Coupled molecular dynamics first-principles calculation method for surface particle adsorption on gas cooled reactor cladding

Abstract

The application discloses a kind of coupling molecular dynamics first principle's gas cooled reactor cladding surface particle adsorption calculation method, steps are as follows: (1) based on computational fluid dynamics and particle discrete phase model establishes numerical simulation framework, including cladding, break, flow channel modeling, grid drawing, boundary condition setting;(2) according to the first principle of molecular dynamics, the binding surface energy of fission product molecules released into the gas gap and the cladding material molecular base is calculated;(3) establish the particle deposition model including particle's own attribute, effective modulus, relaxation time and surface energy;(4) the binding surface energy is implanted into the particle deposition model, and the particle deposition model is used as the wall boundary, and the gas-solid two-way coupling calculation of particle deposition is carried out.The method solves the problem that traditional macroscopic model depends on empirical parameters, realizes high-precision simulation based on physical mechanism, reveals the mechanism of micro-interface properties on macroscopic deposition behavior, and predicts complex deposition morphology.

Description

Technical Field

[0001] This invention belongs to the field of radioactive leakage status assessment in gas-cooled reactor accidents, specifically involving the behavioral analysis of solid fission products being adsorbed by the cladding or entering the coolant circuit under different operating conditions and breach sizes and shapes. Background Technology

[0002] In advanced nuclear energy systems such as high-temperature gas-cooled reactors, the release, transport, and deposition of fission products in solid particle form under cladding failure accidents are crucial for assessing the radioactive source term and containment load. Traditional engineering analysis methods typically employ highly simplified empirical models or homogeneous assumptions to estimate particle escape fractions and deposition locations. While computationally efficient, these methods struggle to characterize the complex local geometry, turbulence effects, and true particle-wall interactions at the failure site. This results in significant uncertainty and strong conservatism in the predictions, potentially impacting the accuracy and cost-effectiveness of safety analyses.

[0003] With the maturation of computational fluid dynamics and discrete phase models, it has become possible to perform refined numerical reproduction of particle behavior using gas-solid two-phase flow simulations. However, the accuracy of existing CFD-DPM methods in simulating the deposition behavior of micron / submicron particles heavily relies on key model parameters such as the rebound / adhesion criteria after particle-wall collisions. These parameters are usually derived from macroscopic experimental fitting or simplified theoretical formulas, and cannot truly reflect the microscopic physicochemical state of a specific material surface under complex conditions such as irradiation, high temperature, and oxidation, as well as its atomic-scale interactions with particles, resulting in inherent defects in the simulation at the mechanistic level.

[0004] Therefore, the main shortcoming of existing technologies lies in the scale gap between microscopic mechanisms and macroscopic simulations. On the one hand, while AIMD can reveal the essence of interfacial interactions, its scale is limited to the nanometer scale and cannot be directly used for engineering system analysis. On the other hand, while macroscopic engineering simulations can handle system-scale flow and transport, their underlying physical models lack input of real physical parameters from more fundamental scales. This disconnect hinders a deep understanding and high-fidelity prediction of the complex cross-scale physical process of fission product migration and deposition. Summary of the Invention

[0005] To overcome the problems existing in the prior art, the present invention aims to provide a calculation method for particle adsorption behavior on the cladding surface of a gas-cooled reactor that couples first principles of molecular dynamics with a particle deposition model. This method breaks away from the traditional particle deposition model's reliance on empirical parameters and adopts a cross-physical-scale modeling method from molecular dynamics to classical mechanics. It constructs a particle deposition model under the influence of multiple factors and uses gas-solid two-phase flow numerical simulation to evaluate the adsorption behavior of solid fission products on the cladding surface or their migration within a mixed inert gas loop after the fuel cladding of a gas-cooled reactor is damaged.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for calculating particle adsorption on the cladding surface of a gas-cooled reactor coupled with first-principles calculations of molecular dynamics includes the following steps: Step 1: Use modeling and meshing software to establish the structural model of the air gap-break-flow channel. Then, import the mesh file into the computational fluid dynamics software FLUENT to complete the setting of the physical properties of the mixed inert gas working fluid, the discrete phase model of the particles, and the boundary conditions of pressure, velocity, and temperature. The specific steps are as follows: Step 1-1: Use Design Modeler to build the geometric model. Divide the air gap, opening, and flow channel into a combination of multiple hexahedrons according to their own shapes to meet the requirements of structured mesh drawing. Steps 1-2: Import the geometric model into Ansys Meshing. The mesh drawing algorithm uses Multizones, and the two ends of the geometric structure along the flow channel direction are used as the source and end faces of Multizones sweep. Set the mesh size for the two ends, first divide the gap mesh, then divide the air gap and flow channel mesh, thus completing the drawing of the hexahedral structured mesh, and import it into FLUENT. Steps 1-3: Calculate the density, specific heat capacity, thermal conductivity, and kinematic viscosity of the mixed inert gas working fluid in FLUENT using the gas state equation and property equation, and implant the user-defined function (UDF) provided by FLUENT software to describe the inert gas properties. Steps 1-4: Enable the Discrete Phase Model (DPM) for particles, set the two-way coupling between particles and the flow field, and the particle tracking time step; enable the mechanical models for gravity, drag, thermophoretic force, pressure gradient force, and additional mass force; enable the random walk model in the turbulence fluctuation effect module, and use message passing for parallel particle computation; create a new particle release nozzle, set the particle size, initial velocity, initial temperature, release time period, and particle flow rate to complete the preparation for particle tracking. Steps 1-5: Enable the Mixture two-phase model in FLUENT, set it to implicit, enable implicit volume forces, set the interface model to discrete, and set two components. The main component is a mixed inert gas, whose properties have been set in Steps 1-3. The secondary component is a mixed fission gas, whose properties are obtained by querying the Nist database and weighting the average according to the content ratio of various fission gases. Set the flow channel inlet as a mass flow rate boundary and set the mass flow rate. Set the outlet as a pressure boundary and set the flow channel working pressure. Use temperature boundaries for all solid walls and set the wall temperature. Set the time step of the flow field to ensure that the particle time step is at most 1 / 10 of the flow field time step. Step 2: Use Material Studio to establish models of free molecules of solid fission products and molecular clusters of the substrate material. Use first-principles AIMD to calculate the potential energy of the free molecules and the substrate molecular clusters in their stable states. Treat the two as a whole after connecting them with electron pairs and calculate the potential energy after stabilization. Use the difference between the potential energy of the initial separated state and the combined state as the surface energy of the combination between the free molecules of solid fission products and the substrate material. Step 3: Modify the existing particle deposition model using the binding surface energy calculated in Step 2, and implant FLUENT through a UDF. The specific details are as follows: Step 3-1: The first part of the particle deposition model is to determine whether particles can be adsorbed when they enter the first mesh layer near the wall, which requires comparing particle velocities. u p Particle critical wall escape velocity u Cr The size of the particle determines whether it will bounce off the wall if the particle velocity is greater; otherwise, it will be adsorbed onto the wall. The critical wall escape velocity is fitted by particle properties, effective modulus, relaxation time, and surface energy. Step 3-2: The second part of the particle deposition model involves determining whether particles adsorbed by the wall can be re-entrained and re-enter the airflow. This requires comparing the shear velocity of the actual airflow at the wall. u τ Critical wall shear velocity u * The size of the particles determines whether they are completely deposited. If the actual shear velocity of the wall airflow is less than the critical wall shear velocity, the particles are considered to be completely deposited; otherwise, they are resuspended in the airflow. Step 3-3: The combined surface energy calculated using first principles is implanted into the first part of the particle deposition model. In addition to setting the temperature, after DPM is enabled in step 1-4, a DPM boundary will appear on the wall boundary. The particle deposition model is then implanted into this boundary to determine whether particles can be deposited on the wall. Step 4: First, initialize the particle deposition model, ensuring the initial particle deposition count is 0. Open the particle deposition count monitoring file and record the particle deposition count and location information. First, set the interface between the breach and the flow channel geometry as a solid wall, i.e., close the breach, and perform steady-state flow field calculations. Then, restore it to the internal surface, i.e., open the breach, and perform gas-solid two-phase flow calculations for inert gas-particle bidirectional coupled CFD-DPM. After the calculation is completed, export the particle deposition count. Calculate the particle deposition rate based on the initial particle quantity and operating conditions. Simultaneously, observe the final particle distribution and assess the escape of radioactive products.

[0007] The present invention has the following advantages and effects: (1) Improve simulation accuracy and reliability By combining surface energy, derived from molecular dynamics and first-principles calculations of microscopic interfaces, with the latter as a key parameter, and embedding it into a macroscopic computational fluid dynamics-discrete phase model (CFD-DPM), macroscopic particle deposition prediction is grounded in solid physical mechanisms rather than relying on empirical assumptions. Through parameter transfer, the crucial influence of microstructure (such as damaged surface morphology and chemical state) on macroscopic particle transport and deposition is directly demonstrated.

[0008] (2) Deepen the understanding of complex physical processes Because the particle deposition model used in this invention comprehensively considers the effects of particle properties, relaxation time, effective modulus, surface energy, various particle forces, and flow field parameters, and uses the refined simulation technology CFD-DPM to track particles, it can simulate and predict particle-surface chemical reactions, surface roughness effects, etc., which are difficult to handle by traditional models, and obtain more realistic deposition morphology and distribution.

[0009] (3) Significantly enhance engineering design and safety analysis capabilities Numerical models can be established for different cladding materials and damage morphologies (crack size and shape). The simulation scheme of this invention can be used to evaluate the product retention capacity, providing a theoretical tool for the optimized design of accident-resistant fuel (ATF) cladding and containment internal components. It can also be used to evaluate the deposition efficiency of particles under different coolant flow rates and temperatures, providing a quantitative basis for the formulation of accident management measures (such as filtration and flushing).

[0010] Meanwhile, the present invention verifies the gas-solid numerical simulation scheme by conducting inert gas mixed gas flow field circular tube flow experiments and particle deposition experiments in rectangular tubes, which can basically guarantee the accuracy of the method. Attached Figure Description

[0011] Figure 1 This is a flowchart of the method of the present invention.

[0012] Figure 2 Model the entire flow path from air gap to break to triangular channel.

[0013] Figure 3 This is to verify the flow field simulation method of the present invention. Figure 4 This is to verify the particle deposition method of the present invention. Detailed Implementation

[0014] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings: like Figure 1 As shown, the present invention provides a method for calculating particle adsorption on the cladding surface of a gas-cooled reactor based on first-principles calculations coupled with molecular dynamics, comprising the following steps: Step 1: Establish the structural model of the air gap-break-flow channel using modeling and meshing software. Then, import the mesh file into the computational fluid dynamics (CFD) software FLUENT to complete the setting of the mixed inert gas working fluid properties, the particle discrete phase model, and the pressure, velocity, and temperature boundary conditions. The overall process is as follows: Figure 2 As shown, the specific content is as follows: Step 1-1: Use Design Modeler to build the geometric model. Divide the air gap, opening, and flow channel into a combination of multiple hexahedrons according to their own shapes to meet the requirements of structured mesh drawing. Steps 1-2: Import the geometry file into Ansys Meshing. The mesh drawing algorithm uses Multizones, and the two ends of the geometry along the flow channel direction are used as the source and end faces of Multizones sweep. Set the mesh size for the two ends, first divide the gap mesh, then divide the air gap and flow channel mesh, thus completing the drawing of the hexahedral structured mesh, and import it into FLUENT. Steps 1-3: Calculate the density, specific heat capacity, thermal conductivity, and kinematic viscosity of the mixed inert gas working fluid in FLUENT using the gas state equation and property equation, and implant the user-defined function (UDF) provided by FLUENT software to describe the inert gas properties. Steps 1-4: Enable the Discrete Phase Model (DPM) for particles, set the two-way coupling between particles and the flow field, and the particle tracking time step; enable the mechanical models for gravity, drag, thermophoretic force, pressure gradient force, and additional mass force; enable the random walk model in the turbulence fluctuation effect module, and use message passing for parallel particle computation; create a new particle release nozzle, set the particle size, initial velocity, initial temperature, release time period, and particle flow rate to complete the preparation for particle tracking. Steps 1-5: Enable the Mixture two-phase model in FLUENT, set it to implicit, enable implicit volume forces, set the interface model to discrete, and set two components. The main component is a mixed inert gas, whose properties have been set in Steps 1-3. The secondary component is a mixed fission gas, whose properties are obtained by querying the Nist database and weighting the average according to the content ratio of various fission gases. Set the flow channel inlet as a mass flow rate boundary and set the mass flow rate. Set the outlet as a pressure boundary and set the flow channel working pressure. Use temperature boundaries for all solid walls and set the wall temperature. Set the time step of the flow field to ensure that the particle time step is at most 1 / 10 of the flow field time step. Step 2: Model the free molecules of the solid fission products and the molecular clusters of the substrate material using Material Studio. First-principles AIMD is used to calculate the potential energy of the free molecules and the substrate molecular clusters in their stable states. The two are then considered as a whole after being connected by electron pairs, and their stable potential energy is calculated. The difference between the potential energy of the initial separated state and the bound state is taken as the binding surface energy between the free molecules of the solid fission products and the substrate material. The calculation steps for the binding surface energy are as follows: First-principles molecular dynamics is a computational method based on quantum mechanics used to simulate the dynamical behavior of atomic and molecular systems. For each crystal plane, its surface energy is calculated using the following formula. : (1) In the formula, E s Represents the total surface energy. E b This represents the total energy of physical fitness. A This represents the crystal plane area. The interfacial energy and separation work of the interface model are: (2) (3) In the formula, E int Indicates the interface capabilities, W sep Represents the work done by separation. E tot This represents the total energy of the original interface. E bulk-up Represents the energy of free molecules. E bulk-down Represents the energy of the base molecules. A This represents the crystal plane area. Interfacial adsorption energy reflects the bonding strength between particles. Comparing interfacial adsorption energies, a negative adsorption energy indicates exothermic adsorption, meaning spontaneous adsorption occurs; a larger absolute value indicates better adsorption performance. A positive adsorption energy indicates endothermic adsorption, meaning heating or other conditions are required at this location, and the adsorbed material is unstable. It can quantitatively determine the adsorption performance of fission products on the shell surface. E 吸附 High and low: (4) In the formula, the three types of energy on the right side of the equation E 体系 , E 原子 , E 基底 , respectively, represent the stabilization energy after bonding, the stabilization energy of CsI, and the stabilization energy of the substrate material Mo-Re alloy, in eV, from which the bonding surface energy is obtained; Step 3: Modify the existing particle deposition model using the binding surface energy calculated in Step 2, and implant FLUENT through a UDF. The specific details are as follows: Step 3-1: The first part of the particle deposition model is to determine whether particles can be adsorbed when they enter the first mesh layer near the wall, which requires comparing particle velocities. u p Particle critical wall escape velocity u Cr The size of the particle determines its escape velocity. If the particle velocity is greater, the particle is bounced off; otherwise, it is adsorbed onto the wall. The critical wall escape velocity is fitted using particle properties, effective modulus, relaxation time, and surface energy. The calculation method is as follows: First, define the effective parameters after the particles come into contact with the substrate material, including the effective modulus. E Pa, reduction radius R m, reduction mass m kg and effective surface energy γ J / m 2 As shown below: (5) In the formula, v i , E i , R i , m i and γ i These represent Poisson's ratio, Young's modulus, particle radius, particle mass, and surface energy, respectively. i =1, 2). 1 represents particles; 2 represents the substrate material. Simultaneously, the coefficient of restitution... e Defined as: (6) In the formula, u i and u r These are the incident velocity and the rebound velocity, respectively, in m / s; E ki and E kr Let J be the incident kinetic energy and the rebound kinetic energy, respectively. According to the law of conservation of energy, the coefficient of restitution is obtained. e for: (7) when e When =0: (8) In the formula, B is an empirical constant, 1.5; Ad Represents the dimensionless adhesion number. γ + This represents dimensionless adhesion force. τ + The dimensionless relaxation time is represented by its root, which is the critical adhesion velocity. The unique positive root can be obtained through a numerical bisection method. Multiple critical adhesion velocity values ​​can be obtained for particles and surfaces with different properties. The critical adhesion velocity can then be obtained through direct fitting. u c Explicit expression: (9) In the formula, γ Indicates effective surface energy. τ Indicates relaxation time. ρ Indicates density, E Indicates the effective modulus. R This represents the particle size. When the particle velocity exceeds the critical adhesion velocity, the particle rebounds. The magnitude of the recovery coefficient is calculated using equation (7), and the particle velocity after rebound is... u r =eu i The particle velocity direction is mirror-symmetric to the incident direction about the wall normal, and it detaches from the wall; when the particle velocity is less than or equal to the critical adhesion velocity, the particle is adsorbed, and in subsequent time steps, it is necessary to determine whether the particle can be resuspended.

[0015] Step 3-2: The second part of the particle deposition model involves determining whether particles, after being adsorbed by the wall, can be re-entrained and re-enter the airflow. This requires comparing the actual shear velocity of the wall airflow with the critical wall shear velocity. If the actual shear velocity of the wall airflow is less than the critical wall shear velocity, the particles are considered completely deposited; otherwise, they are resuspended and re-enter the airflow. The critical wall shear velocity... The calculation method is as follows: (10) In the formula, F po-b This represents the adhesion force between the wall surface and the particles. β Indicates the radius of the protrusion on the particle surface. n b =1, 2, ... represents the average spacing between bumps. n u It is a constant greater than 1. C c This represents the slip correction factor, where π is the mathematical constant pi. d The particle diameter is α Indicates the contact angle. f Re is the coefficient of friction. s Let Reynolds number be 1. f mEmpirical constants. When the actual shear velocity of the wall airflow is greater, the particle tangential velocity is assigned to the tangential velocity of the wall airflow, and the normal velocity is obtained from the simplified energy conservation of the actual shear velocity and the critical shear velocity. This causes the particles to detach from the wall, and vice versa.

[0016] Step 3-3: The combined surface energy calculated using first principles is implanted into the first part of the particle deposition model. In addition to setting the temperature, after DPM is enabled in step 1-4, a DPM boundary will appear on the wall boundary. The particle deposition model is then implanted into this boundary to determine whether particles can be deposited on the wall. Step 4: After completing the above steps, first initialize the particle deposition model, ensuring the initial particle deposition count is 0. Open the particle deposition count monitoring file and record the particle deposition count and location information. First, set the interface between the breach and the channel geometry as a solid wall, i.e., close the breach, and perform steady-state flow field calculations. Then, restore it to an internal surface, i.e., open the breach, and perform gas-solid two-phase flow calculations for inert gas-particle bidirectional coupled CFD-DPM. After the calculation is completed, export the particle deposition count. Calculate the particle deposition rate based on the initial particle quantity and operating conditions. Simultaneously, observe the final particle distribution and assess the escape of radioactive products. Dimensionless particle deposition rate. The calculation is performed using the following formula: (2) In the formula, L The length along the channel axis is expressed in meters (m). W Indicates the width of the pipe cross-section, in meters (m). U 0 represents the average flow velocity along the axis, in m / s; N Indicates the number of particles entering or depositing; u * The turbulent friction velocity in the flow channel is expressed in m / s. The particle relaxation time is used for different operating conditions. describe: (3) In the formula, τ p The relaxation time of the particle is expressed in seconds. τ e The vortex survival time is expressed in seconds. μ and ν The dynamic viscosity and kinematic viscosity of the airflow, respectively, are expressed in Pa·s and m. 2 / s, C c This represents the slip correction factor.

[0017] The above steps enable cross-scale coupling of molecular dynamics and computational fluid dynamics, and allow for the analysis of the escape of fission products. The numerical simulation scheme is validated through experiments involving heating a circular tube with a mixture of inert gases and the deposition of particles within a rectangular tube. Figure 3 The variation of the average temperature along the axis of the circular tube wall in the experiment was compared with the results of numerical simulation, and it was found that the trends of the two are in good agreement. Figure 4 The difference between the dimensionless deposition rate of particles in the rectangular tube and the numerical simulation results was compared, and the error could be kept within 30%, thus verifying the accuracy of the calculation in this invention.

Claims

1. A method for calculating particle adsorption on the cladding surface of a gas-cooled reactor coupled with first-principles calculations of molecular dynamics, characterized in that: Includes the following steps: Step 1: Use modeling and meshing software to establish the structural model of air gap-break-flow channel, and then import the mesh file into the computational fluid dynamics software FLUENT to complete the setting of the physical properties of the mixed inert gas working fluid, the particle discrete phase model, and the pressure, velocity, and temperature boundary conditions; Step 2: Use Material Studio to establish models of free molecules of solid fission products and molecular clusters of the substrate material. Use first-principles AIMD to calculate the potential energy of the free molecules and the substrate molecular clusters in their stable states. Treat the two as a whole after connecting them with electron pairs and calculate the potential energy after stabilization. Use the difference between the potential energy of the initial separated state and the combined state as the surface energy of the combination between the free molecules of solid fission products and the substrate material. Step 3: Modify the particle deposition model using the binding surface energy calculated in Step 2, and then implant FLUENT via UDF. The specific details are as follows: Step 3-1: The first part of the particle deposition model is to determine whether particles can be adsorbed when they enter the first mesh layer near the wall, which requires comparing particle velocities. u p Particle critical wall escape velocity u Cr The size of the particle determines whether it will bounce off the wall if the particle velocity is greater; otherwise, it will be adsorbed onto the wall. The critical wall escape velocity is fitted by particle properties, effective modulus, relaxation time, and surface energy. Step 3-2: The second part of the particle deposition model involves determining whether particles adsorbed by the wall can be re-entrained and re-enter the airflow. This requires comparing the shear velocity of the actual airflow at the wall. u τ Critical wall shear velocity u * The size of the particles determines whether they are completely deposited. If the actual shear velocity of the wall airflow is less than the critical wall shear velocity, the particles are considered to be completely deposited; otherwise, they are resuspended in the airflow. Step 3-3: The combined surface energy calculated using first principles is implanted into the first part of the particle deposition model. In addition to setting the temperature, after enabling DPM, a DPM boundary will appear on the wall boundary. The particle deposition model is implanted into this boundary to determine whether particles can be deposited on the wall. Step 4: First, initialize the particle deposition model, ensuring the initial particle deposition count is 0. Open the particle deposition count monitoring file and record the particle deposition count and location information. First, set the interface between the breach and the flow channel geometry as a solid wall, i.e., close the breach, and perform steady-state flow field calculations. Then, restore it to the internal surface, i.e., open the breach, and perform gas-solid two-phase flow calculations for inert gas-particle bidirectional coupled CFD-DPM. After the calculation is completed, export the particle deposition count. Calculate the particle deposition rate based on the initial particle quantity and operating conditions. Simultaneously, observe the final particle distribution and assess the escape of radioactive products.

2. The method for calculating particle adsorption on the cladding surface of a gas-cooled reactor based on first-principles calculations of coupled molecular dynamics, as described in claim 1, is characterized in that: Step 1 specifically includes the following steps: Step 1-1: Use Design Modeler to build the geometric model. Divide the air gap, opening, and flow channel into a combination of multiple hexahedrons according to their own shapes to meet the requirements of structured mesh drawing. Steps 1-2: Import the geometric model into Ansys Meshing. The mesh drawing algorithm uses Multizones, and the two ends of the geometric structure along the flow channel direction are used as the source and end faces of Multizones sweep. Set the mesh size for the two ends, first divide the gap mesh, then divide the air gap and flow channel mesh, thus completing the drawing of the hexahedral structured mesh, and import it into FLUENT. Steps 1-3: Calculate the density, specific heat capacity, thermal conductivity, and kinematic viscosity of the mixed inert gas working fluid in FLUENT using the gas state equation and property equation, and implant the user-defined function (UDF) provided by FLUENT software to describe the inert gas properties. Steps 1-4: Enable the Discrete Phase Model (DPM) for particles, set the two-way coupling between particles and the flow field, and the particle tracking time step; enable the mechanical models for gravity, drag, thermophoretic force, pressure gradient force, and additional mass force; enable the random walk model in the turbulence fluctuation effect module, and use message passing for parallel particle computation; create a new particle release nozzle, set the particle size, initial velocity, initial temperature, release time period, and particle flow rate to complete the preparation for particle tracking. Steps 1-5: Enable the Mixture two-phase model in FLUENT, set it to implicit, enable implicit volume forces, set the interface model to discrete, and set two components. The main component is a mixture of inert gases, whose properties have been set in Steps 1-3. The secondary component is a mixture of fission gases, whose properties are obtained by querying the Nist database and then weighting the average according to the content ratio of each fission gas. Set the flow channel inlet as the mass flow rate boundary and set the mass flow rate. The outlet is a pressure boundary, and the working pressure of the flow channel is set; all solid walls are temperature boundaries, and the wall temperature is set; the time step of the flow field is set to ensure that the particle time step is at most 1 / 10 of the flow field time step.

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