Calculation method of dynamic load of particle scouring based on discrete element material model
By employing a particle scouring dynamic load calculation method based on a discrete element material model, combined with Hertz contact theory and momentum conservation model, the problem of insufficient computational efficiency and accuracy in large-scale particle collision simulation is solved, achieving efficient and accurate load calculation and providing reliable input for the evaluation and life prediction of engine thermal protection components.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-05-09
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies struggle to achieve a good balance between computational efficiency and model accuracy when calculating dynamic loads from particle erosion. This is especially true in large-scale particle collision simulations, where they fail to accurately reflect the randomness, locality, and interaction with surface morphology of particle collisions, resulting in high computational resource consumption or insufficient accuracy.
A method for calculating particle scour dynamic load based on discrete element material model is adopted. By constructing a hierarchical particle collision physical model and combining an improved Hertz contact theory model and a momentum-conserving instantaneous impulse model, the time history of particle scour dynamic load is obtained, which can adapt to different simulation scales and accuracy requirements and achieve efficient and accurate load calculation.
This paper presents a method for efficiently and accurately obtaining the time history of dynamic erosion loads on material surfaces under extreme conditions. This method can provide reliable load input for erosion damage assessment and life prediction of engine thermal protection components, balancing computational efficiency and model accuracy. It is suitable for large-scale particle collision simulation in engineering practice.
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Figure CN122157916A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of thermal protection material performance evaluation technology, specifically to a method for calculating particle erosion dynamic load based on a discrete element material model. Background Technology
[0002] During solid rocket motor operation, the combustion gases often carry a large number of incompletely burned metal particles (such as aluminum oxide) or carbon particles, forming a high-speed gas-particle two-phase flow. These particles continuously and frequently scour the engine's inner walls and thermal protection components (such as gas rotors), which is one of the key factors leading to material erosion, spalling, and even structural failure. Accurately predicting the dynamic load caused by the gas flow particle scouring is the foundation and prerequisite for assessing the erosion morphology, service reliability, and service life of critical hot-end components.
[0003] Currently, there are two main methods for calculating particle erosion loads: one is based on computational fluid dynamics-discrete element coupled simulation, which performs detailed simulations of the trajectory of each particle and its collision with the wall. While this method can reflect details, it consumes enormous computational resources and is difficult to apply to scenarios in actual engines where the number of particles is huge (often exceeding tens of millions) and the collision frequency is extremely high. The second method is based on empirical formulas or averaged load estimation. This type of method is computationally efficient, but it cannot reflect the randomness, locality of particle collisions, and interaction with surface morphology, resulting in limited accuracy and making it difficult to analyze local damage and microscopic failure mechanisms. Therefore, there is an urgent need for a solution that can both reflect the main physical mechanisms and achieve efficient computation. Summary of the Invention
[0004] To address the aforementioned technical problems, this invention primarily focuses on the lack of a method for calculating particle erosion dynamic loads that achieves a good balance between computational efficiency and model accuracy, particularly in large-scale particle collision simulations for practical engineering applications. This invention provides a method for calculating particle erosion dynamic loads based on a discrete element method (DEM) material model. This method constructs a hierarchical particle collision physical model, balancing the computational feasibility and the rationality of the mechanical processes in large-scale particle collision simulations under extreme conditions. It can efficiently and accurately obtain the time history of the erosion dynamic loads on the material surface, providing a reliable load input for erosion damage assessment and life prediction of engine thermal protection components.
[0005] The first objective of this invention is to provide a method for calculating the dynamic load of particle erosion based on a discrete element material model, used for calculating the local dynamic load of particulate flow erosion of thermal protection materials in high-temperature combustion gases, including: The mechanical parameters of the thermal protection material are obtained, as well as the particle flow parameters. The mechanical properties include the first Young's modulus, the first Poisson's ratio, the first density, and the yield displacement. Particle flow parameters are the mechanical parameters of particles in a particle flow, including the second Young's modulus, the second Poisson's ratio, the second density, the average diameter of the particles, and the particle velocity vector. Construct a discrete element material model based on thermal protection materials; Based on the collision simulation of particles with thermal protection materials and the discrete element method material model, the local surface geometry information of particles colliding with thermal protection materials is obtained; wherein, the local surface geometry information is the coordinate matrix of the collision point, and each row of the coordinate matrix represents the actual coordinates of a node; Based on the local surface geometry information, obtain the local surface unit normal vector and radius of curvature; The particle collision normal velocity is obtained based on the local surface unit normal vector and the particle velocity vector; Construct a suitable physical model of particle-surface interaction; wherein, the physical model of particle-surface interaction includes an improved Hertz contact theory model or a momentum-conserving instantaneous impulse model; Based on the mechanical parameters of the thermal protection material, the particle flow parameters, the radius of curvature, and the normal velocity of particle collision, the dynamic load of particle scouring is obtained based on the particle-surface interaction physical model.
[0006] In one embodiment, when the particle-surface interaction physical model is an improved Hertz contact theory model, the process of obtaining the particle scouring dynamic load includes: Based on the local surface unit normal vector and radius of curvature, the equivalent contact parameters of the particle collision point on the surface of the thermal protection material are obtained. The equivalent contact parameters include the equivalent radius of curvature and the equivalent elastic modulus. The current penetration depth is obtained based on the particle collision normal velocity and the collision step size; The elastic force at the time of collision is obtained based on the equivalent radius of curvature, the equivalent elastic modulus, and the current penetration depth. The plastic force at impact is obtained based on the equivalent radius of curvature and equivalent elastic modulus, as well as the current penetration depth and yield displacement. The dynamic load of particle erosion is obtained based on the elastic and plastic forces during the collision.
[0007] In one embodiment, the formula for calculating the elastic force during a collision is:
[0008] In the formula, The elastic force during the collision; It is the equivalent elastic modulus; The equivalent radius of curvature; This represents the current penetration depth.
[0009] In one embodiment, the formula for calculating the plastic force during the collision is:
[0010] In the formula, This refers to the plastic force during a collision; This represents the current penetration depth. This is the yield displacement; It is the equivalent elastic modulus; It is the equivalent radius of curvature.
[0011] In one embodiment, the method further includes updating the penetration depth at the next moment using the current dynamic load, yield displacement, and the penetration depth at the previous moment and the current penetration depth. The particle erosion dynamic load at the next moment is calculated based on the penetration depth at the next moment. If the current penetration depth is ≤0, or the set time is reached, the dynamic load calculation loop will exit.
[0012] In one embodiment, when the particle-surface interaction physical model is a momentum-conserving instantaneous impulse model, the calculation formula for obtaining the particle scouring dynamic load is as follows:
[0013] In the formula, The instantaneous dynamic load of particle erosion; The comprehensive collision recovery coefficient; The normal velocity of the particle; This refers to the time step for numerical computation. The particle mass is calculated using the second density and average diameter.
[0014] In one embodiment, the direction of the instantaneous dynamic load of particle scouring is:
[0015] In the formula, The direction of the impact force; and These represent the projection lengths of the unit normal direction vector at the point of impact onto the x-axis and y-axis, respectively.
[0016] The second objective of this invention is to provide a computer program product, including a computer program that, when executed by a processor, implements a method for calculating particle scour dynamic loads based on a discrete element material model.
[0017] A third objective of this invention is to provide an electronic device comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to execute a method for calculating particle scour dynamic loads based on a discrete element material model by executing the executable instructions.
[0018] The fourth objective of this invention is to provide a system for calculating the dynamic load of particle erosion based on a discrete element material model, comprising: The data acquisition module is used to acquire the mechanical parameters of the thermal protection material and the particle flow parameters. The mechanical performance parameters include the first Young's modulus, the first Poisson's ratio, the first density, and the yield displacement. The particle flow parameters are the mechanical parameters of the particles in the particle flow, including the second Young's modulus, the second Poisson's ratio, the second density, the average diameter of the particles, and the particle velocity vector. The parameter acquisition module is used to construct a discrete element material model based on the thermal protection material; to simulate the collision of particles with the thermal protection material, and based on the discrete element material model, to acquire the local surface geometric information of the particles colliding with the thermal protection material; wherein, the local surface geometric information is a coordinate matrix of the collision points, and each row of the coordinate matrix represents the actual coordinates of a node; based on the local surface geometric information, the local surface unit normal vector and radius of curvature are acquired; based on the local surface unit normal vector and the particle velocity vector, the particle collision normal velocity is acquired. The load calculation module is used to construct an appropriate particle-surface interaction physical model. The particle-surface interaction physical model includes an improved Hertz contact theory model or a momentum-conserving instantaneous impulse model. Based on the mechanical parameters of the thermal protection material, particle flow parameters, radius of curvature, and normal velocity of particle collision, the particle scouring dynamic load is obtained based on the particle-surface interaction physical model.
[0019] The present invention has at least the following beneficial effects: This invention provides a method for calculating the dynamic load of particle erosion based on a discrete element material model. By constructing a hierarchical particle collision physical model, this method takes into account both the computational feasibility of large-scale particle collision simulation under extreme conditions and the rationality of the mechanical process. It can efficiently and accurately obtain the time history of the dynamic load of erosion on the material surface, providing a reliable load input for the assessment of erosion damage and life prediction of engine thermal protection components.
[0020] This invention provides a series of solutions ranging from high-precision Hertz models to high-efficiency momentum models, which can be flexibly selected or coupled according to the simulation scale and accuracy requirements, effectively solving the computational bottleneck problem in the simulation of massive particle collisions.
[0021] The model provided by this invention is based on classical contact mechanics and collision dynamics theory. The parameters have clear physical meanings, can be calibrated experimentally, and the prediction results are highly reliable.
[0022] The calculation method provided by the present invention can be conveniently integrated into existing finite element or discrete element analysis frameworks, and the output load time history can be directly used for subsequent stress, damage, and life analyses, providing a powerful tool for the anti-particle erosion design and performance evaluation of engine components.
[0023] By introducing the local curvature radius, the present invention enables the calculation of the impact force to truly reflect the influence of the component surface geometry, initial defects, or machining textures, making it more in line with engineering practice. Brief Description of the Drawings
[0024] Figure 1 It is a schematic diagram for calculating the particle impact process using the improved Hertz contact theory model and the momentum conservation theory model; Figure 2 It is a time history curve diagram of the impact force at a typical position calculated by using the Hertz contact theory model in the method of the present invention when the center point of the leading edge of the longitudinal section of a certain type of gas rudder is eroded by the particle flow; Figure 3 It is a schematic diagram of the magnitude and direction of the average impact force calculated by using the instantaneous impulse model of momentum conservation in the method of the present invention for all nodes at the leading edge of the longitudinal section of a certain type of gas rudder when eroded by the particle flow. Detailed Embodiments
[0025] In order to illustrate the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following will be described in detail in combination with embodiments.
[0026] In view of the lack in the prior art of a particle erosion dynamic load calculation method that can achieve a good balance between calculation efficiency and model accuracy, especially in large-scale particle collision simulations facing engineering practice. The purpose of the present invention is to provide a particle erosion dynamic load calculation method based on a discrete element material model. By introducing the local curvature radius, the calculation of the impact force can truly reflect the influence of the component surface geometry, initial defects, or machining textures, making it more in line with engineering practice.
[0027] The present invention selects typical materials for solid rocket engine thermal protection such as carbon / carbon composite materials, ceramic matrix composite materials, or copper infiltrated tungsten materials; the particle flow is Al2O3 particles, soot particles, or unburned metal particles carried in the engine gas.
[0028] To achieve the above purpose, as shown in Figure 1 A particle erosion dynamic load calculation method based on a discrete element material model for calculating the local dynamic load of a thermal protection material eroded by a particle flow in high-temperature gas includes: S1. Obtain the mechanical parameters of the thermal protection material; and obtain the particle flow parameters; wherein, the mechanical property parameters include the first Young's modulus, the first Poisson's ratio, the first density, and the yield displacement; Particle flow parameters are the mechanical parameters of particles in a particle flow, including the second Young's modulus, the second Poisson's ratio, the second density, the average diameter of the particles, and the particle velocity vector. This invention determines the mechanical parameters and particle flow parameters of the target material through experimental measurement, literature review, or simulation calibration. The mechanical parameters of the target material were obtained through literature review and verified by mechanical experiments, while the particle flow parameters were obtained from solid rocket motor test runs.
[0029] S2. Obtain the local surface unit normal vector and radius of curvature, and obtain the particle collision normal velocity; Specifically, a discrete element material model is constructed based on the thermal protection material; Based on the collision simulation of particles with thermal protection materials and the discrete element method material model, the local surface geometry information of particles colliding with thermal protection materials is obtained; wherein, the local surface geometry information is the coordinate matrix of the collision point, and each row of the coordinate matrix represents the actual coordinates of a node; Based on the local surface geometry information, obtain the local surface unit normal vector and radius of curvature; The particle collision normal velocity is obtained based on the local surface unit normal vector and the particle velocity vector; S3. Construct a suitable particle-surface interaction physical model; based on the mechanical parameters of the thermal protection material, particle flow parameters, radius of curvature and particle collision normal velocity, obtain the particle scouring dynamic load based on the particle-surface interaction physical model. Among them, the particle-surface interaction physical model includes the improved Hertz contact theory model or the momentum-conserving instantaneous impulse model.
[0030] In this invention, a suitable particle-surface interaction physical model is selected and constructed based on the typical velocity of particle erosion, material properties, and computational efficiency requirements. Two core models are provided: The improved Hertz contact theory model is applicable to low-to-medium frequency scouring with a total number of impacts less than or equal to 100,000. It can accurately describe the continuous curve of impact force change over time during the collision process and takes into account the elastic-plastic deformation of the material.
[0031] The instantaneous impulse model based on momentum conservation is applicable to high-frequency particle collisions with a total number of impacts exceeding 100,000. It simplifies the collision into momentum transfer within a single time step, greatly improving overall computational efficiency at the cost of sacrificing the details of a single collision.
[0032] Based on the selected model, input parameters, and real-time relative motion information between particles and the surface, the impact force or impulse applied to a specific location (mesh node) on the material surface by a single or statistically significant multiple collisions is calculated; that is, the particle erosion dynamic load at a specific location on the surface of the thermal protection material is calculated. When the particle-surface interaction physical model is an improved Hertz contact theory model, the process of obtaining the particle erosion dynamic load includes: Based on the local surface unit normal vector and radius of curvature, the equivalent contact parameters of the particle collision point on the surface of the thermal protection material are obtained. The equivalent contact parameters include the equivalent radius of curvature and the equivalent elastic modulus. The current penetration depth is obtained based on the particle collision normal velocity and the collision step size; The elastic force at the time of collision is obtained based on the equivalent radius of curvature, the equivalent elastic modulus, and the current penetration depth. The plastic force at impact is obtained based on the equivalent radius of curvature and equivalent elastic modulus, as well as the current penetration depth and yield displacement. The dynamic load of particle erosion is obtained based on the elastic and plastic forces during the collision.
[0033] The formula for calculating the elastic force during a collision is:
[0034] In the formula, The elastic force during the collision; It is the equivalent elastic modulus; The equivalent radius of curvature; This represents the current penetration depth.
[0035] The formula for calculating plastic force during a collision is:
[0036] In the formula, This refers to the plastic force during a collision; This represents the current penetration depth. This is the yield displacement; It is the equivalent elastic modulus; It is the equivalent radius of curvature.
[0037] When obtaining the dynamic load of particle scouring based on the improved Hertz contact theory model, it also includes updating the penetration depth at the next moment by using the current dynamic load, yield displacement, and the penetration depth at the previous moment and the current penetration depth. The particle erosion dynamic load at the next moment is calculated based on the penetration depth at the next moment. If the current penetration depth is ≤0, or the set time is reached, the dynamic load calculation loop will exit.
[0038] In this invention, when the particle-surface interaction physical model is a momentum-conserving instantaneous impulse model, the calculation formula for obtaining the particle scouring dynamic load is as follows:
[0039] In the formula, The instantaneous dynamic load of particle erosion; The comprehensive collision recovery coefficient ( ); The normal velocity of the particle; This refers to the time step for numerical computation. The particle mass is calculated using the second density and average diameter.
[0040] The instantaneous impulse model based on momentum conservation condenses the complex continuous collision process into impulse transfer within a single time step, making it suitable for macro-micro coupled simulations involving more than ten million collisions.
[0041] The direction of the instantaneous dynamic load from particle erosion is:
[0042] In the formula, The direction of the impact force; and These represent the projection lengths of the unit normal direction vector at the point of impact onto the x-axis and y-axis, respectively.
[0043] This invention uses the calculated impact force time history curve or equivalent dynamic load as boundary conditions to input into finite element analysis, fatigue analysis or erosion wear model for mechanical response analysis and life assessment of components.
[0044] To illustrate the particle scouring dynamic load calculation method based on the discrete element material model provided by this invention, we will take the evaluation of the local dynamic load of a solid rocket motor's gas rotor under the scouring of a high-temperature gas particle flow as an example.
[0045] A method for calculating particle erosion dynamic load based on a discrete element material model includes: Step 1, Parameter Acquisition: Thermal protection material parameters: The gas rotor material is a high-temperature resistant tungsten-copper infiltrated material, and its Young's modulus was obtained through literature review. Poisson's ratio ,density and yield strength .
[0046] Particle parameters in the particulate stream: Through gas analysis and sampling, it was determined that the scouring particles were mainly Al2O3, with an average diameter of ,density Young's modulus Poisson's ratio Given that the statistical distribution of the normal velocity of particles in the impact region is obtained through flow field simulation. .
[0047] Geometric parameters of thermal protection material: To demonstrate the adaptability of the method of the present invention to complex surface morphology, it is assumed that the cross-section of the gas rudder leading edge is arc-shaped, and the particle collision impacts the entire arc-shaped leading edge along its central normal direction.
[0048] Step 2, Model Selection and Construction: Given the high frequency of particle collisions in the gas turbine's operating environment, a "momentum-conserving instantaneous impulse model" is adopted as the primary calculation model to improve overall computational efficiency. Simultaneously, in critical local regions (the center of the arc-shaped leading edge), a "modified Hertz model" can be used for fine-tuning. Collision recovery coefficient. Calibration was performed through a small number of ballistic impact tests.
[0049] Step 3, Dynamic Load Calculation: Write a calculation program to iteratively process each particle that may collide with the surface at each time step.
[0050] For the vast majority of collisions, the instantaneous impulse model is invoked: based on particle mass, normal velocity, and calibration... Value, calculate impulse Divide by the time step The equivalent nodal force acting on the corresponding grid nodes within that time step is obtained. This data is then added to the load time history of that node.
[0051] For collisions at selected critical locations, the Hertz contact theory model is invoked: based on the local material and geometric parameters of the particles and the surface, the contact radius and equivalent modulus are calculated in real time, and the motion equations are solved through numerical integration to output a complete impact force-time curve. It is used for in-depth analysis of local damage mechanisms.
[0052] Step 4, Load Output and Application: The calculated load time histories (discrete force sequences or equivalent average force sequences) for all surface mesh nodes are summarized and output.
[0053] (i) In this embodiment, the dynamic load is calculated based on Hertz contact theory; Hertz contact theory is specifically adapted to the simulation calculation needs of particle collisions based on discrete element two-dimensional material models. It can calculate different particle impact force curves and impact directions based on variations in particle collision velocity, angle, collision point morphology, particle mechanical properties, and the mechanical properties of the impacted material, achieving more precise and controllable capture of particle collision dynamic loads. Compared to using momentum conservation models, it offers higher accuracy but also requires more computation. Although iterative calculations are still necessary, it is more engineering-feasible than traditional methods using finite element or smoothed particle hydrodynamics for high-precision particle collision simulations, enabling large-scale (millions of collisions) simulations in practical engineering applications. The specific dynamic load calculation process includes: (1) Obtaining local surface geometric information based on discrete element two-dimensional material model: Input: The line number of the collision point Node coordinate matrix 、 Node activation state matrix Mesh size and displacement field 、 .
[0054] Objective: Extract three rows near the collision point. , , The node coordinates are used to determine the surface node. For each row, the first active node from the left is taken, assuming the particle impacts from the left. If all nodes in a row are invalid, the first active node from the left is used. The second active node in the row is used as a replacement.
[0055] Output: one matrix Each row represents a node. Actual coordinates, i.e., initial coordinates plus displacement.
[0056] This embodiment extracts the coordinates of the nodes after actual deformation near the collision point, providing a basis for subsequent calculation of the local radius of curvature. By considering the displacement field of the nodes, it can accurately reflect the geometric morphology of the material surface during dynamic deformation, making the calculation of impact force more consistent with engineering practice, without requiring excessive computational resources.
[0057] (2) Impact dynamic load calculation: Based on local surface geometry and particle parameters, the normal contact force during the collision process is solved by time integration, specifically including the following: 1) Calculate the local normal and radius of curvature: Since the particle diameter is much smaller than the mesh size, the effect of a single collision is only affected by the surface topography near the collision node. The calculation utilizes the coordinates of the collision point and its adjacent left and right surface nodes: if the three points are collinear, the normal is perpendicular to the connecting line; otherwise, the center of a circle is fitted using the three points, and the normal direction points from the center to the middle node. The radius of curvature is the distance from the center to the node. Output: Unit normal vector. and local radius of curvature .
[0058] This embodiment uses three-point fitting of the local radius of curvature to accurately capture the local geometric features of any complex surface, such as pits, bumps, and processing textures, thus achieving an equivalent radius of curvature. The calculations are more accurate, which is impossible with the traditional uniform plane assumption. This significantly improves the accuracy of impact force prediction, but the method requires the particle size to be much smaller than the mesh size because it requires that particles only affect the impacted node and its adjacent nodes. Since the nodes used are only the three surface nodes output by the surface geometry information acquisition module, the computational cost is quite small.
[0059] 2) Equivalent contact parameters: Equivalent radius of curvature :
[0060] In the formula, Let be the radius of curvature of the particle; Local radius of curvature Equivalent elastic modulus :
[0061] In the formula, This is the second Young's modulus of the particle; The second Poisson's ratio; The first Young's modulus of thermal protective materials; The first Poisson's ratio; This embodiment treats the particles and the material as two elastic bodies and uses equivalent parameters from Hertzian contact theory. This approach retains the classical foundation of contact mechanics while simplifying the calculation. The parameters have clear physical meanings and are easy to calibrate experimentally, reflecting the characteristics of "layered modeling and clear physical mechanisms." This method is also a conventional calculation method in engineering.
[0062] 3) Velocity decomposition: Particle velocity vector Projecting onto the normal direction yields the normal velocity component. and its size is .
[0063] 4) Initialize penetration depth: The initial normal velocity is greater than zero. Assuming contact begins at the first time step, let the initial penetration depth be... ,in, From arrive The step size. It should be noted that the penetration depth refers to the distance at which the particle is considered to have penetrated the heat-resistant material during the iteration process. In the iterative calculation, the penetration depth first increases and then decreases, representing the process of the particle impacting the material, deforming it, and then being detached from the material due to the reaction force of the material.
[0064] 5) Master time loop (from arrive Step length ): For each time step, calculate the current normal contact force: Based on the Hertz contact model, the elastic force is calculated as follows:
[0065] When the penetration depth exceeds the yield displacement At that time, its plastic force is:
[0066] The total normal force is:
[0067] The penetration depth is updated in the next time step using a center-difference scheme:
[0068] in, The net force points in the direction of restoration; For particle mass; From arrive Step size; The penetration depth at the next moment; The current penetration depth; This represents the penetration depth at the previous moment.
[0069] Record the magnitude of the force at the current moment. The direction of the force is taken as the normal direction. From the perspective of, and standardized to Interval.
[0070] Update penetration depth and normal velocity:
[0071]
[0072]
[0073] Termination condition: If If the total time is reached, the output will be truncated and the loop will exit.
[0074] It should be noted that the elastic force term strictly follows Hertzian contact theory, ensuring accuracy under small deformations. The introduction of a plastic force term, when the penetration depth exceeds the yield displacement, simulates the plastic deformation and energy dissipation of the material, making the impact force curve closer to the real physical process—a significant improvement over the classical Hertzian model. The use of an explicit time integration scheme (central difference approach) provides good numerical stability and seamless integration with the time step of the discrete element method (DEM) main program, facilitating engineering implementation. Each step updates the force in real time based on the current penetration depth, capturing loading, unloading, and even multiple impacts during the impact process. Compared to traditional methods using SPH and improved finite element methods for particle collision simulation, this approach is more computationally efficient and meets practical engineering needs.
[0075] 6) Output: Time series It may be shortened due to early termination; Impact sequence ; Final force direction (angle, degrees) .
[0076] (3) Application in overall simulation: The main program for two-dimensional impact erosion simulation calls the above functions as follows: Collision detection: The impact position of each particle collision is generated based on the particle collision probability distribution, and the collision node is determined accordingly.
[0077] Get local surface: Call the local geometry information acquisition function to obtain the coordinates of three surface nodes near the collision node.
[0078] Calculate the impact force: The time history of the impact force is calculated; see [link / reference]. Figure 2 As shown, the impact force curve; it should be noted that the time history of the dynamic load, i.e. the impact force, is a curve.
[0079] Apply momentum: Calculate and update the velocity of the collision node based on the impact force curve, thereby driving the subsequent fracture and erosion process.
[0080] This embodiment seamlessly integrates high-precision impact force calculation into discrete element material simulation, providing accurate load input for studying material damage, fracture, and erosion caused by particle scouring. Because the impact force calculation considers local morphology and material elasticity-plasticity, subsequent erosion morphology prediction is more accurate, demonstrating the beneficial effect of this invention's "strong engineering applicability." Although the model introduces iterative calculations, the overall efficiency is still a qualitative leap compared to using commercial software for high-precision particle collision simulation to obtain impact loads due to the low computational cost of the above process. It can be used for dynamic load calculation in particle collision component erosion simulation at collision frequencies of millions of times.
[0081] (ii) In this embodiment, the instantaneous dynamic load is calculated based on the instantaneous impulse model of momentum conservation; This model is applicable to ultra-high-speed or high-volume particle collision scenarios, significantly improving computational efficiency while adhering to fundamental physical laws. Simulation results have verified that it can effectively handle the erosion problem of internal flow field components in solid-fuel engines, which experience over ten million particle collisions per second.
[0082] (1) Acquisition of local surface geometric information: The process is exactly the same as the local geometry information acquisition step in the Hertz model. This step also reflects the advantage of "considering surface topography," allowing the momentum model to determine the direction of the force based on the actual surface normal, rather than a simple planar assumption.
[0083] (2) Calculation of dynamic load: A simplified model based on the conservation of momentum is adopted, assuming that the momentum is completely converted into an instantaneous impulse on the surface during the particle impact process, and that the magnitude of the impact force is equal to the normal momentum rate of the particle, with the direction being outward along the surface normal.
[0084] 1) Input parameters: Local surface node coordinate matrix ( ).
[0085] Particle mass (kg).
[0086] : Particle incident velocity (m / s).
[0087] : Particle incident velocity direction (in radians, relative to the x-axis).
[0088] 2) Calculate the local normal: The local normal was calculated using the same method as the Hertz contact model.
[0089] 3) Velocity decomposition: The particle velocity vector is represented as:
[0090] In the formula, This is the particle velocity vector; The magnitude of the particle incident velocity; The direction of the particle incident velocity.
[0091] Calculate the normal velocity component:
[0092] Normal velocity magnitude: .
[0093] 4) Calculate the impact force: Magnitude of force: Based on the rate of change of momentum, assuming the impact time is extremely short, the total impulse equals the change of momentum. The calculation formula is as follows:
[0094] in, The comprehensive collision recovery coefficient ( ), For particle mass, For the normal velocity of the particle, This method uses a numerical calculation time step to condense a complex, continuous collision process into impulse transfer within a single time step.
[0095] Direction of force: Take the angle (in radians) of the local surface normal direction. ; and These represent the projection lengths of the unit normal direction vector at the point of impact onto the x-axis and y-axis, respectively.
[0096] In this embodiment, the instantaneous impulse model based on momentum conservation condenses the complex contact process into momentum transfer within a single time step, avoiding the computational overhead of iteratively solving for penetration depth. This results in extremely high computational efficiency, making it suitable for macroscopic simulations of particle collisions exceeding tens of millions of times. Through the restitution coefficient... The adjustable momentum transfer efficiency retains some physical meaning, enabling the model to maintain a certain level of accuracy while being extremely efficient; the normal velocity and direction are both obtained based on the actual surface geometry, ensuring the correct load direction and avoiding cumulative errors caused by directional deviations.
[0097] 5) Output: Impact force magnitude (scalar, unit: N) ; Impact direction (radius) It aligns with the direction of the normal. See also Figure 3 As shown, this is a schematic diagram of the surface impact load distribution.
[0098] (3) Application in overall simulation: This function is called within the program to calculate the impact force generated by particle collisions and apply it to the nodes. The calling process is as follows: Collision detection: Determine the row where the collision point is located based on randomly generated impact locations. and column .
[0099] Get the local surface: Call the local surface geometry information acquisition function to obtain the coordinates of three nodes near the point.
[0100] Calculate the impact force: calculate the magnitude of the force. and direction .
[0101] Apply momentum: Multiply the impact force by the time step (or treat it as an equivalent average force) to convert it into a velocity increment, update the velocity of the collision node, and thus drive the subsequent fracture and erosion process.
[0102] It should be noted that this simplified version avoids complex contact mechanics iterations, resulting in high computational efficiency, making it particularly suitable for massive collision scenarios requiring rapid estimation of impact effects. By using two models in a layered manner (a globally efficient model + a locally high-precision model), this invention achieves a balance between overall computational efficiency and the accuracy of analysis in key areas, and is specifically tailored to the unique particle collision simulation calculation requirements of solid rocket motor internal environment component erosion, which features high particle impact frequency, long working time, and high collision velocity.
[0103] In summary, this invention provides a method for calculating high-frequency particle erosion dynamic loads based on a discrete element material model. The material is located in the internal environment of a solid rocket motor or similar extreme conditions with a two-phase flow of gas and particles, where the particle size in the flow should be significantly smaller than the mesh size. This invention constructs a particle collision model based on Hertz contact theory or the law of conservation of momentum, calculating the dynamic load exerted by the particle flow on the material surface mesh while balancing computational efficiency and model accuracy. Compared to traditional methods that rely on commercial software to perform detailed simulations of each particle collision, this method is more suitable for the two-phase flow environment of solid rocket motors with an extremely high number of collisions (over 10 million), providing a new approach for evaluating the particle erosion resistance of engine components such as gas turbine rudders and throat liners.
[0104] This invention provides a computer program product, including a computer program that, when executed by a processor, implements a method for calculating particle scour dynamic load based on a discrete element material model.
[0105] This invention provides an electronic device, comprising: A processor; and a memory for storing executable instructions of the processor; The processor is configured to execute a method for calculating particle scour dynamic loads based on a discrete element material model by executing the executable instructions.
[0106] This invention provides a system for calculating the dynamic load of particle erosion based on a discrete element material model, comprising: The data acquisition module is used to acquire the mechanical parameters of the thermal protection material and the particle flow parameters. The mechanical performance parameters include the first Young's modulus, the first Poisson's ratio, the first density, and the yield displacement. The particle flow parameters are the mechanical parameters of the particles in the particle flow, including the second Young's modulus, the second Poisson's ratio, the second density, the average diameter of the particles, and the particle velocity vector. The parameter acquisition module is used to construct a discrete element material model based on the thermal protection material; to simulate the collision of particles with the thermal protection material, and based on the discrete element material model, to acquire the local surface geometric information of the particles colliding with the thermal protection material; wherein, the local surface geometric information is a coordinate matrix of the collision points, and each row of the coordinate matrix represents the actual coordinates of a node; based on the local surface geometric information, the local surface unit normal vector and radius of curvature are acquired; based on the local surface unit normal vector and the particle velocity vector, the particle collision normal velocity is acquired. The load calculation module is used to construct an appropriate particle-surface interaction physical model. The particle-surface interaction physical model includes an improved Hertz contact theory model or a momentum-conserving instantaneous impulse model. Based on the mechanical parameters of the thermal protection material, particle flow parameters, radius of curvature, and normal velocity of particle collision, the particle scouring dynamic load is obtained based on the particle-surface interaction physical model.
[0107] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for calculating the dynamic load of particle erosion based on a discrete element material model, characterized in that, Calculation of local dynamic loads for particulate flow erosion of thermal protection materials in high-temperature combustion gases, including: The mechanical parameters of the thermal protection material are obtained, as well as the particle flow parameters. The mechanical properties include the first Young's modulus, the first Poisson's ratio, the first density, and the yield displacement. Particle flow parameters are the mechanical parameters of particles in a particle flow, including the second Young's modulus, the second Poisson's ratio, the second density, the average diameter of the particles, and the particle velocity vector. Construct a discrete element material model based on thermal protection materials; Based on the collision simulation of particles with thermal protection materials and the discrete element method material model, the local surface geometry information of particles colliding with thermal protection materials is obtained; wherein, the local surface geometry information is the coordinate matrix of the collision point, and each row of the coordinate matrix represents the actual coordinates of a node; Based on the local surface geometry information, obtain the local surface unit normal vector and radius of curvature; The particle collision normal velocity is obtained based on the local surface unit normal vector and the particle velocity vector; Construct a suitable physical model of particle-surface interaction; wherein, the physical model of particle-surface interaction includes an improved Hertz contact theory model or a momentum-conserving instantaneous impulse model; Based on the mechanical parameters of the thermal protection material, the particle flow parameters, the radius of curvature, and the normal velocity of particle collision, the dynamic load of particle scouring is obtained based on the particle-surface interaction physical model.
2. The method for calculating particle erosion dynamic load based on discrete element material model according to claim 1, characterized in that, When the particle-surface interaction physical model is an improved Hertz contact theory model, the process of obtaining the particle scouring dynamic load includes: Based on the local surface unit normal vector and radius of curvature, the equivalent contact parameters of the particle collision point on the surface of the thermal protection material are obtained. The equivalent contact parameters include the equivalent radius of curvature and the equivalent elastic modulus. The current penetration depth is obtained based on the particle collision normal velocity and the collision step size; The elastic force at the time of collision is obtained based on the equivalent radius of curvature, the equivalent elastic modulus, and the current penetration depth. The plastic force at impact is obtained based on the equivalent radius of curvature and equivalent elastic modulus, as well as the current penetration depth and yield displacement. The dynamic load of particle erosion is obtained based on the elastic and plastic forces during the collision.
3. The method for calculating particle erosion dynamic load based on discrete element material model according to claim 2, characterized in that, The formula for calculating the elastic force during a collision is: In the formula, The elastic force during the collision; It is the equivalent elastic modulus; The equivalent radius of curvature; This represents the current penetration depth.
4. The method for calculating particle erosion dynamic load based on discrete element material model according to claim 2, characterized in that, The formula for calculating plastic force during a collision is: In the formula, This refers to the plastic force during a collision; This represents the current penetration depth. This is the yield displacement; It is the equivalent elastic modulus; It is the equivalent radius of curvature.
5. The method for calculating particle erosion dynamic load based on discrete element material model according to claim 4, characterized in that, It also includes updating the penetration depth at the next moment by using the current dynamic load, yield displacement, and the penetration depth at the previous moment and the current penetration depth; The particle erosion dynamic load at the next moment is calculated based on the penetration depth at the next moment. If the current penetration depth is ≤0, or the set time is reached, the dynamic load calculation loop will exit.
6. The method for calculating particle erosion dynamic load based on discrete element material model according to claim 1, characterized in that, When the particle-surface interaction physical model is a momentum-conserving instantaneous impulse model, the calculation formula for obtaining the particle scouring dynamic load is as follows: In the formula, The instantaneous dynamic load of particle erosion; The comprehensive collision recovery coefficient; The normal velocity of the particle; This refers to the time step for numerical computation. The particle mass is calculated using the second density and average diameter.
7. The method for calculating particle erosion dynamic load based on discrete element material model according to claim 6, characterized in that, The direction of the instantaneous dynamic load from particle erosion is: In the formula, The direction of the impact force; and These represent the projection lengths of the unit normal direction vector at the point of impact onto the x-axis and y-axis, respectively.
8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the particle scouring dynamic load calculation method based on the discrete element material model as described in any one of claims 1 to 7.
9. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to execute the particle scour dynamic load calculation method based on the discrete element material model according to any one of claims 1 to 7 by executing the executable instructions.
10. A system for calculating the dynamic load of particle erosion based on the discrete element material model as described in claim 1, characterized in that, include: The data acquisition module is used to obtain the mechanical parameters of the thermal protection material; And obtain particle flow parameters; among which, mechanical property parameters include first Young's modulus, first Poisson's ratio, first density and yield displacement; particle flow parameters are the mechanical parameters of particles in the particle flow, including second Young's modulus, second Poisson's ratio, second density and average particle diameter and particle velocity vector; The parameter acquisition module is used to construct a discrete element material model based on the thermal protection material; to simulate the collision of particles with the thermal protection material, and based on the discrete element material model, to acquire the local surface geometric information of the particles colliding with the thermal protection material; wherein, the local surface geometric information is a coordinate matrix of the collision points, and each row of the coordinate matrix represents the actual coordinates of a node; based on the local surface geometric information, the local surface unit normal vector and radius of curvature are acquired; based on the local surface unit normal vector and the particle velocity vector, the particle collision normal velocity is acquired. The load calculation module is used to construct an appropriate particle-surface interaction physical model. The particle-surface interaction physical model includes an improved Hertz contact theory model or a momentum-conserving instantaneous impulse model. Based on the mechanical parameters of the thermal protection material, particle flow parameters, radius of curvature, and normal velocity of particle collision, the particle scouring dynamic load is obtained based on the particle-surface interaction physical model.