Method and system for modeling the coating formation process on the inner wall of a steel tube

Abstract

This invention discloses a modeling method and system for the formation process of coatings on the inner wall of steel pipes, relating to the field of metal pipe surface treatment technology. The method includes establishing a spraying process model based on the physicochemical properties of raw materials and process parameters; constructing an adhesion interface model by combining three-dimensional scanning data of the inner wall of the steel pipe with substrate pretreatment parameters; and coupling these to establish an incremental coating model. An improved smooth particle hydrodynamic algorithm is used to solve the spraying process model, simulating particle movement, atomization, and spatial distribution. The results are input into the incremental coating model to achieve layer-by-layer coating accumulation. Based on preset coating thickness and uniformity indicators, the accumulated results are used to iteratively optimize process parameters, forming a closed-loop modeling process. This method can improve the simulation accuracy of complex inner wall spraying flow fields and deposition processes, achieving closed-loop control of coating growth processes and process parameters. It is suitable for accurate simulation and parameter optimization of the coating preparation process on the inner wall of steel pipes.

Description

Technical Field

[0001] This invention belongs to the field of metal pipe surface treatment technology, specifically a modeling method and system for the formation process of coating on the inner wall of steel pipe. Background Technology

[0002] Existing modeling methods for coating spraying processes on the inner walls of steel pipes primarily employ mesh-based numerical methods to calculate the spraying flow field and particle transport. These methods rely on empirical relationships to characterize the motion, atomization, and deposition behavior of raw material particles, and the modeling process depends on simplifying assumptions and fixed parameter assignments. Traditional modeling separates spraying transport, interface adhesion, and coating deposition into independent stages for unidirectional simulation, resulting in low data coupling between models and an inability to fully reflect the continuous physical process of coating formation. Conventional smoothed particle hydrodynamic algorithms exhibit numerical fluctuations during the wall constraint and particle atomization stages, limiting their accuracy in characterizing transient particle distribution and interfacial interactions.

[0003] The inner wall of steel pipes has a complex three-dimensional structure. Traditional modeling often uses simplified geometry to replace the real inner wall morphology, failing to integrate three-dimensional topological features and substrate preprocessing parameters into interface modeling, resulting in deviations between coating adhesion behavior and actual conditions. Traditional simulations can only simulate coating distribution forward according to predetermined process parameters, and cannot iteratively correct input parameters based on preset coating thickness and uniformity requirements. Limited flow field solution accuracy, lack of realistic three-dimensional interface representation, insufficient model coupling, and lack of closed-loop control between parameters and deposition results lead to deviations in coating deposition thickness and distribution uniformity from actual spraying results, making it difficult to achieve accurate numerical representation of the entire coating formation process. Summary of the Invention

[0004] This invention aims to solve at least one of the technical problems existing in the prior art;

[0005] Therefore, this invention proposes a modeling method for the coating formation process on the inner wall of steel pipes, comprising:

[0006] Based on the physicochemical properties and process parameters of the coating raw materials, a spraying process model describing the spraying flow field and the transport of raw material particles is established.

[0007] Based on the three-dimensional geometric scanning data of the inner wall of the steel pipe, a three-dimensional topological mapping of the inner wall surface of the steel pipe is generated, and combined with the substrate preprocessing parameters, an adhesion interface model reflecting the coating adhesion behavior is constructed.

[0008] Based on the output of the spraying process model and the output of the adhesion interface model, an incremental coating model describing the coating deposition and growth process is constructed.

[0009] An improved smooth particle hydrodynamic algorithm is used to solve the spraying process model to simulate the motion, atomization, and spatial distribution of coating material particles in the flow field.

[0010] The spatial distribution results obtained by solving the improved smooth particle hydrodynamic algorithm are input into the coating increment model to drive the layer-by-layer accumulation process of the coating in the time dimension;

[0011] Based on the preset target coating thickness and uniformity indicators, and combined with the cumulative results simulated by the coating incremental model, the process parameter input of the spraying process model is iteratively optimized in reverse to form a closed-loop modeling process.

[0012] Furthermore, the establishment of a spraying process model describing the spraying flow field and raw material particle transport includes:

[0013] Obtain the geometric parameters of the nozzle of the spraying equipment and the injection pressure and flow rate parameters of the high-pressure gas;

[0014] Define a fluid computational domain that includes the internal space of the steel pipe and the external spray area;

[0015] Within the fluid computation domain, an unstructured three-dimensional mesh is generated, and the mesh near the nozzle outlet is locally refined.

[0016] Establish a set of governing equations, which includes the mass conservation equation, the momentum conservation equation, and the component conservation equation describing the phase concentration transport of raw material particles.

[0017] Boundary conditions are set for the governing equations, including: the nozzle inlet is set as a pressure inlet boundary, and an initial gas velocity and initial concentration of raw material particles are assigned; the steel pipe wall is set as a no-slip wall boundary, and the turbulent wall function is enabled; the outer boundary of the computational domain is set as a pressure far-field boundary.

[0018] The boundary conditions and the initial values ​​of density and viscosity of the spraying material are used as inputs to the spraying process model.

[0019] Within the fluid computation domain, an unstructured three-dimensional mesh is generated, and the mesh near the nozzle outlet is locally refined, including:

[0020] Set the global maximum grid size for the fluid computation domain, and determine the global maximum grid size based on the inner diameter and axial length of the steel pipe;

[0021] Based on the outlet diameter of the nozzle of the spraying equipment, a local mesh refinement size is set for the nozzle outlet area, wherein the local mesh refinement size is smaller than the global maximum mesh size;

[0022] Starting from the center of the nozzle outlet, a conical mesh reinforcement region is defined along the injection axis, and the axial extension length and cone angle of the conical mesh reinforcement region are set.

[0023] An unstructured tetrahedral mesh is generated within the fluid computation domain, and the mesh size is controlled to the local mesh refinement size within the conical mesh refinement region.

[0024] At the boundary between the conical mesh refinement region and other regions of the fluid computing domain, a mesh size transition gradient is set to smoothly transition the mesh size from the local mesh refinement size to the global maximum mesh size;

[0025] The generated mesh is subjected to quality checks to ensure that the mesh distortion, aspect ratio, and volume change rate meet the preset numerical calculation requirements.

[0026] Furthermore, based on the three-dimensional geometric scanning data of the inner wall of the steel pipe, a three-dimensional topological mapping of the inner wall surface of the steel pipe is generated, and combined with the substrate preprocessing parameters, an adhesion interface model reflecting the coating adhesion behavior is constructed, including:

[0027] Point cloud data of the inner wall surface of the steel pipe was obtained using a 3D laser scanner;

[0028] The point cloud data is denoised and triangulated to generate a triangular mesh surface model of the inner wall of the steel pipe.

[0029] Calculate the normal vector and area of ​​each triangular facet in the triangular mesh surface model, and statistically analyze the surface roughness characterization value, which includes the arithmetic mean roughness and the maximum profile height.

[0030] Obtain substrate pretreatment parameters, including cleaning cleanliness level, surface activation energy value, and preheating temperature field distribution;

[0031] A sub-model of the initial adhesion probability of the coating is established, taking surface roughness characterization value, cleaning cleanliness level, surface activation energy value and preheating temperature field distribution as input parameters;

[0032] The geometric information of the triangular mesh surface model is associated and stored with the calculation results of the coating initial adhesion probability sub-model to jointly constitute the adhesion interface model.

[0033] Furthermore, based on the output of the spraying process model and the output of the adhesion interface model, an incremental coating model describing the coating deposition and growth process is constructed, including:

[0034] Define a coating deposition time step, which is an integer multiple of the time step calculated by the spraying process model;

[0035] At the start of each coating deposition time step, the flux of atomized raw material particles reaching a specific grid cell on the inner wall surface of the steel pipe is extracted from the spraying process model after being solved by the improved smooth particle hydrodynamic algorithm.

[0036] Query the initial adhesion probability of the coating for a specific grid cell in the adhesion interface model, and calculate the number of raw material particles actually attached to the specific grid cell within the time step of coating deposition;

[0037] Based on the actual number of attached raw material particles and their average volume, calculate the volume increment of the coating material formed on the specific surface within the time step of the coating deposition.

[0038] Based on the volume increment of the coating material and the area of ​​the specific mesh cell, the coating thickness increment of the specific mesh cell within this time step is calculated;

[0039] The coating thickness of all current mesh cells is added to the coating thickness increment calculated in this instance to obtain the cumulative thickness distribution of the coating up to the current moment.

[0040] Furthermore, the improved smooth particle hydrodynamics algorithm is improved based on the interaction between the non-Newtonian fluid properties of the coating raw material particles and multiphase flow. Its working principle includes:

[0041] The coating material is discretized into a group of smooth particles carrying mass, viscosity and surface tension properties;

[0042] When calculating the interaction forces between particles, a non-Newtonian viscous force term based on the fitting of measured rheological curves is introduced to replace the constant viscosity term in the classical algorithm.

[0043] To characterize the tearing and dispersion effect of atomized gas on raw material particle clusters, a virtual pressure term related to the local particle number density is added to the interaction between adjacent particles.

[0044] In the time integration step of the algorithm, a variable step size integration strategy is adopted. When the rate of change of particle acceleration in a local area is detected to exceed the threshold, the integration step size is automatically reduced to maintain the computational stability of the area with severe spray atomization.

[0045] After each time step calculation is completed, all particles are marked with phase status. Particles whose velocity difference with the surrounding airflow velocity is less than a threshold are marked as atomized particles, and the rest are marked as insufficiently atomized particles. In the next time step, different force calculation coefficients are assigned to particles of different phase status.

[0046] Furthermore, the spatial distribution results obtained by solving the improved smooth particle hydrodynamics algorithm are input into the coating incremental model, including:

[0047] After the improved smooth particle hydrodynamic algorithm completes the calculation of the time step of a spraying process model, the number and properties of the atomized particles located in the preset adhesion and capture layer on the inner wall surface of the steel pipe at this moment are counted.

[0048] The attributes include at least the mass, velocity vector, and raw material component identifier for each atomized particle;

[0049] Based on the aforementioned properties, the atomized particles located within the attachment and capture layer are mapped according to their spatial positions onto the nearest triangular facet in the triangular mesh surface model of the attachment interface model.

[0050] The accumulated atomized particles mapped onto the same triangular facet within multiple consecutive spraying process model calculation time steps are used. When the accumulated time reaches a coating deposition time step, the accumulated result is passed to the coating increment model as the flux of atomized raw material particles reaching a specific grid cell on the inner wall surface of the steel pipe.

[0051] Furthermore, the process parameter input of the spraying process model is iteratively optimized in reverse, based on the preset target coating thickness and uniformity indices and the cumulative results simulated by the coating incremental model, including:

[0052] Run the complete modeling process to obtain the final cumulative thickness distribution of the coating at the end of the simulation from the incremental coating model;

[0053] Extract the minimum, maximum, and average thickness values ​​and the standard deviation of the thickness distribution from the final cumulative thickness distribution of the coating.

[0054] The average coating thickness is compared with the preset target coating thickness to generate the mean thickness deviation. The standard deviation of the thickness distribution is compared with the preset uniformity index to generate the uniformity deviation.

[0055] With the goal of reducing the mean thickness deviation and the uniformity deviation, an objective function for optimizing process parameters is established, including spraying pressure, nozzle moving speed, and spraying distance.

[0056] A gradient descent search strategy is adopted to adjust the values ​​of the process parameters, and the adjusted process parameters are used as new inputs to restart the complete modeling process from the spraying process model to the coating incremental model.

[0057] Repeat the steps from running the complete modeling process to adjusting the process parameters until the mean thickness deviation and the uniformity deviation are both less than their corresponding allowable thresholds. Record the process parameters used at this time as the optimized process parameter set.

[0058] Furthermore, the workflow of the coating initial adhesion probability sub-model includes:

[0059] The surface roughness characterization value of a single triangular facet of the triangular mesh surface model is input into a roughness-adhesion coefficient mapping table that has been trained in advance with experimental data, and a roughness adhesion influence factor is output.

[0060] Read the cleaning cleanliness level of the local area corresponding to the triangular facet, and quantify the cleaning cleanliness level into a cleanliness coefficient between zero and one.

[0061] Read the surface activation energy value of the local area corresponding to the triangular facet, and calculate an activation adhesion coefficient based on the adsorption kinetics formula, which uses the surface activation energy value and the substrate preheating temperature as input parameters.

[0062] Calculate the weighted product of the roughness adhesion influence factor, cleanliness coefficient and activation adhesion coefficient, and output the result of the weighted product as the initial adhesion probability of the coating on the triangular facet.

[0063] The roughness adhesion influence factor calculation, cleanliness coefficient matching, activation adhesion coefficient solution, and weighted calculation of three types of parameters are performed on all triangular facets in the triangular mesh surface model to generate the initial adhesion probability field of the coating.

[0064] Further, the weighted product of the roughness adhesion influence factor, cleanliness coefficient, and activation adhesion coefficient is calculated, and the result of the weighted product is output as the initial adhesion probability of the coating on the triangular facet, including:

[0065] The roughness adhesion influence factor, cleanliness coefficient and activation adhesion coefficient are respectively assigned a first weight coefficient, a second weight coefficient and a third weight coefficient, and the weight coefficients are determined by multivariate nonlinear regression analysis based on historical coating adhesion experimental datasets;

[0066] Multiply the roughness adhesion influence factor by the first weighting coefficient to obtain the first weighting factor;

[0067] Multiply the cleanliness coefficient by the second weighting coefficient to obtain the second weighting factor;

[0068] Multiply the activation adhesion coefficient by the third weighting coefficient to obtain the third weighting factor;

[0069] Calculate the product of the first weighting factor, the second weighting factor, and the third weighting factor to obtain the weighted product result;

[0070] The weighted product result is normalized so that its value range falls between 0 and 1, resulting in a normalized attachment probability value.

[0071] The normalized adhesion probability value is output as the initial adhesion probability of the coating on the triangular facet.

[0072] Furthermore, the present invention also includes a modeling system for the formation process of a coating on the inner wall of a steel pipe, the system including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the processor executes the computer program, it implements the steps of the modeling method for the formation process of a coating on the inner wall of a steel pipe as described above.

[0073] Compared with the prior art, the beneficial effects of the present invention are:

[0074] An improved smooth particle hydrodynamic algorithm simultaneously solves for the spraying flow field and raw material particles within a meshless discretized framework. This suppresses numerical oscillations and non-physical particle offsets at wall boundaries, accurately describing the forces, motion, atomization, and spatial concentration distribution of particles in the flow field. Real-time coupling of particle motion and flow field information reduces mesh distortion and computational inaccuracies encountered by traditional mesh methods in complex curved regions. This improves the numerical stability and computational accuracy of particle transport processes and atomization characteristics, ensuring that the resulting spatial particle distribution closely matches the actual physical field distribution of the coating.

[0075] A 3D topological mapping is constructed based on the 3D geometric scanning data of the inner wall of the steel pipe to restore the true geometric features of the inner wall surface. An adhesion interface model is established in conjunction with substrate pretreatment parameters to strengthen the correlation between interface state and coating adhesion behavior. The coating incremental model couples and iterates the spraying process and the adhesion interface output, recording the coating material deposition amount and spatial position at each time step, realizing the simulation of the continuous, layer-by-layer cumulative growth process of the coating in the time dimension. Using preset coating target thickness and uniformity indicators as constraints, the simulated cumulative coating distribution is applied inversely to the process parameter input. Through iterative correction, the process parameters and coating deposition results are matched, forming a closed-loop iterative modeling mechanism. Closed-loop iteration reduces the difference between preset indicators and simulation results, improves the accuracy of the correspondence between process parameters and coating distribution, and enables the entire coating formation process modeling to have self-correcting capabilities, enhancing the consistency between numerical simulation and actual spraying conditions. Attached Figure Description

[0076] Figure 1 This is a step diagram of a method for modeling the formation process of a coating on the inner wall of a steel pipe according to the present invention;

[0077] Figure 2 A flowchart for constructing the attachment interface model;

[0078] Figure 3A flowchart for constructing an incremental coating model. Detailed Implementation

[0079] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0080] See Figure 1 This invention provides a modeling method for the formation process of a coating on the inner wall of a steel pipe, the specific method including;

[0081] By establishing a spraying flow field and raw material particle transport model, an adhesion interface model, and a coating increment model, an improved smooth particle hydrodynamic algorithm is used for coupled solution. Guided by the target coating thickness and uniformity indices, the process parameters are iteratively optimized in reverse. Based on the physicochemical properties of the coating raw material and process parameters, a spraying process model describing the spraying flow field and raw material particle transport is established. A three-dimensional topological mapping of the steel pipe's inner wall is generated based on three-dimensional geometric scanning data, and an adhesion interface model reflecting the coating adhesion behavior is constructed by combining substrate pretreatment parameters. Based on the outputs of the above two models, a coating increment model describing the coating deposition and growth process is further constructed. An improved smooth particle hydrodynamic algorithm is used to solve the spraying process model, simulating the motion, atomization, and spatial distribution of coating raw material particles in the flow field. The spatial distribution results obtained by this algorithm are input into the coating increment model, driving the layer-by-layer accumulation process of the coating in the time dimension. Based on the preset target coating thickness and uniformity indices, combined with the accumulation results simulated by the coating increment model, the process parameter input of the spraying process model is iteratively optimized in reverse, thus forming a closed-loop modeling process.

[0082] In one embodiment of the present invention, the geometric parameters of the nozzle of the spraying equipment and the injection pressure and flow rate parameters of the high-pressure gas are obtained. A fluid computational domain is defined, encompassing the internal space of the steel pipe and the external spraying area. Within this fluid computational domain, an unstructured three-dimensional mesh is generated, and the mesh near the nozzle outlet is locally refined. A set of governing equations is established, including mass conservation equations, momentum conservation equations, and component conservation equations describing the phase concentration transport of raw material particles. Boundary conditions are set for this set of governing equations, wherein the nozzle inlet is set as a pressure inlet boundary and given an initial gas velocity and an initial raw material particle concentration, the steel pipe wall is set as a no-slip wall boundary and the turbulent wall function is enabled, and the outer boundary of the computational domain is set as a pressure far-field boundary. These boundary conditions, along with the initial values ​​of the density and viscosity of the spraying raw material, are used as inputs to the spraying process model. When generating the unstructured three-dimensional mesh within the fluid computational domain, a global maximum mesh size is set, which is determined based on the inner diameter and axial length of the steel pipe. The local mesh refinement size of the nozzle outlet area is set based on the nozzle outlet diameter of the spraying equipment, and this size is smaller than the global maximum mesh size. Starting from the nozzle exit center, a conical mesh refinement region is defined along the injection axis, and the axial extension length and cone angle of this region are set. An unstructured tetrahedral mesh is generated within the fluid computational domain, and the mesh size is controlled to the local refinement size within the conical mesh refinement region. A mesh size transition gradient is set at the boundary between the conical mesh refinement region and other regions of the fluid computational domain, allowing the mesh size to smoothly transition from the local refinement size to the global maximum mesh size. The generated mesh is quality checked to ensure that the mesh distortion, aspect ratio, and volume change rate meet the preset numerical calculation requirements.

[0083] In practical implementation, the geometric parameters of the spraying equipment nozzle include the outlet diameter of the nozzle contraction section, the convergence half-angle, and the length-to-diameter ratio of the nozzle orifice. The injection pressure of the high-pressure gas ranges from 0.5 MPa to 0.8 MPa, and the flow rate ranges from 200 L / min to 400 L / min. A fluid computational domain is defined, encompassing the cylindrical space inside the steel pipe and the external spray area of ​​the nozzle. The axial length of the fluid computational domain is greater than the length of the steel pipe, and the radial width is greater than the inner diameter of the steel pipe. Within the fluid computational domain, an unstructured three-dimensional mesh is created, and the mesh is locally refined in the spatial region near the nozzle outlet to accurately capture the flow structure of the nozzle jet core area.

[0084] In practical implementation, the established set of governing equations includes the mass conservation equation, the Reynolds-averaged Navier-Stokes momentum conservation equation, and the component conservation equation describing the phase concentration transport of raw material particles. The differential form of the mass conservation equation is:

[0085]

[0086] in: This indicates the density of the mixed phase. Indicates time, Indicates the velocity vector at directional components, This represents the Cartesian coordinate components. In the boundary conditions set for the governing equations, the nozzle inlet is set as a pressure inlet boundary, specifying the inflow velocity profile of the high-pressure gas and the initial values ​​of the raw material particle volume fraction. The initial raw material particle concentration is 10% to 20%. The inner wall of the steel pipe is set as a no-slip wall boundary, and standard wall functions are used to handle near-wall turbulence. The outer far-field boundary of the computational domain is set as a pressure far-field boundary to simulate pressure conditions in an open environment. These boundary conditions, along with the initial values ​​of the density and non-Newtonian viscosity of the sprayed raw material, are used as input parameters for the spraying process model.

[0087] In some embodiments, during the generation of an unstructured 3D mesh within the fluid computational domain, the global maximum mesh size of the fluid computational domain is calculated based on the inner diameter and axial length of the steel pipe. The value of the global maximum mesh size is controlled within the range of one-twentieth to one-thirtieth of the inner diameter of the steel pipe. The local mesh refinement size of the nozzle exit region is determined based on the nozzle exit diameter of the spraying equipment. The local mesh refinement size is set to one-tenth to one-fifth of the nozzle exit diameter, and is always smaller than the global maximum mesh size. Starting from the center point of the nozzle exit section, a conical mesh refinement region is defined along the positive direction of the spray axis. The axial extension length of the conical mesh refinement region is set to 10 to 15 times the nozzle exit diameter, and the cone angle of the conical mesh refinement region is set to 15° to 30° to ensure that the spray cone angle completely covers the refinement region.

[0088] In practice, an unstructured tetrahedral element mesh is generated within the fluid computational domain. Within the conical mesh refinement region, the maximum side length of the tetrahedral elements is constrained to be equal to the local mesh refinement size to achieve fine resolution of the near-field vortex ring structure and shock wave structure of the nozzle. A continuous mesh size transition zone is established between the outer edge of the conical mesh refinement region and the rest of the fluid computational domain. Within this transition zone, the size of the tetrahedral elements linearly increases from the local mesh refinement size to the global maximum mesh size to ensure the continuity of the spatial derivatives of the flow field variables. The generated tetrahedral mesh is quality-assessed, checking the twist, aspect ratio, and relative volume change rate of the mesh elements. If twist greater than 0.85, aspect ratio greater than 50, or negative volume is found, the meshing parameters are readjusted and iterative optimization is performed.

[0089] Optionally, the turbulence intensity at the nozzle inlet pressure inlet boundary is set to 5% to 10%, and the turbulence viscosity ratio is set to 10 to 100 to accommodate the strong shear characteristics of the high-pressure gas jet. It is understood that the conical grid refinement region near the nozzle outlet is not limited to a perfect circular cone shape, but can be expanded into a double-cone or elliptical cone region depending on the actual spray pattern. It is understood that the source term in the component conservation equation can be extended based on the evaporation and polymerization reaction kinetics of the raw material particles, but in the basic implementation, only the passive transport of the particulate phase is considered.

[0090] In one embodiment of the present invention, see [reference] Figure 2Point cloud data of the inner wall surface of a steel pipe is acquired using a 3D laser scanner. This point cloud data is then denoised and triangularly meshed to generate a triangular mesh surface model of the inner wall of the steel pipe. The normal vector and area of ​​each triangular facet in this model are calculated, and surface roughness characterization values, including arithmetic mean roughness and maximum profile height, are statistically analyzed. Substrate pretreatment parameters, including cleaning cleanliness level, surface activation energy, and preheating temperature field distribution, are obtained. A sub-model for the initial adhesion probability of the coating is established, using the surface roughness characterization value, cleaning cleanliness level, surface activation energy, and preheating temperature field distribution as input parameters. The geometric information of the triangular mesh surface model is associated with and stored with the calculation results of this sub-model, forming the adhesion interface model. In the workflow of the initial adhesion probability sub-model, the surface roughness characterization value of a single triangular facet is input into a roughness-adhesion coefficient mapping table pre-trained using experimental data, outputting a roughness adhesion influence factor. The cleaning cleanliness level of the corresponding local area of ​​the triangular facet is read and quantified into a cleanliness coefficient between zero and one. The surface activation energy value of the local region corresponding to the triangular facet is read, and the activation adhesion coefficient is calculated based on the adsorption kinetics formula, which uses the surface activation energy value and the substrate preheating temperature as input parameters. The weighted product of the roughness adhesion influence factor, cleanliness coefficient, and activation adhesion coefficient is calculated, and this product result is output as the initial coating adhesion probability of the triangular facet. The above calculation, matching, solving, and weighting operation steps are performed on all triangular facets in the triangular mesh surface model to generate the initial coating adhesion probability field. During the weighted product calculation, corresponding first, second, and third weighting coefficients are set for the roughness adhesion influence factor, cleanliness coefficient, and activation adhesion coefficient, respectively. These weighting coefficients are determined through multivariate nonlinear regression analysis based on historical coating adhesion experimental datasets. The first weighting factor is obtained by multiplying the roughness adhesion influence factor by the first weighting coefficient, the second weighting factor is obtained by multiplying the cleanliness coefficient by the second weighting coefficient, and the third weighting factor is obtained by multiplying the activation adhesion coefficient by the third weighting coefficient. The product of the three weighting factors is calculated to obtain the weighted product result. The result is then normalized so that its value range falls between 0 and 1, resulting in the normalized adhesion probability value. This value is then used as the output of the initial adhesion probability of the coating.

[0091] In the specific implementation, point cloud data of the inner wall of the steel pipe is acquired using a 3D laser scanner. The ranging accuracy of the 3D laser scanner is 0.05 mm, the scanning angle interval is 0.1 degrees, and the acquired point cloud data density is 500 to 800 points per square centimeter. Gaussian filtering is applied to the original point cloud data to remove outliers and measurement noise. The Delaunay triangulation algorithm is used to convert the denoised point cloud into a continuous triangular mesh surface model. The average side length of the triangular mesh is 0.2 mm to 0.5 mm to balance geometric accuracy and computational cost. The unit normal vector and projected area of ​​each triangular facet in the triangular mesh surface model are calculated, and surface roughness characterization values ​​are statistically analyzed based on height undulation data. The surface roughness characterization values ​​include the arithmetic mean roughness and the maximum profile height within an evaluation reference range of 0.8 mm in length. The typical range of the arithmetic mean roughness is Ra5 μm to Ra25 μm, and the typical range of the maximum profile height is Rz40 μm to Rz150 μm.

[0092] In practice, the substrate pretreatment parameters are derived from the process record database at the production site. Cleaning cleanliness levels are divided into three grades: A, B, and C, corresponding to surface grease residue levels of less than 1 mg / m², 1-5 mg / m², and greater than 5 mg / m², respectively. The surface activation energy value is obtained through X-ray photoelectron spectroscopy, measured in kilojoules per mole. The preheating temperature field distribution is measured using an infrared thermal imager, with a temperature measurement error of less than ±2 degrees Celsius. The established sub-model for the initial coating adhesion probability uses the arithmetic mean roughness of a single triangular facet, the cleaning cleanliness level, the surface activation energy value, and the local preheating temperature as independent input variables. Through built-in mapping relationships and calculation rules, it outputs the initial coating adhesion probability.

[0093] In some embodiments, the workflow of the initial adhesion probability sub-model is as follows: The arithmetic mean roughness of a single triangular facet is input into a pre-stored roughness-adhesion coefficient mapping table. This mapping table stores the corresponding adhesion influence factors at roughness intervals of 0.5 micrometers and outputs roughness adhesion influence factors ranging from 0.6 to 1.0. The cleanliness level corresponding to the mesh cell to which the triangular facet belongs is read. The quantification rule is that level A corresponds to a cleanliness coefficient of 0.95, level B corresponds to 0.75, and level C corresponds to 0.5. The surface activation energy value and substrate preheating temperature at the same location are read, and the activation adhesion coefficient is calculated based on the adsorption kinetics formula. The adsorption kinetics formula is:

[0094]

[0095] in: To activate the adhesion coefficient, Pre-exponential factor, This represents the surface activation energy value. This is the universal gas constant. The substrate preheating temperature is set. The weighted product of the roughness adhesion influence factor, cleanliness coefficient, and activation adhesion coefficient is calculated to obtain the unnormalized adhesion tendency value, which is used as the intermediate calculation result for the triangular facet. The above steps are iteratively performed on all triangular facets of the triangular mesh surface model to generate an initial coating adhesion probability field covering the entire inner wall of the steel pipe. The probability values, along with the vertex coordinates and normal vectors of the triangular facets, are stored in the data structure of the adhesion interface model.

[0096] In some embodiments, the weighted product calculation adopts a fixed weight allocation method. The first weight coefficient corresponds to the roughness adhesion influence factor and has a value of 0.35; the second weight coefficient corresponds to the cleanliness coefficient and has a value of 0.45; and the third weight coefficient corresponds to the activation adhesion coefficient and has a value of 0.20. The roughness adhesion influence factor is multiplied by the first weight coefficient to obtain the first weighted factor, the cleanliness coefficient is multiplied by the second weight coefficient to obtain the second weighted factor, and the activation adhesion coefficient is multiplied by the third weight coefficient to obtain the third weighted factor. The three are then multiplied together to obtain the original weighted product. The original weighted product is linearly normalized to map it to the interval between 0 and 1, as shown in the formula: ,in This is the normalized attachment probability value. This is the original weighted product of the current triangular facets. and These are the minimum and maximum values ​​of the original weighted product across the entire field, respectively. The final output is... As the initial adhesion probability of the coating.

[0097] In the process of coating the inner wall of steel pipes, the adhesion behavior of coating raw material particles to the substrate surface can be regarded as a joint event in which three necessary conditions are simultaneously satisfied: the substrate surface must have sufficient roughness to provide mechanical anchoring points, the surface must have sufficient cleanliness to avoid contaminants hindering the direct contact between particles and the substrate, and the surface activation energy must reach a certain threshold to drive the physical or chemical bonding between particles and the substrate. If any one of these three conditions is severely deficient, adhesion will fail, and the other conditions cannot compensate for this deficiency. For example, even if the surface cleanliness and activation energy are extremely high, if the roughness is too low, there is a lack of mechanical interlocking between the particles and the smooth surface, and the coating is still easily peeled off; similarly, even if the roughness and activation energy meet the requirements, if residual oil on the surface leads to insufficient cleanliness, the contaminant layer will block the effective bonding between particles and the substrate; furthermore, if the roughness and cleanliness are good but the surface activation energy is too low, the particles cannot overcome the interfacial energy barrier to complete spreading and adhesion. Therefore, the initial adhesion probability of the coating should, in its physical essence, be expressed as the product of the probabilities of satisfying each of the three independent necessary conditions, rather than a nonlinearly additive algebraic sum. Based on this, this application adopts a weighted product form:

[0098]

[0099] Calculate the adhesion probability, where , , These are the roughness adhesion influence factor, cleanliness coefficient, and activation adhesion coefficient, respectively. , , The corresponding weighting coefficients are shown. This product form accurately reflects the physical fact that "a severe deficiency of any necessary factor will lead to an adhesion probability approaching zero," while the weighted summation form incorrectly allows a high value of one factor to compensate for a low value of another, thus outputting a physically impossible high adhesion probability. The weighting coefficients obtained by fitting three hundred sets of historical coating peeling experimental data through multivariate nonlinear regression minimize the sum of squared residuals between the product calculation result and the measured adhesion rate. Therefore, this model not only does not deviate from the actual process but also closely reflects the adhesion behavior in the actual spraying process than the linear superposition model.

[0100] Optionally, the roughness-adhesion coefficient mapping table is constructed based on plasma spraying experiments on standard test plates with ten different roughnesses. Each experiment is repeated five times, and the average adhesion rate is used as the mapping node. It is understood that the cleanliness level classification can be expanded to four or five levels depending on the specific coating system, but the quantification coefficient must still be maintained between 0 and 1. Optionally, the pre-exponential factor in the adsorption kinetics formula... The adhesion probability can be calibrated using a microbalance adsorption experiment, but the calibration values ​​vary considerably for different raw material systems. It can be understood that if the substrate preheating temperature field changes over time, the initial adhesion probability sub-model of the coating can dynamically update the activation adhesion coefficient according to the time series, thereby refreshing the adhesion probability field.

[0101] In one embodiment of the present invention, see [reference] Figure 3 The time step for coating deposition is defined as an integer multiple of the time step calculated by the spraying process model. At the beginning of each coating deposition time step, the flux of atomized raw material particles reaching a specific grid cell on the inner wall surface of the steel pipe is extracted from the spraying process model after being solved by an improved smooth particle hydrodynamic algorithm. The initial adhesion probability of the coating for the corresponding specific grid cell in the adhesion interface model is queried, and the number of raw material particles actually attached to the grid cell within that time step is calculated. Based on the actual number of attached raw material particles and their average volume, the volume increment of the coating material formed on the grid cell within that time step is calculated. Based on this volume increment and the area of ​​the grid cell, the coating thickness increment of the grid cell within that time step is calculated. The coating thickness of all grid cells at the current time is summed with the thickness increment calculated in this time step to obtain the cumulative thickness distribution of the coating up to the current time.

[0102] In practical implementation, the time step for coating deposition is defined as follows: The computation time step of the spraying process model is The two satisfy a multiple relationship. ,multiple It is a positive integer and its value ranges from 10 to 50, for example, when When set to 0.0001 seconds, The time step can be taken from 0.001 seconds to 0.005 seconds. At the beginning of each coating deposition time step, the flux of atomized raw material particles reaching a specific grid cell on the inner wall surface of the steel pipe is extracted from the spraying process model after solving the improved smooth particle hydrodynamic algorithm. The unit of the flux of atomized raw material particles is the number of particles passing through per square meter per second.

[0103] In practical implementation, the initial adhesion probability of the coating for a specific grid cell in the adhesion interface model is queried. The initial adhesion probability ranges from 0 to 1. The number of raw material particles actually attached to a specific grid cell within the coating deposition time step is calculated using the following formula:

[0104]

[0105] in: This represents the actual number of raw material particles that adhered. This represents the flux of the atomized feed particles. This represents the initial adhesion probability of the coating. For the area of ​​a specific grid cell, The time step for coating deposition is defined as follows: Based on the actual number of attached raw material particles and their average volume, the volume increment of the coating material formed on a specific grid cell within the time step of coating deposition is calculated. The average volume of a single raw material particle is derived from the particle size distribution statistics, which follows a normal distribution with a median particle size of 30 to 60 micrometers.

[0106] In some embodiments, the coating thickness increment of a specific mesh cell within a given time step is calculated based on the volume increment of the coating material and the area of ​​that specific mesh cell. The expression for the coating thickness increment is as follows: ,in For the volume increment of the coating material, This represents the area of ​​a grid cell. The coating thickness of all current grid cells is summed with the calculated coating thickness increment to obtain the cumulative thickness distribution of the coating up to the current time. This cumulative thickness distribution is stored in a two-dimensional array, where the row index corresponds to the axial segment number of the steel pipe, and the column index corresponds to the circumferential grid number. Refer to Table 1 to show the calculation of grid cells at three different locations within a certain coating deposition time step:

[0107] Table 1: Calculation Table of Coating Thickness Increment and Cumulative Thickness

[0108] G_101 12.5 480 0.027 2.16 102.36 G_205 11.8 520 0.029 2.46 98.54 G_310 13.2 450 0.025 1.89 105.21

[0109] Optionally, when calculating the actual number of attached particles, if the mesh cell is located in the sprayed shadow area, the flux of atomized raw material particles can be corrected by multiplying it by a line-of-sight occlusion coefficient, which is between 0.3 and 0.8. It is understood that the volume increment of the coating material can also consider the packing efficiency factor of the raw material particles, which is between 0.85 and 0.95, to reflect the porosity effect caused by particle overlap. Optionally, the calculation of the coating thickness increment can use an equivalent dense thickness model, i.e., dividing the volume increment by the theoretical dense density rather than the loose density. It is understood that the cumulative thickness distribution update operation is performed synchronously after each coating deposition time step to ensure the consistency of the coating growth state.

[0110] In one embodiment of the invention, the volume dynamics algorithm is improved based on the non-Newtonian fluid properties of the coating material particles and their interaction with multiphase flow. The coating material is discretized into a group of smooth particles carrying mass, viscosity, and surface tension properties. When calculating the interaction forces between particles, a non-Newtonian viscous force term based on the fitting of measured rheological curves is introduced to replace the constant viscosity term in the classical algorithm. A virtual pressure term related to the local particle number density is added to the interaction between adjacent particles to characterize the tearing and dispersing effect of the atomized gas on the material particle cluster. In the time integration step of the algorithm, a variable step-size integration strategy is adopted. When the rate of change of particle acceleration in a local region is detected to exceed a threshold, the integration step size is automatically reduced to maintain the computational stability of the area with severe atomization. After each time step calculation, all particles are phase-labeled. Particles whose velocity difference from the surrounding airflow velocity is less than a threshold are labeled as atomized particles, and the rest are labeled as insufficiently atomized particles. Different force calculation coefficients are assigned to particles of different phases in the next time step. After the algorithm completes the calculation of a spraying process model time step, it counts the number and attributes of atomized particles located in the preset adhesion trapping layer on the inner wall surface of the steel pipe at that moment. These attributes include at least the mass, velocity vector, and raw material component identifier of each particle. Based on these attributes, the atomized particles located in the adhesion trapping layer are mapped to the nearest triangular facet in the triangular mesh surface model of the adhesion interface model according to their spatial position. The atomized particles mapped to the same triangular facet are accumulated over multiple consecutive spraying process model calculation time steps. When the accumulated time reaches a coating deposition time step, the accumulated result is passed to the coating increment model as the flux of atomized raw material particles reaching a specific mesh cell on the inner wall surface of the steel pipe.

[0111] In practical implementation, the improved smooth particle hydrodynamic algorithm is modified based on the non-Newtonian fluid properties of the coating material particles and their interaction with multiphase flow. The coating material is discretized into a group of smooth particles, each carrying mass, viscosity properties, and surface tension parameters. The total number of smooth particles is set to 100,000 to 2 million. When calculating the interaction force between smooth particles, a non-Newtonian viscous force term based on the fitting of measured rheological curves is introduced to replace the constant viscosity term in the classic smooth particle hydrodynamic algorithm. The shear rate dependence of the non-Newtonian viscous force term is fitted using the Carreau-Yasuda model, with fitting parameters obtained from a rotational rheometer at shear rates of 1 to 10,000 s⁻¹. -1 Measurement data within the range. A virtual pressure term related to the local particle number density is added to the interaction between adjacent smooth particles. The coefficient of the virtual pressure term is set to 0.01~0.05 to characterize the tearing and dispersion effect of the atomized gas on the raw material particle cluster, thereby enhancing the accuracy of diffusion simulation at the spray edge.

[0112] In practical implementation, a variable step-size integration strategy is adopted in the time integration step of the improved smooth particle hydrodynamics algorithm, with a standard time step of 1×10⁻⁶. -6 s, when the rate of change of acceleration of smooth particles in a local region exceeds the threshold of 1×10 9 When the velocity is m / s³, the time step is automatically reduced to 1 / 10 of its original size to maintain computational stability in areas of intense spray atomization. After each time step calculation, all smooth particles are labeled with their phase state. Smooth particles whose velocity difference from the surrounding airflow velocity is less than a threshold of 5 m / s are labeled as atomized particles, and the rest are labeled as insufficiently atomized particles. In the next time step, different force calculation coefficients are assigned to smooth particles of different phase states. The aerodynamic coefficient for atomized particles is set to 0.02, and the aerodynamic coefficient for insufficiently atomized particles is set to 0.008. The improved smooth particle hydrodynamic algorithm completes the calculation of a spraying process model with a time step (e.g., 1×10⁻⁶). -5 After solving for s), the number and properties of atomized particles located in the preset attachment and capture layer on the inner wall surface of the steel pipe at this moment are counted. The thickness of the attachment and capture layer is set to 0.5 mm. The properties include at least the mass, velocity vector and raw material component identifier of each atomized particle.

[0113] In some embodiments, based on the spatial coordinate attributes of the atomized particles, the atomized particles located within the adhesion trapping layer are mapped to the nearest triangular facet in the triangular mesh surface model of the adhesion interface model according to their spatial position. The mapping rule adopts the nearest neighbor projection algorithm, and the projection error is controlled within 0.1 mm. The atomized particles mapped to the same triangular facet within multiple consecutive spraying process model calculation time steps are accumulated. When the accumulated time reaches a coating deposition time step, the accumulated result is passed to the coating incremental model. The accumulated result includes the total mass flux, average velocity vector, and raw material component ratio, serving as the flux of atomized raw material particles reaching a specific mesh cell on the inner wall surface of the steel pipe. Refer to Table 2, which shows the attributes and mapping results of five atomized particles within the adhesion trapping layer at a certain moment:

[0114] Table 2: Properties of Atomized Particles and Triangular Patch Mapping Table

[0115] P01023 It has been atomized 42.5 125.3 152.34 56.78 -32.91 T_1042 P01024 It has been atomized 38.2 118.7 153.06 57.03 -33.52 T_1042 P01567 It has been atomized 41.8 132.5 210.88 48.99 -28.17 T_2085 P01892 It has been atomized 39.6 121.9 211.53 49.47 -27.86 T_2085 P01943 It has been atomized 44.1 127.4 212.14 48.76 -29.08 T_2091

[0116] In one embodiment of the present invention, a complete modeling process is run to obtain the final cumulative thickness distribution of the coating at the end of the simulation from the coating incremental model. The minimum, maximum, and average coating thicknesses, as well as the standard deviation of the thickness distribution, are extracted from this distribution. The average coating thickness is compared with a preset target coating thickness to generate a thickness mean deviation, and the standard deviation of the thickness distribution is compared with a preset uniformity index to generate a uniformity deviation. With reducing these two deviations as the optimization objective, a process parameter optimization objective function is established, involving process parameters including spray pressure, nozzle movement speed, and spraying distance. A gradient descent search strategy is used to adjust the values ​​of these process parameters, and the adjusted parameters are used as new inputs to restart the complete modeling process from the spraying process model to the coating incremental model. The above steps of running the complete process and adjusting parameters are repeated until both the thickness mean deviation and the uniformity deviation are less than their corresponding allowable thresholds. The process parameters used at this point are recorded as the optimized process parameter set.

[0117] In practice, a complete modeling process is executed, including sequential calculations from the spraying process model, the adhesion interface model, and the coating increment model, until the spraying simulation time reaches the preset total duration. The final cumulative coating thickness distribution at the end of the simulation is obtained from the coating increment model. The final cumulative coating thickness distribution is stored in a two-dimensional matrix. The row index of the matrix corresponds to the segment number along the axial direction of the steel pipe, and the column index corresponds to the circumferential grid number. Each element represents the coating thickness value of the corresponding grid cell. From the final cumulative coating thickness distribution, the minimum, maximum, and average coating thicknesses, as well as the standard deviation of the thickness distribution, are extracted. The average thickness is calculated using the arithmetic mean method, and the standard deviation of the thickness distribution reflects the degree of fluctuation in coating thickness on the inner wall surface of the steel pipe.

[0118] In practical implementation, the average coating thickness is compared with a preset target coating thickness, set at 200 micrometers, generating a thickness mean deviation, which is the absolute value of the difference between the target thickness and the simulated average thickness. The standard deviation of the thickness distribution is compared with a preset uniformity index, set at 15 micrometers, generating a uniformity deviation, which is the absolute value of the difference between the simulated standard deviation and the uniformity index. With reducing the thickness mean deviation and uniformity deviation as the optimization objective, an objective function for optimizing process parameters is established. These process parameters include spray pressure, nozzle movement speed, and spraying distance. The mathematical form of the objective function is:

[0119]

[0120] in: The objective function value, For process parameter vectors, To simulate the average coating thickness, To preset the target coating thickness, To simulate the standard deviation of thickness distribution, To preset the uniformity index, , These are the weighting coefficients, which are 0.6 and 0.4 respectively.

[0121] Throughout the simulation process, the spraying process model uses spray pressure as the primary factor. Nozzle movement speed Spraying distance As boundary conditions and initial input parameters, an improved smooth particle hydrodynamics algorithm is used to solve for the flow field and particle transport, thereby affecting the flux of atomized raw material particles reaching the inner wall surface of the steel pipe. The adhesion interface model outputs the adhesion probability based on local surface roughness, cleanliness, and activation energy. The coating increment model combines particle flux and adhesion probability to calculate the coating thickness increment of each grid cell. Therefore, the average coating thickness is... with standard deviation Essentially , , implicit functions, i.e.

[0122]

[0123] However, these two functions lack closed analytical expressions and can only be evaluated point-by-point through numerical simulation. To implement a gradient descent search strategy without explicit mathematical expressions, a numerical gradient approximation method based on the finite difference method is adopted: for the current combination of process parameters... Apply a small perturbation to each parameter. , , Calculate the perturbed objective function values ​​sequentially. , , Then use the central difference formula

[0124]

[0125] Calculate the approximate partial derivatives of the objective function with respect to each process parameter, where the values ​​of the disturbances are determined based on the physical dimensions and numerical ranges of each parameter: the disturbance of the injection pressure. The value is 0.01 MPa, representing the disturbance of the nozzle moving speed. The value is 10 mm / s, representing the disturbance of the spraying distance. The value is set to 5mm. After obtaining approximate values ​​for each partial derivative, the update rule is applied according to gradient descent:

[0126]

[0127] Simultaneously adjust three process parameters, including the learning rate. Initially set to 0.1, if the objective function value after this iteration... Compared to If the learning rate increases, reduce it to 0.5 times the current value and recalculate the update step until the objective function value decreases or the maximum number of retries is reached. Each iteration requires running the entire simulation process from the spraying process model, adhesion interface model to the coating increment model to obtain the updated objective function value. This process is repeated until the thickness mean deviation is reached. With uniformity deviation The optimization terminates when all parameters are less than their respective allowable thresholds. The combination of process parameters recorded at this point is the optimized set of process parameters. The above parameter optimization method based on numerical gradient does not rely on an explicit analytical expression of the objective function for the process parameters. It can achieve gradient descent search solely based on the numerical relationship between the input and output of the simulation process. Therefore, the technical solution is complete, clear, and reproducible, and there is no issue of insufficient disclosure.

[0128] In some embodiments, a gradient descent search strategy is used to adjust the values ​​of the process parameters. The learning rate of gradient descent is set to 0.1, and the initial combination of process parameters is: spray pressure 0.6 MPa, nozzle moving speed 300 mm / s, and spraying distance 120 mm. In each iteration, the partial derivatives of the objective function with respect to each process parameter are calculated, and the parameters are adjusted according to the sign and magnitude of the partial derivatives. If the objective function value increases, the learning rate is reduced to 0.05. The adjusted process parameters are used as new inputs, and the complete modeling process from the spraying process model to the coating incremental model is restarted to complete one iteration of optimization. The steps from running the complete modeling process to adjusting the process parameters are repeated. The iteration is terminated when the mean thickness deviation is less than 5 micrometers and the uniformity deviation is less than 2 micrometers. The process parameters used at this time are recorded as the optimized process parameter set.

[0129] Optionally, the weighting coefficients of the objective function for optimizing process parameters can be adjusted according to the coating application scenario. When the thickness uniformity of the anti-corrosion coating is emphasized, the weighting coefficients can be increased. Up to 0.6. It is understood that the gradient descent search strategy can employ a variant with momentum to accelerate convergence, with the momentum coefficient set to 0.9 to reduce oscillations. Optionally, the iteration termination condition can be relaxed to a thickness mean deviation of less than 8 micrometers and a uniformity deviation of less than 3 micrometers to shorten the optimization cycle. It is understood that the process parameter set may also include auxiliary parameters such as nozzle oscillation frequency and spraying angle, but the basic implementation only optimizes the three core parameters.

[0130] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. A method for modeling the formation process of a coating on the inner wall of a steel pipe, characterized in that, The method includes: Based on the physicochemical properties and process parameters of the coating raw materials, a spraying process model describing the spraying flow field and the transport of raw material particles is established. Based on the three-dimensional geometric scanning data of the inner wall of the steel pipe, a three-dimensional topological mapping of the inner wall surface of the steel pipe is generated, and combined with the substrate preprocessing parameters, an adhesion interface model reflecting the coating adhesion behavior is constructed. Based on the output of the spraying process model and the output of the adhesion interface model, an incremental coating model describing the coating deposition and growth process is constructed. An improved smooth particle fluid dynamics algorithm based on the interaction between the non-Newtonian fluid properties of coating raw material particles and multiphase flow is used to solve the spraying process model to simulate the motion, atomization and spatial distribution of coating raw material particles in the flow field. The spatial distribution results obtained by solving the improved smooth particle hydrodynamic algorithm are input into the coating increment model to drive the layer-by-layer accumulation process of the coating in the time dimension; Based on the preset target coating thickness and uniformity indicators, and combined with the cumulative results simulated by the coating incremental model, the process parameter input of the spraying process model is iteratively optimized in reverse to form a closed-loop modeling process.

2. The method for modeling the coating formation process on the inner wall of a steel pipe according to claim 1, characterized in that, The establishment of a spraying process model describing the spraying flow field and raw material particle transport includes: Obtain the geometric parameters of the nozzle of the spraying equipment and the injection pressure and flow rate parameters of the high-pressure gas; Define a fluid computational domain that includes the internal space of the steel pipe and the external spray area; Within the fluid computation domain, an unstructured three-dimensional mesh is generated, and the mesh near the nozzle outlet is locally refined. Establish a set of governing equations, which includes the mass conservation equation, the momentum conservation equation, and the component conservation equation describing the phase concentration transport of raw material particles. Boundary conditions are set for the governing equations, including: the nozzle inlet is set as a pressure inlet boundary, and an initial gas velocity and initial concentration of raw material particles are assigned; the steel pipe wall is set as a no-slip wall boundary, and the turbulent wall function is enabled; the outer boundary of the computational domain is set as a pressure far-field boundary. The boundary conditions and the initial values ​​of density and viscosity of the spraying material are used as inputs to the spraying process model. Within the fluid computation domain, an unstructured three-dimensional mesh is generated, and the mesh near the nozzle outlet is locally refined, including: Set the global maximum grid size for the fluid computation domain, and determine the global maximum grid size based on the inner diameter and axial length of the steel pipe; Based on the outlet diameter of the nozzle of the spraying equipment, a local mesh refinement size is set for the nozzle outlet area, wherein the local mesh refinement size is smaller than the global maximum mesh size; Starting from the center of the nozzle outlet, a conical mesh reinforcement region is defined along the injection axis, and the axial extension length and cone angle of the conical mesh reinforcement region are set. An unstructured tetrahedral mesh is generated within the fluid computation domain, and the mesh size is controlled to the local mesh refinement size within the conical mesh refinement region. At the boundary between the conical mesh refinement region and other regions of the fluid computing domain, a mesh size transition gradient is set to smoothly transition the mesh size from the local mesh refinement size to the global maximum mesh size; The generated mesh is subjected to quality checks to ensure that the mesh distortion, aspect ratio, and volume change rate meet the preset numerical calculation requirements.

3. The method for modeling the coating formation process on the inner wall of a steel pipe according to claim 2, characterized in that, The three-dimensional geometric scanning data based on the inner wall of the steel pipe generates a three-dimensional topological mapping of the inner wall surface of the steel pipe, and, combined with substrate preprocessing parameters, constructs an adhesion interface model reflecting the coating adhesion behavior, including: Point cloud data of the inner wall surface of the steel pipe was obtained using a 3D laser scanner; The point cloud data is denoised and triangulated to generate a triangular mesh surface model of the inner wall of the steel pipe. Calculate the normal vector and area of ​​each triangular facet in the triangular mesh surface model, and statistically analyze the surface roughness characterization value, which includes the arithmetic mean roughness and the maximum profile height. Obtain substrate pretreatment parameters, including cleaning cleanliness level, surface activation energy value, and preheating temperature field distribution; A sub-model of the initial adhesion probability of the coating is established, taking surface roughness characterization value, cleaning cleanliness level, surface activation energy value and preheating temperature field distribution as input parameters; The geometric information of the triangular mesh surface model is associated and stored with the calculation results of the coating initial adhesion probability sub-model to jointly constitute the adhesion interface model.

4. The method for modeling the coating formation process on the inner wall of a steel pipe according to claim 3, characterized in that, Based on the outputs of the spraying process model and the adhesion interface model, an incremental coating model describing the coating deposition and growth process is constructed, including: Define a coating deposition time step, which is an integer multiple of the time step calculated by the spraying process model; At the start of each coating deposition time step, the flux of atomized raw material particles reaching a specific grid cell on the inner wall surface of the steel pipe is extracted from the spraying process model after being solved by the improved smooth particle hydrodynamic algorithm. Query the initial adhesion probability of the coating for a specific grid cell in the adhesion interface model, and calculate the number of raw material particles actually attached to the specific grid cell within the time step of coating deposition. Based on the actual number of attached raw material particles and their average volume, calculate the volume increment of the coating material formed on the specific grid cell within the time step of the coating deposition; Based on the volume increment of the coating material and the area of ​​the specific mesh cell, the coating thickness increment of the specific mesh cell within this time step is calculated; The coating thickness of all current mesh cells is added to the coating thickness increment calculated in this instance to obtain the cumulative thickness distribution of the coating up to the current moment.

5. The method for modeling the coating formation process on the inner wall of a steel pipe according to claim 4, characterized in that, The improved smooth particle hydrodynamics algorithm is based on the interaction between the non-Newtonian fluid properties of the coating raw material particles and multiphase flow. Its working principle includes: The coating material is discretized into a group of smooth particles carrying mass, viscosity and surface tension properties; When calculating the interaction forces between particles, a non-Newtonian viscous force term based on the fitting of measured rheological curves is introduced to replace the constant viscosity term in the classical algorithm. To characterize the tearing and dispersion effect of atomized gas on raw material particle clusters, a virtual pressure term related to the local particle number density is added to the interaction between adjacent particles. In the time integration step of the algorithm, a variable step size integration strategy is adopted. When the rate of change of particle acceleration in a local area is detected to exceed the threshold, the integration step size is automatically reduced to maintain the computational stability of the area with severe spray atomization. After each time step calculation is completed, all particles are marked with phase status. Particles whose velocity difference with the surrounding airflow velocity is less than a threshold are marked as atomized particles, and the rest are marked as insufficiently atomized particles. In the next time step, different force calculation coefficients are assigned to particles of different phase status.

6. The method for modeling the coating formation process on the inner wall of a steel pipe according to claim 5, characterized in that, The spatial distribution results obtained by solving the improved smooth particle hydrodynamic algorithm are input into the coating incremental model, including: After the improved smooth particle hydrodynamic algorithm completes the calculation of the time step of a spraying process model, the number and properties of the atomized particles located in the preset adhesion and capture layer on the inner wall surface of the steel pipe at this moment are counted. The attributes include at least the mass, velocity vector, and raw material component identifier for each atomized particle; Based on the aforementioned properties, the atomized particles located within the attachment and capture layer are mapped according to their spatial positions onto the nearest triangular facet in the triangular mesh surface model of the attachment interface model. The accumulated atomized particles mapped onto the same triangular facet within multiple consecutive spraying process model calculation time steps are used. When the accumulated time reaches a coating deposition time step, the accumulated result is passed to the coating increment model as the flux of atomized raw material particles reaching a specific grid cell on the inner wall surface of the steel pipe.

7. The method for modeling the coating formation process on the inner wall of a steel pipe according to claim 1, characterized in that, The process parameter input of the spraying process model is iteratively optimized in reverse, based on the preset target coating thickness and uniformity indicators and the cumulative results simulated by the coating incremental model, including: Run the complete modeling process to obtain the final cumulative thickness distribution of the coating at the end of the simulation from the incremental coating model; Extract the minimum, maximum, and average thickness values ​​and the standard deviation of the thickness distribution from the final cumulative thickness distribution of the coating. The average coating thickness is compared with the preset target coating thickness to generate the mean thickness deviation. The standard deviation of the thickness distribution is compared with the preset uniformity index to generate the uniformity deviation. With the goal of reducing the mean thickness deviation and the uniformity deviation, an objective function for optimizing process parameters is established, including spraying pressure, nozzle moving speed, and spraying distance. A gradient descent search strategy is adopted to adjust the values ​​of the process parameters, and the adjusted process parameters are used as new inputs to restart the complete modeling process from the spraying process model to the coating incremental model. Repeat the steps from running the complete modeling process to adjusting the process parameters until the mean thickness deviation and the uniformity deviation are both less than their corresponding allowable thresholds. Record the process parameters used at this time as the optimized process parameter set.

8. The method for modeling the coating formation process on the inner wall of a steel pipe according to claim 3, characterized in that, The workflow of the coating initial adhesion probability sub-model includes: The surface roughness characterization value of a single triangular facet of the triangular mesh surface model is input into a roughness-adhesion coefficient mapping table that has been trained in advance with experimental data, and a roughness adhesion influence factor is output. Read the cleaning cleanliness level of the local area corresponding to the triangular facet, and quantify the cleaning cleanliness level into a cleanliness coefficient between zero and one. Read the surface activation energy value of the local area corresponding to the triangular facet, and calculate an activation adhesion coefficient based on the adsorption kinetics formula, which uses the surface activation energy value and the substrate preheating temperature as input parameters. Calculate the weighted product of the roughness adhesion influence factor, cleanliness coefficient and activation adhesion coefficient, and output the result of the weighted product as the initial adhesion probability of the coating on the triangular facet. The roughness adhesion influence factor calculation, cleanliness coefficient matching, activation adhesion coefficient solution, and weighted calculation of three types of parameters are performed on all triangular facets in the triangular mesh surface model to generate the initial adhesion probability field of the coating.

9. The method for modeling the coating formation process on the inner wall of a steel pipe according to claim 8, characterized in that, Calculate the weighted product of the roughness adhesion influence factor, cleanliness coefficient, and activation adhesion coefficient, and output the result of the weighted product as the initial adhesion probability of the coating on the triangular facet, including: The roughness adhesion influence factor, cleanliness coefficient and activation adhesion coefficient are respectively assigned a first weight coefficient, a second weight coefficient and a third weight coefficient, and the weight coefficients are determined by multivariate nonlinear regression analysis based on historical coating adhesion experimental datasets; Multiply the roughness adhesion influence factor by the first weighting coefficient to obtain the first weighting factor; Multiply the cleanliness coefficient by the second weighting coefficient to obtain the second weighting factor; Multiply the activation adhesion coefficient by the third weighting coefficient to obtain the third weighting factor; Calculate the product of the first weighting factor, the second weighting factor, and the third weighting factor to obtain the weighted product result; The weighted product result is normalized so that its value range falls between 0 and 1, resulting in a normalized attachment probability value. The normalized adhesion probability value is output as the initial adhesion probability of the coating on the triangular facet.

10. A modeling system for the formation process of a coating on the inner wall of a steel pipe, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the modeling method for the formation process of coating on the inner wall of a steel pipe as described in any one of claims 1 to 9.

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