Simulation method for atomization process of external mixing type air nozzle

Abstract

The invention discloses an external mixing type air nozzle atomization process simulation method, which comprises a multi-scale atomization mathematical model and numerical simulation based on the multi-scale atomization mathematical model, the multi-scale atomization mathematical model divides a flow field component into a continuous phase and a dispersed phase based on an Euler-Lagrange coupling method, the Lagrange method is used for describing the movement of small-scale coating particles, and the numerical simulation is carried out based on the continuous phase and the dispersed phase. Establishing a big and small droplet identification conversion mechanism, and selecting Reynolds average simulation to establish a turbulence model; based on numerical simulation of a model, a geometric model is firstly constructed to generate a computational domain, a coordinate system is established, then a key region is divided and encrypted by using a hybrid grid, and simulation is performed by controlling the number of grids in combination with a dynamic adaptive technology. Direct and indirect verification experiments prove that the model is correct; the problems that an existing model is incomplete in description, poor in fidelity and low in calculation efficiency are solved, the time cost is saved, the simulation result is closer to reality, accurate data can be provided for analysis of the atomization phenomenon, and the spraying quality and the production efficiency are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of air spray atomization simulation, and in particular to a simulation method for an external-mix air nozzle atomization process. Background Art

[0002] Air spraying is widely used in industrial production, and numerical simulation of its entire process is crucial for verifying the rationality of spray parameter settings and spray gun trajectory planning in intelligent spraying. The physical process of air spraying mainly includes the paint atomization process and the spray film formation process. Currently, the numerical simulation methods for spray film formation are relatively mature, but the existing air impact paint atomization model has many problems. Existing multiphase flow modeling methods for air spray atomization processes mainly include simple engineering models and quasi-direct numerical simulation. Simple engineering models are empirical atomization models, such as the Rosin-Rammler distribution, Log-Normal distribution, and TAB (Taylor Analogy Breakup) model commonly used for droplet diameter distribution. These models have low computational complexity and are easy to couple with the spray flow field. However, due to oversimplification, their universality and accuracy are poor, human factors have a significant impact on the calculation results, and they can only describe the secondary breakup process of the paint. Quasi-direct numerical simulation uses interface capture technology to directly identify the liquid atomization process and can produce a fine atomization structure. However, the computational complexity increases dramatically with the increase in the number of paint droplets in the atomization flow field, and it is not suitable for variable parameter paint atomization simulation to verify the rationality of spray parameter settings. Summary of the Invention

[0003] In view of the above-mentioned defects in the prior art, the technical problem to be solved by the present invention is to provide a simulation method for the atomization process of an external mix air nozzle that can effectively solve the above-mentioned technical problems.

[0004] To achieve the above-mentioned purpose, the present invention provides a simulation method for the atomization process of an external mixing air nozzle, including atomization process modeling, a large liquid mass motion model of the paint, a paint particle motion model, an atomization flow field turbulence model and numerical simulation based on the established model; atomization process modeling: using a multi-scale numerical model method to process multiphase flow, and classifying different components in the flow field into continuous phase and discrete phase; selecting Reynolds average simulation to build a turbulence model to achieve effective simulation of the atomization process; large liquid mass motion model of the paint: using the fluid volume method based on the Euler method to track the gas-liquid interface, and describing the large liquid mass motion by solving related equations; incorporating surface tension into the momentum conservation equation, and calculating its effect on the large liquid mass motion based on the interface characteristics; paint particle motion model: using the Lagrangian method to describe the small-scale paint particle motion process, identifying droplets and dividing regions through algorithms, and screening conversion particles using numerical and physical standards; using the DPM model to establish a transmission model to predict the motion trajectory, considering multiple forces; using the Rayleigh-Taylor instability theory to describe the secondary breakup process and parameters; atomization flow field turbulence model: using Realizable The k-ε model calculates the gas-liquid two-phase turbulent motion and describes the turbulent characteristics through transport equations; numerical simulation based on the established model: construct a geometric model to generate the calculation domain and establish a coordinate system; use hybrid meshing and encrypt key areas, combined with dynamic adaptive technology to control the number of meshes; set gas-liquid two-phase parameters, environmental conditions and solution algorithms; obtain residual maps and spray mist shapes through simulation to analyze the atomization state and flow field stability.

[0005] Furthermore, the large liquid blob motion model of the coating is specifically: the fluid volume method based on the Euler method is used to capture the gas-liquid two-phase interface during the atomization process. In the VOF model transport equation, each variable and property parameter is determined by the volume fraction of each phase. The gas-liquid two-phase interface is tracked by solving the continuity equation of the volume fraction of the gas-liquid phase, and the mass conservation equation and momentum conservation equation of the gas-liquid two-phase flow are established at the same time; the surface tension of the coating is introduced into the momentum conservation equation through the source term. The surface tension is proportional to the average density, and its magnitude is related to the pressure and curvature radius factors on both sides of the interface. The influence of surface tension on the movement of large liquid blobs of coating is calculated by the formula.

[0006] Furthermore, the paint particle motion model is specifically as follows: for paint particles with small scale and small volume in the air spray atomization flow field, the Lagrangian method is used to model the particles, the nearest neighbor search algorithm is used to identify droplets, the parameter G is set to mark the grid cells, and the droplet area to be converted is divided; at the same time, numerical and physical standards are used to determine whether the droplets are converted into Lagrangian particles. The numerical standard is set according to the liquid volume limit, and the physical standard is set according to the sphericity of the droplets. Droplets that meet the standards are removed from the continuous phase described by the Euler method and converted into Lagrangian particles; a Lagrangian particle transport model is established based on the DPM model in CFD, and the motion trajectory of the droplets is predicted by solving the force balance equation of the particle phase in the Lagrangian reference frame. The resistance of the fluid to the droplets, the effect of gravity, and the force generated by rotation are taken into account to describe the force conditions of the paint droplets in the flow field;

[0007] The Rayleigh-Taylor instability theory is used to describe the secondary breakup process of droplets. The occurrence of secondary breakup of droplets and the particle size of broken droplets are predicted through the formula of surface wave growth frequency, wavelength and critical breakup time.

[0008] Furthermore, the turbulence model of the atomization flow field is specifically to use the Realizable k-ε model in the two-equation turbulence model to calculate the turbulent motion of the gas-liquid two-phase during the atomization process. This model modifies the turbulent dissipation rate equation based on the standard k-ε turbulence model, and describes the turbulent motion in the atomization flow field through the transport equation of turbulent kinetic energy k and turbulent dissipation rate ε. Compared with the standard k-ε turbulence model, the Realizable k-ε model uses the formula to calculate the turbulent eddy viscosity, where C μ It is no longer a constant, but a function related to the strain rate tensor, the average rotation rate, the system rotation angular velocity and the turbulence field (k and ε), which improves the simulation accuracy of the turbulence characteristics of the atomized flow field.

[0009] Furthermore, the numerical simulation based on the established model is specifically to construct a spray atomization geometric model, import the SpaceClaim component in the Fluent platform to generate a calculation domain, and the calculation domain includes the central atomization hole, auxiliary atomization hole, fan control hole and paint inlet hole, as well as the external flow field area, and establish the atomization cap coordinate system; the calculation domain is meshed using a polyhedron and hexahedron hybrid grid. At the same time, combined with the characteristics of the spray flow field during the atomization process, the two-phase inlet part, the gas-liquid jet intersection area and the liquid jet breakup physical quantity change area are locally meshed, and the dynamic adaptive mesh encryption technology is used to control the overall mesh number of the calculation domain; the gas phase is defined as the first phase and the liquid phase as the second phase, and the physical properties of the gas and liquid phases and the corresponding inlet conditions are set. The ambient pressure is set to one atmosphere and the gravitational acceleration is 9.8m / s 2 , using adaptive time step, the initial calculation time step is 1×10 -7s, the total calculation time of the numerical simulation is 5ms, the SIMPLEC algorithm is used to discretely solve the atomization flow control equation, the second-order upwind format is used for the convection terms in all flow equations and scalar equations, and the first-order implicit format is used for the transient terms; the iterative residual diagram of the numerical simulation of paint atomization is obtained through numerical simulation, and the spray mist shape when the atomization time is 5ms is obtained by displaying the isosurface with a paint volume fraction of 0.002. The results show that the paint has been preliminarily atomized at this time, part of the liquid paint is atomized into fine particles, and part exists in the form of discontinuous large liquid clumps. The particles on the central axis of the nozzle are denser than those on both sides, and the spray flow field within the calculation domain within a range of 30mm from the nozzle is stable.

[0010] Furthermore, in the paint large liquid mass motion model, in the VOF model transport equation, each variable and property parameter is shared by all phases and is determined by the volume fraction of each phase. The initial atomization process of air involves two phases, air and paint. The volume fractions of the air phase and the paint phase are defined as For any control volume in the atomization space, the tracking of the gas-liquid interface is accomplished by solving the continuity equation of the volume fraction of the gas-liquid phase. The continuity equation of the gas-liquid two-phase volume fraction and the constraints of the two-phase volume fraction for air spray are:

[0011]

[0012] Where t represents time (s); ρ g and ρ l Represent the density of air and paint respectively; v g and v l Represent the velocity vectors of the air phase and the coating phase respectively; S g and S l Represent the mass sources of the air phase and the coating phase respectively; mlg represents the mass transfer from the coating phase to the air phase; m gl Represents the mass transfer from the air phase to the coating phase;

[0013] According to the modeling assumption, there is no mass transfer or heat transfer between gas and liquid during the atomization process. Therefore, the atomization flow control equation only needs to establish the mass conservation equation and momentum conservation equation of the gas-liquid two-phase flow, which are:

[0014]

[0015] Where, ρ q and u represent the q-phase volume fraction, q-phase density, and q-phase velocity, respectively. When the subscript q is l or g, it represents the coating phase and air phase, respectively;

[0016] p represents the pressure of the two phases; σ is the dynamic viscosity; g represents the local acceleration of gravity; and f represents the source term generated by the surface tension σ. The surface tension of the coating is generated by the attraction between the molecules in the coating. It acts on the coating surface, balancing the radially inward attraction between the coating molecules and the radially outward pressure gradient force on the surface, maintaining the original state of the coating. In the VOF method, the surface tension is introduced into the momentum conservation equation as an original term. Considering the special characteristics of the surface tension that always flows along the surface of the liquid coating and considering only the force perpendicular to the interface, the following relationship exists:

[0017]

[0018] Where σ is the surface tension coefficient, p l and p g Respectively represent the pressure of the coating phase and the air phase on both sides of the interface, R l and R g They represent the curvature radius in the orthogonal direction of the interface between the coating phase and the air phase;

[0019] The interface curvature is defined based on the divergence of the unit normal vector, i.e.

[0020]

[0021] Where κ represents the curvature of the interface, Represents the unit normal vector, and its expression is

[0022] Where n represents the normal direction of the interface, and is the gradient of the volume fraction of the coating phase, that is,

[0023] According to the divergence theorem, the force on the surface can be expressed as a volume force, which is the source term of the momentum equation and has the following form:

[0024]

[0025] The atomization process involves only two fluid phases, air and paint.

[0026] Then, the formula becomes:

[0027] The formula shows that the surface tension source term is proportional to the average density ρ.

[0028] Furthermore, in the coating particle motion model, the volume, center of mass position and motion speed of the coating droplet are continuously updated during the identification process of the coating droplet. Numerical and physical standards are used to determine whether the droplet is converted into a Lagrangian particle. The numerical standard is set according to the liquid volume limit, and the critical volume V for conversion is determined. cri, the volume of all convertible droplets V tran Must not be greater than this value, that is:

[0029] The equivalent sphere radius Rcri is an integer multiple of the grid size Δx; the physical standard is set based on the sphericity of the droplet, that is:

[0030]

[0031] Among them, R max is the maximum distance from any point on the liquid structure to the center of mass, and α is usually a positive integer less than 5. Droplets that meet the above criteria will be removed from the continuous phase described by the Euler method and converted into Lagrangian particles. At the same time, the volume fraction of the coating phase in the grid of the area where these droplets are located is converted to 0, and the volume fraction of the gas phase is converted to 1, that is, At this time, the volume of the Lagrangian particle V p =∫ p dx, center of mass Movement speed

[0032] Furthermore, the Lagrangian particle transport model is established based on the DPM model in CFD. The motion trajectory of the droplet is predicted by solving the force balance equation of the particle phase in the Lagrangian reference frame. The force on the droplet in the flow field follows Newton's second law. According to the force analysis, the force balance state equation of the unit mass of the paint droplet is

[0033] Among them, m p Indicates the mass of the coating droplet; F p Indicates the force acting on the droplet, where only the resistance F of the fluid on the droplet is considered drag , gravity acts on gravitation and the force F generated by the rotation R ,Right now:

[0034] F p =F drag +F gravitation +F R

[0035] The resistance F encountered by the paint droplet during its movement drag , which is mainly caused by the relative motion of the fluid and the droplets in the flow field, and its expression is:

[0036] The gravitational force per unit mass of the droplet is:

[0037] The additional force F caused by the rotation of paint particles during the paint atomization process RIt is a component of its acceleration and affects the motion trajectory of particles in the atomization flow field. The rotational force F R Consists of Coriolis force and centripetal force effects:

[0038]

[0039] Where ω is the angular velocity of the droplet; ρ p is the density of the coating droplet; R p is the vector connecting the axis and the droplet position;

[0040] Furthermore, the Rayleigh-Taylor instability is a type of interfacial instability characterized by unstable waves generated by disturbances on the droplet surface caused by airflow or other droplet impacts. This unstable wave is also called a surface wave. As the surface wave develops along the flow of the paint droplet, its amplitude and wavelength also increase. When the surface wave reaches the critical breakup wavelength, the paint droplet undergoes secondary breakage.

[0041] According to the Rayleigh-Taylor instability theory, the growth frequency of the surface wave of the coating droplet can be expressed as:

[0042]

[0043] Where, Ω RT represents the maximum growth rate of surface waves; g m is the acceleration of the coating droplet in the direction of motion; the corresponding droplet surface wavelength can be obtained by the following formula:

[0044] Where C RT is the droplet breakup radius constant, which is set to 0.1;

[0045] The droplet breakup condition in the Rayleigh-Taylor instability theory is that the surface wave growth time exceeds the critical breakup time τ RT , critical crushing time τ RT and the particle size of the crushed droplets r c The expression is:

[0046] Where C τ represents the Rayleigh-Taylor breakup time constant, which is 0.5.

[0047] Furthermore, in the atomization flow field turbulence model, the gas-liquid turbulent motion of the atomization flow field is under the Euler framework.

[0048] The transport equations for turbulent kinetic energy k and turbulent dissipation rate ε in the Realizable k-ε model are expressed as follows:

[0049]

[0050] Where Gk represents the turbulent kinetic energy generation term caused by the mean velocity gradient,

[0051] G b is the term for turbulent kinetic energy generated by buoyancy,

[0052] Among them, Pr t is the turbulent Prandtl number, g i is the gravity vector in the i-th direction;

[0053] C 3ε is a constant that characterizes the influence of buoyancy on the turbulent dissipation rate. Where v represents the velocity component of the fluid in the direction of gravity, and u represents the velocity component of the fluid in the direction perpendicular to gravity;

[0054] σ k and σ ε are the Prandtl numbers representing the turbulent kinetic energy k and the turbulent dissipation rate ε, respectively;

[0055] Other constants:

[0056] C 1ε =1.44; C2=1.9; σ k =1.0;σ ε =1.2;

[0057] The Realizable k-ε model is calculated using the following formula:

[0058] Where C μ is no longer a constant, but is related to the strain rate tensor S ij and the average rotation rate System rotation angular velocity ω k And the functions related to the turbulence field (k and ε) are expressed as follows:

[0059] Where,

[0060] A0 and As are constants, A0=4.04, in,

[0061] The beneficial effects of the present invention are: the present invention effectively solves the problems of incomplete description of the atomization process of the existing model, poor simulation fidelity and low computational efficiency, saves a lot of time and cost for the intelligent spraying process, the simulation results are closer to the actual atomization process, provides more accurate data for analyzing the atomization phenomenon, and improves the spraying quality and production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a schematic diagram of the spray atomization process.

[0063] Figure 2 Schematic diagram of the recognition mechanism of droplets to be converted.

[0064] Figure 3 It is a structural diagram of the atomizing cap.

[0065] Figure 4 It is a schematic diagram of the cross-sectional dimensions of the atomizing cap.

[0066] Figure 5 It is a schematic diagram of the atomization calculation domain.

[0067] Figure 6 It is a schematic diagram of the coordinate system of the three-dimensional air cap model.

[0068] Figure 7 This is a schematic diagram of the mixed polyhedron-hexahedron grid computational domain division.

[0069] Figure 8 This is a schematic diagram of the gas and liquid inlet grid encryption.

[0070] Figure 9 This is a schematic diagram of the dynamic adaptive encryption effect of the XOZ plane grid.

[0071] Figure 10 This is a schematic diagram of the dynamic adaptive encryption effect of the YOZ plane grid.

[0072] Figure 11 This is a schematic diagram of the iterative residual of the numerical simulation of paint atomization.

[0073] Figure 12 It is a schematic diagram of XOZ plane fog shape.

[0074] Figure 13 This is a schematic diagram of the YOZ plane fog shape. DETAILED DESCRIPTION

[0075] like Figures 1 to 13 As shown, a simulation method for the atomization process of an external-mix air nozzle includes atomization process modeling, a large liquid mass motion model of the coating, a coating particle motion model, an atomization flow field turbulence model, and numerical simulation based on the established model;

[0076] Atomization process modeling: Multi-phase flow is processed using a multi-scale numerical model method, and different components in the flow field are classified into continuous and discrete phases. Reynolds average simulation is used to build a turbulence model to achieve effective simulation of the atomization process.

[0077] Coating large liquid blob motion model: Using the volume of fluid method based on the Euler method to track the gas-liquid interface, the motion of the large liquid blob is described by solving the relevant equations. Surface tension is incorporated into the momentum conservation equation, and its effect on the motion of the large liquid blob is calculated based on the interface characteristics.

[0078] Paint particle motion model: The Lagrangian method is used to describe the motion process of small-scale paint particles. Algorithms are used to identify droplets and divide them into regions. Numerical and physical criteria are used to screen and convert particles. The DPM model is used to establish a transmission model to predict the motion trajectory, considering various forces. The Rayleigh-Taylor instability theory is used to describe the secondary breakage process and parameters.

[0079] Atomization flow field turbulence model: The Realizable k-ε model is used to calculate the gas-liquid two-phase turbulent motion, and the turbulent characteristics are described by the transport equation;

[0080] Numerical simulation based on model establishment: Construct a geometric model to generate the computational domain and establish a coordinate system; use hybrid meshing and refine key areas, combining dynamic adaptive technology to control the number of meshes; set gas-liquid two-phase parameters, environmental conditions, and solution algorithms; obtain residual maps and spray mist shapes through simulation to analyze the atomization state and flow field stability;

[0081] The further modeling process is:

[0082] 1. Atomization process modeling

[0083] The paint atomization process is essentially a turbulent two-phase flow of gas and liquid. The mathematical model constructed in this paper comprises two core modules: a multiphase flow model and a turbulence model. A multiscale numerical modeling approach is employed to address the coexistence of air / liquid paint mixtures and discrete particles in the spray flow field. Separately modeling the continuous phase medium (air and liquid paint) and the discrete phase particles allows for a precise description of the gas-liquid interface dynamics while also balancing computational efficiency requirements. This effectively balances the inaccuracy of traditional engineering models with the computationally intensive nature of direct numerical simulations.

[0084] Turbulence modeling utilizes the Reynolds-averaged simulation (RANS) method, which offers significant advantages over direct numerical simulation and large eddy simulation: it is less sensitive to boundary conditions, requires relatively few computational resources, and performs well in complex flow regimes (such as separated and secondary flows). The Realizable k-ε model was specifically selected for its higher accuracy in predicting the diffusion rate of cylindrical liquids.

[0085] The model is built on two key assumptions: first, the non-Newtonian fluid coating is simplified to a Newtonian fluid model based on its low viscosity; second, given the millisecond-scale atomization duration, solvent evaporation and heat exchange processes are ignored. These simplifications significantly improve computational efficiency while maintaining model accuracy.

[0086] 2. Coating large liquid mass movement model

[0087] The large-volume paint motion model is used to simulate the large-scale gas-liquid two-phase motion during paint atomization, from the initial diffusion of the liquid paint into the gas phase to its atomization into paint particles by the air or its movement outside the atomization flow field. The simulation focuses on identifying the interface between the air and the paint. The volume-of-fluid (VOF) method, based on the Euler method, is used to capture the gas-liquid interface during atomization. This method, an interface tracking method within an Euler grid system, tracks the volume fraction of each fluid across the entire region by solving a set of momentum equations, thereby modeling the coupling of two or more fluids. The VOF method is primarily used for predicting atomization or jet breakup, bubble motion in liquids, and steady-state or transient tracking of any gas-liquid interface. The method must be used only when the two or more fluids do not mix. The air and liquid paint do not mix during air spray atomization, which falls within the scope of the VOF method.

[0088] (1) Control equation

[0089] In the VOF model transport equation, all variables and property parameters are shared by all phases and determined by the volume fraction of each phase. The initial air atomization process involves two phases, air and paint, with the volume fractions of the air phase and paint phase defined as . For any control volume in the atomization space, tracking the gas-liquid interface is accomplished by solving the continuity equation for the volume fraction of the gas-liquid phase. The continuity equation for the gas-liquid volume fraction of air spray and the constraints for the two-phase volume fraction are:

[0090]

[0091] Where t represents time (s), ρ g and ρ l Represents the density of air and paint (kg / m 3 ), v g and v l Represent the velocity vectors of the air phase and the coating phase (m / s), S g and S l Represent the mass sources of air phase and coating phase respectively, m lg Represents the mass transfer from the coating phase to the air phase; m gl Represents the mass transfer from the air phase to the coating phase.

[0092] According to the modeling assumption, there is no mass transfer or heat transfer between gas and liquid during the atomization process. Therefore, the atomization flow control equation only needs to establish the mass conservation equation and momentum conservation equation of the gas-liquid two-phase flow, which are:

[0093]

[0094] Where, ρ q and represent the q phase volume fraction and q phase density kg / m 3 ) and q phase velocity (m / s), when the subscript q is l or g, it represents the coating phase and air phase respectively; p represents the pressure of the two phases (N / m 2 ); is the dynamic viscosity (N·s / m 2 ); g represents the local acceleration of gravity (m / s 2 ) represents the source term generated by the surface tension σ.

[0095] (2) Surface tension

[0096] The surface tension of a coating is caused by the intermolecular attraction within the coating. It acts on the coating surface, balancing the radially inward intermolecular attraction and the radially outward pressure gradient on the surface, maintaining the coating's original state. In the VOF method, surface tension can be introduced into the momentum conservation equation (Equation 5) as an original term. Considering the special nature of surface tension, which always extends along the surface of the liquid coating and only considering forces perpendicular to the interface, the following relationship exists:

[0097]

[0098] Where σ is the surface tension coefficient (N / m), p l and p g Respectively represent the pressure of the coating phase and the air phase on both sides of the interface (Pa), R l and R g Respectively represent the curvature radius (m) in the direction perpendicular to the interface between the coating phase and the air phase.

[0099] The interface curvature is defined based on the divergence of the unit normal vector, i.e.

[0100]

[0101] Where κ represents the curvature of the interface, Represents the unit normal vector, and its expression is

[0102]

[0103] Where n represents the normal direction of the interface, and is the gradient of the volume fraction of the coating phase, that is,

[0104]

[0105] According to the divergence theorem, the force on the surface can be expressed as a volume force, which is the source term of the momentum equation and has the following form:

[0106]

[0107] The atomization process involves only two fluid phases, air and paint.

[0108] κ i =-κ j (Formula 11)

[0109]

[0110] Then, the formula (Formula 10) becomes:

[0111]

[0112] Formula (13) shows that the surface tension source term is proportional to the average density ρ.

[0113] 3. Paint particle motion model

[0114] For the small, volume-considered paint particles in the air spray atomization flow field, a computationally efficient Lagrangian method is used to model the particle motion by tracking information such as particle position and velocity. The paint particle motion model primarily includes the droplet recognition and conversion mechanism and the droplet transport model.

[0115] (1) Droplet recognition and conversion mechanism

[0116] The droplets generated during the atomization process must be identified, and only those that meet the size standards can be converted into discrete phase particles for tracking. The interaction between the gas and liquid phases mainly occurs at the gas-liquid interface. Therefore, the identification of the droplets to be converted starts from the gas-liquid interface. The core idea of ​​the droplet identification mechanism is the nearest neighbor search algorithm, such as Figure 2 shown.

[0117] First, set a parameter G to mark the grid cells at the gas-liquid interface: the grid containing the liquid phase, i.e. Marked as G=1 (yellow); the grid of pure gas phase, i.e. Marked as G = 0 (white). The continuous grid (G = 1) area will be divided into an independent unit, and the grids in all units are marked as G = 2 (red). At the same time, continue to search for its adjacent grids. If a grid (G = 1) is found, it will be divided into the same unit and marked as G = 2. When no grid with the mark G = 1 is found, the search is stopped. All areas in the computational domain are marked and divided using the above search method. The grid contained in each unit represents the liquid area to be converted into Lagrangian particles.

[0118] During the identification process of the paint droplet, the volume, center of mass position and movement speed of the droplet are continuously updated, and numerical and physical criteria are used to determine whether the droplet is converted into a Lagrangian particle. Among them, the numerical criteria are set according to the liquid volume limit, and the critical volume V for conversion is determined. cri , the volume of all convertible droplets V tran Must not be greater than this value, that is:

[0119]

[0120] Among them, the equivalent sphere radius R cri is an integer multiple of the grid size Δx.

[0121] The physical standard is based on the sphericity of the droplet, namely:

[0122]

[0123] Among them, R max It is the maximum distance from any point on the liquid structure to the center of mass, and α is usually a positive integer less than 5.

[0124] The droplets that meet the above criteria will be removed from the continuous phase described by the Euler method and converted into Lagrangian particles. At the same time, the volume fraction of the coating phase in the grid of the area where these droplets are located is converted to 0, and the volume fraction of the gas phase is converted to 1, that is, At this time, the volume of the Lagrangian particle V p =∫ p dx, center of mass Movement speed

[0125] (2) Lagrangian particle transport model

[0126] The Lagrangian particle transport model is based on the DPM model in CFD. It mainly predicts the motion trajectory of the droplet by solving the force balance equation of the particle phase in the Lagrangian reference frame. The force on the droplet in the flow field follows Newton's second law. According to the force analysis, the force balance state equation of the unit mass of the paint droplet is:

[0127]

[0128] In, m p Indicates the mass of coating droplets (kg / s); F p Indicates the force acting on the droplet (N), where only the resistance F of the fluid on the droplet is considered drag , gravity F gravitation and the force F generated by the rotation R ,Right now:

[0129] F p =F drag+F gravitation +F R (Formula 17)

[0130] The resistance F encountered by the paint droplet during its movement drag , which is mainly caused by the relative motion of the fluid and the droplets in the flow field, and its expression is:

[0131]

[0132] The gravitational force per unit mass of the droplet is:

[0133]

[0134] The additional force F caused by the rotation of paint particles during the paint atomization process R It is a component of its acceleration and has a significant impact on the motion trajectory of particles in the atomization flow field. R Consists of Coriolis force and centripetal force effects:

[0135]

[0136] Where ω is the angular velocity of the droplet (rad / s); is the density of the coating droplet (kg / m 3 );R p is the vector connecting the axis and the droplet position.

[0137] (3) Secondary crushing model

[0138] In a spray flow field, large droplets produced by primary atomization are in a non-steady state. Under the continuous impact of high-speed airflow and surrounding moving fluid, they undergo secondary breakup. This secondary breakup mechanism plays a key role in improving liquid atomization and enhancing gas-liquid mixing efficiency. The dynamics of this process can be described using the Rayleigh-Taylor instability theory.

[0139] Rayleigh-Taylor instability is a typical interfacial instability phenomenon, manifesting as disturbance waves generated on the surface of a droplet by the impact of external airflow or other droplets. These wave characteristics are defined as surface waves. As the droplet flows, the amplitude and wavelength of the surface waves show a continuous growth trend. When the fluctuation parameters reach a critical breakup threshold, the droplet undergoes a structural secondary breakup process.

[0140] According to the Rayleigh-Taylor instability theory, the growth frequency of the surface wave of the coating droplet can be expressed as:

[0141]

[0142] Where, Ω RT represents the maximum growth rate of surface waves; g m is the acceleration of the coating droplet in the direction of motion, (m / s2 ); the corresponding droplet surface wavelength can be obtained by the following formula:

[0143]

[0144] Where C RT is the droplet breakup radius constant, which is generally taken as 0.1.

[0145] The droplet breakup condition in the Rayleigh-Taylor instability theory is that the surface wave growth time exceeds the critical breakup time τ RT , critical crushing time τ RT and the particle size of the crushed droplets r c The expression is:

[0146]

[0147] Where C τ Represents the Rayleigh-Taylor breakup time constant, which is typically 0.5.

[0148] 4. Turbulence model of atomization flow field

[0149] The Realizable k-ε model, a two-equation turbulence model, is used to calculate the turbulent motion of the gas-liquid phase during the atomization process. This model modifies the turbulent dissipation rate equation based on the standard k-ε turbulence model, effectively resolving the anomaly in the cylindrical jet dissipation rate found in other k-ε turbulence models. Because the atomization process of air spray paint is a complex cylindrical jet behavior, the Realizable k-ε model is a more appropriate description of its turbulent motion.

[0150] (1) Turbulent transport equation

[0151] In the gas-liquid turbulent motion of the atomized flow field under the Euler framework, the transport equations of turbulent kinetic energy k and turbulent dissipation rate ε in the Realizable k-εε model are expressed as follows:

[0152]

[0153] Where G k represents the turbulent kinetic energy generation term caused by the mean velocity gradient,

[0154] G b is the term for turbulent kinetic energy generated by buoyancy, Among them, Pr t is the turbulent Prandtl number, g i is the gravity vector in the i-th direction;

[0155] C 3ε is a constant that characterizes the influence of buoyancy on the turbulent dissipation rate. Where v represents the velocity component of the fluid in the direction of gravity, and u represents the velocity component of the fluid in the direction perpendicular to gravity;

[0156] σ k and σ ε The Prandtl number represents the turbulent kinetic energy k and the turbulent dissipation rate ε respectively;

[0157] Other constants: C2=1.9;σ k =1.0;C 1ε =1.44;σ ε =1.2

[0158] (2) Turbulent eddy viscosity modeling

[0159] Compared with the standard k-ε turbulence model, the Realizable k-ε model uses the following formula for calculation:

[0160]

[0161] Where C μ is no longer a constant, but is related to the strain rate tensor S ij and the average rotation rate System rotation angular velocity ω k And the functions related to the turbulence field (k and ε) are expressed as follows:

[0162]

[0163] Where,

[0164] A0 and A s is a constant, A0=4.04, in,

[0165] The numerical simulation based on the established model is as follows:

[0166] 5. Numerical simulation of air spray atomization

[0167] (1) Computational domain settings

[0168] The fluid computational domain is used to define the calculation range for spray atomization simulations and is generated from the paint atomization geometry model. Thermal analysis of air spray atomization characteristics aims to analyze the paint atomization characteristics during static spraying. The spray atomization geometry model is primarily considered for the air spray gun structure and the external flow field region. To maximize computational resources, the geometry model can be simplified to generate the smallest and most efficient numerical simulation domain possible. Non-atomizing structures or regions within the geometry model can be simplified. For example, only the atomizer cap structure needs to be retained within the spray gun structure, and the external flow field range can be adjusted as needed.

[0169] This embodiment uses the Japanese Iwata W-71 paint spray gun, and its atomizing cap 3D model and cross-sectional view can be seen Figure 3 and Figure 4 The center of the atomizer cap is the paint inlet hole, and the circular ring concentric with the paint inlet hole is the central atomizer hole. Two auxiliary atomizer holes are arranged on both sides of the central atomizer hole. A fan-shaped control hole is set on the trumpet mouth on both sides of the atomizer cap. For specific size parameters, see Table (1) Atomizer Cap Size Parameters;

[0170] Table 1-Dimension parameter of air cap

[0171] Table (1) Atomizer Cap Dimensions

[0172]

[0173]

[0174] Import the established paint atomization geometry model into the SpaceClaim component in the Fluent platform to generate the calculation domain, such as Figure 5 As shown in the figure, the top surfaces of the small cylinders in the upper part of the calculation domain represent the gas and liquid inlet holes such as the central atomization hole, auxiliary atomization hole, fan control hole and paint inlet hole. The surface in contact with the cylinder represents the surface of the atomization cap. The rest is the external flow field area. The bottom radius of the external flow field area is 12mm and the length is 50mm. In order to facilitate the description of the numerical simulation results, the atomization cap coordinate system is established as follows: Figure 6 As shown, the center of the bottom surface of the atomizing cap is taken as the coordinate origin, which is located at the center of the paint outlet hole; the X direction is defined as the short axis direction of the spray flow field, and the Y direction is defined as the long axis direction of the spray flow field.

[0175] (2) Computational grid division

[0176] Meshing is a very important step in numerical simulation. This step is to discretize the atomized fluid domain into grid units. By solving all grid nodes, the flow field information at different times and spaces can be obtained. Therefore, the grid has a direct impact on the simulation results. The computational meshing of air spray atomization numerical simulation focuses on the following two aspects:

[0177] First, select the appropriate grid type according to the geometric characteristics of the simulation domain. The grids used in CFD calculations can be divided into structured grids, unstructured grids, and hybrid grids according to the topological structure rules. Structured grids have the characteristics of small calculation scale, high calculation accuracy, and fast calculation convergence speed, but the geometric characteristics of the nozzle are relatively complex, and it is very difficult to divide it into high-quality hexahedral grids; unstructured grids have strong applicability and can quickly generate body-fitting grids in geometric models of any shape, but the accuracy of the description of the actual scene is relatively poor, which is not conducive to high-precision numerical simulation; hybrid grids use unstructured grid division for the external area and structured grid division for the internal area, which fully utilizes the advantages of the first two.

[0178] In view of the high irregularity of the boundary of the atomized geometric model and the need for high-quality meshes for atomization simulation, a hybrid mesh is used in the computational domain. Currently, the hybrid meshes available in CFD include tetrahedron and hexahedron hybrid meshes and polyhedron and hexahedron hybrid meshes, such as Figure 7 In the specific implementation process, according to the needs, the hybrid grid of polyhedron and hexahedron (hexahedron core grid) is selected to mesh the computational domain.

[0179] Secondly, considering the characteristics of the spray flow field during the atomization process, local mesh encryption is used for sensitive areas to ensure that the mesh direction is consistent with the flow direction. CFD calculations have special requirements for computational meshes. For example, the near-wall viscosity effect requires a denser body-fitting mesh, and the mesh size and quality requirements are higher in areas where the flow field gradient changes greatly. High-quality meshes are necessary to obtain high-fidelity results, and the consistency of the mesh direction and the flow direction is beneficial to reducing discrete errors. Therefore, when dividing the mesh into the computational domain of the atomization numerical simulation, it is necessary to encrypt the areas where the physical quantities change dramatically, such as the two-phase inlet, the gas-liquid jet intersection area, and the liquid jet breakup, to ensure that the mesh direction is basically consistent with the fluid movement direction. Figure 8 This is a schematic diagram of the gas and liquid inlet encryption.

[0180] As the number of computational grids increases, computational costs increase significantly. Furthermore, computational accuracy is not absolutely positively correlated with the number of grids. Furthermore, the spatial state of the atomized flow field changes rapidly, and the characteristics of these changes vary from region to region. Sometimes, the physical quantities of the fluid in the atomized region fluctuate dramatically, while other regions remain relatively stable. Therefore, dynamic adaptive mesh refinement (DAM) is employed to control the overall number of grids in the computational domain while ensuring that local grid sizes meet accuracy requirements, maximizing computational efficiency.

[0181] During the numerical simulation, meshes containing more than 5% of the coating volume fraction are adaptively encrypted. The encryption level is level 3 and the encryption frequency is once every 3 time steps. Particles with a volume less than 10-16m3 are automatically discarded. The dynamic adaptive encryption effect is as follows: Figure 9 and Figure 10 As shown in the figure, they are the dynamic adaptive encryption effect diagrams of XOZ plane and YOZ plane grid. Figure 9 and Figure 10 It can be seen that there are three levels of mesh refinement in the area where the coating liquid column and coating droplet are located, which are regarded as the continuous phase during the numerical simulation.

[0182] (3) Solution conditions and solver settings

[0183] The atomization process of paint subjected to air impact involves two phases: gas and liquid. The gas phase is defined as the primary phase, and the liquid phase as the secondary phase. Air is the gas phase material. The physical properties of the paint are measured using instruments such as a density meter, viscosity cup, and surface tension meter. The physical properties of the gas and liquid phases and their corresponding inlet conditions are shown in Table 2.

[0184] Table 2: Gas-liquid two-phase physical parameters and corresponding inlet conditions

[0185]

[0186] The ambient pressure is set to one atmosphere and the acceleration due to gravity is 9.8 m / s 2 , using adaptive time step, the initial calculation time step is 1×10 -7 s, and the total numerical simulation time is 5ms. The SIMPLEC algorithm is used to discretize the atomization flow control equations. The second-order upwind scheme is used for the convection terms in all flow equations and scalar equations, and the first-order implicit scheme is used for the transient terms.

[0187] (4) Numerical simulation results

[0188] Figure 11 This is the iterative residual plot for the paint atomization numerical simulation, demonstrating good convergence throughout the simulation. The simulation was powered by an Intel Xeon(R) Gold 6242 CPU. Using 60 CPU cores to compute a single example of multi-scale paint atomization numerical simulation took approximately 54 hours. Simulating the same paint atomization process using an atomization model based on the Euler-Euler method took approximately 150 hours, a reduction of approximately two-thirds.

[0189] When post-processing the calculation results, by displaying the isosurface with a coating volume fraction of 0.002, the spray shape when the atomization time is 5ms can be obtained, as shown in the following example: Figure 12 and Figure 13 As shown in the figure. The continuous phase paint is shown in blue, and the discrete phase paint is displayed as black particles at actual scale. The display range is the entire calculation domain (Z = 50mm). It can be seen that at the atomization time formula of 5ms, the paint has been initially atomized by the high-speed air ejected from the central atomization hole, auxiliary atomization holes, and fan control holes. Within the calculated spray flow field, part of the liquid paint is atomized into fine particles, while part exists in the form of discontinuous large liquid clumps. The particles are denser on the center axis of the nozzle than on both sides. The dynamic image of the paint volume fraction in the numerical simulation results shows that the spray flow field within 30mm of the nozzle in the calculation domain is basically stable at this time.

[0190] The present invention also includes numerical simulation verification, which is a key link to ensure the reliability of numerical simulation and is mainly carried out through two aspects: grid independence test and experimental verification.

[0191] Mesh independence test: Numerical simulation results are affected by meshing. Analysis of mesh parameters for different mesh sizes revealed that varying the mesh size between 0.1 and 0.5 mm increases the number of meshes and the average quality, while minimizing the change in minimum orthogonal quality. Simulations using velocity changes in the flow field as a metric indicate that for mesh sizes ≤ 0.2 mm, simulation results are unaffected by mesh quality and number, leading to the selection of 0.2 mm as the optimal mesh length.

[0192] Experimental verification: A combination of direct and indirect experimental methods is used. Direct verification includes verification of the paint atomization morphology and particle size; indirect verification is carried out through spray film formation experiments and numerical simulation to compare the coating film thickness.

[0193] Verification of paint atomization morphology: The spray flow field shape was photographed with a high-speed camera and compared with the simulation results. The measured mist shape after processing was consistent with the simulation results. However, the inside of the measured mist shape was denser, mainly due to the limitations of the optical equipment and the neglect of some tiny particles in the simulation.

[0194] Verification of paint atomized particle size: Particle size was measured using a particle size analyzer and compared with simulation results. This confirmed that the spray was completely atomized at an axial extension of 27.5 mm. Areas less than 30 mm from the nozzle axis were considered incompletely atomized, while those greater than 30 mm were considered fully atomized. While there were discrepancies between the simulation and experimental results in different particle size ranges, they were generally within acceptable limits.

[0195] Verification of spray film formation: First, numerical simulations of spray film formation were performed, followed by experimental spray film formation. Finally, the film thickness results were compared. The results showed good agreement between the simulated and experimental film thickness trends. However, the experimental film exhibited uneven distribution, with thickness being lower in the center and higher at the sides. This was primarily due to factors such as drying and curing, as well as the position of the spray needle. Overall, the numerical simulations and experiments were highly consistent in many respects, confirming the accuracy of the established atomization mathematical model and numerical simulations.

[0196] This paper establishes a numerical simulation process for air spray paint atomization and completes the simulation, validating the model and simulation through experiments. The simulation process optimizes the computational domain, rationally divides the grid, performs local encryption, and employs adaptive techniques. The verification process determines the optimal grid size and completes direct and indirect experimental verification.

Claims

1. A simulation method for the atomization process of an external mix air nozzle, characterized in that: Including atomization process modeling, paint large liquid mass motion model, paint particle motion model, atomization flow field turbulence model and numerical simulation based on the established model; Atomization process modeling: Multi-phase flow is processed using a multi-scale numerical model method, and different components in the flow field are classified into continuous and discrete phases. Reynolds average simulation is used to build a turbulence model to achieve effective simulation of the atomization process. Coating large liquid blob motion model: The air-liquid interface is tracked using the fluid volume method based on the Euler method, and the motion of the large liquid blob is described by solving the relevant equations; Incorporate surface tension into the momentum conservation equation and calculate its effect on the motion of large liquid masses based on the interface characteristics; Paint particle motion model: The Lagrangian method is used to describe the motion process of small-scale paint particles. Algorithms are used to identify droplets and divide them into regions. Numerical and physical criteria are used to screen and convert particles. The DPM model is used to establish a transmission model to predict the motion trajectory, considering various forces. The Rayleigh-Taylor instability theory is used to describe the secondary breakage process and parameters. Atomization flow field turbulence model: The Realizable k-ε model is used to calculate the gas-liquid two-phase turbulent motion, and the turbulent characteristics are described by the transport equation; Numerical simulation based on model establishment: Construct a geometric model to generate the computational domain and establish a coordinate system; use hybrid meshing and encrypt key areas, combining dynamic adaptive technology to control the number of meshes; set gas-liquid two-phase parameters, environmental conditions, and solution algorithms; obtain residual maps and spray mist shapes through simulation to analyze the atomization state and flow field stability.

2. The method for simulating the atomization process of an external-mix air nozzle according to claim 1, wherein: Specifically, the large liquid mass motion model of the coating uses a volume of fluid method based on the Euler method to capture the gas-liquid interface during the atomization process. In the VOF model transport equation, each variable and property parameter is determined by the volume fraction of each phase. The gas-liquid interface is tracked by solving the continuity equation of the volume fraction of the gas-liquid phase, and the mass conservation equation and momentum conservation equation of the gas-liquid two-phase flow are established at the same time. The surface tension of the coating is introduced into the momentum conservation equation as a source term. The surface tension is proportional to the average density, and its magnitude is related to the pressure and curvature radius on both sides of the interface. The influence of surface tension on the movement of large liquid clumps of coating is calculated by the formula.

3. The method for simulating the atomization process of an external mix air nozzle according to claim 2, wherein: Specifically, the paint particle motion model uses the Lagrangian method to model small-scale paint particles with a small volume share in the air spray atomization flow field. Droplets are identified through a nearest neighbor search algorithm, and the parameter G is set to mark grid cells to divide the droplet area to be converted. At the same time, numerical and physical standards are used to determine whether the droplets are converted into Lagrangian particles. The numerical standard is set according to the liquid volume limit, and the physical standard is set according to the sphericity of the droplets. Droplets that meet the standards are removed from the continuous phase described by the Euler method and converted into Lagrangian particles. A Lagrangian particle transport model is established based on the DPM model in CFD. The droplet trajectory is predicted by solving the force balance equation of the particle phase in the Lagrangian reference frame. The force acting on the paint droplet in the flow field is described by considering the fluid resistance, gravity, and the force generated by rotation. The Rayleigh-Taylor instability theory is used to describe the secondary breakup process of droplets. The occurrence of secondary breakup of droplets and the particle size of broken droplets are predicted through the formula of surface wave growth frequency, wavelength and critical breakup time.

4. The method for simulating the atomization process of an external mix air nozzle according to claim 3, wherein: Specifically, the atomization flow field turbulence model uses the Realizable k-ε model in the two-equation turbulence model to calculate the turbulent motion of the gas-liquid two-phase during the atomization process. This model modifies the turbulent dissipation rate equation based on the standard k-ε turbulence model and describes the turbulent motion in the atomization flow field through the transport equations of turbulent kinetic energy k and turbulent dissipation rate ε. Compared with the standard k-ε turbulence model, the Realizable k-ε model uses the formula to calculate the turbulent eddy viscosity, where C μ It is no longer a constant, but a function related to the strain rate tensor, the average rotation rate, the system rotation angular velocity and the turbulence field (k and ε), which improves the simulation accuracy of the turbulence characteristics of the atomized flow field.

5. The method for simulating the atomization process of an external mix air nozzle according to claim 4, wherein: The numerical simulation based on the established model specifically involves constructing a spray atomization geometric model and importing the SpaceClaim component in the Fluent platform to generate a calculation domain. The calculation domain includes the central atomization hole, auxiliary atomization holes, fan control holes and paint inlet holes, as well as the external flow field area, and establishes the atomization cap coordinate system. The computational domain is meshed using a hybrid grid of polyhedrons and hexahedrons. Taking into account the characteristics of the spray flow field during atomization, local mesh refinement is performed at the two-phase inlet, the gas-liquid jet intersection, and the region where the liquid jet breakup physical quantity changes. Dynamic adaptive mesh refinement technology is used to control the overall mesh size in the computational domain. Define the gas phase as the first phase and the liquid phase as the second phase, set the physical properties of the gas and liquid phases and the corresponding inlet conditions, set the ambient pressure to one atmosphere, and the gravitational acceleration to 9.8m / s 2 , using adaptive time step, the initial calculation time step is 1×10 -7 s, the total numerical simulation calculation time is 5ms, the SIMPLEC algorithm is used to discretely solve the atomization flow control equations, the second-order upwind scheme is used for the convection terms in all flow equations and scalar equations, and the first-order implicit scheme is used for the transient terms; The iterative residual diagram of the numerical simulation of paint atomization is obtained through numerical simulation. By displaying the isosurface with a paint volume fraction of 0.002, the spray mist shape when the atomization time is 5ms is obtained. The results show that the paint has been preliminarily atomized at this time. Part of the liquid paint is atomized into fine particles, and part exists in the form of discontinuous large liquid clumps. The particles on the central axis of the nozzle are denser than those on both sides, and the spray flow field within the calculation domain within 30mm away from the nozzle is stable.

6. The method for simulating the atomization process of an external mix air nozzle according to claim 5, wherein: In the paint large liquid mass motion model, in the VOF model transport equation, each variable and property parameter is shared by all phases and is determined by the volume fraction of each phase. The initial atomization process of air involves two phases, air and paint. The volume fractions of the air phase and the paint phase are defined as For any control volume in the atomization space, the tracking of the gas-liquid interface is accomplished by solving the continuity equation of the volume fraction of the gas-liquid phase. The continuity equation of the gas-liquid two-phase volume fraction and the constraints of the two-phase volume fraction for air spray are: Where, t represents time (s); ρ g and ρ l Represent the density of air and paint respectively; v g and v l represent the velocity vectors of the air phase and the coating phase respectively; S g and S l represent the mass sources of air phase and coating phase respectively; m lg Represents the mass transfer from the coating phase to the air phase; m gl Represents the mass transfer from the air phase to the coating phase; According to the modeling assumption, there is no mass transfer or heat transfer between gas and liquid during the atomization process. Therefore, the atomization flow control equation only needs to establish the mass conservation equation and momentum conservation equation of the gas-liquid two-phase flow, which are: Where, ρ q and u represent the q-phase volume fraction, q-phase density, and q-phase velocity, respectively. When the subscript q is l or g, it represents the coating phase and air phase, respectively; p represents the pressure of the two phases acting together; p is the dynamic viscosity; g represents the local acceleration of gravity; f represents the source phase generated by the surface tension σ; The surface tension of a coating is caused by the attraction between molecules in the coating. It acts on the coating surface, balancing the radially inward attraction between the coating molecules and the radially outward pressure gradient force on the surface, maintaining the original state of the coating. In the VOF method, surface tension is introduced into the momentum conservation equation as an original term. Considering the special characteristics of surface tension that always extends along the surface of the liquid coating and considering only the force perpendicular to the interface, the following relationship exists: Where σ is the surface tension coefficient, p l and p g Respectively represent the pressure of the coating phase and the air phase on both sides of the interface, R l and R g They represent the curvature radius in the orthogonal direction of the interface between the coating phase and the air phase; The interface curvature is defined based on the divergence of the unit normal vector, i.e. Where κ represents the curvature of the interface, Represents the unit normal vector, and its expression is Where n represents the normal direction of the interface, and is the gradient of the volume fraction of the coating phase, that is, According to the divergence theorem, the force on the surface can be expressed as a volume force, which is the source term of the momentum equation and has the following form: The atomization process involves only two fluid phases, air and paint. k i =-k j Then, the formula becomes: The formula shows that the surface tension source term is proportional to the average density ρ.

7. The method for simulating the atomization process of an external mix air nozzle according to claim 6, wherein: In the coating particle motion model, the volume, center of mass position, and velocity of the droplet are continuously updated during the identification process of the coating droplet. Numerical and physical criteria are used to determine whether the droplet is converted into a Lagrangian particle. The numerical criteria are set according to the liquid volume limit, and the critical volume V for conversion is determined. cri , the volume of all convertible droplets V tran Must not be greater than this value, that is: Among them, the equivalent sphere radius R cri is an integer multiple of the grid size Δx. The physical standard is based on the sphericity of the droplet, namely: Among them, R max It is the maximum distance from any point on the liquid structure to the center of mass, and α is usually a positive integer less than 5; The droplets that meet the above criteria will be removed from the continuous phase described by the Euler method and converted into Lagrangian particles. At the same time, the volume fraction of the coating phase in the grid of the area where these droplets are located is converted to 0, and the volume fraction of the gas phase is converted to 1, that is, At this time, the volume of the Lagrangian particle V p =∫ p dx, center of mass Movement speed 8. The method for simulating the atomization process of an external mix air nozzle according to claim 7, wherein: The Lagrangian particle transport model is based on the DPM model in CFD. The motion trajectory of the droplet is predicted by solving the force balance equation of the particle phase in the Lagrangian reference frame. The force on the droplet in the flow field follows Newton's second law. According to the force analysis, the force balance state equation of the unit mass of the paint droplet is: Among them, m p Indicates the mass of coating droplets (kg / s); F p Indicates the force acting on the droplet (N), where only the drag force Fdrag and gravity F are considered. gravitation and the force F generated by the rotation R ,Right now: F p =F drag +F gravitation +F R The resistance F encountered by the paint droplet during its movement drag , which is mainly caused by the relative motion of the fluid and the droplets in the flow field, and its expression is: The gravitational force per unit mass of the droplet is: The additional force F caused by the rotation of paint particles during the paint atomization process R It is a component of its acceleration and affects the motion trajectory of particles in the atomization flow field. The rotational force F R Consists of Coriolis force and centripetal force effects: Where ω is the angular velocity of the droplet; ρ p is the density of the coating droplet; R p is the vector connecting the axis and the droplet position.

9. The method for simulating the atomization process of an external mix air nozzle according to claim 8, wherein: Rayleigh-Taylor instability is a type of interfacial instability characterized by unstable waves generated by disturbances on the droplet surface caused by airflow or other droplet impacts. These unstable waves are also called surface waves. As the surface waves develop along the flow of the paint droplet, their amplitude and wavelength continue to grow. When the surface waves reach the critical breakup wavelength, the paint droplet undergoes secondary breakage. According to the Rayleigh-Taylor instability theory, the growth frequency of the surface wave of the coating droplet can be expressed as: Where, Ω RT represents the maximum growth rate of surface waves; g m is the acceleration of the coating droplet in the direction of motion; the corresponding droplet surface wavelength can be obtained by the following formula: Where C RT is the droplet breakup radius constant, which is set to 0.1; The droplet breakup condition in the Rayleigh-Taylor instability theory is that the surface wave growth time exceeds the critical breakup time τ RT , critical crushing time τ RT and the particle size of the crushed droplets r c The expression is: Where C τ represents the Rayleigh-Taylor breakup time constant, which is 0.

5.

10. The method for simulating the atomization process of an external mix air nozzle according to claim 9, wherein: In the atomization flow field turbulence model, the gas-liquid turbulent motion of the atomization flow field is carried out under the Euler framework. The transport equations for turbulent kinetic energy k and turbulent dissipation rate ε in the Realizable k-ε model are expressed as follows: Where G k represents the turbulent kinetic energy generation term caused by the mean velocity gradient, G b is the term for turbulent kinetic energy generated by buoyancy, Among them, Pr t is the turbulent Prandtl number, g i is the gravity vector in the i-th direction; C 3ε is a constant that characterizes the influence of buoyancy on the turbulent dissipation rate. Where v represents the velocity component of the fluid in the direction of gravity, and u represents the velocity component of the fluid in the direction perpendicular to gravity; σ k and σ ε are the Prandtl numbers representing the turbulent kinetic energy k and the turbulent dissipation rate ε, respectively; Other constants: C 1ε =1.44; C2=1.9; σ k =1.0;σ ε =1.2; The Realizable k-ε model is calculated using the following formula: Where C μ is no longer a constant, but is related to the strain rate tensor S ij and the average rotation rate System rotation angular velocity ω k And the functions related to the turbulence field (k and ε) are expressed as follows: Where, A0 and A s is a constant, A0=4.04, in,

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