A numerical simulation method for narrow-pulse laser-induced shock waves

Abstract

This invention discloses a numerical simulation method for narrow-pulse laser-induced shock waves, comprising: acquiring laser parameters and metal target parameters; calculating the spatial distribution of laser energy, dividing the laser ablation region into a grid, and generating a two-dimensional numerical grid; constructing a laser ablation simulation model based on a metal phase transition heat transfer model and introducing the particle evaporation backscattering coefficient; simulating the propagation state of shock waves induced by vapor expansion within a set time interval, obtaining the state physical quantities of vapor flow outside the Knudsen layer as the initial boundary conditions of the shock wave in the shock wave model; and updating the fluid medium parameters based on the governing equations of the shock wave model and the ambient gas state during the shock wave propagation simulation, iteratively calculating the instantaneous evolution characteristics of the shock wave at different time lengths within the time interval. This invention can accurately predict the dynamic evolution characteristics of shock waves during laser ablation, providing technical support for fields such as laser processing, laser propulsion, and laser shock enhancement.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology of laser-matter interaction, and in particular to a method for numerical simulation of narrow-pulse laser-induced shock waves. Background Technology

[0002] With the rapid development of laser technology, laser-induced shock wave technology has been widely used in materials processing, laser propulsion, and laser shock strengthening. However, because laser-induced shock waves involve multi-physics coupling (such as thermodynamic processes, phase transitions, and vaporization effects), existing research methods still have certain limitations in accurately predicting the evolution characteristics of shock waves. Traditional experimental techniques are limited by temporal resolution and spatial capture capabilities, while a single theoretical model is insufficient to fully describe the complex behavior of shock waves.

[0003] Therefore, how to provide a high-precision numerical simulation method for the dynamic evolution characteristics of laser-induced shock waves is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] In response to the aforementioned research status and existing problems, this invention provides a numerical simulation method for narrow-pulse laser-induced shock waves. By constructing a multi-physics coupled numerical simulation framework, it can accurately predict the dynamic evolution characteristics of shock waves during laser ablation. In particular, considering the interaction between laser-induced shock waves and metal ablation and vaporization effects, it provides important theoretical support and technical guarantee for applications in high-end technology fields such as laser processing, laser propulsion, and laser shock strengthening.

[0005] The present invention provides a numerical simulation method for narrow-pulse laser-induced shock waves, comprising the following steps:

[0006] S1: Obtain laser parameters and metal target parameters;

[0007] S2: Using the laser energy in the laser parameters as a heat source term, calculate the spatial distribution of the laser energy, and use the finite element method to divide the laser ablation region of the metal target into a mesh to generate a two-dimensional numerical mesh.

[0008] S3: Based on the metal phase transition heat transfer model, the metal phase transition process and the phase interface movement process are described. The particle evaporation backscattering coefficient is introduced to construct a laser ablation simulation model. The laser ablation simulation model is used to simulate the propagation state of the shock wave caused by the steam expansion during the laser ablation process within a set time interval in the two-dimensional numerical grid, and the ablation interface is dynamically updated to obtain the state physical quantities of the steam flow outside the Knudsen layer.

[0009] S4: Construct a shock wave model, using the state physical quantities of the Knudsen layer vapor flow within the time interval as the initial boundary conditions of the shock wave in the shock wave model, and using the conservation equations of the fluid medium state changes before and after the shock wave as the governing equations of the shock wave model. The fluid medium includes Knudsen layer vapor and ambient gas.

[0010] S5: Based on the control equations of the shock wave model, the fluid medium parameters are updated in combination with the ambient gas state during the shock wave propagation simulation, and the instantaneous evolution characteristics of the shock wave at different time lengths within the time interval are obtained by iterative calculation.

[0011] Preferably, the laser parameters in S1 include: laser peak power, laser pulse width, and laser beam radius; the metal target parameters include: metal density, specific heat capacity, and thermal conductivity.

[0012] Preferably, the metal phase change heat transfer model includes three stages of phase change heat transfer equations: a no-phase-change heat transfer stage where the ablation interface temperature is below the metal melting point, a solid-liquid phase change heat transfer stage where the ablation interface temperature is between the metal melting point and boiling point, and a gas-liquid phase change heat and mass transfer stage where the ablation interface temperature is above the boiling point; wherein:

[0013] The dynamic specific heat capacity considering the latent heat of fusion is adopted in the solid-liquid phase transition stage;

[0014] The dynamic specific heat capacity, which takes into account the latent heat of melting and the latent heat of vaporization, is used in the gas-liquid phase change stage.

[0015] Preferably, based on the phase change heat transfer equations of the three stages, solid-liquid interface control equations and gas-liquid interface control equations with respect to temperature, shock wave pressure, fluid medium velocity, and density are obtained.

[0016] Preferably, as the evaporation process continues, a Knudsen layer is generated on the surface of the metal target. The distribution function at the gas-liquid interface in the laser ablation simulation model introduces a backscattering coefficient, expressed as:

[0017] f (+) =f(P sat ,T s ,0),V z >0

[0018]

[0019] The steam back pressure introduces a backscattering coefficient, expressed as:

[0020]

[0021] In the formula, f (+) f (-)Let V represent the forward scattering and backscattering distribution functions, respectively. x V y V z P represents the components of the particle velocity in each direction. sat Let be the saturated vapor pressure, u be the velocity of the backscattered particle, and k be the velocity of the backscattered particle. B Where is the Boltzmann constant, M is the atomic mass of the metal, and T is the... v ρ represents the steam temperature outside the Knudsen layer. v The vapor density outside the Knudsen layer, β R T is the backscattering coefficient. s This represents the ablation interface temperature.

[0022] Preferably, the step in S3, which uses the laser ablation simulation model to simulate the propagation state of the shock wave caused by steam expansion during laser ablation within a set time interval in the two-dimensional numerical grid, and obtains the state physical quantities of the steam flow outside the Knudsen layer, includes:

[0023] Based on the jump relationship in the Knudsen layer, the relationship between the Knudsen layer and the physical quantities of steam flow in the target material is obtained:

[0024]

[0025] In the formula, P represents the most probable rate. v T represents the vapor pressure outside the Knudsen layer. s Here, γ is the ablation interface temperature, γ is the specific heat of vapor, and R is the ideal gas constant.

[0026] According to the Hertz-Knudsen equation, the evaporation rate of the target surface is expressed as:

[0027]

[0028] The Mach number Ma for the steam flow state outside the Knudsen layer is expressed as:

[0029]

[0030] In the formula, U is the flow velocity of the fluid medium outside the Knudsen layer, and C is the local speed of sound;

[0031] The state physical quantities for obtaining the steam flow outside the Knudsen layer include: the steam pressure P outside the Knudsen layer. v , Knudsen layer outer steam temperature T v And the Mach number Ma of the steam flow state outside the Knudsen layer.

[0032] Preferably, the construction of the shock wave model in S4 includes:

[0033] During the evolution of the shock wave induced by pulsed laser ablation of the target, the governing equation is a conservation equation dominated by inertial force, and its expression is as follows:

[0034]

[0035] The fundamental equations of shock waves derived from the conservation equations are as follows:

[0036] Mass conservation equation: ρ1(D-u1)=ρ0(D-u0);

[0037] Momentum conservation equation: ρ1(D-u1) 2 +P1=ρ0(D-u0) 2 +P0;

[0038] Energy conservation equation:

[0039] In the formula: D is the shock wave velocity, subscripts 1 and 0 represent the state behind and before the shock wave, respectively, and ρ is the density. It is a velocity vector. It is a momentum vector, P is absolute pressure, and e is total internal energy. It is a volume force vector, Q is the volume heat source, and g is the gravitational acceleration;

[0040] Based on the Hugoniot relation, the changes in pressure and density of the fluid medium passing through both ends of the wavefront are obtained:

[0041]

[0042] The relationship between pressure and wave velocity on both sides of the shock wave is derived as follows:

[0043]

[0044] In the formula, γ is the specific heat of steam;

[0045] During the propagation of the shock wave, based on the relationship between the flow velocity u and the local sound speed c, and given the wavefront state and the moving velocity of the shock wave front, the velocity of the flow field behind the wave is obtained by solving:

[0046]

[0047] Preferably, in step S5, the calculation result of the outer boundary of the Knudsen layer is used as the initial boundary condition for the shock wave model, wherein the vapor pressure P outside the Knudsen layer is... vThe Mach number Ma of the vapor flow state outside the P0 and Knudsen layers is used to calculate the velocity u0, and the density of the background gas is used as ρ0. The instantaneous evolution characteristics of the shock wave under different time lengths within the time interval are obtained by iterative calculation, including the shock wave velocity D and the wavefront pressure P1.

[0048] This invention establishes a multi-physics coupling model, including heat conduction, phase transition, vaporization, and shock wave propagation processes. Based on the finite element method, the model is numerically discretized and iteratively solved. A metal ablation model considering backscattering coefficients and evaporation effects is established, enabling the processing of complex ablation surfaces and the quantitative analysis of shock wave propagation laws. The coupling mechanism of laser energy absorption, heat conduction, phase transition, and shock wave propagation is described. Compared with existing technologies, this invention provides a comprehensive and accurate numerical simulation method for laser-induced shock waves, with the following beneficial effects:

[0049] High-precision shock wave prediction: This invention can efficiently predict the dynamic evolution characteristics of shock waves during laser ablation through precise numerical simulation, significantly improving the accuracy of laser ablation and shock wave characteristic prediction, and providing a theoretical basis for practical applications in laser processing, laser propulsion and other fields.

[0050] Multi-physics coupling simulation framework: This invention realizes a complete numerical simulation framework for the interaction between laser ablation and shock waves by coupling multiple physical fields such as heat conduction, phase change, evaporation, gas dynamics and shock wave propagation. It can comprehensively reflect the complex physical phenomena in the laser ablation process, and improves the accuracy of shock wave characteristic prediction, especially in the accurate description of complex physical phenomena under the action of high-power laser.

[0051] Applicable to a variety of materials and working conditions: The method of this invention has high applicability and can be adjusted and optimized for different metal materials and laser working conditions. It is widely applicable to numerical simulation in fields such as laser ablation and impact strengthening.

[0052] Supporting high-power laser technology: This invention provides strong numerical support for high-power laser processing, laser shock peening and other technologies, and is of great value, especially in the accurate description of the interaction between laser and matter under high temperature and high pressure. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely embodiments of the present invention, and those skilled in the art can obtain other drawings based on the provided drawings without creative effort.

[0054] Figure 1A flowchart of a method for numerical simulation of narrow-pulse laser-induced shock waves provided in an embodiment of the present invention;

[0055] Figure 2 This is a schematic diagram of laser ablation mesh division provided in an embodiment of the present invention;

[0056] Figure 3 This is a schematic diagram of the instantaneous evolution and calculation results of the shock wave provided in an embodiment of the present invention. Figure 1 ;

[0057] Figure 4 This is a schematic diagram of the instantaneous evolution and calculation results of the shock wave provided in an embodiment of the present invention. Figure 2 . Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] This invention discloses a numerical simulation method for narrow-pulse laser-induced shock waves. The technical concept is as follows: First, laser parameters are set and target material is selected. Then, a multiphysics coupling model is established, including a laser energy absorption model, a heat conduction model, a phase transition and vaporization model, and a shock wave propagation model. Second, the finite element method is used for numerical discretization and computational domain partitioning. Third, iterative solutions and dynamic updates are performed, including dynamic updates of the ablation interface. Finally, output and analysis are performed, including visualization analysis of shock wave propagation laws and data such as ablation depth and mass changes.

[0060] like Figure 1 As shown, the steps in this embodiment include:

[0061] S1: Obtain laser parameters and metal target parameters;

[0062] S2: Using the laser energy in the laser parameters as a heat source term, calculate the spatial distribution of the laser energy, and use the finite element method to mesh the laser ablation region of the metal target to generate a two-dimensional numerical mesh.

[0063] S3: Description of metal phase transformation process and phase interface movement process based on metal phase transformation heat transfer model, introduce particle evaporation backscattering coefficient, and construct laser ablation simulation model; use laser ablation simulation model to simulate the propagation state of shock wave caused by steam expansion during laser ablation in a two-dimensional numerical grid within a set time interval, and dynamically update the ablation interface to obtain the state physical quantities of steam flow outside the Knudsen layer.

[0064] S4: Construct a shock wave model, using the state physical quantities of the Knudsen layer vapor flow within the time interval as the initial boundary conditions of the shock wave in the shock wave model, and using the conservation equations of the fluid medium state changes before and after the shock wave as the governing equations of the shock wave model. The fluid medium includes the Knudsen layer vapor and the ambient gas.

[0065] S5: Based on the control equations of the shock wave model, the fluid medium parameters are updated in combination with the ambient gas state during the shock wave propagation simulation, and the instantaneous evolution characteristics of the shock wave at different time lengths within the time interval are obtained by iterative calculation.

[0066] In one embodiment, in step S1, according to different task requirements, laser parameters are first set, including: laser peak power, laser pulse width, and laser beam radius. The initial velocity of the target boundary is 0, the initial temperature is 20°C, and the ambient pressure is 1 standard atmosphere. A suitable metal target is then selected. For the selected metal, mathematical expressions for the changes in material parameters such as density, specific heat capacity, and thermal conductivity with temperature are obtained, thereby providing the necessary thermophysical data for subsequent numerical calculations.

[0067] In one embodiment, after obtaining the laser parameters and the state parameters of the metal target, the laser energy is determined as the heat source term, and the spatial distribution of the laser energy is calculated. Based on the laser ablation region, the reverse direction of the laser beam is determined as the z-axis, and the horizontal direction as the r-axis. The computational domain for laser ablation of the metal is divided using a mapped mesh, while other regions use a free triangular mesh, ultimately generating a two-dimensional numerical mesh. This mesh provides the basis for spatial discretization in subsequent numerical solutions, ensuring the accuracy of the simulation results and computational efficiency.

[0068] In one embodiment, when a laser is incident on the surface of a metal target, reflection, absorption, and transmission will occur. According to the law of conservation of energy and Fresnel's equations, the absorption rate of the target to the laser can be expressed as:

[0069]

[0070] In the formula, ε0 represents the vacuum dielectric constant, v represents the incident light angular frequency, c represents the speed of light in vacuum, ρ is the material resistivity, and λ is the incident laser wavelength. After the target absorbs the laser, it will undergo processes such as temperature rise, convection, and radiation.

[0071] Heat conduction:

[0072] According to Fourier's law:

[0073]

[0074] In the formula, q represents energy density and k is the thermal conductivity of the material.

[0075] convection:

[0076] According to Newton's law of cooling:

[0077] Q=AhΔT

[0078] In the formula, Q represents heat flow rate, h represents surface heat transfer coefficient, A represents heat transfer area, and ΔT represents surface temperature difference.

[0079] Thermal radiation:

[0080] According to the Stefan-Boltzmann law:

[0081]

[0082] In the formula, T is the material surface temperature, T0 is the ambient temperature, and q r For heat flux density, ε is a constant, and ε is the surface emissivity.

[0083] In one embodiment, the metal phase change heat transfer model includes three stages of phase change heat transfer equations: a no-phase-change heat transfer stage where the ablation interface temperature is below the metal melting point, a solid-liquid phase change heat transfer stage where the ablation interface temperature is between the metal melting point and boiling point, and a gas-liquid phase change heat and mass transfer stage where the ablation interface temperature is above the boiling point; wherein:

[0084] The dynamic specific heat capacity considering the latent heat of fusion is adopted in the solid-liquid phase transition stage;

[0085] The dynamic specific heat capacity, which takes into account the latent heat of melting and the latent heat of vaporization, is used in the gas-liquid phase change stage.

[0086] In this embodiment, after the target material absorbs laser energy, its temperature rises to the solid-liquid phase transition point. According to the phase transition heat transfer theory, the heat transfer equation will be:

[0087]

[0088] In the formula, f s Let C be the solid fraction, L be the latent heat of phase transition, and C be the solid fraction. p ρ is the specific heat capacity, T is the temperature, ρ is the density, and f is the density. s Let t be the solid phase ratio, k be the thermal conductivity, t be the time, the direction of the laser beam action be the z-axis, and the horizontal direction be the r-axis.

[0089] When f s When = 1, the target material is a solid pure phase. Therefore:

[0090]

[0091] Substituting into the phase change heat transfer equation and rearranging, we get:

[0092]

[0093] Since the phase transition region exists, the latent heat of phase transition needs to be addressed. Therefore, the specific heat capacity needs to be described using a dynamic specific heat capacity method.

[0094] C p =C p0 +L m D m

[0095] In the formula, L m Indicates latent heat of fusion. The overall value represents the latent heat of fusion, T. m Indicates the melting point of the target material, ΔT m Indicates the melting transition region, C p0 It has a constant heat capacity.

[0096] The heat capacity for the gas-liquid phase transition stage will be modified as follows:

[0097] C p =C p0 +L m D m +L v D v

[0098] In the formula, L v Indicates latent heat of vaporization. T represents the latent heat of vaporization. b Indicates the melting point of the target material, ΔT b This indicates the evaporation transition zone.

[0099] In one embodiment, the solid-liquid interface control equation and the gas-liquid interface control equation are obtained based on the three-stage phase change heat transfer equation, with respect to temperature, shock wave pressure, fluid medium velocity, and density.

[0100] In this embodiment, the governing equations for the solid-liquid interface can be obtained by combining the above relationships with the formulas:

[0101] mass conservation equation:

[0102]

[0103] Momentum conservation equation:

[0104]

[0105] Energy conservation equation:

[0106]

[0107] In the formula, T is the temperature. Let C be the velocity vector, ρ be the density, and C be the velocity vector. pWhere P is the specific heat capacity and P is the pressure. is the identity matrix, k is the thermal conductivity, and μ is the dynamic viscosity. Darcy friction:

[0108]

[0109] In the formula, K is the Carman-Kozeny permeability coefficient, C is the Carman-Kozeny constant, and b is a minimal constant to control the denominator from being zero. ε is the porosity, i.e., the liquid volume fraction in the solid-liquid phase transition process.

[0110]

[0111] Using the above relationships and formulas, we can also obtain the governing equations for the gas-liquid interface. Considering the Marangoni effect, the expression is:

[0112]

[0113] In the formula, μ is the surface tension coefficient. This is the normal vector of the gas-liquid interface.

[0114] Based on the above theoretical process, the temperature rise and solid-liquid phase transition of the target can be obtained by calculating the actual energy injected into the target by laser. Accurate estimation of this part will play a crucial role in the calculation and analysis of the mass migration process of laser-ablated metal targets.

[0115] In one embodiment, the physical quantities of vapor flow state outside the Knudsen layer in the laser ablation model are obtained, and then the interface is input into the shock wave model as the initial boundary conditions of the initial shock wave. During the pulsed laser ablation process, evaporation occurs at the outermost surface of the material.

[0116] It should be noted that the so-called "providing an interface" means that a series of time-series values ​​of the physical quantities of steam flow outside the Knudsen layer obtained within a time interval are continuously input into the shock wave model through the interface.

[0117] Based on phase change heat transfer theory, the solution is performed within a two-dimensional numerical grid. The simulation considers the phase change behavior of the metal, the movement of the phase interface, and the backscattering effect of particle evaporation during laser ablation, establishing an ablation model coupling phase change and heat conduction. As the evaporation process continues, a Knudsen layer is generated on the surface of the metal target. By solving for the metal temperature distribution within the time step, the state physical quantities of the vapor flow outside the Knudsen layer within the current time step are obtained. The distribution function at the gas-liquid interface in the laser ablation simulation model incorporates the backscattering coefficient, expressed as:

[0118] f (+) =f(Psat ,T s ,0),V z >0

[0119]

[0120] The steam back pressure introduces a backscattering coefficient, expressed as:

[0121]

[0122] In the formula, f (+) f (-) Let V represent the forward scattering and backscattering distribution functions, respectively. x V y V z P represents the components of the particle velocity in each direction. sat Let be the saturated vapor pressure, u be the velocity of the backscattered particle, and k be the velocity of the backscattered particle. B Where is the Boltzmann constant, M is the atomic mass of the metal, and T is the... v ρ represents the steam temperature outside the Knudsen layer. v The vapor density outside the Knudsen layer, β R T is the backscattering coefficient. s This represents the ablation interface temperature.

[0123] The backscattering coefficient is:

[0124]

[0125] MA is the Mach number, represented as:

[0126]

[0127] In the formula, γ is the specific heat of steam, and U is the steam flow velocity outside the Knudsen layer.

[0128] Introducing the backscattering coefficient β R As an evaluation of the probability distribution of forward particles leaving the gas-liquid interface and returning to the system due to collisions with spatial particles, the probability distribution of vapor scattering from the interface and returning to the system will also vary greatly due to the large differences in the outgoing velocity of particles leaving the interface. Therefore, dynamically linking the backscattering coefficient with the process variables can more realistically reflect the physical reality of the process. Under phase equilibrium conditions, that is, when the saturated vapor pressure equals the external pressure, the number of particles outgoing from the gas-liquid interface and the number of particles returning are the same, and the net flux is zero.

[0129] It should be noted that during laser ablation, evaporation typically occurs on the outermost layer of the target surface. After leaving the target surface, the vapor particles follow a Maxwell velocity distribution, and the net flux of the particles is determined by the surface-evaporated particles and the backscattered particles. Based on the dynamic evolution of the evaporation process, the vapor flow generated at the interface creates a high-temperature, high-pressure environment outside the Knudsen layer. These vapor flow state physical quantities (such as velocity, pressure, and temperature) are used as initial conditions and input into the shock wave model as the initial boundary conditions for the shock wave.

[0130] In one embodiment, the step in S3, which uses a laser ablation simulation model to simulate the propagation state of shock waves caused by steam expansion during laser ablation within a set time interval in a two-dimensional numerical grid, and obtains the state physical quantities of steam flow outside the Knudsen layer, includes:

[0131] Based on the jump relationship in the Knudsen layer, the relationship between the Knudsen layer and the physical quantities of steam flow in the target material is obtained:

[0132]

[0133] In the formula, P represents the most probable rate. v T represents the vapor pressure outside the Knudsen layer. s γ is the ablation interface temperature, γ is the specific heat of vapor, the specific value of which is taken as 5 / 3, and R is the ideal gas constant.

[0134] To fully determine the surface state, the saturated vapor pressure at the interface and the flow state of the external gas are required. For the vaporization process, considering the high-temperature, high-pressure environment under high power density, and assuming the metal vapor is represented as a compressible flow, the complete form of the Clausius-Clapeyron equation is adopted. Based on the slope of the tangent to the two-phase coexistence curve given by the Clausius-Clapeyron equation, the change of the saturated vapor pressure *sat* with temperature can be described as follows:

[0135]

[0136] The enthalpy change ΔH during the phase transition is described using the Watson equation. v :

[0137]

[0138] In the formula, T b T represents the melting point and boiling point of the target material under normal pressure. C ΔH represents the critical temperature of the target material. v0 Typical temperature T b The phase transition enthalpy is usually taken as the value corresponding to the boiling point under standard atmospheric pressure.

[0139] ΔH v Substituting the Clausius-Clapeyron equations into the numerical simulation of laser ablation, the saturated vapor pressure P is obtained through iterative integration using a partial differential equation interface. sat It also couples with other physical fields.

[0140] According to the Hertz-Knudsen equation, the evaporation rate of the target surface is expressed as:

[0141]

[0142] The state physical quantities for obtaining the steam flow outside the Knudsen layer include: the steam pressure P outside the Knudsen layer. v , Knudsen layer outer steam temperature T v And the Mach number Ma of the steam flow state outside the Knudsen layer.

[0143] In one embodiment, S4, constructing the shock wave model includes:

[0144] During the ablation of a target material by a high-intensity laser, the target material undergoes a strong phase transition due to the absorption of a large amount of laser energy, forming a high-speed jet. The instantaneous velocity of the ablation products reaches the speed of sound. The high-speed ablation products push compressed air, causing abrupt changes in physical parameters such as medium density and pressure, thus forming a shock wave. Laser-induced shock waves manifest as high-speed moving curved surfaces with rapidly changing physical parameters, i.e., the so-called "fronts." To study this phenomenon, a shock wave model was established. Short-pulse laser-induced shock waves are characterized by high Mach numbers and high Reynolds numbers; therefore, inertial forces dominate their evolution. The conservation equations, neglecting viscosity and thermal conduction, have the following form.

[0145] The governing equations are as follows:

[0146]

[0147] In the formula, ρ is density. It is a velocity vector. It is a momentum vector, P is absolute pressure, and e is total internal energy. is the volume force vector, Q is the volume heat source, and g is the gravitational acceleration. The fundamental equation for shock waves, derived from the conservation equations, is applicable to any compressible medium, and its expression is as follows:

[0148] Mass conservation equation: ρ1(D-u1)=ρ0(D-u0);

[0149] Momentum conservation equation: ρ1(D-u1) 2 +P1=ρ0(D-u0) 2 +P0;

[0150] Energy conservation equation:

[0151] In the formula: D is the shock wave velocity, and subscripts 1 and 0 represent the states behind and before the shock wave, respectively. According to thermodynamic relations, the expressions for internal energy and enthalpy are:

[0152]

[0153]

[0154] When a laser induces a phase transition in a target material to generate a shock wave in a background air environment, if the wavefront state and the equation of state e = e(p,ρ) are known, then there are four unknowns: the shock wave velocity D, and the physical quantities u1, ρ1, and P1 behind the wave. To completely determine the motion parameters of the shock wave, at least one of these four quantities must be known. By examining the flow characteristics of the shock wave, the velocity of the shock wave front in any medium can be obtained solely based on the mass conservation equation:

[0155]

[0156] Considering the conservation of momentum, for a given shock wave front velocity D, we will obtain a point (P0, τ0) on the (P, τ) plane with a slope of ρ0. 2 (D-u0) 2 Rayleigh line:

[0157]

[0158] In the formula, τ = 1 / ρ is the specific volume. Combining the energy conservation equation and the Rayleigh line, the following relationship can be derived:

[0159]

[0160] Based on the Hugoniot relation, the changes in pressure and density of the fluid medium passing through both ends of the wavefront are obtained:

[0161]

[0162] The relationship between pressure and wave velocity on both sides of the shock wave is derived as follows:

[0163]

[0164] In the formula, γ is the specific heat of steam, D is the shock wave velocity, u0, ρ0, P0, and e0 represent the velocity, density, pressure, and specific internal energy of the fluid medium undisturbed by the wavefront, respectively, and u1, ρ1, P1, and e1 represent the velocity, density, pressure, and specific internal energy of the flow field after the shock wave, respectively. In the propagation of the shock wave, the speed of sound is a crucial concept, used to describe the propagation speed of minute disturbances in the medium. In a moving reference frame following gas flow: when the flow velocity u is less than the speed of sound c, the pressure disturbance moves downstream at a velocity c+u and upstream at a velocity cu, expanding in all directions as a spherical wave; when u is greater than c, the pressure disturbance does not propagate upstream but expands within the cone downstream of the sound source. The speed of sound in the medium is not only related to the inherent properties of the medium but also to its state, expressed as:

[0165]

[0166] Based on the above relationships, the energy conservation equation can be expressed as:

[0167]

[0168] Given the wavefront state and the velocity of the shock wave front, the solution behind the wave is uniquely determined. The velocity of the flow field behind the wave can be expressed as:

[0169]

[0170] By solving the governing equations in the shock wave model, the instantaneous evolution characteristics of the shock wave at different time steps are calculated and obtained.

[0171] In one embodiment, S5 considers the dynamic behavior of the gas after laser ablation, especially the expansion process of high-temperature, high-pressure steam. In the shock wave model, the Knudsen layer extralayer steam flow state Ma and the shock wave pressure source term P are incorporated into the ablation model. v An interface is provided to be input into the shock wave model as initial boundary conditions, and the shock wave region is meshed to provide necessary numerical discretization support for simulating the instantaneous evolution characteristics of the shock wave. The specific execution process is as follows:

[0172] The pressure jump relationship on both sides is described by the temperature and pressure jump relationship of the Knudsen layer. The calculation results of the outer boundary of the Knudsen layer are used as the initial boundary conditions of the shock wave model. Substituted into the governing equation, the instantaneous evolution characteristics of the shock wave are calculated through the governing equation. The instantaneous evolution characteristics of the shock wave at different time lengths within the time interval are obtained by iterative calculation, including: shock wave velocity D and wavefront pressure P1.

[0173] The following is a case study of ablation of aluminum metal using nanosecond lasers, which details the specific steps and calculation process of implementing this invention.

[0174] In this embodiment, aluminum metal is selected as the target material, and nanosecond laser is used for ablation simulation. The entire process, from setting laser parameters and obtaining the thermophysical parameters of the metal target material to establishing and calculating the shock wave model, is described in detail.

[0175] Laser parameter setting and metal target selection stage:

[0176] Based on the requirements of laser ablation, the key parameters of the laser are set, specifically including:

[0177] Laser energy: E = 4 mJ;

[0178] Laser pulse width t p =15ns;

[0179] Laser beam radius r0 = 250 μm;

[0180] The selected metal target material is aluminum, and the thermophysical parameters of the material are as follows:

[0181]

[0182] These physical parameters not only determine the thermal response characteristics of the metal target, but also directly affect the calculation accuracy of heat conduction and phase transition processes during the simulation. The combination of laser parameters and the thermophysical properties of the target affects the temperature rise of the metal surface, phase transition behavior, and the formation of the final shock wave.

[0183] Laser energy transfer and computational domain mesh generation stage:

[0184] In numerical simulations, when a laser irradiates a metal target, energy enters the metal through thermal conduction. Based on the laser's peak power and pulse width, the spatiotemporal energy distribution of the laser can be calculated using the following formula:

[0185]

[0186] In the formula, Q s Let E be the energy density per unit area, E be the laser energy, x be the direction perpendicular to the beam, and t be the energy density per unit area. p α is the pulse width, r0 is the laser radius, and α is the absorption rate of the laser by the target material.

[0187] Then, the surface of the metal target and the region beneath it are discretized and meshed. A two-dimensional plane is chosen as the computational domain to simulate the heat distribution on the surface and inside of the metal target, ensuring numerical accuracy. The minimum mesh size is 1e-4 mm, and it is able to capture metal temperature changes and phase transition processes, such as... Figure 2 As shown.

[0188] After refining the computational domain into a grid, a sufficiently high spatial resolution is provided for numerical solutions, which helps to accurately capture changes in temperature, pressure and other fields.

[0189] Phase change heat transfer model and ablation process stages:

[0190] When a metal is irradiated with a laser, its temperature gradually rises until it reaches the metal's melting point T. m At this point, a phase transition begins, and the metal changes from a solid to a liquid state. Further heating to the boiling point T... b Metals can evaporate.

[0191] This embodiment uses a phase change heat transfer model to describe this process, employing the following heat transfer equations:

[0192]

[0193] When the temperature reaches T m At that point, some of the metal begins to melt; and when the temperature reaches T... b At this point, the metal enters the evaporation stage. During this process, the metal's thermal properties (specific heat capacity, thermal conductivity) change significantly. Therefore, dynamic specific heat capacity and dynamic thermal conductivity are used to accurately describe the heat conduction process of the metal.

[0194] For most metallic materials, the thermophysical parameters of the target material undergo significant changes during the melting process. The solid-liquid phase transition coexistence state can be simplified by approximating the process using the porous medium heat transfer—enthalpy porosity method. The enthalpy porosity method treats the solid-liquid coexistence region as a porous medium, using the concept of porosity in porous media to represent the liquid fraction in the solid. When the target material is entirely solid, its porosity is 0, and the liquid velocity in this region is 0. When the target material is entirely liquid, its porosity is 1, and the liquid velocity in this region is equal to the velocity in the liquid phase region. In the solid-liquid coexistence region, the fluid properties are described by the Carman-Kozeny equation and Darcy's law.

[0195] Laser ablation simulation stage:

[0196] During laser ablation, vapor evaporates from the metal surface, generating steam. As the steam particles detach from the metal surface, they follow a Maxwell velocity distribution, forming a Knudsen layer. Within this layer, the behavior of the steam particles influences the generation and propagation of shock waves.

[0197] The steam flow state is described by the following formula:

[0198] 1. Introduce the backscattering coefficient:

[0199] f (+) =f(ρ sat ,T s ,0),V z>0

[0200]

[0201] 2. After introducing the backscattering coefficient, the backscattering coefficient is then applied to the steam backpressure:

[0202]

[0203] 3. Based on the jump relationship in the Knudsen layer, the relationship between the Knudsen layer and the physical quantities of the target material vapor flow is obtained:

[0204]

[0205] 4. The vapor flow state outside the Knudsen layer can be described by the Mach number Ma:

[0206]

[0207] The establishment and solution stage of the shock wave model:

[0208] A two-dimensional shock wave propagation model was established to simulate the propagation of shock waves induced by vapor expansion during laser ablation. Based on gas dynamics theory, the model employs the spatially discontinuous Galerkin method for discretization and captures strongly discontinuous shock waves. Simultaneously, a third-order Runge-Kutta time-stepping method is used to obtain the weak form of the partial differential equations. After spatial discretization, the Runge-Kutta time-stepping method, explicitly expressed in the time domain, allows for the solution of conservation equations in both time and space, describing the generation, propagation, and characteristics of shock waves during laser ablation.

[0209] The governing equations include:

[0210]

[0211] The Hugoniot relation can be used to describe the changes in pressure and density of a medium passing through both ends of the wavefront:

[0212]

[0213] Based on the above theory, the relationship between the pressure on both sides of the shock wave and the wave velocity can be derived:

[0214]

[0215] The initial boundary condition pressure P of these steam flows v The Mach number Ma will be used as input to the shock wave model to determine the initial boundary conditions of the shock wave.

[0216] By solving these governing equations, this invention can simulate the propagation process of shock waves and obtain key parameters such as wave velocity and wavefront pressure. Figure 3-4 The figure shows the instantaneous position and velocity of the shock wave propagation corresponding to multiple evolution stages of laser ablation of a metal target. These calculation results provide important theoretical basis for the shock wave effect in practical applications.

[0217] The present invention provides a detailed description of a narrow-pulse laser-induced shock wave numerical simulation method. Specific examples have been used to illustrate the principle and implementation of the invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​the invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​the invention. Therefore, the content of this specification should not be construed as a limitation of the invention.

[0218] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A method of numerical simulation of a narrow-pulse laser-induced shock wave, characterized in that, The method comprises the following steps: S1: obtaining laser parameters and metal target parameters; S2: taking laser energy in the laser parameters as a heat source term, calculating a spatial distribution of the laser energy, performing mesh division on a laser ablation region of the metal target by using a finite element method, and generating a two-dimensional numerical mesh; S3: based on a metal phase change heat transfer model, introducing a particle evaporation backscattering coefficient, and constructing a laser ablation simulation model; using the laser ablation simulation model to simulate a propagation state of a shock wave caused by vapor expansion in a laser ablation process in the two-dimensional numerical mesh within a set time interval, and dynamically updating an ablation interface to obtain state physical quantities of vapor flow outside a Knudsen layer; S4: constructing a shock wave model, taking the state physical quantities of the vapor flow outside the Knudsen layer within the time interval as initial boundary conditions of the shock wave in the shock wave model, and taking conservation equations of state changes of fluid media before and after the shock wave as control equations of the shock wave model, the fluid media including the vapor outside the Knudsen layer and ambient gas; S5: based on the control equations of the shock wave model, updating fluid medium parameters in combination with ambient gas state in a shock wave propagation simulation process, and iteratively calculating to obtain instantaneous evolution characteristics of the shock wave under different time steps within the time interval; The metal phase change heat transfer model includes phase change heat transfer equations of three stages: a non-phase change heat transfer stage in which the ablation interface temperature is lower than the melting point of the metal, a solid-liquid phase change heat transfer stage in which the ablation interface temperature is between the melting point and the boiling point of the metal, and a gas-liquid phase change heat transfer and mass transfer stage in which the ablation interface temperature is higher than the boiling point; wherein: The dynamic specific heat capacity considering the latent heat of melting is used in the solid-liquid phase change stage; The dynamic specific heat capacity considering the latent heat of melting and the latent heat of evaporation is used in the gas-liquid phase change stage; After the target absorbs laser energy, the temperature rises to the solid-liquid phase change point, according to the phase change heat transfer theory, the heat transfer equation will be: In the formula, is the solid phase rate, is the latent heat of phase change, is the specific heat capacity, is the temperature, is the density, is the solid phase ratio, k is the thermal conductivity, t is the time, and the direction opposite to the action of the laser beam is z the axis, and the horizontal direction is r the axis; When = 1, the target material is a solid pure phase, then: After the phase change heat transfer equation is arranged, it can be obtained that: Because of the existence of the phase change transition zone, the latent heat of phase change needs to be processed, so the specific heat capacity needs to be described by using the dynamic specific heat capacity: wherein represents the latent heat of fusion, , the overall latent heat of fusion coefficient, represents the melting point of the target material, represents the melting transition region, is the constant heat capacity; For the gas-liquid phase change stage the heat capacity will be modified as: wherein represents the latent heat of evaporation, represents the latent heat of evaporation coefficient, represents the melting point of the target material, represents the evaporation transition zone; According to the phase change heat transfer equations of the three stages, the solid-liquid phase interface control equation and the gas-liquid phase interface control equation about the temperature, the shock wave pressure, the fluid medium velocity and the density are obtained; the solid-liquid phase interface control equation can be obtained by using the above relationship in combination with the formula: Mass conservation equation: Momentum conservation equation: Energy conservation equation: wherein T is the temperature, V is the velocity vector, p is the density, Cp is the specific heat capacity, p is the pressure, I is the identity matrix, k k is the thermal conductivity, μ μ is the dynamic viscosity; D is the Darcy friction factor: wherein is the Carman-Kozeny permeability coefficient, is the Carman-Kozeny constant, is a very small constant to control the denominator not to be zero; is the porosity, i.e. the volume fraction of the liquid phase during the solid-liquid phase change process: The gas-liquid phase interface control equation can also be obtained by using the above relationship in combination with the formula, and the expression is: wherein is the surface tension coefficient, is the gas-liquid interface normal vector.

2. The method of claim 1, wherein, The laser parameters in S1 include: laser peak power, laser pulse width, and laser beam radius; the metal target parameters include: density, specific heat capacity, and thermal conductivity of the metal.

3. The method of claim 1, wherein, With the continuous evaporation process, a Knudsen layer is generated on the surface of the metal target, the backscattering coefficient is introduced into the distribution function at the gas-liquid phase interface in the laser ablation simulation model, and is expressed as: The backscattering coefficient is introduced into the vapor recoil pressure, and is expressed as: wherein , respectively denote the forward and backward scattering distribution functions, V x , V y , V z are respectively the components of the particle velocity in each direction, is the saturated vapor pressure, u is the backscattered particle velocity, is the Boltzmann constant, M is the metal atomic mass, T v is the vapor temperature outside the Knudsen layer, is the vapor density outside the Knudsen layer, is the backscattering coefficient, T s is the ablation interface temperature.

4. The method of claim 3, wherein, The step of simulating propagation states of shock waves caused by vapor expansion in a time interval of laser ablation in the two-dimensional numerical grid by using the laser ablation simulation model in the S3 comprises: According to the jump relationship in the Knudsen layer, the relationship between the Knudsen layer and the target vapor flow physical quantity is obtained: wherein represents the most probable velocity, is the vapor pressure outside the Knudsen layer, is the ablating interface temperature, is the specific heat of vapor, R is the ideal gas constant; According to the Hertz-Knudsen equation, the target surface evaporation rate is represented as: Knudsen layer outside the vapor flow state mach number is expressed as: wherein is the flow velocity of the fluid medium outside the Knudsen layer, is the local sound speed; The state physical quantities of the vapor flow outside the Knudsen layer include: vapor pressure outside the Knudsen layer vapor temperature outside the Knudsen layer T v and Mach number of the vapor flow outside the Knudsen layer .

5. The method of claim 1, wherein, The S4 comprises: In the evolution process of the shock wave motion induced by the pulsed laser ablation target, the conservation equation with inertia force as the dominant is used as the control equation, and the expression is as follows: The basic equation of the shock wave derived from the conservation equation is as follows: Mass conservation equation: ; Momentum conservation equation: ; Energy conservation equation: ; where: is the shock wave speed, the subscripts 1 and 0 represent the state behind and ahead of the shock wave, respectively, is the density, is the velocity vector, is the momentum vector, is the absolute pressure, is the total energy of internal energy, is the volume force vector, is the volume heat source, is the gravitational acceleration; According to the Hugoniot relationship, the change state of the pressure and the density of the fluid medium passing through the two ends of the rear wave front is obtained: The relationship between the pressure and the wave velocity on both sides of the shock wave is derived: wherein Cp is the specific heat of the vapor; During the propagation of the shock wave, the flow velocity is determined from the relation between the local sound speed and the given wave front state and shock wave front movement speed, and the solution is obtained as follows: 。 6. The method of claim 5, wherein, The S5 is calculated with the Knudsen layer outer boundary calculation results as the starting boundary conditions of the shock wave model, wherein the steam pressure outside the Knudsen layer As P 0, the Mach number of the steam flow state outside the Knudsen layer For calculating the velocity u 0, the density of the background gas as ​ 0, the instantaneous evolution characteristics of the shock wave under different time intervals and time steps are obtained by iterative calculation, including the shock wave velocity D , the wave front pressure .

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