Method for predicting drag force of spherical particles in supersonic transition-rarefied flow

Abstract

The invention relates to the technical field of supersonic gas-particle two-phase flow analysis, in particular to a method for predicting drag force of spherical particles in supersonic transition-rarefied flow, which comprises the following steps: collecting a plurality of flow field parameters of the supersonic transition-rarefied flow, collecting size parameters of the spherical particles, and calculating a rarefied correction coefficient based on the flow field parameters and the size parameters; determining a dimensionless coefficient of the incoming flow density based on the rarefied correction coefficient; the particle temperature of the spherical particles is collected, and the dimensionless coefficient of the particle temperature is determined based on the particle temperature and the rarefaction correction coefficient; obtaining an incoming flow velocity, and determining a dimensionless coefficient of the incoming flow velocity based on the incoming flow velocity and the rarefied correction coefficient; according to the dimensionless coefficient of the incoming flow density, the dimensionless coefficient of the particle temperature and the dimensionless coefficient of the incoming flow velocity, a drag force predicted value of the spherical particles is obtained through calculation; according to the method, high-precision prediction of the supersonic particle drag force from the transition drainage basin to the free molecular drainage basin can be realized.

Description

Technical Field

[0001] This invention relates to the field of supersonic gas-particle two-phase flow analysis technology, specifically to a method for predicting the drag force of spherical particles in supersonic transition-rare flow. Background Technology

[0002] The rarefaction effect is a prevalent scientific problem in many engineering applications. The Knudsen number (Kn) is a key parameter characterizing the rarefaction of a flow field, defined as the ratio of the mean free path of molecules to the characteristic length of the flow field. When Kn approaches infinity, it is called free molecular flow; when Kn << 1, it is called continuous flow. When the Knudsen number is in the middle range, the flow field is mainly in the transition region and the rarefaction region of near-free molecular flow. The rarefaction effect also exists in supersonic gas-particle two-phase flow. For example, a large number of solid microparticles are generated during semiconductor processing. Since the characteristic scale of the flow field itself is submicron or even nanometer scale, comparable to the mean free path of molecules, the rarefaction effect of the gas-particle two-phase flow field is significant. High-speed aircraft ablate heat shield materials during high-altitude flight, or probes operating in dusty environments on the surface of the moon or Mars, both generate a large number of solid particles. Due to the low air density and large mean free path of molecules, this also leads to a strong rarefaction effect. Furthermore, solid rocket motors eject microparticles such as alumina, and local rarefaction effects also exist in the high Mach number expansion region of the jet. Only by accurately predicting the flow field and particle behavior in gas-particle two-phase flow can we accurately assess issues such as material surface erosion characteristics and engine thrust. Among these factors, particle drag is one of the main factors determining the accuracy of particle behavior prediction. Under the same transitional flow conditions, the particle velocity variation with flow distance obtained from different drag prediction methods can differ by up to 100%. Therefore, it is essential to establish an accurate particle drag prediction method.

[0003] Currently, there are three main categories of methods for predicting particle drag in transition-rabblende flows. The first category is based on the free molecular flow theory, which provides the force exerted by the flow field on the particles. This approach relies on the premise that the mean free path of molecules is much larger than the particle size, and the collision frequency between molecules is negligible compared to the collision frequency between molecules and particles. However, in practical engineering problems, the ideal free molecular flow conditions are difficult to satisfy, leading to significant errors in particle drag. The second category is based on particle drag models proposed under continuous flow conditions, which improve prediction accuracy under rarefied conditions by adding a "rabblende correction coefficient," such as the Cunningham-Millikan-Davies (CMD) model. Carlson and Henderson models also use this idea to correct for rarefied effects in continuous flow particle drag models. However, as the rarefaction increases, the flow field structure around particles differs significantly from that in continuous flow, with compressibility and viscous effects weakening. The rarefaction correction effect of this type of method is usually limited, leading to increased prediction errors. The third type of method couples the rarefied modified continuous flow drag force model with the theoretical solution of free molecular flow, using parameters such as Mach number and Reynolds number as criteria for applicability or as coupling weights between the two models, thereby improving prediction accuracy under near-free molecular flow conditions. However, this method directly couples the theoretical solution of free molecular flow with the continuous flow modified model, thus failing to accurately reflect the influence of rarefied effects in the transition region, resulting in poor prediction accuracy for particle drag force. Therefore, high-precision prediction methods for particle drag force in supersonic transition-rarely flow are still relatively lacking. Summary of the Invention

[0004] In view of the above problems, the present invention provides a method for predicting the drag force of spherical particles in supersonic transition-rare flow, which solves the technical problem that the prior art cannot achieve high-precision prediction of supersonic particle drag force from the transition flow domain to the free molecular flow domain.

[0005] This invention provides a method for predicting the drag force of spherical particles in supersonic transition-rarely flowing flow. Step S1: Collect multiple flow field parameters of supersonic transition-rarely flowing flow and collect the size parameters of spherical particles. Calculate the rarefaction correction coefficient based on the flow field parameters and size parameters.

[0006] Step S2: Determine the dimensionless coefficient of the incoming flow number density based on the rarefaction correction coefficient;

[0007] Step S3: Collect the particle temperature of the spherical particles, and determine the dimensionless coefficient of the particle temperature based on the particle temperature and the dilution correction coefficient.

[0008] Step S4: Obtain the incoming flow velocity, and determine the dimensionless coefficient of the incoming flow velocity based on the incoming flow velocity and the rarefaction correction coefficient;

[0009] Step S5: Calculate the predicted drag force of the spherical particles using the dimensionless coefficients of the incoming flow number density, particle temperature, and incoming flow velocity.

[0010] Preferably, step S1 specifically includes:

[0011] The dynamic viscosity coefficient, density, and pressure of the incoming gas molecules and the diameter of the spherical particles are collected for the supersonic transition-rare flow. The particle Knudsen number is calculated from the dynamic viscosity coefficient, density, and pressure of the incoming gas molecules and the diameter of the spherical particles. The rarefaction correction function is then calculated based on the particle Knudsen number to obtain the rarefaction correction coefficient.

[0012] Preferably, in step S1, the expressions for the particle Knudsen number and the rarefaction correction coefficient are:

[0013]

[0014] Where Kn is the Knudsen number based on particle diameter; d is the particle diameter; λ is the mean free path of the incoming gas molecules; μ is the dynamic viscosity coefficient of the incoming gas molecules; ρ is the density of the incoming gas molecules; p is the pressure of the incoming gas molecules; f Kn C1, C2, and C3 are the rarefaction correction coefficients, respectively. C1 = 2.31, C2 = 0.942, and C3 = 0.298. exp(·) represents the calculation of the natural index.

[0015] Preferably, step S2 specifically includes:

[0016] The dimensionless coefficient of the flux number density, calculated from the rarefaction correction factor, is expressed as:

[0017] F n (f Kn )=exp(-C n / f Kn )

[0018] Among them, F n C is the dimensionless coefficient of the incoming flow number density; n C is a constant coefficient among the dimensionless coefficients of the number density. n =0.66.

[0019] Preferably, step S3 specifically includes:

[0020] The particle temperature of spherical particles is collected, and the dimensionless coefficient of the particle temperature is calculated from the particle temperature and the dilution correction factor. The expression is as follows:

[0021]

[0022] in, T is a dimensionless coefficient representing the temperature of the particles.p T represents the particle temperature. pref For reference particle temperature, T is a constant coefficient in the dimensionless coefficient of particle temperature. pref =300K, C Tp =1.1.

[0023] Preferably, step S4 specifically includes:

[0024] Obtain the incoming flow velocity, and calculate the dimensionless coefficient of the incoming flow velocity from the incoming flow velocity and the rarefaction correction factor. The expression is:

[0025]

[0026] Among them, F u u is a dimensionless coefficient representing the incoming flow velocity. p The velocity u is the relative velocity between the particle velocity and the macroscopic velocity of the incoming gas molecules, which is the incoming velocity in the particle coordinate system. pref For reference flow velocity, C u C is a constant coefficient in the dimensionless coefficient of the incoming flow velocity. u =0.12.

[0027] Preferably, step S5 specifically includes:

[0028] The predicted drag force of the spherical particles is calculated from the dimensionless coefficients of the incoming flow number density, particle temperature, and incoming flow velocity.

[0029] The expression is:

[0030]

[0031] Among them, F D C is the predicted drag force of spherical particles. D C is the particle resistance coefficient; D The expression is:

[0032]

[0033] Where S is the molecular velocity ratio of the incoming gas, σ p T is the surface fitness coefficient of the particles. g Let S be the temperature of the incoming gas, and m1 and m2 be auxiliary functions related to the integral series; the expressions for S, m1, and m2 are:

[0034]

[0035] Where Ma is the particle Mach number, i.e., the incoming Mach number in the particle coordinate system, γ is the gas specific heat ratio, erf[s] and serf[s] are the error function and its differential form, respectively, s represents the independent variable of the error function, and t represents the integral variable of the error function.

[0036] Compared with the prior art, the present invention has at least the following beneficial effects:

[0037] (1) The method for predicting the drag force of spherical particles in supersonic transition-rare flow provided by this invention can accurately predict the drag coefficient of particles based on molecular kinetic parameters such as incoming flow number density, incoming flow temperature, particle temperature, and incoming flow velocity without relying on continuous flow model correction. It achieves a form consistent with the theoretical solution of free molecular flow, expands the applicable operating conditions range of the method, and improves the convenience of engineering calculation and design.

[0038] (2) This invention provides a method for obtaining dimensionless coefficients related to incoming flow number density, particle temperature, and incoming flow velocity, which effectively reflects the rarefaction effect in the transitional flow domain. Unlike existing traditional methods that only perform rarefaction corrections on continuous flows or simply couple free molecular flows and continuous flow models, this invention enables a more accurate description and capture of the physical essence in the transitional-rare flow region.

[0039] (3) Compared with existing prediction methods, the present invention can control the maximum prediction error within 5% under typical conditions, which significantly improves the accuracy of supersonic spherical particle drag prediction in transition-sparse watersheds. Attached Figure Description

[0040] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0041] Figure 1 The flowchart illustrates the method for predicting the drag force of spherical particles in a supersonic transition-rare flow provided by this invention.

[0042] Figure 2 This diagram illustrates the variation of particle flow velocity with flow distance, calculated using gas-particle two-phase flow, under the transition flow condition of Kn = 0.08 provided by the present invention.

[0043] Figure 3 This diagram illustrates a comparison of the drag coefficient of supersonic particles calculated using wind tunnel testing, DSMC numerical simulation, free molecular flow theoretical solutions, and existing methods under wind tunnel testing conditions conducted in Kane.

[0044] Figure 4This diagram illustrates a comparison of the drag coefficient of supersonic particles obtained by wind tunnel testing conducted at Wegener and under supplementary high rarefaction conditions, with calculations obtained by wind tunnel testing, DSMC numerical simulation, free molecular flow theory solutions, and existing methods. Detailed Implementation

[0045] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0046] In existing technologies, under the same transitional flow conditions, the particle velocity variation with flow distance obtained by different drag prediction methods can differ by up to 100%, for example... Figure 2 As shown. To address this problem, this invention proposes a method for predicting the drag force of spherical particles under supersonic conditions from the transition flow domain to the free molecular flow domain, and provides the applicable range of the Knudsen number. The drag force prediction method of this invention is based on molecular kinetic parameters, maintaining a form consistent with the theoretical solution of free molecular flow, thus allowing it to revert to the form of the theoretical solution of free molecular flow when the Knudsen number approaches infinity.

[0047] The Knudsen number of the particles in this invention is applicable in the range of Kn≥0.05. If the Knudsen number meets this requirement, the particle drag coefficient and drag force can be calculated using the method of this invention.

[0048] like Figure 1 As shown, a method for predicting the drag force of spherical particles in supersonic transition-rare flow is disclosed. The specific implementation steps are as follows:

[0049] Step S1: Collect multiple flow field parameters of the supersonic transition-rarely flow, collect the size parameters of the spherical particles, and calculate the rarefaction correction coefficient based on the flow field parameters and size parameters;

[0050] In this step, the present invention first obtains the dynamic viscosity coefficient, density, and pressure of the incoming molecules of the supersonic transition-rare flow; and obtains the diameter of the spherical particles.

[0051] In some embodiments, the dynamic viscosity coefficient μ of the incoming molecules in the supersonic transition-rare flow can be calculated using relevant parameters obtained from experimental observations, taking into account known gas types and temperature conditions. The density and pressure of the incoming flow can be obtained by consulting standard atmospheric model data based on specific flight altitudes or experimental conditions, or directly measured in wind tunnel experiments using equipment such as high-precision pressure sensors. Furthermore, the incoming flow density and pressure parameters can be obtained through numerical simulation methods such as computational fluid dynamics (CFD) and particle simulation (e.g., direct Monte Carlo simulation, DSMC) by setting boundary conditions and flow parameters.

[0052] In some embodiments, if the spherical particles are products with known particle specifications, the diameter of the spherical particles can be obtained directly using the nominal particle size data provided by the manufacturer; if the spherical particles are unknown particles, the diameter of the spherical particles can be measured by experimental techniques such as laser particle size analyzer and scanning electron microscope (SEM) imaging analysis.

[0053] This invention calculates the Knudsen number of particles based on the dynamic viscosity coefficient, density, and pressure of the incoming molecules, as well as the diameter of the spherical particles. The expression is as follows:

[0054]

[0055] Where Kn is the Knudsen number based on particle diameter; d is the particle diameter; λ is the mean free path of the incoming molecules; μ is the dynamic viscosity coefficient of the molecules; ρ is the density of the incoming gas molecules; and p is the pressure of the incoming gas molecules.

[0056] After obtaining the Knsen number of the particles, it can be determined whether Kn≥0.05 is satisfied. If the Knsen number satisfies this requirement, then the scope of application of this invention is determined to be satisfied.

[0057] The rarefaction correction function is calculated based on the particle Knudsen number, and the rarefaction correction coefficient is obtained. The expression is as follows:

[0058]

[0059] Among them, f Kn C1, C2, and C3 are the rarefaction correction coefficients, and C3 are the constant coefficients in the rarefaction correction function. exp(·) represents the calculation of the natural index.

[0060] In some embodiments, the values ​​of C1, C2, and C3 are C1 = 2.31, C2 = 0.942, and C3 = 0.298. Testing has shown that the rarefaction correction coefficients obtained from these parameters enable the method proposed in this invention to obtain relatively accurate particle drag prediction results.

[0061] Step S2: Determine the dimensionless coefficient of the incoming flow number density based on the rarefaction correction coefficient;

[0062] In this step, the dimensionless coefficient of the incoming flow number density is calculated from the rarefaction correction factor, and the expression is:

[0063] F n (f Kn )=exp(-C n / f Kn )

[0064] Among them, F n C is the dimensionless coefficient of the incoming flow number density; n These are constant coefficients in the dimensionless coefficients of the number density, and their values ​​can be determined by fitting and testing.

[0065] In some embodiments, C n The value is C n =0.66.

[0066] Step S3: Obtain the particle temperature of the spherical particles, and determine the dimensionless coefficient of the particle temperature based on the particle temperature and the dilution correction coefficient.

[0067] In this step, the particle temperature of the spherical particles is first obtained. For short-duration particle motion or particles with high specific heat capacity, the heat transfer time can be considered too short, resulting in a negligible change in particle temperature, which is the same as the temperature when the particle enters the flow field. Specifically, if the particle is in thermal equilibrium with the incoming gas when it enters the flow field, the particle temperature can be directly taken as the temperature of the incoming gas. If the particle temperature change is not negligible, for nanoscale or microparticles whose temperature is difficult to measure directly, the particle temperature can be estimated using theoretical calculations or numerical simulations, based on the system's heat transfer model and known ambient temperature, airflow parameters, and the energy exchange relationship between the particle and the environment. The appropriate method can be selected to obtain the particle temperature based on the actual operating conditions and the specific characteristics of the particles used.

[0068] In this step, the dimensionless coefficient of particle temperature is calculated from the particle temperature and the dilution correction factor, expressed as:

[0069]

[0070] in, T is a dimensionless coefficient representing the temperature of the particles. p T represents the particle temperature. pref For reference particle temperature, This is a constant coefficient in the dimensionless coefficient of particle temperature, with reference particle temperature T. pref and constant coefficients It is a set of corresponding values ​​determined by fitting and testing to ensure high prediction accuracy across all particle temperatures.

[0071] In some embodiments, T pref and The value is T pref =300K,

[0072] Step S4: Obtain the incoming flow velocity, and determine the dimensionless coefficient of the incoming flow velocity based on the incoming flow velocity and the rarefaction correction coefficient;

[0073] The incoming flow velocity can be obtained in several ways: directly by measuring it using wind tunnel or jet flow experiments with velocity measuring instruments; or indirectly by calculating it indirectly using fluid dynamics formulas based on parameters such as the mass flow rate, cross-sectional area, and known gas density of the incoming gas. Alternatively, the incoming flow velocity can be obtained by setting boundary conditions and flow parameters using computational fluid dynamics (CFD) or particle simulations (such as the DSMC method). The specific measurement or acquisition method can be selected based on experimental conditions, equipment accuracy, and the characteristics of the flow environment to ensure the accuracy and reliability of the obtained incoming flow velocity parameters.

[0074] The dimensionless coefficient for calculating the incoming flow velocity from the incoming flow velocity and the rarefaction correction factor is expressed as:

[0075]

[0076] Among them, F u u is a dimensionless coefficient representing the incoming flow velocity. p The velocity u is the relative velocity between the particle velocity and the macroscopic velocity of the incoming gas molecules, which is the incoming velocity in the particle coordinate system. pref For reference flow velocity, C u This is a constant coefficient in the dimensionless coefficient of the incoming flow velocity, with reference to the incoming flow velocity u. pref And constant coefficient C u It is a set of corresponding values ​​determined by fitting and testing to ensure high prediction accuracy under all incoming flow velocities.

[0077] In some embodiments, u pref and C u The value of is u pref =1000m / s, C u =0.12.

[0078] Step S5: Calculate the predicted drag force of the spherical particles using the dimensionless coefficients of the incoming flow number density, particle temperature, and incoming flow velocity.

[0079] In this step, the predicted drag force of the spherical particle is calculated using the three dimensionless coefficients mentioned above, and the expression is as follows:

[0080]

[0081] Among them, F D C is the predicted drag force of spherical particles. D C is the particle drag coefficient. D The expression is:

[0082]

[0083] Where S is the molecular velocity ratio of the incoming gas; σ p The surface fitness coefficient of the particles can be determined experimentally; T g The temperature of the incoming gas is obtained similarly to that of the incoming density and pressure, and can be derived from atmospheric parameters at the flight altitude, experimental conditions, or numerical simulations. m1 and m2 are auxiliary functions related to the integral series. The expressions for S, m1, and m2 are:

[0084]

[0085]

[0086] Where Ma is the particle Mach number, i.e. the incoming Mach number in the particle coordinate system, γ is the gas specific heat ratio, erf[s] and serf[s] are the error function and the differential form of the error function, respectively, s represents the independent variable of the error function, and t represents the integral variable of the error function.

[0087] This invention can significantly improve the prediction accuracy of drag force of supersonic spherical particles in transition-dilute watersheds. Under typical conditions, the maximum prediction error is less than 5%, which is significantly better than existing prediction methods.

[0088] To illustrate the effectiveness of the method proposed in this invention, the above technical solution of this invention will be described in detail below through specific embodiments.

[0089] Example 1

[0090] like Figure 3 The diagram shows the particle drag coefficient curves under the following conditions: both the inflow temperature and particle temperature are 400K; particle Mach numbers are 2.45, 2.05, 2.08, 2.40, and 2.24; and Reynolds numbers are 41.01, 38.15, 39.06, 47.07, and 59.10. The corresponding particle Knudsen numbers are 0.089, 0.080, 0.079, 0.076, and 0.056, all of which are within the scope of this invention. The wind tunnel test results under the above conditions are given by Kane in his 1951 article, "Sphere Drag Data at Supersonic Speeds and Low Reynolds Numbers".

[0091] The particle drag coefficient predicted by this invention was compared with the corresponding wind tunnel test results, DSMC numerical simulation results, free molecular flow theoretical solutions, the model proposed by Loth in his 2008 paper "Compressibility and Rarefaction Effects on Dragofa Spherical Particle", the model proposed by Henderson in his 1976 paper "Drag Coefficients of Spheres in Continuum and Rarefied Flows", and the model proposed by Carlson in his 1976 paper "Particle Drag and Heat Transfer in Rocket Nozzles". It can be seen that within the applicable range of transition-rarely flowing systems of this invention, the predicted results are basically consistent with the experimental results and DSMC numerical simulation results, with a maximum error of 5%. Among other models, the Loth model and the Henderson model, which have higher prediction accuracy, have maximum errors of 21.00% and 13.22%, respectively.

[0092] Example 2

[0093] like Figure 4 The figure shows the particle drag coefficient curves under the following conditions: 1) Inflow and particle temperatures are the same (292.45 K, 292.75 K, 292.95 K, 292.55 K), particle Mach numbers are 4.01, 4.10, 4.17, 3.87, and Reynolds numbers are 66.33, 79.34, 97.37, 105.00, and the corresponding particle Knudsen numbers are 0.090, 0.077, 0.068, and 0.055, all within the applicability range of the model of this invention. The wind tunnel test results under the above conditions are given by Wegener et al. in their 1951 article, "Wind Tunnel Measurements of Sphere Drag at Supersonic Speeds and Low Reynolds Numbers". In addition, eight equally distributed conditions with a high degree of rarefaction were added, with both the inflow temperature and particle temperature at 300K, a particle Mach number of 4, and Reynolds numbers ranging from 0.73 to 54.85, corresponding to particle Knudsen numbers of 8.17 to 0.11.

[0094] The particle drag coefficient predicted by this invention was compared with the corresponding wind tunnel test results, DSMC numerical simulation results, free molecular flow theoretical solutions, and predictions from the Loth model, Henderson model, and Carlson model. It can be seen that within the applicable range of transition-rarely flowing systems of this invention, the predicted results are basically consistent with the experimental results and DSMC numerical simulation results, with a maximum error of 3.78%. Among the other models, the Loth model and Henderson model, which have higher prediction accuracy, have maximum errors of 18.94% and 11.36%, respectively.

[0095] While the specific embodiments of the present invention depict actions or steps in a particular order, this should be understood as requiring such actions or steps to be performed in the specific order shown or in sequential order, or requiring all illustrated actions or steps to be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations.

[0096] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the drag force of spherical particles in a supersonic transition-rare flow, characterized in that, Includes the following steps: Step S1: Collect multiple flow field parameters of the supersonic transition-rarely flow, collect the size parameters of the spherical particles, and calculate the rarefaction correction coefficient based on the flow field parameters and size parameters; Step S2: Determine the dimensionless coefficient of the incoming flow number density based on the rarefaction correction coefficient; Step S3: Collect the particle temperature of the spherical particles, and determine the dimensionless coefficient of the particle temperature based on the particle temperature and the dilution correction coefficient. Step S4: Obtain the incoming flow velocity, and determine the dimensionless coefficient of the incoming flow velocity based on the incoming flow velocity and the rarefaction correction coefficient; Step S5: Calculate the predicted drag force of the spherical particles using the dimensionless coefficients of the incoming flow number density, particle temperature, and incoming flow velocity.

2. The method for predicting the drag force of spherical particles in supersonic transition-rare flow according to claim 1, characterized in that, Step S1 specifically includes: The dynamic viscosity coefficient, density, and pressure of the incoming gas molecules and the diameter of the spherical particles are collected for the supersonic transition-rare flow. The particle Knudsen number is calculated from the dynamic viscosity coefficient, density, and pressure of the incoming gas molecules and the diameter of the spherical particles. The rarefaction correction function is then calculated based on the particle Knudsen number to obtain the rarefaction correction coefficient.

3. The method for predicting the drag force of spherical particles in supersonic transition-rare flow according to claim 2, characterized in that, In step S1, the expressions for the particle Knudsen number and the rarefaction correction coefficient are: Where Kn is the Knudsen number based on particle diameter; d is the particle diameter; λ is the mean free path of the incoming gas molecules; μ is the dynamic viscosity coefficient of the incoming gas molecules; ρ is the density of the incoming gas molecules; p is the pressure of the incoming gas molecules; f Kn C1, C2, and C3 are the rarefaction correction coefficients, respectively. C1 = 2.31, C2 = 0.942, and C3 = 0.

298. exp(·) represents the calculation of the natural index.

4. The method for predicting the drag force of spherical particles in supersonic transition-rare flow according to claim 3, characterized in that, Step S2 specifically includes: The dimensionless coefficient of the flux number density, calculated from the rarefaction correction factor, is expressed as: F n (f Kn )=exp(-C n / f Kn ) Among them, F n C is the dimensionless coefficient of the incoming flow number density; n C is a constant coefficient among the dimensionless coefficients of the number density. n =0.

66.

5. The method for predicting the drag force of spherical particles in supersonic transition-rare flow according to claim 4, characterized in that, Step S3 specifically includes: The particle temperature of spherical particles is collected, and the dimensionless coefficient of the particle temperature is calculated from the particle temperature and the dilution correction factor. The expression is as follows: Among them, F Tp T is a dimensionless coefficient representing the temperature of the particles. p T represents the particle temperature. pref For reference particle temperature, C Tp T is a constant coefficient in the dimensionless coefficient of particle temperature. pref =300K, C Tp =1.

1.

6. The method for predicting the drag force of spherical particles in supersonic transition-rare flow according to claim 5, characterized in that, Step S4 specifically includes: Obtain the incoming flow velocity, and calculate the dimensionless coefficient of the incoming flow velocity from the incoming flow velocity and the rarefaction correction factor. The expression is: Among them, F u u is a dimensionless coefficient representing the incoming flow velocity. p The velocity u is the relative velocity between the particle velocity and the macroscopic velocity of the incoming gas molecules, which is the incoming velocity in the particle coordinate system. pref For reference flow velocity, C u C is a constant coefficient in the dimensionless coefficient of the incoming flow velocity. u =0.

12.

7. The method for predicting the drag force of spherical particles in supersonic transition-rarely flowing water according to claim 6, characterized in that, Step S5 specifically includes: The predicted drag force of the spherical particles is calculated from the dimensionless coefficients of the incoming flow number density, particle temperature, and incoming flow velocity. The expression is: Among them, F D C is the predicted drag force of spherical particles. D C is the particle resistance coefficient; D The expression is: Where S is the molecular velocity ratio of the incoming gas, σ p T is the surface fitness coefficient of the particles. g Let S be the temperature of the incoming gas, and m1 and m2 be auxiliary functions related to the integral series; the expressions for S, m1, and m2 are: Where Ma is the particle Mach number, i.e. the incoming Mach number in the particle coordinate system, γ is the gas specific heat ratio, erf[s] and serf[s] are the error function and the differential form of the error function, respectively, s represents the independent variable of the error function, and t represents the integral variable of the error function.

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