A method and system for droplet coalescence based on DEM

Abstract

The application belongs to the technical field of droplet coalescence, and discloses a droplet coalescence method and system based on DEM, which comprises the following steps: acquiring the physical properties and initial motion state of droplets in a simulation domain; calculating the relative distance between the droplets and judging whether the droplets are in contact; for the droplet pair in contact, calculating the attraction force according to the overlap amount; updating the motion state of the droplets according to the attraction force, and recalculating the overlap amount between the droplets; based on the updated overlap amount, transferring a certain volume of liquid phase material from the first droplet to the second droplet in the droplet pair, and updating the radii of the two droplets; according to the law of conservation of momentum, updating the motion state of the droplet pair, and iteratively executing the above steps until the coalescence termination condition is met, and outputting the coalesced droplet state. The application realizes the whole process simulation of droplets from close to complete fusion, and strictly guarantees the conservation of mass and momentum.

Description

Technical Field

[0001] This invention relates to the field of droplet agglomeration technology, and in particular to a droplet agglomeration method and system based on DEM. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] In many industrial processes such as spray drying, fuel combustion, and gas-liquid separation, the collision and coalescence of droplets are key physical phenomena affecting system efficiency and product quality. High-precision numerical simulations are essential for understanding and optimizing these processes.

[0004] Traditional numerical simulation methods typically simplify droplet coalescence into an instantaneous process: once two droplets come into contact or geometrically overlap, they immediately merge into a new spherical droplet. This simplified model suffers from significant physical distortions. 1. Process distortion: It completely ignores the gradual dynamic process of droplets moving closer to each other, deforming and eventually merging, and cannot reflect the microscopic dynamics of coagulation.

[0005] 2. Lack of mechanical mechanism: The mutual attraction between droplets dominated by surface tension before and after contact was not explicitly simulated, resulting in a lack of physical basis for the droplet approach behavior.

[0006] 3. Conservation laws are difficult to guarantee: When the instantaneous merging algorithm processes the redistribution of mass and momentum at the moment of merging, it is often difficult to strictly guarantee the conservation of momentum, which leads to deviations in the simulation results and affects the numerical stability.

[0007] Some existing improved algorithms attempt to introduce criteria such as the critical Stokes number or Weber number to determine whether coagulation occurs. However, these methods are essentially criteria for "whether to merge" rather than models for "how to merge," and still cannot simulate asymptotic, dynamic coagulation processes. Furthermore, while the discrete element method (DEM) has advantages in simulating particulate matter, its application in droplet coagulation, especially considering dynamic processes and strict conservation laws, is still insufficient.

[0008] Therefore, developing a DEM algorithm that can accurately simulate the progressive coagulation of droplets, strictly conserve energy, and has a sound physical mechanism is of great significance for the accurate simulation of large-scale droplet systems. Summary of the Invention

[0009] To address the aforementioned issues, this invention proposes a droplet coagulation method and system based on DEM. By introducing a surface tension attraction model and establishing a progressive volume transfer and momentum conservation update mechanism based on overlap, the entire process of droplet coagulation from approach to complete fusion is simulated, strictly ensuring the conservation of mass and momentum.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a droplet coagulation method based on DEM, comprising the following steps: Obtain the physical properties and initial motion state of the droplet within the simulation domain; The relative distance between droplets is calculated based on the acquired data, and whether the droplets are in contact is determined based on the relative distance. For droplet pairs that are in contact, the attractive force driven by surface tension is calculated based on their geometric overlap. Based on the attractive force, the motion state of the droplets is updated by solving the equation of motion, and the overlap between the droplets is recalculated; Based on the updated overlap, a certain volume of liquid phase material is transferred from the first droplet in the droplet pair to the second droplet, and the radii of the two droplets are updated. According to the law of conservation of momentum, update the motion state of the droplet pair, iterate through the above steps until the agglomeration termination condition is met, and output the state of the agglomerated droplets.

[0011] As an alternative implementation, the surface tension-driven attractive force is calculated using the following formula: ; in, The surface tension coefficient, This represents the geometric overlap.

[0012] As an alternative implementation, the transfer of a certain volume of liquid phase material from the first droplet to the second droplet in the droplet pair specifically involves: The transfer volume is calculated based on the updated overlap and the radius of the first droplet. The transfer volume is then subtracted from the volume of the first droplet and added to the volume of the second droplet, wherein the volume of the first droplet is less than or equal to the volume of the second droplet.

[0013] As an alternative implementation, the radii of the first and second droplets are updated, specifically as follows: The radius of the first droplet is directly reduced by the size of the updated overlap, and the radius of the second droplet is recalculated based on its updated volume.

[0014] As an alternative implementation method, the motion state of the droplet pair is updated according to the law of conservation of momentum, specifically as follows: Calculate the change in momentum caused by volume transfer, and update the motion state of the second droplet based on the change in momentum.

[0015] As an alternative implementation, the coagulation termination condition is that the radius of the first droplet is lower than a preset threshold.

[0016] Secondly, the present invention provides a droplet coagulation system based on DEM, comprising: The data acquisition module is configured to acquire the physical properties and initial motion state of the droplets within the simulation domain. The attraction calculation module is configured to: calculate the relative distance between droplets based on the acquired data, determine whether the droplets are in contact based on the relative distance, and for droplet pairs that are in contact, calculate the attraction driven by surface tension based on their geometric overlap. The motion update module is configured to update the motion state of the droplets by solving the motion equations based on the attraction force, and recalculate the overlap between the droplets. The volume transfer module is configured to: transfer a certain volume of liquid phase material from the first droplet to the second droplet in the droplet pair based on the updated overlap amount, and update the radii of the two droplets; The loop control module is configured to update the motion state of the droplet pair according to the law of conservation of momentum, iteratively execute the above steps until the agglomeration termination condition is met, and output the state of the agglomerated droplets.

[0017] Thirdly, the present invention provides an electronic device including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described in the first aspect.

[0018] Fourthly, the present invention provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in the first aspect.

[0019] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the method described in the first aspect.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention proposes a droplet coalescence method based on DEM with high physical realism: by introducing a progressive attraction model driven by surface tension and a volume transfer mechanism based on overlap, the entire process of droplets from contact, approach to fusion is fully reproduced, breaking through the physical distortion limitations of traditional instantaneous merging models.

[0021] This invention proposes a droplet coagulation method based on DEM, which strictly adheres to the laws of conservation of mass and momentum at every time step, ensuring the numerical stability and physical reliability of the simulation results.

[0022] This invention proposes a droplet coagulation method based on DEM, which has broad application prospects: This invention can more accurately simulate the dynamic behavior of droplet groups and has important engineering application and scientific research value in fields involving droplet coagulation, such as spray combustion, fuel injection, meteorological cloud physics, and chemical separation.

[0023] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0024] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0025] Figure 1 This is a flowchart of a droplet coagulation method based on DEM according to the present invention. Detailed Implementation

[0026] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0027] It should be noted that the following detailed description is exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0028] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form as well. Furthermore, it should be understood that the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but includes other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0029] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0030] Example 1 like Figure 1As shown, this embodiment provides a droplet coagulation method based on DEM, including the following steps: Obtain the physical properties and initial motion state of the droplet within the simulation domain; The relative distance between droplets is calculated based on the acquired data, and whether the droplets are in contact is determined based on the relative distance. For droplet pairs that are in contact, the attractive force driven by surface tension is calculated based on their geometric overlap. Based on the attractive force, the motion state of the droplets is updated by solving the equation of motion, and the overlap between the droplets is recalculated; Based on the updated overlap, a certain volume of liquid phase material is transferred from the first droplet in the droplet pair to the second droplet, and the radii of the two droplets are updated, wherein the volume of the first droplet is less than or equal to the volume of the second droplet. According to the law of conservation of momentum, update the motion state of the droplet pair, iterate through the above steps until the agglomeration termination condition is met, and output the state of the agglomerated droplets.

[0031] The specific solution of the present invention is as follows: Step 1: Parameter Initialization. Set the physical parameters of the droplets, including the surface tension coefficient, and simultaneously set simulation parameters, such as the coagulation termination threshold and DEM time step. Read the initial spatial distribution and motion state of the droplet swarm, including the droplet position and velocity.

[0032] Step 2, Contact Detection. Within each DEM time step, traverse all droplet pairs and calculate the droplet center-to-center distance. dij Determine the droplet contact condition, i.e., determine whether the conditions are met. dij <= ( Ri + Rj (The droplets have contacted and overlapped), where, Ri and Rj These are the radii of the two droplets, respectively.

[0033] Step 3, Calculation of attractive force. For droplet pairs that are in contact, calculate their geometric overlap using the formula: Δ = ( Ri + Rj ) - dij and surface tension attraction F (i.e., attractive force driven by surface tension), where , is the surface tension coefficient.

[0034] Step 4: Motion Solution. The calculated attractive force is embedded into the Newton's second law equations of motion of the DEM (Discrete Element Method) to solve for the updated droplet velocity and position. The DEM obtains the interaction forces between the droplets, integrates the equations of motion at each time step to obtain the updated droplet velocity, and integrates again to obtain the updated droplet position. The equations of motion after embedding the attractive force are as follows: ; These include gravity, liquid bridge force, contact force, and viscous resistance.

[0035] Step 5: Volume transfer.

[0036] Step 501: For overlapping droplet pairs, recalculate the droplet overlap amount after updating the position: Δ = ( Ri + Rj ) - dij .

[0037] Step 502: Identify the larger and smaller droplets: Compare the current volumes of the two overlapping droplets and identify the larger droplet. i and smaller droplets j If the two droplets have the same volume, the one with the smaller number is the droplet. i The larger number indicates a droplet. j .

[0038] Step 503: Calculate the transfer volume Δ V According to the geometric model, the overlap Δ and the droplet radius are... Rj Calculate the volume to be transferred in this round. .

[0039] Step 504: Perform volume transfer and radius update to update the droplets. j The volume and radius of the large droplet are updated. i Volume and radius of the small droplet. j new radius Rj' = Rj -Δ. Large droplets i new volume Vi' = Vi +Δ V Its new radius .

[0040] Step 6: Update the droplet displacement based on the conservation of momentum.

[0041] Step 601: Calculate the momentum transfer amount .

[0042] Step 602: Update the velocity of large droplets ,in .

[0043] Step 603: Adjust the droplet position according to the updated velocity to prepare for the calculation of the next time step.

[0044] Step 7: Iteration and Termination Judgment. Inspect the small droplets. j radius Rj' When the radius of a small droplet is smaller than a preset coagulation termination threshold, the small droplet is considered to have been completely absorbed and removed from the simulation domain. Large droplets... i This is the final droplet after agglomeration, and its volume is the sum of the volumes of the two droplets. If agglomeration is not complete, the algorithm returns to step 2 to enter the loop of the next time step, removing the smaller droplet and transferring its volume completely to the larger droplet in contact, until the calculation stops. At this point, the dynamic droplet agglomeration calculation result based on DEM is obtained.

[0045] Example 2 This embodiment provides a droplet coagulation system based on DEM, including: The data acquisition module is configured to acquire the physical properties and initial motion state of the droplets within the simulation domain. The attraction calculation module is configured to: calculate the relative distance between droplets based on the acquired data, determine whether the droplets are in contact based on the relative distance, and for droplet pairs that are in contact, calculate the attraction driven by surface tension based on their geometric overlap. The motion update module is configured to update the motion state of the droplets by solving the motion equations based on the attraction force, and recalculate the overlap between the droplets. The volume transfer module is configured to: transfer a certain volume of liquid phase material from the first droplet to the second droplet in the droplet pair based on the updated overlap amount, and update the radii of the two droplets; The loop control module is configured to update the motion state of the droplet pair according to the law of conservation of momentum, iteratively execute the above steps until the agglomeration termination condition is met, and output the state of the agglomerated droplets.

[0046] It should be noted that the above modules correspond to the steps in Embodiment 1, and the examples and application scenarios implemented by the above modules and their corresponding steps are the same, but are not limited to the content disclosed in Embodiment 1. It should also be noted that the above modules can be executed in a computer system as part of the system.

[0047] In further embodiments, the following is also provided: An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the method described in Embodiment 1. For brevity, further details are omitted here.

[0048] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0049] A computer-readable storage medium for storing computer instructions that, when executed by a processor, perform the method of Embodiment 1.

[0050] The method in Example 1 can be directly executed by a hardware processor, or it can be executed by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.

[0051] A computer program product includes a computer program that, when executed by a processor, implements the method in Embodiment 1.

[0052] The present invention also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer-executable instructions, such as instructions included in program modules, which execute in a device on a target real or virtual processor to perform the processes / methods described above. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc., that perform specific tasks or implement specific abstract data types. In various embodiments, the functionality of program modules can be combined or divided among program modules as needed. The machine-executable instructions for the program modules can execute within a local or distributed device. In a distributed device, the program modules can reside in both local and remote storage media.

[0053] The computer program code used to implement the methods of the present invention may be written in one or more programming languages. This computer program code may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the computer or other programmable data processing device, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a computer, partially on a computer, as a stand-alone software package, partially on a computer and partially on a remote computer, or entirely on a remote computer or server.

[0054] In the context of this invention, computer program code or related data may be carried by any suitable carrier to enable a device, apparatus, or processor to perform the various processes and operations described above. Examples of carriers include signals, computer-readable media, and the like. Examples of signals may include electrical, optical, radio, sound, or other forms of propagation signals, such as carrier waves, infrared signals, etc.

[0055] Those skilled in the art will recognize that the units and algorithm steps described in conjunction with the embodiments herein can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0056] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A droplet coagulation method based on DEM, characterized in that, Includes the following steps: Obtain the physical properties and initial motion state of the droplet within the simulation domain; The relative distance between droplets is calculated based on the acquired data, and whether the droplets are in contact is determined based on the relative distance. For droplet pairs that are in contact, the attractive force driven by surface tension is calculated based on their geometric overlap. Based on the attractive force, the motion state of the droplets is updated by solving the equation of motion, and the overlap between the droplets is recalculated; Based on the updated overlap, a certain volume of liquid phase material is transferred from the first droplet to the second droplet in the droplet pair, and the radii of the two droplets are updated; wherein the volume of the first droplet is less than or equal to the volume of the second droplet; the current volumes of the two overlapping droplets are compared, and the droplet i with the larger volume and the droplet j with the smaller volume are identified. If the volumes of the two droplets are equal, the smaller droplet is identified as droplet i, and the larger droplet is identified as droplet j; small droplet j new radius Rj' = Rj -Δ; Large droplets i new volume Vi' = Vi +Δ V Its new radius ; According to the law of conservation of momentum, the motion state of the droplet pair is updated, and the above steps are iteratively executed until the agglomeration termination condition is met, and the state of the agglomerated droplets is output; the agglomeration termination condition is that the radius of the first droplet is lower than a preset threshold.

2. The droplet coagulation method based on DEM as described in claim 1, characterized in that, The surface tension-driven attractive force is calculated using the following formula: ； in, The surface tension coefficient, This represents the geometric overlap.

3. The droplet coagulation method based on DEM as described in claim 1, characterized in that, The transfer of a certain volume of liquid phase substance from the first droplet to the second droplet in the droplet pair specifically involves: The transfer volume is calculated based on the updated overlap and the radius of the first droplet. The transfer volume is then subtracted from the volume of the first droplet and added to the volume of the second droplet, wherein the volume of the first droplet is less than or equal to the volume of the second droplet.

4. The droplet coagulation method based on DEM as described in claim 1, characterized in that, Update the radii of the first and second droplets as follows: The radius of the first droplet is directly reduced by the size of the updated overlap, and the radius of the second droplet is recalculated based on its updated volume.

5. The droplet coagulation method based on DEM as described in claim 1, characterized in that, According to the law of conservation of momentum, the motion state of the droplet pair is updated as follows: Calculate the change in momentum caused by volume transfer, and update the motion state of the second droplet based on the change in momentum.

6. A droplet coagulation system based on DEM, characterized in that, include: The data acquisition module is configured to acquire the physical properties and initial motion state of the droplets within the simulation domain. The attraction calculation module is configured to: calculate the relative distance between droplets based on the acquired data, determine whether the droplets are in contact based on the relative distance, and for droplet pairs that are in contact, calculate the attraction driven by surface tension based on their geometric overlap. The motion update module is configured to update the motion state of the droplets by solving the motion equations based on the attraction force, and recalculate the overlap between the droplets. The volume transfer module is configured to: transfer a certain volume of liquid phase material from the first droplet to the second droplet in the droplet pair based on the updated overlap amount, and update the radii of the two droplets; wherein the volume of the first droplet is less than or equal to the volume of the second droplet; compare the current volumes of the two overlapping droplets, identify the larger droplet i and the smaller droplet j, and if the two droplet volumes are equal, the smaller droplet is identified as droplet i, and the larger droplet is identified as droplet j; small droplet j new radius Rj' = Rj -Δ; Large droplets i new volume Vi' = Vi +Δ V Its new radius ; The loop control module is configured to update the motion state of the droplet pair according to the law of conservation of momentum, iteratively execute the above steps until the agglomeration termination condition is met, and output the state of the agglomerated droplets; the agglomeration termination condition is that the radius of the first droplet is lower than a preset threshold.

7. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the method according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, perform the method described in any one of claims 1-5.

9. A computer program product, characterized in that, Includes a computer program, which, when executed by a processor, implements the method described in any one of claims 1-5.

Images