CN109190260B - Laser-arc hybrid welding three-dimensional transient numerical simulation method - Google Patents
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Abstract
The invention relates to a three-dimensional transient numerical simulation method for laser-arc hybrid welding, which solves the problems that the prior laser arc welding simulation method does not realize the overall calculation and can not truly reproduce the hybrid welding process. The invention realizes the overall accurate numerical solution of the evolution law of the pores, the molten pool, the plasma and the metal steam of the laser-TIG electric arc hybrid welding, and can be used for the theoretical research and the process optimization of the laser-TIG electric arc hybrid welding.
Description
Technical Field
The invention belongs to a welding numerical simulation method, and particularly relates to a laser-arc hybrid welding three-dimensional transient numerical simulation method.
Technical Field
The laser-electric arc hybrid welding can combine the advantages of two heat sources, namely laser and electric arc, and realize advantage complementation; compared with electric arc welding, the laser-electric arc hybrid welding has the advantages of large fusion depth, high speed, small residual stress and deformation; compared with laser welding, the laser-electric arc hybrid welding has the advantages of enhanced bridging capacity, easy adjustment of welding seam components, reduced cold brittleness phase tendency and improved pinhole stability. The laser-arc hybrid welding has unique advantages, can realize high-quality and high-efficiency welding manufacture, becomes a welding technology with wide application prospect, and has important application in the fields of ocean, nuclear power and the like.
As shown in fig. 1, the laser and the electric arc are directly used as heat sources to act on the material, so that the material is subjected to multi-state transformation such as melting, gasification and ionization, a molten pool, a small hole, photoinduced metal vapor/plasma, electric arc plasma and the like coexist, severe physical changes such as extremely high temperature, high pressure, high speed, instantaneous and the like exist in a millimeter-scale area, and the complex physical processes and characteristics make it difficult to deeply research the composite welding mechanism by adopting an experimental method. Meanwhile, the laser-arc hybrid welding combines two heat sources, the technological parameters of the laser-arc hybrid welding are further increased, and more difficulties are brought to obtaining the optimal technological parameters through an experimental method. The numerical simulation method can be used for carrying out visual quantitative analysis on all physical quantities and evolution rules thereof in the laser-arc hybrid welding process, and can reveal the evolution rules of pinholes, a molten pool, plasma and metal steam along with time in the welding process, so that the numerical simulation has important significance in the application of laser-arc hybrid welding research.
The laser-arc hybrid welding process is extremely complex, physical modeling is difficult, the density, temperature, potential, speed and the like on two sides of an interface are suddenly changed in an extremely small space scale, so that the characteristics of large gradient and high nonlinearity are caused near the interface, a unified solution dual-phase flow model is difficult to solve, and accurate solution of the interface position is difficult to obtain. In view of the above difficulties, those skilled in the art either neglect to calculate the arc and metal vapor only for the molten pool, see Z Gao, et al, analysis of the world porous ceramic stationary Laser-MIG hybrid welding, the International journal Advanced Manufacturing Technology,2009,44(9-10):870, or neglect to calculate the arc only for the molten pool, see Y.T.Cho, et al, numerical analysis of the hybrid planar Manufacturing by Nd: YAGlaser and gas porous arc & Laser Technology,2011,43(3):711 and 720, and there is no current report on the overall numerical calculation implementation of Laser-arc hybrid welding. However, the behavior of the plasma during hybrid welding directly determines the thermal effect on the weld pool, and the metal vapor generated by the local violent evaporation of the weld pool will also change the composition and properties of the plasma. Therefore, the method of only calculating the molten pool or only calculating the electric arc can not truly reproduce the composite welding process, and is not beneficial to the research of the interaction mechanism of the laser-electric arc composite welding.
Disclosure of Invention
The invention provides a laser-arc hybrid welding three-dimensional transient numerical simulation method, which solves the problems that the conventional laser arc welding simulation method does not realize integral calculation and can not truly reproduce the hybrid welding process, can realize the integrated simulation calculation of melting, solidification and evaporation behaviors, heat transfer flow of arc plasma, laser plume gas and metal molten pool and electromagnetic field evolution in the laser-TIG arc hybrid welding process, can reproduce the physical process more comprehensively and truly, is convenient to carry out deeper theoretical research, and can further promote the engineering application of laser-arc hybrid welding.
The invention provides a laser-arc hybrid welding three-dimensional transient numerical simulation method, which comprises the steps of establishing a geometric model, setting an initial value, updating a time step, updating physical parameters, solving an electromagnetic field, decomposing a space discontinuity, calculating a gas region state, calculating a workpiece region state, updating a molten pool free interface and judging, and is characterized in that:
firstly, establishing a geometric model:
establishing a geometric model by adopting three-dimensional modeling software, wherein the geometric model is a cuboid, the geometric model comprises a workpiece area, an electrode area and a gas area, and the workpiece area is the cuboid and has the same length and width as the geometric model; the electrode area is a cylinder or a cylinder with one end being a cone, when the electrode area is a cylinder, the included angle between the central axis of the electrode area and the vertical direction is 0-60 degrees, and when the electrode area is a cylinder with one end being a cone, the diameter of the bottom surface of the cone is the same as that of the cylinder; the vertical distance between the end part of the electrode area and the workpiece area is 1 mm-10 mm; the gas area is the rest area of the geometric model except the workpiece area and the electrode area;
the region of the geometric model except the electrode region is a calculation region;
carrying out grid division on the calculation region by adopting grid division software, wherein the grid is a cuboid or a cube, and the side length of the cuboid or the cube is 10-500 mu m;
secondly, setting an initial value:
given the boundary conditions of the computation region: the environment temperature is 300-1000K, the electrode temperature is 3000-3500K, the environment pressure is 0.1-10 atm, and the bottom potential of the workpiece is 0V;
setting the initial value of the physical quantity of each grid center point in the whole calculation area: potential 0V, current density 0A/m2The magnetic field intensity is 0T, the speed is 0m/s, the temperature is 300-1000K, the pressure is 0.1-10 atm, and the mass percentage content of the metal steam is 0;
setting an accumulation time variable tsumCalculating the cutoff time t as 0end＝0.1～10s；
Setting the time step Δ tiIs an initial time step Δ t0，Δt0＝1×10-7～1×10-6s, performing the fourth step;
step three, updating the time step:
calculating the maximum time step for gas region stability calculation
Then calculating the maximum time step length of stable calculation of the workpiece region
Take (Δ t)0,Δtg,Δtm) The minimum value of the three is used as the updated time step delta tiCarrying out the step four;
where, i is 1,2 …, which indicates the i-th step, the maximum condition number Cmax＝0.5～1.0，ug_x,ug_y,ug_zGas velocity at the center point of the gas area grid
Component in three directions x, y, z, um_x,um_y,um_zThe velocity of the molten pool being the central point of the grid of the region of the workpiece
Components in the x, y, z directions; the sizes of the grids in the x direction, the y direction and the z direction are respectively delta x, delta y and delta z;
fourthly, updating physical property parameters:
setting physical property parameters in the whole calculation region:
the gas area is filled with mixed gas of protective gas and metal steam, the protective gas is one or more of argon, helium and carbon dioxide, and the metal steam is the metal steam of the workpiece material; calculating the mass percentage content and the temperature of the metal steam in the mixed gas as initial values for the first time, and acquiring the mass percentage content and the temperature of the metal steam in the mixed gas in the next time step from the substeps (7.2) and (7.3);
conductivity σ of the gas mixtureeDensity rhogViscosity [ mu ] ofgSpecific heat capacity CpgCoefficient of thermal conductivity kgAnd net gas emissivityNThe composition and temperature of the mixed gas at the center of each grid are directly determined;
the workpiece material of the workpiece area is iron-based alloy or non-ferrous metal alloy; corresponding conductivity σeDensity rhomViscosity [ mu ] ofmSpecific heat capacity CpmCoefficient of thermal conductivity kmThermal expansion coefficient β, surface tension coefficient gamma, and thermal capillary coefficient
Work potential
Emissivity of radiationrDirectly determined by the workpiece material and temperature at each grid center;
fifthly, solving the electromagnetic field:
solving for the electromagnetic field throughout the calculation area:
welding current is introduced in the welding process, an electromagnetic field is generated in the whole calculation area, welding current of 30-300A is given through the electrodes, and potential of the center points of all grids in the whole calculation area is calculated and obtained
Current density
And magnetic induction intensity
Distribution, the calculation equation is as follows:
wherein the vacuum dielectric constant is0Magnetic loss of potential at center point of grid
Gradient operator
Divergence operator
Rotation operator
Laplacian operator
Electrical conductivity sigmaeRespectively adopting the mixed gas in the gas area and the corresponding conductivity of the workpiece material in the workpiece area during calculation;
sixthly, spatial discontinuous decomposition:
performing space discontinuous decomposition by taking the upper surface of a workpiece area as an interface in the first calculation and taking an updated free interface of a molten pool as an interface in the subsequent calculation, and dividing the whole calculation area into a gas area and a workpiece area, wherein the gas area is an arc-metal vapor area and the workpiece area is a workpiece solid-liquid area; defining interface boundary points as intersection points of grid central point connecting lines at two sides of a free interface of the molten pool and the free interface of the molten pool;
seventhly, calculating the gas area state:
the method comprises the following substeps of calculating the flow field, the temperature field and the metal vapor distribution of the gas region in sequence:
(7.1) calculating the gas area flow field: calculating the gas velocity of the center points of all grids in the gas area
Gas pressure PgThe calculation formula is as follows:
wherein
Is the acceleration of gravity;
setting the gas velocity of the boundary point of the gas zone and the workpiece zone at the free interface of the molten bath
And gas pressure Pg_sRespectively as follows:
wherein the evaporation recoil pressure PrBy using pressure based on the environmentObtaining a recoil pressure model;
(7.2) calculating the gas zone temperature field: calculating the gas temperature T of the central point of all grids in the gas areagThe calculation formula is as follows:
wherein k isbBoltzmann constant, e is elementary charge, t is time,
a differential operator;
calculating the heat flow q of the boundary point of the interface into the gas region at the free interface of the molten pool of the gas region and the workpiece regiongas：
Wherein T isgs、TmsAcquiring the temperatures of a gas area and a workpiece area which are boundary points of an interface respectively by adopting a virtual flow method; k is a radical ofeffIs the effective thermal conductivity, k, of the boundary point of the interfaceeff＝0.5×(kg(Tgs)+kg(Tms))，kg(Tgs)、kg(Tms) Respectively is the temperature Tgs、TmsThe corresponding gas thermal conductivity; the effective thickness of the boundary layer of the free interface of the molten pool is 0.1 mm-0.4 mm;
(7.3) calculating the gas zone metal vapor diffusion: calculating the mass percentage content C of the metal vapor at the central points of all grids in the gas areavaporThe calculation formula is as follows:
wherein D is the mass diffusion coefficient of the metal vapor, and the value can be obtained by a second viscosity approximation method;
setting the metal vapour quality of boundary point of each interface at the free interface of molten pool in gas region and workpiece regionAmount percentage of Cvapor：
Eighthly, calculating the state of the workpiece area:
sequentially calculating a flow field and a temperature field of a workpiece region, and comprising the following substeps:
(8.1) calculating the flow field of the workpiece area: calculating the molten pool speed of the central points of all grids in the workpiece area
Pressure P of the molten bathmThe calculation formula is as follows:
wherein the temperature T of the central point of the grid of the workpiece areamTaking the ambient temperature during the first calculation; the next time step is calculated by adopting the calculated value of the last time step (7.2);
reference temperature TrefTaking the melting point temperature of a workpiece material; K. c is the seepage coefficient, relaxation coefficient and liquidus fraction flClosely related:
wherein d is a constant closely related to the size of dendrite spacing, and d is 0.05mm to 0.5 mm; fraction of liquid phase flLinear with temperature:
wherein, Tl、TsThe liquidus temperature and solidus temperature of the workpiece material, respectively;
calculating the normal pressure P of the molten pool at the boundary point of the interface at the free interface of the molten pool in the gas area and the workpiece areafAnd the tangential force of the molten pool
Wherein
Normal vector and tangent vector of the free interface of the molten pool, kappa is the curvature of the free interface of the molten pool, PeffFor effective pressure of gas region to workpiece region, take Peff＝max(Pr,Pg)；
(8.2) calculating the temperature field of the workpiece area: calculating the temperature T of the central point of all grids in the workpiece areamThe calculation formula is as follows:
wherein the workpiece absorbs the energy of the laser beam qlaserAcquiring by adopting a ray tracing method; the laser is fiber laser or Nd, namely YAG laser, the power is 100W-10000W, and the spot radius is 0.1 mm-0.5 mm;
calculating the heat flow q of the boundary point of the interface into the workpiece region at the free interface of the molten pool of the gas region and the workpiece regionmatel：
Wherein σ is Stefan-Boltzmann constant, T∞Is the ambient temperature, qevapHeat loss for evaporation;
ninthly, updating a free interface of the molten pool:
molten pool velocity through all grid center points of workpiece area
Calculating the distance phi from the central point of each grid to the interface in the area, wherein the obtained equivalent surface with phi equal to 0 is the updated free interface of the molten pool, and the calculation formula is as follows:
the normal vector and curvature of the free interface of the molten pool are solved as follows:
in the fifth step to the ninth step, all the involved calculation equations are dispersed by adopting a finite difference method or a finite volume method, and the time step delta t isiSolving is carried out internally;
tenthly, judging:
will tsum+ΔtiIs given to tsumJudging whether t is presentsum＜tendIf yes, turning to the step three, updating the time step, otherwise, ending the calculation.
In the first step, the three-dimensional modeling Software is AutoCAD of American Autodesk Software company, UG of Germany Siemens PLM Software company or Pro/E of American parameter technology company; the cuboid of the geometric model is 5 mm-500 mm long, 5 mm-500 mm wide and 5 mm-200 mm high; the cuboid of the workpiece area is 1 mm-100 mm high; when the electrode area is a cylinder, the diameter of the cylinder is 1 mm-4 mm, the height is 1 mm-150 mm, when the electrode area is a cylinder with one end being a cone, the cone angle is 30-120 degrees, the diameter of the cylinder is 1 mm-4 mm, and the height is 1 mm-150 mm; the gridding software is Hypermesh of Altair corporation, Gridgen of Pointwise corporation, or Patran of MSC.
6. In the fourth step, the electric conductivity σ of the mixed gas is determined by the composition and temperature of the mixed gaseDensity rhogViscosity [ mu ] ofgSpecific heat capacity CpgCoefficient of thermal conductivity kgAnd gas purifying agentCoefficient of radiationNReference is made to the substances from Mougenot J, et al, plasma-assisted interaction in structured input-gas configuration, journal of Physics D: Applied Physics,2013,46(13):135206, or Murphy A B, et al, modeling of thermal plasma for arc welding, the roll of the shifting gas properties and of metallic force. journal of Physics D: Applied Physics,2009,42(19):194006, or Murphy AB, the effects of metallic in arc welding, journal of Physics D: Applied Physics,2010,43(43): 434001;
the corresponding electrical conductivity σ of the workpiece material being determined directly from the workpiece material and the temperatureeDensity rhomViscosity [ mu ] ofmSpecific heat capacity CpmCoefficient of thermal conductivity kmThermal expansion coefficient β, surface tension coefficient gamma, and thermal capillary coefficient
Work potential
Emissivity of radiationrObtained by calculation using the Material Performance calculation Software JMatPro, Inc. of Sente Software, UK, either cited by Wei HL, et al, original of grain orientation reduction solution of an aluminium alloy, acta materials, 2016,115:123-131, or by Wu C S.computer correlation of this-dimensional correlation in transforming MIG well locations, engineering compositions, 1992,9(5): 529-537.
In the sub-step (7.1), the recoil pressure model based on the environmental pressure is as follows: s. Pang, et. Explosition of duration reduction Laser welding indirect representations. journal of Laser Applications 2015,27(2): 022007; in the sub-step (7.2), the virtual stream method is as follows: fedkiw R P, et al, A non-oscilloscopic Eulerapaach to interfaces in multimaterial flows Journalo f computational physics,1999,152(2): 457-; in the sub-step (7.3), the second viscosity approximation method is as follows: A.B.Murphy.A composition of transactions of differentiation in thermoplasmas. journal of Physics D: Applied Physics,1996,29(7): 1922.
In the sub-step (8.2), the ray tracing method is as follows: computing the energy density of the laser deep fusion welding small holes with arbitrary shapes, the laser technology 2010,34(05) 614-618; in the step (8.2), the heat loss q is evaporatedevapThe calculation method is as follows: wu D, et al.infraduction of scatter formation in fiber laser welding of5083aluminum alloy&Mass Transfer,2017,113:730-740。
The invention can be realized by high-level programming languages such as C + + computer, and can simulate the three-dimensional dynamic behaviors of electric arc, molten pool, small hole and metal vapor in the laser-electric arc welding process by the computer.
The invention solves the whole calculation area uniformly when solving the electromagnetic field, divides the integral calculation area with multiple phases (liquid phase, solid phase, electric arc and metal vapor) into a gas area (electric arc-metal vapor area) and a workpiece area (workpiece solid-liquid area) through the instantaneous free interface of the workpiece molten pool when solving the concentration of the flow field, the temperature field and the metal vapor, respectively calculates two areas with physical and mathematical discontinuity in a minimum time step, and carries out bidirectional sequential coupling at the interface position in a boundary loading mode through respective calculation data. The method provided by the invention can well solve the problem of nonlinear solution near the interface, realize the heat transfer flow of a molten pool and arc plasma, the diffusion behavior of metal vapor, free interface evolution and electromagnetic field in the laser-arc hybrid welding process, realize integrated simulation calculation, more comprehensively and truly reproduce the physical process, facilitate deeper theoretical research and further promote the engineering application of the laser-arc hybrid welding.
Drawings
FIG. 1 is a schematic view of a laser-arc hybrid welding process;
FIG. 2 is a block flow diagram of the present invention;
FIG. 3 is a schematic view of an overall spatial intermittent decomposition with dashed lines indicating the free interface of the molten bath;
FIG. 4 shows the simulation results of the temperature field in example 1 of the present invention, wherein the unit of the numerical quantity is K;
FIG. 5 shows the velocity field simulation results of example 1 of the present invention, in which the numerical quantity is m/s;
FIG. 6 shows the results of the mass percentage simulation of the metal vapor in example 1 of the present invention;
FIG. 7 shows the simulation results of current density distribution in example 1 of the present invention, in which the unit of digital quantity is A/m2。
Detailed Description
The invention is further illustrated below with reference to specific embodiments and the accompanying drawings.
Embodiment 1, the flowchart of which is shown in fig. 2, includes a geometric model building step, an initial value setting step, a time step updating step, a physical property parameter updating step, an electromagnetic field solving step, a spatial intermittent decomposition step, a gas region state calculating step, a workpiece region state calculating step, a molten pool free interface updating step, and a judgment step:
firstly, establishing a geometric model:
establishing a geometric model by using three-dimensional modeling software, wherein the geometric model is a cuboid, and is 14mm in length, 10mm in width and 12mm in height; the geometric model comprises a workpiece area, an electrode area and a gas area, wherein the workpiece area is a cuboid, the length and the width of the workpiece area are the same as those of the geometric model, and the height of the workpiece area is 4 mm; the electrode area is a cylinder, the diameter of the cylinder is 2mm, the height of the cylinder is 3mm, the included angle between the central axis of the electrode area and the vertical direction is 30 degrees, and the vertical distance between the end part of the electrode area and the workpiece area is 5 mm; the gas area is the rest area of the geometric model except the workpiece area and the electrode area; the three-dimensional modeling Software is UG of Siemens PLM Software company in Germany;
the region of the geometric model except the electrode region is a calculation region;
carrying out grid division on the calculation region by adopting grid division software, wherein the grid is a cube, and the side length of the cube is 100 micrometers; the grid division software is Hypermesh of Altair company in America;
secondly, setting an initial value:
given the boundary conditions of the computation region: the environment temperature is 300K, the electrode temperature is 3000K, the environment pressure is 1atm, and the bottom potential of the workpiece is 0V;
setting the initial value of the physical quantity of each grid center point in the whole calculation area: potential 0V, current density 0A/m2The magnetic field intensity is 0T, the speed is 0m/s, the temperature is 300K, the pressure is 1atm, and the mass percentage of the metal vapor is 0;
setting an accumulation time variable tsumCalculating the cutoff time t as 0end＝1.5s；
Setting the time step Δ tiIs an initial time step Δ t0，Δt0＝1×10-7s, performing the fourth step;
step three, updating the time step:
calculating the maximum time step for gas region stability calculation
Then calculating the maximum time step length of stable calculation of the workpiece region
Take (Δ t)0,Δtg,Δtm) The minimum value of the three is used as the updated time step delta tiCarrying out the step four;
where, i is 1,2 …, which indicates the i-th step, the maximum condition number Cmax＝0.8，ug_x,ug_y,ug_zGas velocity at the center point of the gas area grid
Component in three directions x, y, z, um_x,um_y,um_zThe velocity of the molten pool being the central point of the grid of the region of the workpiece
Components in the x, y, z directions; the sizes of the grids in the x direction, the y direction and the z direction are respectively delta x, delta y and delta z;
fourthly, updating physical property parameters:
setting physical property parameters in the whole calculation region:
the gas area is filled with mixed gas of protective gas and metal steam, the protective gas is argon, and the metal steam is metal steam of a workpiece material; calculating the mass percentage content and the temperature of the metal steam in the mixed gas as initial values for the first time, and acquiring the mass percentage content and the temperature of the metal steam in the mixed gas in the next time step from the substeps (7.2) and (7.3);
conductivity σ of the gas mixtureeDensity rhogViscosity [ mu ] ofgSpecific heat capacity CpgCoefficient of thermal conductivity kgAnd net gas emissivityNThe composition and temperature of the mixed gas at the center of each grid are directly determined; the electrical conductivity σ of the gas mixture being determined by the composition and temperature of the gas mixtureeDensity rhogViscosity [ mu ] ofgSpecific heat capacity CpgCoefficient of thermal conductivity kgAnd net gas emissivityNCited from MougenotJ, et al, plasma-field pore interaction in tubular input-gassconfiguration, journal of Physics D: Applied Physics,2013,46(13): 135206;
the workpiece material of the workpiece area is 316L stainless steel; corresponding conductivity σeDensity rhomViscosity [ mu ] ofmSpecific heat capacity CpmCoefficient of thermal conductivity kmThermal expansion coefficient β, surface tension coefficient gamma, and thermal capillary coefficient
Work potential
Emissivity of radiationrDirectly determined by the workpiece material and temperature at each grid center; the corresponding electrical conductivity σ of the workpiece material being determined directly from the workpiece material and the temperatureeDensity rhomViscosity [ mu ] ofmSpecific heat capacity CpmCoefficient of thermal conductivity kmThermal expansion coefficient β, surface tension coefficient gamma, and thermal capillary coefficient
Work byPotential energy
Emissivity of radiationrThe material property calculation Software JMatPro of Sente Software company in England is adopted for calculation and acquisition;
fifthly, solving the electromagnetic field:
solving for the electromagnetic field throughout the calculation area:
welding current is introduced in the welding process, an electromagnetic field is generated in the whole calculation area, the welding current of 150A is given through the electrodes, and the potential of the center points of all grids in the whole calculation area is obtained through calculation
Current density
And magnetic induction intensity
Distribution, the calculation equation is as follows:
wherein the vacuum dielectric constant is0Magnetic loss of potential at center point of grid
Gradient operator
Divergence operator
Rotation operator
Laplacian operator
Electrical conductivity sigmaeRespectively adopting the mixed gas in the gas area and the corresponding conductivity of the workpiece material in the workpiece area during calculation;
sixthly, spatial discontinuous decomposition:
performing spatial intermittent decomposition by taking the upper surface of a workpiece area as an interface in the first calculation and taking an updated free interface of a molten pool as an interface in the subsequent calculation, and dividing the whole calculation area into a gas area and a workpiece area as shown in fig. 3, wherein the gas area is an arc-metal vapor area, and the workpiece area is a workpiece solid-liquid area; defining interface boundary points as intersection points of grid central point connecting lines at two sides of a free interface of the molten pool and the free interface of the molten pool;
seventhly, calculating the gas area state:
the method comprises the following substeps of calculating the flow field, the temperature field and the metal vapor distribution of the gas region in sequence:
(7.1) calculating the gas area flow field: calculating the gas velocity of the center points of all grids in the gas area
Gas pressure PgThe calculation formula is as follows:
wherein
Acceleration of gravity;
setting the gas velocity of the boundary point of the gas zone and the workpiece zone at the free interface of the molten bath
And gas pressure Pg_sRespectively as follows:
wherein the evaporation recoil pressure PrObtaining by adopting a recoil pressure model based on the environmental pressure; the recoil pressure model based on the environmental pressure is as follows: s. Pang, et al. Explosition of duration depth variant laser welding under variable temporal representation. journal of laser applications 2015,27(2): 022007;
(7.2) calculating the gas zone temperature field: calculating the gas temperature T of the central point of all grids in the gas areagThe calculation formula is as follows:
wherein k isbBoltzmann constant, e is elementary charge, t is time,
a differential operator;
calculating the heat flow q of the boundary point of the interface into the gas region at the free interface of the molten pool of the gas region and the workpiece regiongas：
Wherein T isgs、TmsAcquiring the temperatures of a gas area and a workpiece area which are boundary points of an interface respectively by adopting a virtual flow method; k is a radical ofeffIs the effective thermal conductivity, k, of the boundary point of the interfaceeff＝0.5×(kg(Tgs)+kg(Tms))，kg(Tgs)、kg(Tms) Respectively is the temperature Tgs、TmsThe corresponding gas thermal conductivity; the effective thickness of the boundary layer of the free interface of the molten pool is 0.1 mm; the virtual stream method is as follows: fedkiw R P, et al, A non-oscillotory Eulerian approach to interfaces in multimaterial flows [ J ] method].Journal ofcomputational physics,1999,152(2):457-492；
(7.3) calculating the gas zone metal vapor diffusion: calculating the mass percentage content C of the metal vapor at the central points of all grids in the gas areavaporThe calculation formula is as follows:
wherein D is the mass diffusion coefficient of the metal vapor, and the value can be obtained by a second viscosity approximation method; the second viscosity approximation method is as follows: A.B.Murphy.A composition of transactions of differentiation in thermoplasmas. journal of Physics D: Applied Physics,1996,29(7): 1922;
setting the mass percentage content C of metal steam at each interface boundary point at the free interface of a molten pool of a gas area and a workpiece areavapor：
Eighthly, calculating the state of the workpiece area:
sequentially calculating a flow field and a temperature field of a workpiece region, and comprising the following substeps:
(8.1) calculating the flow field of the workpiece area: calculating the molten pool speed of the central points of all grids in the workpiece area
Pressure P of the molten bathmThe calculation formula is as follows:
wherein the temperature T of the central point of the grid of the workpiece areamTaking the ambient temperature during the first calculation; the next time step is calculated by adopting the calculated value of the last time step (7.2);
reference temperature TrefTaking the melting point temperature of a workpiece material; K. c is the seepage coefficient, relaxation coefficient and liquidus fraction flClosely related:
wherein d is a constant closely related to the size of the dendrite spacing, and d is 0.1 mm; fraction of liquid phase flLinear with temperature:
wherein, Tl、TsThe liquidus temperature and solidus temperature of the workpiece material, respectively;
calculating the normal pressure P of the molten pool at the boundary point of the interface at the free interface of the molten pool in the gas area and the workpiece areafAnd the tangential force of the molten pool
Wherein
Normal vector and tangent vector of the free interface of the molten pool, kappa is the curvature of the free interface of the molten pool, PeffFor effective pressure of gas region to workpiece region, take Peff＝max(Pr,Pg)；
(8.2) calculating the temperature field of the workpiece area: calculating the temperature T of the central point of all grids in the workpiece areamThe calculation formula is as follows:
wherein the workpiece absorbs the energy of the laser beam qlaserThe laser is obtained by adopting a ray tracing method, the laser is an optical fiber laser, the power is 2000W, and the radius of a light spot is 0.3 mm; the ray tracing method is as follows: computing the energy density of the laser deep fusion welding small holes with arbitrary shapes, the laser technology 2010,34(05) 614-618;
calculating the heat flow q of the boundary point of the interface into the workpiece region at the free interface of the molten pool of the gas region and the workpiece regionmatel：
Wherein σ is Stefan-Boltzmann constant, T∞Is the ambient temperature, qevapHeat loss for evaporation; heat loss q by evaporationevapThe calculation method is as follows: wu D, et al, understanding of spray formation in fiber laser welding of5083aluminum alloy&MassTransfer,2017,113:730-740；
Ninthly, updating a free interface of the molten pool:
molten pool velocity through all grid center points of workpiece area
Calculating the distance phi from the central point of each grid to the interface in the area, wherein the obtained equivalent surface with phi equal to 0 is the updated free interface of the molten pool, and the calculation formula is as follows:
the normal vector and curvature of the free interface of the molten pool are solved as follows:
in the fifth step to the ninth step, all the related calculation equations are dispersed by adopting a finite difference method, and the time step delta t isiSolving is carried out internally;
tenthly, judging:
will tsum+ΔtiIs given to tsumJudging whether t is presentsum＜tendIf yes, turning to the step three, updating the time step, otherwise, ending the calculation.
After the calculation is finished, an open source visualization program Paraview is adopted to perform visualization processing on simulation data obtained in the simulation process, and fig. 4 to 7 are transient results of the laser-arc hybrid welding temperature field, the speed field, the metal vapor distribution and the current density distribution simulated in the embodiment.
Embodiment 2, the flowchart of which is shown in fig. 1, includes a geometric model building step, an initial value setting step, a time step updating step, a physical property parameter updating step, an electromagnetic field solving step, a spatial intermittent decomposition step, a gas region state calculating step, a workpiece region state calculating step, a molten pool free interface updating step, and a judgment step:
firstly, establishing a geometric model:
same as example 1;
secondly, setting an initial value:
given the boundary conditions of the computation region: the environment temperature is 1000K, the electrode temperature is 3500, the environment pressure is 10atm, and the bottom potential of the workpiece is 0V;
setting the initial value of the physical quantity of each grid center point in the whole calculation area: potential 0V, current density 0A/m2The magnetic field intensity is 0T, the speed is 0m/s, the temperature is 1000K, the pressure is 10atm, and the mass percentage of the metal vapor is 0;
setting an accumulation time variable tsumCalculating the cutoff time t as 0end＝10s；
Setting the time step Δ tiIs an initialStep of time Δ t0，Δt0＝1×10-6s, performing the fourth step;
step three, updating the time step:
same as example 1;
fourthly, updating physical property parameters:
setting physical property parameters in the whole calculation region:
the gas area is filled with mixed gas of protective gas and metal vapor, the protective gas is helium, and the metal vapor is metal vapor of a workpiece material; calculating the mass percentage content and the temperature of the metal steam in the mixed gas as initial values for the first time, and acquiring the mass percentage content and the temperature of the metal steam in the mixed gas in the next time step from the substeps (7.2) and (7.3);
conductivity σ of the gas mixtureeDensity rhogViscosity [ mu ] ofgSpecific heat capacity CpgCoefficient of thermal conductivity kgAnd net gas emissivityNThe composition and temperature of the mixed gas at the center of each grid are directly determined; the electrical conductivity σ of the gas mixture being determined by the composition and temperature of the gas mixtureeDensity rhogViscosity [ mu ] ofgSpecific heat capacity CpgCoefficient of thermal conductivity kgAnd net gas emissivityNFrom Murphy AB, et al modeling of thermal plastics for arc welding, the roll of the shifting gas properties and of the metal vacuum. journal of Physics D: applied Physics,2009,42(19): 194006;
the workpiece material of the workpiece area is 304 stainless steel; corresponding conductivity σeDensity rhomViscosity [ mu ] ofmSpecific heat capacity CpmCoefficient of thermal conductivity kmThermal expansion coefficient β, surface tension coefficient gamma, and thermal capillary coefficient
Work potential
Emissivity of radiationrDirectly determined by the workpiece material and temperature at each grid center; from workpiece materialThe electrical conductivity σ corresponding to the material of the workpiece determined directly by the temperatureeDensity rhomViscosity [ mu ] ofmSpecific heat capacity CpmCoefficient of thermal conductivity kmThermal expansion coefficient β, surface tension coefficient gamma, and thermal capillary coefficient
Work potential
Emissivity of radiationrThe citation is from: wu C S.computer correlation of thread-dimensional correlation in transforming MIG wells engineering computations,1992,9(5): 529-;
fifthly, solving the electromagnetic field:
same as example 1;
sixthly, spatial discontinuous decomposition:
same as example 1;
seventhly, calculating the gas area state:
(7.1) same as in example 1;
(7.2) the same procedure as in example 1 was repeated except that the thickness was changed to 0.4 mm;
(7.3) same as in example 1;
eighthly, calculating the state of the workpiece area:
same as example 1;
ninthly, updating a free interface of the molten pool:
same as example 1;
tenthly, judging:
same as example 1;
after the calculation is finished, the simulation data obtained in the simulation process is visualized by adopting visualization processing software Tecplot 360 of the American Tecplot company, and the transient results of the laser-arc hybrid welding temperature field, the speed field, the metal vapor distribution and the current density distribution can be obtained.
Embodiment 3, the flowchart of which is shown in fig. 1, includes a geometric model building step, an initial value setting step, a time step updating step, a physical property parameter updating step, an electromagnetic field solving step, a spatial intermittent decomposition step, a gas region state calculating step, a workpiece region state calculating step, a molten pool free interface updating step, and a judgment step:
firstly, establishing a geometric model:
establishing a geometric model by using three-dimensional modeling software, wherein the geometric model is a cuboid, and is 500mm long, 400mm wide and 200mm high; the geometric model comprises a workpiece area, an electrode area and a gas area, wherein the workpiece area is a cuboid, the length and the width of the workpiece area are the same as those of the geometric model, and the height of the workpiece area is 40 mm; the electrode area is a cone, the cone angle is 120 degrees, the diameter of the bottom surface of the cone is the same as that of the cylinder, the diameter of the cylinder is 4mm, the height of the cylinder is 150mm, the included angle between the axis in the electrode area and the vertical direction is 60 degrees, and the vertical distance between the end part of the electrode area and the workpiece area is 10 mm; the region of the geometric model except the electrode region is a calculation region; the three-dimensional modeling software is Pro/E of American parameter technology company;
the gas area is the rest area of the geometric model except the workpiece area and the electrode area;
carrying out grid division on the calculation region by adopting grid division software, wherein the grid is a cuboid, and the side length of the cuboid is 500 microns, the width of the cuboid is 200 microns, and the height of the cuboid is 200 microns; the grid division software is Gridgen of the American Pointwise company;
the second to fourth steps are the same as in example 1;
fifthly, solving the electromagnetic field:
welding current is introduced in the welding process, an electromagnetic field is generated in the whole calculation area, and the welding current of 300A is given through the electrode; otherwise, the same as example 1;
the sixth step to the seventh step are the same as those in the embodiment 1;
eighthly, calculating the state of the workpiece area:
(8.1) the same procedure as in example 1 was repeated except that d was 0.5 mm;
(8.2) the laser is Nd, namely YAG laser, the power is 10000W, and the spot radius is 0.5 mm; otherwise, the same as example 1;
nine to ten steps are the same as in example 1;
embodiment 4, the flowchart of which is shown in fig. 1, includes a geometric model building step, an initial value setting step, a time step updating step, a physical property parameter updating step, an electromagnetic field solving step, a spatial intermittent decomposition step, a gas region state calculating step, a workpiece region state calculating step, a molten pool free interface updating step, and a judgment step:
firstly, establishing a geometric model:
the geometric model is a cuboid, the length is 5mm, the width is 5mm, and the height is 4 mm; the height of the workpiece area is 1 mm; the electrode area is a cone, the cone angle is 30 degrees, the diameter of the bottom surface of the cone is the same as that of the cylinder, the diameter of the cylinder is 1mm, the height of the cylinder is 1mm, the included angle between the central axis of the electrode area and the vertical direction is 60 degrees, and the vertical distance between the end part of the electrode area and the workpiece area is 2 mm;
the grid is a cube, and the side length of the cube is 20 micrometers;
otherwise, the same as example 1;
secondly, setting an initial value:
calculating the cut-off time tend0.1 s; otherwise, the same as example 1;
the third to fourth steps are the same as in example 1;
fifthly, solving the electromagnetic field:
welding current is introduced in the welding process, an electromagnetic field is generated in the whole calculation area, and 30A welding current is given through the electrodes; otherwise, the same as example 1;
the sixth step to the seventh step are the same as those in the embodiment 1;
eighthly, calculating the state of the workpiece area:
(8.1) taking d as 0.05mm, and the rest is the same as the example 1;
(8.2) the laser is a fiber laser, the power is 100W, and the radius of a light spot is 0.1 mm; otherwise, the same as example 1;
nine to ten steps are the same as in example 1;
the method realizes the numerical simulation calculation of the laser-TIG hybrid welding under the condition of the process parameters of the embodiment, and can simultaneously solve the evolution law of solid phase, liquid phase, metal vapor and plasma in the hybrid welding process. By simply modifying the embodiment and the implementation mode in the implementation scheme, the numerical simulation of the laser-TIG hybrid welding of different shielding gas types, different workpiece materials and different process parameters can be realized by adopting the method disclosed by the invention, the expansibility is good, and the method has application potential in the aspects of mechanism research of the hybrid welding and engineering process parameter formulation.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (5)
1. A three-dimensional transient numerical simulation method for laser-arc hybrid welding comprises the steps of establishing a geometric model, setting an initial value, updating a time step, updating physical property parameters, solving an electromagnetic field, performing spatial discontinuous decomposition, calculating a gas region state, calculating a workpiece region state, updating a molten pool free interface and judging, and is characterized in that:
firstly, establishing a geometric model:
establishing a geometric model by adopting three-dimensional modeling software, wherein the geometric model is a cuboid, the geometric model comprises a workpiece area, an electrode area and a gas area, and the workpiece area is the cuboid and has the same length and width as the geometric model; the electrode area is a cylinder or a cylinder with one end being a cone, when the electrode area is a cylinder, the included angle between the central axis of the electrode area and the vertical direction is 0-60 degrees, and when the electrode area is a cylinder with one end being a cone, the diameter of the bottom surface of the cone is the same as that of the cylinder; the vertical distance between the end part of the electrode area and the workpiece area is 1 mm-10 mm; the gas area is the rest area of the geometric model except the workpiece area and the electrode area;
the region of the geometric model except the electrode region is a calculation region;
carrying out grid division on the calculation region by adopting grid division software, wherein the grid is a cuboid or a cube, and the side length of the cuboid or the cube is 10-500 mu m;
secondly, setting an initial value:
given the boundary conditions of the computation region: the environment temperature is 300-1000K, the electrode temperature is 3000-3500K, the environment pressure is 0.1-10 atm, and the bottom potential of the workpiece is 0V;
setting the initial value of the physical quantity of each grid center point in the whole calculation area: potential 0V, current density 0A/m2The magnetic field intensity is 0T, the speed is 0m/s, the temperature is 300-1000K, the pressure is 0.1-10 atm, and the mass percentage content of the metal steam is 0;
setting an accumulation time variable tsumCalculating the cutoff time t as 0end＝0.1～10s；
Setting the time step Δ tiIs an initial time step Δ t0，Δt0＝1×10-7～1×10-6s, performing the fourth step;
step three, updating the time step:
calculating the maximum time step for gas region stability calculation
Then calculating the maximum time step length of stable calculation of the workpiece region
Take (Δ t)0,Δtg,Δtm) The minimum value of the three is used as the updated time step delta tiCarrying out the step four;
where, i is 1,2 …, which indicates the i-th step, the maximum condition number Cmax＝0.5～1.0，ug_x,ug_y,ug_zGas velocity at the center point of the gas area grid
At three of x, y and zComponent of direction, um_x,um_y,um_zThe velocity of the molten pool being the central point of the grid of the region of the workpiece
Components in the x, y, z directions; the sizes of the grids in the x direction, the y direction and the z direction are respectively delta x, delta y and delta z;
fourthly, updating physical property parameters:
setting physical property parameters in the whole calculation region:
the gas area is filled with mixed gas of protective gas and metal steam, the protective gas is one or more of argon, helium and carbon dioxide, and the metal steam is the metal steam of the workpiece material; calculating the mass percentage content and the temperature of the metal steam in the mixed gas as initial values for the first time, and acquiring the mass percentage content and the temperature of the metal steam in the mixed gas in the next time step from the substeps (7.2) and (7.3);
conductivity σ of the gas mixtureeDensity rhogViscosity [ mu ] ofgSpecific heat capacity CpgCoefficient of thermal conductivity kgAnd net gas emissivityNThe composition and temperature of the mixed gas at the center of each grid are directly determined;
the workpiece material of the workpiece area is iron-based alloy or non-ferrous metal alloy; corresponding conductivity σeDensity rhomViscosity [ mu ] ofmSpecific heat capacity CpmCoefficient of thermal conductivity kmThermal expansion coefficient β, surface tension coefficient gamma, and thermal capillary coefficient
Work potential
Emissivity of radiationrDirectly determined by the workpiece material and temperature at each grid center;
fifthly, solving the electromagnetic field:
solving for the electromagnetic field throughout the calculation area:
in the welding processWelding current is input, an electromagnetic field is generated in the whole calculation area, welding current of 30-300A is given through the electrodes, and the potential of the center points of all grids in the whole calculation area is obtained through calculation
Current density
And magnetic induction intensity
Distribution, the calculation equation is as follows:
wherein the vacuum dielectric constant is0Magnetic loss of potential at center point of grid
Gradient operator
Divergence operator
Rotation operator
Laplacian operator
Electrical conductivity sigmaeRespectively adopting the mixed gas in the gas area and the corresponding conductivity of the workpiece material in the workpiece area during calculation;
sixthly, spatial discontinuous decomposition:
performing space discontinuous decomposition by taking the upper surface of a workpiece area as an interface in the first calculation and taking an updated free interface of a molten pool as an interface in the subsequent calculation, and dividing the whole calculation area into a gas area and a workpiece area, wherein the gas area is an arc-metal vapor area and the workpiece area is a workpiece solid-liquid area; defining interface boundary points as intersection points of grid central point connecting lines at two sides of a free interface of the molten pool and the free interface of the molten pool;
seventhly, calculating the gas area state:
the method comprises the following substeps of calculating the flow field, the temperature field and the metal vapor distribution of the gas region in sequence:
(7.1) calculating the gas area flow field: calculating the gas velocity of the center points of all grids in the gas area
Gas pressure PgThe calculation formula is as follows:
wherein
Is the acceleration of gravity;
setting the gas velocity of the boundary point of the gas zone and the workpiece zone at the free interface of the molten bath
And gas pressure Pg_sRespectively as follows:
wherein the evaporation recoil pressure PrObtaining by adopting a recoil pressure model based on the environmental pressure;
(7.2) calculating the gas zone temperature field: calculating the gas temperature T of the central point of all grids in the gas areagThe calculation formula is as follows:
wherein k isbBoltzmann constant, e is elementary charge, t is time,
a differential operator;
calculating the heat flow q of the boundary point of the interface into the gas region at the free interface of the molten pool of the gas region and the workpiece regiongas：
Wherein T isgs、TmsAcquiring the temperatures of a gas area and a workpiece area which are boundary points of an interface respectively by adopting a virtual flow method; k is a radical ofeffIs the effective thermal conductivity, k, of the boundary point of the interfaceeff＝0.5×(kg(Tgs)+kg(Tms))，kg(Tgs)、kg(Tms) Respectively is the temperature Tgs、TmsThe corresponding gas thermal conductivity; the effective thickness of the boundary layer of the free interface of the molten pool is 0.1 mm-0.4 mm;
(7.3) calculating the gas zone metal vapor diffusion: calculating the mass percentage content C of the metal vapor at the central points of all grids in the gas areavaporMeter for measuringThe calculation formula is as follows:
wherein D is the mass diffusion coefficient of the metal vapor, and the value can be obtained by a second viscosity approximation method;
setting the mass percentage content C of metal steam at each interface boundary point at the free interface of a molten pool of a gas area and a workpiece areavapor：
Eighthly, calculating the state of the workpiece area:
sequentially calculating a flow field and a temperature field of a workpiece region, and comprising the following substeps:
(8.1) calculating the flow field of the workpiece area: calculating the molten pool speed of the central points of all grids in the workpiece area
Pressure P of the molten bathmThe calculation formula is as follows:
wherein the temperature T of the central point of the grid of the workpiece areamTaking the ambient temperature during the first calculation; the next time step is calculated by adopting the calculated value of the last time step (7.2);
reference temperature TrefTaking the melting point temperature of a workpiece material; K. c is the seepage coefficient, relaxation coefficient and liquidus fraction flClosely related:
wherein d is a constant closely related to the size of dendrite spacing, and d is 0.05mm to 0.5 mm; fraction of liquid phase flLinear with temperature:
wherein, Tl、TsThe liquidus temperature and solidus temperature of the workpiece material, respectively;
calculating the normal pressure P of the molten pool at the boundary point of the interface at the free interface of the molten pool in the gas area and the workpiece areafAnd the tangential force of the molten pool
Wherein
Normal vector and tangent vector of the free interface of the molten pool, kappa is the curvature of the free interface of the molten pool, PeffFor effective pressure of gas region to workpiece region, take Peff＝max(Pr,Pg)；
(8.2) calculating the temperature field of the workpiece area: calculating the temperature T of the central point of all grids in the workpiece areamThe calculation formula is as follows:
wherein the workpiece absorbs the energy of the laser beam qlaserAcquiring by adopting a ray tracing method; the laser is fiber laser or Nd, namely YAG laser, the power is 100W-10000W, and the spot radius is 0.1 mm-0.5 mm;
calculating the boundary point of the interface into the workpiece zone at the free interface of the molten pool between the gas zone and the workpiece zoneOf heat flow qmatel：
Wherein σ is Stefan-Boltzmann constant, T∞Is the ambient temperature, qevapHeat loss for evaporation;
ninthly, updating a free interface of the molten pool:
molten pool velocity through all grid center points of workpiece area
Calculating the distance phi from the central point of each grid to the interface in the area, wherein the obtained equivalent surface with phi equal to 0 is the updated free interface of the molten pool, and the calculation formula is as follows:
the normal vector and curvature of the free interface of the molten pool are solved as follows:
in the fifth step to the ninth step, all the involved calculation equations are dispersed by adopting a finite difference method or a finite volume method, and the time step delta t isiSolving is carried out internally;
tenthly, judging:
will tsum+ΔtiIs given to tsumJudging whether t is presentsum＜tendIf yes, turning to the step three, updating the time step, otherwise, ending the calculation.
2. The laser-arc hybrid welding three-dimensional transient numerical simulation method of claim 1, characterized in that: in the first step, the three-dimensional modeling software is AutoCAD of American Autodesk software company, UG of Germany Siemens PLMSofware company or Pro/E of American parameter technology company; the cuboid of the geometric model is 5 mm-500 mm long, 5 mm-500 mm wide and 5 mm-200 mm high; the cuboid of the workpiece area is 1 mm-100 mm high; when the electrode area is a cylinder, the diameter of the cylinder is 1 mm-4 mm, the height is 1 mm-150 mm, when the electrode area is a cylinder with one end being a cone, the cone angle is 30-120 degrees, the diameter of the cylinder is 1 mm-4 mm, and the height is 1 mm-150 mm;
the gridding software is Hypermesh of Altair corporation, Gridgen of Pointwise corporation, or Patran of MSC.
3. The laser-arc hybrid welding three-dimensional transient numerical simulation method of claim 1, characterized in that: in the fourth step, the electric conductivity σ of the mixed gas is determined by the composition and temperature of the mixed gaseDensity rhogViscosity [ mu ] ofgSpecific heat capacity CpgCoefficient of thermal conductivity kgAnd net gas emissivityNReference is made to the substances from Mougenot J, et al, plasma-field poolvination in structured input-gas configuration, journal of Physics D: Applied Physics,2013,46(13):135206, or Murphy A B, et al, modeling of thermal plasma for arc welding: the roll of the shifting gas properties and of metallic publication. journal of Physics D: Applied Physics,2009,42(19):194006, or Murphy AB.the effects of metallic publication in arc welding. journal of Physics D: Applied Physics,2010,43(43): 434001;
the corresponding electrical conductivity σ of the workpiece material being determined directly from the workpiece material and the temperatureeDensity rhomViscosity [ mu ] ofmSpecific heat capacity CpmCoefficient of thermal conductivity kmThermal expansion coefficient β, surface tension coefficient gamma, and thermal capillary coefficient
Work potential
Emissivity of radiationrThe material property calculation Software JMatPro of Sente Software company in England is adopted for calculationObtained from either Wei H L, the equivalent, the original, the orientation reducing, the identification of an aluminum alloy, acta materials, 2016,115: 123-.
4. The laser-arc hybrid welding three-dimensional transient numerical simulation method of claim 1, characterized in that: in the sub-step (7.1), the recoil pressure model based on the environmental pressure is as follows: s. Pang, et al. exhibition of duration reduction Laser welding under variable electromagnetic Applications. journal of Laser Applications 2015,27(2): 022007; in the sub-step (7.2), the virtual stream method is as follows: fedkiw R P, et al, A non-oscillotory Eulerian approach in multimaterial flows, Journal of computational physics,1999,152(2) 457-; in the sub-step (7.3), the second viscosity approximation method is as follows: A.B.Murphy.A composition of transactions of differentiation in thermoplasmas. journal of Physics D: Applied Physics,1996,29(7): 1922.
5. The laser-arc hybrid welding three-dimensional transient numerical simulation method of claim 1, characterized in that: in the sub-step (8.2), the ray tracing method is as follows: computing the energy density of the laser deep fusion welding small holes with arbitrary shapes, the laser technology 2010,34(05) 614-618; in the step (8.2), the heat loss q is evaporatedevapThe calculation method is as follows: wu D, et al.infraduction of scatter formation in fiber laser welding of5083aluminum alloy&Mass Transfer,2017,113:730-740。
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