Computational method of granular dispersion of densely packed charge bed under plasma jet action based on CFD-DEM

Abstract

The application discloses a kind of based on CFD-DEM's dense charge bed particle scattering calculation method under plasma jet action, comprising: using the zero-dimensional mathematical physics model of capillary ablation plasma generation including pulse circuit discharge, capillary ablation, plasma jet, obtain the curve fitting formula of plasma jet temperature and pressure change with time;Obtain the initial information of dense charge bed;Establish the geometric model of dense charge bed, set the geometric dimension parameter of dense charge bed model, carry out mesh division, establish the dense charge bed plasma jet point fire model in CFD solver;Establish particle model in DEM solver;Coupling Fluent and Edem calculation software, carry out transient calculation solution, carry out numerical calculation to CFD solver simultaneously, obtain simulation result data.The application can obtain the instantaneous velocity distribution of particle motion in chamber and the final accumulation of particle in chamber.

Description

Technical Field

[0001] This invention belongs to the field of electrothermal chemical emission technology, and in particular, it is a method for calculating the particle distribution of a dense charge bed under the action of plasma jet based on CFD-DEM. Background Technology

[0002] Electrothermal-chemical guns are a novel firing technology that converts electrical and chemical energy into kinetic energy. Compared to traditional artillery, electrothermal-chemical guns exhibit superior internal ballistic performance, improving ignition consistency and increasing firing rate. However, compared to traditional artillery igniting with propellant gases, the initial stage of its internal ballistics is more complex. This is because, at the initial moment of firing, propellant particles are concentrated around the ignition tube, and a high-temperature, high-pressure plasma jet is ejected from the ignition port, causing the energetic propellant particles to move into free space within the chamber. During this process, intense energy and momentum exchange occurs between the energetic particles, resulting in complex gas-solid flows.

[0003] Understanding the gas-particle flow within the propellant chamber is crucial in the early stages of internal ballistics, but predicting it is complex. It has been confirmed that the formation of an initial reverse pressure differential affects the stability of the internal ballistics of an artillery piece and can even lead to safety incidents (such as chamber explosions), primarily due to the uneven distribution of propellant particles caused by the compression of the propellant bed. Therefore, detailed simulations of the gas-particle flow within a dense propellant bed are essential for optimizing the charging, design, and ignition sequence. However, traditional Eulerian-Eulerian methods neglect the interactions between particles and their collisions with the chamber walls, failing to study the particle motion and dispersion behavior under the influence of airflow at the particle scale. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating particle dispersion in a dense charge bed under the action of plasma jet based on CFD-DEM, so as to study the motion and dispersion of particles in a cylindrical charge chamber under the action of plasma jet, and obtain the instantaneous motion of particles in the dense charge bed and the final static accumulation morphology.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A method for calculating particle distribution in a dense charge bed under plasma jet action based on CFD-DEM includes the following steps:

[0007] Step 1: Using a zero-dimensional mathematical physics model of capillary ablation to generate plasma, which includes pulse circuit discharge, capillary ablation, and plasma jet, the curve fitting formula of plasma jet temperature and pressure changing with time is obtained by calculation.

[0008] Step 2: Obtain the initial information of the dense charge bed, including the initial temperature and pressure of the fluid in the chamber, the geometry and dimensions of the dense charge bed, and the plasma jet ignition structure;

[0009] Step 3: Use 3D modeling software to establish a geometric model of the dense charge bed, set the geometric dimension parameters of the dense charge bed model, use tetrahedral mesh to mesh the geometric model of the dense charge bed, and establish a plasma jet ignition model of the dense charge bed in the CFD solver.

[0010] Step 4: Establish the particle model in the DEM solver, which includes particle simulation calculation parameters, particle contact model, and initial particle generation.

[0011] Step 5: Couple the two calculation software programs Fluent and Edem, and use an implicit pressure-velocity coupling algorithm to perform transient calculations. Based on the set time step and calculation time step, perform numerical calculations on the CFD solver simultaneously to obtain simulation results data.

[0012] The significant advantages of this invention compared to existing technologies are:

[0013] The present invention adopts the above technical solution, which can realize the study of the motion and dispersion of particles in a cylindrical drug chamber under the action of plasma jet, and obtain the instantaneous velocity distribution of the particles in the drug chamber and the final accumulation of the particles in the drug chamber. Attached Figure Description

[0014] Figure 1 This is a schematic flowchart of a method for particle dispersion in a dense charge bed under the action of plasma jet based on CFD-DEM according to the present invention.

[0015] Figure 2 This is a schematic diagram of the original three-dimensional model of the compacted charge bed in the embodiment;

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

[0017] Figure 4 This is a schematic diagram showing the distribution and structure of the central ignition tube inside the compacted charge bed in the embodiment;

[0018] Figure 5 The numerical calculation and function fitting curve of the plasma jet generated by capillary ablation in the embodiment are shown.

[0019] Figure 6 This is a diagram showing the accumulation of particles in a compacted drug bed after the particles have come to a standstill, as described in the embodiment.

[0020] Figure 7 This is the instantaneous particle velocity cloud map at 6ms in the embodiment. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

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

[0023] Step 1: Using a zero-dimensional mathematical physics model that includes pulsed circuit discharge, capillary ablation, and plasma jet to generate plasma, the curve fitting formulas for the changes in plasma jet temperature and pressure over time are obtained through calculation.

[0024] Step 1-1, the circuit of the pulse discharge system is as follows: Figure 2 As shown, the structure includes a step-up device consisting of an autotransformer, an isolation transformer, and a step-up transformer; a capacitor energy storage structure consisting of a rectifier stack, a current-limiting resistor, and a capacitor bank; and a discharge structure consisting of a plasma generator, a discharge switch, and a discharge trigger. Ignoring the effects of stray inductance and stray capacitance, the mathematical model for pulsed discharge of plasma jets generated by capillary ablation is as follows:

[0025]

[0026] P=IU-I 2 R s

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

[0028] The formula for calculating the equivalent resistance R′ of a plasma mixture 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, and σ p K is the conductivity of the plasma. b Here, ε₀ is the Boltzmann constant, Z is the plasma charge number, e is the electron charge number, and T is the electron charge number. p The temperature of the plasma is given by lnΛ, where lnΛ is the Coulomb logarithm, and a, b, c are constants related to the types of particles in the plasma. e This represents the number of free electrons.

[0032] Steps 1-2, the mathematical model of capillary ablation for generating plasma jets is as follows:

[0033]

[0034] The above formula assumes that the plasma generated by capillary ablation is the main component, and other forms of plasma generation are negligible. The plasma in the capillary is in a state of local thermodynamic equilibrium. Radiation in the capillary is calculated using the "blackbody radiation model." The capillary ablation material is polyethylene, and during the ablation process, its C-C bonds are broken, generating a large number of CH2 free radicals. The number of other free radicals and molecules is very small and negligible. Where N... CH2 E represents the number of CH2 free radicals. CC Here, f is the C / C bond energy, f is the radiation coefficient, and T is the T / C bond energy. p σ 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 mathematical model of plasma jet generation by capillary ablation 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 internal pressure. Assuming the plasma is a critical flow, where m0 is the mass of the plasma ejected from the capillary, r0 is the nozzle radius, and γ... p R is the specific heat ratio of the plasma. p p is the plasma gas constant. p m is the plasma jet pressure. p m is the mass of the plasma generated by capillary ablation, and m1 is the mass of the remaining plasma in the capillary. C and m H These are the masses of a carbon atom and a hydrogen atom, respectively.

[0039] Steps 1-4 require supplementing the energy equation and plasma state equation, and calculating the data for plasma jet temperature and pressure.

[0040] The formula for calculating the energy equation is as follows:

[0041]

[0042] The above equation assumes that the plasma is in thermodynamic equilibrium and that the particle energy follows the Maxwell distribution. T represents the average kinetic energy of the plasma. p This represents the plasma temperature, and k is the Boltzmann constant.

[0043]

[0044] In the formula, N1 represents the number of plasmas, and E CH For CH bond energy, W i N is the electron ionization energy, N0 is the number of ejected plasmas, N e This represents the number of electrons.

[0045] The plasma state equation is as follows:

[0046]

[0047] The above equation is the classical plasma state equation that takes into account the partial ionization caused by the Coulomb force, p p ′ represents the pressure correction term that includes interparticle forces.

[0048] Steps 1-5: Taking the initial discharge voltage as U = 9kV, the calculations are as follows: Figure 3 The numerical calculation curve of the plasma jet generated by capillary ablation was obtained by curve fitting using an exponential equation, and the fitting formulas for the change of plasma jet temperature and pressure over time are 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] In the above formula, exp represents the natural exponent.

[0052] Step 2: Obtain the initial information of the dense charge bed, which includes the initial temperature and pressure of the fluid in the chamber, the geometry and dimensions of the dense charge bed, and the 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 The data shows that the charge bed has a cylindrical structure with L = 490 mm and a diameter 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 ignition tube, which is located in the center of the powder chamber. There are 14 ignition holes with a diameter of 6 mm distributed on the tube, arranged in four symmetrical rows. The figure uses x and y coordinates to show the size, structure and position distribution of the central ignition tube.

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

[0056] Step 3-1: Use Ansys meshing to mesh the geometric model of the dense charge bed. The mesh size is controlled at 12mm, and the minimum mesh size at the central ignition tube nozzle is 2mm. The central ignition tube nozzle is designated as the pressure inlet. The wall surface is a non-slip wall surface, and the contact type between the wall surface and the particles is bounce.

[0057] Step 3-2: The turbulence model adopts the Realizable k-ε turbulence model. The calculation time step for the fluid is determined, which is generally 1-100 times the calculation time step for the particulate phase. A calculation time step of 1×10⁻⁶ is chosen. -6 The total calculation time is 0.7 seconds.

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

[0059] Step 4-1: Based on the known properties of gunpowder particles, calibrate the simulation parameters of the simulated gunpowder particles, select the Hertz-Mindlin no-slip contact model, and adopt 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 by the red dashed line is the particle generation area. Particles are generated in the particle generation factory 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 as 1×10 based on the Rayleigh time step of the particles. -6 The total calculation time is 0.7s. The formula for calculating the Rayleigh time step for particles is as follows.

[0064]

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

[0066] Step 5: Couple the two calculation software programs Fluent and Edem, and use an implicit pressure-velocity coupling algorithm to perform transient calculations. Based on the set time step and calculation time step, perform numerical calculations simultaneously on the CFD solver (Fluent) and the DEM solver (Edem) to obtain simulation results data.

[0067] Step 5-1: In the CFD-DEM coupled calculation, the plasma phase is treated as a continuous phase, and its motion is solved based on the Navier-Stokes equations. The governing equations are as follows:

[0068]

[0069] In the formula p f ρ f ε f Let μ represent the pressure, density, and gas volume fraction within the grid of the fluid phase, respectively; g is the acceleration due to gravity; and μ is the fluid viscosity coefficient. t U is the turbulent viscosity coefficient, S is the momentum exchange source term, and u is the turbulent viscosity coefficient. f,i u represents the fluid velocity interpolated to particle i. f,j x represents the fluid velocity interpolated to particle j. i Indicates the position of particle i, x j This indicates the position of particle j.

[0070] In CFD-DEM coupled calculations, particles are treated as discrete phases, and their motion follows Newton's mechanical equations within the Lagrange framework. The governing equations are as follows:

[0071]

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

[0073] In gas-solid two-phase flow, the momentum exchange between particles and the gas phase is mainly reflected in the drag force. The formula for calculating the drag force on 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 v is the fluid velocity interpolated to particle i. s,i Let β be the velocity of particle i, β be the interphase momentum exchange coefficient, and ε be the velocity of particle i. s It is the solid volume fraction within the current grid.

[0076] The Gidaspow drag model is used, and its specific expression is as follows:

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

[0078]

[0079] When ε f When ≤0.8:

[0080]

[0081] In the formula, γ is the drag correction factor, and Re s U is the particle Reynolds number. f v is the fluid velocity. s The velocity is the solid phase velocity.

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

[0083] This invention employs the above technical solution, based on the CFD-DEM method and coupled with a zero-dimensional mathematical and physical model of plasma generated by capillary ablation, to study the motion and dispersion of particles in a cylindrical propellant chamber under the action of a plasma jet, and to obtain a simulated motion and accumulation of gunpowder particles in the propellant chamber.

Claims

1. A method for calculating particle distribution in a dense charge bed under plasma jet action based on CFD-DEM, characterized in that, Includes the following steps: Step 1: Using a zero-dimensional mathematical physics model of capillary ablation to generate plasma, which includes pulse circuit discharge, capillary ablation, and plasma jet, the curve fitting formula of plasma jet temperature and pressure changing with time is obtained by calculation. Zero-dimensional mathematical physics models include: Pulse discharge mathematical model: P = IU-I 2 R s In the above formula, R s t is stray resistance, C is capacitor bank capacitance, U is discharge voltage, I is discharge current, P is power received by plasma load, R′ is equivalent resistance of plasma mixture, and t is time. Mathematical model of capillary ablation: Where N CH2 E represents the number of CH2 free radicals. CC Here, f is the C / C bond energy, f is the radiation coefficient, and T is the T / C bond energy. p σ is the temperature of the plasma, σ is the Stefan-Boltzmann constant, r1 is the capillary radius, and l1 is the capillary length. Mathematical model of plasma jet: Where m0 is the mass of the plasma ejected from the capillary, r0 is the nozzle radius, and γ p R is the specific heat ratio of the plasma. p p is the plasma gas constant. p m is the plasma jet pressure. p m is the mass of the plasma generated by capillary ablation, and m1 is the mass of the remaining plasma in the capillary. C and m H These are the masses of a carbon atom and a hydrogen atom, respectively. Step 2: Obtain the initial information of the dense charge bed, including the initial temperature and pressure of the fluid in the chamber, the geometry and dimensions of the dense charge bed, and the plasma jet ignition structure; Step 3: Use 3D modeling software to establish a geometric model of the dense charge bed, set the geometric dimension parameters of the dense charge bed model, use tetrahedral mesh to mesh the geometric model of the dense charge bed, and establish a plasma jet ignition model of the dense charge bed in the CFD solver. Step 4: Establish the particle model in the DEM solver, which includes particle simulation calculation parameters, particle contact model, and initial particle generation. Step 5: Couple the Fluent and Edem calculation software, and use an implicit pressure-velocity coupling algorithm for transient calculation. Based on the set time step and calculation time step number, perform numerical calculations synchronously on the CFD solver to obtain simulation results data; specifically including: Step 5-1: In the CFD-DEM coupled calculation, the plasma phase is treated as a continuous phase, and its governing equations are as follows: In the formula p f ρ f ε f Let μ represent the pressure, density, and gas volume fraction within the grid of the fluid phase, respectively; g is the acceleration due to gravity; and μ is the fluid viscosity coefficient. t U is the turbulent viscosity coefficient, S is the momentum exchange source term, and u is the turbulent viscosity coefficient. f,i u represents the fluid velocity interpolated to particle i. f,j x represents the fluid velocity interpolated to particle j. i Indicates the position of particle i, x j Indicates the position of particle j; In CFD-DEM coupled calculations, particles are treated as discrete phases, and their governing equations are as follows: In the formula, m p It refers to particle mass, v p It is the translational velocity of the particle, F P For pressure gradient force, F d For drag force, F c For the collision contact force, ω p It is the particle angular velocity, I P It is the moment of inertia, Ln is the vector radius from the particle's center of mass to the contact point, N is the number of all particles colliding with the current particle, and f τ,ij It is the tangential collision contact force between discrete particles; In gas-solid two-phase flow, the momentum exchange between particles and the gas phase is mainly reflected in the drag force. The formula for calculating the drag force on a single particle i in the flow field is as follows: In the above formula, V s For particle volume, u f,i v is the fluid velocity interpolated to particle i. s,i Let β be the velocity of particle i, β be the interphase momentum exchange coefficient, and ε be the velocity of particle i. s It is the solid volume fraction within the current grid. Step 5-2: Obtain the plasma jet flow data and simulation time in the CFD solution; obtain the instantaneous particle spatial distribution and particle instantaneous velocity cloud map in the DEM solver.

2. The method for calculating particle distribution in a dense charge bed under plasma jet action based on CFD-DEM according to claim 1, characterized in that, Step 3 specifically includes: Step 3-1: Use Ansys meshing to mesh the geometric model of the compacted charge bed, designate the central ignition pipe nozzle as the pressure inlet, use a non-slip wall surface, and set the contact type between the wall surface and the particles to bounce. Step 3-2: The Realizable k-ε turbulence model is adopted for the turbulence model. The fluid calculation time step and the total calculation time are determined.

3. The method for calculating particle distribution in a dense charge bed under plasma jet action based on CFD-DEM according to claim 1, characterized in that, Step 4 specifically includes: Step 4-1: Based on the known properties of gunpowder particles, calibrate the simulation parameters of the simulated gunpowder particles, select the Hertz-Mindlin no-slip contact model, and adopt the standard rolling friction model. Step 4-2: Generate particles in the particle generation plant according to the filling porosity. After 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.

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

5. The method for calculating particle distribution in a dense charge bed under plasma jet action based on CFD-DEM according to claim 1, characterized in that, When ε f When >0.8: Among them, C D This is the drag coefficient; When ε f When ≤0.8: In the formula, γ is the drag correction factor, and Re s U is the particle Reynolds number. f v is the fluid velocity. s The velocity is the solid phase velocity.

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