Method and device for predicting wall friction coefficient of turbulent boundary layer, and storage medium

Abstract

The application relates to a method and device for predicting a wall friction coefficient of a turbulent boundary layer and a storage medium. The application obtains basic parameters of the turbulent boundary layer in a target scene and constructs a power function relationship between the adverse pressure gradient and the wall friction coefficient. Then, the target pressure gradient, the target boundary layer displacement thickness and the target wall shear stress of the target scene collected in real time are used to calculate the target adverse pressure gradient of the turbulent boundary layer at the current time. Finally, the power function relationship is used to predict the target wall friction coefficient of the turbulent boundary layer under the target adverse pressure gradient. The strong coupling effect of the adverse pressure gradient on the wall friction is directly taken into account in the calculation framework, the problem of velocity profile distortion caused by the neglect of the adverse pressure gradient in the traditional scheme based on the wall law is solved, and the prediction error of the wall friction coefficient is reduced. Moreover, high prediction accuracy can be maintained even in a complex geometric scene.

Description

Technical Field

[0001] This application relates to the fields of fluid mechanics and aerodynamics, specifically to a method, apparatus, and storage medium for predicting the wall friction coefficient of a turbulent boundary layer. Background Technology

[0002] The wall friction coefficient is a core parameter in fluid mechanics, characterizing the shear stress generated by viscosity in a fluid near a solid wall. This parameter directly impacts critical engineering issues such as fluid drag prediction, turbulent boundary layer structure analysis, aircraft / ship drag reduction design, and pipeline efficiency optimization. Particularly in computational fluid dynamics, the wall friction coefficient is a crucial input for setting boundary conditions in turbulence models, and its accuracy directly determines the reliability of flow field simulations. Therefore, developing high-precision and adaptable methods for calculating the wall friction coefficient is of great significance for improving industrial design and simulation capabilities. Traditional methods for predicting the wall friction coefficient typically assume the flow is in equilibrium, making it difficult to characterize effects such as boundary layer thickening and velocity profile distortion under adverse pressure gradients. Consequently, they exhibit significant shortcomings in the presence of pressure gradients (especially adverse pressure gradients), leading to severe distortion in the calculated wall friction coefficient and consequently, low reliability in turbulence model flow field simulations. Summary of the Invention

[0003] The purpose of this application is to provide a method, apparatus and storage medium for predicting the wall friction coefficient of turbulent boundary layer, in order to solve the problem of low accuracy in traditional methods for predicting the friction force of turbulent boundary layer.

[0004] To achieve the above objectives, the first aspect of this application provides a method for predicting the wall friction coefficient of a turbulent boundary layer, comprising:

[0005] Obtain the basic parameters of the turbulent boundary layer in the target scene, and construct a power function relationship between the adverse pressure gradient and the wall friction coefficient of the turbulent boundary layer in the target scene based on the basic parameters;

[0006] The target pressure gradient, target boundary layer displacement thickness, and target wall shear stress of the turbulent boundary layer in the target scenario are obtained in real time through numerical simulation or experimental measurement.

[0007] The target adverse pressure gradient of the turbulent boundary layer at the current moment is calculated based on the target pressure gradient, the target boundary layer displacement thickness, and the target wall shear stress.

[0008] The target wall friction coefficient of the turbulent boundary layer under the target adverse pressure gradient is predicted based on the power function relationship.

[0009] A second aspect of this application provides a device for predicting the wall friction coefficient of a turbulent boundary layer, comprising:

[0010] A construction module is used to obtain the basic parameters of the turbulent boundary layer in the target scene, and to construct a power function relationship between the adverse pressure gradient and the wall friction coefficient of the turbulent boundary layer in the target scene based on the basic parameters;

[0011] The acquisition module is used to acquire, in real time, the target pressure gradient, target boundary layer displacement thickness, and target wall shear stress of the turbulent boundary layer in the target scene through numerical simulation or experimental measurement.

[0012] The calculation module is used to calculate the target adverse pressure gradient of the turbulent boundary layer at the current moment based on the target pressure gradient, the target boundary layer displacement thickness, and the target wall shear stress.

[0013] The prediction module is used to predict the target wall friction coefficient of the turbulent boundary layer under the target adverse pressure gradient based on the power function relationship.

[0014] A third aspect of this application provides a computer-readable storage medium storing a program that can be loaded by a processor and executed by the above-described method for predicting the wall friction coefficient of a turbulent boundary layer.

[0015] The beneficial effects of this application are:

[0016] This application obtains the fundamental parameters of the turbulent boundary layer in the target scenario and constructs a power function relationship between the adverse pressure gradient and the wall friction coefficient. Then, by real-time acquisition of the target pressure gradient, target boundary layer displacement thickness, and target wall shear stress in the target scenario, the target adverse pressure gradient of the turbulent boundary layer at the current moment is calculated. Finally, the target wall friction coefficient of the turbulent boundary layer under the target adverse pressure gradient is predicted based on the constructed power function relationship. This application directly incorporates the strong coupling effect of the adverse pressure gradient on wall friction into the calculation framework, reducing the problem of velocity profile distortion caused by neglecting the adverse pressure gradient in empirical formulas based on the wall law in traditional schemes, and reducing the prediction error of the wall friction coefficient. Furthermore, it does not rely on a closed turbulence model or a high-precision near-wall network; through direct calculation of the fundamental parameters, it reduces the interference of numerical noise on the results and maintains high prediction accuracy even in complex geometric scenarios.

[0017] Other features and advantages of this application will be described in detail in the following detailed description section. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating a method for predicting the wall friction coefficient of a turbulent boundary layer provided in this application embodiment;

[0019] Figure 2This is a schematic diagram of a power function fitting curve for a turbulent boundary layer provided in a specific embodiment of this application;

[0020] Figure 3 This is a schematic diagram of the structure of a device for predicting the wall friction coefficient of a turbulent boundary layer provided in an embodiment of this application. Detailed Implementation

[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] In the description of this application, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this application, "a plurality of" means two or more, unless otherwise explicitly specified. In this application, the term "exemplary" is used to mean "used as an example, illustration, or description." Any embodiment described as "exemplary" in this application is not necessarily to be construed as being more preferred or advantageous than other embodiments. The following description is provided to enable any person skilled in the art to implement and use this application. In the following description, details are set forth for illustrative purposes. It should be understood that those skilled in the art will recognize that this application can be implemented without using these specific details. In other instances, well-known structures and processes will not be described in detail to avoid unnecessary detail that would obscure the description of this application. Therefore, this application is not intended to be limited to the embodiments shown, but is consistent with the broadest scope of the principles and features disclosed in this application.

[0023] Figure 1 This is a flowchart illustrating a method for predicting the wall friction coefficient of a turbulent boundary layer provided in an embodiment of this application. Figure 1 As shown, this prediction method may include steps 101-104, which will be described in detail below.

[0024] Step 101: Obtain the basic parameters of the turbulent boundary layer in the target scene, and construct a power function relationship between the adverse pressure gradient and the wall friction coefficient of the turbulent boundary layer in the target scene based on the basic parameters.

[0025] The target scenario refers to a typical engineering scenario where the method of this application is applicable to a turbulent boundary layer with an adverse pressure gradient. This is typically a scenario with tail flow and a high proportion of frictional drag, because tail shape changes easily generate adverse pressure gradients, requiring accurate prediction of the wall friction coefficient for design optimization. As an example, the target scenario of this application can include: the turbulent boundary layer at the tail of an aircraft, the turbulent boundary layer at the tail of a ship, and the turbulent boundary layer at the tail of an underwater vehicle. The turbulent boundary layer at the tail of an aircraft refers to the turbulent boundary layer at the tail of the aircraft fuselage and wings, characterized by a strong adverse pressure gradient in high-speed airflow. The turbulent boundary layer at the tail of a ship refers to the turbulent boundary layer at the tail of the ship and near the propeller, with water as the medium, characterized by low-speed, high Reynolds number flow, generating an adverse pressure gradient due to tail shape changes. The turbulent boundary layer at the tail of an underwater vehicle can include the turbulent boundary layer at the tail of a submarine or torpedo, with water as the medium, characterized by weak to strong adverse pressure gradients under fully submerged flow and low-noise design requirements.

[0026] The basic parameters are the original data used to construct the power function relationship. They need to be strongly matched with the flow characteristics of the target scenario to ensure the model's adaptability to the actual scenario. Based on the above target scenario, the basic parameters of the turbulent boundary layer in the target scenario are obtained from at least one of the following: numerical simulation results of the turbulent boundary layer at the tail of an aircraft, the tail of a ship, or the tail of an underwater vehicle; measurement data of the turbulent boundary layer at the tail of an aircraft model or the tail of a ship model in a wind tunnel test; and measurement data of the turbulent boundary layer of an underwater vehicle model in a water tunnel test.

[0027] Numerical simulation results refer to the simulation of the turbulent boundary layer of a target scenario using computational fluid dynamics, such as wall analytical large eddy simulation (WRLES) solving the Navier-Stokes equations and Reynolds-averaged Navier-Stokes equations (RANS), outputting flow field data and extracting parameters. Wind tunnel test measurement data refers to the measurement of pressure distribution and velocity gradient of the tail boundary layer using pressure sensors and hot-wire anemometers on a scaled-down aircraft or ship model built in a wind tunnel, which is then converted into basic parameters. Water tunnel test measurement data refers to the measurement of parameters of the tail turbulent boundary layer using particle image velocimetry and wall shear force sensors on a scaled-down underwater vehicle model in a water tunnel. Obtaining basic parameters by combining numerical simulation and experimental measurements ensures comprehensive data coverage across various target scenarios. This combined approach is applicable at different stages of engineering design, reducing reliance on a single data source.

[0028] The basic parameters of this application's embodiments are directly derived from simulations or experiments of similar scenarios, ensuring that the power function relationship can accurately capture the scenario-specific flow patterns, providing a standardized tool for predicting the wall friction coefficient under adverse pressure gradients, reducing the cost of repetitive research and development, and lowering prediction errors.

[0029] Step 102: Obtain the target pressure gradient, target boundary layer displacement thickness, and target wall shear stress of the turbulent boundary layer in the target scenario in real time through numerical simulation or experimental measurement.

[0030] For actual flow processes in target scenarios, such as the turbulent boundary layer at the tail of an aircraft during flight or the water flow boundary layer at the tail of a ship during navigation, target parameters can be obtained by acquiring data in real time through numerical simulation or experimental measurements. Numerical simulation dynamically calculates the current flow state and outputs real-time flow data. Experimental measurements directly measure pressure distribution, velocity gradient, etc., near the wall using sensors, and convert these into target parameters.

[0031] The target parameters in this embodiment may include the target pressure gradient, the target boundary layer displacement thickness, and the target wall shear stress. The target pressure gradient refers to the rate of pressure change along the flow direction at the current moment. The target displacement boundary layer is the mainstream velocity deficit thickness required for low-velocity fluid to be displaced into the mainstream from within the thickness boundary layer; it characterizes the degree of interference caused by the boundary layer's displacement effect on the mainstream at the current moment. The target wall shear stress refers to the frictional stress between the wall and the fluid at the current moment. Real-time acquisition of these target parameters can reflect the instantaneous changes in the flow state, solving the problem that traditional static models are difficult to adapt to dynamic scenarios. It is compatible with numerical simulation and experimental measurement, allowing for the selection of different acquisition methods based on the target scenario to meet different needs. Direct data acquisition for the target scenario can reduce parameter deviations caused by scenario differences, providing high-quality data input for subsequent adverse pressure gradient calculations.

[0032] Step 103: Calculate the target adverse pressure gradient of the turbulent boundary layer at the current moment based on the target pressure gradient, the target boundary layer displacement thickness, and the target wall shear stress.

[0033] The target adverse pressure gradient is a parameter characterizing the strength of the adverse pressure gradient in the turbulent boundary layer at the current moment. Its magnitude directly reflects the degree of non-equilibrium in the flow; for example, the larger the target adverse pressure gradient, the easier it is for the flow to separate. Integrating the three real-time acquired target parameters into a dimensionless target adverse pressure gradient reduces the input dimension of subsequent predictions and lowers computational complexity. The magnitude of the target adverse pressure gradient can intuitively reflect the current adverse pressure gradient strength, facilitating rapid judgment of the flow state. Furthermore, as an input to the power function, it can provide suitable parameters for calculating the wall friction coefficient, ensuring the consistency of the model.

[0034] Step 104: Predict the target wall friction coefficient of the turbulent boundary layer under the target adverse pressure gradient based on the power function relationship.

[0035] The target wall friction coefficient is a dimensionless parameter characterizing the frictional resistance between the wall and the fluid. It is a core indicator for evaluating flow resistance and optimizing design. The smaller the target wall friction coefficient, the lower the frictional resistance. By inputting the target adverse pressure gradient into the power function relationship constructed in step 101, the target wall friction coefficient at the current moment can be obtained through back-calculation. This eliminates the need to repeatedly solve equations or rely on complex models; the result can be obtained solely through algebraic operations, reducing computation time and meeting the real-time requirements of engineering projects.

[0036] This application directly incorporates the strong coupling effect of the adverse pressure gradient on wall friction into the computational framework, reducing the problem of velocity profile distortion caused by neglecting the adverse pressure gradient in the empirical formula based on the wall law in traditional schemes, and lowering the prediction error of the wall friction coefficient. Furthermore, it does not rely on a closed turbulence model or a high-precision near-wall network; by directly calculating the basic parameters, it reduces the interference of numerical noise on the results, maintaining high prediction accuracy even in complex geometric scenarios.

[0037] In step 101, multiple sets of basic parameters of the turbulent boundary layer in the target scenario can be acquired offline. Before real-time prediction, parameters covering multiple operating conditions of the target scenario can be pre-collected through numerical simulation or experiments as training data for constructing power function relationships. For example, the operating conditions corresponding to the target scenario can cover variables such as different incoming flow velocities and tail shape. Pressure gradient, boundary layer displacement thickness, and wall shear stress are extracted under each operating condition to form a basic database containing hundreds to thousands of data sets, ensuring coverage of the full range of data, including weak, moderate, and strong adverse pressure gradients.

[0038] Then, based on the fundamental parameters, the sample adverse pressure gradient and the sample wall friction coefficient are calculated, and multiple sets of sample data pairs are obtained based on these parameters. Both the sample adverse pressure gradient and the sample wall friction coefficient are calculated based on the fundamental parameters, and these two parameters can form multiple sets of sample data pairs, each corresponding to the flow state under a specific operating condition. These sample data pairs transform the fundamental parameters into dimensionless parameter pairs with more clearly defined physical meanings, directly characterizing the relationship between the adverse pressure gradient intensity and the wall friction drag.

[0039] Finally, the least squares method was used to fit multiple sets of sample data pairs to obtain the power function relationship between the adverse pressure gradient and the wall friction coefficient of the turbulent boundary layer in the target scenario. Least squares fitting is a mathematical optimization method that minimizes the squared error between the actual data and the model predictions to solve for the coefficients of the power function, ensuring a good fit to the sample data. The power function relationship is a nonlinear quantitative mapping between the adverse pressure gradient and the wall friction coefficient, and its form is determined by the flow characteristics of the target scenario.

[0040] For example, suppose It is the inverse pressure gradient. Let the wall friction coefficient be a power function that satisfies the following formula: Where A, B, and C are the fitting coefficients. Using sample data pairs as input, the values ​​of the fitting coefficients can be solved using the least squares method. During the fitting process, the goodness of fit can be verified to ensure that the power function relationship accurately reflects the nonlinear relationship between the adverse pressure gradient and the wall friction coefficient, so that the wall friction coefficient can be quickly calculated based on the real-time calculated adverse pressure gradient.

[0041] This application's embodiments cover the target scenario's operating conditions with multiple sets of basic parameters, reducing the model's limitations caused by single operating conditions. The inclusion of strong adverse pressure gradient samples solves the problem of traditional empirical formulas failing under strong adverse pressure gradients, ensuring the power function relationship maintains high accuracy across the entire adverse pressure gradient range. Sample data pairs are directly calculated based on flow parameters, preserving the coupling relationship between the adverse pressure gradient and the wall friction coefficient, reducing overfitting or distortion of physical meaning caused by pure mathematical fitting. The least squares optimization process ensures the minimum average error of the overall data, improving prediction stability compared to local fitting methods. By combining offline fitting with online invocation of the power function relationship, complex flow field analysis and parameter calculations are pre-processed as a one-time calculation. In the real-time prediction stage, only parameter input and solution are required, eliminating the need to repeatedly process massive amounts of basic data, improving computational efficiency and meeting the real-time requirements of rapid response in engineering projects.

[0042] Taking the acquisition of multiple sets of fundamental parameters from offline data through numerical simulation as an example, the target scene can first be numerically simulated. The Navier-Stokes (NS) equations can be solved using computational fluid dynamics methods to obtain the flow field data of the turbulent boundary layer in the target scene. For example, a three-dimensional geometric model including tail details can be constructed using fluid dynamics methods, dividing it into structured and unstructured networks. Then, boundary conditions are set, such as inflow velocity, pressure, and no-slip conditions at the walls. By solving the three-dimensional incompressible or compressible NS equations, steady-state or transient flow field data can be obtained. The output flow field data can include, but is not limited to, global pressure and velocity fields, with the velocity and pressure distribution near the walls being the core data for extracting fundamental parameters.

[0043] Then, based on the flow field data, sample pressure gradient, sample boundary layer displacement thickness, and sample wall shear stress of the turbulent boundary layer are extracted. The sample pressure gradient is a sample of the pressure rate along the flow direction; a positive value indicates an adverse pressure gradient, which is a key factor leading to flow separation. The sample boundary layer displacement thickness is a sample of the mainstream velocity deficit thickness required for low-velocity fluid within the boundary layer to be displaced into the mainstream, reflecting the degree of boundary layer interference with the mainstream. The sample wall shear stress is a sample of the frictional stress between the wall and the fluid, determined by both fluid viscosity and wall velocity; its magnitude affects the wall friction coefficient.

[0044] As an example, the dynamic viscosity coefficient of the fluid and the tangential velocity gradient along the wall can be obtained from the flow field data. The dynamic viscosity coefficient can be determined based on the fluid type and operating conditions; for example, the dynamic viscosity coefficient of air at 20°C under standard atmospheric pressure can be 1.81 × 10⁻⁶. -5 The dynamic viscosity coefficient of water is 1.002 × 10 Pa·s. -3 Pa·s is used as a known constant input. The tangential velocity gradient at the wall is obtained by extracting the flow velocity profile near the wall from the flow field data and calculating the gradient using the central difference method.

[0045] Then, based on the dynamic viscosity coefficient and flow velocity gradient, the shear stress on the sample wall is calculated, reflecting the frictional intensity between the wall and the fluid. The shear stress on the sample wall can be calculated using the following formula:

[0046] ;

[0047] in, For the shear stress of the sample wall, The dynamic viscosity coefficient is... This represents the flow velocity gradient.

[0048] As another example, we can obtain the streamwise velocity at a set height above the wall in the flow field data, as well as the potential velocity at the outer edge of the turbulent boundary layer. The streamwise velocity is extracted from the flow field data along the wall normal (y-direction), i.e., the streamwise velocity values ​​at different heights y. The potential velocity at the outer edge of the boundary layer is the velocity at the outer edge of the boundary layer; the upper limit of integration is actually taken to... The location.

[0049] Then, based on the flow velocity at the set height of the wall and the potential flow velocity at the outer edge of the turbulent boundary layer, the sample boundary layer displacement thickness is calculated. The sample boundary layer displacement thickness can be calculated using the following formula:

[0050] ;

[0051] in, The sample boundary layer displacement thickness, Wall height The flow velocity at that location, The velocity is the potential flow velocity at the outer edge.

[0052] Finally, multiple sets of fundamental parameters are determined based on the sample pressure gradient, sample boundary layer displacement thickness, and sample wall shear stress. The pressure distribution along the flow direction (x-direction) is extracted from the flow field data. The average pressure near the wall within the boundary layer is taken, and the sample pressure gradient is calculated using the first-order difference method. Under each operating condition, the extracted sample pressure gradient, sample boundary layer displacement thickness, and sample wall shear stress are combined to form a set of fundamental parameters. Ultimately, a fundamental parameter library covering multiple operating conditions can be constructed based on these multiple sets of fundamental parameters.

[0053] The embodiments of this application are based on numerical simulations that strictly adhere to the fundamental laws of fluid mechanics, resulting in flow field data that more closely approximates real flow compared to estimates obtained using empirical formulas. The calculation of sample wall shear stress and sample boundary layer displacement thickness employs fluid mechanics definitions, ensuring physical consistency of parameters, reducing errors introduced by human assumptions, and improving the accuracy of basic parameter calculations. Numerical simulations can flexibly set extreme or difficult-to-experiment conditions to obtain fundamental parameters that are difficult to cover in traditional experiments, making them particularly suitable for non-equilibrium flow scenarios such as strong adverse pressure gradients, thus solving the problem of limited sensor placement in traditional experiments.

[0054] In this embodiment, the sample adverse pressure gradient and sample wall friction coefficient can be calculated based on fundamental parameters to construct multiple sets of sample data pairs. The sample adverse pressure gradient is a comprehensive quantitative indicator of the influence of the turbulent boundary layer. Its physical meaning is the ratio of the product of the boundary layer displacement thickness and the pressure gradient to the wall shear stress. It only reflects whether the adverse pressure gradient or the wall friction force dominates, and is a key indicator for judging whether the flow tends to separate. The sample wall friction coefficient is a standardized measure of wall friction resistance. By correlating the wall shear stress with the incoming flow pressure, the influence of operating parameters such as fluid density and velocity is eliminated, making the friction resistance comparable under different operating conditions in different target scenarios.

[0055] As an example, the sample inverse pressure gradient can be calculated using the following formula:

[0056] ;

[0057] in, For the sample inverse pressure gradient, The sample boundary layer displacement thickness, The shear stress on the sample wall, the The sample pressure gradient is calculated based on the extracted baseline data. When the sample pressure gradient is positive, the sample reverse pressure gradient increases with the increase of the sample pressure gradient or the sample boundary layer displacement thickness, and decreases with the increase of the sample wall shear stress, directly quantifying the proportion of the reverse pressure gradient intensity relative to the wall friction effect.

[0058] As another example, the sample wall friction coefficient can be obtained through the following steps. First, obtain the sample inflow density and sample inflow velocity from the flow field data. The sample inflow velocity is the mainstream velocity unaffected by the boundary layer. Then, calculate the sample wall friction coefficient based on the sample wall shear stress, the sample inflow density, and the square of the sample inflow velocity. The sample wall friction coefficient can be calculated using the following formula:

[0059] ;

[0060] in, The coefficient of friction of the sample wall. For the shear stress of the sample wall, For the sample flow density, The original flow velocity. The ratio of the sample wall shear stress to the incoming flow pressure is called the sample wall friction coefficient, which is a dimensionless parameter that characterizes the ratio of the wall shear stress to the incoming flow pressure.

[0061] The sample adverse pressure gradient and sample wall friction coefficient are based on classical definitions in fluid mechanics, rather than purely mathematical variables. This ensures that the sample data accurately reflects the physical laws of flow and reduces the likelihood of mathematically plausible but physically contradictory power functions in subsequent fitting. For example, an abnormal increase in the wall friction coefficient may occur as the adverse pressure gradient increases. Both the sample adverse pressure gradient and sample wall friction coefficient are dimensionless parameters, eliminating the influence of dimensions such as length, velocity, and density on the data. This allows for comparative analysis of adverse pressure gradients and wall friction coefficients from different target scenarios within a single power function model, eliminating the need for separate modeling for different media or scales. Furthermore, it is easier for engineers to understand and use, requiring no complex dimension conversions, thus improving the engineering applicability of this prediction method.

[0062] In one specific embodiment, experiments have shown that the relationship between the wall friction coefficient and the adverse pressure gradient under an adverse pressure gradient can be expressed as follows: . Figure 2 This is a schematic diagram of a power function fitting curve for a turbulent boundary layer provided in a specific embodiment of this application. Figure 2 As shown, taking a turbulent boundary layer with an adverse pressure gradient as an example, the horizontal axis represents the friction coefficient, and the vertical axis represents the adverse pressure gradient. Orange dots represent coarse-grid simulation data with lower resolution, used for rapid calculation. Blue squares represent fine-grid simulation data; the finer mesh provides higher accuracy in the near-wall region, resulting in results closer to real flow. The characteristic locations along the flow direction (x is the flow direction coordinate, D is the characteristic length of the target scene, such as the model diameter) reflect the evolution of the adverse pressure gradient with the flow direction. The R-squared value, 0.9516, indicates that the power function relationship explains 95.16% of the data, demonstrating excellent fitting performance. Figure 2The negative correlation between the adverse pressure gradient and the wall friction coefficient is intuitively presented. When the adverse pressure gradient increases, the wall friction coefficient decreases significantly. The consistency between fine-mesh and coarse-mesh data verifies the stability and universality of the power function relationship. The prediction method of this application is used to calculate the wall friction coefficient under adverse pressure gradient conditions, especially in regions with strong adverse pressure gradients, where the accuracy is significantly improved. Furthermore, the power function relationship is used to... and A curve is fitted, and the wall friction coefficient can be quickly calculated based on the fitted formula.

[0063] Figure 3 This is a schematic diagram of the structure of a device 300 for predicting the wall friction coefficient of a turbulent boundary layer provided in an embodiment of this application. Figure 3 As shown, the prediction device 300 may include a construction module 301, an acquisition module 302, a calculation module 303, and a prediction module 304. The construction module 301 acquires the basic parameters of the turbulent boundary layer in the target scenario and constructs a power function relationship between the adverse pressure gradient and the wall friction coefficient of the turbulent boundary layer in the target scenario based on these basic parameters. The acquisition module 302 acquires the target pressure gradient, target boundary layer displacement thickness, and target wall shear stress of the turbulent boundary layer in the target scenario in real time through numerical simulation or experimental measurement. The calculation module 303 calculates the target adverse pressure gradient of the turbulent boundary layer at the current moment based on the target pressure gradient, target boundary layer displacement thickness, and target wall shear stress. The prediction module 304 predicts the target wall friction coefficient of the turbulent boundary layer under the target adverse pressure gradient based on the power function relationship.

[0064] The construction module 301 may include an acquisition unit, a pairing unit, and a fitting unit. The acquisition unit is used to acquire multiple sets of basic parameters of the turbulent boundary layer in the target scene, acquired offline. The pairing unit is used to calculate the sample adverse pressure gradient and sample wall friction coefficient based on the basic parameters, and obtain multiple sets of sample data pairs based on the sample adverse pressure gradient and the sample wall friction coefficient. The fitting unit is used to fit the multiple sets of sample data pairs using the least squares method to obtain the power function relationship between the adverse pressure gradient and the wall friction coefficient of the turbulent boundary layer in the target scene.

[0065] The acquisition unit is also used to perform numerical simulations of the target scene, solve the Navier-Stokes equations using computational fluid dynamics methods, and obtain flow field data of the turbulent boundary layer in the target scene; based on the flow field data, extract the sample pressure gradient, sample boundary layer displacement thickness, and sample wall shear stress of the turbulent boundary layer; and determine multiple sets of basic parameters based on the sample pressure gradient, sample boundary layer displacement thickness, and sample wall shear stress.

[0066] Specifically, the acquisition unit is also used to acquire the dynamic viscosity coefficient of the fluid in the flow field data, as well as the flow velocity gradient along the wall tangentially; based on the dynamic viscosity coefficient and the flow velocity gradient, the sample wall shear stress is calculated; the sample wall shear stress is calculated using the following formula:

[0067] ;

[0068] in, For the shear stress of the sample wall, The dynamic viscosity coefficient, This represents the flow velocity gradient.

[0069] The acquisition unit is also used to acquire the flow velocity at a set height above the wall and the potential velocity at the outer edge of the turbulent boundary layer from the flow field data; based on the flow velocity at the set height above the wall and the potential velocity at the outer edge of the turbulent boundary layer, the sample boundary layer displacement thickness is calculated; the sample boundary layer displacement thickness is calculated using the following formula:

[0070] ;

[0071] in, The sample boundary layer displacement thickness, Wall height The flow velocity at that location, The velocity is the potential flow velocity at the outer edge.

[0072] In this embodiment, the sample inverse pressure gradient is calculated using the following formula:

[0073] ;

[0074] in, For the sample inverse pressure gradient, The sample boundary layer displacement thickness, The shear stress on the sample wall, the The pressure gradient is the sample pressure gradient.

[0075] The group unit is also used to acquire the sample inflow density and sample inflow velocity from the flow field data; based on the sample wall shear stress, the sample inflow density, and the square of the sample inflow velocity, the sample wall friction coefficient is calculated; the sample wall friction coefficient is calculated using the following formula:

[0076] ;

[0077] in, The coefficient of friction of the sample wall. For the shear stress of the sample wall, For the sample flow density, The sample inflow velocity.

[0078] In this embodiment, the power function relationship satisfies the following formula:

[0079] ;

[0080] in, It is the inverse pressure gradient. Let be the wall friction coefficient, and A, B, and C be the fitting coefficients, respectively.

[0081] In this application embodiment, the target scenario may include: the turbulent boundary layer at the tail of an aircraft, the turbulent boundary layer at the tail of a ship, and the turbulent boundary layer at the tail of an underwater vehicle.

[0082] The basic parameters of the turbulent boundary layer in the target scenario obtained in the construction module 301 are derived from at least one of the following: numerical simulation results of the turbulent boundary layer at the tail of an aircraft, the tail of a ship, or the tail of an underwater vehicle; measurement data of the turbulent boundary layer at the tail of an aircraft model or the tail of a ship model in a wind tunnel test; and measurement data of the turbulent boundary layer of an underwater vehicle model in a water tunnel test.

[0083] This application also provides a computer-readable storage medium storing a program that can be loaded and executed by a processor. This program is one of the methods for predicting the wall friction coefficient of a turbulent boundary layer in this application. Those skilled in the art will understand that all or part of the functions of the various methods in the above embodiments can be implemented in hardware or by a computer program. When all or part of the functions in the above embodiments are implemented by a computer program, the program can be stored in a computer-readable storage medium, which may include: read-only memory, random access memory, disk, optical disk, hard disk, etc. The computer executes the program to achieve the above functions. For example, the program can be stored in the device's memory. When the processor executes the program in the memory, all or part of the above functions can be achieved. Alternatively, when all or part of the functions in the above embodiments are implemented by a computer program, the program can also be stored in a server, another computer, disk, optical disk, flash drive, or portable hard drive, etc. It can be downloaded or copied to the local device's memory, or the local device's system can be updated. When the processor executes the program in the memory, all or part of the functions in the above embodiments can be achieved.

[0084] The above examples illustrate this application only to aid understanding and are not intended to limit its scope. Those skilled in the art to which this application pertains can make various simple deductions, modifications, or substitutions based on the ideas presented.

Claims

1. A method for predicting the wall friction coefficient of a turbulent boundary layer, characterized in that, include: Acquire multiple sets of basic parameters of the turbulent boundary layer in the target scene obtained offline; Based on the aforementioned basic parameters, the sample reverse pressure gradient and the sample wall friction coefficient are calculated, and multiple sets of sample data pairs are obtained based on the sample reverse pressure gradient and the sample wall friction coefficient. The least squares method is used to fit multiple sets of sample data pairs to obtain the power function relationship between the adverse pressure gradient of the turbulent boundary layer and the wall friction coefficient in the target scene; The target pressure gradient, target boundary layer displacement thickness, and target wall shear stress of the turbulent boundary layer in the target scenario are obtained in real time through numerical simulation or experimental measurement. The target adverse pressure gradient of the turbulent boundary layer at the current moment is calculated based on the target pressure gradient, the target boundary layer displacement thickness, and the target wall shear stress. Based on the power function relationship, the target wall friction coefficient of the turbulent boundary layer under the target adverse pressure gradient is predicted. The sample inverse pressure gradient is calculated using the following formula: ； in, The inverse pressure gradient of the sample, The sample boundary layer displacement thickness, For the sample wall cut For the sample pressure gradient; The calculation of the sample wall friction coefficient based on the aforementioned basic parameters includes: Obtain the sample inflow density and sample inflow velocity from the flow field data; The coefficient of friction of the sample wall is calculated based on the shear stress of the sample wall, the sample flow density, and the square of the sample flow velocity. The coefficient of friction of the sample wall surface is calculated using the following formula: ； in, The coefficient of friction of the sample wall is given. The shear stress on the sample wall is... The sample flow density, The sample inflow velocity.

2. The prediction method according to claim 1, characterized in that, The acquisition of multiple sets of basic parameters of the turbulent boundary layer in the target scene obtained offline includes: Numerical simulation is performed on the target scenario, and the Navier-Stokes equations are solved using computational fluid dynamics methods to obtain the flow field data of the turbulent boundary layer in the target scenario. Based on the flow field data, the sample pressure gradient, sample boundary layer displacement thickness, and sample wall shear stress of the turbulent boundary layer are extracted. Multiple sets of basic parameters are determined based on the sample pressure gradient, the sample boundary layer displacement thickness, and the sample wall shear stress.

3. The prediction method according to claim 2, characterized in that, Based on the flow field data, the sample wall shear stress of the turbulent boundary layer is extracted, including: Obtain the dynamic viscosity coefficient of the fluid and the tangential velocity gradient of the wall in the flow field data; The shear stress on the sample wall is calculated based on the dynamic viscosity coefficient and the flow velocity gradient. The shear stress on the sample wall is calculated using the following formula: ； in, The shear stress on the sample wall is... The dynamic viscosity coefficient is... The flow velocity gradient is given.

4. The prediction method according to claim 2, characterized in that, Based on the flow field data, the sample boundary layer displacement thickness of the turbulent boundary layer is extracted, including: Obtain the flow velocity at a set height from the wall in the flow field data, and the potential flow velocity at the outer edge of the turbulent boundary layer; The displacement thickness of the sample boundary layer is calculated based on the flow velocity at the set height of the wall and the potential flow velocity at the outer edge of the turbulent boundary layer. The sample boundary layer displacement thickness is calculated using the following formula: ； in, The sample boundary layer displacement thickness, Wall height The flow velocity at that location, The outer edge potential flow velocity is given.

5. The prediction method according to claim 1, characterized in that, The power function relationship satisfies the following formula: ； in, The inverse pressure gradient, Let be the wall friction coefficient, and A, B, and C be the fitting coefficients, respectively.

6. The prediction method according to any one of claims 1 to 5, characterized in that, The target scenarios include: the turbulent boundary layer at the tail of an aircraft, the turbulent boundary layer at the tail of a ship, and the turbulent boundary layer at the tail of an underwater vehicle. The multiple sets of basic parameters of the turbulent boundary layer in the target scene acquired offline are derived from at least one of the following: Numerical simulation results of the turbulent boundary layer at the tail of the aircraft, the turbulent boundary layer at the tail of the ship, or the turbulent boundary layer at the tail of the underwater vehicle; Measurement data of the turbulent boundary layer at the tail of an aircraft model or a ship model during wind tunnel testing; and Measurement data of the turbulent boundary layer of an underwater vehicle model during a water tunnel test.

7. A device for predicting the wall friction coefficient of a turbulent boundary layer, characterized in that, include: A construction module is used to acquire multiple sets of basic parameters of the turbulent boundary layer in the target scene collected offline; calculate the sample adverse pressure gradient and sample wall friction coefficient based on the basic parameters, and obtain multiple sets of sample data pairs based on the sample adverse pressure gradient and the sample wall friction coefficient; fit the multiple sets of sample data pairs using the least squares method to obtain the power function relationship between the adverse pressure gradient and the wall friction coefficient of the turbulent boundary layer in the target scene; The acquisition module is used to acquire, in real time, the target pressure gradient, target boundary layer displacement thickness, and target wall shear stress of the turbulent boundary layer in the target scene through numerical simulation or experimental measurement. The calculation module is used to calculate the target adverse pressure gradient of the turbulent boundary layer at the current moment based on the target pressure gradient, the target boundary layer displacement thickness, and the target wall shear stress. The prediction module is used to predict the target wall friction coefficient of the turbulent boundary layer under the target adverse pressure gradient based on the power function relationship. The sample inverse pressure gradient is calculated using the following formula: ； in, The inverse pressure gradient of the sample, The sample boundary layer displacement thickness, For the sample wall cut For the sample pressure gradient; The calculation of the sample wall friction coefficient based on the aforementioned basic parameters includes: Obtain the sample inflow density and sample inflow velocity from the flow field data; The coefficient of friction of the sample wall is calculated based on the shear stress of the sample wall, the sample flow density, and the square of the sample flow velocity. The coefficient of friction of the sample wall surface is calculated using the following formula: ； in, The coefficient of friction of the sample wall is given. The shear stress on the sample wall is... The sample flow density, The sample inflow velocity.

8. 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 6 for the method of predicting the wall friction coefficient of the turbulent boundary layer.

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