Turbulent boundary layer inner and outer region normalization method and device and storage medium

Abstract

The invention relates to a turbulence boundary layer inner and outer region normalization method and device and a storage medium. The method comprises the following steps: firstly, determining an outer zone scale based on the thickness of a turbulent boundary layer, time-average axial velocity distribution and edge velocity; and then calculating a local shear stress parameter based on the dynamic viscosity, the local axial velocity gradient and the wall shear stress. And calculating by adopting a set normalization formula to obtain the target speed loss after normalization processing. A local shear stress parameter based on a local axial velocity gradient is introduced, so that the correction force for velocity loss can be enhanced, and the divergence phenomenon of an inner section is effectively inhibited. Meanwhile, the local shear stress parameter of the outer region tends to be a constant due to the stable velocity gradient, and it is ensured that the velocity loss profile of the outer region keeps good self-similarity. Therefore, according to the turbulence boundary layer inner and outer region normalization method, inner region divergence reduction and outer region good self-similarity maintenance can be taken into consideration, so that the normalization precision of the inner and outer regions of the turbulence boundary layer is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fluid mechanics, in particular to a method and device for normalizing inner and outer regions of a turbulent boundary layer and a storage medium. BACKGROUND

[0002] In the tail contraction section of an aircraft, a ship or other vehicles, the turbulent boundary layer (TBL) is often affected by adverse pressure gradient, which leads to frequent energy exchange between the inner and outer regions of the boundary layer, and even causes flow separation. In the traditional method, the normalization of the velocity deficit of the boundary layer usually uses the edge velocity or the wall friction velocity as the characteristic scale, but these methods cannot guarantee the self-similarity of the inner and outer region velocity profiles under adverse pressure gradient conditions. In the traditional technology, the outer region scale proposed by Zagarola and Smits can improve the normalization effect of the outer region, but the inner region still has divergence problems. Therefore, the traditional normalization method of the turbulent boundary layer under adverse pressure gradient cannot adapt to the differences in flow characteristics between the inner and outer regions. SUMMARY

[0003] The purpose of the present application is to provide a method and device for normalizing inner and outer regions of a turbulent boundary layer and a storage medium, to solve the problem of low precision in normalizing the inner and outer regions of a turbulent boundary layer under traditional adverse pressure gradient.

[0004] To achieve the above-mentioned purpose, the first aspect of the present application provides a method for normalizing inner and outer regions of a turbulent boundary layer, comprising: obtaining the time-averaged axial velocity distribution, the local axial velocity gradient and the edge velocity of the turbulent boundary layer under adverse pressure gradient conditions; determining the outer region scale based on the boundary layer thickness, the time-averaged axial velocity distribution and the edge velocity of the turbulent boundary layer; calculating the local shear stress parameter based on the dynamic viscosity, the local axial velocity gradient and the wall shear stress; calculating the target velocity deficit after normalization by using a set normalization formula based on the local shear stress parameter, the edge velocity and the outer region scale.

[0005] The second aspect of the present application provides a device for normalizing inner and outer regions of a turbulent boundary layer, comprising: an acquisition module for acquiring the time-averaged axial velocity distribution, the local axial velocity gradient and the edge velocity of the turbulent boundary layer under adverse pressure gradient conditions; a determination module for determining the outer region scale based on the boundary layer thickness, the time-averaged axial velocity distribution and the edge velocity of the turbulent boundary layer; a calculation module for calculating the local shear stress parameter based on the dynamic viscosity, the local axial velocity gradient and the wall shear stress; a normalization module, configured to calculate a normalized target velocity deficit based on the local shear stress parameter, the edge velocity and the outer region scale according to a preset normalization formula.

[0006] The third aspect of the present application provides a computer readable storage medium, which stores a program capable of being loaded and executed by a processor to perform the method for normalizing the inner and outer regions of the turbulent boundary layer.

[0007] The present application has the following advantages: The present application first determines the outer region scale based on the thickness of the turbulent boundary layer, the time-averaged axial velocity distribution and the edge velocity. Then, the local shear stress parameter is calculated based on the dynamic viscosity, the local axial velocity gradient and the wall shear stress. Finally, the normalized target velocity deficit is calculated according to the preset normalization formula. Since the local shear stress parameter of the inner region will significantly increase with the increase of the local axial velocity gradient, the introduction of the local shear stress parameter based on the local axial velocity gradient can enhance the correction of the velocity deficit and effectively suppress the divergence of the inner region profile. At the same time, the local shear stress parameter of the outer region tends to be constant due to the stable velocity gradient, which can reduce the interference of the normalization advantage of the outer region scale and ensure the good self-similarity of the outer region velocity deficit profile. Therefore, the method for normalizing the inner and outer regions of the turbulent boundary layer can reduce the divergence of the inner region and maintain the good self-similarity of the outer region, thereby improving the accuracy of normalizing the inner and outer regions of the turbulent boundary layer.

[0008] Other features and advantages of the present application will be described in detail in the following specific embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0009] Figure 1 FIG. 1 is a flowchart of a method for normalizing the inner and outer regions of a turbulent boundary layer according to an embodiment of the present application; Figure 2 FIG. 2 is a schematic diagram of a dimensionless time-averaged axial velocity distribution under the outer region scale according to an embodiment of the present application; Figure 3 FIG. 3 is a schematic diagram of a dimensionless time-averaged axial velocity distribution under the inner region scale according to an embodiment of the present application; Figure 4 FIG. 4 is a schematic diagram of an axial average velocity deficit profile using the outer region scale according to an embodiment of the present application; Figure 5 FIG. 5 is a schematic diagram of an axial average velocity deficit profile dimensionless under the outer region scale according to an embodiment of the present application; Figure 6 FIG. 6 is a schematic diagram of an axial average velocity deficit profile under the joint action of the local shear stress parameter, the outer region scale and the edge velocity according to an embodiment of the present application; Figure 7 Fig. 1 is a structural schematic diagram of a device for normalizing inner and outer zones of a turbulent boundary layer according to an embodiment of the present application. DETAILED DESCRIPTION

[0010] The technical solutions in the embodiments of the present application will be clearly and completely described in connection with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person skilled in the art without creative work fall within the scope of protection of the present application.

[0011] In the description of the present application, it should be understood that the terms "first", "second" are used only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more of the features. In the description of the present application, the meaning of "multiple" is two or more, unless otherwise specifically limited. In the present application, the word "exemplary" is used to mean "serving as an example, instance, or illustration". Any embodiment described as "exemplary" in the present application is not necessarily to be construed as preferred or advantageous over other embodiments. In order to enable any person skilled in the art to implement and use the present application, the following description is given. In the following description, details are listed for the purpose of explanation. It should be understood that a person skilled in the art can realize the present application without using these specific details. In other examples, well-known structures and processes will not be described in detail to avoid unnecessary details making the description of the present application obscure. Therefore, the present application is not intended to be limited to the embodiments shown, but is consistent with the broadest scope consistent with the principles and features disclosed in the present application.

[0012] Figure 1 Fig. 2 is a flowchart of a method for normalizing inner and outer zones of a turbulent boundary layer according to an embodiment of the present application. As shown in the figure, the method can include steps 101-104, which will be described in detail below. Figure 1

[0013] Step 101, obtaining time-averaged axial velocity distribution, local axial velocity gradient and edge velocity of the turbulent boundary layer under adverse pressure gradient conditions.

[0014] ​Adverse pressure gradient (APG) refers to the condition that the pressure of fluid gradually increases in the flow direction, which is a typical flow characteristic of the aircraft tail section, the ship tail contraction section and other engineering scenarios. Due to the sharp velocity gradient in the inner region of the turbulent boundary layer and the relatively stable outer region, under the adverse pressure gradient condition, the flow characteristics of the inner and outer regions of the turbulent boundary layer are significantly different. Turbulent boundary layer (TBL) refers to the region near the wall surface (such as the tail of an aircraft or the tail of a ship) formed by the viscous effect of the wall surface and the turbulent fluctuations when the fluid (such as air or water) flows through the solid wall surface.

[0015] Time-averaged axial distribution velocity refers to the collection of time-averaged axial (i.e. fluid flow direction) velocities at different wall distances perpendicular to the wall surface in the turbulent boundary layer, reflecting the variation of velocity in the turbulent boundary layer with spatial position. Time-averaged axial distribution velocity is the basic data for calculating boundary layer thickness, displacement thickness and original velocity deficit.

[0016] Local axial velocity gradient refers to the rate of change of time-averaged axial velocity at a certain wall distance, which is the core parameter for describing the local flow intensity. Local axial velocity gradient is the only dynamic variable for calculating local shear stress and determines the correction characteristics of local shear stress parameters, which can reflect the non-equilibrium flow characteristics under adverse pressure gradient.

[0017] The edge velocity of the turbulent boundary layer refers to the time-averaged axial velocity of the outer edge of the boundary layer (i.e. the region where the time-averaged axial velocity no longer changes with wall distance). The edge velocity is the reference quantity for calculating the velocity deficit, and is the basis for calculating the boundary layer thickness and displacement thickness, and is also the basis for the outer region scale and normalization formula.

[0018] Therefore, time-averaged axial velocity distribution, local shear stress parameters and edge velocity are the original data support for the calculation of subsequent outer region scale and local shear stress parameters.

[0019] In step 101, the time-averaged axial velocity distribution corresponding to different wall distances can be obtained by wall-resolved large eddy simulation or experimental measurement. Wall-resolved large eddy simulation (WRLES) is a high-precision numerical simulation method that directly resolves small-scale turbulent fluctuations near the wall by densifying the grid in the near-wall region, without relying on empirical wall functions, and can accurately output flow parameters in the turbulent boundary layer. Experimental measurement refers to a method of collecting flow data through physical experiments, which is a direct means of obtaining real flow data. The wall distance is the vertical distance from the solid wall to a certain point in the fluid, which is a key geometric parameter for describing the spatial position of the boundary layer. WRLES can directly resolve turbulent fluctuations, and experimental measurement can directly collect real flow data, both of which can reduce the error caused by empirical models and ensure that the time-averaged axial velocity accurately reflects the non-equilibrium flow characteristics of the inner region with large velocity gradient and the outer region with relatively stable under adverse pressure gradient.

[0020] Then, the local axial velocity gradient is obtained by numerically differentiating the time-averaged axial velocity distribution. Since the time-averaged axial velocity usually exists in the form of discrete points (e.g., grid points from simulation output and sampling points from experimental measurement), it cannot be directly calculated by analytical derivative, and needs to be approximated by numerical methods. Therefore, after smoothing and denoising the obtained time-averaged axial velocity distribution data, the discrete point fluctuations caused by simulation numerical oscillation or experimental measurement noise can be eliminated. Then, a numerical differentiation method such as central finite difference method is used for numerical differentiation to ensure the continuity of the global local axial velocity gradient. In one example, if the time-averaged axial velocity distribution comes from WRLES simulation, the result of local axial velocity gradient can be directly output without additional numerical differentiation. If it is experimental data, it needs to be corrected by adjacent gradient consistency test to ensure compliance with the physical law under adverse pressure gradient.

[0021] Finally, the edge velocity is obtained by measuring the outer edge of the turbulent boundary layer. The outer edge of the turbulent boundary layer refers to the transition area between the turbulent boundary layer and the free stream, where the time-averaged axial velocity no longer changes significantly with the wall distance, and the influence of turbulent fluctuations has decayed to a negligible level. Based on the time-averaged axial velocity distribution data, a curve is drawn showing the change of time-averaged axial velocity with wall distance, and the starting position of the stable region of time-averaged axial velocity is found. Then, from the direction far away from the wall, the wall is traced back, and when the change rate of time-averaged axial velocity is less than or equal to a certain value, such as 1%, the position can be considered as the outer edge of the boundary layer. If experimental measurement is used, the probe or laser sheet can be directly moved to the region where the time-averaged axial velocity no longer changes to locate the outer edge position. Then, the edge velocity is detected by experimental measurement or numerical simulation, and data verification is performed to check whether the edge velocity complies with the physical law.

[0022] Step 102, determining the outer region scale based on the boundary layer thickness, the time-averaged axial velocity distribution, and the edge velocity of the turbulent boundary layer.

[0023] The conventional normalization method directly uses the edge velocity as the outer region scale. However, under the adverse pressure gradient, the outer region fluid kinetic energy is consumed by the pressure, and the velocity distribution of the outer region of the turbulent boundary layer is distorted. Therefore, only the edge velocity cannot reflect the equivalent velocity scale of the actual flow in the outer region, which easily leads to the fact that the velocity deficit profile in the outer region cannot remain self-similar. Therefore, the embodiments of the present application determine the outer region scale based on the boundary layer thickness, the time-averaged axial velocity distribution, and the edge velocity of the turbulent boundary layer, correct the edge velocity through the geometric characteristics and flow equivalent characteristics of the turbulent boundary layer, obtain the outer region normalization characteristic scale that adapts to the adverse pressure gradient condition, and solve the problem that the conventional outer region scale has poor self-similarity under the adverse pressure gradient.

[0024] In step 102, the displacement thickness of the turbulent boundary layer can be calculated based on the time-averaged axial velocity distribution and the edge velocity of the turbulent boundary layer. Then, the outer region scale is calculated based on the displacement thickness, the edge velocity, and the boundary layer thickness.

[0025] The boundary layer thickness is a geometric boundary reference of the outer region scale. The boundary layer thickness refers to the radial distance at which the turbulent fluctuation velocity decays to a set percentage of the free stream velocity, and the judgment standard is the distance from the wall when the time-averaged axial velocity is a set percentage of the edge velocity. It is a geometric characteristic scale of the turbulent boundary layer.

[0026] In an example, the time-averaged axial velocity distribution and the edge velocity can be detected. When the time-averaged axial velocity is detected to be a set percentage of the edge velocity, the distance from the wall at the current time is taken as the boundary layer thickness. Specifically, the distance from the wall that satisfies the time-averaged axial velocity being a set percentage of the edge velocity can be found based on the time-averaged axial velocity and the edge velocity, and the distance from the wall is taken as the boundary layer thickness. For example, the set percentage can be 2%. When the time-averaged axial velocity decays to 2% of the edge velocity, the influence of the turbulent fluctuation has been greatly weakened, and the fluid flow approaches the free stream state. At this time, the distance from the wall can be regarded as the physical interface between the turbulent boundary layer and the free stream.

[0027] Therefore, the boundary layer thickness is the geometric anchor for the subsequent flow resistance quantification, that is, the displacement thickness calculation delimits a clear spatial range. If there is no geometric anchoring of the boundary layer thickness, the integral calculation of the displacement thickness will result in distorted results due to no clear upper limit of integration, and therefore the boundary layer thickness is the geometric basis for ensuring the subsequent correction accuracy.

[0028] The displacement thickness is an equivalent quantitative index of the flow resistance effect of the turbulent boundary layer. In an example, the displacement thickness can satisfy the following formula: ; wherein, is the displacement thickness, is the boundary layer thickness, is the time-averaged axial velocity distribution, is the edge velocity, is the perpendicular distance from the wall.

[0029] The integral term reflects the degree of flow blockage at a certain distance from the wall. The closer to the wall, the smaller the degree of blockage, and the closer the integral term is to 0. Conversely, the closer to the wall, the greater the degree of blockage, and the closer the integral term is to 1. By integrating the integral term between 0 and 1, the blockage effects of all positions in the turbulent boundary layer are superimposed to obtain an equivalent thickness. The greater the displacement thickness, the stronger the avoidance of overall blockage to the outer zone flow. Therefore, the displacement thickness is the core bridge connecting the geometric scale and the flow characteristics, which can convert the time-averaged axial velocity distribution under adverse pressure gradient into a quantifiable physical quantity, and provide flow characteristic basis for subsequent edge velocity correction.

[0030] In an example, the outer zone scale can satisfy the following formula: .

[0031] wherein, reflects the relative strength of flow blockage, the displacement thickness is the equivalent blockage thickness, and the boundary layer thickness is the geometric total thickness. The greater the ratio of the two, the higher the proportion of blockage effect in the entire turbulent boundary layer. The outer zone scale is the product of the edge velocity and the relative strength of flow blockage, and the essence is to adapt the equivalent velocity scale of the outer zone flow under adverse pressure gradient. Under adverse pressure gradient, the relative strength increases, and the outer zone scale will be smaller than the edge velocity, which can offset the self-similarity destruction caused by the distortion of the outer zone velocity distribution. Therefore, the outer zone scale of the embodiments of the present application can solve the limitations of the traditional edge velocity, retain the free flow benchmark attribute of the edge velocity, and integrate the geometric and flow characteristics of the turbulent boundary layer itself. The scale parameter is corrected by using the characteristics of the turbulent boundary layer itself, rather than relying on external assumptions. The non-equilibrium flow under adverse pressure gradient can be accurately adapted, and the outer zone velocity loss can maintain good self-similarity under the scale, which provides reliable outer zone scale support for subsequent inner and outer zone collaborative normalization.

[0032] Step 103, calculating the local shear stress parameter based on the dynamic viscosity, the local axial velocity gradient, and the wall shear stress.

[0033] Kinematic viscosity is an inherent physical property of fluid, which reflects the ability of fluid to resist shear deformation. Wall shear stress is the shear stress at fixed wall, which is a direct embodiment of viscous action between wall and fluid, and is a reference quantity of local shear stress. Local shear stress is the shear stress at a certain spatial position in turbulent boundary layer, which is generated by fluid viscosity and turbulent fluctuations, and is a core physical quantity to describe the ability loss and shear intensity at this position.

[0034] In step 103, the local shear stress can be calculated based on the kinematic viscosity and the local axial velocity gradient. Specifically, the spatial distribution of the local axial velocity gradient is extracted, the kinematic viscosity of the fluid is determined, and the units of the local axial velocity gradient and the kinematic viscosity are unified. Then, the local shear stress is calculated at each distance from the wall by point-by-point calculation of the local axial velocity gradient according to the calculation formula of the local shear stress.

[0035] In one example, the local shear stress can satisfy the following formula: ; wherein, is the local shear stress, is the time-averaged axial velocity distribution, is the vertical distance from the wall, is the local axial velocity gradient, is the kinematic viscosity.

[0036] By taking the square root of the local axial velocity gradient, the energy distribution characteristics of turbulent fluctuations can be matched, so that the local shear stress is more consistent with the non-equilibrium flow law under adverse pressure gradient. Then, by multiplying the kinematic viscosity, the local shear stress at this position can be obtained, and finally the spatial distribution data of the local shear stress is formed, which corresponds to the local axial velocity gradient one by one.

[0037] In addition, it can also be checked whether the distribution law of the local shear stress conforms to the physical logic. For example, under the adverse pressure gradient, the local axial velocity gradient in the inner region is large, and the local shear stress increases significantly. The local axial velocity in the outer region is stable, and the local shear stress tends to be constant. If the local shear stress appears abnormal distribution, it can be traced back to the determination step of the local axial velocity gradient, and the numerical differentiation accuracy is checked to ensure the reliability of the local shear stress calculation.

[0038] Converting the local flow intensity into a quantifiable shear stress parameter provides a physically meaningful input parameter for subsequent correction of the divergent inner region. Moreover, it can adapt to the non-equilibrium flow characteristics under adverse pressure gradient, and the calculation logic is simple and has no additional cost.

[0039] Then, based on the local shear stress and the wall shear stress, the local shear stress parameter is calculated. The wall shear stress can be calculated based on the local axial velocity gradient, and the value near the wall region is extracted. Alternatively, the wall shear stress at the wall can be directly output by WRLES numerical simulation. According to the calculation formula of the local shear stress parameter, the local shear stress parameter at each distance from the wall is calculated point by point.

[0040] In one example, the local shear stress parameter satisfies the following formula: ; wherein, is the wall shear stress, is the local shear stress parameter.

[0041] The ratio of the local shear stress to the wall shear stress can reflect the relative strength of the shear stress at that position relative to the wall shear stress. Then, the cubic root of the ratio is taken, which can amplify the change range of the inner region ratio and enhance the correction strength of the inner region. At the same time, the ratio of the outer region is less affected, reducing the destruction of the characteristics of the outer region. Finally, the spatial distribution data of the local shear stress parameter is obtained, the local shear stress parameter of the inner region is greater than 1 and has a larger value, and the local shear stress parameter of the outer region is approximately equal to 1 and tends to be a constant.

[0042] In addition, the local shear stress parameter of the inner region can also be verified. If the local shear stress parameter of the inner region has an abnormal value and is too large, the calculation of the local shear stress can be checked for errors. If the local shear stress parameter of the outer region fluctuates too much, for example, more than ±5%, the accuracy of the shear stress is re-verified to ensure the stability of the local shear stress parameter in the outer region, which provides protection for the subsequent normalization of the self-similarity of the outer region.

[0043] When the local shear stress of the inner region increases, the ratio increases, and the local shear stress parameter also significantly increases, which can enhance the correction strength of the velocity deficit and offset the divergence trend caused by the change of the velocity gradient distance under the adverse pressure gradient. In this way, the inner region can be corrected specifically to solve the pain point of divergence in the inner region. At the same time, when the local shear stress of the outer region is stable and the ratio is constant, the normalization advantage of the outer region scale can be ensured to be unaffected, achieving the goal of inhibiting divergence in the inner region and preserving self-similarity in the outer region. The local shear stress parameter is a dimensionless parameter and is not affected by the fluid medium and working condition parameters, which can be adapted to different adverse pressure gradient intensities and different engineering scenarios, expanding the range of use. Moreover, the flow characteristics and the depth of the correction parameter are bound, and the parameter is obtained from the previous steps without additional cost.

[0044] Step 104, based on the local shear stress parameter, the edge velocity and the outer region scale, a set of normalization formulas are used to calculate the target velocity deficit after normalization processing.

[0045] The target velocity deficit is a normalized dimensionless velocity deficit value, which can reflect the normalized characteristics of the velocity deficit of a point in the turbulent boundary layer under adverse pressure gradient, and is used to realize the uniform self-similarity of the internal and external velocity profiles. The core parameters in the previous steps are corresponded according to the wall distance and extracted. For each wall distance, the original velocity deficit is calculated point by point, that is, the edge velocity is subtracted from the time-averaged axial velocity distribution. Then, the target velocity deficit can be obtained by calculating according to the normalization formula for each wall distance.

[0046] In one example, the set normalization formula satisfies the following formula: ; Wherein, is the target velocity deficit, is the time-averaged axial velocity distribution, is the edge velocity, is the external scale, is the local shear stress parameter.

[0047] Through experimental verification, the scaling coefficient is 2, which can optimize the coincidence accuracy of the internal and external velocity profiles, so that the coincidence degree of the normalized profile reaches the optimum. Through the product of the local shear stress parameter and the scaling coefficient, and then multiplied by the original velocity deficit, the numerator is obtained. The composite scale designed by combining the external scale and the edge velocity can reduce the problem of internal divergence or external distortion caused by a single scale. Finally, the ratio of the numerator to the denominator is the target velocity deficit at the wall distance. By integrating the target velocity deficits at all wall distances, the spatial distribution of the normalized velocity deficit can be obtained.

[0048] Through the normalization formula, the local shear stress parameter in the internal region is significantly increased, and the correction strength is amplified through the numerator, which offsets the divergence trend caused by the sharp change of the internal velocity gradient. The local shear stress parameter in the external region is approximately equal to 1 and tends to be stable, which can maintain good self-similarity, and finally realize the technical goal of high coincidence degree of internal and external profiles. The input parameters are all from the previous steps, without the need for additional experiments or simulations, the formula structure is simple, and the calculation amount is small. It can be embedded in the Computational Fluid Dynamics (CFD) software or experimental data processing system through programming, to realize the rapid application in engineering.

[0049] In the embodiments of the present application, the turbulent boundary layer under adverse pressure gradient conditions can include the turbulent boundary layer of the aircraft tail cone section or the ship tail contraction section. When the airflow passes through the tail cone, the flow passage gradually contracts from the fuselage section. When the airflow passes through the ship tail, the ship tail line type changes from wide to narrow, and the water flow passage contracts. Therefore, the flow direction of the aircraft tail cone section and the ship tail under adverse pressure gradient conditions gradually increases, which is easy to produce internal divergence, and the internal and external regions cannot be considered together.

[0050] The target velocity deficit can be applied to calculate flow parameters in a near-wall region, to predict wall friction, to verify a turbulence model in computational fluid dynamics software, to calculate a boundary layer shape factor, to provide a calculation basis, or to predict flow separation.

[0051] The velocity profile corresponding to the target velocity deficit is coincident within a distance range greater than a first set value and less than a second set value. The first set value and the second set value are a distance range for coincidence, for example, the first set value can be 0.01, and the second set value can be 1. The velocity profile corresponding to the target velocity deficit refers to a normalized velocity profile with respect to a wall distance obtained by backstepping or directly from the target velocity deficit. The relative wall distance refers to a ratio of the wall distance to the boundary layer thickness, which can uniformly describe the position of the boundary layer under different sizes and different working conditions. Through the velocity profile corresponding to the target velocity deficit, the velocity profile shapes of different interfaces are basically coincident in the whole region from the near-wall to the outer edge of the boundary layer, achieving the core effect of uniformity and self-similarity of the inner and outer regions.

[0052] The normalized method of the inner and outer regions of the turbulent boundary layer of the aircraft tail fin under an adverse pressure gradient is taken as an example. In order to explore the velocity deficit phenomenon of the turbulent boundary layer under the adverse pressure gradient, the average axial velocity profile of 9 positions on the aircraft tail fin can be taken. As shown in Figure 2 , a non-dimensionalized time-averaged axial velocity distribution diagram under the outer region scale in an embodiment of the present application is shown in Figure 2 . The time-averaged axial velocity and the wall distance are respectively and non-dimensionalized. The velocity deficit under the adverse pressure gradient is manifested as a downward shift of the average velocity profile curve, and the degree of shift gradually increases with the development of the boundary layer. The flow instability of the front end and the rear end corner of the tail fin will affect the velocity profile, so the middle 4 positions are taken for analysis. As shown in Figure 3 , a non-dimensionalized time-averaged axial velocity distribution diagram under the inner region scale in an embodiment of the present application is shown in Figure 3 . and are respectively and non-dimensionalized. The wall friction velocity and the ratio of kinematic viscosity to friction velocity are used to obtain the non-dimensionalized form. As can be seen from the figure, The velocity profiles in the inner region are coincident as a curve and basically accord with the traditional logarithmic law. However, when and the boundary layer is not out, the velocity profile curve begins to diverge, and at the same , the of the downstream boundary layer is less than that of the upstream boundary layer, which is a typical feature of the turbulent boundary layer of the inclined plate adverse pressure gradient.

[0053] The outer region scale dimensionless axial average velocity deficit profile is shown in Figure 4 . Figure 4 is a schematic diagram of the outer region scale axial average velocity deficit profile in an embodiment of the present application.

[0054] The velocity difference and the wall radial distance are dimensionless by using the edge velocity and the boundary layer thickness . Obviously, only makes the boundary position velocity deficit of / =0;1 coincide, and the velocity deficit along the flow direction between 0-1 increases, but does not make the axial average velocity deficit profile of the tail vertebrae at four positions self-similar. Further, the outer region scale is used instead of dimensionless, and the formula is as follows: .

[0055] Figure 5 is a schematic diagram of the outer region scale dimensionless axial average velocity deficit profile in an embodiment of the present application. Figure 5 The results of dimensionless are given, and when / >0.1, the velocity profile is located in the outer region of the boundary layer, i.e., outside the logarithmic region, and presents good coincidence. However, when / <0.1, the velocity profile is located in the inner region of the boundary layer, and presents a divergent state and diverges more as it is closer to the wall, can make the velocity deficit in the outer region of the boundary layer self-similar, but cannot have the same effect on the velocity deficit in the inner region.

[0056] To change the divergent trend of dimensionless in the inner region of the boundary layer, and to maintain the advantage of dimensionless in the outer region of the boundary layer, the This causes the velocity deficit at the boundary layer to coincide. Therefore, it is necessary to construct a physical parameter that takes into account the interaction between the large-scale turbulent structure in the outer region and the small-scale turbulent structure in the inner region of the boundary layer. The embodiments of this application use local shear stress within the boundary layer based on the local velocity gradient. Introducing a dimensionless dimension, the formula is as follows: .

[0057] Local shear stress The velocity gradient is large in the inner region of the boundary layer and increases closer to the wall, thus having the ability to cancel or suppress it. The dimensionless velocity deficit profile exhibits divergence in the inner region, while the velocity gradient in the outer region is small and changes slowly. The dimensionless advantage has a relatively small impact. Utilizing wall shear stress... Local shear stress within the boundary layer Perform dimensionless processing, and It is a number between 0 and 1. To amplify its effect, it is cubed to obtain a parameter based on the local velocity gradient of the boundary layer, denoted as . : .

[0058] Figure 6 This is a schematic diagram of the axial average velocity deficit profile under the combined effects of local shear stress parameters, outer zone scale, and edge velocity in a specific embodiment of this application. Figure 6 As shown, the curves can be considered to be basically overlapping, and the speed loss profile before the improvement is in / The significant divergence observed when the inequality is less than 0.1 has disappeared, and the original graph shows... / The overlap of the outer region of the boundary layer is still good even with a value >0.1, indicating that the boundary layer defined in the embodiments of this application is valid. It did indeed achieve the expected results. (See image) The curves with a value <0.1 are slightly more dispersed than those in other regions because the average velocity stability in the transition zone within the boundary layer is poor, and the calculation of the velocity slope has some uncertainty. The calculation depends on the average velocity.

[0059] Figure 7 This is a schematic diagram of a device 700 for normalizing the inner and outer regions of a turbulent boundary layer, as provided in an embodiment of this application. Figure 7 As shown, the device 700 for normalizing the inner and outer regions of the turbulent boundary layer may include an acquisition module 701, a determination module 702, a calculation module 703, and a normalization module 704.

[0060] The acquisition module 701 is configured to acquire a time-averaged axial velocity distribution, a local axial velocity gradient, and an edge velocity of a turbulent boundary layer under adverse pressure gradient conditions.

[0061] The determination module 702 is configured to determine an outer region scale based on a boundary layer thickness, the time-averaged axial velocity distribution, and the edge velocity of the turbulent boundary layer.

[0062] The calculation module 703 is configured to calculate a local shear stress parameter based on a dynamic viscosity, the local axial velocity gradient, and a wall shear stress.

[0063] The normalization module 704 is configured to calculate a normalized target velocity deficit based on the local shear stress parameter, the edge velocity, and the outer region scale by using a set normalization formula.

[0064] In the embodiments of the present application, the acquisition module 701 can include a first measurement unit, a second measurement unit, and a third measurement unit.

[0065] The first measurement unit is configured to acquire the time-averaged axial velocity distribution corresponding to different wall distances by analyzing a wall surface through a large eddy model or experimental measurement.

[0066] The second measurement unit is configured to obtain the local axial velocity gradient by numerically differentiating the time-averaged axial velocity distribution.

[0067] The third measurement unit is configured to acquire the edge velocity by measuring an outer edge of the turbulent boundary layer.

[0068] In the embodiments of the present application, the determination module 702 can include a first determination unit and a second determination unit.

[0069] The first determination unit is configured to calculate a displacement thickness of the turbulent boundary layer based on the time-averaged axial velocity distribution and the edge velocity of the turbulent boundary layer.

[0070] The second determination unit is configured to calculate the outer region scale based on the displacement thickness, the edge velocity, and the boundary layer thickness.

[0071] In the embodiments of the present application, the displacement thickness can satisfy the following formula: ; The outer region scale can satisfy the following formula: ; wherein, is the displacement thickness, is the boundary layer thickness, is the time-averaged axial velocity distribution, is the edge velocity, is the outer region scale, is a vertical distance from a wall surface.

[0072] In the embodiment of the present application, the device 700 for normalizing the inner and outer regions of the turbulent boundary layer can further comprise a determining module. The determining module is configured to In the embodiment of the present application, the determining module 702 can further comprise a detecting unit and a responding unit.

[0073] The detecting unit is configured to detect the time-averaged axial velocity distribution and the edge velocity.

[0074] The responding unit is configured to take the distance from the wall at the current time as the boundary layer thickness when the time-averaged axial velocity is detected to be a set percentage of the edge velocity.

[0075] In the embodiment of the present application, the calculating module 703 can comprise a first calculating unit and a second calculating unit.

[0076] The first calculating unit is configured to calculate the local shear stress based on the dynamic viscosity and the local axial velocity gradient.

[0077] The second calculating unit is configured to calculate the local shear stress parameter based on the local shear stress and the wall shear stress.

[0078] The local shear stress satisfies the following formula: ; The local shear stress parameter satisfies the following formula: ; wherein, is the local shear stress, is the time-averaged axial velocity distribution, is the vertical distance from the wall, is the local axial velocity gradient, is the dynamic viscosity, is the wall shear stress, is the local shear stress parameter.

[0079] In the embodiment of the present application, the set normalization formula satisfies the following formula: ; wherein, is the target velocity deficit, is the time-averaged axial velocity distribution, is the edge velocity, is the outer region scale, is the local shear stress parameter.

[0080] In the embodiments of the present application, the turbulent boundary layer under adverse pressure gradient conditions can include a turbulent boundary layer of a tail cone section of an aircraft or a tail contraction section of a ship, the target velocity deficit can be applied to computational fluid dynamics wall treatment, wall friction resistance prediction, near-wall turbulent flow model verification, boundary layer shape factor calculation or flow separation prediction, and the velocity profile corresponding to the target velocity deficit is coincident at a relative wall distance greater than a first set value and less than a second set value.

[0081] The embodiments of the present application also provide a computer readable storage medium, which stores a program capable of being loaded and executed by a processor to perform any one of the methods for normalizing inner and outer zones of a turbulent boundary layer.

[0082] Those skilled in the art can understand that all or part of the functions of the various methods in the above embodiments can be implemented in the form of hardware or in the form of a computer program. When all or part of the functions in the above embodiments are implemented in the form of a computer program, the program can be stored in a computer readable storage medium, and the storage medium can include a read-only memory, a random access memory, a magnetic disk, an optical disk, a hard disk, etc. The above functions are implemented by executing the program in a computer. For example, the program is stored in a memory of a device, and when the program in the memory is executed by a processor, the above all or part of the functions can be implemented. In addition, when all or part of the functions in the above embodiments are implemented in the form of a computer program, the program can also be stored in a server, another computer, a disk, an optical disk, a flash disk or a mobile hard disk, etc. The program is saved in a memory of a local device by downloading or copying, or the system of the local device is updated to a new version, and when the program in the memory is executed by a processor, the above all or part of the functions in the embodiments of the present application can be implemented.

[0083] The above describes the present application by applying specific examples, which is only used to help understand the present application and does not limit the present application. Those skilled in the art of the present application can make some simple deductions, deformations or substitutions according to the idea of the present application.

Claims

1. A method for normalizing the inner and outer regions of a turbulent boundary layer, characterized in that, include: Obtain the time-averaged axial velocity distribution, local axial velocity gradient, and edge velocity of the turbulent boundary layer under adverse pressure gradient conditions; The outer region scale is determined based on the boundary layer thickness of the turbulent boundary layer, the time-averaged axial velocity distribution, and the edge velocity. Local shear stress parameters are calculated based on dynamic viscosity, local axial velocity gradient, and wall shear stress. Based on the local shear stress parameters, the edge velocity, and the outer region scale, the normalized target velocity loss is calculated using a set normalization formula.

2. The method according to claim 1, characterized in that, Obtain the time-averaged axial velocity distribution, local axial velocity gradient, and edge velocity of the turbulent boundary layer under adverse pressure gradient conditions, including: The time-averaged axial velocity distribution corresponding to different distances from the wall was obtained by analyzing the large eddy model of the wall or by experimental measurement. The local axial velocity gradient is obtained by numerically differentiating the time-averaged axial velocity distribution. The edge velocity is obtained by measuring the outer edge of the turbulent boundary layer.

3. The method according to claim 1, characterized in that, The determination of the outer region scale based on the boundary layer thickness of the turbulent boundary layer, the time-averaged axial velocity distribution, and the edge velocity includes: Based on the time-averaged axial velocity distribution and the edge velocity of the turbulent boundary layer, the displacement thickness of the turbulent boundary layer is calculated. The outer region scale is calculated based on the displacement thickness, the edge velocity, and the boundary layer thickness.

4. The method according to claim 3, characterized in that, The displacement thickness satisfies the following formula: ； The outer region scale satisfies the following formula: ； in, The displacement thickness is... The boundary layer thickness is... The time-averaged axial velocity distribution is described above. The edge velocity, The outer region scale, This is the vertical distance from the wall.

5. The method according to claim 1, characterized in that, Before the step of determining the outer region scale based on the boundary layer thickness of the turbulent boundary layer, the time-averaged axial velocity distribution, and the edge velocity, the method further includes: The time-averaged axial velocity distribution and the edge velocity are detected; When the time-averaged axial velocity is detected to be a set percentage of the edge velocity, the distance from the wall at the current moment is used as the boundary layer thickness.

6. The method according to claim 1, characterized in that, The calculation of local shear stress parameters based on dynamic viscosity, local axial velocity gradient, and wall shear stress includes: Based on the dynamic viscosity and the local axial velocity gradient, the local shear stress is calculated. The local shear stress parameters are calculated based on the local shear stress and the wall shear stress. The local shear stress satisfies the following formula: ； The local shear stress parameters satisfy the following formula: ； in, For the local shear stress, The time-averaged axial velocity distribution is described above. It is the vertical distance from the wall. The local axial velocity gradient is... The dynamic viscosity, The wall shear stress is... The local shear stress parameter is given.

7. The method according to claim 1, characterized in that, The normalization formula set satisfies the following formula: ； in, For the target speed loss, The time-averaged axial velocity distribution is described above. The edge velocity, The outer region scale, The local shear stress parameter is given.

8. The method according to any one of claims 1 to 7, characterized in that, The turbulent boundary layer under the adverse pressure gradient condition includes the turbulent boundary layer of the tail section of an aircraft or the contraction section of the tail of a ship. The target velocity deficit is applied to computational fluid dynamics wall treatment, wall friction resistance prediction, near-wall turbulence model verification, boundary layer shape factor calculation, or flow separation prediction. The velocity profile corresponding to the target velocity deficit coincides within a relative wall distance greater than a first set value and less than a second set value.

9. A device for normalizing the inner and outer regions of a turbulent boundary layer, characterized in that, include: The acquisition module is used to acquire the time-averaged axial velocity distribution, local axial velocity gradient, and edge velocity of the turbulent boundary layer under adverse pressure gradient conditions. The determination module is used to determine the outer region scale based on the boundary layer thickness of the turbulent boundary layer, the time-averaged axial velocity distribution, and the edge velocity. The calculation module is used to calculate local shear stress parameters based on dynamic viscosity, local axial velocity gradient, and wall shear stress. The normalization module is used to calculate the normalized target velocity loss based on the local shear stress parameters, the edge velocity, and the outer region scale using a set normalization formula.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that can be loaded by a processor and executed as described in any one of claims 1 to 8 for normalizing the inner and outer regions of the turbulent boundary layer.

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