Prediction method of compressible channel turbulence average profile

Abstract

The invention discloses a method for predicting the average turbulence profile of a compressible channel, and belongs to the technical field of fluid mechanics engineering calculation and experiments. The prediction method provided by the invention comprises the steps of obtaining basic parameters of compressible channel turbulence to be predicted, wherein the basic parameters comprise a body Reynolds number, a body Mach number, a Prandtt number, a wall surface temperature and a reference temperature; setting initial iteration values for the wall surface density and the wall surface friction speed according to the basic parameters; generating a reference stretching grid by adjusting a stretching coefficient, and generating an initial laminar flow profile; and carrying out iteration on the initial laminar flow profile by using an iteration method until convergence to obtain a predicted compressible average profile. According to the prediction method provided by the invention, profile information such as average speed, temperature, density and the like can be quickly obtained directly according to the volume Reynolds number, the volume Mach number, the Prandtt number, the wall surface temperature and the reference temperature, and the method has remarkable efficiency and accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydrodynamic engineering calculation and experiment, and particularly relates to a method for predicting the mean profile of compressible channel turbulence. Background Art

[0002] Compressible channel turbulence has important application values in many engineering fields such as aerospace and energy power. Accurately predicting the mean profile of compressible channel turbulence is crucial for optimizing engineering designs, improving system performance and safety. Currently, there are mainly three technical routes for fluid profile prediction, but each technical route faces its own limitations:

[0003] 1 Traditional numerical simulation methods

[0004] (1) DNS (Direct Numerical Simulation): Based on the Navier-Stokes equations, although it can accurately capture the anisotropic characteristics of compressible channel turbulence and provide researchers with very detailed and accurate flow field information. However, this simulation method is limited by computing resources. When applied at the engineering scale, it will face the problem of grid magnitude explosion. For example, three-dimensional channel simulation often requires more than hundreds of millions of grids, which makes the calculation cost too high to be widely applied in actual engineering. (2) RANS (Reynolds-averaged) model: Although it reduces the amount of calculation to a certain extent, the error of the calculation results is relatively large and it is difficult to meet the high-precision prediction requirements.

[0005] 2 Experimental measurement techniques

[0006] The existing vertical profile method obtains pipeline flow field data through an electrode array, but faces two major bottlenecks in compressible flow: (1) High-speed flow causes sensor response lag and cannot obtain flow field information in a timely and accurate manner; (2) The cost of a single experiment is relatively high, which greatly limits the number of experiments and the application scope; (3) Measuring the flow very close to the wall is often very difficult. Techniques such as hot wires will interfere with the flow field, while particle image velocimetry technology will have errors due to overly sparse near-wall particles.

[0007] 3 Machine learning prediction models

[0008] The profile prediction method based on machine learning has significantly improved in terms of computational efficiency and can complete predictions in a relatively short time, but it has the problem of lack of physical consistency. In addition, the existing data-driven models have insufficient generalization ability for working conditions with sudden changes in compression ratio (such as M b > 3) and are difficult to accurately predict the fluid profile under such complex working conditions.

[0009] Therefore, it is urgent to develop a prediction method that can quickly and accurately predict the profile of compressible channel turbulence based on the bulk Reynolds number and the bulk Mach number. Summary of the Invention

[0010] The object of the present invention is to solve the problems existing in the prediction of the mean profile of compressible channel turbulence by traditional methods, such as low computational efficiency and poor physical consistency, and to provide a prediction method for predicting the mean profile of compressible channel turbulence based on the bulk Reynolds number and the bulk Mach number.

[0011] The specific technical solution adopted by the present invention is as follows:

[0012] The present invention provides a prediction method for the mean profile of compressible channel turbulence, comprising the following steps:

[0013] S1. Obtain the basic parameters of the compressible channel turbulence to be predicted, where the basic parameters include the bulk Reynolds number, the bulk Mach number, the Prandtl number, the wall temperature, and the reference temperature;

[0014] S2. Obtain the guessed value of the wall density and the guessed value of the wall friction velocity of the compressible channel turbulence to be predicted according to the basic parameters, and use the guessed value of the wall density and the guessed value of the wall friction velocity as the initial iteration value of the wall density and the initial iteration value of the wall friction velocity respectively;

[0015] S3. Adjust the stretching coefficient according to the preset grid resolution to generate a reference stretched grid;

[0016] S4. Generate an initial laminar profile according to the generated reference stretched grid;

[0017] S5. Use the iterative method to iteratively update the initial iteration value of the wall density and the initial iteration value of the wall friction velocity to obtain a new iteration value of the wall density and a new iteration value of the wall friction velocity; iteratively update the initial laminar profile point by point according to the iteration value of the wall density and the iteration value of the wall friction velocity until a satisfactory compressible mean profile is obtained;

[0018] S6. Obtain the residual of the compressible mean profile according to the compressible mean profile, and judge whether the residual is less than the threshold. If so, obtain the mean velocity and the mean temperature of the obtained compressible mean profile and output them; if not, update the iteration value of the wall density and the iteration value of the wall friction velocity, repeat step S5 and re-obtain the residual of the iterated compressible mean profile and judge until the residual is less than the threshold.

[0019] Further, in step S2, the method for obtaining the initial iteration value of the wall density is:

[0020]

[0021] where ρ w represents the initial iteration value of the wall density, ρ b represents the bulk density of the gas in the channel, and M b represents the bulk Mach number of the gas in the channel;

[0022] The method for obtaining the initial iteration value of the wall friction velocity is as follows:

[0023]

[0024] where,

[0025]

[0026] ρ c = ρ w T w / T c

[0027]

[0028] where, u τ represents the initial iteration value of the wall friction velocity, u b represents the bulk velocity of the gas in the channel, M b represents the bulk Mach number, represents the characteristic Reynolds number, ρ w represents the initial iteration value of the wall density, ρ c represents the fluid density at the center of the channel, μ c represents the viscosity at the center of the channel, μ ref represents the kinematic viscosity at the reference temperature, T w represents the wall temperature, T c represents the temperature at the center of the channel, Re b represents the bulk Reynolds number.

[0029] Furthermore, the bulk density of the gas in the channel is used as the reference density, and the dimensionless value is 1.0.

[0030] Furthermore, the steps for generating the reference stretched grid in step S3 include:

[0031] S31. Preset an initial grid through the preset number of grid points and the initial stretching coefficient, and obtain the height of the first layer of the initial grid;

[0032] S32. Obtain the difference between the height of the first layer of the initial grid and the reference resolution, and adjust the initial stretching coefficient according to the difference to obtain the adjusted stretching coefficient;

[0033] S33. Generate an adjusted stretched grid according to the adjusted stretching coefficient, and determine whether the adjusted stretched grid meets the requirements of the reference resolution. If so, the adjusted stretched grid is used as the reference stretched grid; if not, the current adjusted stretched grid is used as the initial grid, and step S32 is repeated until the resolution of the generated adjusted stretched grid meets the reference resolution.

[0034] Furthermore, the iterative step in step S5 includes:

[0035] S51. Generate an incompressible velocity profile based on the iterative value of the wall friction velocity and the iterative value of the wall density;

[0036] S52. Interpolate and calculate the corresponding incompressible velocity reference value according to the incompressible velocity profile;

[0037] S53. Obtain the current compressible average velocity value at any prediction point in the laminar profile after iteration, use the average temperature-velocity relationship to obtain the compressible average temperature value, and further use the ideal gas formula and the viscosity formula to obtain the corresponding compressible average density and compressible average viscosity values;

[0038] S54. Repeat step S53, obtain the compressible average density profile and the compressible viscosity profile through point-by-point iteration, and convert the compressible average velocity value of the current prediction point to the corresponding value in the incompressible state;

[0039] S55. Obtain the deviation value between the corresponding value in the incompressible state of the compressible average velocity value of the current prediction point and the incompressible reference value, and determine whether the deviation value is less than the preset deviation. If so, perform the iteration of the next prediction point; if not, use the iteration method to update the compressible average velocity value of the current prediction point;

[0040] S56. Repeat steps S53 - S55 until the deviation of each prediction point is less than the preset deviation, so as to obtain the compressible average profile under the current iterative value of the wall friction velocity and the iterative value of the wall density.

[0041] Furthermore, the deviation value of the prediction point is the difference between the corresponding value in the incompressible state after the conversion of the compressible average velocity value and the incompressible velocity reference value.

[0042] Preferably, the iteration method all adopts the Newton iteration method.

[0043] The present invention has the following beneficial effects compared with the prior art:

[0044] The prediction method provided by the present invention can directly obtain profile information such as average velocity and temperature based on the basic parameters of compressible channel turbulence, with remarkable efficiency and accuracy. The prediction method provided by the present invention greatly improves the analysis efficiency of high Mach number flows, provides timely and comprehensive flow field data support for engineers and researchers, enables engineers and researchers to comprehensively and accurately grasp complex flow states in a short time, and significantly enhances the reliability and efficiency of complex flow analysis. This rapid response ability not only improves work efficiency but also provides strong support for timely optimizing designs and adjusting parameters, avoiding the cumbersome process of traditional methods that require multiple simulations to obtain complete flow field data, thus providing a more convenient, efficient, and reliable means for the research and application of compressible channel flows. Brief Description of the Drawings

[0045] Figure 1 It is a flowchart of the prediction method provided in this embodiment;

[0046] Figure 2 For Mach number M b = 1.5, bulk Reynolds number Re b = 7667 for result comparison;

[0047] Figure 3 For Mach number M b = 1.5, bulk Reynolds number Re b = 13100 for result comparison;

[0048] Figure 4 For Mach number M b = 1.5, bulk Reynolds number Re b = 17000 for result comparison;

[0049] Figure 5 For Mach number M b = 1.5, bulk Reynolds number Re b = 70000 for result comparison;

[0050] Figure 6 For Mach number M b = 3.0, bulk Reynolds number Re b = 34000 for result comparison. Detailed Embodiments

[0051] To make the above objects, features, and advantages of the present invention more apparent and understandable, the following describes the specific embodiments of the present invention in detail with reference to the accompanying drawings. Many specific details are set forth in the following description to facilitate a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below. The technical features in the various embodiments of the present invention can be combined correspondingly without conflict.

[0052] The present invention provides a method for predicting the mean profile of compressible channel turbulence, which is particularly applicable to the prediction requirements of the mean profile of high Mach number compressible flows (M b ≥ 1.5). It can quickly obtain the mean velocity, temperature, density, and dynamic viscosity profiles based on the basic parameters of compressible channel turbulence, thus solving the problems of low computational efficiency and poor physical consistency existing in the traditional and machine learning methods for predicting the compressible channel flow profile. This method is applicable to scenarios such as internal flow analysis of aerospace engines, monitoring of oil and gas pipelines, and design of nuclear reactor cooling systems.

[0053] As Figure 1 shown, in a preferred implementation of the present invention, this embodiment provides a method for predicting the mean profile of compressible channel turbulence, which includes the following steps S1 to S6. The specific implementation processes are described separately below.

[0054] S1. Obtain the basic parameters of the compressible channel turbulence to be predicted, where the basic parameters include the bulk Reynolds number, bulk Mach number, Prandtl number, wall temperature, and reference temperature.

[0055] S2. Obtain the guessed values of the wall density and wall friction velocity of the compressible channel turbulence to be predicted based on the basic parameters, and use the guessed values of the wall density and wall friction velocity as the initial iteration values of the wall density and wall friction velocity, respectively.

[0056] It should be noted that the guessed values of the wall density and wall friction velocity, that is, the initial iteration values of the wall density and wall friction velocity, can be determined according to the scaling law formula (Reference: Xia Z.H., Song Y.B., Zhu X.K. Skin-friction scaling in compressible turbulent channel flows [J]. AIAA Journal, 2025 (Under review).), so as to obtain an initial prediction closer to the actual working conditions.

[0057] The method for obtaining the initial iteration value of the wall density is:

[0058]

[0059] Among them, ρ w represents the initial iterative value of the wall density, and ρ b represents the bulk density of the gas in the channel, and M b represents the bulk Mach number of the gas in the channel. The bulk density ρ b of the gas in the channel is also the reference density, and the dimensionless value is 1.0.

[0060] In this embodiment, according to the obtained bulk Reynolds number Re b , bulk Mach number M b , Prandtl number Pr, wall temperature T w and reference temperature T ref , the central temperature T c and central viscosity μ c are calculated.

[0061]

[0062] Among them, T w represents the wall temperature, M b represents the bulk Mach number, μ c represents the central viscosity of the channel, T ref represents the reference temperature, and T s = 110.4K.

[0063] After that, the initial iterative value of the wall friction velocity is obtained:

[0064]

[0065] Among them,

[0066]

[0067] ρ c = ρ w T w / T c

[0068] Among them, u τ represents the initial iterative value of the wall friction velocity, u b represents the bulk velocity of the gas in the channel, M b represents the bulk Mach number, represents the characteristic Reynolds number, ρ w represents the initial iterative value of the wall density, ρ c represents the fluid density at the center of the channel, μ c represents the central viscosity of the channel, μ ref represents the dynamic viscosity at the reference temperature, and T wDenote the wall temperature, T c Denote the channel center temperature, Re b Denote the bulk Reynolds number.

[0069] Accurate initial iteration values can reduce the number of iterations during the calculation process. The closer the initial iteration value is to the true operating condition value, the faster the solver converges. Using the scaling law formula (Reference: Xia Z.H., Song Y.B., Zhu X.K. Skin-friction scaling in compressible turbulent channel flows[J]. AIAA Journal, 2025(Under review).) to predict the initial iteration values of wall density and wall friction velocity can greatly reduce the number of iteration steps, thereby saving calculation time and calculation resources.

[0070] S3. Generate a reference stretched grid by adjusting the stretching coefficient according to the preset grid resolution.

[0071] In this embodiment, step S3 is specifically as follows:

[0072] S31. Preset an initial grid through the preset number of grid points and the initial stretching coefficient, and obtain the height of the first layer of the initial grid;

[0073] S32. Obtain the difference between the height of the first layer of the initial grid and the reference resolution, and adjust the initial stretching coefficient based on this difference to obtain an adjusted stretching coefficient;

[0074] S33. Generate an adjusted stretched grid according to this adjusted stretching coefficient, and determine whether the adjusted stretched grid meets the requirements of the reference resolution. If so, this adjusted stretched grid is used as the reference stretched grid; if not, the current adjusted stretched grid is used as the initial grid, and step S32 is repeated until the resolution of the generated adjusted stretched grid meets the reference resolution.

[0075] In this embodiment, it is possible to determine whether the generated stretched grid meets the requirements of the reference resolution by comparing the height of the first layer of the generated grid. The formula for grid generation is as follows:

[0076]

[0077] Where

[0078]

[0079] In the formula, Re τ is the friction Reynolds number, y represents the distance between the prediction point and the wall, y +The dimensionless normal coordinate representing the wall coordinate, j is an integer from 0, 1, 2... ny - 1, b is the adjustment stretching coefficient, μ w represents the wall viscosity, μ ref represents the kinematic viscosity at the reference temperature, T w represents the wall temperature, T ref represents the reference temperature, T s = 110.4K.

[0080] In this embodiment, the adjustment stretching coefficient b is not a fixed value, but can be optimized and adjusted according to the stretching grid generated last time. Continuously optimize the adjustment stretching coefficient b. When the adjustment stretching coefficient b can make the resolution of the grid meet the requirements, the stretching grid generated based on this adjustment stretching coefficient b can basically meet the requirements of the reference resolution.

[0081] S4. Generate an initial laminar profile according to the generated reference stretching grid.

[0082] Generate an initial velocity laminar profile according to the grid distribution of the reference stretching grid

[0083] u(y) = -1.5y 2 + 3y,

[0084] In the formula, y represents the distance between the prediction point and the wall.

[0085] S5. Use the iterative method to iteratively update the initial iteration values of the wall density and the wall friction velocity, and obtain new iteration values of the wall density and the wall friction velocity; according to the iteration values of the wall density and the wall friction velocity, iteratively update the initial laminar profile point by point until a compressible average profile that meets the requirements is obtained.

[0086] In this embodiment, step S5 is specifically as follows:

[0087] S51. Generate an incompressible velocity profile based on the iteration value of the wall friction velocity and the iteration value of the wall density;

[0088] S52. Interpolate and calculate the corresponding incompressible velocity reference value based on the incompressible velocity profile;

[0089] S53. Obtain the current compressible average velocity value of any prediction point in the iterated laminar profile, use the average temperature - velocity relationship to obtain the compressible average temperature value, and further use the ideal gas formula and the viscosity formula to obtain the corresponding compressible average density and compressible average viscosity values;

[0090] S54. Repeat step S53, obtain the compressible average density profile and the compressible viscosity profile through point - by - point iteration, and convert the compressible average velocity value of the current prediction point to the corresponding value in the incompressible state;

[0091] S55. Obtain the deviation value between the corresponding value in the incompressible state of the compressible average velocity value at the current prediction point and the incompressible reference value, and determine whether the deviation value is less than the preset deviation. If so, perform iteration for the next prediction point; if not, update the compressible average velocity value at the current prediction point using the iteration method.

[0092] S56. Repeat steps S53 - S55 until the deviation of each prediction point is less than the preset deviation, thereby obtaining the compressible average profile under the current wall friction velocity iteration value and wall density iteration value.

[0093] In this embodiment, the wall density iteration value and the wall friction velocity iteration value are continuously iteratively updated through the initial iteration values of the wall density and the wall friction velocity. The initial velocity laminar profile is iterated using the wall density iteration value and the wall friction velocity iteration value through the iteration method. After the compressible average density profile and the compressible viscosity profile of the current prediction point i are obtained, the compressible average velocity value of the prediction point i needs to be stored, and then the (0, i] prediction points are used to iterate the (i + 1)-th prediction point.

[0094] In this embodiment, the iteration method used is the Newton iteration method. First, recalculate the characteristic Reynolds number based on the current wall friction velocity iteration value, the current wall density iteration value, and the channel center temperature, and generate an incompressible velocity profile. With the help of the model of the incompressible mixing length and the total stress relationship to close the total stress balance equation, use the ZSYX transformation Y + = y * and find the incompressible average velocity profile U + (Y + ):

[0095]

[0096] Y + = ∫f I dy + and U + = ∫g I du + where

[0097] In this embodiment, uppercase letters U, Y, and the subscript "in" are used to represent the incompressible state.

[0098]

[0099] Among them, R core≈0.27,

[0100] In this embodiment, through the mean temperature-velocity relationship (Reference: Zhu X.K., Zhang P., Yang X.S., et al. A unified framework for mean temperature analysis in compressible turbulent channel flows[J]. Journal of Fluid Mechanics, 2025(Under review).), the compressible mean temperature profile is obtained based on the current compressible mean velocity profile:

[0101]

[0102]

[0103] where B q represents the dimensionless wall heat flux, M τ represents the wall friction Mach number, Pr represents the Prandtl number, y * represents the wall normal distance, γ = 1.4 represents the specific heat ratio of the gas in the channel, n = 10,

[0104] In this embodiment, according to the ideal gas assumption and the normal isobaric assumption, the density profile can be obtained by the following formula

[0105]

[0106] where ρ w represents the initial wall density iteration value, T w represents the wall temperature, and T(y) represents the temperature profile.

[0107] The viscosity profile can be obtained by the following formula:

[0108]

[0109] where T ref represents the reference temperature, and in the considered symmetric isothermal channel, T w = T ref , μ ref represents the dimensionless reference dynamic viscosity, and T s = 110.4K.

[0110] In this embodiment, according to the mean temperature and viscosity, the semi-local normal coordinate of the i-th point at the prediction point can be obtained

[0111]

[0112] Among them, the subscript i represents the value at the i-th point.

[0113] According to the above results, the corresponding incompressible reference value can be interpolated and calculated:

[0114] U in,ref = interp1(Y + , U + , y * )

[0115] Among them, interp1(x, y, x i ) represents interpolating and calculating the function value at x based on the function value y corresponding to x i .

[0116] In this embodiment, taking the acquisition of the average velocity profile as an example, the profile value of the transformed incompressible velocity profile at the i-th point of the prediction point is obtained through the compressible velocity transformation formula (Reference: Zhu X.K., Song Y.B., Yang X.S., et al. Velocity transformation for compressible wall - bounded turbulence—An approach through the mixing length hypothesis[J]. Science China Physics, Mechanics & Astronomy, 2024, 67(9).) That is, the corresponding value in the incompressible state of the compressible average velocity value:

[0117]

[0118]

[0119] Among them,

[0120]

[0121] In the formula, k = 0.57, r core ≈ 0.27, r = 1 - y + / Re τ .

[0122] Then judge whether the deviation value of the velocity at this point is less than the preset deviation ε = 1e -6, if not, update the compressible average velocity value of this point and continue the iteration until the deviation value is less than the preset deviation; if so, perform the iteration for the next prediction point, the (i + 1)-th point, until the entire compressible average velocity profile is obtained.

[0123] S6. Obtain the residual based on the current compressible average profile, and determine whether the residual is less than the threshold value. If so, obtain the average velocity and average temperature of the obtained compressible average profile and output them; if not, update the wall density iteration value and the wall friction velocity iteration value, repeat step S5, and re-obtain the residual of the iterated compressible average profile and determine until the residual is less than the threshold value.

[0124] In this embodiment, calculate the residual based on the currently obtained average velocity profile

[0125]

[0126] Determine whether it is less than the threshold value. If not, use the iterative method to update the wall density and wall friction velocity iteration values, and repeat steps S5 and S6 until the residual is less than the threshold value. If so, output the average velocity and average temperature profiles. Where h represents the half-width of the channel, and the dimensionless value is usually 1.

[0127] According to the ideal gas assumption and the normal isobaric assumption, the density profile can be obtained from the following formula

[0128]

[0129] In the formula, ρ w represents the initial wall density iteration value, T w represents the wall temperature, and T(y) represents the temperature profile.

[0130] The viscosity profile can be obtained from the following formula:

[0131]

[0132] In the formula, T ref represents the reference temperature, and in the considered symmetric isothermal channel, T w = T ref , μ ref represents the dimensionless reference kinetic viscosity, and T s = 110.4K.

[0133] In this embodiment, use images to show the comparison between the prediction results obtained by using this prediction method and the profile results obtained from the DNS database under different bulk Mach numbers and bulk Reynolds numbers. The red dashed line is the compressible profile predicted by the present invention, and the black solid line is the compressible profile obtained from the DNS database; u + = u / u τrepresents the dimensionless average velocity of the wall surface, T / T w represents the ratio of the average temperature to the wall temperature, y + represents the dimensionless wall normal coordinate. Figure 2 The comparison of results with Mach number 1.5 and bulk Reynolds number 7667 is shown; Figure 3 The comparison of results with Mach number 1.5 and bulk Reynolds number 13100 is shown; Figure 4 The comparison of results with Mach number 1.5 and bulk Reynolds number 17000 is shown; Figure 5 The comparison of results with Mach number 1.5 and bulk Reynolds number 70000 is shown; Figure 6 The comparison of results with Mach number 3.0 and bulk Reynolds number 34000 is shown. It can be found through comparison that the predicted results (red dashed lines) obtained by using this prediction method all correspond well to the results in the database (black solid lines), demonstrating the accuracy of the present invention.

[0134] The embodiments described above are only a preferred solution of the present invention, but they are not intended to limit the present invention. Those of ordinary skill in the relevant technical field can still make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all technical solutions obtained by means of equivalent replacement or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A prediction method for the mean profile of compressible channel turbulence, characterized in that It includes the following steps: S1. Obtain the basic parameters of the compressible channel turbulence to be predicted, where the basic parameters include the bulk Reynolds number, bulk Mach number, Prandtl number, wall temperature, and reference temperature; S2. Obtain the guessed value of the wall density and the guessed value of the wall friction velocity of the compressible channel turbulence to be predicted according to the basic parameters, and use the guessed value of the wall density and the guessed value of the wall friction velocity as the initial iteration value of the wall density and the initial iteration value of the wall friction velocity respectively; S3. Adjust the stretching coefficient according to the preset grid resolution to generate a reference stretched grid; S4. Generate an initial laminar profile according to the generated reference stretched grid; S5. Use the iterative method to iteratively update the initial iteration value of the wall density and the initial iteration value of the wall friction velocity to obtain a new iteration value of the wall density and a new iteration value of the wall friction velocity; Iteratively update the initial laminar profile point by point according to the iteration value of the wall density and the iteration value of the wall friction velocity until a compressible mean profile that meets the requirements is obtained; S6. Obtain the residual of the compressible mean profile according to the compressible mean profile, and judge whether the residual is less than the threshold. If so, obtain the average velocity and average temperature of the obtained compressible mean profile and output them; If not, update the iteration value of the wall density and the iteration value of the wall friction velocity, repeat step S5 and re-obtain the residual of the iterated compressible mean profile and judge until the residual is less than the threshold.

2. The prediction method of the average profile of compressible channel turbulence according to claim 1, characterized in that In step S2, the method for obtaining the initial iteration value of the wall density is: Among them, ρ w represents the initial iteration value of the wall density, and ρ b represents the bulk density of the gas in the channel, and M b represents the bulk Mach number of the gas in the channel; The method for obtaining the initial iteration value of the wall friction velocity is: Among them, ρ c = ρ w T w / T c Among them, u τ represents the initial iteration value of the wall friction velocity, u b represents the bulk velocity of the gas in the channel, M b represents the bulk Mach number, represents the characteristic Reynolds number, ρ w represents the initial iteration value of the wall density, ρ c represents the fluid density at the center of the channel, μ c represents the viscosity at the center of the channel, μ ref represents the kinematic viscosity at the reference temperature, T w represents the wall temperature, T c represents the temperature at the center of the channel, Re b represents the bulk Reynolds number.

3. The prediction method of the average profile of compressible channel turbulence according to claim 2, characterized in that The bulk density of the gas in the channel is used as the reference density, and the dimensionless value is 1.

0.

4. The prediction method of the average profile of compressible channel turbulence according to claim 1, characterized in that The generation steps of the reference stretched grid in step S3 include: S31. Preset an initial grid through the preset number of grid points and the initial stretching coefficient, and obtain the height of the first layer of the grid of the initial grid; S32. Obtain the difference between the height of the first layer of the grid of the initial grid and the reference resolution, and adjust the initial stretching coefficient according to the difference to obtain an adjusted stretching coefficient; S33. Generate an adjusted stretched grid according to the adjusted stretching coefficient, and judge whether the adjusted stretched grid meets the requirements of the reference resolution. If so, the adjusted stretched grid is used as the reference stretched grid; If not, the current adjusted stretched grid is used as the initial grid, and step S32 is repeated until the resolution of the generated adjusted stretched grid meets the reference resolution.

5. The prediction method of the average profile of compressible channel turbulence according to claim 1, characterized in that The iterative steps in step S5 include: S51. Generate an incompressible velocity profile according to the iteration value of the wall friction velocity and the iteration value of the wall density; S52. Interpolate and calculate the corresponding incompressible velocity reference value according to the incompressible velocity profile; S53. Obtain the current compressible mean velocity value of any prediction point in the iterated laminar profile, use the mean temperature-velocity relationship to obtain the compressible mean temperature value, and further use the ideal gas formula and the viscosity formula to obtain the corresponding compressible mean density and compressible mean viscosity values; S54. Repeat step S53 to obtain the compressible average density profile and the compressible viscosity profile through point-by-point iteration, and convert the compressible average velocity value at the current prediction point to the corresponding value in the incompressible state; S55. Obtain the deviation value between the corresponding value in the incompressible state of the compressible average velocity value at the current prediction point and the incompressible reference value, and determine whether the deviation value is less than the preset deviation. If so, proceed to the iteration of the next prediction point; if not, use the iteration method to update the compressible average velocity value at the current prediction point; S56. Repeat steps S53 - S55 until the deviation of each prediction point is less than the preset deviation, thus obtaining the compressible average profile at the current wall friction velocity iteration value and the wall density iteration value.

6. The prediction method of the average profile of compressible channel turbulence according to claim 5, characterized in that The deviation value of the prediction point is the difference between the corresponding value in the incompressible state after the conversion of the compressible average velocity value and the incompressible velocity reference value.

7. The prediction method of the average profile of compressible channel turbulence according to claim 1, characterized in that The iteration method all adopts the Newton iteration method.

Images