A method for generating wide-speed-range turbulent boundary layer inlet information

Abstract

This invention relates to a method for generating inlet information of a wide-velocity-domain turbulent boundary layer, the method comprising: S1, based on the average velocity U under the Van Driest transform... VD Incoming flow velocity U e Incoming flow temperature T e Temperature T at the wall surface w Wall friction speed u τ S1. Obtain turbulent average flow information; the turbulent average flow information includes: average velocity, average density, and average temperature; S2. Based on the preset first random number vector ζ, the preset second random number vector ξ, the density gradient wavenumber vector k, and the turbulent energy spectrum E(k), m energy spectra E(k) are pre-divided into multiple slices. m S3. Based on the average turbulent flow information and the turbulent fluctuation information, generate turbulent boundary layer inlet information.

Description

Technical Field

[0001] This invention relates to the field of large eddy simulation or direct simulation of turbulent boundary layer induction conditions in computational fluid dynamics numerical simulation technology, and particularly to a method for generating induction information of a wide velocity domain turbulent boundary layer from low-speed incompressible flow to hypersonic compressible flow. Background Technology

[0002] In computational fluid dynamics numerical simulations, the spatially evolving turbulent boundary layer is highly sensitive to its upstream conditions. When using large eddy simulation (LES) or direct numerical simulation (DMS) to simulate the turbulent boundary layer, the inlet boundary conditions are particularly crucial, directly impacting the success of the numerical calculation. This is because the fluctuation information at the turbulence inlet is derived from the upstream spatial turbulence development and evolution, typically provided by experimental upstream numerical simulations of turbulence statistics. Subsequent simulations usually require boundary conditions based on these statistics. For LES or DMS, information on the evolution of fluctuations over time is needed. Whether the provided fluctuation information conforms to the characteristics of true turbulence, and consequently whether the derived downstream fully developed turbulence closely approximates real turbulence, becomes a key technical issue in ensuring the accuracy and reliability of the computational simulation.

[0003] Currently, methods for generating boundary layer inlet turbulence mainly include database methods, recovery / transformation methods, and synthesis methods. Database methods involve obtaining turbulent inlet information from an established database and then applying (or transforming) it to the inlet conditions. Recovery / transformation methods involve setting up a recovery plane in the downstream region of the flow, extracting flow information at that plane, and transforming the information from the recovery plane to the inlet plane through a series of transformations. Synthesis methods simulate stochastic processes, directly evolving pulsation information from statistical information. Synthesis methods can be categorized into synthetic stochastic Fourier methods, digital filtering methods, synthetic coherent eddies methods, and synthetic body force methods. Stochastic synthesis methods primarily generate turbulent pulsation information using random numbers and were initially used in computational wind engineering.

[0004] However, in existing methods, the inlet boundary layer often requires a long evolution over a considerable distance and time to obtain a turbulent boundary layer that meets certain realistic turbulence characteristics and requirements, which poses a significant challenge to the numerical simulation of turbulent boundary layers. Furthermore, existing methods are only applicable to simulating incompressible turbulent boundary layers, or only applicable to calculating compressible turbulent boundary layers; few algorithms can generate inlet conditions for turbulent boundary layers across a wide velocity range. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] In view of the aforementioned shortcomings and deficiencies of existing technologies, this invention provides a method for generating inlet information of a wide-velocity-domain turbulent boundary layer. This method solves the problem that in existing methods, the inlet boundary layer often requires a long evolution over a considerable distance and time to obtain a turbulent boundary layer that meets the characteristics and requirements of true turbulence. Furthermore, the evolved turbulence information may contain perturbation factors from the generation perturbation technique, which poses a significant challenge to the accuracy of numerical simulations of turbulent boundary layers. In addition, most existing methods are only applicable to simulating incompressible turbulent boundary layers or only applicable to calculating compressible turbulent boundary layers.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the main technical solutions adopted by the present invention include:

[0009] This invention provides a method for generating inlet information of a wide-velocity-range turbulent boundary layer, comprising:

[0010] S1. Average velocity under Van Driest transformation Incoming flow velocity Incoming flow temperature Temperature at the wall surface Wall friction speed To obtain turbulent average flow information;

[0011] The turbulent average flow information includes: average velocity, average density, and average temperature;

[0012] S2, based on the preset first random number vector , preset second random number vector density gradient The wavenumber vector k and the turbulent energy spectrum E(k) are m energy spectra pre-divided into multiple slices. To obtain information on turbulent fluctuations;

[0013] The turbulent fluctuation information includes: velocity fluctuation, density fluctuation, and temperature fluctuation;

[0014] S3. Based on the turbulent average flow information and the turbulent fluctuation information, generate turbulent boundary layer inlet information.

[0015] Preferably, S1 specifically includes:

[0016] S11. Average velocity under Van Driest transformation Incoming flow velocity Incoming flow temperature Temperature at the wall surface Wall friction speed The distribution of average velocity U is obtained by using formulas (1), (2), and (3).

[0017] Formula (1) is:

[0018] (1);

[0019] Formula (2) is:

[0020] (2);

[0021] Formula (3) is:

[0022] (3);

[0023] The average velocity under the Van Driest transform;

[0024] for Dimensionless form;

[0025] y is the normal coordinate of the wall;

[0026] Let y be the dimensionless form of the wall normal coordinate;

[0027] Indicates the boundary layer thickness under the Van Driest transform;

[0028] C1 is the first preset constant;

[0029] This is the second preset constant;

[0030] b is the third preset constant;

[0031] d is the fourth preset constant;

[0032] C is the fifth preset constant;

[0033] This is the sixth preset constant;

[0034] in, ; ;

[0035] Indicates the Mach number of the incoming flow;

[0036] Indicates the incoming flow velocity;

[0037] U represents the average velocity;

[0038] r is the recovery factor;

[0039] Specific heat ratio;

[0040] Indicates the incoming flow temperature;

[0041] Indicates the temperature at the wall surface;

[0042] The velocity is the wall friction velocity.

[0043] S12. Based on the average velocity U, obtain the average temperature using formula (4). Distribution;

[0044] The formula (4) is:

[0045] (4);

[0046] in,

[0047]

[0048] Average temperature;

[0049] T aw To restore temperature;

[0050] S13, based on the average temperature The average density is obtained using formula (5). ;

[0051] The formula (5) is:

[0052] (5);

[0053] in, The incoming flow density;

[0054] The average density.

[0055] Preferably,

[0056] The second preset constant The value is 11;

[0057] The value of the third preset constant b is 0.33;

[0058] The value of the fourth preset constant d is 0.41;

[0059] The value of the fifth preset constant C is 5.6;

[0060] The value of the first preset constant C1 is (-log(0.41) / 0.41)+5.6;

[0061] The sixth preset constant The value is 0.45.

[0062] Preferably,

[0063] The value of the recovery factor r is greater than 0.8 and less than 1;

[0064] The specific heat ratio The value is 1.4.

[0065] Preferably, S2 specifically includes:

[0066] S21. Based on the preset first random number vector , preset second random number vector density gradient The wavenumber vector k and the turbulent energy spectrum E(k) are the m-th energy spectrum of a pre-divided multi-slice array. Formula (6) is used to obtain the magnitude of the velocity fluctuation at time t at each point in the computational domain. ;

[0067] The formula (6) is:

[0068] (6);

[0069] in,

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] The expected value is 0 and the variance is . The angular frequency of a normal distribution;

[0078] x represents the coordinate vector corresponding to a point within the computational domain;

[0079] k m Represents the characteristic scale of wavenumber space;

[0080] The first random number vector is preset;

[0081] This is a pre-defined second random number vector;

[0082] Represents the gradient operator;

[0083] Represents the density gradient;

[0084] k represents the wavenumber vector;

[0085] It represents the wavenumber vector of the nth mode in the mth wavenumber space;

[0086] It is the m-th energy spectrum among the multiple energy spectra into which the pre-obtained turbulent energy spectrum E(k) is divided;

[0087] Represents the length scale of turbulence;

[0088] m is the number of turbulence spectrum segments in wavenumber space;

[0089] n represents the nth level mode;

[0090] N represents the set number of modes;

[0091] k max The maximum wave number set;

[0092] This represents the value used to make the wavenumber space dimensionless.

[0093] a is a random number uniformly distributed between 0 and 1;

[0094] S22. Regarding the magnitude of velocity fluctuations at each point in space at time t. Using pre-acquired turbulence intensity-velocity fluctuation distribution curves, the magnitude of velocity fluctuations at each point in space at time t is determined. Polynomial fitting is performed to obtain the distribution pattern of velocity fluctuations within the turbulent boundary layer;

[0095] S23. Measure the magnitude of the velocity fluctuations at each point in the space at time t. By combining the velocity fluctuation distribution pattern within the turbulent boundary layer, the velocity fluctuations are obtained. ;

[0096] S24, according to the speed pulsation Average velocity U, average temperature The temperature fluctuation is obtained using formula (7);

[0097] The formula (7) is:

[0098] ;

[0099] in, It's a temperature fluctuation;

[0100] S25, according to the temperature fluctuation Average temperature Average density Density pulsation is obtained using formula (8);

[0101] The formula (8) is:

[0102] (8);

[0103] It is a density pulsation.

[0104] Preferably,

[0105] The turbulent energy spectrum E(k) in S21 is obtained according to the von Karman spectral model;

[0106] In the von Karman spectral model, for uniform isotropic turbulence, the expression for the spectral function corresponding to the flow direction is Equation (9), the expression for the spectral function corresponding to the wall normal is Equation (10), and the expression for the spectral function corresponding to the spanwise direction is Equation (11).

[0107] The formula (9) is:

[0108] (9);

[0109] I u Indicates the turbulence intensity in terms of direction of flow;

[0110] L u The turbulent integral scale representing the direction of flow;

[0111] f represents frequency. Where k is the wave number;

[0112] Turbulent energy spectrum function indicating flow direction;

[0113] The formula (10) is:

[0114] (10);

[0115] I v Indicates the turbulence intensity in the direction normal to the wall;

[0116] Lv The integral scale of turbulence in the direction normal to the wall;

[0117] The turbulent energy spectrum function representing the wall normal;

[0118] The formula (11) is:

[0119] (11);

[0120] I w Indicates the spanwise turbulence intensity;

[0121] L w Represents the spanwise integral scale of turbulence;

[0122] The spanwise turbulent energy spectrum function;

[0123] In the von Karman spectral model, for non-uniform anisotropic turbulence, the expression for the spectral function corresponding to the flow direction is Equation (12), the expression for the spectral function corresponding to the spanwise direction is Equation (13), and the expression for the spectral function corresponding to the wall normal direction is Equation (14).

[0124] The formula (12) is:

[0125] (12);

[0126] The formula (13) is:

[0127] (13);

[0128] The formula (14) is:

[0129] (14).

[0130] Preferably,

[0131] The turbulence intensity I u Value, span I w The value of the wall normal velocity I v The values ​​are all preset;

[0132] The turbulent integral scale L in the direction of flow u The value of the spanwise turbulence integral scale L w The value of the wall-normal turbulent integral scale L v The values ​​are all preset.

[0133] Preferably, S3 specifically includes:

[0134] S31, based on the average velocity U and the velocity fluctuation The inlet velocity of the turbulent boundary layer is synthesized using formula (15);

[0135] The formula (15) is:

[0136] (15);

[0137] u is the inlet velocity of the turbulent boundary layer;

[0138] S32, based on the average density and the density pulsation The inlet density of the turbulent boundary layer is synthesized using formula (16);

[0139] The formula (16) is:

[0140] (16);

[0141] The This represents the inlet density of the turbulent boundary layer.

[0142] S33, Based on the average temperature and the temperature fluctuations The inlet temperature of the turbulent boundary layer is synthesized using formula (17);

[0143] The formula (17) is:

[0144] (17);

[0145] T is the inlet temperature of the turbulent boundary layer;

[0146] S34, Based on the turbulent boundary layer inlet density , inlet velocity u of turbulent boundary layer, average density Average temperature The inlet energy of the turbulent boundary layer is obtained by formula (18);

[0147] Formula (18) is as follows:

[0148] (18);

[0149] Where e is the inlet energy of the turbulent boundary layer;

[0150] R is the universal gas constant, with a value of 286.9 J / (kg·K).

[0151] Preferably, the method further includes:

[0152] S4. Based on the turbulent boundary layer inlet information, the turbulent boundary layer is simulated using the large eddy simulation method or the direct numerical simulation method, and the simulation results are obtained.

[0153] The turbulent boundary layer inlet information includes: turbulent boundary layer inlet density, turbulent boundary layer inlet velocity, turbulent boundary layer inlet temperature, and turbulent boundary layer inlet energy.

[0154] Preferably,

[0155] The value of the recovery factor r is equal to 0.9.

[0156] (III) Beneficial Effects

[0157] The beneficial effects of the present invention are as follows: The method for generating inlet information of a wide velocity domain turbulent boundary layer of the present invention decomposes the turbulent physical quantities into average flow information and pulsation information in the generation process. Accordingly, the generation process of inlet information of a wide velocity domain turbulent boundary layer mainly includes three aspects: generating average flow information of turbulence, turbulent pulsation information and synthesizing inlet information of turbulent boundary layer. In the process of generating turbulent pulsation information, the influence of flow compressibility is taken into account by formula (14), which solves the problem of excessively long transition zone in the simulation process of turbulent boundary layer. Attached Figure Description

[0158] Figure 1 This is a flowchart of a method for generating inlet information of a wide velocity domain turbulent boundary layer according to the present invention;

[0159] Figure 2 This refers to the boundary layer inlet information generated using a method for generating wide velocity-domain turbulent boundary layer inlet information according to the present invention.

[0160] Figure 3 According to Figure 2 The vorticity isosurface based on the Q criterion is obtained by performing high-precision large eddy simulation of the turbulent boundary layer using boundary layer inlet information.

[0161] Figure 4 This is a schematic diagram of the turbulent velocity fluctuation distribution.

[0162] Figure 5 This is a schematic diagram of the average velocity distribution;

[0163] Figure 6 This is a schematic diagram of the wall friction coefficient distribution;

[0164] Figure 7 The downstream velocity spectrum of the flow;

[0165] Figure 8 The downstream density spectrum;

[0166] Figure 9The schematic diagram illustrates a method for generating inlet information of a wide-velocity-range turbulent boundary layer, which can evolve from a method for incompressible flows to a general method applicable to flows ranging from incompressible to strongly compressible. Detailed Implementation

[0167] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0168] To better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present invention can be understood more clearly and thoroughly, and that the scope of the present invention can be fully conveyed to those skilled in the art.

[0169] See Figure 1 This embodiment provides a method for generating inlet information of a wide-velocity-range turbulent boundary layer, including:

[0170] S1. Average velocity under Van Driest transformation Incoming flow velocity Incoming flow temperature Temperature at the wall surface Wall friction speed To obtain information on turbulent average flow.

[0171] The turbulent average flow information includes: average velocity, average density, and average temperature.

[0172] S2, based on the preset first random number vector , preset second random number vector density gradient The wavenumber vector k and the turbulent energy spectrum E(k) are m energy spectra pre-divided into multiple slices. To obtain information on turbulent fluctuations.

[0173] The turbulent fluctuation information includes: velocity fluctuation, density fluctuation, and temperature fluctuation.

[0174] S3. Based on the turbulent average flow information and the turbulent fluctuation information, generate turbulent boundary layer inlet information.

[0175] In practical applications of this embodiment, S1 specifically includes:

[0176] S11. Average velocity under Van Driest transformation Incoming flow velocity Incoming flow temperature Temperature at the wall surface Wall friction speed The distribution of average velocity U is obtained by using formulas (1), (2), and (3).

[0177] Formula (1) is:

[0178] (1).

[0179] Formula (2) is:

[0180] (2).

[0181] Formula (3) is:

[0182] (3).

[0183] The average velocity under the Van Driest transform; for , dimensionless form; y is the wall normal coordinate; Let y be the dimensionless form of the wall normal coordinate; This represents the boundary layer thickness under the Van Driest transform; C1 is the first preset constant. b is the second preset constant; b is the third preset constant;

[0184] d is the fourth preset constant; C is the fifth preset constant; This is the sixth preset constant.

[0185] in, ; ;

[0186] This indicates the Mach number of the incoming flow. This represents the incoming flow velocity. U is the average velocity; r is the recovery factor.

[0187] Specific heat ratio; Indicates the incoming flow temperature; Indicates the temperature at the wall surface; The velocity is the wall friction velocity.

[0188] S12. Based on the average velocity U, obtain the average temperature using formula (4). Distribution;

[0189] The formula (4) is:

[0190] (4);

[0191] in,

[0192] ;

[0193] This represents the average temperature.

[0194] T aw To restore temperature.

[0195] S13, based on the average temperature The average density is obtained using formula (5). .

[0196] The formula (5) is:

[0197] (5).

[0198] in, The incoming flow density; The average density.

[0199] In the practical application of this embodiment, the second preset constant The value of the first preset constant is 11; the value of the third preset constant b is 0.33; the value of the fourth preset constant d is 0.41; the value of the fifth preset constant C is 5.6; the value of the first preset constant C1 is (-log(0.41) / 0.41)+5.6; the value of the sixth preset constant is 11; the value of the third preset constant b is 0.33; the value of the fourth preset constant d is 0.41; the value of the fifth preset constant C is 5.6; the value of the sixth preset constant C1 is (-log(0.41) / 0.41)+5.6; the value of the sixth preset constant C1 is 11; the value of the third preset constant b is 0.33; the value of the fourth preset constant d is 0.41; the value of the fifth preset constant C is 5.6; the value of the first preset constant C1 is (-log(0.41) / 0. The value is 0.45.

[0200] In the practical application of this embodiment, the value of the recovery factor r is greater than 0.8 and less than 1; the specific heat ratio The value is 1.4.

[0201] In practical applications of this embodiment, S2 specifically includes:

[0202] For any given three-dimensional energy spectrum It can be discretized into many single chips. The combination of can be expressed by the formula:

[0203] (twenty one);

[0204] Where k represents the space wavenumber, This represents the Dirichlet function.

[0205] For the m-th energy spectrum Its corresponding pulsation velocity It can be represented as:

[0206] (twenty two);

[0207] spectral frequency It follows a normal distribution. Let j represent the coordinate value in the j-direction, and t represent a certain moment. , where 'a' is a random number uniformly distributed between 0 and 1.

[0208] Consider the continuity equation:

[0209] (twenty three);

[0210] This represents the pulsating velocity component in the i-direction.

[0211] Analysis shows that for incompressible flow, the condition of zero divergence can be strictly guaranteed, that is:

[0212] (twenty four).

[0213] The above equation allows the continuity equation to be automatically satisfied.

[0214] For compressible flows, since the density varies, the effect of compressibility on mass conservation must be considered. This means that the mass flux divergence must be zero under compressible conditions.

[0215] (25);

[0216] Decomposing equation (25) yields:

[0217] (26);

[0218] The synthesis obtained from equation (22) Substituting the expression into equation (26), we obtain equation (27):

[0219] (27);

[0220] Equations (25) and (27) are equivalent, which means that satisfying equation (27) satisfies the condition that the mass flux divergence is zero. Therefore, a non-zero unit vector H is constructed to introduce the compressibility effect into the stochastic synthetic turbulence algorithm:

[0221] ;

[0222] in, This is a source of compressibility effects.

[0223] Construct the following random number vector and ,in, , .

[0224] like Figure 9 As shown, it can first be assumed that Together with k, they form a plane A, whose normal vector is H. and (Use the diagram consistently) (represented by) is the preset first random number vector. and the preset second random number vector (Use the diagram consistently) (represented by) the components after subtracting the components in the normal direction from each of the components, and thus... and Being within plane A means that the newly generated random number vector and and k and p are coplanar with A. Furthermore, according to the expressions for p and q, p is in... In the direction of the normal to plane B, which is jointly determined by k and q, q is located... In the direction of the normal to plane C, which is jointly determined by p and k, A, B, and C clearly represent the same plane, which we will name D. Therefore, p and q are both perpendicular to the plane. Since k is perpendicular to the mass flux, equation (27) is satisfied, and thus equation (27) holds. In summary, the condition that the mass flux divergence is zero under compressible conditions is satisfied, thus enabling the DSRFG method, which was originally only applicable to incompressible flows, to be developed into a general method applicable to flows from incompressible to strongly compressible. It should be noted that in all previous random generation methods for compressible turbulence, no constraint was made on the zero mass flux divergence. This caused the introduced velocity disturbance to accumulate and form a mass source term, which in turn caused the disturbance to be distorted and affected the subsequent evolution of the flow. The method for generating wide-velocity turbulent boundary layer inlet information in this embodiment makes this constraint for the first time and proposes a generation algorithm that satisfies this constraint, completely solving the problem that the introduced random velocity disturbance does not strictly satisfy the mass conservation condition of compressibility. This is also the key technology that enables the method for generating wide-velocity turbulent boundary layer inlet information in this embodiment to shorten the transition zone length by 2 / 3 compared to existing schemes.

[0225] S21. Based on the preset first random number vector , preset second random number vector density gradient The wavenumber vector k and the turbulent energy spectrum E(k) are m energy spectra pre-divided into multiple slices. Formula (6) is used to obtain the magnitude of the velocity fluctuation at time t at each point in the computational domain. ;

[0226] The formula (6) is:

[0227] (6);

[0228] in,

[0229] .

[0230] .

[0231] .

[0232] .

[0233] .

[0234] .

[0235] .

[0236] The expected value is 0 and the variance is . The angular frequency of a normal distribution; x represents the coordinate vector corresponding to a point in the computational domain; k m Represents the characteristic scale of wavenumber space; The first random number vector is preset; This is a pre-defined second random number vector; Represents the gradient operator; The density gradient is represented by k; the wavenumber vector is represented by k. It represents the wavenumber vector of the nth mode in the mth wavenumber space; It is the m-th energy spectrum among the multiple energy spectra into which the pre-obtained turbulent energy spectrum E(k) is divided;

[0237] The length scale of turbulence is represented; m is the number of turbulence spectrum slices in wavenumber space; n represents the nth mode; N represents the set number of modes; k max The maximum wave number set; represents the value used to make the wavenumber space dimensionless; a is a random number uniformly distributed between 0 and 1.

[0238] S22. Regarding the magnitude of velocity fluctuations at each point in space at time t. Using pre-acquired turbulence intensity-velocity fluctuation distribution curves, the magnitude of velocity fluctuations at each point in space at time t is determined. Polynomial fitting is performed to obtain the distribution pattern of velocity fluctuations within the turbulent boundary layer.

[0239] S23. Measure the magnitude of the velocity fluctuations at each point in the space at time t. By combining the velocity fluctuation distribution pattern within the turbulent boundary layer, the velocity fluctuations are obtained. .

[0240] S24, according to the speed pulsation Average velocity U, average temperature The temperature fluctuation is obtained using formula (7).

[0241] The formula (7) is:

[0242] (7);

[0243] in, It's a temperature fluctuation.

[0244] S25, according to the temperature fluctuation Average temperature Average density Density pulsation is obtained using formula (8).

[0245] The formula (8) is:

[0246] (8);

[0247] It is a density pulsation.

[0248] In the practical application of this embodiment, the turbulent energy spectrum E(k) in S21 is obtained according to the von Karman spectral model.

[0249] In the von Karman spectral model, for uniform isotropic turbulence, the expression for the spectral function corresponding to the flow direction is Equation (9), the expression for the spectral function corresponding to the wall normal is Equation (10), and the expression for the spectral function corresponding to the spanwise direction is Equation (11).

[0250] The formula (9) is:

[0251] (9);

[0252] I u Indicates the turbulence intensity in the direction of flow.

[0253] L u The turbulent integral scale representing the flow direction.

[0254] f represents frequency. Where k is the wave number.

[0255] Turbulent energy spectrum function representing the direction of flow.

[0256] The formula (10) is:

[0257] (10);

[0258] I v This represents the turbulence intensity in the direction normal to the wall.

[0259] L v The integral scale of turbulence is represented by the wall normal.

[0260] The turbulent energy spectrum function represents the direction of the wall normal.

[0261] The formula (11) is:

[0262] (11);

[0263] I w This indicates the spanwise turbulence intensity.

[0264] L w Represents the spanwise integral scale of turbulence.

[0265] This represents the spanwise turbulent energy spectrum function.

[0266] In the von Karman spectral model, for non-uniform anisotropic turbulence, the expression for the spectral function corresponding to the flow direction is Equation (12), the expression for the spectral function corresponding to the spanwise direction is Equation (13), and the expression for the spectral function corresponding to the wall normal is Equation (14).

[0267] The formula (12) is:

[0268] (12).

[0269] The formula (13) is:

[0270] (13).

[0271] The formula (14) is:

[0272] (14).

[0273] In the practical application of this embodiment, the turbulence intensity I u Value, span I w The value of the wall normal velocity I v The values ​​are all preset.

[0274] The turbulent integral scale L in the direction of flow u The value of the spanwise turbulence integral scale L w The value of the wall-normal turbulent integral scale Lv The values ​​are all preset.

[0275] In practical applications of this embodiment, S3 specifically includes:

[0276] S31, based on the average velocity U and the velocity fluctuation The inlet velocity of the turbulent boundary layer is synthesized using formula (15).

[0277] The formula (15) is:

[0278] (15);

[0279] u is the inlet velocity of the turbulent boundary layer.

[0280] S32, based on the average density and the density pulsation The inlet density of the turbulent boundary layer is synthesized using formula (16).

[0281] The formula (16) is:

[0282] (16);

[0283] The This represents the inlet density of the turbulent boundary layer.

[0284] S33, Based on the average temperature and the temperature fluctuations The inlet temperature of the turbulent boundary layer is synthesized using formula (17).

[0285] The formula (17) is:

[0286] (17);

[0287] T is the inlet temperature of the turbulent boundary layer.

[0288] S34, Based on the turbulent boundary layer inlet density , inlet velocity u of turbulent boundary layer, average density Average temperature The inlet energy of the turbulent boundary layer is obtained by using formula (18).

[0289] Formula (18) is as follows:

[0290] (18);

[0291] Where e is the inlet energy of the turbulent boundary layer.

[0292] R is the universal gas constant, with a value of 286.9 J / (kg·K).

[0293] In practical applications of this embodiment, the method further includes:

[0294] S4. Based on the turbulent boundary layer inlet information, the turbulent boundary layer is simulated using the large eddy simulation method or the direct numerical simulation method, and the simulation results are obtained.

[0295] The turbulent boundary layer inlet information includes: turbulent boundary layer inlet density, turbulent boundary layer inlet velocity, turbulent boundary layer inlet temperature, and turbulent boundary layer inlet energy.

[0296] In the practical application of this embodiment, the value of the recovery factor r is equal to 0.9.

[0297] Specific example: Large eddy simulation of a flat plate turbulent boundary layer with a Mach number of 2.33 and a Reynolds number of 2540 based on momentum thickness.

[0298] Constructing a three-dimensional computational domain, such as Figure 2 As shown, the computational domain size used is The number of grids is Near the wall, the mesh is refined with equal lengths in both the flow and spanwise directions. The dimensionless mesh spacings in the flow and spanwise directions are respectively... The dimensionless first-layer mesh spacing of the wall normal is The computational accuracy is 4th order, the number of solution points in the computational domain is 5.25 million, the wall adopts adiabatic boundary conditions, the spanwise boundary conditions are periodic boundary conditions, the upper surface of the computational domain adopts far-field boundary conditions or slip wall boundary conditions, the inlet is supersonic inlet conditions, the outlet is supersonic pressure outlet conditions, and the location where the turbulent boundary layer inlet conditions are applied has been marked in the figure.

[0299] Generate a random number file in .txt text format. Select the von Karman spectrum as the input spectrum and choose 200 spectral sample points with a frequency range of 1,000 to 200,000.

[0300] The turbulence intensities chosen for the flow direction, wall normal, and spanwise directions are 0.07, 0.0338, and 0.047, respectively, and the turbulence scale is 0.6 times the thickness of the inlet turbulent boundary layer.

[0301] The method for generating wide-velocity-domain turbulent boundary layer inlet information from this embodiment is run on a GPU to achieve high-precision large eddy simulation of the turbulent boundary layer, and the simulation results are as follows: Figure 3-7 As shown, where Figure 3 The vorticity isosurface based on the Q criterion (colored with u) Figure 3 Appearing in This represents the distance between the flow inlet and the location where true turbulence develops. This indicates the given laminar boundary layer thickness. Figure 4 The distribution of turbulent velocity fluctuations. Figure 5 For the average velocity distribution, Figure 6 The distribution of wall friction coefficient, Figure 7 This presents the spectrum of the downstream flow and compares it with theoretical empirical formulas and other numerical simulation results. Figure 4-7 It can be seen that the results obtained by the current method agree well with those obtained by other methods. Figure 3 and Figure 6 As can be seen, the distance from the flow inlet to the location where the real turbulence is obtained is reduced by about 2 / 3 compared to the typical methods implemented in existing literature.

[0302] The present invention provides a method for generating inlet conditions for a wide-velocity-domain turbulent boundary layer. During the generation process, turbulent physical quantities are decomposed into mean flow information and fluctuation information. Therefore, the generation process mainly includes three aspects: generating mean flow information, fluctuation information, and synthesizing inlet information for the turbulent boundary layer. In the process of generating fluctuation information, the influence of flow compressibility is considered through formula (14). (As can be seen from formula 14, since the turbulence generation process at each point is independent, it is suitable for GPU parallel computing, meaning that the flow information at each point within the inlet turbulent boundary layer can be obtained simultaneously without waiting, which helps improve computational efficiency.) This largely solves the problem of excessively long transition zones in turbulent boundary layer simulation.

[0303] The technical solution proposed in this invention takes into account the influence of flow compressibility, which effectively solves the problem of excessively long transition zones in turbulent boundary layer simulation. By adopting the parallel principle of GPU, it achieves high computational efficiency with fewer computing resources. While ensuring computational accuracy, it significantly shortens the distance from the flow inlet to the location of the true turbulence. The form of the input spectrum can be varied, making it easy to implement. It also has good parallel performance, meets the conditions for application, and can be integrated into existing industrial fluid calculation software.

[0304] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0305] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions.

[0306] It should be noted that any reference numerals placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In claims that enumerate several means, several of these means may be embodied by the same hardware. The use of the terms first, second, third, etc., is merely for convenience of expression and does not indicate any order. These terms can be understood as part of the component names.

[0307] Furthermore, it should be noted that in the description of this specification, the terms "one embodiment," "some embodiments," "embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0308] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the claims should be interpreted to include both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0309] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, then this invention should also include these modifications and variations.

Claims

1. A method for generating inlet information of a wide-velocity-domain turbulent boundary layer, characterized in that, S1. Average velocity under Van Driest transformation Incoming flow velocity Incoming flow temperature Temperature at the wall surface Wall friction speed To obtain turbulent average flow information; The turbulent average flow information includes: average velocity, average density, and average temperature; S2, based on the preset first random number vector The preset second random number vector density gradient The wavenumber vector k and the turbulent energy spectrum E(k) are m energy spectra pre-divided into multiple slices. The process involves acquiring turbulent fluctuation information, including velocity fluctuations, density fluctuations, and temperature fluctuations. Specifically, S2 includes: S21. Based on the preset first random number vector The preset second random number vector density gradient The wavenumber vector k and the turbulent energy spectrum E(k) are the m-th energy spectrum of a pre-divided multi-slice array. Formula (6) is used to obtain the magnitude of the velocity fluctuation at time t at each point in the computational domain. ; The formula (6) is: （6）； in, ; ; ； ； ； ； ； The expected value is 0 and the variance is . The angular frequency of a normal distribution; x represents the coordinate vector corresponding to a point in the computational domain; k m Represents the characteristic scale of wavenumber space; The first random number vector is preset; This is a pre-defined second random number vector; Represents the gradient operator; The density gradient is represented by k; the wavenumber vector is represented by k. It represents the wavenumber vector of the nth mode in the mth wavenumber space; It is the m-th energy spectrum among the multiple energy spectra into which the pre-obtained turbulent energy spectrum E(k) is divided; The length scale of turbulence is represented; m is the number of turbulence spectrum slices in wavenumber space; n represents the nth mode; N represents the set number of modes; k max The maximum wavenumber set; This represents the value used to make the wavenumber space dimensionless; a is a random number uniformly distributed between 0 and 1; S22. Regarding the magnitude of velocity fluctuations at each point in space at time t. Using pre-acquired turbulence intensity-velocity fluctuation distribution curves, the magnitude of velocity fluctuations at each point in space at time t is determined. Polynomial fitting is performed to obtain the distribution pattern of velocity fluctuations within the turbulent boundary layer; S23. Measure the magnitude of the velocity fluctuations at each point in the space at time t. By combining the velocity fluctuation distribution pattern within the turbulent boundary layer, the velocity fluctuations are obtained. ; S24, according to the speed pulsation Average velocity U, average temperature The temperature fluctuation is obtained using formula (7); formula (7) is: ;in, It's a temperature fluctuation; Indicates the Mach number of the incoming flow; Specific heat ratio; S25, according to the temperature fluctuation Average temperature Average density Density pulsation is obtained using formula (8); formula (8) is: (8); Density pulsation; S3. Based on the turbulent average flow information and the turbulent fluctuation information, generate turbulent boundary layer inlet information.

2. The method according to claim 1, characterized in that, S1 specifically includes: S11. Average velocity under Van Driest transformation Incoming flow velocity Incoming flow temperature Temperature at the wall surface Wall friction speed The distribution of average velocity U is obtained by using formulas (1), (2), and (3). Formula (1) is: （1）； Formula (2) is: （2）； Formula (3) is: （3）； The average velocity under the Van Driest transform; for Dimensionless form; y is the normal coordinate of the wall; Let y be the dimensionless form of the wall normal coordinate; Indicates the boundary layer thickness under the Van Driest transform; C1 is the first preset constant; This is the second preset constant; b is the third preset constant; d is the fourth preset constant; C is the fifth preset constant; This is the sixth preset constant; in, ; ; Indicates the incoming flow velocity; U represents the average velocity; r is the recovery factor; Indicates the incoming flow temperature; Indicates the temperature at the wall surface; The wall friction speed; S12. Based on the average velocity U, obtain the average temperature using formula (4). Distribution; The formula (4) is: （4）； in, ； Average temperature; T aw To restore temperature; S13, based on the average temperature The average density is obtained using formula (5). ; The formula (5) is: （5）； in, The incoming flow density; The average density.

3. The method according to claim 2, characterized in that, The second preset constant The value is 11; The value of the third preset constant b is 0.33; The value of the fourth preset constant d is 0.41; The value of the fifth preset constant C is 5.6; The value of the first preset constant C1 is (-log(0.41) / 0.41)+5.6; The sixth preset constant The value is 0.

45.

4. The method according to claim 2, characterized in that, The value of the recovery factor r is greater than 0.8 and less than 1; The specific heat ratio The value is 1.

4.

5. The method according to claim 4, characterized in that, The turbulent energy spectrum E(k) in S21 is obtained according to the von Karman spectral model; In the von Karman spectral model, for uniform isotropic turbulence, the expression for the spectral function corresponding to the flow direction is Equation (9), the expression for the spectral function corresponding to the wall normal is Equation (10), and the expression for the spectral function corresponding to the spanwise direction is Equation (11). The formula (9) is: （9）； I u indicates the turbulence intensity of the flow L u integral scale of turbulence representing the direction of flow; f represents frequency. Where k is the wave number; Turbulent energy spectrum function indicating flow direction; The formula (10) is: （10）； I v represents the wall-normal turbulent intensity; L v represents the turbulent integral scale of the wall normal direction; The turbulent energy spectrum function representing the wall normal; The formula (11) is: （11）； I w Indicates the spanwise turbulence intensity; L w Represents the spanwise integral scale of turbulence; The spanwise turbulent energy spectrum function; In the von Karman spectral model, for non-uniform anisotropic turbulence, the expression for the spectral function corresponding to the flow direction is Equation (12), the expression for the spectral function corresponding to the spanwise direction is Equation (13), and the expression for the spectral function corresponding to the wall normal is Equation (14). The formula (12) is: （12）； The formula (13) is: （13）； The formula (14) is: （14）。 6. The method according to claim 5, characterized in that, The turbulence intensity I u Value, span I w The value of the wall normal velocity I v The values ​​are all preset; The turbulent integral scale L in the direction of flow u The value of the spanwise turbulence integral scale L w The value of the wall-normal turbulent integral scale L v The values ​​are all preset.

7. The method according to claim 6, characterized in that, S3 specifically includes: S31, based on the average velocity U and the velocity fluctuation The inlet velocity of the turbulent boundary layer is synthesized using formula (15); The formula (15) is: （15）； u is the inlet velocity of the turbulent boundary layer; S32, based on the average density and the density pulsation The inlet density of the turbulent boundary layer is synthesized using formula (16); The formula (16) is: （16）； The This represents the inlet density of the turbulent boundary layer. S33, based on the average temperature and the temperature fluctuations The inlet temperature of the turbulent boundary layer is synthesized using formula (17); The formula (17) is: （17）； T is the inlet temperature of the turbulent boundary layer; S34, Based on the turbulent boundary layer inlet density , inlet velocity u of turbulent boundary layer, average density Average temperature The inlet energy of the turbulent boundary layer is obtained by formula (18); Formula (18) is as follows: （18）； Where e is the inlet energy of the turbulent boundary layer; R is the universal gas constant, with a value of 286.9 J / (kg·K).

8. The method according to claim 7, characterized in that, The method further includes: S4. Based on the turbulent boundary layer inlet information, the turbulent boundary layer is simulated using the large eddy simulation method or the direct numerical simulation method, and the simulation results are obtained. The turbulent boundary layer inlet information includes: turbulent boundary layer inlet density, turbulent boundary layer inlet velocity, turbulent boundary layer inlet temperature, and turbulent boundary layer inlet energy.

9. The method according to claim 8, characterized in that, The value of the recovery factor r is equal to 0.9.

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