Boundary model of rarefied gas and multi-scale rough solid surface action and calculation method
By employing ray tracing principles and Monte Carlo sampling techniques, combined with boundary models of rarefied gases and multi-scale rough solid surfaces, the problem of existing models being unable to accurately account for the effects of roughness has been solved, achieving accurate calculation of gas molecule reflection velocities and improving flow simulation.
Patent Information
- Application Number
- CN202511475046.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-15
- Publication Date
- 2026-02-06
AI Technical Summary
In existing rarefied gas flow simulations, traditional models cannot accurately account for the influence of multi-scale rough solid surfaces on the gas-solid interface, resulting in insufficient reliability and accuracy of rarefied gas flow simulations.
Using ray tracing and Monte Carlo sampling techniques, combined with the micro-nano scale roughness of solid surfaces, the reflection velocity distribution of gas molecules on multi-scale rough solid surfaces is calculated. Through molecular dynamics simulation and scattering kernel functions, the collision probability and velocity changes of gas molecules are obtained, taking into account the true roughness morphology of the solid surface.
It enables accurate calculation of the reflection velocity of gas molecules on rough solid surfaces, is applicable to both isotropic and anisotropic surfaces, improves the accuracy and flexibility of rarefied gas flow simulation, and satisfies the reciprocity condition.
Smart Images
Figure CN121480353A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of rarefied gas dynamics, in particular to a boundary model and a calculation method for the interaction of rarefied gas with a multi-scale rough solid surface. BACKGROUND
[0002] Rarefied gas flow is widely used in modern industry, involving high altitude, high temperature, high speed, vacuum, microscale and many other fields, such as hypersonic flight of spacecraft in near space, physical / chemical vapor deposition process (LPPVD / LPCVD) in vacuum environment, and emerging micro-electro-mechanical systems (MEMS). With the decrease of system characteristic scale, or the increase of average free path between gas molecules, the discrete atomic nature of the gas medium gradually emerges, and the traditional description based on continuous medium (such as Navier-Stokes equation) and no-slip boundary condition will bring huge deviation. Especially in the transition flow region (0.1Kn<10) and free molecular flow region (Kn>10), the influence of the boundary will extend to the whole flow field, thus determining and controlling many special rarefied gas flow phenomena. Therefore, developing accurate boundary conditions is an indispensable part of accurately simulating rarefied gas flow.
[0003] The gas-solid interface interaction model is a boundary condition suitable for the simulation of rarefied gas flow in all flow regions. Currently, the widely used is the empirical phenomenological model, such as Maxwell and Cercignani-Lampis-Lord (CLL) model. These phenomenological models have many defects in accuracy and usability, which restricts the reliability of rarefied gas flow simulation. Recently, the physical modeling method is an effective means to develop more advanced gas-solid interface interaction models, such as the improved washboard model which reasonably considers three-dimensional scattering, adsorption / desorption and other physical mechanisms, thus more accurately reflecting the changes of gas molecule incident and reflection velocity distribution function on the boundary.
[0004] There are various scales of roughness on the solid surface, from the smallest atomic scale to the nanometer / micrometer scale. However, all current gas-solid interface interaction models cannot directly consider the influence of these roughness on the gas-solid interaction characteristics. The most perfect improved washboard model so far also only uses the assumption of flat attractive potential well, so it can only consider atomic scale roughness, and cannot reflect the influence of larger micro / nano scale roughness.
[0005] Therefore, it is necessary to provide a boundary model and a calculation method for the interaction of rarefied gas with a multi-scale rough solid surface to solve the above problems. SUMMARY
[0006] To provide more accurate boundary conditions for studying rarefied gas flow, this invention provides a boundary model and calculation method for the interaction between rarefied gas and multi-scale rough solid surfaces, in order to solve existing problems.
[0007] The boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface of the present invention adopts the following technical solution, wherein the solid surface includes roughness at the atomic scale and micro / nano scale, and further includes: Based on the micro-nano scale roughness of the solid surface, the distribution function of the local normal direction at each point on the solid surface is obtained; through molecular dynamics simulation, the reflection velocity distribution of gas molecules on the atomically rough solid surface is calculated, and the scattering kernel function of local collisions is determined based on the reflection velocity fitting. Based on the incident velocity of the gas molecules, obtain the velocity direction of the gas molecules; perform coordinate transformation on the incident velocity according to the local normal direction to obtain the transformed target incident velocity; use the target incident velocity as the velocity before the collision and obtain the velocity of the gas molecules after the collision according to the scattering kernel function; transform the velocity of the gas molecules after the collision to the target velocity in the global coordinate system. The system determines whether the gas molecules are moving in the opposite direction based on the target velocity. If they are not moving in the opposite direction, it obtains the forward collision probability between the gas molecules and the collision point based on the principles of ray tracing, the distribution function of the local normal direction, and the velocity direction of the gas molecules, and samples the next collision point for collision. If they are moving in the opposite direction, it obtains the direct reflection probability of the gas molecules leaving the solid surface. If the direct reflection probability is greater than the preset probability value, the gas molecules leave the solid surface. If the direct reflection probability is less than or equal to the preset probability value, it obtains the reverse collision probability between the gas molecules and the collision point based on the principles of ray tracing, the distribution function of the local normal direction, and the velocity direction of the gas molecules, and samples the next collision point for collision, until the gas molecules leave the solid surface, thus obtaining the reflection velocity of the gas molecules on the rough solid surface.
[0008] A further technical solution of the present invention utilizes non-contact optical scanning technology to scan the solid surface and obtain the micro-nano scale roughness of the solid surface.
[0009] A further technical solution of the present invention provides that the expression for the distribution function is:
[0010] In the formula, It is the distribution function; The polar angle of the local normal vector direction of the solid surface at the point of collision; It is the azimuth angle of the local normal vector direction of the solid surface at the point of collision.
[0011] In a further technical solution of the present invention, the scattering kernel function is one of specular reflection, diffuse reflection, Maxwell scattering kernel, and CLL scattering kernel function.
[0012] A further technical solution of the present invention provides the following expression for the incident velocity of gas molecules:
[0013] In the formula, denoted as the incident velocity of the gas molecules; This represents the x-axis component of the incident velocity of the gas molecules. This represents the y-axis component of the incident velocity of the gas molecules. Let be the component of the incident velocity of the gas molecules along the z-axis.
[0014] A further technical solution of the present invention provides the following expression for the velocity direction of gas molecules:
[0015]
[0016] In the formula, denoted as the incident velocity of the gas molecules; This represents the component of the incident velocity of the gas molecules along the x-axis in the global coordinate system. This represents the component of the incident velocity of the gas molecules along the y-axis in the global coordinate system. This represents the component of the incident velocity of the gas molecules along the z-axis in the global coordinate system. The polar angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; Let be the azimuth angle of the current velocity of the gas molecules in the global coordinate system of the solid surface. The global coordinate system is established by taking the plane of the macroscopic surface of the solid as the OXY plane of the global coordinate system and the outward normal of the plane of the macroscopic surface of the solid as the positive z-axis.
[0017] A further technical solution of the present invention provides an expression for the forward collision probability as follows:
[0018] In the formula, This represents the probability of a gas molecule colliding head-on with the collision point. This is the distribution function of the local normal direction at various points on the solid surface; The polar angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; This is the azimuth angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; The polar angle of the local normal vector direction of the solid surface at the point of collision; It is the azimuth angle of the local normal vector direction of the solid surface at the point of collision.
[0019] A further technical solution of the present invention provides an expression for the probability of a reverse collision:
[0020] In the formula, This represents the probability of a gas molecule colliding backwards with the collision point. This is the distribution function of the local normal direction at various points on the solid surface; The polar angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; This is the azimuth angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; The polar angle of the local normal vector direction of the solid surface at the point of collision; It is the azimuth angle of the local normal vector direction of the solid surface at the point of collision.
[0021] A further technical solution of the present invention provides an expression for the direct reflection probability as follows:
[0022] In the formula, This represents the probability of direct reflection of gas molecules. This is the distribution function of the local normal direction at various points on the solid surface; The polar angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; This is the azimuth angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; The polar angle of the local normal vector direction of the solid surface at the point of collision; It is the azimuth angle of the local normal vector direction of the solid surface at the point of collision.
[0023] A further technical solution of the present invention is that the preset probability threshold is a random number uniformly distributed between 0 and 1.
[0024] The beneficial effects of this invention are: This invention calculates the collision probability of gas molecules at different positions based on the roughness of the solid surface and the incident velocity of gas molecules, using the principle of ray tracing. Collision positions are then randomly selected based on this probability. At each local collision point, the gas molecule velocity is transformed according to the local normal direction of the surface, and the velocity of the gas molecules after the collision is calculated based on the local collision scattering kernel function. After each local collision, the subsequent collisions that may occur are tracked and calculated based on the new velocity of the gas molecules, ensuring the reversibility of the collision trajectory of gas molecules on the micro / nano-scale rough surface. Finally, the reflection velocity of the gas molecules leaving the rough solid surface is obtained. This boundary model employs physical modeling methods based on the fiber optic tracing principle and Monte Carlo sampling technology, considering the influence of atomic-scale and micro / nano-scale roughness of the solid surface on the gas-solid interface process, achieving accurate and efficient calculation of the gas molecule reflection velocity. Compared with existing technologies, this invention directly considers the real roughness of the solid surface, is applicable to isotropic and anisotropic surfaces, and can accommodate multiple scattering kernels in local collisions, strictly satisfying the reciprocity condition. It has better accuracy, usability, and flexibility than existing gas-solid interface interaction models. Attached Figure Description
[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0026] Figure 1 This is a schematic diagram of a boundary model for the interaction between a rarefied gas and a multi-scale rough solid surface according to the present invention. Figure 2 This is a flowchart illustrating the calculation method of a boundary model for the interaction between a rarefied gas and a multi-scale rough solid surface according to the present invention. Figure 3 The reflection velocity distribution function obtained in the molecular beam scattering experimental example demonstrated in this invention is... A projection of a plane; Figure 4 The reflection velocity distribution function obtained in the molecular beam scattering experimental example demonstrated in this invention is... A projection of a plane; Figure 5 The reflection velocity distribution function obtained in the molecular beam scattering experimental example demonstrated in this invention is... A projection of a plane. Detailed Implementation
[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0028] This invention provides an embodiment of a boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface. In this embodiment, the solid surface includes roughness at both the atomic and micro / nano scales. The interaction process between gas molecules and the solid surface is divided into two spatiotemporal scales: local collisions and global collisions. Based on the principle of ray tracing, the reversible collision trajectories of gas molecules on the globally micro / nano-scale rough surface are calculated. At each local collision, a suitable scattering kernel model is selected to describe the change in gas molecule velocity caused by the atomic-scale roughness. Therefore, as... Figure 1 and 2 As shown, it includes: S1. Obtain the distribution function of the local normal direction at each point on the solid surface and the scattering kernel function of local collisions; Specifically, based on the micro-nano scale roughness of the solid surface, the distribution function of the local normal direction at each point on the solid surface is obtained; through molecular dynamics simulation, the reflection velocity distribution of gas molecules on the atomically rough solid surface is calculated, and the scattering kernel function of local collisions is determined based on the reflection velocity fitting.
[0029] For example, in one specific embodiment, a non-contact optical scanning technique is used to scan the solid surface to obtain the micro-nano scale roughness of the solid surface. In this embodiment, a white light interferometer is used, but a laser confocal microscope, a phase-shifting interferometer, and a digital holographic microscope can also be used.
[0030] For example, in one specific embodiment, the expression for the distribution function is:
[0031] In the formula, It is the distribution function; The polar angle of the local normal vector direction of the solid surface at the point of collision; It is the azimuth angle of the local normal vector direction of the solid surface at the point of collision.
[0032] For example, in one specific embodiment, the scattering kernel function that satisfies the reciprocity condition is one of the following: specular reflection, diffuse reflection, Maxwell scattering kernel, and CLL scattering kernel function. Alternatively, an improved washboard model that satisfies the reciprocity condition can also be used. It should be noted that as the roughness at the atomic scale increases, the scattering behavior tends to be diffuse reflection, that is, the fitness coefficient approaches 1. The boundary model strictly satisfies the modeling constraints of the boundary conditions, including nonnegativity, normalization, and reciprocity.
[0033] Among them, specular reflection is:
[0034] In the formula, The velocity of the gas molecules before the local collision; The velocity of gas molecules after a local collision This represents the local outward normal vector of the solid surface at the point of collision. This represents the local normal component of the velocity after the collision; This is the delta function.
[0035] Diffuse reflection is:
[0036] In the formula, Boltzmann constant, Mass of gas molecules The temperature is the surface temperature of the solid.
[0037] The Maxwell scattering kernel function is:
[0038] In the formula, This represents the adaptation coefficient for local collisions.
[0039] The CLL scattering kernel function is:
[0040] In the formula, The tangential component of the velocity of gas molecules before the local collision is the decomposition of the local normal vector at the point of collision. The normal component of the velocity of gas molecules before the local collision is the decomposition of the local normal vector at the point of collision. It represents the tangential component of the velocity of gas molecules after a local collision, which is the decomposition of the local normal vector at the point of collision. It represents the normal component of the velocity of gas molecules after a local collision, which is the decomposition of the local normal vector at the point of collision. The energy adaptation coefficient for the tangential velocity component; The energy adaptation coefficient for the normal velocity component; , It is a zero-order Bessel function of the first kind.
[0041] S2. Obtain the velocity of gas molecules after collision and the target velocity converted to the global coordinate system; Specifically, the velocity direction of the gas molecules is obtained based on their incident velocity; the target incident velocity is obtained by performing coordinate transformation on the incident velocity based on the local normal direction; the target incident velocity is used as the velocity before the collision, and the velocity of the gas molecules after the collision is obtained based on the scattering kernel function; the velocity of the gas molecules after the collision is transformed into the target velocity in the global coordinate system.
[0042] For example, in one specific embodiment, the expression for the incident velocity of gas molecules is:
[0043] In the formula, denoted as the incident velocity of the gas molecules; This represents the x-axis component of the incident velocity of the gas molecules. This represents the y-axis component of the incident velocity of the gas molecules. Let be the component of the incident velocity of the gas molecules along the z-axis.
[0044] For example, in one specific embodiment, the expression for the velocity direction of gas molecules is:
[0045]
[0046] In the formula, denoted as the incident velocity of the gas molecules; This represents the component of the incident velocity of the gas molecules along the x-axis in the global coordinate system. This represents the component of the incident velocity of the gas molecules along the y-axis in the global coordinate system. This represents the component of the incident velocity of the gas molecules along the z-axis in the global coordinate system. The polar angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; Let be the azimuth angle of the current velocity of the gas molecules in the global coordinate system of the solid surface, where , for example Figure 1 As shown, the plane containing the macroscopic surface of the solid is used as the OXY plane of the global coordinate system, and the outward normal of the plane containing the macroscopic surface of the solid is taken as the positive z-axis direction to establish the global coordinate system. It should be noted that the polar angle of the direction... The angle between the velocity vector of gas molecules and the positive z-axis; azimuth angle. Let be the angle between the velocity vector of gas molecules in the OXY plane of the global coordinate system and the positive x-axis.
[0047] For example, the transformed target incident velocity is obtained by performing a coordinate transformation on the incident velocity according to the local normal direction, that is:
[0048] In the formula, The incident velocity; The target incident velocity (velocity before collision).
[0049] For example, in one specific embodiment, the target incident velocity is substituted into the scattering kernel function of the local collision. The Monte Carlo sampling method was used to sample and obtain the velocities of gas molecules after collisions. .
[0050] For example, in one specific embodiment, the velocity of gas molecules after collision is obtained. After that, The target velocity is obtained by transforming back to the global coordinate system. .
[0051]
[0052] S3. Obtain the reflection velocity of gas molecules on a rough solid surface; Specifically, the system determines whether the gas molecules are moving in the opposite direction based on the target velocity. If they are not moving in the opposite direction, the system obtains the forward collision probability between the gas molecules and the collision point based on the principles of ray tracing, the distribution function of the local normal direction, and the velocity direction of the gas molecules, and samples the next collision point for collision. If they are moving in the opposite direction, the system obtains the direct reflection probability of the gas molecules leaving the solid surface. If the direct reflection probability is greater than a preset probability value, the gas molecules leave the solid surface. If the direct reflection probability is less than or equal to the preset probability value, the system obtains the reverse collision probability between the gas molecules and the collision point based on the principles of ray tracing, the distribution function of the local normal direction, and the velocity direction of the gas molecules, and samples the next collision point for collision, until the gas molecules leave the solid surface, thus obtaining the reflection velocity of the gas molecules on the rough solid surface.
[0053] For example, in one specific embodiment, the z-axis component of the target velocity in global coordinates is used as an example. To determine whether gas molecules are reversed, if... If the gas molecules have not yet collided in the opposite direction, then subsequent collisions are inevitable. Continue calculating the probability of a forward collision. The Monte Carlo method is used to sample the next collision point and perform a collision.
[0054]
[0055] like If the gas molecules have already reversed direction, then based on the principle of ray tracing, the probability of direct reflection of the gas molecules leaving the solid surface is calculated. :
[0056] The probability threshold is a random number uniformly distributed between 0 and 1. If the random number is less than... If the gas molecules successfully leave the solid surface, then they are considered to have successfully escaped. Otherwise, the gas molecules need to undergo subsequent collisions, and the probability of a reverse collision needs to be calculated. The Monte Carlo method is used to sample the next collision point, and a collision is performed. The probability of a reverse collision is calculated. for:
[0057] This process is repeated until the gas molecules successfully leave the solid surface, ultimately obtaining the reflection speed of the gas molecules on the rough solid surface.
[0058] It should be noted that the boundary model is based on the actual micro-nano-scale roughness of the solid surface and uses the fiber optic tracking principle to track the reversible collision trajectories of gas molecules on the rough surface. It is applicable to both isotropic and anisotropic rough surfaces.
[0059] The present invention will be described below with reference to specific parameters: Using a single molecular beam scattering experiment as an example, the reflection velocity distribution of gas molecules on an isotropic, randomly distributed Gaussian rough surface is calculated. The direction angle distribution density of the local normal vector of the micro-nano scale roughness is assumed to be:
[0060] The scattering kernel function was selected as the CLL kernel function:
[0061] Among them, the tangential energy fitness coefficient The normal energy fitness coefficient is 0.2. It is 0.5. Solid surface temperature The K value is 300 K, the incident gas molecules are argon atoms, and the atomic mass is... It is 6.63e-26 kg. The incident velocity of a single molecular beam is... .
[0062] The Monte Carlo random sampling algorithm was used to calculate the reflection velocity of a sample of 10 million gas molecules, and the reflection velocity distribution function was statistically analyzed. , and The projection of the plane, the distribution function is shown by equipotential lines as follows: Figure 3 , Figure 4 and Figure 5 As shown. These results demonstrate the distribution of gas molecule reflection velocities under the demonstration example conditions, from which it can be seen that: The components are asymmetrically distributed, which is a typical phenomenon caused by the different collision probabilities at different locations (windward and leeward sides) on a rough surface, and is consistent with the phenomenon observed experimentally in the literature. The components are symmetrically distributed, which is a result of using an isotropic solid surface in the demonstration example; The components are displayed with and The components exhibit a certain degree of coupling correlation, which demonstrates the complex mechanism by which different velocity components influence and transform each other during the gas-solid interaction process.
[0063] 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 spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface, wherein the solid surface includes roughness at the atomic and micro / nano scales, characterized in that, Also includes: Based on the micro-nano scale roughness of the solid surface, the distribution function of the local normal direction at each point on the solid surface is obtained; through molecular dynamics simulation, the reflection velocity distribution of gas molecules on the atomically rough solid surface is calculated, and the scattering kernel function of local collisions is determined based on the reflection velocity fitting. Based on the incident velocity of the gas molecules, obtain the velocity direction of the gas molecules; perform coordinate transformation on the incident velocity according to the local normal direction to obtain the transformed target incident velocity; use the target incident velocity as the velocity before the collision and obtain the velocity of the gas molecules after the collision according to the scattering kernel function; transform the velocity of the gas molecules after the collision to the target velocity in the global coordinate system. The system determines whether the gas molecules are moving in the opposite direction based on the target velocity. If they are not moving in the opposite direction, it obtains the forward collision probability between the gas molecules and the collision point based on the principles of ray tracing, the distribution function of the local normal direction, and the velocity direction of the gas molecules, and samples the next collision point for collision. If they are moving in the opposite direction, it obtains the direct reflection probability of the gas molecules leaving the solid surface. If the direct reflection probability is greater than the preset probability value, the gas molecules leave the solid surface. If the direct reflection probability is less than or equal to the preset probability value, it obtains the reverse collision probability between the gas molecules and the collision point based on the principles of ray tracing, the distribution function of the local normal direction, and the velocity direction of the gas molecules, and samples the next collision point for collision, until the gas molecules leave the solid surface, thus obtaining the reflection velocity of the gas molecules on the rough solid surface.
2. The boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface according to claim 1, characterized in that, Non-contact optical scanning technology is used to scan solid surfaces and obtain the micro-nano scale roughness of solid surfaces.
3. The boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface as described in claim 1, characterized in that, The expression for the distribution function is: In the formula, It is the distribution function; The polar angle of the local normal vector direction of the solid surface at the point of collision; It is the azimuth angle of the local normal vector direction of the solid surface at the point of collision.
4. The boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface according to claim 1, characterized in that, The scattering kernel function is one of the following: specular reflection, diffuse reflection, Maxwell scattering kernel, and CLL scattering kernel function.
5. The boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface according to claim 1, characterized in that, The expression for the incident velocity of gas molecules is: In the formula, denoted as the incident velocity of the gas molecules; This represents the x-axis component of the incident velocity of the gas molecules. This represents the y-axis component of the incident velocity of the gas molecules. Let be the component of the incident velocity of the gas molecules along the z-axis.
6. The boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface according to claim 1, characterized in that, The expression for the direction of gas molecule velocity is: In the formula, denoted as the incident velocity of the gas molecules; This represents the component of the incident velocity of the gas molecules along the x-axis in the global coordinate system. This represents the component of the incident velocity of the gas molecules along the y-axis in the global coordinate system. This represents the component of the incident velocity of the gas molecules along the z-axis in the global coordinate system. The polar angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; Let be the azimuth angle of the current velocity of the gas molecules in the global coordinate system of the solid surface. The global coordinate system is established by taking the plane of the macroscopic surface of the solid as the OXY plane of the global coordinate system and the outward normal of the plane of the macroscopic surface of the solid as the positive z-axis.
7. The boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface according to claim 1, characterized in that, The expression for the probability of a forward collision is: In the formula, This represents the probability of a gas molecule colliding head-on with the collision point. This is the distribution function of the local normal direction at various points on the solid surface; The polar angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; This is the azimuth angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; The polar angle of the local normal vector direction of the solid surface at the point of collision; It is the azimuth angle of the local normal vector direction of the solid surface at the point of collision.
8. The boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface according to claim 1, characterized in that, The expression for the probability of a reverse collision is: In the formula, This represents the probability of a gas molecule colliding backwards with the collision point. This is the distribution function of the local normal direction at various points on the solid surface; The polar angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; This is the azimuth angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; The polar angle of the local normal vector direction of the solid surface at the point of collision; It is the azimuth angle of the local normal vector direction of the solid surface at the point of collision.
9. The boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface according to claim 1, characterized in that, The expression for the direct reflection probability is: In the formula, This represents the probability of direct reflection of gas molecules. This is the distribution function of the local normal direction at various points on the solid surface; The polar angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; This is the azimuth angle of the current velocity of the gas molecules in the global coordinate system of the solid surface; The polar angle of the local normal vector direction of the solid surface at the point of collision; It is the azimuth angle of the local normal vector direction of the solid surface at the point of collision.
10. The boundary model and calculation method for the interaction between a rarefied gas and a multi-scale rough solid surface according to claim 1, characterized in that, The preset probability threshold is a random number that is uniformly distributed between 0 and 1.