A neural network-based method for predicting heat flux on cylindrical wall in hypersonic rarefied flow

Abstract

A neural network-based method for predicting heat flux on the wall of a cylinder under hypersonic rarefied flow. In the offline phase, a parameter setting standard is obtained through a Direct Simulation Monte Carlo algorithm verified for heat flux independence. The neural network is then trained using normalized DSMC simulation samples based on this standard. In the online phase, for the problem of flow around a cylinder under hypersonic argon flow, the multi-point heat flux coefficient of the cylinder wall is obtained based on the existing connections within the neural network and the corresponding training parameters for a wide range of known values ​​of the incoming flow Knudsen number, temperature ratio, and Mach number. This method enables rapid and accurate prediction of the heat flux coefficient of the cylinder wall under hypersonic argon flow under a wide range of rarefied flow conditions. Twenty-one test results demonstrate that the stagnation point heat flux error is within 1.5%, and the maximum wall heat flux error does not exceed 4.8%. The calculation speed is close to that of the theoretical formula.

Description

Technical Field

[0001] The present invention relates to a technology in the field of hypersonic aircraft, specifically a method for predicting the heat flux on a cylindrical wall under hypersonic rarefied flow based on a neural network. Background Art

[0002] Thermal protection systems are used to protect hypersonic vehicles from the harsh effects of aerodynamic heating during high-speed flight. Accurately predicting wall heat flux is key to their design. Currently, there are three main approaches for predicting heat flux at hypersonic speeds: theory, experiment, and numerical simulation. Theoretical formulas are often used for rapid engineering estimates, but they are not very accurate and are primarily used for calculations in continuous flow regimes. Experiments are limited by demanding flight conditions. And numerical simulations, due to computational resource constraints, cannot quickly estimate heat flux under specific operating conditions. Furthermore, all three approaches are limited by the demarcation of boundaries between different flow domains. Therefore, there is an urgent need for a method that can quickly and accurately predict wall heat flux in rarefied flows. Summary of the Invention

[0003] In response to the above-mentioned deficiencies in the prior art, the present invention proposes a neural network-based method for predicting the heat flux on the wall of a cylinder under hypersonic rarefied flow, which can quickly and accurately predict the heat flux coefficient of the cylinder wall under hypersonic argon flow under a wide range of rarefied flow conditions. The 21 results of the test set show that the error of the stagnation heat flux is within 1.5%, the maximum error of the wall heat flux does not exceed 4.8%, and the calculation speed is close to that of the theoretical formula.

[0004] The present invention is achieved through the following technical solutions:

[0005] The present invention relates to a neural network-based method for predicting heat flux on a cylindrical wall under hypersonic rarefied flow. In an offline phase, a parameter setting standard is obtained through a Direct Simulation Monte Carlo (DSMC) algorithm after heat flux independence verification. Then, a neural network is trained using normalized DSMC simulation samples under this standard. In an online phase, for a problem of flow around a cylinder under a hypersonic argon flow, multi-point heat flux coefficient values ​​on the cylindrical wall are obtained based on existing connection relationships in the neural network and corresponding training parameters for a known wide range of incoming flow Knudsen number, temperature ratio, and Mach number values.

[0006] The rarefied flow refers to a flow with an incoming Knudsen number greater than 0.01.

[0007] The DSMC method is a direct simulation Monte Carlo method of a hard sphere model with a variable diameter, an NTC collision scheme, and a load balancing parallel scheme based on the number of particles in the grid. The specific steps include:

[0008] 1) Flow field initialization, that is, scattering simulated particles in the flow field according to the incoming flow conditions.

[0009] 2) Particle movement, that is, the particles are moved at a uniform speed within a certain time step according to their velocities in three directions, and reflection is considered if they come into contact with the boundary.

[0010] 3) Particle index, which determines the grid number where each particle is located.

[0011] 4) Collision and chemical reaction: determine the collision pairs of each grid and the corresponding chemical reaction process, and redistribute the energy and velocity of the particles.

[0012] 5) Sampling: statistics on the type, total number, speed and energy of particles in each grid.

[0013] 6) Output: calculate macro information such as temperature, pressure, and velocity based on the particle statistics in each grid.

[0014] The heat flux independence verification means that the wall heat flux results obtained by DSMC calculation are closely related to the setting of calculation parameters, and the parameter setting standards need to be determined. First, the grid is set to 0.2 times the local molecular free path, the time step is 0.1 times the local molecular collision time, the wall grid is 180, the sub-grid is 2*2, the initial grid particle number is 200, and the sampling times are 100,000 times to obtain accurate values ​​for subsequent reference. Then, the independence verification is performed on the grid and time step respectively, and the parameter setting standards are obtained as follows: the grid is 1 times the local molecular free path, the time step is 0.33 times the local molecular collision time, and the heat flux error can be controlled within 0.1%, ensuring the accuracy of the subsequently established samples.

[0015] The normalization is to map the input parameters to [0, 1] using the maximum and minimum values ​​of their respective ranges, wherein the Knudsen number is first logarithmized and then mapped to [0, 1].

[0016] The problem of flow around a cylinder under hypersonic argon flow refers to the problem related to the flow field of a two-dimensional cylinder under the conditions where the incoming gas is argon and the speed is greater than Mach 5.

[0017] The wide range mentioned above refers to the following: Knudsen number Kn ∞ Range [0.0072,14.47], temperature ratio T w / T s Range [0.012, 0.2], Mach number Ma range [5, 20], where: T w is the cylinder wall temperature, T s is the stagnation temperature calculated based on the incoming flow temperature, Mach number and specific heat ratio theory.

[0018] The neural network includes: an input unit, a first hidden layer unit, a second hidden layer unit and an output unit, wherein: the input unit performs dimensionless processing based on information on the minimum number of variables required to determine the wall heat flux, and obtains the result of predicting the heat flux under hypersonic rarefied flow using three dimensionless parameters; the first hidden layer unit and the second hidden layer unit iteratively adjust the number of neurons based on error information obtained from neural network training, and obtain the final result of selecting the number of hidden layer neurons; the output unit performs uniform arrangement processing based on the distribution position information of important heat flux information on the 1 / 4 cylindrical wall, and obtains 9 heat flux prediction position results from 0° to 80°.

[0019] The input unit consists of three input layers, the two hidden layer units consist of 20 neurons and 15 neurons respectively, and the output unit consists of nine output layers. The layers are fully connected, that is, each neuron is connected to each neuron in the next layer, and each connection corresponds to a specific weight. Each neuron in the hidden layer and each output corresponds to a specific base value. The weights and base values ​​are the training parameters. The training parameters are obtained by training the DSMC simulation results of 102 points randomly selected from a wide range. The loss function is the mean square error, and it is optimized using the Levenberg–Marquardt algorithm. The convergence condition is that the mean square error is less than 0.001 or the number of iterations reaches 2500 steps.

[0020] The multiple points on the cylindrical wall refer to: starting from the stationary point, a total of 9 points are selected in sequence with a step length of 10°, covering a range of 0° to 80°.

[0021] Technical Effects

[0022] The present invention uses a neural network to establish a proxy model and predict the heat flux of the cylindrical wall under hypersonic rarefied flow. Compared with the existing technology, it can quickly and accurately predict the heat flux coefficient of the cylindrical wall under hypersonic argon flow under a wide range of rarefied flow conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Schematic diagram of the calculation process of the direct simulation Monte Carlo method;

[0024] Figure 2 Schematic diagram of neural network structure;

[0025] Figure 3 Schematic diagram of the comparison results of the wall stagnation point heat flux for the two-dimensional flow around a circular cylinder;

[0026] Figure 4 Schematic diagram of the error distribution of heat flux at the wall stagnation point of the two-dimensional cylinder flow problem;

[0027] Figure 5Schematic diagram of the wall heat flux comparison results for the two-dimensional flow around a circular cylinder;

[0028] In the figure: (a) is Kn ∞ , (b) is T w / T s , (c) is Ma, ANN is the prediction result of the present invention. DETAILED DESCRIPTION

[0029] like Figure 1 As shown, this embodiment involves a neural network-based method for predicting the heat flux on the cylindrical wall under hypersonic rarefied flow. For a two-dimensional argon cylinder flow problem, 7 to 21 groups of different incoming flow conditions, cylinder radius and wall temperature are given. The neural network-based prediction model and the DSMC method are used to calculate the stagnation point heat flux and compare the results.

[0030] After specific practical experiments, the above method was run with three dimensionless parameters under the specific environment setting of hypersonic rarefied flow, and the experimental data that can be obtained are: the heat flux coefficient of nine points on the cylindrical wall under each set of flow conditions.

[0031] The seven groups of different incoming flow conditions, cylinder radius and wall temperature specifically refer to:

[0032] No. Ma p(Pa) t(K) r(m) Tw(K) <![CDATA[Kn ∞ ]]> <![CDATA[T w / T s ]]> 1 12.5 1.04268 35.5265 0.001 200 0.3236 0.106 2 12.5 83.6585 71.0531 0.001 400 0.0100 0.106 3 12.5 0.01423 106.58 0.01 600 10.0000 0.106 4 12.5 0.926731 188.291 0.01 200 0.3236 0.02 5 12.5 0.021975 62.7636 0.1 600 0.3236 0.18 6 6 0.065856 145.071 0.1 200 0.3236 0.106 7 18 0.010073 34.6029 0.1 400 0.3236 0.106

[0033] The 21 groups of different incoming flow conditions, cylinder radius and wall temperature specifically refer to: 21 groups of conditions are randomly selected within a wide range.

[0034] The comparison of stagnation point heat flow results in this embodiment is shown in the figure below. Figure 3 .

[0035] The stagnation point heat flux error distribution diagram in this embodiment is as follows: Figure 4 .

[0036] This embodiment shows that when randomly selecting points within a wide range, accurate stagnation point heat flow results can be obtained using a prediction model based on a neural network, with a maximum error of no more than 1.5%.

[0037] The results comparison diagram in this embodiment is as follows Figure 5 .

[0038] This embodiment shows that accurate results can be obtained using a prediction model based on a neural network at the boundaries and center of a wide range, with a maximum error not exceeding 4.8%.

[0039] Compared with the existing technology, this method has high accuracy (<5%) and a calculation speed close to that of the theoretical formula.

[0040] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principles and purpose of the present invention. The scope of protection of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. All implementation schemes within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for predicting heat flux on a cylindrical wall under hypersonic rarefied flow based on a neural network, characterized in that: In the offline phase, a parameter setting standard is obtained through direct simulation Monte Carlo (DSMC) algorithm verification based on heat flow independence. A neural network is then trained using normalized DSMC simulation samples based on this standard. In the online phase, for the flow around a cylinder in a hypersonic argon flow, the multi-point heat flux coefficient on the cylinder wall is obtained based on the existing connections within the neural network and the corresponding training parameters for a wide range of known values ​​of the incoming flow Knudsen number, temperature ratio, and Mach number. The neural network includes: an input unit, a first hidden layer unit, a second hidden layer unit, and an output unit, wherein: the input unit performs dimensionless processing based on information on the minimum number of variables required to determine the wall heat flux, and obtains a result of predicting the heat flux under hypersonic rarefied flow using three dimensionless parameters; the first hidden layer unit and the second hidden layer unit iteratively adjust the number of neurons based on error information obtained from neural network training, and obtain the final result of selecting the number of hidden layer neurons; the output unit performs uniform arrangement processing based on the distribution position information of important heat flux information on the 1 / 4 cylindrical wall, and obtains 9 heat flux prediction position results from 0° to 80°.

2. The method for predicting heat flux on a cylindrical wall under hypersonic rarefied flow based on a neural network according to claim 1, characterized in that: The rarefied flow refers to a flow with an incoming Knudsen number greater than 0.

01.

3. The method for predicting heat flux on a cylindrical wall under hypersonic rarefied flow based on a neural network according to claim 1, characterized in that: The DSMC method is a direct simulation Monte Carlo method of a hard sphere model with a variable diameter, an NTC collision scheme, and a load balancing parallel scheme based on the number of particles in the grid. The specific steps include: 1) Flow field initialization, that is, scattering simulated particles in the flow field according to the incoming flow conditions; 2) Particle movement, that is, the particles are moved at a constant speed within a certain time step according to their velocities in three directions, and reflection is considered if they come into contact with the boundary; 3) Particle index, which determines the grid number where each particle is located; 4) Collision and chemical reaction: determine the collision pairs and corresponding chemical reaction processes of each grid, and redistribute the energy and velocity of particles; 5) Sampling: statistics on the type, total number, speed and energy of particles in each grid; 6) Output: Calculate temperature, pressure, and velocity information based on the particle statistics within each grid.

4. The method for predicting heat flux on a cylindrical wall under hypersonic rarefied flow based on a neural network according to claim 1, wherein: The heat flux independence verification means that the wall heat flux results obtained by DSMC calculation are closely related to the setting of calculation parameters, and the parameter setting standard needs to be determined. Specifically, the grid is first set to 0.2 times the local molecular free path, the time step is 0.1 times the local molecular collision time, the wall grid is 180, the subgrid is 2*2, the initial grid particle number is 200, and the sampling times are 100,000 times to obtain accurate values ​​as subsequent references. Then, independence verification is performed on the grid and time step respectively, and the parameter setting standard is obtained as follows: the grid is 1 times the local molecular free path, the time step is 0.33 times the local molecular collision time, and the heat flux error can be controlled within 0.1%, ensuring the accuracy of the subsequently established samples.

5. The method for predicting heat flux on a cylindrical wall under hypersonic rarefied flow based on a neural network according to claim 1, wherein: The normalization is to map the input parameters to [0, 1] using the maximum and minimum values ​​of their respective ranges, wherein the Knudsen number is first logarithmized and then mapped to [0, 1].

6. The method for predicting heat flux on a cylindrical wall under hypersonic rarefied flow based on a neural network according to claim 1, wherein: The problem of flow around a cylinder under hypersonic argon flow refers to the problem related to the flow field of a two-dimensional cylinder under the conditions where the incoming gas is argon and the speed is greater than Mach 5.

7. The method for predicting heat flux on a cylindrical wall under hypersonic rarefied flow based on a neural network according to claim 1, wherein: The wide range mentioned above refers to the following: Knudsen number Kn ∞ Range [0.0072, 14.47], temperature ratio T w / T s Range [0.012, 0.2], Mach number Ma range [5, 20], where: T w is the cylinder wall temperature, T s is the stagnation temperature calculated based on the incoming flow temperature, Mach number and specific heat ratio theory.

8. The method for predicting heat flux on a cylindrical wall under hypersonic rarefied flow based on a neural network according to claim 1, wherein: The input unit consists of three input layers, the two hidden layer units consist of 20 neurons and 15 neurons respectively, and the output unit consists of nine output layers. Full connection is adopted between layers, that is, each neuron is connected to each neuron in the next layer, each connection corresponds to a specific weight, each neuron in the hidden layer and each output corresponds to a specific basic value, and the weight and basic value are training parameters. The training parameters are obtained by training the DSMC simulation results of 102 points randomly selected in a wide range. The loss function is the mean square error and is optimized using the Levenberg-Marquardt algorithm. The convergence condition is that the mean square error is less than 0.001 or the number of iteration steps reaches 2500 steps.

9. The method for predicting heat flux on a cylindrical wall under hypersonic rarefied flow based on a neural network according to claim 1, wherein: The multiple points on the cylindrical wall refer to: starting from the stationary point, a total of 9 points are selected in sequence with a step length of 10°, covering a range of 0° to 80°.

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