A spacecraft aerodynamic drag calculation method and system based on free molecule flow

Abstract

The application provides a spacecraft aerodynamic drag calculation method and system based on free molecular flow. The method constructs a three-dimensional geometric model of a spacecraft, defines a free molecular flow calculation domain, and simulates the dynamic behavior of particles by combining particle tracking technology to accurately calculate the aerodynamic drag of the spacecraft in the atmospheric environment. Compared with traditional aerodynamic calculation methods, the application can reflect the aerodynamic characteristics in the free molecular flow state with higher precision, especially in the rarefied atmospheric environment, and the details that may be ignored by traditional methods are more accurately simulated. The method can simulate multiple reflections of particles and spacecraft surfaces through full trajectory tracking and an accurate gas-surface interaction model, and then calculate more accurate aerodynamic forces, and finally extract the drag coefficient, which has high applicability and reliability.

Description

Technical Field

[0001] This application belongs to the field of spacecraft aerodynamic drag calculation technology, specifically relating to a spacecraft aerodynamic drag calculation method and system based on free molecular flow. Background Technology

[0002] During flight, spacecraft experience air resistance from the atmosphere, which directly impacts key factors such as performance, stability, and fuel consumption. Accurately predicting the aerodynamic characteristics of spacecraft is a crucial aspect of aerospace design. Traditional aerodynamic calculation methods, such as approximate calculations based on turbulence models and analytical models based on viscous flow, are typically suitable for relatively dense fluid environments. However, these methods face many limitations in high-altitude, thin atmospheres, or near-vacuum environments, especially under conditions of extremely low airflow density, where the effectiveness of fluid dynamic models is significantly reduced. With increasingly demanding spacecraft design requirements, particularly the rise of high-speed, ultra-high-altitude missions, traditional methods often struggle to obtain accurate results when dealing with aerodynamic drag in low-density, low-pressure environments.

[0003] In rarefied gas environments, collisions between molecules become sparse and irregular, and the calculation of aerodynamic drag typically needs to take into account the characteristics of free molecular flow. In free molecular flow, collisions between molecules and object surfaces are primarily elastic, and the motion of gas molecules depends more on their initial conditions, such as molecular density, velocity, and temperature. For spacecraft surfaces, the interactions between molecules and the surface further increase the computational complexity.

[0004] Traditional aerodynamic drag calculation methods often cannot accurately handle these influencing factors, resulting in large errors in the calculation results. This is especially true in actual spacecraft design, where high precision is required, and traditional calculation methods often fail to meet practical needs.

[0005] To overcome this challenge, an increasing number of researchers are applying molecular dynamics models to spacecraft aerodynamic analysis. Calculations of free molecular flows can not only accurately simulate the interaction between molecules and object surfaces in rarefied gas environments, but also perform detailed calculations of aerodynamic drag using particle tracking methods. However, current technologies still face limitations in terms of the accuracy, computational efficiency, and applicability of particle tracking. For example, in large-scale spacecraft aerodynamic drag calculations, the computational load of particle tracking is enormous. Improving computational efficiency while maintaining accuracy is a crucial direction for current technological development. Summary of the Invention

[0006] One objective of this application is to provide a method and system for calculating aerodynamic drag of spacecraft based on free molecular flow, which aims to overcome the problem that traditional aerodynamic calculation methods cannot accurately calculate aerodynamic drag in rarefied gas environments.

[0007] To achieve the above objectives, the first aspect of this application provides a method for calculating spacecraft aerodynamic drag based on free molecular flow, comprising the following steps: Construct a three-dimensional geometric model of the spacecraft and define the free molecular flow computational domain, set the gas-surface interaction model and spacecraft surface properties; Based on the constructed free molecular flow computational domain and the set spacecraft surface properties, the atmospheric environment inlet parameters are coupled to the boundary of the free molecular flow computational domain to generate the initial states of multiple simulated particles. Based on the initial state of the generated simulated particles, particle tracking initialization is performed; Based on the particle tracking initialization results, particle-wall collision full trajectory tracking is performed for each simulated particle, and the total momentum entering and leaving the boundary of the free molecular flow computational domain of all simulated particles is recorded during the tracking process. Based on the recorded difference between the total momentum upon entry and the total momentum upon exit, the aerodynamic forces acting on the spacecraft are calculated, and drag is extracted from them without dimensioning.

[0008] According to a specific embodiment of this application, the construction of a three-dimensional geometric model of the spacecraft and the definition of a free molecular flow computational domain include: Construct a three-dimensional model of the spacecraft and build a closed cubic free molecular flow computational domain centered on the spacecraft, and make the minimum distance between the boundary of the free molecular flow computational domain and the surface of the spacecraft 5-10 times the characteristic size of the spacecraft.

[0009] According to a specific embodiment of this application, the setting of the gas-surface interaction model and spacecraft surface properties includes: The computational domain of the free molecular flow is divided into a structured mesh; Material property parameters are assigned to each grid cell on the spacecraft surface, and either the Maxwell hybrid reflection model or the Cercignani-Lampis-Lord model is selected as the gas-surface interaction model to calculate the reflection velocity when particles collide with the spacecraft surface.

[0010] According to a specific embodiment of this application, the step of coupling atmospheric environment inlet parameters to the computational domain boundary to generate the initial state of simulated particles includes: Obtain multiple atmospheric environment inlet parameters to be calculated; the atmospheric environment inlet parameters include atmospheric number density. ,temperature Average molecular weight Macroscopic incoming flow velocity and the proportion of atmospheric components; Based on the obtained atmospheric environment inlet parameters, the initial states of multiple simulated particles are generated by random sampling according to the drift Maxwell distribution on the boundary of the free molecular flow computational domain. The drift Maxwell distribution is as follows: ; The initial velocity vector of each simulated particle is obtained by sampling based on the Box-Muller algorithm. Simultaneously, the initial position coordinates of each simulated particle are generated by randomly sampling at the boundary of the computational domain in a uniform distribution. .

[0011] According to a specific embodiment of this application, the particle tracking initialization includes: Calculate the weighting factor w for each simulated particle; The weighting factor w is calculated using the following formula: in To simulate the total number of particles, To calculate the domain boundary normal vector, This is the total area of ​​the domain boundary; Set the maximum number of reflections N for each simulated particle. max The N max For 50-100 times.

[0012] According to a specific embodiment of this application, the step of performing particle-wall full trajectory tracking for each simulated particle and recording the momentum of the particle entering and leaving the boundary of the computational domain includes: The initial position of the simulated particle from the boundary of the free molecular flow computational domain With initial velocity Upon entering the computational domain, record its entering momentum. , =m*w*v0; The simulated particles were made to move in uniform linear motion with an initial velocity v0, and collisions with the spacecraft surface were detected. The trajectory equation of the simulated particle is r(t) = r curr +v0⋅t (t≥0), where t is the motion time of the simulated particle.

[0013] According to a specific embodiment of this application, the detection of collisions with the spacecraft surface includes: Based on the trajectory equation, the intersection calculation between the ray and the spacecraft surface mesh is performed to obtain the first collision time tc, the collision point coordinates rc, and the molecular incident angle θ. Collision determination is based on the initial collision time tc: If no collision is detected, record its departure momentum. ,in The velocity vector at the point of escape; If a collision is detected, the velocity vector v of the simulated particle after reflection is calculated based on the material properties of the collision wall, the established gas-surface interaction model, and the incident angle θ. out Then perform multiple reflection loop tracing; The multiple reflection loop tracing includes: Update the current position and velocity of the simulated particle to the collision point rc and reflection velocity vout, and repeat the sub-steps of uniform linear motion and collision detection until the simulated particle collides with the spacecraft surface. max After the collision, it escapes from the boundary of the computational domain and its departure momentum is recorded.

[0014] According to the specific implementation of this application, after completing the particle-wall full trajectory tracking of all simulated particles, according to... Calculate the weighted sum of the entry momentum of all simulated particles per unit time to obtain the total entry momentum; and according to... The weighted sum of the momentum of all simulated particles leaving the ground per unit time is calculated to obtain the total momentum of departure.

[0015] According to a specific embodiment of this application, the step of calculating the aerodynamic force on the spacecraft based on the difference between the total momentum entering and leaving the computational domain boundary is as follows: The total aerodynamic force was calculated. ; The step of extracting drag from aerodynamic forces and making it dimensionless further includes: The total aerodynamic force Macroscopic velocity along atmospheric flow Directional decomposition yields resistance. ; according to Transform the dimensionless resistance into a resistance coefficient. ; in For the incoming flow pressure, This is the reference area for the spacecraft.

[0016] According to a specific embodiment of this application, this application also provides a spacecraft aerodynamic drag calculation system based on free molecular flow, used to perform the above-described method, including: Geometric modeling module: used to construct the three-dimensional geometric model of the spacecraft and the computational domain of free molecular flow; Environment Coupling Module: Used to acquire atmospheric environment inlet parameters and couple them to the boundary of the free molecular flow computational domain; Particle generation module: Used to generate the initial state of simulated particles at the boundary of the computational domain; Trajectory tracking module: used to perform full trajectory tracking of particle-wall collisions; Momentum statistics module: used to record the momentum of particles entering and leaving the boundary of the computational domain; Aerodynamic calculation module: used to calculate the drag experienced by the spacecraft based on the momentum difference.

[0017] Compared with the prior art, the above-described solutions of this application have at least the following beneficial effects: (1) This application achieves the simulation of the entire process of multiple collisions between gas molecules and the spacecraft surface by precisely coupling the three-dimensional geometric model of the spacecraft with the free molecular flow computational domain and combining it with a high-precision particle tracking method. This method can completely record the momentum changes of particles entering and leaving the computational domain, thereby accurately calculating the aerodynamic forces on the spacecraft and extracting the drag coefficient. Compared with traditional methods that ignore sparse collisions between molecules or approximate free molecular flow, this application significantly improves the accuracy of aerodynamic drag calculation under thin atmospheric conditions, and is especially suitable for high-altitude and low-density environments, making the prediction of spacecraft aerodynamic performance more reliable and providing a solid data foundation for design optimization. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings: Figure 1 This is a flowchart illustrating a spacecraft aerodynamic drag calculation method based on free molecular flow, as described in this application. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that an article or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such an article or device. Without further limitation, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the article or device that includes said element.

[0021] The following is in conjunction with the appendix Figure 1 Detailed description of optional embodiments of this application.

[0022] like Figure 1 As shown in the specific embodiments of this application, this application provides a method for calculating spacecraft aerodynamic drag based on free molecular flow, including the following steps: Construct a three-dimensional geometric model of the spacecraft and define the free molecular flow computational domain, set the gas-surface interaction model and spacecraft surface properties; Based on the constructed free molecular flow computational domain and the set spacecraft surface properties, the atmospheric environment inlet parameters are coupled to the boundary of the free molecular flow computational domain to generate the initial states of multiple simulated particles. Based on the initial state of the generated simulated particles, particle tracking initialization is performed; Based on the particle tracking initialization results, particle-wall collision full trajectory tracking is performed for each simulated particle, and the total momentum entering and leaving the boundary of the free molecular flow computational domain of all simulated particles is recorded during the tracking process. Based on the recorded difference between the total momentum entering and leaving the spacecraft, the aerodynamic forces acting on the spacecraft are calculated, and the drag is extracted from them.

[0023] As an optional implementation, firstly, a three-dimensional geometric model of the spacecraft is constructed based on the spacecraft's design drawings or three-dimensional model files.

[0024] As an optional embodiment, the model includes a full-size three-dimensional geometric model of all exposed structures such as the body, solar array, antenna, deep cavity, and slits, preserving all geometric details that affect molecular collisions and reflections, ensuring that the multiple reflection effects of complex structures can be accurately captured.

[0025] As an optional embodiment, a closed free molecular flow computational domain is defined, which is centered on the spacecraft and has a cubic structure. The minimum distance between the boundary of the computational domain and the surface of the spacecraft is 5-10 times the characteristic size of the spacecraft.

[0026] As an optional implementation, the characteristic dimensions of the spacecraft typically refer to the spacecraft's reference length, such as the overall fuselage length, maximum cross-sectional diameter, wingspan, or theoretical tip-to-base distance. The specific values ​​are determined based on the shape characteristics and calculation objectives, with the maximum width or main body diameter commonly used as a benchmark. This ensures that the computational domain boundary is outside the spacecraft's aerodynamic disturbance range, that the atmospheric molecules at the boundary are undisturbed incoming molecules, and that all reflected molecules after colliding with the spacecraft ultimately escape from the computational domain boundary without molecular stagnation, thus ensuring the accuracy and comprehensiveness of the simulation results.

[0027] As an optional embodiment, this step also requires setting a gas-surface interaction model.

[0028] As an optional implementation, by dividing the free molecular flow computational domain into a structured grid, the region where gas molecules interact with the spacecraft surface can be accurately described. At the same time, the grid is locally refined in areas with high incidence of multiple reflections, such as cavities and gaps, and the position and normal vector of each grid cell at the boundary of the computational domain are recorded, providing a basis for subsequent molecular momentum flux statistics.

[0029] As an alternative embodiment, each grid cell represents a portion of the spacecraft surface and is assigned corresponding material properties.

[0030] As an optional embodiment, the material properties include energy fitness coefficient α, normal momentum fitness coefficient σn, and tangential momentum fitness coefficient σt. The parameters support nonlinear changes with molecular incident angle θ and surface temperature Tw. The parameter change function is obtained by fitting experimental data or molecular dynamics simulation and stored as an interpolation table to adapt to various aerospace materials such as polyimide, OSR sheet, aluminum alloy, and aluminized film.

[0031] As an optional implementation, a suitable gas-surface interaction model is selected. Common models include the Maxwell mixed reflection model and the Cercignani-Lampis-Lord model. These models can accurately simulate the collision process between particles and the spacecraft surface, calculate the reflection velocity, and thus affect subsequent particle tracking and aerodynamic drag calculations.

[0032] As an optional implementation, after constructing the computational domain and setting the gas-surface interaction model, the next step is to obtain the environmental ingress parameters to be calculated, with each set of parameters corresponding to a different orbital environmental condition.

[0033] As an optional embodiment, the environmental inlet parameters include atmospheric number density n. ∞ Temperature T ∞ Average molecular mass m, macroscopic inflow velocity v ∞The atmospheric composition percentage; these parameters can be calculated using international reference atmospheric models (NRLMSISE-00, JB2008) based on orbital altitude, F10.7 solar radio flux, and geomagnetic index Ap. These parameters allow for the random generation of initial states for multiple simulated particles at the boundary of the free molecular flow computational domain.

[0034] As an optional embodiment, a drift Maxwell distribution is used to generate the initial velocity vector of the simulated particles, and the Box-Muller algorithm is used for velocity sampling. Based on the Box-Muller algorithm, the initial velocity vector v of each simulated particle is obtained, and at the same time, the initial position coordinates r0 of each simulated particle are generated by random sampling at the boundary of the computational domain in a uniform distribution.

[0035] As an optional embodiment, the drift Maxwell distribution is: .

[0036] As an optional implementation, the position coordinates of simulated particles are randomly sampled in a uniform distribution based on atmospheric inlet parameters to ensure that the particle distribution conforms to the characteristics of the actual atmospheric environment. This process provides initial conditions for subsequent particle tracking, ensuring the accuracy and representativeness of the simulation.

[0037] As an optional implementation, the core objective of particle tracking initialization is to calculate a weighting factor w for each simulated particle. This weighting factor w represents the contribution of each simulated particle, where each simulated particle represents w real atmospheric molecules. The weighting factor ensures that the simulated molecular flux is consistent with the molecular flux of the real atmosphere, and is specifically determined by the number of particles, the normal vector of the computational domain boundary, and the total area of ​​the computational domain boundary. By calculating the weighting factor for each simulated particle, the influence of different particles on aerodynamic drag can be weighted in subsequent aerodynamic calculations.

[0038] As an optional embodiment, the weighting factor w is calculated by the following formula: in To simulate the total number of particles, To calculate the domain boundary normal vector, This is the total area of ​​the domain boundary.

[0039] As an optional implementation, this step also requires setting the maximum number of reflections, Nmax, for each simulated particle. This value is typically set to 50 to 100 times to limit the number of reflections the particle makes within the computational domain, preventing excessive simulation time or computational load. Proper initialization provides sufficient basis for tracking the trajectory of each particle, thereby ensuring the accuracy of the simulation results.

[0040] As an optional implementation, once particle tracking initialization is complete, the next step is to perform particle-wall full trajectory tracking.

[0041] As an optional implementation, each simulated particle, upon entering the free molecular flow computational domain, will undergo uniform linear motion with an initial velocity. By detecting collisions between the particles and the spacecraft surface, it can be determined whether the particles interact with the spacecraft.

[0042] As an optional implementation, when a particle comes into contact with the spacecraft surface, its trajectory is first described by the trajectory equation r(t) = rcurr + v0⋅t, where t is the simulated particle motion time. By performing an intersection calculation between the ray and the spacecraft surface mesh, the time of the first collision between the particle and the spacecraft surface, the coordinates of the collision point, and the molecular incident angle can be accurately obtained.

[0043] As an optional embodiment, the intersection calculation of the ray and the spacecraft surface mesh is performed as follows: For the spacecraft surface mesh, the molecular trajectory equation and the plane equation of the mesh patch are combined to determine whether there is a geometric intersection between the trajectory ray direction and the mesh patch plane and calculate the coordinates of the intersection point. The centroid coordinate method or cross product method is used to determine whether the intersection point is located within the effective area of ​​the mesh patch. The intersection point closest to the current starting position of the simulated particle is selected as the actual collision point. The coordinates of the point are recorded and the incident angle of the molecule is calculated based on the normal vector of the mesh patch.

[0044] As an optional implementation, once a collision occurs, the velocity vector of the simulated particle is adjusted according to a gas-surface interaction model. Based on the incident angle θ and the material properties at the collision point, the velocity vector of the simulated particle after reflection is calculated, and multiple reflection cycles are performed. This process continuously updates the current position and velocity of the simulated particle until the particle escapes from the computational domain boundary after 50 to 100 reflections. After each reflection, the simulated particle continues to be simulated as moving at a uniform linear velocity until all reflections are completed and the particle leaves the computational domain.

[0045] As an optional implementation, during particle tracking, the entry and exit momentum are recorded each time a simulated particle enters or leaves the computational domain of the free molecular flow. The entry momentum is calculated by multiplying the particle's mass and velocity vector, while the exit momentum is calculated based on the particle's reflected velocity as it leaves the computational domain. These momentum records provide fundamental data for subsequent aerodynamic calculations.

[0046] As an optional implementation, after tracking all simulated particles, the weighted sum of the total ingress and outgress momentum is used to calculate the total aerodynamic force acting on the spacecraft. Based on this momentum data, the ingress and outgress momentum per unit time can be obtained, thereby calculating the difference in aerodynamic force and ultimately the aerodynamic drag acting on the spacecraft.

[0047] As an optional implementation, the total aerodynamic force is then decomposed according to the macroscopic velocity direction of the incoming atmospheric flow to extract the drag. To obtain a dimensionless drag coefficient, the drag needs to be further standardized with the incoming kinetic pressure and the spacecraft's reference area to obtain the final aerodynamic drag coefficient.

[0048] As an optional embodiment, the step of calculating the aerodynamic forces acting on the spacecraft based on the difference between the total momentum entering and leaving the computational domain boundary is as follows: The total aerodynamic force was calculated. ; As an optional embodiment, the step of extracting drag from aerodynamic forces further includes: The total aerodynamic force Macroscopic velocity along atmospheric flow Directional decomposition yields resistance. ; according to Transform the dimensionless resistance into a resistance coefficient. ; in For the incoming flow pressure, This is the reference area for the spacecraft.

[0049] As an optional embodiment, this application also provides a spacecraft aerodynamic drag calculation system based on free molecular flow, comprising: Geometric modeling module: used to construct the three-dimensional geometric model of the spacecraft and the computational domain of free molecular flow; Environment Coupling Module: Used to acquire atmospheric environment inlet parameters and couple them to the boundary of the free molecular flow computational domain; Particle generation module: Used to generate the initial state of simulated particles at the boundary of the computational domain; Trajectory tracking module: used to perform full trajectory tracking of particle-wall collisions; Momentum statistics module: used to record the momentum of particles entering and leaving the boundary of the computational domain; Aerodynamic calculation module: used to calculate the drag experienced by the spacecraft based on the momentum difference.

[0050] As an optional embodiment, the following is a specific calculation process of a spacecraft aerodynamic drag calculation method based on free molecular flow according to this application: In this embodiment, a spacecraft geometric model for aerodynamic calculations was first constructed. This geometric model fully considers the complexity of the spacecraft's shape, including the main body, solar panels, antennas, thruster nozzles, and other protruding structures that may affect the molecular flow field. High-precision computer-aided design software was used in constructing the geometric model to ensure that the dimensions, shapes, and relative positions of all spacecraft components are completely consistent with actual engineering data.

[0051] Subsequently, a free molecular flow computational domain was established around the geometric model. The size of the computational domain was determined based on the spacecraft dimensions and the expected aerodynamic environment to ensure that the particles at the boundary accurately represent the physical processes of free molecular inflow and outflow. The boundary of the computational domain was divided into an inflow ingress surface and an outflow reflective surface to correspond to incident particles flowing into the spacecraft surface and reflected particles leaving the computational domain, respectively. To ensure that the simulation results are consistent with actual high-altitude, rarefied atmospheric conditions, the boundary size of the computational domain is typically set to 5-10 times the maximum external dimensions of the spacecraft, and a mesh is generated to accurately capture collision information between particles and the spacecraft surface during trajectory tracking.

[0052] After determining the computational domain, simulated particles are generated based on preset atmospheric environment inlet parameters. These atmospheric environment inlet parameters include key physical quantities such as atmospheric number density, temperature, average molecular mass, and macroscopic inflow velocity. These parameters are obtained through international reference atmospheric models (such as the NRLMSISE-00 model) and are dynamically adjusted according to the spacecraft's orbital altitude, attitude, and flight speed.

[0053] The particle velocities were randomly sampled using a drifting Maxwell distribution to generate the initial velocity direction and magnitude for each simulated particle. Simultaneously, each particle was assigned a weighting factor representing the number of real atmospheric molecules corresponding to a single simulated particle, ensuring that the simulated molecular flux remained consistent with the real molecular flux. A high-performance random number generation algorithm was employed during particle generation to guarantee that the statistical characteristics of the initial particle state were consistent with the actual free molecular flow field. The velocity, energy, and momentum statistics of the generated particle swarm met the expected physical distribution requirements through a distribution function verification. Furthermore, the influence of the spacecraft's relative wind direction was considered in the particle generation stage to ensure the uniformity and correct orientation of the incoming particles on the incident surface, thus realistically reflecting the physical characteristics of the free molecular flow.

[0054] Subsequently, trajectory tracking was performed on all generated simulated particles. The trajectory tracking adopted a linear motion model, in which the particles moved along the direction of their initial velocity in the free molecular flow computational domain until they collided with the spacecraft surface.

[0055] When a particle comes into contact with the spacecraft surface, the reflection velocity is calculated based on a gas-surface interaction model. Gas-surface interaction models include the Maxwell mixed reflection model or the Cercignani-Lampis-Lord model, which can be selected based on different material properties.

[0056] In this process, the material properties of every point on the spacecraft surface are precisely mapped, including surface temperature, energy fitness coefficient, normal momentum fitness coefficient, and tangential momentum fitness coefficient. These coefficients are dynamically adjusted as the molecular incident angle and surface temperature change. Through this process, particles are reflected multiple times by the complex geometric surface until they reach N... max Subsequently, the free molecular flow escapes from the boundary of the computational domain, and its momentum and energy exchange processes can be accurately captured. Simultaneously, the trajectory tracking process employs a parallel computing architecture, distributing the motion task of millions of particles across multiple computational cores. High-performance computing clusters are used to achieve parallel processing of large-scale particle tracking, significantly improving computational efficiency. For each particle, its final momentum is recorded as it leaves the computational domain, forming a complete dataset of particle momentum changes, providing a foundation for subsequent aerodynamic calculations.

[0057] Based on particle trajectory tracking, momentum statistics of simulated particles are performed. In this process, the momentum information of each particle entering and leaving the computational domain is first recorded to ensure that the momentum change of each particle is recorded in detail. Since the aerodynamic force on the spacecraft is determined by the combined effect of the momentum changes of all particles, it is necessary to calculate the total momentum of the particles when entering and leaving the computational domain.

[0058] Therefore, the total momentum of all simulated particles entering the computational domain is first calculated. For each entering particle, its momentum is determined by the particle's mass and velocity, i.e. ,in For the mass of the particle, Let be the velocity of the particle. Based on the momentum data of all particles, calculate the total momentum of all particles entering the particle. .

[0059] Similarly, for a particle leaving the computational domain, its momentum is also determined by the particle's mass and its exit velocity, i.e. ,in The velocity of the particle as it leaves the ground. The total momentum of the particle as it leaves the ground. It can be obtained by summing the momentum of all the particles that leave the particle.

[0060] By statistically analyzing the momentum of all particles entering and exiting the spacecraft, the total aerodynamic force acting on the spacecraft can be determined. According to Newton's third law, aerodynamic force can be calculated by the difference between the total momentum entering and exiting per unit time: This process actually reflects the interaction between the spacecraft and the surrounding free molecular fluid. The molecular flow entering the spacecraft carries momentum, while the molecular flow leaving the spacecraft releases momentum; this momentum exchange process generates aerodynamic forces.

[0061] After calculating the aerodynamic force, its decomposition in the direction of the incoming atmospheric flow is further considered to obtain the aerodynamic drag. .

[0062] Aerodynamic drag is one of the most important physical quantities in the interaction between a spacecraft and atmospheric flow, determining key performance indicators such as orbital variation and thermal load. The formula for calculating aerodynamic drag is: in This is the angle between the direction of the aerodynamic force and the direction of the incoming flow relative to the spacecraft. In practical calculations, it is usually assumed that the aerodynamic force is parallel to the normal direction of the spacecraft surface; therefore, drag can be determined by the component of the aerodynamic force along the direction of the incoming flow.

[0063] Furthermore, the drag coefficient It is an important dimensionless quantity for evaluating the influence of aerodynamic forces, and it can be calculated using the following formula: in, It comes from the flow pressure. This is the spacecraft's reference area. This formula allows the calculated aerodynamic forces to be converted into dimensionless quantities related to the spacecraft's geometry and the atmospheric environment. (Drag coefficient) It is an important indicator of the aerodynamic performance of spacecraft, and is often used to evaluate the aerodynamic efficiency and flight stability of different design schemes.

[0064] This embodiment employs an efficient parallel computing architecture to handle trajectory tracking and momentum statistics of large-scale particles.

[0065] Specifically, the particle tracking process significantly improves computational efficiency by distributing tasks to multiple computing cores for parallel execution. Each computing core independently tracks particle trajectories and calculates related momentum changes, ultimately aggregating the results from all cores to the main computing unit. This not only effectively shortens computation time but also enables the handling of larger-scale particle swarms while ensuring the accuracy of the calculation results.

[0066] To improve simulation accuracy, the number of simulated particles is typically large, potentially reaching millions or even more. The initial velocity, mass, and trajectory parameters of each particle are carefully designed to ensure that the simulation results accurately reflect the molecular flow characteristics of the real environment. The simulated particles are randomly distributed along the boundary of the computational domain, following a drift Maxwell distribution, and their velocity and direction conform to the statistical characteristics of the atmospheric environment. In this way, the behavior of the simulated particles can realistically reflect the molecular flow in the aerodynamic environment.

[0067] Furthermore, considering that spacecraft may encounter different aerodynamic environments at different stages of flight, atmospheric environmental parameters can be dynamically adjusted based on the spacecraft's orbit, altitude, and attitude changes in practical applications. This is fully demonstrated in the practical application of this embodiment, ensuring the accuracy of aerodynamic analysis results through real-time updated meteorological data and spacecraft status information.

[0068] Through the above process, this embodiment achieves high-precision aerodynamic calculations for spacecraft based on free molecular flow, providing reliable theoretical support for spacecraft design and orbit prediction. By combining aerodynamic drag with other mechanical factors (such as spacecraft mass and gravity), spacecraft design can be further optimized, improving its flight stability and orbital accuracy.

[0069] Finally, it should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0070] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for calculating aerodynamic drag of spacecraft based on free molecular flow, characterized in that, Includes the following steps: Construct a three-dimensional geometric model of the spacecraft and define the free molecular flow computational domain, set the gas-surface interaction model and spacecraft surface properties; Based on the constructed free molecular flow computational domain and the set spacecraft surface properties, the atmospheric environment inlet parameters are coupled to the boundary of the free molecular flow computational domain to generate the initial states of multiple simulated particles. Based on the initial state of the generated simulated particles, particle tracking initialization is performed; Based on the particle tracking initialization results, particle-wall collision full trajectory tracking is performed for each simulated particle, and the total momentum entering and leaving the boundary of the free molecular flow computational domain of all simulated particles is recorded during the tracking process. Based on the recorded difference between the total momentum upon entry and the total momentum upon exit, the aerodynamic forces acting on the spacecraft are calculated, and drag is extracted from them without dimensioning.

2. The method according to claim 1, characterized in that, The construction of the three-dimensional geometric model of the spacecraft and the definition of the free molecular flow computational domain include: Construct a three-dimensional model of the spacecraft and build a closed cubic free molecular flow computational domain centered on the spacecraft, and make the minimum distance between the boundary of the free molecular flow computational domain and the surface of the spacecraft 5-10 times the characteristic size of the spacecraft.

3. The method according to claim 1, characterized in that, The defined gas-surface interaction model and spacecraft surface properties include: The computational domain of the free molecular flow is divided into a structured mesh; Material property parameters are assigned to each grid cell on the spacecraft surface, and either the Maxwell hybrid reflection model or the Cercignani-Lampis-Lord model is selected as the gas-surface interaction model to calculate the reflection velocity when particles collide with the spacecraft surface.

4. The method according to claim 1, characterized in that, The process of coupling atmospheric environment inlet parameters to the computational domain boundary to generate the initial state of simulated particles includes: Obtain multiple atmospheric environment inlet parameters to be calculated; the atmospheric environment inlet parameters include atmospheric number density. ,temperature Average molecular weight Macroscopic incoming flow velocity and the proportion of atmospheric components; Based on the obtained atmospheric environment inlet parameters, the initial states of multiple simulated particles are generated by random sampling according to the drift Maxwell distribution on the boundary of the free molecular flow computational domain. The drift Maxwell distribution is as follows: ; The initial velocity vector of each simulated particle is obtained by sampling based on the Box-Muller algorithm. Simultaneously, the initial position coordinates of each simulated particle are generated by randomly sampling at the boundary of the computational domain in a uniform distribution. .

5. The method according to claim 2, characterized in that, The particle tracking initialization includes: Calculate the weighting factor w for each simulated particle; The weighting factor w is calculated using the following formula: in To simulate the total number of particles, To calculate the domain boundary normal vector, This is the total area of ​​the domain boundary; Set the maximum number of reflections N for each simulated particle. max The N max For 50-100 times.

6. The method according to claim 1, characterized in that, The process of performing particle-wall full trajectory tracking for each simulated particle and recording the momentum of the particle entering and leaving the computational domain boundary includes: The initial position of the simulated particle from the boundary of the free molecular flow computational domain With initial velocity Upon entering the computational domain, record its entering momentum. , =m*w*v0; The simulated particles were made to move in uniform linear motion with an initial velocity v0, and collisions with the spacecraft surface were detected. The trajectory equation of the simulated particle is r(t) = r curr +v0⋅t (t≥0), where t is the motion time of the simulated particle.

7. The method according to claim 6, characterized in that, The method of detecting collisions with the spacecraft surface includes: Based on the trajectory equation, the intersection calculation between the ray and the spacecraft surface mesh is performed to obtain the first collision time tc, the collision point coordinates rc, and the molecular incident angle θ. Collision determination is based on the initial collision time tc: If no collision is detected, record its departure momentum. ,in The velocity vector at the point of escape; If a collision is detected, the velocity vector v of the simulated particle after reflection is calculated based on the material properties of the collision wall, the established gas-surface interaction model, and the incident angle θ. out Then perform multiple reflection loop tracing; The multiple reflection loop tracing includes: Update the current position and velocity of the simulated particle to the collision point rc and reflection velocity vout, and repeat the sub-steps of uniform linear motion and collision detection until the simulated particle collides with the spacecraft surface. max After the collision, it escapes from the boundary of the computational domain and its departure momentum is recorded.

8. The method according to claim 7, characterized in that, After completing the full trajectory tracing of particle-wall collisions for all simulated particles, according to Calculate the weighted sum of the entry momentum of all simulated particles per unit time to obtain the total entry momentum; and according to... The weighted sum of the momentum of all simulated particles leaving the ground per unit time is calculated to obtain the total momentum of departure.

9. The method according to claim 8, characterized in that, The steps for calculating the aerodynamic forces acting on the spacecraft based on the difference between the total momentum entering and leaving the computational domain boundary are as follows: The total aerodynamic force was calculated. ; The step of extracting drag from aerodynamic forces and making it dimensionless further includes: The total aerodynamic force Macroscopic velocity along atmospheric flow Directional decomposition yields resistance. ; according to Transform the dimensionless resistance into a resistance coefficient. ; in For the incoming flow pressure, This is the reference area for the spacecraft.

10. A spacecraft aerodynamic drag calculation system based on free molecular flow, used to execute the method according to any one of claims 1-9, characterized in that, include: Geometric modeling module: used to construct the three-dimensional geometric model of the spacecraft and the computational domain of free molecular flow; Environment Coupling Module: Used to acquire atmospheric environment inlet parameters and couple them to the boundary of the free molecular flow computational domain; Particle generation module: Used to generate the initial state of simulated particles at the boundary of the computational domain; Trajectory tracking module: used to perform full trajectory tracking of particle-wall collisions; Momentum statistics module: used to record the momentum of particles entering and leaving the boundary of the computational domain; Aerodynamic calculation module: used to calculate the drag experienced by the spacecraft based on the momentum difference.

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