Gas-solid interaction scattering kernel model modeling method based on corrected characteristic temperature

Abstract

The invention discloses a gas-solid interaction scattering nuclear model modeling method based on a corrected characteristic temperature, and the method comprises the steps: determining the average incident energy according to the macroscopic temperature and macroscopic speed of incident gas; calculating tangential and normal energy adaptation coefficients and a total energy adaptation coefficient according to given tangential and normal momentum adaptation coefficients; constructing a gas reflection temperature based on the average incident energy, the wall surface temperature and the total energy adaptation coefficient; calculating tangential correction characteristic temperature according to the reflection temperature and the tangential momentum adaptation coefficient; calculating a normal correction characteristic temperature according to the reflection temperature and the normal momentum adaptation coefficient; and respectively replacing the wall surface temperatures of the tangential and normal scattering nuclei of the original CLL model with the tangential and normal corrected characteristic temperatures to obtain a gas-solid interaction scattering nucleus model based on the corrected characteristic temperatures. According to the method, the characteristic temperature of the original CLL model is corrected according to the incoming flow parameters on the premise that the number of adjustable parameters is not increased, and the simulation precision of the gas scattering behavior is improved.

Description

Technical Field

[0001] This invention relates to the field of gas-solid surface boundary modeling technology for hypersonic vehicles, and more specifically, to a predictive modeling method for the scattering behavior of gas molecules on the surface of a vehicle under high-speed rarefied flow conditions. Background Technology

[0002] With the rapid development of flight technology, hypersonic vehicles are increasingly operating in large airspaces, often in high-temperature, high-speed, and low-density gas environments during flight. In these environments, the mean free path of gas molecules is comparable to the characteristic scale of the vehicle, resulting in significant discontinuities and non-equilibrium in the flow. The rarefied gas effect becomes a key factor influencing the aerodynamic and thermal characteristics of the vehicle.

[0003] Under the aforementioned conditions, traditional continuum mechanics methods, represented by the Navier-Stokes equations, are no longer applicable. Direct Simulation Monte Carlo (DSMC) based on molecular kinetic theory has become the primary method for simulating hypersonic rarefied flows. In DSMC, the gas-solid interaction between the gas and the spacecraft surface is crucial in determining the flow field structure and the accuracy of surface aerodynamic / thermal predictions. Its mathematical core is a scattering kernel model describing the scattering behavior of gas molecules on a solid surface. Literature indicates that, under the same computational conditions, the aerodynamic errors calculated using different scattering kernel models can reach over 14%, and the aerodynamic-thermal errors can reach over 46%.

[0004] Among numerous scattering kernel models, the Maxwell and Cercignani-Lampis-Lord (CLL) models are the most widely used, with most other models derived from them. The Maxwell model simplifies wall scattering as a linear superposition of diffuse and specular reflections based on the tangential momentum fitness coefficient, offering a simple form but failing to accurately describe the true scattering process. The CLL model introduces independent tangential momentum and normal energy fitness coefficients, enabling a more flexible description of molecular scattering behavior and reproducing the leaf-shaped reflection distribution results in high-speed molecular beam experiments. However, when there is a significant temperature difference between the gas and solid surface, or a large incident macroscopic velocity, the CLL model, with its limited adjustable parameters and fixed wall temperature as a characteristic temperature, cannot accurately reflect the adaptation of different energy modes on the solid surface, nor the non-equilibrium transport behavior of translational energy in different directions. This leads to a significant deviation between the CLL model's calculations and the underlying molecular dynamics simulations, hindering the improvement of boundary condition modeling accuracy in the DSMC method. To improve the modeling accuracy of scattering nuclei, most subsequent models have adopted the method of adding adjustable parameters to the model. However, such parameters often need to be determined by molecular dynamics simulations or experimental measurements, which makes them too complex to be widely applied. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a modeling method for gas-solid interaction scattering kernels based on modified characteristic temperature, thereby improving the modeling accuracy of gas-solid interaction scattering kernels with a small number of adjustable parameters.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] This invention provides a modeling method for a gas-solid interaction scattering kernel model based on a modified characteristic temperature. The specific steps are as follows:

[0008] Step 1: Based on the macroscopic temperature of the incident gas With macro speed Determine the average incident energy Ei of the gas.

[0009] Step 2: Based on the given tangential momentum adaptation coefficient σ t Normal momentum adaptation coefficient σ n Calculate the tangential energy fitness coefficient α t Normal energy fitness coefficient α n And the total energy fitness coefficient α.

[0010] Step 3: Based on the average incident energy E of the gas i Wall temperature (or characteristic temperature of the object surface) T w And the total energy adaptation coefficient α, the reflection temperature T of the constructed gasr .

[0011] Step 4: Based on the reflection temperature T r With the tangential momentum adaptation coefficient σ t Calculate the tangentially corrected characteristic temperature T t According to the reflection temperature T r With normal momentum adaptation coefficient σ n Calculate the normal correction characteristic temperature T n .

[0012] Step 5: Adjust the tangential correction characteristic temperature T t and normal correction characteristic temperature T n Replace the wall temperatures T of the tangential and normal scattering nuclei in the original CLL model respectively. w A gas-solid interaction scattering nucleus model based on the modified characteristic temperature was obtained.

[0013]

[0014]

[0015] in, and These represent the tangential incident velocity and the tangential reflected velocity of the gas molecules, respectively. and These represent the normal incident velocity and the normal reflected velocity of the gas molecules, respectively. This represents the tangential scattering nucleus, characterizing the gas molecules' scattering... When the tangential incident velocity is incident within the interval, The probability of tangential reflection velocity within the interval. The scattering nucleus is the normal scattering nucleus; m is the gas molecule mass, and k is the Boltzmann constant. It is a zeroth-order modified Bessel function of the first kind.

[0016] Preferably, the average incident energy in step one is... The calculation method is as follows:

[0017]

[0018] in, Let represent the macroscopic temperature of the incident gas, and s represent the macroscopic velocity of the incident gas. Compared to the most probable speed, The angle between the macroscopic velocity and the normal vector of the object's surface, and the expression for the complementary error function erfc, are:

[0019]

[0020] in, Let be the independent variable of the complementary error function erfc. It is the integral variable.

[0021] Preferably, the calculation method for the tangential, normal, and total energy fitness coefficients in step two is as follows:

[0022]

[0023]

[0024]

[0025] Preferably, the expression for the reflection temperature Tr in step three is:

[0026]

[0027] Preferably, based on the characteristics of the CLL scattering nuclear reflection distribution function, the tangentially corrected characteristic temperature T in step four is... t and normal correction characteristic temperature T n The expression is:

[0028]

[0029]

[0030] Based on the above steps, the scattering kernel model obtained by this invention only requires the tangential momentum adaptation coefficient σ. t and normal momentum adaptation coefficient σ n Two parameters are adjustable, and the remaining parameters can be calculated based on the known incoming flow conditions. Therefore, the number of adjustable parameters is the same as that of the original CLL model.

[0031] The beneficial effects of this invention are as follows:

[0032] Compared to other modified scattering kernel models, this invention can consider physical effects such as translational energy exchange and gas-solid temperature difference caused by high-temperature and high-speed gas incidence without increasing the number of adjustable parameters in the original CLL model. This improves the simulation accuracy of gas scattering behavior and can be further applied as boundary conditions in particle simulation methods such as DSMC to enhance the accuracy of aerodynamic and thermal prediction of hypersonic vehicles. Attached Figure Description

[0033] Figure 1 This is a flowchart of the present invention.

[0034] Figure 2The graph shows a comparison of the tangential and normal reflection velocity distribution functions calculated using the MCLL model, CLL model, and molecular dynamics (MD) method of this invention when nitrogen is scattered (reflected) on a smooth platinum metal surface at a wall temperature of 300K and under condition 1 in Table 1.

[0035] Figure 3 The graph shows a comparison of the tangential and normal reflection velocity distribution functions calculated using the MCLL model, CLL model, and MD method of this invention when nitrogen scatters on a smooth platinum metal surface under the condition of 300K wall temperature and working condition 2 in Table 1.

[0036] Figure 4 The graph shows a comparison of the tangential and normal reflection velocity distribution functions calculated using the MCLL model of this invention, the original CLL model, and the MD method when nitrogen scatters on a smooth platinum metal surface at a wall temperature of 300K and under condition 3 in Table 1.

[0037] Figure 5 The graph shows a comparison of the tangential and normal reflection velocity distribution functions calculated using the MCLL model, CLL model, and MD method of this invention when nitrogen scatters on a smooth platinum metal surface at a wall temperature of 300K and under condition 4 in Table 1. Detailed Implementation

[0038] The invention will now be further described with reference to the accompanying drawings.

[0039] like Figure 1 As shown, this invention provides a gas-solid interaction scattering kernel modeling method based on modified characteristic temperature. The method modifies the characteristic temperature of the original CLL model according to known incoming flow parameters, thereby correcting the original CLL model and improving the simulation accuracy of gas scattering behavior. Specifically, it includes the following steps:

[0040] Step 1: Based on the macroscopic flow parameters of the incident gas (macroscopic temperature of the incident gas) With macro speed Determine the average incident energy Ei of the gas:

[0041]

[0042] In the formula, Let represent the macroscopic temperature of the incident gas, and s represent the macroscopic velocity of the incident gas. (The vector sum of the tangential and normal incident velocities) and the most probable velocity The ratio, Let represent the angle between the macroscopic velocity and the normal vector of the object's surface (object surface normal vector), erfc be the complementary error function, and k be the Boltzmann constant. Let m be the molecular mass, then the most probable velocity... The calculation method is as follows:

[0043]

[0044] Step 2: Based on the given tangential momentum adaptation coefficient σ t Normal momentum adaptation coefficient σ n Calculate the tangential energy fitness coefficient α t Normal energy fitness coefficient α n And the overall energy fitness coefficient α:

[0045]

[0046]

[0047]

[0048] Step 3: Based on the average incident energy E of the gas i Wall temperature T w And the total energy fitness coefficient α, based on the definition of the total energy fitness coefficient, the expression for the reflection temperature Tr is constructed as follows:

[0049]

[0050] Step 4: Based on the characteristics of the CLL scattering kernel reflection distribution function, according to the reflection temperature T r With the tangential momentum adaptation coefficient σ t Calculate the tangentially corrected characteristic temperature T t According to the reflection temperature T r With normal momentum adaptation coefficient σ n Calculate the normal correction characteristic temperature T n Corrected characteristic temperature T t With T n The expression is:

[0051]

[0052]

[0053] Step 5: Adjust the tangential correction characteristic temperature T t and normal correction characteristic temperature T n Replace the wall temperatures T of the tangential and normal scattering nuclei in the original CLL model respectively. w The gas-solid interaction scattering kernel model based on the modified characteristic temperature is obtained as follows:

[0054]

[0055]

[0056] In the formula, and These represent the tangential incident velocity and the tangential reflected velocity of the gas molecules, respectively. and These represent the normal incident velocity and the normal reflected velocity of the gas molecules, respectively. This represents the tangential scattering nucleus, characterizing the gas molecules' scattering... When the tangential incident velocity is incident within the interval, The probability of tangential reflection velocity within the interval. It is a normal scattering nucleus; It is a zeroth-order modified Bessel function of the first kind.

[0057] In DSMC flow simulation, in order to update the molecular reflection velocity at the solid wall boundary, the corrected characteristic temperature can be calculated based on the macroscopic temperature and macroscopic velocity of the flow field grid where the boundary element is located. Then, the corrected characteristic temperature can replace the wall temperature of the original CLL model, thus realizing the application of the present invention.

[0058] The following example, using the scattering simulation of nitrogen (N2) on a smooth platinum (Pt) surface, further illustrates the specific implementation of the present invention and verifies its practical effectiveness. In this example, the wall temperature of the platinum is taken as 300K, and the remaining calculation conditions are shown in Table 1. The tangential momentum fitness coefficients and normal momentum fitness coefficients in Table 1 are obtained from classical molecular dynamics simulations.

[0059] Table 1

[0060] Operating condition number macroscopic temperature of incident gas Tangential incident velocity Normal incident velocity Tangential momentum fit coefficient Normal momentum adaptation coefficient 1 400K 300m / s 0 0.213 0.570 2 400K 300m / s 200m / s 0.197 0.531 3 2300K 0 0 0.099 0.307 4 1500K 500m / s 400m / s 0.095 0.343

[0061] Based on the parameters for each operating condition in Table 1, a large number of incident nitrogen molecules can be generated. For the scattering behavior of a single nitrogen molecule after colliding with the platinum surface, the improved CLL scattering model of this invention can be used to calculate the reflection velocity. The calculation process for the reflection velocity is based on existing technology, and the final tangential reflection velocity is obtained. With normal reflection velocity The formula is as follows:

[0062]

[0063]

[0064] Among them, the intermediate variable u t0 u t1 and u n0 u n1 The expression is as follows:

[0065]

[0066]

[0067] Among them, r1, r2, r3, and r4 are four random numbers generated from a uniform distribution of 0 to 1.

[0068] Based on the above process, the reflection velocities of a large number of incident nitrogen molecules after colliding with the wall under different operating conditions can be obtained. By statistically analyzing the reflection velocities of nitrogen molecules under each operating condition, the probability density function (PDF) of the reflection velocity of nitrogen molecules on the platinum surface can be obtained. The probability density functions of the reflection velocities obtained statistically in the tangential and normal directions of the platinum surface are the tangential reflection velocity distribution function PDF1 and the normal reflection velocity distribution function PDF2.

[0069] For the four calculation scenarios in Table 1, the calculation results of this invention (denoted as Modified CLL, MCLL), the calculation results of the original CLL model, and the simulation results of molecular dynamics (MD) are compared. The comparison results are as follows: Figures 2-5 As shown.

[0070] from Figures 2-5 It can be seen that the reflection velocity distribution calculated by the MCLL model obtained in this invention is largely consistent with the MD calculation results, significantly improving the excessively high peak values ​​of the tangential and normal reflection velocity distributions in the original CLL model. Furthermore, for the normal reflection velocity distribution, MCLL corrects the issue of the excessively small peak position of the distribution function in the original CLL model.

[0071] from Figure 2 It can be seen that, even without the presence of a normal incident velocity, the MCLL model can still correct the change in the normal reflection velocity distribution caused by the tangential incident velocity. This indicates that the MCLL model can describe the translational energy transport behavior between different directions, that is, the behavior of the tangential translational energy of the tangential incident velocity being transferred to the translational energy in the normal direction.

[0072] from Figure 4 It can be seen that even when only the gas-solid temperature difference exists and macroscopic velocity is absent, the MCLL model can still correct the difference between the original CLL model and the MD calculation results, indicating that the MCLL model can characterize the change in reflection velocity caused by the gas-solid temperature difference effect. Figure 5 It can be seen that the MCLL model can also handle situations where there is a large gas-solid temperature difference and macroscopic velocity at the same time.

[0073] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the protection scope of the present invention.

Claims

1. A modeling method for gas-solid interaction scattering kernels based on modified characteristic temperature, characterized in that: The specific steps are as follows: Step 1: Based on the macroscopic temperature of the incident gas With macro speed Determine the average incident energy Ei of the gas; Step 2: Based on the given tangential momentum adaptation coefficient σ t Normal momentum adaptation coefficient σ n Calculate the tangential energy fitness coefficient α t Normal energy fitness coefficient α n And the overall energy fitness coefficient α; Step 3: Based on the average incident energy E of the gas i Wall temperature T w And the total energy adaptation coefficient α, the reflection temperature T of the constructed gas r ; Step 4: Based on the reflection temperature T r With the tangential momentum adaptation coefficient σ t Calculate the tangentially corrected characteristic temperature T t According to the reflection temperature T r With normal momentum adaptation coefficient σ n Calculate the normal correction characteristic temperature T n ; Step 5: Adjust the tangential correction characteristic temperature T t and normal correction characteristic temperature T n Replace the wall temperatures T of the tangential and normal scattering nuclei in the original CLL model, respectively. w We obtain a gas-solid interaction scattering kernel model based on the modified characteristic temperature: in, and These represent the tangential incident velocity and the tangential reflected velocity of the gas molecules, respectively. and These represent the normal incident velocity and the normal reflected velocity of the gas molecules, respectively. Represents the tangential scattering nucleus, characterizing gas molecules in the direction of scattering. When the tangential incident velocity is incident within the interval, The probability of tangential reflection velocity within the interval. It is a normal scattering nucleus; m is the molecular mass of the gas, and k is the Boltzmann constant. It is a zeroth-order modified Bessel function of the first kind.

2. The modeling method for a gas-solid interaction scattering kernel model based on a modified characteristic temperature according to claim 1, characterized in that: The average incident energy in step one The calculation is as follows: in, Let represent the macroscopic temperature of the incident gas, and s represent the macroscopic velocity of the incident gas. Compared to the most probable speed, The angle between the macroscopic velocity and the normal vector of the object's surface, and the expression for the complementary error function erfc, are: in, Let be the independent variable of the complementary error function erfc. It is the integral variable.

3. The modeling method for a gas-solid interaction scattering kernel model based on a modified characteristic temperature according to claim 1, characterized in that: The tangential, normal, and total energy fitness coefficients in step two are calculated as follows: 。 4. The modeling method for a gas-solid interaction scattering kernel model based on a modified characteristic temperature according to claim 1, characterized in that: The expression for the reflection temperature Tr in step three is: 。 5. The modeling method for a gas-solid interaction scattering kernel model based on a modified characteristic temperature according to claim 1, characterized in that: In step four, the tangential correction characteristic temperature T t and normal correction characteristic temperature T n The expression is: 。

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