Airfoil surface air spraying numerical simulation method based on CFD-DEM bidirectional coupling

Abstract

The invention discloses a wing surface air spraying numerical simulation method based on a CFD-DEM bidirectional coupling method. The wing surface air spraying numerical simulation method comprises the steps that geometric models of an air spraying gun nozzle and a wing are established in three-dimensional modeling software; extracting a fluid domain and dividing a computational grid; cFD-DEM coupling calculation is carried out, air is regarded as a continuous phase, coating liquid drops are regarded as a discrete phase, a discrete element method (DEM) is used for initializing the discrete phase, and a computational fluid dynamics (CFD) method is used for setting and solving fluid phase flow field characteristics; the flow field information is transmitted to the discrete phase, and then the force acting on each particle is calculated; particle translation and rotation motion data are obtained through a DEM solver, and the volume fraction and momentum exchange of the particles are calculated in CFD grid units. According to the method, the airfoil surface air spraying process is subjected to numerical simulation by adopting the bidirectional coupling CFD-DEM method, and the method has an important guiding effect on the actual technological process.

Description

Technical Field

[0001] This invention relates to the field of aerospace engineering technology, and more particularly to the field of gas-liquid two-phase flow calculation, specifically a numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling. Background Technology

[0002] Air spraying is a common surface engineering technique. Its basic principle is to control the spray gun's high-compressed air output, creating high-speed relative motion between the air and paint droplets. This atomizes the paint droplets and delivers them to the surface of the workpiece, forming a uniform coating. Due to its ease of operation, cost-effectiveness, and good film quality, it has broad application prospects in the aerospace field. However, current research on air spraying for film formation mostly focuses on planar or simple surfaces, with limited in-depth studies on complex surfaces with engineering significance.

[0003] Wing surface coating technology is a crucial component of aerospace manufacturing processes. Compared to simpler surface profiles, complex surfaces like wings present greater challenges and higher costs for experimental research due to their large size, variable curvature, and asymmetry. Therefore, it is necessary to develop a reliable and cost-effective numerical simulation method for air spraying of wing surfaces to provide guidance for practical manufacturing processes. Summary of the Invention

[0004] The purpose of this invention is to address the problems existing in the prior art by providing a numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling. This numerical simulation method is used to solve the difficulties and high costs in the research of air spraying on complex and large-sized surfaces, and to guide the coating quality problems that occur in the actual process flow.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A numerical simulation method for air spraying on airfoil surfaces based on CFD-DEM bidirectional coupling is proposed. The steps of this numerical simulation method are as follows:

[0007] S1. Use 3D modeling software to construct 3D models of the air spray gun nozzle, air wing, and flow field respectively;

[0008] S2. Import the three-dimensional models of the air spray gun nozzle, airfoil and flow field constructed in step S1 into Ansys software to obtain an integrated three-dimensional model. Extract the fluid domain of the integrated three-dimensional model and divide the geometric boundary. Perform mesh generation on the integrated three-dimensional model after extracting the fluid domain and dividing the geometric boundary.

[0009] S3. Import all the meshes divided in step S2 into FLUENT software, set the continuous phase property parameters, define the continuous phase boundary conditions of each geometric boundary, initialize the flow field mixing using FLUENT software, and obtain the continuous phase information by solving the continuous phase control equations based on computational fluid dynamics.

[0010] S4. Introduce discrete phase coating droplets into the flow field, set discrete phase attribute parameters, define discrete phase boundary conditions for each geometric boundary, transfer the continuous phase information obtained in step S3 to the discrete phase control equation, solve the discrete phase control equation based on the discrete element method to obtain discrete phase information, and update particle position information, translational motion state information, and rotational motion state information.

[0011] S5. Determine whether the coupled iteration process of steps S3 and S4 has ended. If it has ended, output the information of the continuous phase in the flow field. If it has not ended, transfer the information of the discrete phase obtained in step S4 to the continuous phase control equation in step S3, and continue to solve the information of the continuous phase at each point in the flow field in the next time step based on the computational fluid dynamics method and include it in step S4.

[0012] In step S1, the air spray gun nozzle is a ten-hole nozzle model, which includes a paint inlet hole, a central atomizing hole, four auxiliary atomizing holes, and four fan-shaped control holes; the airfoil in step S1 is the NACA 0012 airfoil; the flow field in step S1 is a cuboid shape minus the airfoil and the bottom surface of the nozzle being the shape of the airfoil surface.

[0013] The number of grids in step S2 is 4,000,000-6,000,000.

[0014] In step S2, the mesh on the surface of the air spray gun nozzle, the surface of the wing, and the center axis of the spraying are locally densified. The minimum unit size of the mesh on the surface of the air spray gun nozzle is set to 0.5 mm, the minimum unit size of the mesh on the surface of the wing is set to 0.7 mm, and the minimum unit size of the mesh on the center axis of the spraying is set to 1.5 mm.

[0015] In step S3, the continuous phase property parameters include density and viscosity; the wing surface and nozzle structure surface are defined as fixed walls, and the conditions of no heat passage and no velocity slip are adopted. The inlet boundary conditions of the paint inlet hole, central atomizing hole, auxiliary atomizing hole and fan control hole are defined as pressure inlet, and the turbulence parameters are characterized by turbulence intensity and hydraulic diameter.

[0016] The continuous phase control equations in step S3 include the continuity equation, the momentum conservation equation, and the implementable equations used for turbulence calculation. Turbulence model, solving the continuous phase control equations and realization Turbulence model until the residual values ​​of all variables are below 10. -4 This allows us to obtain information about the continuous phase at various points in the flow field, including velocity, pressure, density, and viscosity.

[0017] The continuity equation is shown in equation (1), and the momentum conservation equation is shown in equation (2):

[0018] (1)

[0019] (2)

[0020] In equations (1)-(2), This represents the volume fraction of the fluid phase within the unit cell. For fluid phase density, The average velocity of the fluid phase within the unit. To share the burden between the two parties, It is a particle-fluid interaction force. It is the viscous stress tensor;

[0021] The achievable Turbulence model and The transport equations are equations (3) and (4), respectively:

[0022] (3)

[0023] (4)

[0024] In equations (3)-(4), , These are the turbulent kinetic energy generation terms caused by the average velocity gradient and buoyancy, respectively. This relates to the effect of fluctuating expansion on the total dissipation rate in compressible turbulent flow. , It is a constant. , It is the Prandtl number of turbulent flow, which represents the turbulent kinetic energy and the turbulent kinetic energy dissipation rate. , It is a custom source item.

[0025] In step S4, the discrete phase density, viscosity, and surface tension coefficient are set; the discrete phase jet source type is defined as a surface jet source, the incident surface is set as the paint inlet hole, and the jet is ejected along the normal direction of the paint inlet. The initial velocity and mass flow rate are determined, the particle type is selected as inertial particles, and the particle size is determined; the discrete phase boundary conditions of the paint inlet hole, the central atomizing hole, the auxiliary atomizing hole, the fan-shaped control hole, and the surrounding gas phase outlet are defined as escape, the discrete phase boundary condition of the air spray gun nozzle structure surface is reflection, and the discrete phase boundary condition of the wing surface is wall liquid film.

[0026] The discrete phase control equations in step S4 include translational motion described by the basic equation of Newton's second law provided by equation (5) and rotational motion described by Euler's law provided by equation (6):

[0027] (5)

[0028] (6)

[0029] In equations (5)-(6), , , , They are particles The mass, moment of inertia, translational velocity, and angular velocity, It is with particles The number of interacting particles, Indicates particles The elastic force it is subjected to Indicates particles The viscous damping force it is subjected to It is a particle The fluid-particle interaction forces it experiences , These are the tangential torque and rolling friction torque experienced by the particles as they move in the fluid, respectively.

[0030] The discrete phase control equations are solved using the discrete element method until convergence, i.e., the residual values ​​of all variables are less than 10. -4 The fluid-particle interaction forces experienced by each particle were obtained. .

[0031] In step S5, if the coupling iteration process ends, the velocity distribution data of the continuous phase in the flow field, the surface pressure of the part to be coated, and the coating thickness distribution data are output.

[0032] In step S5, if the coupling iteration process has not ended, the particle-fluid interaction force corresponding to each particle in the discrete phase information obtained in step S4 is obtained based on the fluid-particle interaction force, and the particle-fluid interaction force is transferred to the continuous phase control equation in step S3.

[0033] The present invention has the following advantages over the prior art:

[0034] The present invention proposes a numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling. This method is accurate, cost-effective, and efficient. It eliminates the need for time-consuming, costly, and difficult spraying experiments. Numerical simulation can provide the spraying flow field distribution and film formation performance on the wing surface under different operating parameters.

[0035] The present invention proposes a numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling, which has strong scalability and can adjust the wing model, spray gun size, operating parameters, coating properties, etc. according to different needs, and has certain applicability to most working conditions. Attached Figure Description

[0036] Appendix Figure 1 This is a flowchart of a numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling, according to the present invention.

[0037] Appendix Figure 2 This is a schematic diagram of a three-dimensional model of a ten-hole nozzle provided in Embodiment 1 of the present invention;

[0038] Appendix Figure 3 A schematic diagram of a three-dimensional model of air spraying on an airfoil provided in Embodiment 1 of the present invention;

[0039] Appendix Figure 4 The computational domain mesh of the XZ section after local refinement is provided in Embodiment 1 of the present invention;

[0040] Appendix Figure 5 The computational domain mesh of the YZ section after local refinement is provided in Embodiment 1 of the present invention;

[0041] Appendix Figure 6 A trend diagram showing the variation of the flow field gas phase steady-state calculation accuracy with the number of grid divisions, provided for Embodiment 1 of the present invention;

[0042] Appendix Figure 7 A trend diagram showing the variation of the steady-state calculation time of the gas phase flow field with the number of grid divisions, provided for Embodiment 1 of the present invention;

[0043] Appendix Figure 8 The numerical simulation and experimental results of pressure distribution along the X-axis on the surface of the part to be sprayed under four different working conditions are compared and verified for the simulation verification of the present invention.

[0044] Appendix Figure 9 The numerical simulation and experimental results of pressure distribution along the Z-axis on the surface of the part to be sprayed under four different working conditions are compared and verified for the simulation verification of the present invention.

[0045] Appendix Figure 10 Liquid film thickness distribution diagrams under different feed pressures are provided for the example verification of the present invention;

[0046] Appendix Figure 11 The following curves are provided to verify the application of the present invention: the coating efficiency versus feed pressure under different feed pressures.

[0047] Appendix Figure 12 The following curves are provided to verify the application of the present invention, showing the variation of coating uniformity with feed pressure under different feed pressures.

[0048] Appendix Figure 13 The curves showing the variation of spray asymmetry with feed pressure under different feed pressures are provided to verify the examples of the present invention. Detailed Implementation

[0049] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the embodiments set forth herein; rather, they are provided so that the invention will be thorough and complete, and the concept of the exemplary embodiments will be fully conveyed to those skilled in the art. The same reference numerals in the drawings denote the same or similar structures, and therefore their detailed description will be omitted.

[0050] The terms “a,” “one,” “the,” and “the” are used to indicate the existence of one or more elements / components / etc.; the terms “including” and “having” are used to indicate an open-ended meaning of inclusion and that other elements / components / etc. may exist in addition to the listed elements / components / etc.

[0051] This invention provides a numerical simulation method for air spraying on airfoil surfaces based on CFD-DEM bidirectional coupling. The flowchart of this method is as follows: Figure 1 As shown, the specific steps of this numerical simulation method are as follows:

[0052] S1. Use 3D modeling software to construct 3D models of the air spray gun nozzle, airfoil, and flow field to provide a geometric basis for subsequent numerical simulation. The air spray gun nozzle uses a ten-hole nozzle model, which includes one paint inlet hole, one central atomizing hole, four auxiliary atomizing holes, and four fan-shaped control holes. The airfoil is selected as NACA0012. The flow field is a cuboid shape minus the bottom surface of the airfoil and nozzle.

[0053] S2. Import the three-dimensional models of the air spray gun nozzle, wing, and flow field constructed in step S1 into Ansys software to obtain an integrated three-dimensional model. Extract the fluid domain of the integrated three-dimensional model and divide its geometric boundaries. Mesh the integrated three-dimensional model after extracting the fluid domain and dividing the geometric boundaries. The number of meshes is 4,000,000-6,000,000. To ensure calculation accuracy, the meshes on the surface of the air spray gun nozzle, the surface of the wing, and the spraying center axis are locally refined. The minimum unit size of the mesh on the surface of the air spray gun nozzle is set to 0.5 mm, the minimum unit size of the mesh on the surface of the wing is set to 0.7 mm, and the minimum unit size of the mesh on the spraying center axis is set to 1.5 mm.

[0054] S3. Import all the meshes generated in step S2 into FLUENT software, and set the continuous phase property parameters, including density and viscosity. Define the wing surface and nozzle structure surface as fixed walls, and adopt no heat passage and no velocity slip conditions. Define the inlet boundary conditions of the paint inlet hole, central atomizing hole, auxiliary atomizing hole, and fan-shaped control hole as pressure inlets. Turbulence parameters are characterized by turbulence intensity and hydraulic diameter. After initializing the flow field mixing using FLUENT software, solve the continuous phase control equations based on computational fluid dynamics to obtain continuous phase information: velocity, pressure, density, viscosity, velocity distribution data, surface pressure of the part to be coated, and coating thickness distribution data.

[0055] Solving the continuous phase control equations and achieving Turbulence model until the residual values ​​of all variables are below 10. -4 The information of the continuous phase at various points in the flow field at this time is obtained, including velocity, pressure, density, viscosity, velocity distribution data, surface pressure of the part to be coated, and coating thickness distribution data; among which the continuity equation is shown in equation (1) and the momentum conservation equation is shown in equation (2):

[0056] (1)

[0057] (2)

[0058] In equations (1)-(2), This represents the volume fraction of the fluid phase within the unit cell. For fluid phase density, The average velocity of the fluid phase within the unit. To share the burden between the two parties, It is a particle-fluid interaction force. It is the viscous stress tensor;

[0059] It is achievable Turbulence model and The transport equations are equations (3) and (4), respectively:

[0060] (3)

[0061] (4)

[0062] In equations (3)-(4), , These are the turbulent kinetic energy generation terms caused by the average velocity gradient and buoyancy, respectively. This relates to the effect of fluctuating expansion on the total dissipation rate in compressible turbulent flow. , It is a constant. , It is the Prandtl number of turbulent flow, which represents the turbulent kinetic energy and the turbulent kinetic energy dissipation rate. , It is a custom source item;

[0063] S4. Introduce discrete phase coating droplets into the flow field and set the discrete phase density, viscosity, and surface tension coefficient; define the discrete phase jet source type as a surface jet source, set the incident surface as the coating inlet hole, and eject it along the coating inlet normal direction, determine the initial velocity and mass flow rate, select inertial particles as the particle type, and determine the particle size; define the discrete phase boundary conditions of the coating inlet hole, central atomizing hole, auxiliary atomizing hole, fan-shaped control hole, and surrounding gas phase outlet as escape, the discrete phase boundary condition of the air spray gun nozzle structure surface as reflection, and the discrete phase boundary condition of the wing surface as wall liquid film; transfer the velocity, pressure, density, and viscosity information of the continuous phase obtained in step S3 to the discrete phase control equation, and obtain the discrete phase information by solving the discrete phase control equation based on the discrete element method. The discrete phase control equation includes the translational motion described by the basic equation of Newton's second law provided by equation (5) and the rotational motion described by Euler's law provided by equation (6):

[0064] (5)

[0065] (6)

[0066] In equations (5)-(6), , , , They are particles The mass, moment of inertia, translational velocity, and angular velocity, It is with particles The number of interacting particles, Indicates particles The elastic force it is subjected to Indicates particles The viscous damping force it is subjected to It is a particle The fluid-particle interaction forces it experiences , These are the tangential torque and rolling friction torque experienced by the particles as they move in the fluid, respectively.

[0067] The discrete phase control equations are solved using the discrete element method until convergence, i.e., the residual values ​​of all variables are less than 10. -4 The fluid-particle interaction forces experienced by each particle were obtained. And update the particle position information and translational and rotational motion status information;

[0068] S5. Determine whether the coupled iteration process of steps S3 and S4 has ended. If the coupled iteration process has ended, output the velocity distribution data of the continuous phase in the flow field, the surface pressure of the part to be coated, and the coating thickness distribution data. If the coupled iteration process has not ended, the corresponding particle-fluid interaction force can be obtained from the fluid-particle interaction force on each particle obtained in step S4. This force is then transferred to the continuous phase control equation in step S3. Combined with computational fluid dynamics methods, the fluid information at each point in the flow field in the next time step is solved. The above steps are iterated repeatedly until the simulation time ends.

[0069] Example 1

[0070] like Figure 1 As shown, a numerical simulation method for air spraying on airfoil surfaces based on CFD-DEM bidirectional coupling mainly includes the following steps:

[0071] S1. Using 3D modeling software, construct 3D models of the air spray gun nozzle, airfoil, and flow field respectively. In this embodiment, the airfoil is selected as NACA 0012, and the air spray gun nozzle is a classic ten-hole nozzle model, including one paint inlet hole, one central atomizing hole, four auxiliary atomizing holes, and four fan-shaped control holes, such as... Figure 2 As shown, the specific structural parameters are shown in Table 1; the flow field is a cuboid with the bottom surface of the wing surface subtracted from the wing and nozzle, as shown in the schematic diagram. Figure 3 As shown.

[0072] Table 1 Main structural parameters of the nozzle

[0073]

[0074] S2. Import the three-dimensional models of the air spray gun nozzle, airfoil, and flow field constructed in step S1 into Ansys software to obtain an integrated three-dimensional model. Extract the fluid domain of the integrated three-dimensional model and define its geometric boundaries. Mesh the integrated three-dimensional model after extracting the fluid domain and defining the geometric boundaries. Locally refine the mesh in important areas (air spray gun nozzle surface, airfoil surface, and spraying center axis) (minimum element size set to 0.5mm, 0.7mm, and 1.5mm respectively) to ensure calculation accuracy. The XZ and YZ sections of the mesh are shown below. Figure 4 , 5 As shown;

[0075] To ensure the simulation meets computational accuracy requirements while minimizing computational resource consumption, mesh independence needs to be verified. Steady-state calculations of the gas phase in the flow field of the integrated 3D model after mesh generation were performed under the same computational conditions using three mesh numbers: 2434717, 5389687, and 10724314. The results were obtained through curve fitting. Figure 6 , Figure 7 The graph shows the trend of gas-phase steady-state calculation accuracy and calculation time in the flow field as a function of the number of grid divisions; from Figure 6 When the grid number is between 0 and 2M, the computational accuracy increases sharply with the increase in grid number; when the grid number is between 2M and 6M, the increase in computational accuracy slows down, but is still considerable; after the grid number reaches 6M, the increase in computational accuracy becomes increasingly smaller and can almost be ignored. Figure 7 When the grid number is in the range of 0-2M, the computation time increases significantly with the increase in grid number, but the grid number is still relatively small, and the computational accuracy has not yet met the requirements. When the grid number is in the range of 2M-6M, the increase in computation time slows down slightly. Beyond 6M, the increase in computation time increases again, and further increasing the grid number will lead to greater computational resource consumption. Considering both computational accuracy and efficiency, a grid number of 4-6M can be selected.

[0076] S3. Import all the meshes generated in step S2 into the FLUENT software. Since no special gases are generally introduced during air spraying, air can be considered as a continuous phase. Therefore, the continuous phase density is set to 1.225. The viscosity is 1.7894 × 10⁻⁶. -5 The wing surface and nozzle structure surface are defined as fixed walls, and conditions of no heat passage and no velocity slip are adopted. The inlet boundary conditions of the paint inlet hole, central atomizing hole, auxiliary atomizing hole, and fan-shaped control hole are defined as pressure inlets. Turbulence parameters are characterized by turbulence intensity and hydraulic diameter. Specific parameters are shown in Table 2.

[0077] Table 2 Parameters corresponding to pressure inlet

[0078]

[0079] After initializing the flow field using FLUENT software, the continuous phase is calculated based on computational fluid dynamics. The governing equations for the continuous phase include the continuity equation (1) and the momentum conservation equation (2).

[0080] (1)

[0081] (2)

[0082] In equations (1)-(2), This represents the volume fraction of the fluid phase within the unit cell. For fluid phase density, The average velocity of the fluid phase within the unit. To share the burden between the two parties, It is a particle-fluid interaction force. It is the viscous stress tensor;

[0083] It is achievable Turbulence model and The transport equations are equations (3) and (4), respectively:

[0084] (3)

[0085] (4)

[0086] In equations (3)-(4), , These are the turbulent kinetic energy generation terms caused by the average velocity gradient and buoyancy, respectively. This relates to the effect of fluctuating expansion on the total dissipation rate in compressible turbulent flow. , It is a constant. , The Prandt number of turbulent flow is the sum of turbulent kinetic energy and turbulent kinetic energy dissipation rate. , It is a custom source item.

[0087] The continuous phase control equations of the flow field are solved using computational fluid dynamics until convergence (the residual values ​​of all variables are less than 10). -4 This allows us to obtain information about the continuous phase at various points in the flow field, including velocity, pressure, density, viscosity, velocity distribution data, surface pressure of the part to be coated, and coating thickness distribution data.

[0088] S4. Introduce discrete phase coating droplets into the flow field. In this embodiment, the discrete phase density is set to 1200. The viscosity was set to 8×10. -2 The surface tension coefficient was set to 0.07194. The discrete phase jet source type is defined as a surface jet source, with the incident surface set as the paint inlet hole, ejected along the normal direction of the paint inlet, with an initial velocity of 10 m / s and a mass flow rate of 0.001. Without considering factors such as chemical reactions, the particle type is selected as inertial particles, and the particle size is set to a uniform distribution of 50μm. The discrete phase boundary conditions of the coating inlet hole, central atomizing hole, auxiliary atomizing hole, fan-shaped control hole and surrounding gas phase outlet are defined as escape, the discrete phase boundary condition of the nozzle structure surface is reflection, and the discrete phase boundary condition of the wing surface is wall liquid film.

[0089] Discrete phase control equations are constructed based on the Discrete Element Method (DEM). These equations include translational motion described by the basic equation of Newton's second law provided by equation (5) and rotational motion described by Euler's law provided by equation (6).

[0090] (5)

[0091] (6)

[0092] In equations (5)-(6), , , , They are particles The mass, moment of inertia, translational velocity, and angular velocity, It is with particles The number of interacting particles, Indicates particles The elastic force it is subjected to Indicates particles The viscous damping force it is subjected to It is a particle The fluid-particle interaction forces it experiences , These are the tangential torque and rolling friction torque experienced by the particles as they move in the fluid, respectively.

[0093] The discrete phase control equations are solved using the discrete element method until convergence, i.e., the residual values ​​of all variables are less than 10. -4 The fluid-particle interaction forces experienced by each particle were obtained. It also updates the particle position information and translational and rotational motion status information.

[0094] In summary, steps S3 and S4 involve: transferring the velocity, pressure, density, and viscosity of the continuous phase at various points in the flow field to the discrete phase governing equations when the continuous phase calculated in step S3 converges; and solving the discrete phase governing equations using the discrete element method until convergence (when the residual values ​​of all variables are less than 10). -4 This yields the fluid-particle interaction forces acting on each particle. It also updates the particle position information and translational and rotational motion status information.

[0095] S5. Determine whether the coupled iteration process of steps S3 and S4 has ended (whether the simulation time has been reached). If the coupled iteration process has ended, output the velocity distribution data of the continuous phase in the flow field, the surface pressure of the part to be coated, and the coating thickness distribution data. If the coupled iteration process has not ended, the corresponding particle-fluid interaction force can be obtained from the fluid-particle interaction force on each particle obtained in step S4. This force is then transferred to the continuous phase control equation in step S3, and the information of the fluid at each point in the flow field in the next time step is solved by combining computational fluid dynamics methods. The above steps are iterated repeatedly until the simulation time ends.

[0096] Simulation verification

[0097] The numerical simulation method provided in Example 1 was used to simulate existing experiments. The effectiveness of the numerical simulation method was verified by comparing the simulation results with experimental data under different operating conditions. The results are shown in [Figure 1]. Figure 8 and Figure 9 ;Depend on Figure 8 It can be seen that the pressure distribution curves of the plate surface under various working conditions along the X-axis obtained by simulation are in good agreement with the experimental results; from Figure 9 It can be seen that, along the Z-axis, the simulation results agree well with the experimental results when the fan-shaped control pressure is 0.5 bar and 0.75 bar. However, when the fan-shaped control pressure is 0 and 0.25 bar, there are some errors between the simulation results and the experimental results. Considering that the fan-shaped control pressure in subsequent studies will generally be much greater than this value, we consider this error to be within an acceptable range. In summary, the pressure distribution curves of the surface of the part to be sprayed along the X and Z axes under various working conditions obtained by simulation agree well with the existing experimental results, proving the effectiveness of the numerical simulation method.

[0098] Instance verification

[0099] Based on the effectiveness verification of numerical simulation methods, the film quality of spraying under different spray gun operating parameters is compared, providing some guidance for the actual process flow.

[0100] In the case study, the research object was the feed pressure. Numerical simulations of air spraying on the wing surface were performed under feed pressures of 0, 0.2, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0, and 1.2 bar. Based on this method, the spatial flow field distribution, paint particle distribution, and liquid film thickness distribution can be obtained, and the spraying quality can be evaluated.

[0101] In the example verification, the transient calculation time step was set to 5 × 10. -5 The total calculation time is set to 0.5 seconds.

[0102] Instance verification obtained such as Figure 10 The diagram shows the liquid film thickness distribution under different feed pressures; from Figure 10 It can be seen that when the feed pressure is 0, the liquid film shape is a flat, nearly circular shape; as the feed pressure is turned on and initially increased ( =0-0.4 bar), the liquid film shape expands from a flat circle along the Y-axis to a vertical ellipse; continue to increase the feed pressure ( =0.5-0.7 bar), the liquid film shape still appears as a vertical ellipse, but the spray coverage area has slightly decreased, and the area of ​​the central red overspray area has also decreased during this period, which means that the overspray phenomenon has been partially alleviated; further increasing the feed pressure ( =0.8-1.2 bar), the liquid film shape gradually changes from a vertical ellipse to a circle, and the area of ​​the sprayed coverage area increases significantly to a degree visible to the naked eye. In this stage, the central red overspray area also shows the same shape change trend.

[0103] Instance verification obtained such as Figure 11 The curves showing the coating efficiency versus feed pressure under different feed pressures are shown; Figure 11 It can be seen that in the initial stage of starting the feed pressure ( =0-0.6 bar), the spraying efficiency is partially lost along the X-axis, but increases along the Y-axis. Considering both factors, the spraying efficiency fluctuates slightly around 100%, but the change is not significant (i.e., compared to 0-0.6 bar). The initial state of =0 shows little change; during the subsequent increase in feed pressure ( =0.6-1.2 bar), the spraying efficiency drops dramatically in both directions. As the feed pressure increases from 0.6 bar to 1.2 bar, the spraying efficiency drops from about 100% to about 40%.

[0104] Instance verification obtained such as Figure 12The curves showing the coating uniformity under different feed pressures are illustrated. Coating uniformity is characterized by the Comprehensive Relative Mean Deviation (CRMD); the larger this value, the lower the coating uniformity. Figure 12 It can be seen that in the initial stage of starting the feed pressure ( =0-0.4 bar), the overall relative average deviation remains at a high level, which means that at this stage, the spray uniformity is poor and increasing the feed pressure has almost no effect on the spray uniformity; further increasing the feed pressure ( =0.4-1.2 bar), the value of the overall relative average deviation continues to decrease, from about 3.75 to about 3.15. During this stage, increasing the feed pressure can effectively improve the uniformity of spraying.

[0105] Instance verification obtained such as Figure 13 The curves showing the variation of coating asymmetry with feed pressure under different feed pressures are shown; Figure 13 It can be seen that when the feed pressure is 0, the coating asymmetry is at a moderate level, approximately 5.14%; in the initial stage of feed pressure activation ( At feed pressures of 0-0.4 bar, the coating asymmetry increases to 7.38%; however, as the feed pressure increases from 0.4 bar to 0.6 bar, the coating asymmetry continuously decreases, reaching approximately [value missing]. =At around 0.6, the minimum value of about 3.2% is obtained; continue to increase the feed pressure ( =0.6-1.2 bar), the asymmetry first increases, then decreases and then increases again, but overall it shows an increasing trend. This means that further increasing the feed pressure will no longer substantially improve the situation of spray asymmetry.

[0106] Taking all the above factors into account, we can conclude that when the feed pressure is set to a moderate value of 0.4-0.6 bar, although the uniformity of the coating cannot reach the optimal state, the symmetry of the coating is good, the coating efficiency is maintained at a high level, and the overall coating quality is high.

[0107] This invention proposes a numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling. This method is accurate, cost-effective, and efficient, eliminating the need for time-consuming, costly, and difficult spraying experiments. Numerical simulation can provide the spray flow field distribution and film formation on the wing surface under different operating parameters. This numerical simulation method has strong scalability, allowing adjustment of the wing model, spray gun size, operating parameters, and coating properties according to different needs, and is applicable to most working conditions.

[0108] In this embodiment of the invention, the term "multiple" refers to two or more, unless otherwise explicitly defined. The terms "install," "connect," and "fix" should be interpreted broadly. For example, "connect" can mean a fixed connection, a detachable connection, or an integral connection. Those skilled in the art can understand the specific meaning of the above terms in this embodiment of the invention based on the specific circumstances.

[0109] In the description of the embodiments of the present invention, it should be understood that the terms "upper" and "lower" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or unit referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of the present invention.

[0110] In the description of this specification, the terms "an embodiment," "a preferred embodiment," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0111] The above embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention. Technologies not covered in this invention can be implemented using existing technologies.

Claims

1. A numerical simulation method for air spraying on airfoil surfaces based on CFD-DEM bidirectional coupling, characterized in that: The steps of this numerical simulation method are as follows: S1. Use 3D modeling software to construct 3D models of the air spray gun nozzle, air wing, and flow field respectively; S2. Import the three-dimensional models of the air spray gun nozzle, airfoil and flow field constructed in step S1 into Ansys software to obtain an integrated three-dimensional model. Extract the fluid domain of the integrated three-dimensional model and divide the geometric boundary. Perform mesh generation on the integrated three-dimensional model after extracting the fluid domain and dividing the geometric boundary. S3. Import all the meshes divided in step S2 into FLUENT software, set the continuous phase property parameters, define the continuous phase boundary conditions of each geometric boundary, initialize the flow field mixing using FLUENT software, and obtain the continuous phase information by solving the continuous phase control equations based on computational fluid dynamics. S4. Introduce discrete phase coating droplets into the flow field, set discrete phase attribute parameters, define discrete phase boundary conditions for each geometric boundary, transfer the continuous phase information obtained in step S3 to the discrete phase control equation, solve the discrete phase control equation based on the discrete element method to obtain discrete phase information, and update particle position information, translational motion state information, and rotational motion state information. S5. Determine whether the coupled iteration process of steps S3 and S4 has ended. If it has ended, output the information of the continuous phase in the flow field. If it has not ended, transfer the information of the discrete phase obtained in step S4 to the continuous phase control equation in step S3, and continue to solve the information of the continuous phase at each point in the flow field in the next time step based on the computational fluid dynamics method and include it in step S4.

2. The numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling according to claim 1, characterized in that: In step S1, the air spray gun nozzle is a ten-hole nozzle model, which includes a paint inlet hole, a central atomizing hole, four auxiliary atomizing holes, and four fan-shaped control holes; the airfoil in step S1 is the NACA 0012 airfoil; the flow field in step S1 is a cuboid shape minus the airfoil and the bottom surface of the nozzle being the shape of the airfoil surface.

3. The numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling according to claim 1, characterized in that: The number of grids in step S2 is 4,000,000-6,000,000.

4. The numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling according to claim 1 or 3, characterized in that: In step S2, the mesh on the surface of the air spray gun nozzle, the surface of the wing, and the center axis of the spraying are locally densified. The minimum unit size of the mesh on the surface of the air spray gun nozzle is set to 0.5 mm, the minimum unit size of the mesh on the surface of the wing is set to 0.7 mm, and the minimum unit size of the mesh on the center axis of the spraying is set to 1.5 mm.

5. The numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling according to claim 1, characterized in that: In step S3, the continuous phase property parameters include density and viscosity; the wing surface and nozzle structure surface are defined as fixed walls, and the conditions of no heat passage and no velocity slip are adopted. The inlet boundary conditions of the paint inlet hole, central atomizing hole, auxiliary atomizing hole and fan control hole are defined as pressure inlet, and the turbulence parameters are characterized by turbulence intensity and hydraulic diameter.

6. The numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling according to claim 1 or 5, characterized in that: The continuous phase control equations in step S3 include the continuity equation, the momentum conservation equation, and the implementable equations used for turbulence calculation. Turbulence model, solving the continuous phase control equations and realization Turbulence model until the residual values ​​of all variables are below 10. -4 This allows us to obtain information about the continuous phase at various points in the flow field, including velocity, pressure, density, and viscosity.

7. The numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling according to claim 6, characterized in that: The continuity equation is shown in equation (1), and the momentum conservation equation is shown in equation (2): （1） （2） In equations (1)-(2), This represents the volume fraction of the fluid phase within the unit. For fluid phase density, The average velocity of the fluid phase within the unit. To share the burden between the two parties, It is a particle-fluid interaction force. It is the viscous stress tensor; The achievable Turbulence model and The transport equations are equations (3) and (4), respectively: （3） （4） In equations (3)-(4), , These are the turbulent kinetic energy generation terms caused by the average velocity gradient and buoyancy, respectively. This relates to the effect of fluctuating expansion on the total dissipation rate in compressible turbulent flow. , It is a constant. , It is the Prandtl number of turbulent kinetic energy and turbulent kinetic energy dissipation rate. , It is a custom source item.

8. The numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling according to claim 1, characterized in that: In step S4, the discrete phase density, viscosity, and surface tension coefficient are set; the discrete phase jet source type is defined as a surface jet source, the incident surface is set as the paint inlet hole, and the jet is ejected along the normal direction of the paint inlet. The initial velocity and mass flow rate are determined, the particle type is selected as inertial particles, and the particle size is determined; the discrete phase boundary conditions of the paint inlet hole, the central atomizing hole, the auxiliary atomizing hole, the fan-shaped control hole, and the surrounding gas phase outlet are defined as escape, the discrete phase boundary condition of the air spray gun nozzle structure surface is reflection, and the discrete phase boundary condition of the wing surface is wall liquid film.

9. The numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling according to claim 1 or 8, characterized in that: The discrete phase control equations in step S4 include translational motion described by the basic equation of Newton's second law provided by equation (5) and rotational motion described by Euler's law provided by equation (6): （5） （6） In equations (5)-(6), , , , They are particles The mass, moment of inertia, translational velocity, and angular velocity, It is with particles The number of interacting particles, Indicates particles The elastic force it is subjected to Indicates particles The viscous damping force it is subjected to It is a particle The fluid-particle interaction forces it experiences , These are the tangential torque and rolling friction torque experienced by the particles as they move in the fluid, respectively. The discrete phase control equations are solved using the discrete element method until convergence, i.e., the residual values ​​of all variables are less than 10. -4 The fluid-particle interaction forces experienced by each particle were obtained. .

10. The numerical simulation method for air spraying on wing surfaces based on CFD-DEM bidirectional coupling according to claim 9, characterized in that: In step S5, if the coupling iteration process ends, the velocity distribution data of the continuous phase in the flow field, the surface pressure of the part to be coated, and the coating thickness distribution data are output. In step S5, if the coupling iteration process has not ended, the particle-fluid interaction force corresponding to each particle in the discrete phase information obtained in step S4 is obtained based on the fluid-particle interaction force, and the particle-fluid interaction force is transferred to the continuous phase control equation in step S3.

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