Numerical simulation of heat and mass transfer under synergistic effect of ultrasonic vibration and CMT-p arc

Abstract

A numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc is disclosed. The method includes constructing an arc additive manufacturing system and obtaining a sample; building a two-dimensional geometric model; forming a complete numerical model of heat and mass transfer in the ultrasonic-CMT-P arc molten pool; setting boundary and initial conditions; obtaining transient evolution results of the molten pool temperature field, velocity field, and phase distribution; and evaluating the accuracy and reliability of the constructed model. The advantages of this invention are: it enables the synergistic solution of the acoustic field, flow field, thermal field, and electromagnetic field, comprehensively describing the heat and mass transfer behavior under the ultrasonic-CMT-P composite process. By dynamically coupling the ultrasonic displacement boundary conditions, the CMT-P heat and force sources, and the motion law of the moving mesh to the solver, transient numerical solutions of multiple physics fields (acoustic, thermal, mechanical, and magnetic) can be achieved. By comparing the simulated droplet transition morphology with high-speed photographic images over time, and by performing quantitative error analysis on the calculated melt width and depth values ​​with experimental measurements, the accuracy of the model can be dually verified.

Description

Technical Field

[0001] This invention belongs to the field of electric arc forming technology, and specifically relates to a numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P electric arc. Background Technology

[0002] Cold Metal Transfer with Pulsed (CMT-P) combines the advantages of low heat input, stable droplet transfer, and high filling efficiency of the CMT arc with the concentrated energy and deep penetration of the pulsed MIG arc, effectively broadening the heat input range and providing an ideal precision heat source for heat-sensitive materials. To further optimize forming quality and microstructure, ultrasonic vibration is introduced as an external field aid, leveraging its significant advantages such as grain refinement, solute diffusion promotion, and solidification defect suppression to achieve multi-field synergy with the CMT-P arc. Through the unique acoustic flow and cavitation effects of ultrasonic vibration, it is possible to actively intervene in and optimize the thermal-mass coupling behavior of the molten pool while ensuring stable droplet transfer, thereby achieving a synergistic improvement in forming quality and microstructure.

[0003] However, the physical mechanisms within the molten pool during the synergistic interaction of ultrasonic vibration and CMT-P arc are extremely complex, involving multi-physics coupling of thermo-mechanical-magnetic fields. The acoustic flow and cavitation effects generated by ultrasonic vibration in the molten pool significantly alter its flow behavior and heat transfer rate, thereby affecting the temperature field distribution, flow field morphology, and solidification behavior. These factors are the core physical processes that determine the forming quality. Traditional trial-and-error experiments are insufficient for real-time observation of the multi-field evolution within the high-temperature molten pool, and are costly and time-consuming, making it difficult to systematically reveal the intrinsic relationship between ultrasonic amplitude and CMT-P process parameters on the heat and mass transfer behavior of the molten pool.

[0004] Numerical simulation is a crucial tool for revealing the physical mechanisms of the aforementioned composite processes. By establishing accurate multi-field coupled numerical models, the heat and mass transfer behavior of the molten pool under different combinations of process parameters can be quantitatively analyzed, thereby gaining a deeper understanding of the control mechanism of ultrasonic vibration on the molten pool. However, constructing a high-fidelity ultrasonic-CMT-P composite heat source model faces several challenges: on the one hand, it is necessary to accurately describe the dynamic distribution of CMT-P arc heat flux density and pressure; on the other hand, it is necessary to reasonably characterize the influence mechanism of ultrasonic vibration in the molten pool. Currently, systematic numerical simulation studies on the heat and mass transfer behavior under the synergistic effect of ultrasonic-CMT-P are still relatively few. Existing simulation methods are still imperfect in terms of thermo-mechanical-magnetic multi-field coupling algorithms, free interface tracking accuracy, and prediction of solidification structure evolution, thus failing to meet the practical needs of mechanism exploration and parameter optimization for this composite process.

[0005] Currently, the existing technologies mainly adopt the following solutions:

[0006] Option A: Experience-based trial-and-error method. Technicians set CMT-P process parameters and ultrasonic amplitude based on experience, and conduct single-layer or multi-layer deposition experiments. Weld formation, weld width and depth, and grain size are analyzed through cutting, mounting, polishing, and metallographic microscopy. Based on the experimental results and the technicians' experience, a parameter is manually adjusted, and the above process is repeated until the desired forming quality is obtained.

[0007] Option B: Numerical Simulation Method. A transient heat and mass transfer model of the molten pool is established, and the volumetric fluid flow (VOF) method is used to track the evolution of the free surface of the molten pool. By solving the mass, momentum, and energy conservation equations, the temperature and flow field distributions within the molten pool are calculated. Some studies attempt to consider the ultrasonic mechanism in the model to predict the behavior of the molten pool and solidification characteristics under different process parameters. Simulation results are usually presented in the form of temperature gradient and flow field distribution contour maps.

[0008] However, the aforementioned existing technology has the following disadvantages:

[0009] Option A: Experience-based trial and error method

[0010] Relying on operator experience to adjust parameters makes it difficult to quantitatively reveal the influence mechanism of ultrasonic amplitude and CMT-P process parameters on the heat and mass transfer behavior inside the molten pool. This method requires conducting numerous single-layer and multi-layer deposition experiments and obtaining weld formation and microstructure information through destructive testing, resulting in high experimental costs and long development cycles. Because it is impossible to observe the temperature field distribution, flow field morphology, and solidification process inside the high-temperature molten pool in real time, it is difficult to establish the intrinsic correlation between process parameters and molten pool behavior. Furthermore, successful experiences are difficult to effectively replicate across different equipment or operators, resulting in insufficient process stability and portability.

[0011] Option B: Numerical simulation method

[0012] Existing numerical simulation studies mostly focus on the effects of a single CMT arc or a single ultrasonic field, lacking simulation models that can accurately describe the multi-physics coupling behavior of the molten pool under the synergistic effect of ultrasonic vibration and CMT-P pulsed arc. Constructing a high-fidelity composite heat source model faces several challenges: on the one hand, it requires accurately describing the dynamic distribution characteristics of CMT-P arc heat flux density and pressure; on the other hand, it requires a reasonable characterization of the influence mechanism of ultrasonic vibration in the molten pool. Currently, there are relatively few systematic numerical simulation studies on the heat and mass transfer behavior under the synergistic effect of ultrasonic vibration and CMT-P arc, and existing simulation methods are still imperfect in terms of the implementation of thermo-mechanical-acoustic multi-field coupling algorithms, the accuracy of free interface tracking, and the prediction of solidification structure evolution, making it difficult to meet the practical needs of mechanism exploration and process parameter optimization for this composite process. Summary of the Invention

[0013] To address the aforementioned problems, the present invention aims to provide a numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc.

[0014] To achieve the above objectives, the numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc provided by the present invention includes the following steps performed in sequence:

[0015] Step 1: Construct an arc additive manufacturing system for in-situ observation experiments. Under the set experimental conditions, use the system to conduct ultrasonic vibration-assisted CMT-P arc additive manufacturing experiments to obtain an ultrasonic-CMT-P composite process experimental dataset and samples containing electrical signal data, droplet transition images, microscopic morphology images of the molten pool region, and process parameter records.

[0016] Step 2: Divide the above sample into regions to build a two-dimensional geometric model for numerical simulation. Then, divide all regions into quadrilateral meshes and set up dynamic meshes.

[0017] Step 3: Based on the experimental dataset of the ultrasonic-CMT-P composite process obtained in Step 1, a set of control equations covering mass, momentum, energy conservation, fluid volume function equations and ultrasonic vibration simple harmonic motion equations is established using fluid dynamics methods and written into a UDF program through user-defined functions; then the ultrasonic vibration effect and the CMT-P electric arc heat source effect are coupled into the equations in the form of source terms to form a complete numerical model of heat and mass transfer in the ultrasonic-CMT-P electric arc molten pool.

[0018] Step 4: Based on the experimental conditions set in Step 1 and the two-dimensional geometric model established in Step 2, set the boundary conditions and initial conditions for the numerical model of heat and mass transfer in the ultrasonic-CMT-P arc molten pool.

[0019] Step 5: By configuring the ANSYS Fluent solver parameters and loading the UDF program written in Step 3, and combining the boundary conditions and initial conditions set in Step 4, the ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model established in Step 3 is numerically solved to obtain the transient evolution results of the molten pool temperature field, velocity field and phase distribution.

[0020] Step 6: Compare and verify the transient evolution results obtained in Step 5 with the sample obtained under the process parameters in Step 1. By quantifying the geometric characteristics of the molten pool, evaluate the accuracy and reliability of the established ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model.

[0021] In step 1, the method for constructing an arc additive manufacturing system for in-situ observation experiments, and using this system to conduct ultrasonic vibration-assisted CMT-P arc additive manufacturing experiments under set experimental conditions, to obtain an ultrasonic-CMT-P composite process experimental dataset and samples containing electrical signal data, droplet transition images, microscopic morphology images of the molten pool region, and process parameter records, is as follows:

[0022] The arc additive manufacturing system used for in-situ observation experiments includes a welding machine, a high-speed camera, a laser, an ultrasonic automatic frequency tracking digital system, an electrical signal acquisition device, an industrial computer, an industrial robot, and a pure argon protective gas supply system. The high-speed camera and laser are respectively mounted on opposite sides of the substrate. The ultrasonic amplitude rod on the ultrasonic automatic frequency tracking digital system is in close contact with one end of the substrate via a clamp. The industrial robot holds the welding torch on the welding machine and deposits the material according to a planned path. The welding machine is used to melt, feed, and retract the molten wire. The electrical signal acquisition device records electrical signal values, including current and voltage. The pure argon protective gas supply system ensures gas protection during the forming process. The industrial computer is electrically connected to the welding machine, high-speed camera, laser, ultrasonic automatic frequency tracking digital system, electrical signal acquisition device, industrial robot, and pure argon protective gas supply system to process all images and data, providing experimental basis for setting boundary conditions and verifying results for the numerical model described below.

[0023] The substrate is fixed on the worktable; the process parameters for the experiment are set.

[0024] During the experiment, under the control of an industrial computer, pure argon gas supplied by a pure argon protective gas supply system was used as the protective gas. An industrial robot was used to deposit the molten wire from the welding machine onto the substrate using a single-pass, single-layer deposition strategy. During this process, the ultrasonic amplitude rod on the ultrasonic automatic frequency tracking digital system effectively transmitted ultrasonic vibrations to the molten pool area. A highly focused beam was generated using a laser, and a high-speed camera was used to acquire images of the droplet transition form and the evolution of the molten pool morphology in real time. An electrical signal acquisition device was used to record electrical signal values, including current and voltage, thereby preparing the sample.

[0025] Based on the above process parameters, the above samples were wire-cut and sampled. After inlaying, rough grinding, fine grinding and polishing, the microscopic morphology image of the molten pool area was captured under an optical microscope. The experimental dataset of ultrasonic-CMT-P composite process was composed of all electrical signal data, droplet transition images, molten pool morphology images and process parameter records.

[0026] In step 2, the method of dividing the above-mentioned sample into regions to build a two-dimensional geometric model for numerical simulation, and then dividing all regions into quadrilateral meshes and setting dynamic meshes, is as follows:

[0027] The above sample was divided into a fuse domain, a substrate domain, and a protective gas domain bounded by the fuse boundary, thereby constructing a two-dimensional geometric model for numerical simulation. Each half of the sample was used as the substrate domain and the protective gas domain, respectively, and the fuse domain was located within the protective gas domain. Then, ANSYS ICEM software was used to divide all the above regions into quadrilateral meshes with a size of 0.5 mm.

[0028] Considering the wire feeding and retraction actions in the CMT-P process, a moving mesh is set in the two-dimensional geometric model. The upper boundary of the wire domain is used as the velocity inlet. The moving mesh movement speed is set according to the wire feeding speed. The interface between the wire domain and the protective gas domain is set as the sliding mesh boundary to ensure the continuity of boundary conditions during mesh movement.

[0029] In step 3, based on the experimental dataset of the ultrasonic-CMT-P composite process obtained in step 1, a set of control equations covering mass, momentum, energy conservation, fluid volume function equations, and ultrasonic vibration simple harmonic motion equations is established using fluid dynamics methods and written into a UDF program through user-defined functions; then, the ultrasonic vibration effect and the CMT-P arc heat source effect are coupled into the equations as source terms to form a complete numerical model of heat and mass transfer in the ultrasonic-CMT-P arc molten pool.

[0030] 3.1 Basic Assumptions

[0031] ① The feeding and retraction of the molten wire are achieved using dynamic mesh technology. The inlet velocity of the molten droplet is determined based on the analysis of electrical signals and high-speed camera images. It is assumed that the molten droplet generation velocity is equal to the wire feeding velocity.

[0032] ② Ignoring the arc plasma region, the effect of the arc on the molten droplet and the molten pool is loaded into the momentum equation and energy equation in the form of source terms;

[0033] ③ Both the gas phase and the metallic phase are laminar, incompressible Newtonian fluids;

[0034] ④ Heat and mass loss caused by metal vapor are not considered;

[0035] ⑤ The amplitude of ultrasonic vibration in the substrate remains constant.

[0036] 3.2 Mass Conservation Equation

[0037] ;

[0038] in, Density, kg / m³; t is the velocity vector, in m / s; t is time, in s;

[0039] 3.3 Momentum Conservation Equation

[0040] ;

[0041] in, Pressure, Pa; For dynamic viscosity, Pa·s, the dynamic viscosity of liquid metal is taken as 0.005 kg / (m·s); F Darcy Darcy force, used to suppress flow in the solid region; For momentum source term;

[0042] 3.4 Energy Conservation Equation

[0043] ;

[0044] Where h is enthalpy; k is thermal conductivity; S e For energy source terms;

[0045] 3.5 Fluid Volume Function Equation

[0046] ;

[0047] Where α is the volume fraction, α = 1 indicates that the unit is filled with a metallic phase, α = 0 indicates that the unit is filled with a gas phase, and 0 < α < 1 indicates that the unit contains two-phase fluid.

[0048] 3.6 Equation of Simple Harmonic Motion of Ultrasonic Vibration

[0049] ;

[0050] Where x(t) is the vibration displacement at time t; A is the amplitude; ω is the angular frequency, ω=2πf, and f is the ultrasonic frequency in Hz; This is the initial phase;

[0051] The above-mentioned mass, momentum, energy conservation, fluid volume function equations and ultrasonic vibration simple harmonic motion equations are combined into a set of control equations and written into a UDF program through user-defined functions. The UDF program reads the current value and ultrasonic vibration parameters of the current time step in real time, calculates each source term and adds it to the corresponding equation. All equations constitute a complete numerical model of heat and mass transfer in ultrasonic-CMT-P arc molten pool.

[0052] In step 4, the method for setting the boundary and initial conditions for the ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model based on the experimental conditions set in step 1 and the two-dimensional geometric model established in step 2 is as follows:

[0053] 4.1 Boundary Condition Settings

[0054] The two-dimensional geometric model contains the following boundaries, and the types and parameter settings for each boundary are as follows:

[0055] ① Fuse domain inlet boundary conditions

[0056] The type is velocity inlet, located at the upper boundary of the molten wire domain; the wire feeding speed and direction, the timing of each stage of wire feeding and retraction, the initial temperature of the molten droplet, and the phase volume fraction are set.

[0057] ② Boundary conditions at the inlet of the protective gas domain

[0058] The type is a velocity inlet, located on both sides of the fuse zone; the protective gas flow rate, temperature, phase volume fraction, and gas composition are set.

[0059] ③ Pressure outlet boundary conditions

[0060] It is a pressure outlet, located on both sides of the protective gas zone;

[0061] ④ Wall boundary conditions

[0062] The type is a wall, located at the bottom of the substrate domain and on both sides of the substrate domain;

[0063] 4.2 Initial Condition Settings

[0064] Set the initial temperature of the entire computational domain, the initial velocity of the entire computational domain, the phase volume fraction of the filament domain, the phase volume fraction of the substrate domain, and the phase volume fraction of the protective gas domain; solid-liquid phase state.

[0065] In step 5, the method for numerically solving the ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model established in step 3 by configuring the ANSYS Fluent solver parameters, loading the UDF program written in step 3, and combining the boundary conditions and initial conditions set in step 4, to obtain the transient evolution results of the molten pool temperature field, velocity field, and phase distribution is as follows:

[0066] 5.1 Solver and Model Configuration

[0067] Solver algorithm: A pressure-based solver is used, and the time term adopts a transient formula to capture the unsteady characteristics of droplet transition and molten pool evolution; the influence of gravitational acceleration is considered, and the gravitational acceleration is set to -9.8 m / s².

[0068] Multiphase flow model: Enable VOF model, set the main phase as argon gas and the secondary phase as liquid metal; enable surface tension model and define the surface tension coefficient as a function of temperature;

[0069] Dynamic mesh configuration: Layering method is used for mesh topology update, and splitting and folding factors are set; the filament domain is defined as a rigid motion region;

[0070] Discretization scheme and algorithm: Pressure discretization adopts the PRESTO scheme; momentum and energy equations adopt the second-order upwind scheme to ensure calculation accuracy; volume fraction equation adopts the Geo-Reconstruct scheme to ensure clear interface; pressure-velocity coupling adopts the PISO algorithm.

[0071] Time step control: To accurately analyze the periodic changes and high-frequency vibration characteristics of the heat source, the time step is set to Δt = 1 × 10⁻ 5 The maximum number of iterations per time step is set to 40 to meet the accuracy requirements for solving the rapid current changes and high-frequency ultrasonic vibrations during the CMT-P cycle.

[0072] 5.2 UDF Program Loading and Execution

[0073] The UDF program written in step 3 is compiled and loaded using the UDF manager of the ANSYS Fluent solver. This mainly includes: defining global variables and configuring the initial conditions of the computational domain by initializing the UDF; adding volume force source terms and energy source terms corresponding to the arc heat input through momentum source term UDF and energy source term UDF respectively; defining the rigid body motion of the filament domain through dynamic mesh UDF; and controlling the wire feeding and retraction actions according to the timing determined in step 1, thereby accurately simulating the influence of filament feeding on droplet detachment and transition process.

[0074] The numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc provided by this invention has the following beneficial effects:

[0075] 1. Numerical model construction method for multi-physics coupling of ultrasonic vibration and CMT-P arc: The simple harmonic displacement equation of ultrasonic vibration is coupled to the mass, momentum and energy conservation equations in the form of source terms, which can realize the synergistic solution of sound field, flow field, thermal field and electromagnetic field, and fully describe the heat and mass transfer behavior under ultrasonic-CMT-P composite process.

[0076] 2. UDF-based dynamic coupling solution method for ultrasound-CMT-P: Ultrasonic vibration parameters and CMT-P periodic electrical signals are loaded into the control equations in real time through user-defined functions. Ultrasonic displacement boundary conditions, CMT-P heat and force sources and dynamic mesh motion laws are dynamically coupled to the solver, which can realize transient numerical solution of acoustic-thermal-mechanical-magnetic multi-physics fields.

[0077] 3. Multi-source data verification method for heat and mass transfer behavior of ultrasonic-CMT-P molten pool: The simulated droplet transition morphology is compared with high-speed photographic images over time, and the calculated values ​​of melt width and melt depth are compared with the experimental measurements to perform quantitative error analysis, which can achieve dual verification of the model accuracy. Attached Figure Description

[0078] Figure 1 The flowchart of the numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc provided by the present invention is shown.

[0079] Figure 2 This is a schematic diagram of the electric arc additive manufacturing system used for in-situ observation experiments in this invention.

[0080] Figure 3 This is a schematic diagram of the voltage and current signals within one CMT-P cycle in this invention, along with the corresponding high-speed photographic image.

[0081] Figure 4 This is an image of the molten pool morphology taken during the present invention.

[0082] Figure 5 This is a schematic diagram of the two-dimensional geometric model in this invention.

[0083] Figure 6 This is a comparison diagram of the simulated molten pool and the actual molten pool in this invention. Detailed Implementation

[0084] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0085] like Figure 1 As shown, the numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc provided by this invention includes the following steps performed in sequence:

[0086] Step 1: Construct an arc additive manufacturing system for in-situ observation experiments. Under the set experimental conditions, use the system to conduct ultrasonic vibration-assisted CMT-P arc additive manufacturing experiments to obtain an ultrasonic-CMT-P composite process experimental dataset and samples containing electrical signal data, droplet transition images, microscopic morphology images of the molten pool region, and process parameter records.

[0087] like Figure 2As shown, the arc additive manufacturing system used for in-situ observation experiments includes a Fronius Advanced 4000R welding machine, a high-speed camera equipped with a 2000 Hz shooting frequency, an LWIRL808-50W-F laser, an ultrasonic automatic frequency tracking digital system, and a 2000 Hz shooting frequency camera. The system comprises an Advantech USB-4704 electrical signal acquisition device with a sampling frequency of Hz, an Advantech IPC-610-L industrial computer, an ABB industrial robot, and a pure argon protective gas supply system. A high-speed camera and a laser are respectively mounted on opposite sides of the substrate. The high-speed camera is used to acquire real-time images of the molten droplet transition, and the laser is used to generate a highly focused beam. An ultrasonic amplitude rod on the ultrasonic automatic frequency tracking digital system is in close contact with one end of the substrate via a clamp to ensure that ultrasonic vibrations are effectively transmitted to the molten pool area. The industrial robot holds the welding torch on the welding machine and deposits the molten wire according to a planned path. The welding machine is used to melt, feed, and retract the molten wire. The electrical signal acquisition device records electrical signal values, including current and voltage. The pure argon protective gas supply system ensures gas protection during the forming process. The industrial computer is electrically connected to the welding machine, high-speed camera, laser, ultrasonic automatic frequency tracking digital system, electrical signal acquisition device, industrial robot, and pure argon protective gas supply system to process all images and data, providing experimental basis for setting boundary conditions and verifying results for the numerical model described below.

[0088] The substrate is fixed on the worktable and is made of hot-rolled UNS S32750 sheet (150 mm × 80 mm × 8 mm); ER2594 fuse with a diameter of 1.2 mm is selected.

[0089] Figure 3 The voltage and current signals and the corresponding droplet transition image during a CMT-P cycle are presented. The CMT-P cycle consists of alternating CMT and pulse phases, with the CMT phase lasting 17 ms and the pulse phase lasting 22 ms, for a total cycle duration of 39 ms.

[0090] The experimental procedure used the process parameters shown in Table 1. Table 2 lists the chemical composition of the ER2594 fuse and the UNS S32750 substrate.

[0091]

[0092] Before conducting the ultrasonic vibration-assisted CMT-P arc additive manufacturing experiment, the substrate was thoroughly cleaned with alcohol to remove surface contaminants. During the experiment, under the control of an industrial computer, pure argon gas supplied by a pure argon protective gas supply system was used as the protective gas. An industrial robot was used to deposit the molten wire from the welding machine onto the substrate using a single-pass, single-layer deposition strategy. During this process, the ultrasonic amplitude bar on the ultrasonic automatic frequency tracking digital system effectively transmitted ultrasonic vibration to the molten pool area. A highly focused laser beam was generated, and a high-speed camera was used to acquire real-time images of the droplet transition pattern and the evolution of the molten pool morphology. Figure 3 As shown, an electrical signal acquisition device is used to record electrical signal values, including current and voltage, thereby preparing a sample with a length of 150 mm.

[0093] Based on the above process parameters, wire cutting was used to sample the above-mentioned parts. After inlaying, rough grinding, fine grinding, and polishing, microscopic morphology images of the molten pool area were captured under an optical microscope, such as... Figure 4 As shown, the experimental dataset for the ultrasonic-CMT-P composite process consists of all electrical signal data, droplet transition images, molten pool morphology images, and process parameter records.

[0094] Step 2: Divide the above sample into regions to build a two-dimensional geometric model for numerical simulation. Then, divide all regions into quadrilateral meshes and set up dynamic meshes.

[0095] like Figure 5 As shown, the above sample is divided into a fuse domain, a substrate domain, and a protective gas domain enclosed by the fuse boundary, thereby constructing a two-dimensional geometric model for numerical simulation. Each half of the sample is used as the substrate domain and the protective gas domain, respectively, and the fuse domain is located within the protective gas domain. Then, ANSYS ICEM software is used to divide all the above regions into quadrilateral meshes with a size of 0.5 mm.

[0096] Considering the wire feeding and retraction actions in the CMT-P process, a moving mesh is set in the two-dimensional geometric model. The upper boundary of the wire domain is used as the velocity inlet. The moving mesh movement speed is set according to the wire feeding speed. The interface between the wire domain and the protective gas domain is set as the sliding mesh boundary to ensure the continuity of boundary conditions during mesh movement.

[0097] Step 3: Based on the experimental dataset of the ultrasonic-CMT-P composite process obtained in Step 1, a set of control equations covering mass, momentum, energy conservation, fluid volume function equations, and ultrasonic vibration simple harmonic motion equations is established using the fluid dynamics (CFD) method. These equations are then written into a UDF program using user-defined functions (UDF). The ultrasonic vibration effect and the CMT-P arc heat source effect are then coupled into the equations as source terms to form a complete numerical model of heat and mass transfer in the ultrasonic-CMT-P arc molten pool, which is used to simulate the droplet transition and molten pool evolution process.

[0098] 3.1 Basic Assumptions

[0099] To improve computational efficiency while ensuring computational accuracy, the following reasonable assumptions are adopted:

[0100] ① The feeding and retraction of the molten wire are achieved using dynamic mesh technology. The inlet velocity of the molten droplet is determined based on the analysis of electrical signals and high-speed camera images. It is assumed that the molten droplet generation velocity is equal to the wire feeding velocity.

[0101] ② Ignoring the arc plasma region, the effect of the arc on the molten droplet and the molten pool is loaded into the momentum equation and energy equation in the form of source terms;

[0102] ③ Both the gas phase and the metallic phase are laminar, incompressible Newtonian fluids;

[0103] ④ Heat and mass loss caused by metal vapor are not considered;

[0104] ⑤ The amplitude of ultrasonic vibration in the substrate remains constant.

[0105] 3.2 Mass Conservation Equation

[0106] ;

[0107] in, Density, kg / m³; t is the velocity vector, in m / s; t is time, in s;

[0108] 3.3 Momentum Conservation Equation

[0109] ;

[0110] in, Pressure, Pa; For dynamic viscosity, Pa·s, the dynamic viscosity of liquid metal is taken as 0.005 kg / (m·s); F Darcy Darcy force, used to suppress flow in the solid region; For momentum source term;

[0111] 3.4 Energy Conservation Equation

[0112] ;

[0113] Where h is enthalpy; k is thermal conductivity; S e For energy source terms;

[0114] 3.5 Fluid Volume Function Equation

[0115] ;

[0116] Where α is the volume fraction, α = 1 indicates that the unit is filled with a metallic phase, α = 0 indicates that the unit is filled with a gas phase, and 0 < α < 1 indicates that the unit contains two-phase fluid.

[0117] 3.6 Equation of Simple Harmonic Motion of Ultrasonic Vibration

[0118] ;

[0119] Where x(t) is the vibration displacement at time t; A is the amplitude; ω is the angular frequency, ω=2πf, and f is the ultrasonic frequency in Hz; This is the initial phase;

[0120] The above-mentioned mass, momentum, energy conservation, fluid volume function equations and ultrasonic vibration simple harmonic motion equations are combined into a set of control equations and written into a UDF program through user-defined functions (UDF). The UDF program reads the current value and ultrasonic vibration parameters at the current time step in real time, calculates each source term and adds it to the corresponding equation. All equations constitute a complete numerical model of heat and mass transfer in ultrasonic-CMT-P arc molten pool.

[0121] Through the above steps, the final established ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model can accurately simulate the droplet transition, molten pool flow and heat conduction behavior in the ultrasonic vibration-assisted CMT-P arc additive manufacturing process, and output key results such as molten pool temperature field, velocity field and solid fraction distribution, providing theoretical support for sample quality prediction and process optimization.

[0122] Step 4: Based on the experimental conditions set in Step 1 and the two-dimensional geometric model established in Step 2, set the boundary conditions and initial conditions for the numerical model of heat and mass transfer in the ultrasonic-CMT-P arc molten pool to ensure that the simulation results match the actual situation.

[0123] 4.1 Boundary Condition Settings

[0124] like Figure 3 As shown, the two-dimensional geometric model contains the following boundaries, and the type and parameter settings of each boundary are as follows:

[0125] ⑤ Fuse domain inlet boundary conditions

[0126] The type is velocity inlet, located at the upper boundary of the molten wire domain; the wire feed speed is set to 6.2 m / min, and the direction is vertically downward; the timing of each stage of wire feeding and retraction corresponds to the CMT-P cycle in step 1; the initial temperature of the molten droplet is set to the liquidus temperature Tl = 1663 K, and the phase volume fraction α = 1;

[0127] ⑥ Protective gas domain inlet boundary conditions

[0128] The type is a velocity inlet, located on both sides of the fuse zone; the protective gas flow rate is set to 20 L / min; the temperature is set to ambient temperature Ta = 300 K, the phase volume fraction α = 0, and the gas composition is pure argon.

[0129] ⑦ Pressure outlet boundary conditions

[0130] It is a pressure outlet, located on both sides of the protective gas zone;

[0131] ⑧ Wall boundary conditions

[0132] The type is a wall, located at the bottom of the substrate domain and on both sides of the substrate domain;

[0133] 4.2 Initial Condition Settings

[0134] Initial temperature: The initial temperature of the entire computational domain is set to the ambient temperature Ta = 300 K;

[0135] Initial velocity: The initial velocity of the entire computational domain is set to 0 m / s;

[0136] Phase distribution: Fuse domain phase volume fraction α = 1, substrate domain phase volume fraction α = 1, protective gas domain phase volume fraction α = 0;

[0137] Solid-liquid phase state: Initially, all metallic phases are solid, and the liquid phase fraction f l = 0.

[0138] Step 5: By configuring the ANSYS Fluent solver parameters and loading the UDF program written in Step 3, and combining the boundary conditions and initial conditions set in Step 4, the ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model established in Step 3 is numerically solved to obtain the transient evolution results of the molten pool temperature field, velocity field and phase distribution.

[0139] 5.1 Solver and Model Configuration

[0140] Solver algorithm: A pressure-based solver is used, and the time term adopts a transient formula to capture the unsteady characteristics of droplet transition and molten pool evolution; the influence of gravitational acceleration is considered, and the gravitational acceleration is set to -9.8 m / s².

[0141] Multiphase flow model: Enable VOF model, set the main phase as argon gas and the secondary phase as liquid metal; enable surface tension model and define the surface tension coefficient as a function of temperature;

[0142] Dynamic mesh configuration: Layering method is used for mesh topology update, and splitting and folding factors are set; the filament domain is defined as a rigid motion region;

[0143] Discretization scheme and algorithm: Pressure discretization adopts the PRESTO scheme; momentum and energy equations adopt the second-order upwind scheme to ensure calculation accuracy; volume fraction equation adopts the Geo-Reconstruct scheme to ensure clear interface; pressure-velocity coupling adopts the PISO algorithm.

[0144] Time step control: To accurately analyze the periodic changes and high-frequency vibration characteristics of the heat source, the time step is set to Δt = 1 × 10⁻ 5 The maximum number of iterations per time step is set to 40 to meet the accuracy requirements for solving the rapid current changes and high-frequency ultrasonic vibrations during the CMT-P cycle.

[0145] 5.2 UDF Program Loading and Execution

[0146] The UDF program written in step 3 is compiled and loaded using the UDF manager of the ANSYS Fluent solver. This mainly includes: defining global variables and configuring the initial conditions of the computational domain by initializing the UDF; adding volume force source terms and energy source terms corresponding to the arc heat input through momentum source term UDF and energy source term UDF respectively; defining the rigid body motion of the filament domain through dynamic mesh UDF; and controlling the wire feeding and retraction actions according to the timing determined in step 1, thereby accurately simulating the influence of filament feeding on droplet detachment and transition process.

[0147] Step 6: Compare and verify the transient evolution results obtained in Step 5 with the samples obtained under the process parameters in Step 1. By quantifying the geometric characteristics of the molten pool, evaluate the accuracy and reliability of the established ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model.

[0148] like Figure 6 As shown, the verification results indicate that the relative error of the weld width is 4.1% and the relative error of the weld depth is 6.3%. All indicators meet the verification criteria, proving that the established ultrasonic-CMT-P arc weld pool heat and mass transfer numerical model can accurately describe the actual physical process and can be used for subsequent process mechanism analysis and parameter optimization research.

Claims

1. A numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc, characterized in that: The heat and mass transfer numerical simulation method includes the following steps performed in sequence: Step 1: Construct an arc additive manufacturing system for in-situ observation experiments. Under the set experimental conditions, use the system to conduct ultrasonic vibration-assisted CMT-P arc additive manufacturing experiments to obtain an ultrasonic-CMT-P composite process experimental dataset and samples containing electrical signal data, droplet transition images, microscopic morphology images of the molten pool region, and process parameter records. Step 2: Divide the above sample into regions to build a two-dimensional geometric model for numerical simulation. Then, divide all regions into quadrilateral meshes and set up dynamic meshes. Step 3: Based on the experimental dataset of the ultrasonic-CMT-P composite process obtained in Step 1, a set of control equations covering mass, momentum, energy conservation, fluid volume function equations and ultrasonic vibration simple harmonic motion equations is established using fluid dynamics methods and written into a UDF program through user-defined functions; then the ultrasonic vibration effect and the CMT-P electric arc heat source effect are coupled into the equations in the form of source terms to form a complete numerical model of heat and mass transfer in the ultrasonic-CMT-P electric arc molten pool. Step 4: Based on the experimental conditions set in Step 1 and the two-dimensional geometric model established in Step 2, set the boundary conditions and initial conditions for the numerical model of heat and mass transfer in the ultrasonic-CMT-P arc molten pool. Step 5: By configuring the ANSYS Fluent solver parameters and loading the UDF program written in Step 3, and combining the boundary conditions and initial conditions set in Step 4, the ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model established in Step 3 is numerically solved to obtain the transient evolution results of the molten pool temperature field, velocity field and phase distribution. Step 6: Compare and verify the transient evolution results obtained in Step 5 with the sample obtained under the process parameters in Step 1. By quantifying the geometric characteristics of the molten pool, evaluate the accuracy and reliability of the established ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model.

2. The numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc as described in claim 1, characterized in that: In step 1, the method for constructing an arc additive manufacturing system for in-situ observation experiments, and using this system to conduct ultrasonic vibration-assisted CMT-P arc additive manufacturing experiments under set experimental conditions, to obtain an ultrasonic-CMT-P composite process experimental dataset and samples containing electrical signal data, droplet transition images, microscopic morphology images of the molten pool region, and process parameter records, is as follows: The arc additive manufacturing system used for in-situ observation experiments includes a welding machine, a high-speed camera, a laser, an ultrasonic automatic frequency tracking digital system, an electrical signal acquisition device, an industrial computer, an industrial robot, and a pure argon protective gas supply system. The high-speed camera and laser are respectively mounted on opposite sides of the substrate. The ultrasonic amplitude rod on the ultrasonic automatic frequency tracking digital system is in close contact with one end of the substrate via a clamp. The industrial robot holds the welding torch on the welding machine and deposits the material according to a planned path. The welding machine is used to melt, feed, and retract the molten wire. The electrical signal acquisition device records electrical signal values, including current and voltage. The pure argon protective gas supply system ensures gas protection during the forming process. The industrial computer is electrically connected to the welding machine, high-speed camera, laser, ultrasonic automatic frequency tracking digital system, electrical signal acquisition device, industrial robot, and pure argon protective gas supply system to process all images and data, providing experimental basis for setting boundary conditions and verifying results for the numerical model described below. The substrate is fixed on the worktable; the process parameters for the experiment are set. During the experiment, under the control of an industrial computer, pure argon gas supplied by a pure argon protective gas supply system was used as the protective gas. An industrial robot was used to deposit the molten wire from the welding machine onto the substrate using a single-pass, single-layer deposition strategy. During this process, the ultrasonic amplitude rod on the ultrasonic automatic frequency tracking digital system effectively transmitted ultrasonic vibrations to the molten pool area. A highly focused beam was generated using a laser, and a high-speed camera was used to acquire images of the droplet transition form and the evolution of the molten pool morphology in real time. An electrical signal acquisition device was used to record electrical signal values, including current and voltage, thereby preparing the sample. Based on the above process parameters, the above samples were wire-cut and sampled. After inlaying, rough grinding, fine grinding and polishing, the microscopic morphology image of the molten pool area was captured under an optical microscope. The experimental dataset of ultrasonic-CMT-P composite process was composed of all electrical signal data, droplet transition images, molten pool morphology images and process parameter records.

3. The numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc as described in claim 1, characterized in that: In step 2, the method of dividing the above-mentioned sample into regions to build a two-dimensional geometric model for numerical simulation, and then dividing all regions into quadrilateral meshes and setting dynamic meshes, is as follows: The above sample was divided into a fuse domain, a substrate domain, and a protective gas domain bounded by the fuse boundary, thereby constructing a two-dimensional geometric model for numerical simulation. Each half of the sample was used as the substrate domain and the protective gas domain, respectively, and the fuse domain was located within the protective gas domain. Then, ANSYS ICEM software was used to divide all the above regions into quadrilateral meshes with a size of 0.5 mm. Considering the wire feeding and retraction actions in the CMT-P process, a moving mesh is set in the two-dimensional geometric model. The upper boundary of the wire domain is used as the velocity inlet. The moving mesh movement speed is set according to the wire feeding speed. The interface between the wire domain and the protective gas domain is set as the sliding mesh boundary to ensure the continuity of boundary conditions during mesh movement.

4. The numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc as described in claim 1, characterized in that: In step 3, based on the experimental dataset of the ultrasonic-CMT-P composite process obtained in step 1, a set of control equations covering mass, momentum, energy conservation, fluid volume function equations, and ultrasonic vibration simple harmonic motion equations is established using fluid dynamics methods and written into a UDF program through user-defined functions; then, the ultrasonic vibration effect and the CMT-P arc heat source effect are coupled into the equations as source terms to form a complete numerical model of heat and mass transfer in the ultrasonic-CMT-P arc molten pool. 3.1 Basic Assumptions ① The feeding and retraction of the molten wire are achieved using dynamic mesh technology. The inlet velocity of the molten droplet is determined based on the analysis of electrical signals and high-speed camera images. It is assumed that the molten droplet generation velocity is equal to the wire feeding velocity. ② Ignoring the arc plasma region, the effect of the arc on the molten droplet and the molten pool is loaded into the momentum equation and energy equation in the form of source terms; ③ Both the gas phase and the metallic phase are laminar, incompressible Newtonian fluids; ④ Heat and mass loss caused by metal vapor are not considered; ⑤ The amplitude of ultrasonic vibration remains constant in the substrate; 3.2 Mass Conservation Equation ; in, Density, kg / m³; t is the velocity vector, in m / s; t is time, in s; 3.3 Momentum Conservation Equation ; in, Pressure, Pa; For dynamic viscosity, Pa·s, the dynamic viscosity of liquid metal is taken as 0.005 kg / (m·s); F Darcy Darcy force, used to suppress flow in the solid region; For momentum source term; 3.4 Energy Conservation Equation ； Where h is enthalpy; k is thermal conductivity; S e For energy source terms; 3.5 Fluid Volume Function Equation ； Where α is the volume fraction, α = 1 indicates that the unit is filled with a metallic phase, α = 0 indicates that the unit is filled with a gas phase, and 0 < α < 1 indicates that the unit contains two-phase fluid. 3.6 Equation of Simple Harmonic Motion of Ultrasonic Vibration ； Where x(t) is the vibration displacement at time t; A is the amplitude; ω is the angular frequency, ω=2πf, and f is the ultrasonic frequency in Hz; This is the initial phase; The above-mentioned mass, momentum, energy conservation, fluid volume function equations and ultrasonic vibration simple harmonic motion equations are combined into a set of control equations and written into a UDF program through user-defined functions. The UDF program reads the current value and ultrasonic vibration parameters of the current time step in real time, calculates each source term and adds it to the corresponding equation. All equations constitute a complete numerical model of heat and mass transfer in ultrasonic-CMT-P arc molten pool.

5. The numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc as described in claim 1, characterized in that: In step 4, the method for setting the boundary and initial conditions for the ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model based on the experimental conditions set in step 1 and the two-dimensional geometric model established in step 2 is as follows: 4.1 Boundary Condition Settings The two-dimensional geometric model contains the following boundaries, and the types and parameter settings for each boundary are as follows: ① Boundary conditions at the entrance of the fused wire domain The type is velocity inlet, located at the upper boundary of the molten wire domain; the wire feeding speed and direction, the timing of each stage of wire feeding and retraction, the initial temperature of the molten droplet, and the phase volume fraction are set. ② Boundary conditions at the inlet of the protective gas domain The type is a velocity inlet, located on both sides of the fuse zone; the protective gas flow rate, temperature, phase volume fraction, and gas composition are set. ③ Pressure outlet boundary conditions It is a pressure outlet, located on both sides of the protective gas zone; ④ Wall boundary conditions The type is a wall, located at the bottom of the substrate domain and on both sides of the substrate domain; 4.2 Initial Condition Settings Set the initial temperature of the entire computational domain, the initial velocity of the entire computational domain, the phase volume fraction of the filament domain, the phase volume fraction of the substrate domain, and the phase volume fraction of the protective gas domain; solid-liquid phase state.

6. The numerical simulation method for heat and mass transfer under the synergy of ultrasonic vibration and CMT-P arc as described in claim 1, characterized in that: In step 5, the method for numerically solving the ultrasonic-CMT-P arc molten pool heat and mass transfer numerical model established in step 3 by configuring the ANSYS Fluent solver parameters, loading the UDF program written in step 3, and combining the boundary conditions and initial conditions set in step 4, to obtain the transient evolution results of the molten pool temperature field, velocity field, and phase distribution is as follows: 5.1 Solver and Model Configuration Solver algorithm: A pressure-based solver is used, and the time term adopts a transient formula to capture the unsteady characteristics of droplet transition and molten pool evolution; the influence of gravitational acceleration is considered, and the gravitational acceleration is set to -9.8 m / s². Multiphase flow model: Enable VOF model, set the main phase as argon gas and the secondary phase as liquid metal; enable surface tension model and define the surface tension coefficient as a function of temperature; Dynamic mesh configuration: Layering method is used for mesh topology update, and splitting and folding factors are set; the filament domain is defined as a rigid motion region; Discretization scheme and algorithm: Pressure discretization adopts the PRESTO scheme; momentum and energy equations adopt the second-order upwind scheme to ensure calculation accuracy; volume fraction equation adopts the Geo-Reconstruct scheme to ensure clear interface; pressure-velocity coupling adopts the PISO algorithm. Time step control: To accurately analyze the periodic changes and high-frequency vibration characteristics of the heat source, the time step is set to Δt = 1×10⁻ 5 The maximum number of iterations per time step is set to 40 to meet the accuracy requirements for solving the rapid current changes and high-frequency ultrasonic vibrations during the CMT-P cycle. 5.2 UDF Program Loading and Execution The UDF program written in step 3 is compiled and loaded using the UDF manager of the ANSYS Fluent solver. This mainly includes: Global variables are defined by initializing UDF and initial conditions of the computational domain are configured. Volume force source term and energy source term corresponding to arc heat input are added by momentum source term UDF and energy source term UDF respectively. Rigid body motion of the molten wire domain is defined by dynamic mesh UDF and the wire feeding and retraction actions are controlled according to the timing determined in step 1, so as to accurately simulate the influence of molten wire feeding on droplet detachment and transition process.

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