Simulation method, device and equipment for OLED inkjet printing and storage medium

Abstract

The present application relates to the technical field of simulation, and particularly relates to an OLED inkjet printing simulation method, device, equipment and storage medium, the method solves the technical pain point that a single modeling framework is difficult to consider simulation accuracy and calculation efficiency in the prior art by configuring simulation resources in stages, dynamically determining stage switching and sequentially delivering stage information; specifically, stages are divided according to the physical evolution law of the inkjet process, so that each stage model is accurately matched with the dominant physical mechanism, the dynamics characteristics of key behaviors such as ink supply response, liquid column necking, droplet shape adjustment and the like are finely depicted, calculation redundancy of non-key stages is reduced through an adaptive simplification strategy, continuous simulation of the whole process from jet start to droplet deposition is realized, physical quantity conservation and evolution consistency are ensured, simulation accuracy and calculation efficiency are significantly improved compared with traditional methods, pixel deposition consistency is effectively improved, and actual process trial and error cost is reduced.

Description

Technical Field

[0001] This invention relates to the field of simulation technology, and in particular to a simulation method, apparatus, equipment and storage medium for OLED inkjet printing. Background Technology

[0002] Inkjet printing technology has been widely used in fields such as micro-nano structure fabrication, functional material deposition, and display and electronic device manufacturing due to its advantages such as high material utilization, flexible process path, and ability to achieve on-demand deposition and patterning control. In particular, it has gradually become one of the core processes in the manufacturing of organic light-emitting diodes (OLEDs), where material utilization efficiency and deposition accuracy are extremely important.

[0003] The OLED inkjet printing process is a typical unsteady free interface flow problem, which includes multiple unsteady stages such as ink supply response inside the nozzle, free liquid surface extension, formation and breakage of continuous liquid structure, and droplet movement in the gas phase space. The different stages differ significantly in terms of the dominant mechanical mechanism (relative interaction of inertial force, viscous force, and surface tension), time scale, and spatial scale, and the dynamic behavior is highly sensitive to changes in process parameters.

[0004] Existing numerical analysis methods for inkjet printing mostly focus on the characteristics of the final ejection result, such as droplet geometry and deposition location, as the core objective. They achieve simulation evaluation by establishing a correspondence between process parameters and result characteristics. These numerical analysis methods incorporate the entire inkjet process into a unified and simplified modeling framework, using a single physical model, governing equations, and numerical strategies for holistic processing. While they can meet the needs of macroscopic parameter evaluation and trend judgment, they have significant limitations: First, they are difficult to characterize the differences in the dominant physical mechanisms at different stages in detail; second, they cannot accurately reflect the differences in inkjet dynamics response caused by changes in process parameters; and third, they are difficult to balance between the refined process analysis and rapid parameter evaluation required for OLED inkjet printing, and cannot provide sufficient simulation support for ejection stability optimization and process parameter adjustment.

[0005] It is evident that existing technologies still need improvement and enhancement. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, the present invention aims to provide a simulation method for OLED inkjet printing, which achieves synergistic optimization of simulation accuracy and computational efficiency by clarifying stage correlations, quantifying configuration criteria, and refining switching rules.

[0007] The first aspect of this invention provides a simulation method for OLED inkjet printing, comprising: acquiring preset input process parameters and continuously collecting current physical quantities during the simulation process; loading first configuration information corresponding to the initial formation stage and performing simulation operations based on the first configuration information to calculate jetting start-up information; determining whether the entry conditions for the continuous liquid structure formation stage are met according to the input process parameters and the current physical quantities; if so, loading second configuration information corresponding to the continuous liquid structure formation stage and performing simulation operations based on the jetting start-up information and the second configuration information to calculate liquid column morphology information; determining whether the entry conditions for the droplet separation stage are met according to the current physical quantities; if so, loading third configuration information corresponding to the droplet separation stage and performing simulation operations based on the third configuration information. The system performs simulation operations based on information and liquid column morphology information to calculate droplet information. It then determines whether the entry conditions for the initial flight phase are met based on the current physical quantities. If so, it loads the fourth configuration information corresponding to the initial flight phase and performs simulation operations based on the droplet information and the fourth configuration information to calculate stable droplet parameters. Next, it determines whether the entry conditions for the stable flight phase are met based on the current physical quantities. If so, it loads the fifth configuration information corresponding to the stable flight phase and performs simulation operations based on the stable droplet parameters and the fifth configuration information to calculate the final droplet deposition parameters. Finally, it integrates the jet initiation information, liquid column morphology information, droplet information, stable droplet parameters, and final droplet deposition parameters to form a simulation result, which guides the OLED inkjet printing operation.

[0008] Optionally, in a first implementation of the first aspect of the present invention, the step of acquiring preset input process parameters and continuously collecting current physical quantities during the simulation process includes: acquiring preset input process parameters, the input process parameters including nozzle parameters, ink property parameters, driving signal parameters, and gas phase environment parameters; continuously collecting current physical quantities during the simulation process, the current physical quantities including velocity field, pressure field, liquid-gas interface state, liquid geometric parameters, and dynamic parameters; and sequentially performing denoising processing, completion processing, and standardization processing on the current physical quantities to obtain standardized physical quantities.

[0009] Optionally, in a second implementation of the first aspect of the present invention, loading the first configuration information corresponding to the initial formation stage and performing simulation operations based on the first configuration information to calculate the injection start-up information includes: loading the first configuration information corresponding to the initial formation stage, wherein the first configuration information includes a first physical model, a first mesh configuration, a first time step configuration, and a first boundary condition, wherein the first physical model includes the incompressible fluid continuity equation and the Navier-Stokes equation; initializing the simulation calculation domain based on the first configuration information and configuring the initial state parameters of the simulation calculation domain; performing unsteady-state simulation calculations in the simulation calculation domain based on input process parameters and standardized physical quantities, and continuously monitoring the initial deformation state of the free liquid surface; and extracting the injection start-up information when the free liquid surface extension distance is ≥ 1 / 10 of the nozzle inner diameter, wherein the injection start-up information includes the velocity distribution time-series curve at the nozzle outlet, the pressure change waveform inside the nozzle, the initial displacement trajectory of the free liquid surface, and the start-up time point.

[0010] Optionally, in a third implementation of the first aspect of the present invention, the step of determining whether the entry conditions for the continuous liquid structure formation stage are met based on the input process parameters and the current physical quantity, and if so, loading the second configuration information corresponding to the continuous liquid structure formation stage, and performing a simulation operation based on the injection start information and the second configuration information to calculate the liquid column morphology information, includes: calculating the condition judgment value based on the standardized physical quantity, and determining whether the entry conditions for the continuous liquid structure formation stage are met based on the input process parameters and the condition judgment value; if so, loading the second configuration information, the second configuration... The information includes a second physical model, a second mesh configuration, and a second time step configuration. The second physical model includes the Navier-Stokes equations with a CSF surface tension model and an interface tracking method, which is either the volume fraction method or the level set method. The injection start-up information is imported into the current simulation calculation domain as initial conditions, and the simulation calculation is started. The length-to-diameter ratio and morphological change rate of the liquid column are continuously monitored. When the length-to-diameter ratio of the liquid column is ≥3 and the morphological change rate is ≤5%, the liquid column morphological information is extracted. The liquid column morphological information includes the total length of the liquid column, the maximum diameter, the interface curvature distribution, and the internal velocity gradient.

[0011] Optionally, in the fourth implementation of the first aspect of the present invention, the step of determining whether the entry conditions for the droplet separation stage are met based on the current physical quantity, and if so, loading the third configuration information corresponding to the droplet separation stage, and performing a simulation operation based on the third configuration information and the liquid column morphology information to calculate the droplet information, includes: determining whether the entry conditions for the droplet separation stage are met based on the liquid geometric parameters and dynamic parameters; if so, loading the third configuration information, which includes a third physical model, a third mesh configuration, and a third time step configuration, wherein the third physical model adopts the interface tracking method for the continuous liquid structure formation stage; importing the liquid column morphology information into the current simulation calculation domain to initialize the necking fracture calculation module and boundary conditions of the current simulation calculation domain, and then performing simulation calculations and continuously monitoring the necking rate; when the necking rate is ≤ a preset fracture judgment threshold, extracting the droplet information, which includes the droplet mass, equivalent radius, initial velocity, surface morphology, and fracture position coordinates.

[0012] Optionally, in the fifth implementation of the first aspect of the present invention, the step of determining whether the entry conditions for the initial flight stage are met based on the current physical quantity, and if so, loading the fourth configuration information corresponding to the initial flight stage, and performing simulation operations based on the droplet information and the fourth configuration information to calculate stable droplet parameters, includes: determining whether the entry conditions for the initial flight stage are met based on the liquid-gas interface state, liquid geometric parameters, and dynamic parameters; if so, loading the fourth configuration information, which includes a fourth physical model, a fourth mesh configuration, and a fourth time step configuration, wherein the fourth physical model includes the Lagrange momentum equation, the interface tracking model, the coupled Stokes drag model, and the Laplace pressure equation; importing the droplet information into the current simulation calculation domain to initialize the gas phase environment parameters and droplet motion equations of the current simulation calculation domain, and then performing simulation calculations, while continuously monitoring the tail length and the rate of change of interface curvature; when the tail length is less than or equal to 1 / 3 of the droplet's equivalent radius and the rate of change of interface curvature is less than or equal to 1 / 3 of the droplet's equivalent radius and the rate of change of interface curvature is less than or equal to 1 / 3 of the droplet's equivalent radius and the rate of change of interface curvature is less than or equal to 1 / 3 of the droplet's equivalent radius and the droplet's equivalent radius ... At that time, stable droplet parameters are extracted, including the stable equivalent radius of the droplet, the adjusted flight speed, and the surface curvature uniformity.

[0013] Optionally, in the sixth implementation of the first aspect of the present invention, the step of determining whether the entry conditions for the stable flight phase are met based on the current physical quantity, and if so, loading the fifth configuration information corresponding to the stable flight phase, and performing a simulation operation based on the stable droplet parameters and the fifth configuration information to calculate the final deposition parameters of the droplet, includes: determining whether the entry conditions for the stable flight phase are met based on the tail length, the rate of change of interface curvature and the stable droplet parameters; if so, loading the fifth configuration information corresponding to the stable flight phase, the fifth configuration information including a fifth physical model, a fifth mesh configuration and a fifth time step configuration, the fifth physical model including an equivalent particle dynamics model and an empirical formula for air resistance; importing the stable droplet parameters into the current simulation calculation domain, initializing the boundary conditions of the deposition surface, and then performing the simulation calculation steps, while continuously monitoring the distance between the droplet and the deposition surface; when the droplet reaches the deposition surface, extracting the final deposition parameters of the droplet, the final deposition parameters of the droplet including the deposition location coordinates, impact velocity, deposition morphology radius and spreading area.

[0014] A second aspect of the present invention provides a simulation device for OLED inkjet printing, comprising: an acquisition module for acquiring preset input process parameters and continuously collecting current physical quantities during the simulation process; a first simulation module for loading first configuration information corresponding to the initial formation stage and performing simulation operations based on the first configuration information to calculate jetting start-up information; a second simulation module for determining whether the entry conditions for the continuous liquid structure formation stage are met based on the input process parameters and current physical quantities, and if so, loading second configuration information corresponding to the continuous liquid structure formation stage and performing simulation operations based on the jetting start-up information and second configuration information to calculate liquid column morphology information; and a third simulation module for determining whether the entry conditions for the droplet separation stage are met based on the current physical quantities, and if so, loading third configuration information corresponding to the droplet separation stage and performing simulation operations based on the first configuration information. The third simulation module uses the configuration information and liquid column morphology information to perform simulation operations to calculate droplet information; the fourth simulation module is used to determine whether the entry conditions for the initial flight stage are met based on the current physical quantity. If so, it loads the fourth configuration information corresponding to the initial flight stage and performs simulation operations based on the droplet information and the fourth configuration information to calculate stable droplet parameters; the fifth simulation module is used to determine whether the entry conditions for the stable flight stage are met based on the current physical quantity. If so, it loads the fifth configuration information corresponding to the stable flight stage and performs simulation operations based on the stable droplet parameters and the fifth configuration information to calculate the final droplet deposition parameters; the integration module is used to integrate the jet initiation information, liquid column morphology information, droplet information, stable droplet parameters, and final droplet deposition parameters to form simulation results, and guides OLED inkjet printing operations based on the simulation results.

[0015] A third aspect of the present invention provides a simulation device for OLED inkjet printing, the simulation device comprising: a memory and at least one processor, the memory storing instructions; the at least one processor calling the instructions in the memory to cause the simulation device for OLED inkjet printing to perform the various steps of the simulation method for OLED inkjet printing described in any of the preceding claims.

[0016] A fourth aspect of the present invention provides a computer-readable storage medium storing instructions that, when executed by a processor, implement the steps of the simulation method for OLED inkjet printing described in any of the preceding claims.

[0017] The technical solution of this invention solves the technical pain point of existing technologies where a single modeling framework cannot balance simulation accuracy and computational efficiency by configuring simulation resources in stages, dynamically determining stage switching, and orderly transmitting stage information. Specifically, the method divides the process into stages according to the physical evolution of the inkjet process, so that the model of each stage is accurately matched with the dominant physical mechanism. It not only meticulously depicts the dynamic characteristics of key behaviors such as ink supply response, liquid column necking, and droplet shape adjustment, but also reduces the computational redundancy of non-critical stages through an adaptive simplification strategy. This achieves continuous simulation of the entire process from jet initiation to droplet deposition, ensuring the conservation and consistency of physical quantities. The simulation accuracy and computational efficiency are significantly improved compared with traditional methods. It can provide comprehensive and reliable simulation support for parameter optimization and stability control of OLED inkjet printing process, effectively improve pixel deposition consistency, and reduce process trial and error costs. Attached Figure Description

[0018] Figure 1 A logic flowchart of the simulation method for OLED inkjet printing provided in an embodiment of the present invention;

[0019] Figure 2 A schematic diagram of the structure of a simulation device for OLED inkjet printing provided in an embodiment of the present invention;

[0020] Figure 3 This is a schematic diagram of the structure of a simulation device for OLED inkjet printing provided in an embodiment of the present invention. Detailed Implementation

[0021] This invention provides a simulation method, apparatus, device, and storage medium for OLED inkjet printing. In this invention, the terms "first," "second," "third," "fourth," etc. (if applicable) in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0022] This application discloses a simulation method for OLED inkjet printing. For ease of understanding, the specific process of the embodiments of the present invention is described below. Please refer to [link / reference]. Figure 1 One embodiment of the simulation method for OLED inkjet printing in this invention includes:

[0023] 101. Obtain the preset input process parameters and continuously collect the current physical quantities during the simulation process;

[0024] In this embodiment, the current physical quantities are collected and updated synchronously in real time, which can accurately capture the dynamic changes of the physical state during the simulation process. This provides real-time data support for stage switching judgment and model parameter adjustment, ensuring that the simulation process is consistent with the physical evolution law of actual OLED inkjet printing, and laying a data foundation for accurate simulation of subsequent stages.

[0025] 102. Load the first configuration information corresponding to the initial formation stage, and perform simulation operations based on the first configuration information to calculate the injection start information;

[0026] In this embodiment, the core physical behavior of the initial formation stage is that the liquid inside the nozzle establishes a flow field and forms the initial conditions for injection under the action of the driving signal. The first configuration information is a set of simulation settings specifically adapted to the physical characteristics of this stage, which can accurately characterize the transient flow response of the liquid inside the nozzle and the initial deformation process of the free liquid surface, avoiding flow field distortion caused by improper model or mesh settings. Through standardized simulation execution process and clear injection start information extraction conditions, the obtained injection start information is ensured to be complete and accurate, which can provide reliable initial boundary conditions for the subsequent continuous liquid structure formation stage.

[0027] 103. Determine whether the entry conditions for the continuous liquid structure formation stage are met based on the input process parameters and current physical quantities. If so, load the second configuration information corresponding to the continuous liquid structure formation stage, and perform simulation operations based on the injection start information and the second configuration information to calculate the liquid column morphology information.

[0028] In this embodiment, the core physical behavior of the continuous liquid structure formation stage is the continuous outward extension of liquid from the nozzle outlet to form a stable liquid column. The second configuration information is a simulation setting adapted to the physical characteristics of the rapid evolution of the liquid-gas interface and the enhanced dominance of surface tension in this stage, which can accurately capture the outward extension and deformation process of the liquid-gas interface. The extracted liquid column morphology information fully reflects the key characteristics of the liquid column, providing accurate initial geometric and physical state data for the simulation of the necking and fracture process in the subsequent droplet separation stage, and ensuring the simulation continuity between the liquid column formation and droplet separation stages.

[0029] 104. Determine whether the entry conditions for the droplet separation stage are met based on the current physical quantity. If so, load the third configuration information corresponding to the droplet separation stage, and perform simulation operations based on the third configuration information and the liquid column morphology information to calculate the droplet information.

[0030] In this embodiment, the core physical behavior of the droplet separation stage is that the stable liquid column necks under the combined action of inertial force, viscous force, and surface tension, and eventually breaks to form independent droplets. The third configuration information is a simulation setting adapted to the physical characteristics of the necking region, such as severe deformation and large changes in interface curvature, which can accurately capture the subtle deformation of the necking region and the physical state at the moment of breakage. The extracted droplet information fully reflects the core characteristics of droplet generation, providing high-precision initial data for the subsequent simulation of the droplet's motion trajectory and morphological evolution during the flight stage, ensuring the consistency of the simulation logic from droplet generation to flight.

[0031] 105. Determine whether the entry conditions for the initial flight phase are met based on the current physical quantity. If so, load the fourth configuration information corresponding to the initial flight phase, and perform simulation operations based on the droplet information and the fourth configuration information to calculate the stable droplet parameters.

[0032] In this embodiment, the core physical behavior of the initial flight phase is the morphological adjustment of the broken droplet in the gaseous environment. The fourth configuration information is a simulation setting adapted to the physical characteristics of the strong coupling between droplet morphology and flight motion, and surface tension driving morphological retraction in this phase. It can accurately characterize the coupling relationship between droplet morphological adjustment and flight motion. The extracted stable droplet parameters provide high-quality initial data for the simplified simulation of the subsequent stable flight phase, realizing a smooth transition from refined morphological characterization to efficient trajectory calculation, and ensuring the simulation accuracy of the entire droplet flight process.

[0033] 106. Determine whether the entry conditions for the stable flight phase are met based on the current physical quantity. If so, load the fifth configuration information corresponding to the stable flight phase, and perform a simulation operation based on the stable droplet parameters and the fifth configuration information to calculate the final droplet deposition parameters.

[0034] In this embodiment, the core physical behavior of the stable flight phase is that the morphologically stable droplet flies along the trajectory in the gas phase environment and eventually impacts the deposition surface. The fifth configuration information is a simulation setting adapted to the physical characteristics of the droplet's stable morphology, weak interface changes, and dominant motion trajectory in this phase. The extracted final deposition parameters of the droplet directly reflect the core process results of OLED inkjet printing, providing key data support for process parameter optimization and accurately guiding actual printing operations.

[0035] 107. Integrate the jetting start-up information, liquid column morphology information, droplet information, stable droplet parameters, and final droplet deposition parameters to form simulation results, and guide OLED inkjet printing operations based on the simulation results;

[0036] In this embodiment, the integrated content includes the time-series evolution curves of key physical quantities at each stage, statistical analysis of characteristic parameters at each stage, visualization results of the simulation process, and sensitivity analysis of process parameters. The time-series evolution curves include the nozzle pressure change curve, the liquid column length growth curve, and the droplet velocity decay curve. The statistical analysis includes droplet size distribution and deposition position deviation statistics. The visualization results of the simulation process include liquid-gas interface evolution animation and a 3D model of droplet flight trajectory. The sensitivity analysis of process parameters includes the influence of driving voltage on droplet velocity and the influence of ink viscosity on liquid column stability. The resulting simulation results are output in a standardized report format, including data tables, graphs, visualization models, and other forms, making it easy for process engineers to understand and use. The process parameter sensitivity analysis and specific optimization directions provided by the simulation results can directly guide actual printing operations, help quickly locate process problems, reduce the number of process trials and errors, and reduce R&D and production costs. At the same time, the simulation results can serve as a direct basis for configuring parameters of OLED inkjet printing equipment, effectively improving the stability of the printing process and pixel deposition consistency, and promoting the precision and efficiency development of OLED printing technology.

[0037] The OLED inkjet printing simulation method disclosed in this invention solves the technical pain point of existing technologies where a single modeling framework cannot balance simulation accuracy and computational efficiency by configuring simulation resources in stages, dynamically determining stage switching, and orderly transmitting stage information. Specifically, the method divides the process into stages according to the physical evolution of the inkjet process, so that the model of each stage is accurately matched with the dominant physical mechanism. It not only meticulously depicts the dynamic characteristics of key behaviors such as ink supply response, liquid column necking, and droplet shape adjustment, but also reduces the computational redundancy of non-critical stages through an adaptive simplification strategy. It realizes continuous simulation of the entire process from jet initiation to droplet deposition, ensuring the conservation and consistency of physical quantities. The simulation accuracy and computational efficiency are significantly improved compared with traditional methods. It can provide comprehensive and reliable simulation support for parameter optimization and stability control of OLED inkjet printing process, effectively improve pixel deposition consistency, and reduce process trial and error costs.

[0038] Furthermore, in this embodiment of the invention, obtaining preset input process parameters and continuously collecting current physical quantities during the simulation process includes:

[0039] 201. Obtain preset input process parameters, including nozzle parameters, ink property parameters, drive signal parameters, and gas phase environment parameters;

[0040] In this embodiment, the nozzle parameters include geometric features and material properties. The geometric features include the nozzle's inner diameter, length, outlet fillet radius, and outlet taper. The material properties include the nozzle's inner wall roughness and the contact angle with the ink. These nozzle parameters directly affect the flow resistance and adhesion characteristics of the liquid within the nozzle. The ink physical properties include core thermodynamic and hydrodynamic parameters, specifically density, dynamic viscosity, surface tension coefficient, volatility, and the contact angle with the deposition surface. These ink physical properties determine the ink's flow characteristics and interfacial behavior. The call number drive signal parameters include core electrical signal features, specifically drive voltage amplitude, pulse width, rise / fall time, signal frequency, and waveform type, directly controlling the magnitude and timing of the driving force of the ink supply system. The gas phase environment parameters include the environmental physical state, including environmental pressure and temperature, gas dynamic viscosity, and gas composition, affecting the resistance and interfacial evolution during droplet flight.

[0041] 202. Continuously collect the current physical quantities during the simulation process. The current physical quantities include velocity field, pressure field, liquid-gas interface state, liquid geometric parameters, and dynamic parameters.

[0042] In this embodiment, the velocity field acquisition covers the entire region, including the nozzle interior, liquid column region, droplet region, and surrounding gas phase region. The acquisition content includes the instantaneous velocity components of each spatial point in the x, y, and z directions. The pressure field acquisition covers the liquid interior and gas phase region, acquiring the instantaneous static pressure values ​​of each spatial point, focusing on the pressure gradient inside the nozzle, the pressure distribution inside the liquid column, and the pressure abrupt change at the liquid-gas interface, reflecting the transmission and equilibrium state of forces. The liquid-gas interface state acquisition needs to accurately capture dynamic characteristics, including the interface's three-dimensional coordinates, interface curvature distribution, and interface topology, directly reflecting the core process of interface evolution. The liquid geometric parameter acquisition includes key morphological indicators, specifically the liquid column length and diameter, droplet equivalent radius and tail length, liquid column cross-sectional shape, and droplet aspect ratio, to quantify the spatial morphological characteristics of the liquid. The dynamic parameter acquisition includes core indicators reflecting the motion and force state, specifically the Weber number (ratio of inertial force to surface tension), Reynolds number (ratio of inertial force to viscous force), necking rate, rate of change of interface curvature, droplet acceleration, and rate of change of momentum, revealing the dynamic essence of liquid motion.

[0043] 203. Perform noise reduction, completion, and standardization on the current physical quantity in sequence to obtain a standardized physical quantity;

[0044] In this embodiment, the denoising process employs a Gaussian filtering algorithm, with the filter kernel size determined based on the grid size. Weighted averaging smooths numerical fluctuations, removing high-frequency noise caused by numerical discretization and grid distortion in the simulation calculations, while preserving the true trend of physical quantity changes. The completion process uses a linear interpolation algorithm. For missing data in local physical quantities caused by insufficient grid discretization accuracy, truncation of the computational domain boundary, or numerical convergence issues, interpolation is performed based on the distribution pattern of valid data around the missing points to ensure the spatial continuity and integrity of the physical quantity data. The standardization process uses the min-max standardization method to convert physical quantities of different magnitudes and units to the [0, 1] interval, eliminating interference caused by differences in units and magnitudes, facilitating unified quantitative judgment of entry conditions and adaptation of model parameters in subsequent stages.

[0045] Further, in this embodiment of the invention, the loading of the first configuration information corresponding to the initial formation stage, and the execution of simulation operations based on the first configuration information to calculate the injection start information, includes:

[0046] 301. Load the first configuration information corresponding to the initial formation stage. The first configuration information includes a first physical model, a first mesh configuration, a first time step configuration, and a first boundary condition. The first physical model includes the incompressible fluid continuity equation and the Navier-Stokes equation.

[0047] In this embodiment, the core equations of the first physical model are designed based on the physical characteristics of the incompressible liquid flow within the nozzle during the initial formation stage. The expression for the incompressible fluid continuity equation is as follows:

[0048]

[0049] in, , , These represent the velocity components of the fluid in three spatial directions, ensuring that the liquid density remains constant during the simulation, which conforms to the actual physical characteristics of ink flow.

[0050] The Navier-Stokes equations are expressed as follows:

[0051]

[0052] in, For the velocity field, Represents the velocity field Over time The rate of change of fluid motion reflects the unsteady characteristics of fluid motion; For the velocity field gradient, For the density of the liquid, For dynamic viscosity, For pressure field, The Navier-Stokes equations, which describe the conservation of liquid momentum, are used to comprehensively describe the volumetric forces caused by surface tension, covering the effects of core forces such as inertial forces, viscous forces, and pressure gradients. When the nozzle has axisymmetric geometry, the three-dimensional equations can be degenerated into two-dimensional axisymmetric forms, reducing the degrees of freedom in computation and lowering the computational load while ensuring accuracy.

[0053] The first grid configuration explicitly defines the simulation computation domain as the area between the internal flow channel of the nozzle and the external flow channel of the nozzle outlet. The area is meshed using structured hexahedral meshes, with the mesh resolution set to ≤ for critical areas such as the nozzle inner wall and outlet edge. The grid resolution for other areas is set to ≤ To avoid mesh distortion and balance computational accuracy and efficiency;

[0054] The first time step is configured to be 1 / 10 of the driving signal period to ensure that the transient response of the flow field caused by the change of the driving signal can be accurately captured;

[0055] The first boundary conditions include three types of core boundaries: a nozzle wall no-slip boundary, where the velocity components of the liquid at the wall are all 0; an ink supply end pressure-driven boundary, which is converted into a pressure load through the piezoelectric effect based on the driving voltage signal, and the pressure conversion coefficient is determined according to the characteristics of the nozzle piezoelectric material; and a nozzle outlet free boundary, which is connected to the gas phase environment, where the pressure is equal to the ambient pressure and the velocity develops freely.

[0056] 302. Initialize the simulation computing domain based on the first configuration information, and configure the initial state parameters of the simulation computing domain;

[0057] In this embodiment, the initialization of the simulation computation domain includes mesh generation and boundary definition. Based on the range and resolution requirements of the first mesh configuration, a structured hexahedral mesh is generated using mesh generation software. Mesh optimization is performed on areas prone to mesh distortion, such as the nozzle outlet edge and inner wall corners, to ensure that the mesh quality meets the computational convergence requirements. The initial state parameter configuration needs to restore the physical state at the initial moment. The initial state of the liquid is set to be static, with uniform pressure distribution, and the free liquid surface flush with the nozzle outlet. The initial liquid temperature is consistent with the gas phase ambient temperature. The initial contact angle of the free liquid surface is determined according to the characteristics of the ink and nozzle materials to ensure that the initialization state is consistent with the initial state of the actual process.

[0058] 303. Based on the input process parameters and standardized physical quantities, perform unsteady-state simulation calculations in the simulation calculation domain and continuously monitor the initial deformation state of the free liquid surface;

[0059] In this embodiment, the unsteady-state simulation calculation uses the finite volume method to discretize the governing equations. The pressure-velocity coupled solution employs the PISO algorithm (pressure implicit splitting operator method) to ensure computational stability and convergence speed. A second-order upwind discretization scheme is used to improve the calculation accuracy of the convection and diffusion terms. During the calculation, the input process parameters are substituted into the governing equations in real time. The calculation iteration process is adjusted through feedback of standardized physical quantities. After each time step of calculation, the velocity and pressure field data of the entire domain are updated. The iteration convergence criterion is set to the residual of the incompressible fluid continuity equation ≤ And the residuals of the Navier-Stokes equations are ≤ The initial deformation state monitoring of the free liquid surface involves selecting 5-10 feature points at the nozzle outlet edge, recording the three-dimensional displacement data of each feature point in real time, calculating the average outward extension distance of the free liquid surface, and simultaneously monitoring the morphological changes of the free liquid surface.

[0060] 304. When the free liquid surface extension distance is greater than or equal to 1 / 10 of the nozzle inner diameter, extract the injection start information, which includes the velocity distribution time sequence curve at the nozzle outlet, the pressure change waveform inside the nozzle, the initial displacement trajectory of the free liquid surface, and the start time point.

[0061] In this embodiment, the determination of the injection start-up condition adopts the average extension distance threshold mechanism. When the average extension distance of the selected feature points is ≥ 1 / 10 of the nozzle inner diameter, it is determined that the start-up condition is met.

[0062] The velocity distribution time-series curve at the nozzle exit extracts the velocity component data of all grid nodes on the nozzle exit section, covering at least 10 consecutive time steps, forming a curve of the velocity of each node changing with time, reflecting the spatial distribution and temporal evolution characteristics of the exit velocity.

[0063] The pressure change waveform inside the nozzle is extracted to obtain the average pressure value of three characteristic sections: the ink supply end, the middle of the nozzle, and the nozzle outlet. This forms a pressure-time curve that covers a complete cycle of the drive signal and reflects the transmission and attenuation of pressure inside the nozzle.

[0064] The displacement data of the monitoring feature points are extracted from the initial displacement trajectory of the free liquid surface to form displacement curves of each feature point from its initial position to when the start-up conditions are met, reflecting the spatial uniformity and temporal regularity of the free liquid surface deformation.

[0065] The extracted injection start information needs to be verified by mass conservation and signal matching to ensure its validity.

[0066] Further, in this embodiment of the invention, the step of determining whether the entry conditions for the continuous liquid structure formation stage are met based on the input process parameters and current physical quantities, and if so, loading the second configuration information corresponding to the continuous liquid structure formation stage, and performing a simulation operation based on the injection start information and the second configuration information to calculate the liquid column morphology information, includes:

[0067] 401. Calculate the condition judgment value based on the standardized physical quantity, and determine whether the entry conditions for the continuous liquid structure formation stage are met based on the input process parameters and the condition judgment value.

[0068] In this embodiment, a weighted summation algorithm is used to calculate the condition judgment value based on the free surface extension distance and the velocity field gradient. The weighting coefficients are determined based on the simulation accuracy requirements and the importance of the physical quantities. Specifically, the weight of the free surface extension distance is 0.6, the weight of the velocity field gradient is 0.4, and the value of the conditional decision value α ranges from [0, 1]. The entry condition for the continuous liquid structure formation stage is... The dual judgment criteria, which combine liquid surface displacement and flow field intensity, are greater than 0.6 and the average free surface extension distance is greater than or equal to the nozzle inner diameter / 2. This can accurately reflect the physical transition of the liquid from initial start-up to stable extension, avoiding premature or late stage switching due to a single parameter judgment. During the judgment process, the free surface extension distance and velocity field data in the standardized physical quantities are called in real time, and combined with the nozzle inner diameter in the input process parameters, the condition judgment value is dynamically calculated. A judgment is performed after each time step until the entry condition is met.

[0069] 402. If so, load the second configuration information, which includes the second physical model, the second mesh configuration, and the second time step configuration. The second physical model includes the Navier-Stokes equations with the CSF surface tension model and the interface tracking method, wherein the interface tracking method is the volume fraction method or the level set method.

[0070] In this embodiment, the second physical model is optimized for the physical characteristics of rapid evolution of the liquid-gas interface and enhanced surface tension dominance. The Navier-Stokes equations of the surface tension model containing CSF (continuous surface force) introduce a surface tension body force term into the momentum equation, and the expression is:

[0071]

[0072] in, The surface tension coefficient at the liquid-gas interface. For the interface curvature, The normal vector of the interface. The Dirac function is used to represent the force distribution on the interface. The Navier-Stokes equations with the CSF (continuous surface force) surface tension model can accurately characterize the driving effect of surface tension on interface evolution in the momentum equation.

[0073] Interface tracking methods offer two options: Volume Fraction (VOF) method, which describes the interface by tracking the volume fraction of liquid in the mesh (C=1 for pure liquid phase, C=0 for pure gas phase, and 0<C<1 for the interface region), and uses PLIC (Piecewise Linear Interface Reconstruction) technology to improve interface capture accuracy; and Level Set method, which uses implicit functions... ( =0 represents the interface. >0 indicates the liquid phase. <0 represents the gas phase) tracking interface. A re-initialization technique is used to maintain the stability of the interface. Both methods can meet the requirements for accurate capture of interface evolution. Users can choose according to simulation accuracy and computing resources.

[0074] The second mesh configuration explicitly defines the simulation computation domain as extending beyond the nozzle outlet. The region is divided using a non-uniform structured mesh, specifically the liquid-gas interface region (0 < C < 1 or | |< , (for grid size) and near the nozzle outlet (outside the outlet 0- ) Set the grid resolution to ≤ The mesh resolution for the gas phase region far from the interface is set to ≤ By using grid adaptive encryption technology, the computational accuracy of the interface area is ensured while controlling the overall computational load.

[0075] The default value range for the second time step configuration is: ~ The CFL (Courant-Friedrichs-Lewy) condition is satisfied to ensure that the interface displacement within each time step does not exceed the local mesh size, thus avoiding interface distortion. As the liquid column morphology gradually stabilizes, i.e., when the morphology change rate is ≤5%, the time step is widened through an adaptive adjustment mechanism. To improve computational efficiency.

[0076] 403. Import the injection start information as initial conditions into the current simulation calculation domain and start the simulation calculation, continuously monitoring the length-to-diameter ratio and morphological change rate of the liquid column;

[0077] In this embodiment, the import of injection start-up information is achieved through a grid interpolation method. The data such as velocity distribution and pressure change at the nozzle exit extracted in the previous stage are accurately mapped to the corresponding grid nodes in the current simulation calculation domain, ensuring the continuity of data between different calculation domains. After import, the initial volume fraction of the liquid-gas interface (VOF method) or the level set function value (Level Set method) is set. The initial position of the interface is determined based on the initial displacement trajectory of the free liquid surface, maintaining the consistency of boundary conditions. That is, the boundary conditions of the nozzle wall and ink supply end are consistent with the previous stage, and the boundary conditions of the gas phase region are set as pressure outlet.

[0078] The simulation calculation uses the finite volume method to discretize the control equations. The pressure-velocity coupling solution uses the SIMPLEC algorithm (a simplified version of the SIMPLE algorithm) to improve the convergence speed. The discretization scheme uses a second-order precision scheme to ensure the calculation accuracy of the flow field and interface evolution.

[0079] The monitoring of the liquid column length-to-diameter ratio selects the characteristic dimensions of the liquid column. The liquid column length is defined as the straight-line distance from the nozzle outlet to the top of the liquid column, and the maximum diameter of the liquid column is defined as the maximum cross-sectional diameter of the liquid column along the length direction. The length-to-diameter ratio is the ratio of the two, and it is calculated once every 5 time steps. The monitoring of the morphological change rate adopts the liquid column volume change rate, and calculates the ratio of the difference in liquid column volume between two adjacent monitoring times to the liquid column volume at the previous time, which reflects the stability of the liquid column morphology.

[0080] 404. When the length-to-diameter ratio of the liquid column is ≥3 and the rate of change of shape is ≤5%, extract the liquid column shape information, which includes the total length of the liquid column, the maximum diameter, the interface curvature distribution and the internal velocity gradient.

[0081] In this embodiment, the determination of the stability of the liquid column shape adopts a dual standard of liquid column length-to-diameter ratio and shape change rate. The liquid column length-to-diameter ratio ≥3 ensures that the liquid column has formed a sufficient length scale, and the shape change rate ≤5% ensures that the liquid column shape tends to be stable.

[0082] The extraction of liquid column morphology information is performed on the liquid column in a steady state. The total length of the liquid column is the straight-line distance from the top of the liquid column to the nozzle outlet at the steady state, and the maximum diameter is the maximum cross-sectional diameter of the liquid column along the length direction at the steady state. Both are calculated through global grid data statistics.

[0083] To extract the interface curvature distribution, 20-30 feature points uniformly distributed on the surface of the liquid column are selected. The curvature value of each feature point is calculated by the interface tracking method to form a curvature distribution curve, which reflects the smoothness of the liquid column surface and the curvature change law.

[0084] The internal velocity gradient is extracted and the rate of change of velocity in the axial and radial directions of the liquid column is calculated, where the axial direction refers to the length direction and the radial direction refers to the direction perpendicular to the length direction. The central axis of the liquid column and three different radial sections are selected, and the velocity gradient along the axial direction of each section and the velocity gradient along the radial direction at each axial position are calculated to reflect the flow characteristics inside the liquid column.

[0085] All liquid column morphology information must be verified by mass conservation to ensure the accuracy of the information.

[0086] Further, in this embodiment of the invention, the step of determining whether the entry conditions for the droplet separation stage are met based on the current physical quantity, and if so, loading the third configuration information corresponding to the droplet separation stage, and performing a simulation operation based on the third configuration information and the liquid column morphology information to calculate the droplet information, includes:

[0087] 501. Based on the liquid geometric parameters and kinetic parameters, determine whether the entry conditions for the droplet separation stage are met;

[0088] In this embodiment, the entry conditions for the droplet separation stage are based on multi-parameter quantitative determination of liquid column morphology and dynamic state. The core judgment parameters include the liquid column aspect ratio and necking radius in liquid geometry, and the Weber number and necking rate in dynamic parameters. The specific judgment logic is as follows: when the liquid column aspect ratio ≥ 3, the Weber number ≥ 0.8, and the necking radius ≤ 2 times the critical radius, the entry conditions are determined to be met.

[0089] The necking region is defined as the region with the smallest diameter along the length of the liquid column, and the radius of the necking region is 1 / 2 of the average diameter of the region.

[0090] The critical radius is calculated using Rayleigh-Plateau theory, and the formula is as follows:

[0091]

[0092] in, The surface tension coefficient, For the density of the liquid, The characteristic velocity of the droplet;

[0093] The Weber number expression is:

[0094]

[0095] in, For the density of the liquid, The characteristic velocity of the droplet, The characteristic length of the droplet, It is the surface tension coefficient;

[0096] During the determination process, the liquid column length-to-diameter ratio and necking radius data from the liquid geometry parameters, as well as the Weber number and necking rate data from the dynamic parameters, are called in real time. A multi-parameter collaborative determination is performed after each time step until the entry conditions are met.

[0097] 502. If so, then load the third configuration information, which includes the third physical model, the third mesh configuration, and the third time step configuration. The third physical model adopts the interface tracking method for the continuous liquid structure formation stage.

[0098] In this embodiment, the third physical model adopts the interface tracking method of the continuous liquid structure formation stage to ensure the continuity and consistency of interface tracking and avoid interface distortion caused by model switching. At the same time, a new necking fracture calculation module is added, which embeds the critical radius calculation logic of Rayleigh-Plateau theory. The critical radius threshold is updated in real time according to parameters such as liquid column characteristic velocity and surface tension coefficient. Satellite droplet judgment logic is introduced simultaneously. When the volume of the secondary droplet formed after necking fracture is ≥ 5% of the volume of the main droplet, it is judged as a satellite droplet, and its size, velocity and position information are recorded to improve the comprehensiveness of the simulation.

[0099] The third grid configuration explicitly defines the simulation computation domain as outside the nozzle outlet. The region employs a mesh adaptive encryption mechanism, using the curvature change rate of the necked region as the trigger condition. When the interface curvature change rate is ≥ Automatically monitor the neck constriction area and surrounding 10 meters per meter. The mesh within the specified range is refined, and the mesh resolution in the necked area after refinement is ≤ Other areas will use the same grid resolution as the second configuration information, i.e., the interface area ≤ Gas phase region ≤ To ensure the accuracy of the calculation of the necking fracture zone;

[0100] The default value range for the third time step configuration is: ~ The time step is 1 / 5 to 1 / 2 of the continuous liquid structure formation stage, and is dynamically adjusted by monitoring the necking rate. When the necking rate is ≥ When the speed is m / s, the time step is automatically reduced by 50% to ensure accurate capture of the rapid physical changes at the moment of fracture.

[0101] 503. Import the liquid column morphology information into the current simulation calculation domain to initialize the necking fracture calculation module and boundary conditions of the current simulation calculation domain, then execute the simulation calculation and continuously monitor the necking rate;

[0102] In this embodiment, the import of liquid column morphology information is achieved through data mapping and module initialization. Data such as the total length, maximum diameter, interface curvature distribution, and internal velocity gradient of the liquid column are accurately substituted into the corresponding mesh nodes of the current simulation calculation domain. This initializes the core parameters of the necking fracture calculation module, including the initial value of the critical radius, fracture determination accuracy, and satellite droplet determination threshold. The initial value of the critical radius is calculated based on the liquid column's characteristic velocity and surface tension coefficient, and the fracture determination accuracy is ≤ [missing value]. The threshold for satellite droplet determination is that the volume percentage of secondary droplets is ≥5%.

[0103] The boundary conditions are initialized in the same way as the previous stage. The boundary conditions of the nozzle wall and ink supply end remain unchanged. The surface tension coefficient and contact angle of the liquid-gas interface remain continuous. The boundary conditions of the gas phase region are set to pressure outlet to ensure the continuity of the force field and flow field.

[0104] The simulation calculation employs the finite volume method to discretize the control equations, and uses an explicit scheme for time integration, such as the Euler explicit method, which can quickly respond to the drastic changes in the necking region. The pressure-velocity coupled solution uses the PISO algorithm to ensure computational stability, and the discretization scheme adopts a second-order upwind scheme to improve computational accuracy. For monitoring the necking rate, 3-5 feature points in the necking region are selected, and the radius change data of each feature point over time are recorded in real time. The calculated necking rate is the decrease in radius per unit time. The interface curvature change and internal pressure distribution of the necking region are monitored simultaneously to comprehensively understand the dynamic characteristics of the necking process.

[0105] 504. When the necking rate is less than or equal to the preset fracture determination threshold, extract the droplet information, which includes the droplet's mass, equivalent radius, initial velocity, surface morphology, and fracture location coordinates.

[0106] In this embodiment, the fracture determination threshold is the critical radius r_c calculated by Rayleigh-Plateau theory. When the average radius of the necking region is ≤ r_c, the liquid column is determined to have fractured. This threshold can accurately reflect the critical fracture state after the balance between surface tension and inertial force, ensuring the physical rationality of the fracture timing determination.

[0107] The extraction of droplet information is performed separately for the main droplet and satellite droplets formed after fracture. The mass of the droplet is calculated by volume fraction integration of the droplet region (VOF method) or volume calculation based on level set function (Level Set method), combined with ink density. The equivalent radius is converted to the radius of an equivalent sphere based on the droplet mass and density. The initial velocity is calculated by integrating the velocity field of the droplet region to obtain the centroid velocity, which is the weighted average velocity of all grid nodes within the droplet. The surface morphology is described by the volume fraction distribution of the droplet surface (VOF method) or level set function value (Level Set method), including surface roughness, the presence of a trailing structure, and the length of the trailing structure. The fracture location coordinates are determined by the coordinates of the feature points at the necking fracture, and the coordinates of the center node of the fracture region are selected as the fracture location.

[0108] All droplet information must be verified by mass conservation to ensure accuracy.

[0109] Further, in this embodiment of the invention, the step of determining whether the entry conditions for the initial flight phase are met based on the current physical quantity, and if so, loading the fourth configuration information corresponding to the initial flight phase, and performing a simulation operation based on the droplet information and the fourth configuration information to calculate the stable droplet parameters, includes:

[0110] 601. Based on the liquid-gas interface state, liquid geometric parameters, and dynamic parameters, determine whether the entry conditions for the initial flight phase are met.

[0111] In this embodiment, the entry condition for the initial flight phase is determined by a multi-parameter quantitative assessment based on droplet separation state and morphological stability. The core assessment parameters include droplet separation state in the liquid-gas interface state, droplet equivalent radius fluctuation in liquid geometry parameters, and velocity stability in dynamic parameters. The specific assessment logic is as follows: the droplet is completely separated from the original liquid column, that is, the volume fraction of the droplet region and the liquid column region do not overlap; the droplet equivalent radius fluctuation is ≤5%, specifically, the percentage of equivalent radius change over 10 consecutive time steps is ≤5%; the droplet centroid velocity fluctuation is ≤3%, specifically, the percentage of velocity change over 10 consecutive time steps is ≤3%. When all three conditions are met simultaneously, the entry condition is deemed met.

[0112] During the determination process, the separation state is verified in real time by calling the liquid-gas interface state data. The equivalent radius fluctuation is calculated through liquid geometric parameters, and the velocity fluctuation is calculated through kinetic parameters. A multi-parameter collaborative determination is performed after each time step to ensure that the entry timing accurately reflects the physical state of the droplet in the initial stage of independent flight after detaching from the liquid column.

[0113] 602. If so, then load the fourth configuration information, which includes the fourth physical model, the fourth mesh configuration, and the fourth time step configuration. The fourth physical model includes the Lagrange momentum equation, the interface tracking model, the coupled Stokes resistance model, and the Laplace pressure equation.

[0114] In this embodiment, the fourth physical model is designed to address the strong coupling between droplet morphology and flight motion, and the physical characteristics of surface tension driving morphological retraction. The Lagrange momentum equation is used to describe the motion of the droplet's center of mass, accurately depicting the overall motion of the droplet. The interface tracking model continues the VOF method or Level Set method from the previous stage, continuously updating the volume fraction or level set function value of the droplet surface to capture subtle morphological changes such as tailing retraction and surface smoothing, ensuring the continuity of interface evolution. The coupled Stokes drag model is used to describe the hindering effect of gas phase viscosity on droplet motion, and its expression is:

[0115]

[0116] in, For gas dynamic viscosity, The characteristic radius of the droplet is used, which is suitable for low Reynolds number (Re≤1) conditions. When the Reynolds number >1, a Re-related correction term is introduced to automatically correct the drag coefficient to improve the accuracy of drag calculation.

[0117] The Laplace pressure equation is used to describe the internal pressure difference of droplets caused by surface tension, which drives the droplet shape to retract into a lower-energy sphere, accurately depicting the driving effect of surface tension on shape adjustment.

[0118] The fourth grid configuration explicitly defines the simulation computation domain as being outside the droplet center. For the region, an adaptive meshing technique based on interface curvature is used, where the interface curvature ≥ The mesh is refined per meter along the droplet surface and tail region, with the refined mesh resolution ≤ Gas phase region grid resolution ≤ Balancing form detail capture with computational efficiency;

[0119] The default value range for the fourth time step configuration is: ~ The fourth-order Runge-Kutta integral method is used to solve the droplet motion equation. This method has high-order accuracy, can effectively suppress numerical dispersion, and ensure the accuracy of the coupled calculation of droplet motion and morphological evolution. The time step satisfies the CFL condition.

[0120] 603. Import the droplet information into the current simulation calculation domain to initialize the gas phase environment parameters and droplet motion equations of the current simulation calculation domain, then perform simulation calculations and continuously monitor the tail length and interface curvature change rate.

[0121] In this embodiment, the import of droplet information is achieved through data mapping. Data such as the droplet's mass, equivalent radius, initial velocity, surface morphology, and fracture location coordinates are accurately substituted into the current simulation calculation domain to initialize the initial conditions of the droplet's motion equations. Specifically, the initial position of the centroid is the fracture location coordinates, and the initial velocity is the extracted initial droplet velocity. At the same time, the initial volume fraction or level set function value of the interface is set based on the droplet surface morphology data. The gas phase environment parameters are initialized based on the gas phase environment parameters in the input process parameters. The initial state of the gas phase in the calculation domain is set to be static, with uniform pressure equal to the ambient pressure, and constant temperature equal to the ambient temperature, ensuring that the gas phase environment is consistent with the actual process.

[0122] The simulation employs a coupled flow field-interface-motion solution strategy. Simultaneously, it solves the internal flow field of the droplet based on the Navier-Stokes equations, determines the liquid-gas interface evolution based on the VOF / Leave lSet method, and determines the droplet's center-of-mass motion based on the Lagrange momentum equation. At each time step, the global flow field, interface state, and droplet motion parameters are updated. The iterative convergence criterion is set as the residual of the incompressible fluid continuity equation ≤ The residuals of the Navier–Stokes equations are ≤ ;

[0123] The tail length is monitored by selecting the straight-line distance from the tip of the droplet tail to the maximum cross-section of the droplet body, and is calculated once every 3 time steps; the interface curvature change rate is monitored by selecting 15-20 feature points evenly distributed on the droplet surface, calculating the ratio of the curvature difference between adjacent time steps to the time step, and taking the average value as the interface curvature change rate.

[0124] 604. When the tail length is less than or equal to 1 / 3 of the droplet's equivalent radius and the rate of change of interface curvature is less than or equal to 1 / 3 of the droplet's equivalent radius, the following conditions apply: At that time, stable droplet parameters are extracted, including the stable equivalent radius of the droplet, the adjusted flight velocity, and the surface curvature uniformity.

[0125] In this embodiment, the stability of the droplet morphology is determined using a dual standard: tail length and rate of change of curvature. A tail length ≤ 1 / 3 of the droplet's equivalent radius indicates that the tail structure has essentially retracted, and the rate of change of interface curvature ≤ This indicates that the surface morphology of the droplet tends to be stable, and this dual standard can accurately reflect the physical transition of the droplet from an unstable morphology to a stable morphology.

[0126] The extraction of stable droplet parameters is performed on droplets after their shape has stabilized. The stable equivalent radius is calculated based on the droplet volume at the moment of shape stabilization, reflecting the actual size of the droplet after shape stabilization. The adjusted flight velocity is the velocity of the droplet's center of mass at the moment of shape stabilization, obtained by integrating the Lagrange momentum equation, reflecting the actual flight velocity of the droplet after shape adjustment. The surface curvature uniformity γ is calculated by the ratio of the standard deviation of the curvature of each feature point on the droplet surface to the average curvature. When γ ≤ 5%, the surface curvature is considered uniform. This parameter quantifies the smoothness of the droplet surface.

[0127] All parameters of stable droplets must be verified by mass and momentum conservation to ensure the accuracy of the information.

[0128] Further, in this embodiment of the invention, the step of determining whether the entry conditions for the stable flight phase are met based on the current physical quantity, and if so, loading the fifth configuration information corresponding to the stable flight phase, and performing a simulation operation based on the stable droplet parameters and the fifth configuration information to calculate the final droplet deposition parameters, includes:

[0129] 701. Based on the tail length, the rate of change of interface curvature, and the stable droplet parameters, determine whether the entry conditions for the stable flight phase are met;

[0130] In this embodiment, the entry condition for the stable flight phase is a multi-parameter quantitative determination based on morphological stability and parameter consistency. The core determination parameters include tail length, rate of change of interface curvature, and surface curvature uniformity among the stable droplet parameters. The specific determination logic is: tail length ≤ 1 / 3 of the droplet's equivalent radius, rate of change of interface curvature ≤ When the three conditions of surface curvature uniformity ≥95% are met simultaneously, it is determined that the entry condition is met. This judgment logic fully verifies the stability of the droplet morphology and ensures that when entering the stable flight stage, the droplet has formed a stable structure of approximately spherical shape, and there are no significant changes in the internal flow field and surface morphology. There is no need to perform fine interface tracking and morphology characterization, which provides a physical basis for model simplification.

[0131] During the determination process, the tail length and interface curvature change rate data monitored in the previous stage are called in real time. Combined with the surface curvature uniformity in the stable droplet parameters, a multi-parameter collaborative determination is performed after each time step until the entry conditions are met.

[0132] 702. If so, then load the fifth configuration information corresponding to the stable flight phase. The fifth configuration information includes the fifth physical model, the fifth grid configuration, and the fifth time step configuration. The fifth physical model includes the equivalent particle dynamics model and the empirical formula for air resistance.

[0133] In this embodiment, the fifth physical model is designed for the physical characteristics of droplet morphology stability, weak interface changes, and dominant motion trajectory. The equivalent particle dynamics model treats the droplet as a rigid particle with mass concentrated at the center of mass, ignores the subtle changes in the internal flow field and surface morphology, focuses on the motion trajectory calculation of the droplet's center of mass, and greatly simplifies the computational complexity.

[0134] Empirical formulas for air resistance are used to accurately describe the viscous drag of gas relative to liquid droplets. The expression is:

[0135]

[0136] in, It is the drag coefficient. It is air density. It is the cross-sectional area of ​​the droplet. It is the droplet velocity and drag coefficient. Different empirical formulas are used depending on the different values ​​of the Reynolds number Re: when Re≤1 =24 / Re; when 1 < Re ≤ 1000 =0.44; when Re > 1000, =0.1, to ensure the accuracy of drag calculation under different flight conditions;

[0137] The fifth grid configuration explicitly defines the simulation computation domain as the area along the droplet's flight trajectory ± The region uses a coarse-structured mesh, eliminating the need for fine meshing on the droplet surface. The mesh resolution is set to ≤ This significantly reduces the number of grid cells and lowers the consumption of computing resources.

[0138] The default value range for the fifth time step configuration is: ~ The time step s is 10 to 20 times the time step of the initial flight phase. Under the premise of satisfying the CFL condition, the number of time steps is significantly reduced, and the computational efficiency is improved. The time integration adopts the Lagrange integration method to ensure the accuracy of trajectory calculation.

[0139] 703. Import the stable droplet parameters into the current simulation calculation domain, initialize the deposition surface boundary conditions, then execute the simulation calculation steps, and continuously monitor the distance between the droplet and the deposition surface;

[0140] In this embodiment, the import of stable droplet parameters directly initializes the core parameters of the equivalent particle dynamics model. The stable equivalent radius of the droplet is used to calculate the cross-sectional area of ​​the droplet. The adjusted flight velocity is used as the initial velocity of the droplet's center of mass. The droplet mass is used to calculate the momentum change.

[0141] The initialization of the boundary conditions of the deposition surface is based on the process requirements. The deposition surface is defined as a fixed wall surface. The physical properties of the deposition surface are set, including surface roughness and contact angle with ink, to provide boundary constraints for the subsequent spread calculation of droplet impact deposition.

[0142] The simulation calculation uses the Lagrange method to track the trajectory of the droplet's center of mass. After each time step, the resistance experienced by the droplet is calculated using the empirical formula for air resistance. Combined with gravity, the velocity and position of the droplet are updated using the Lagrange momentum equation. During the calculation, it is determined in real time whether the droplet collides with the deposition surface. When the distance between the droplet and the deposition surface is ≤ the stable equivalent radius of the droplet / 2, it indicates that a collision has occurred. The distance between the droplet and the deposition surface is monitored by selecting the projection distance of the droplet's center of mass onto the normal direction of the deposition surface. This calculation is performed after each time step to ensure that the moment when the droplet reaches the deposition surface is captured in a timely manner.

[0143] 704. When the droplet reaches the deposition surface, the final deposition parameters of the droplet are extracted, including the deposition location coordinates, impact velocity, deposition morphology radius and spreading area.

[0144] In this embodiment, the criterion for determining when a droplet reaches the deposition surface is that the distance between the droplet's centroid and the deposition surface is ≤ 1 / 2 of the droplet's stable equivalent radius. This criterion is determined based on the geometric relationship of a spherical droplet impacting a plane and can accurately reflect the moment when the droplet initially contacts the deposition surface.

[0145] The extraction of final droplet deposition parameters is based on data from the instant of droplet impact on the deposition surface and after the droplet has stabilized. The deposition location coordinates are the three-dimensional coordinates of the centroid of the droplet when it impacts the deposition surface, directly reflecting the deposition accuracy. The impact velocity is the three-dimensional component of the centroid velocity at the instant of droplet impact, reflecting the magnitude of the kinetic energy of the droplet impacting the deposition surface. The deposition morphology radius is the maximum radius of the droplet after impact when it has stabilized on the deposition surface, i.e., when the rate of change of the spread area is ≤1%, calculated by integrating the volume fraction of the spread area. The spread area is the area of ​​the spread area on the deposition surface after droplet impact, calculated based on the deposition morphology radius.

[0146] All deposition parameters must be verified by mass conservation to ensure the accuracy of the information.

[0147] The simulation method for OLED inkjet printing in the embodiments of the present invention has been described above. The simulation device for OLED inkjet printing in the embodiments of the present invention will be described below. Please refer to [link / reference]. Figure 2 One embodiment of the OLED inkjet printing simulation device in this invention includes:

[0148] The acquisition module 801 is used to acquire preset input process parameters and continuously collect current physical quantities during the simulation process;

[0149] The first simulation module 802 is used to load the first configuration information corresponding to the initial formation stage, and perform simulation operations based on the first configuration information to calculate the injection start information;

[0150] The second simulation module 803 is used to determine whether the entry conditions for the continuous liquid structure formation stage are met based on the input process parameters and the current physical quantity. If so, it loads the second configuration information corresponding to the continuous liquid structure formation stage and performs simulation operations based on the injection start information and the second configuration information to calculate the liquid column morphology information.

[0151] The third simulation module 804 is used to determine whether the entry conditions for the droplet separation stage are met based on the current physical quantity. If so, it loads the third configuration information corresponding to the droplet separation stage and performs simulation operations based on the third configuration information and the liquid column morphology information to calculate the droplet information.

[0152] The fourth simulation module 805 is used to determine whether the entry conditions for the initial flight stage are met based on the current physical quantity. If so, it loads the fourth configuration information corresponding to the initial flight stage and performs simulation operations based on the droplet information and the fourth configuration information to calculate the stable droplet parameters.

[0153] The fifth simulation module 806 is used to determine whether the entry conditions for the stable flight phase are met based on the current physical quantity. If so, it loads the fifth configuration information corresponding to the stable flight phase and performs simulation operations based on the stable droplet parameters and the fifth configuration information to calculate the final droplet deposition parameters.

[0154] The integration module 807 is used to integrate the jetting start-up information, liquid column morphology information, droplet information, stable droplet parameters and final droplet deposition parameters to form simulation results, and guide OLED inkjet printing operations based on the simulation results.

[0155] Based on the same ideas as the methods in the above embodiments, the apparatus provided in this application can implement the methods in the above embodiments.

[0156] above Figure 2 The simulation device for OLED inkjet printing in this embodiment of the invention is described in detail from the perspective of modular functional entities. The simulation device for OLED inkjet printing in this embodiment of the invention is described in detail from the perspective of hardware processing.

[0157] Figure 3This is a schematic diagram of the structure of an OLED inkjet printing simulation device 900 provided in an embodiment of the present invention. The OLED inkjet printing simulation device 900 can vary significantly due to different configurations or performance characteristics. It may include one or more central processing units (CPUs) 910 and memory 920, and one or more storage media 930 (e.g., one or more mass storage devices) storing application programs 933 or data 932. The memory 920 and storage media 930 can be temporary or persistent storage. The program stored in the storage media 930 may include one or more modules (not shown in the diagram), each module including a series of instruction operations on the OLED inkjet printing simulation device 900. Furthermore, the processor 910 may be configured to communicate with the storage media 930 and execute the series of instruction operations in the storage media 930 on the OLED inkjet printing simulation device 900 to implement the steps of the OLED inkjet printing simulation method provided in the above-described method embodiments.

[0158] The OLED inkjet printing simulation device 900 may also include one or more power supplies 940, one or more wired or wireless network interfaces 950, one or more input / output interfaces 960, and / or one or more operating systems 931, such as Windows Server, Unix, Linux, FreeBSD, etc. Those skilled in the art will understand that... Figure 3 The illustrated OLED inkjet printing simulation device structure does not constitute a limitation on the OLED inkjet printing simulation device, and may include more or fewer components than illustrated, or combine certain components, or have different component arrangements.

[0159] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when executed on a computer, cause the computer to perform the steps of a simulation method for OLED inkjet printing.

[0160] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system, device, or unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0161] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0162] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A simulation method for OLED inkjet printing, characterized in that, include: Obtain preset input process parameters and continuously collect current physical quantities during the simulation process; Load the first configuration information corresponding to the initial formation stage, and perform simulation operations based on the first configuration information to calculate the injection start information; Based on the input process parameters and current physical quantities, it is determined whether the entry conditions for the continuous liquid structure formation stage are met. If so, the second configuration information corresponding to the continuous liquid structure formation stage is loaded, and a simulation operation is performed based on the injection start information and the second configuration information to calculate the liquid column morphology information. Based on the current physical quantity, determine whether the entry conditions for the droplet separation stage are met. If so, load the third configuration information corresponding to the droplet separation stage, and perform simulation operations based on the third configuration information and the liquid column morphology information to calculate the droplet information. Based on the current physical quantity, determine whether the entry conditions for the initial flight phase are met. If so, load the fourth configuration information corresponding to the initial flight phase, and perform simulation operations based on the droplet information and the fourth configuration information to calculate the stable droplet parameters. Based on the current physical quantity, determine whether the entry conditions for the stable flight phase are met. If so, load the fifth configuration information corresponding to the stable flight phase, and perform simulation operations based on the stable droplet parameters and the fifth configuration information to calculate the final droplet deposition parameters. The jetting start-up information, liquid column morphology information, droplet information, stable droplet parameters, and final droplet deposition parameters are integrated to form simulation results, and the simulation results are used to guide OLED inkjet printing operations.

2. The simulation method for OLED inkjet printing according to claim 1, characterized in that, The process of acquiring preset input process parameters and continuously collecting current physical quantities during the simulation includes: Obtain preset input process parameters, including nozzle parameters, ink property parameters, drive signal parameters, and gas phase environment parameters; The simulation continuously collects current physical quantities, including velocity field, pressure field, liquid-gas interface state, liquid geometric parameters, and dynamic parameters. The current physical quantity is sequentially subjected to denoising, completion, and standardization processes to obtain a standardized physical quantity.

3. The simulation method for OLED inkjet printing according to claim 2, characterized in that, The loading of the first configuration information corresponding to the initial formation stage, and the execution of simulation operations based on the first configuration information to calculate the injection start information, includes: Load the first configuration information corresponding to the initial formation stage. The first configuration information includes a first physical model, a first mesh configuration, a first time step configuration, and a first boundary condition. The first physical model includes the incompressible fluid continuity equation and the Navier-Stokes equation. The simulation computing domain is initialized based on the first configuration information, and the initial state parameters of the simulation computing domain are configured. Based on the input process parameters and standardized physical quantities, unsteady-state simulation calculations are performed in the simulation calculation domain, and the initial deformation state of the free liquid surface is continuously monitored. When the free surface extension distance is greater than or equal to 1 / 10 of the nozzle inner diameter, the injection start information is extracted. The injection start information includes the velocity distribution time sequence curve at the nozzle outlet, the pressure change waveform inside the nozzle, the initial displacement trajectory of the free surface, and the start time point.

4. The simulation method for OLED inkjet printing according to claim 3, characterized in that, The process involves determining whether the entry conditions for the continuous liquid structure formation stage are met based on the input process parameters and current physical quantities. If so, the second configuration information corresponding to the continuous liquid structure formation stage is loaded, and a simulation operation is performed based on the injection start information and the second configuration information to calculate the liquid column morphology information, including: The condition judgment value is calculated based on the standardized physical quantity, and the entry conditions for the continuous liquid structure formation stage are determined based on the input process parameters and the condition judgment value. If so, then load the second configuration information, which includes the second physical model, the second mesh configuration, and the second time step configuration. The second physical model includes the Navier-Stokes equations with the CSF surface tension model and the interface tracking method, wherein the interface tracking method is the volume fraction method or the level set method. The injection start information is imported into the current simulation calculation domain as the initial condition and the simulation calculation is started, and the length-to-diameter ratio and morphological change rate of the liquid column are continuously monitored. When the length-to-diameter ratio of the liquid column is ≥3 and the rate of change of shape is ≤5%, the liquid column shape information is extracted. The liquid column shape information includes the total length of the liquid column, the maximum diameter, the interface curvature distribution, and the internal velocity gradient.

5. The simulation method for OLED inkjet printing according to claim 4, characterized in that, The step involves determining whether the entry conditions for the droplet separation stage are met based on the current physical quantity. If so, the third configuration information corresponding to the droplet separation stage is loaded, and a simulation operation is performed based on the third configuration information and the liquid column morphology information to calculate the droplet information, including: Based on the liquid geometry and kinetic parameters, determine whether the entry conditions for the droplet separation stage are met; If so, then load the third configuration information, which includes the third physical model, the third mesh configuration, and the third time step configuration. The third physical model adopts the interface tracking method for the continuous liquid structure formation stage. The liquid column morphology information is imported into the current simulation calculation domain to initialize the necking fracture calculation module and boundary conditions of the current simulation calculation domain. Then, the simulation calculation is performed and the necking rate is continuously monitored. When the necking rate is less than or equal to a preset fracture determination threshold, droplet information is extracted. The droplet information includes the droplet's mass, equivalent radius, initial velocity, surface morphology, and fracture location coordinates.

6. The simulation method for OLED inkjet printing according to claim 5, characterized in that, The step involves determining whether the entry conditions for the initial flight phase are met based on the current physical quantity. If so, the fourth configuration information corresponding to the initial flight phase is loaded, and a simulation operation is performed based on the droplet information and the fourth configuration information to calculate the stable droplet parameters, including: Based on the liquid-gas interface state, liquid geometric parameters, and dynamic parameters, determine whether the entry conditions for the initial flight phase are met. If so, then load the fourth configuration information, which includes the fourth physical model, the fourth mesh configuration, and the fourth time step configuration. The fourth physical model includes the Lagrange momentum equation, the interface tracking model, the coupled Stokes resistance model, and the Laplace pressure equation. The droplet information is imported into the current simulation calculation domain to initialize the gas phase environment parameters and droplet motion equations of the current simulation calculation domain. Then, the simulation calculation is performed, and the tail length and interface curvature change rate are continuously monitored. When the tail length is less than or equal to 1 / 3 of the droplet's equivalent radius and the rate of change of interface curvature is less than or equal to 1 / 3 of the droplet's equivalent radius, the rate of change of interface curvature is less than or equal to 1 / 3 of the droplet's equivalent radius. At that time, stable droplet parameters are extracted, including the stable equivalent radius of the droplet, the adjusted flight speed, and the surface curvature uniformity.

7. The simulation method for OLED inkjet printing according to claim 6, characterized in that, The step involves determining whether the entry conditions for the stable flight phase are met based on the current physical quantity. If so, the fifth configuration information corresponding to the stable flight phase is loaded, and a simulation operation is performed based on the stable droplet parameters and the fifth configuration information to calculate the final droplet deposition parameters, including: The entry conditions for the stable flight phase are determined based on the tail length, the rate of change of interface curvature, and the stable droplet parameters. If so, then load the fifth configuration information corresponding to the stable flight phase. The fifth configuration information includes the fifth physical model, the fifth grid configuration, and the fifth time step configuration. The fifth physical model includes the equivalent particle dynamics model and the empirical formula for air resistance. The stable droplet parameters are imported into the current simulation domain, and the boundary conditions of the deposition surface are initialized. Then, the simulation calculation steps are executed, and the distance between the droplet and the deposition surface is continuously monitored. When the droplet reaches the deposition surface, the final deposition parameters of the droplet are extracted. These final deposition parameters include the deposition location coordinates, impact velocity, deposition morphology radius, and spreading area.

8. A simulation device for OLED inkjet printing, characterized in that, include: The acquisition module is used to acquire preset input process parameters and continuously collect current physical quantities during the simulation process; The first simulation module is used to load the first configuration information corresponding to the initial formation stage, and perform simulation operations based on the first configuration information to calculate the injection start information; The second simulation module is used to determine whether the entry conditions for the continuous liquid structure formation stage are met based on the input process parameters and the current physical quantity. If so, the second configuration information corresponding to the continuous liquid structure formation stage is loaded, and the simulation operation is performed based on the injection start information and the second configuration information to calculate the liquid column morphology information. The third simulation module is used to determine whether the entry conditions for the droplet separation stage are met based on the current physical quantity. If so, it loads the third configuration information corresponding to the droplet separation stage and performs simulation operations based on the third configuration information and the liquid column morphology information to calculate the droplet information. The fourth simulation module is used to determine whether the entry conditions for the initial flight stage are met based on the current physical quantity. If so, it loads the fourth configuration information corresponding to the initial flight stage and performs simulation operations based on the droplet information and the fourth configuration information to calculate the stable droplet parameters. The fifth simulation module is used to determine whether the entry conditions for the stable flight phase are met based on the current physical quantity. If so, it loads the fifth configuration information corresponding to the stable flight phase and performs simulation operations based on the stable droplet parameters and the fifth configuration information to calculate the final droplet deposition parameters. An integration module is used to integrate the jetting start-up information, liquid column morphology information, droplet information, stable droplet parameters, and final droplet deposition parameters to form simulation results, and guide OLED inkjet printing operations based on the simulation results.

9. A simulation device for OLED inkjet printing, characterized in that, The OLED inkjet printing simulation device includes: a memory and at least one processor, wherein the memory stores instructions; At least one of the processors invokes the instructions in the memory to cause the OLED inkjet printing simulation device to perform the steps of the OLED inkjet printing simulation method as claimed in any one of claims 1-7.

10. A computer-readable storage medium storing instructions thereon, characterized in that, When the instructions are executed by the processor, they implement the various steps of the simulation method for OLED inkjet printing as described in any one of claims 1-7.

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