, select the Hertz-Mindlin non-sliding contact model, and use the standard rolling friction model; the simulation parameters of the particles are shown in Table 1.

[0060] Table 1 Particle simulation parameters

[0061]

[0062] Step 4-2, Figure 3 The virtual particle factory marked with a red dotted line is the particle generation area. In the particle generation factory, particles are generated according to the filling porosity. After the particle generation is completed, the calculation case is exported and the calculation time is set to 0.

[0063] Step 4-3: Determine the solid phase calculation time step to be 1×10 based on the Rayleigh time step of the particles. -6 s, the total calculation time is 0.7s, and the particle Rayleigh time step calculation formula is as follows.

[0064]

[0065] In the above formula, Yi is the particle Young's modulus, ρ s is the particle density, R i is the particle radius, ν i is the particle Poisson's ratio.

[0066] Step 5, couple the two computing software Fluent and Edem, use the implicit pressure-velocity coupling algorithm to perform transient calculation and solution, based on the set time step and calculation time step, perform numerical calculations on the CFD solver (Fluent) and the DEM solver (Edem) simultaneously to obtain the simulation result data.

[0067] Step 5-1, in the CFD-DEM coupled calculation, the plasma phase is regarded as a continuous phase, and its motion is solved based on the Navier-Stokes equation, and its control equation is as follows:

[0068]

[0069] Where p f , f , ε f They represent the pressure, density, and volume fraction of gas in the grid, respectively. g is the acceleration of gravity. μ is the viscosity coefficient of the fluid. t is the turbulent viscosity coefficient, S is the momentum exchange source term, u f,i represents the fluid velocity interpolated to particle i, u f,j represents the fluid velocity interpolated to particle j, x i represents the position of particle i, x j represents the position of particle j.

[0070] In the CFD-DEM coupling calculation, particles are regarded as discrete phases, and their motion follows the Newtonian mechanics equations under the Lagrangian framework. The governing equations are as follows:

[0071]

[0072] In the above formula, m p is the particle mass, v p is the particle translational velocity, F P is the pressure gradient force, F d is the drag force, F c is the collision contact force. p is the particle angular velocity, I P is the moment of inertia, Ln is the vector radius from the particle mass center to the contact point. N is the number of all particles that collide with the current particle, f τ,ij is the tangential collision contact force between discrete particles.

[0073] In gas-solid two-phase flow, the momentum exchange between particles and gas is mainly reflected in the drag force. The drag force calculation formula for a single particle i in the flow field is as follows:

[0074]

[0075] In the above formula, Vs is the particle volume, u f,i is the fluid velocity interpolated to particle i, v s,i is the velocity of particle i, β is the phase momentum exchange coefficient, ε s is the solid volume fraction in the current grid.

[0076] The Gidaspow drag model is used, which is specifically expressed as follows:

[0077] When ε f >0.8: In the above formula, C D is the drag coefficient,

[0078]

[0079] When ε f ≤0.8:

[0080]

[0081] Where γ is the drag correction factor, Re s is the particle Reynolds number, u f is the fluid velocity, v s is the solid phase velocity.

[0082] Step 5-2, in CFD solution, the flow data and simulation time of plasma jet can be obtained; in DEM solver, the instantaneous particle spatial distribution and particle instantaneous velocity cloud map can be obtained, such as Figure 6 , 7 .

[0083] The present invention adopts the above technical scheme, based on the CFD-DEM method and coupled with the zero-dimensional mathematical physics model of plasma generated by capillary ablation, to realize the study of the movement and scattering of particles in a cylindrical chamber under the action of a plasma jet, and obtain the movement and accumulation of simulated gunpowder particles in the chamber.

Claims

1. A method for calculating the particle dispersion of a dense charge bed under the action of a plasma jet based on CFD-DEM, characterized in that: The following steps are involved: Step 1, using a zero-dimensional mathematical physics model of plasma generated by capillary ablation including pulse circuit discharge, capillary ablation, and plasma jet, and obtaining a curve fitting formula of the change of plasma jet temperature and pressure over time by calculation; Step 2, obtaining initial information of the dense charge bed, including initial temperature and pressure of the fluid in the chamber, geometric structure and size of the dense charge bed, and plasma jet ignition structure; Step 3, using 3D modeling software to establish a dense charge bed geometric model, set the geometric size parameters of the dense charge bed model, use tetrahedral meshes to mesh the dense charge bed geometric model, and establish a dense charge bed plasma jet ignition model in a CFD solver; Step 4, establishing a particle model in the DEM solver, including particle simulation calculation parameters, particle contact model, and initial particle generation; Step 5, couple the two computing software Fluent and Edem, use the implicit pressure-velocity coupling algorithm to perform transient calculation and solution, based on the set time step and calculation time step, perform numerical calculation on the CFD solver synchronously to obtain the simulation result data.

2. The method for calculating the particle distribution of a dense charge bed under the action of a plasma jet based on CFD-DEM according to claim 1 is characterized in that: Zero-dimensional mathematical physics models include: Pulse discharge mathematical model: P = IU-I 2 R s In the above formula, R s is the stray resistance, C is the capacitor bank capacitance, U is the discharge voltage, I is the discharge current, P is the power received by the plasma load, R' is the plasma mixture equivalent resistance, and t is the time; Capillary ablation mathematical model: Where N CH2 Indicates the number of CH2 radicals, E CC is the CC bond energy, f is the radiation coefficient, T p is the temperature of the plasma, σ is the Stefan-Boltzmann constant, r1 is the capillary radius, and l1 is the capillary length; Plasma jet mathematical model: Where m0 is the mass of plasma ejected from the capillary, r0 is the nozzle radius, γ p is the specific heat ratio of plasma, R p is the plasma gas constant, p p is the plasma jet pressure, m p is the mass of plasma generated by capillary ablation, m1 is the mass of plasma remaining in the capillary, and m C and m H are the masses of carbon and hydrogen atoms respectively.

3. The method for calculating the particle distribution of a dense charge bed under the action of a plasma jet based on CFD-DEM according to claim 1 is characterized in that: Step 3 specifically includes: Step 3-1, mesh the geometric model of the dense charge bed using Ansysmeshing, designate the central fire tube nozzle as the pressure inlet, use a no-slip wall for the wall, and the contact type between the wall and the particles is rebound; Step 3-2, the turbulence model adopts the Realizable k-ε turbulence model, determines the fluid calculation time step, and calculates the total time.

4. The method for calculating the particle distribution of a dense charge bed under the action of a plasma jet based on CFD-DEM according to claim 1 is characterized in that: Step 4 specifically includes: Step 4-1, calibrate the simulation parameters of the simulated gunpowder particles according to the known properties of the gunpowder particles, select the Hertz-Mindlin non-sliding contact model, and use the standard rolling friction model; Step 4-2, generate particles according to the filling porosity in the particle generation factory, and after the particle generation is completed, export the calculation case and set the calculation time to 0; Step 4-3, determine the solid phase calculation time step based on the Rayleigh time step of the particles.

5. The method for calculating the particle distribution of a dense charge bed under the action of a plasma jet based on CFD-DEM according to claim 1, characterized in that: The particle Rayleigh time step calculation formula is as follows: In the above formula, Y i is the particle Young's modulus, ρ s is the particle density, R i is the particle radius, ν i is the particle Poisson's ratio.

6. The method for calculating the particle distribution of a dense charge bed under the action of a plasma jet based on CFD-DEM according to claim 1, characterized in that: Step 5 specifically includes: Step 5-1, in the CFD-DEM coupled calculation, the plasma phase is regarded as a continuous phase, and its governing equation is as follows: Where p f , f , ε f They represent the pressure, density, and volume fraction of gas in the grid, respectively. g is the acceleration of gravity. μ is the viscosity coefficient of the fluid. t is the turbulent viscosity coefficient, S is the momentum exchange source term, u f,i represents the fluid velocity interpolated to particle i, u f,j represents the fluid velocity interpolated to particle j, x i represents the position of particle i, x j represents the position of particle j; In the CFD-DEM coupled calculation, the particles are regarded as discrete phases, and the governing equations are as follows: In the formula, m p is the particle mass, v p is the particle translational velocity, F P is the pressure gradient force, F d is the drag force, F c is the collision contact force. p is the particle angular velocity, I P is the moment of inertia, Ln is the vector radius from the particle mass center to the contact point, N is the number of all particles that collide with the current particle, and f τ,ij is the tangential collision contact force between discrete particles; In gas-solid two-phase flow, the momentum exchange between particles and gas is mainly reflected in drag. The drag calculation formula for a single particle i in the flow field is as follows: In the above formula, V s is the particle volume, u f,i is the fluid velocity interpolated to particle i, v s,i is the velocity of particle i, β is the phase momentum exchange coefficient, ε s is the solid volume fraction in the current grid; Step 5-2, obtain the flow data and simulation time of the plasma jet in CFD solution; obtain the instantaneous particle spatial distribution and particle instantaneous velocity cloud map in DEM solver.

7. The method for calculating the particle distribution of a dense charge bed under the action of a plasma jet based on CFD-DEM according to claim 6 is characterized in that: When ε f >0.8: Among them, C D is the drag coefficient; When ε f ≤0.8: Where γ is the drag correction factor, Re s is the particle Reynolds number, u f is the fluid velocity, v s is the solid phase velocity.

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