A method for calculating friction force suitable for any flow surface of an aircraft

Abstract

The application provides a friction force calculation method suitable for any flow wall surface of an aircraft, comprising: generating a full-area grid of the aircraft wall surface, calculating characteristic information corresponding to the grid, solving a flow field by using an adaptive solver, obtaining flow variables, and interpolating the velocity gradient of the grid cell center to the wall surface; decomposing the wall surface velocity into normal and tangential components, and directly constructing an accurate calculation formula of each axial component of the friction force by using a directional derivative mathematical analysis formula, a velocity gradient and a wall surface normal vector, so as to ensure that the friction force is strictly perpendicular to the wall surface normal; and finally outputting the friction force data for aerodynamic force integration. The application theoretically strictly ensures the perpendicularity of the wall surface friction force and the wall surface normal, solves the problems of direction deviation and inconsistent physical description existing in the prior art, does not need to reconstruct the velocity gradient twice, maintains the numerical precision, is suitable for complex working conditions such as steady flow and unsteady flow and separation flow, and provides precise support for large aircraft aerodynamic design.

Description

Technical Field

[0001] This invention relates to the field of aircraft technology, and more specifically to a method for calculating friction force applicable to any flowing wall surface of an aircraft. Background Technology

[0002] In computational fluid dynamics numerical simulations and engineering applications, the interaction between fluids and the solid walls of aircraft is one of the core research topics. Due to the viscosity of the fluid itself, when the fluid flows over the solid walls of an aircraft, it generates a frictional force along the tangential direction of the wall. This frictional force is strictly perpendicular to the normal direction of the wall and is a direct manifestation of the interaction between fluid viscosity and the solid walls of the aircraft. For aircraft moving in a fluid, this type of frictional force usually manifests as resistance to the forward motion of the aircraft. Therefore, those skilled in the art also refer to this type of frictional force, generated by the combined action of fluid viscosity and the relative motion between the fluid and the aircraft on the solid surface of the aircraft, as frictional drag.

[0003] Accurate prediction and calculation of wall friction are crucial reference data for aircraft design, directly determining the rationality of aerodynamic layout optimization and power system matching design. They also represent a current technical challenge in computational fluid dynamics. Compared to the accuracy of lift prediction, computational fluid dynamics' prediction accuracy for wall friction (frictional drag) is generally low, indicating a significant technical shortcoming. Particularly in the cruise state of large transport aircraft, prediction errors in wall friction can directly lead to substantial errors in the assessment of key technical indicators and range, severely impacting the feasibility, safety, and economy of transport aircraft design schemes, and hindering the development of aerodynamic design technology for large transport aircraft.

[0004] Currently, the commonly used method in this field for calculating wall friction is to obtain the wall friction force by directly performing a dot product operation between the viscous stress tensor and the unit normal vector of the wall. Specifically, the commonly used method for calculating the wall friction force of aircraft... The calculation method is based on the viscous stress tensor and the unit normal vector of the wall. The dot product of is specifically calculated as follows: , This calculation method seems to lack sufficient theoretical basis and cannot strictly guarantee that the direction of the wall friction force is perpendicular to the wall normal. In this case, the normal stress component of the wall... for: , The following can be easily obtained from the viscous stress constitutive equation of Stokes fluid: , Verification of wall normal stress components using existing calculation methods. Whether it is zero, the mass conservation equation in the flow equation is equivalent to: , Considering the speed on the solid surface of the aircraft u No slip condition If the flow around the aircraft is steady, then we have It is easy to see that the velocity divergence is zero on the solid wall of the aircraft, that is: , That is, for steady flow problems, the normal stress components can be further... Simplified to: , Even under the constraints of steady flow, it is difficult to guarantee that the wall friction force calculated using currently widely adopted methods is strictly perpendicular to the unit normal vector of the wall, especially since fluid flow around the solid wall of an aircraft may experience flow separation and reattachment. Based on this, some researchers have directly subtracted the component of the friction force calculated along the wall normal vector to ensure that the friction force vector is strictly perpendicular to the wall normal vector. However, this calculation method lacks a rigorous physical basis and fails to provide sufficient justification for subtracting the normal component.

[0005] Therefore, practical verification has shown that the existing calculation method has clear technical defects. It not only lacks solid theoretical support, but also cannot technically guarantee that the calculated direction of the wall friction force is strictly perpendicular to the wall normal, which is inconsistent with the physical characteristics of wall friction force in actual engineering scenarios, resulting in directional deviations in the calculation results. At the same time, the method has poor applicability in complex aircraft flow scenarios such as steady / unsteady flow and attachment / separation flow, and the calculation accuracy is difficult to meet the engineering requirements such as fine design of aircraft, thus affecting the rationality of engineering design. Summary of the Invention

[0006] The purpose of this invention is to propose a friction calculation method applicable to arbitrary flowing surfaces of aircraft. Specifically, it provides a complete calculation expression of friction force on arbitrary flowing curved surfaces of an aircraft, based on the mathematical definition of solid wall friction. The friction calculation method proposed in this invention effectively overcomes the problem of traditional methods where the friction force calculated on aircraft walls is not perpendicular to the wall normal, thus achieving accurate calculation of the friction force on solid walls of aircraft.

[0007] This invention proposes a method for calculating friction force on any flowing wall surface of an aircraft, comprising the following steps: Step 1: Calculate the generation of the computational mesh. Generate a full-area mesh around the outer wall of the aircraft to be simulated. The full-area mesh is bounded by the solid wall of the aircraft and covers all key flow areas. The full-area mesh can be a structured mesh, an unstructured mesh, or a combination of structured and unstructured meshes. Step 2: Calculation of mesh feature information. For structured meshes in the whole-region mesh, calculate their mesh transformation derivative and mesh transformation Jacobian. For unstructured meshes in the whole-region mesh, directly calculate their area and volume. Step 3: Solve the flow field, solve for the conserved variables in the Navier-Stokes equations, including velocity vector, pressure, density, temperature, energy, and viscosity coefficient, and calculate the velocity gradient. Interpolate the velocity gradient values ​​stored at the center of the computational grid cells to the solid wall grid of the aircraft to obtain the velocity gradient of the wall grid. Step 4: Calculate the wall friction force. Calculate the unit normal vector of the wall mesh, as well as the velocity vectors of the wall mesh normal and tangential directions. Calculate the wall mesh normal velocity gradient along the wall mesh normal direction based on the wall mesh velocity gradient. Calculate the solid wall friction force of the aircraft based on the wall mesh normal gradient. Step 5: Aerodynamic integration, outputting the frictional force data of the solid wall of the aircraft according to the post-processing requirements for the extraction and application of flow field characteristic data.

[0008] Preferably, step 4: calculating the wall friction force involves calculating the unit normal vector of the wall mesh, as well as the velocity vectors of the wall mesh normal and tangential directions, and calculating the wall mesh normal velocity gradient along the wall mesh normal direction based on the wall mesh velocity gradient. The solid wall friction force of the aircraft is then calculated based on the wall mesh normal gradient. The specific calculation process is as follows: 4.1: Calculate the unit normal vector of the wall mesh and the area vector of the solid wall mesh of the aircraft in Cartesian coordinates. for: ,in, , and Cartesian coordinate system The unit coordinate basis vector, , and They are area vectors respectively exist , and The projected area of ​​the direction, the area vector of the wall mesh. Normalization yields the unit normal vector of the wall mesh. for: , in, The area vector of the wall mesh The absolute value, , , for exist , and Component of direction; 4.2: Calculate the velocity vectors of the wall mesh in the normal and tangential directions, and the velocity vectors of the aircraft wall mesh. ,Will Along the wall mesh normal And tangential decomposition, to obtain the mesh normal along the aircraft wall. normal velocity vector of the wall mesh for: , in, for exist , and Components of direction, It is the normal velocity of the aircraft wall mesh, i.e., the normal velocity vector of the wall mesh. The projection component along the direction of the unit normal vector n on the wall. velocity along the tangential direction of the spacecraft wall grid for , its in , and The directional components are: , in, for exist , and Component of direction; 4.3: Based on the wall mesh velocity gradient, calculate the gradient of the wall mesh normal velocity along the wall mesh normal direction. , , 4.4: Based on the calculated normal gradient of the wall mesh, the frictional force of the solid wall of the aircraft is calculated. Each component: , satisfy That is, the frictional force of the solid wall of the aircraft. Completely perpendicular to the normal of the aircraft wall, wherein, They are respectively exist , and The directional component.

[0009] Preferably, the Navier-Stokes equation in step 3 is: , in, Let the flow field variables be those to be determined. , and They are respectively , and Convection current in the direction: , and They are respectively , and Viscous flux in the direction: , in, Represents time, Represents the density of the fluid. and They represent the fluid along , and velocity components in the direction, It is more than always , For specific heat ratio, The hydrostatic pressure is given by the fluid's equation of state. For a calorimetrically perfect gas, it has: , For temperature, The gas constant is The normal stress is in the x-direction. For the shear stress in the x and y planes, For the shear stress in the x and z planes, The normal stress is in the y-direction. For the shear stress in the y and z planes, The normal stress is in the z-direction. , , for , and Energy density flux of viscous flux in a given direction.

[0010] Preferably, step 3, the flow field solution, further includes the following steps: for the structured grid in the whole-region grid, the flow field is solved using a structured grid solver based on the finite difference method or the finite volume method; for the unstructured grid in the whole-region grid, the flow field is solved using an unstructured grid solver based on the finite volume method.

[0011] Preferably, in step 3, the calculated velocity gradient value is interpolated to the solid wall mesh of the aircraft to obtain the wall mesh velocity gradient. This includes: for a structured mesh solver based on the finite difference method, if the calculated velocity gradients are all stored at the center of the computational grid cells, the velocity gradient values ​​are interpolated to the wall mesh to obtain the wall mesh velocity gradient; for an unstructured mesh solver based on the finite volume method, the calculated velocity gradients are all stored at the center of the computational grid cells, and the velocity gradient values ​​are interpolated to the solid wall mesh to obtain the wall mesh velocity gradient.

[0012] Preferably, the key flow region in step 1 includes: the wall boundary layer region, the wing-body blending point of the aircraft, the trailing edge of the wing, the tail, and the engine nacelle where there are abrupt changes in aerodynamic shape or curvature.

[0013] To address the specific technical deficiencies of the existing technologies, this invention proposes a method for calculating friction force on arbitrary flowing walls of aircraft. Starting from the physical definition of wall friction force, this method, through clear technical logic derivation, theoretically ensures that the direction of wall friction force is strictly perpendicular to the wall normal vector, fully considering the physical characteristics of aircraft wall friction force. It is widely applicable to various actual flow problems of aircraft, such as steady / unsteady attachment or separation flows. Furthermore, this method directly calculates wall friction force based on the numerical value of the wall velocity gradient, eliminating the need to reconstruct the velocity gradient on the wall. Compared to existing methods that reconstruct the velocity gradient, this method is not only more direct but also effectively maintains the numerical discretization accuracy requirements in aircraft design, improving the accuracy of wall friction force calculation. This solves the technical problems of low accuracy, poor applicability, and inconsistency with engineering realities in existing calculation methods. It provides accurate technical data support for the aerodynamic design and range assessment of aircraft (especially large transport aircraft), possessing clear engineering practicality and technical improvement value. Attached Figure Description

[0014] To more clearly illustrate the technical solutions of this application, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a schematic diagram for calculating the friction force on the aircraft wall. Detailed Implementation

[0016] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0017] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0018] Figure 1 This is a schematic diagram for calculating the friction force on the wall of an aircraft. The friction force calculation method proposed in this invention, applicable to any flowing wall of an aircraft, includes the following steps: Step 1: Mesh Generation. A full-area mesh is generated around the outer wall of the aircraft to be simulated. The mesh is bounded by the solid wall of the aircraft and must cover all key flow regions. The mesh can be either structured or unstructured. For ease of calculation, the mesh region can be divided into blocks, with some areas being structured and others unstructured. The mesh processing calculation in this step does not affect the implementation of the friction calculation method proposed in this invention.

[0019] The critical flow region refers to the fluid flow area near the aircraft wall where fluid viscosity causes significant changes in the fluid flow state, directly and significantly influencing wall friction (frictional drag). This region is the core flow field area that determines the accuracy of friction calculations, as its flow characteristics directly govern the generation and distribution of wall friction. The criteria for identifying this region are: flow field areas in and around the aircraft wall where the velocity gradient is significant, viscous shearing is prominent, and the magnitude and distribution of wall friction are directly determined. Examples include the wall boundary layer region, and areas with significant aerodynamic changes or curvature variations, such as the wing-body blending point, wing trailing edge, tail, and engine nacelles.

[0020] Step 2: Calculation of mesh feature information. For structured meshes, the corresponding mesh transformation derivative and mesh transformation Jacobian are generally calculated. For unstructured meshes, the corresponding area and volume are generally calculated directly. The calculation method of mesh feature information in this step does not affect the implementation of the friction calculation method proposed in this invention.

[0021] Step 3: Solve the flow field. Solve for the flow field variables, which are the conserved variables in the Navier-Stokes equations (NS equations), including physical variables such as density, velocity, pressure, and temperature in the flow. The NS equations are a set of governing equations for fluid dynamics composed of conservation of mass, momentum, and energy.

[0022] For structured meshes, a structured mesh solver based on the finite difference method or the finite volume method is used to solve them. For unstructured meshes, an unstructured mesh solver based on the finite volume method is generally used to solve them.

[0023] The flow field solution process requires obtaining all velocity gradient values. For structured mesh solvers based on the finite difference method, if the calculated velocity gradients are all stored at the center of the computational mesh cells, then the velocity gradient values ​​near the wall need to be interpolated to the solid wall. Generally, for unstructured mesh solvers based on the finite volume method, the calculated velocity gradients are all stored at the center of the computational mesh cells, and the velocity gradient values ​​also need to be interpolated to the solid wall mesh.

[0024] In this step, complete flow state information can be obtained, including velocity, pressure, density, temperature or energy, and viscosity coefficient.

[0025] For ease of understanding, all relevant formulas are provided in the embodiments of this invention. Generally, the Cartesian coordinate system... The physical equations satisfied by the viscous compressible flow of the lower orbital vehicle, namely the Navier-Stokes equations, are as follows: , in For the flow field variables to be determined . Represents the density of the fluid. and They represent the fluid along , and velocity components in the direction, It is more than always . For specific heat ratio, The hydrostatic pressure is generally given by the fluid's equation of state. For calorimetrically perfect gases, it is: . For temperature, is the gas constant.

[0026] In the above equation and They are respectively , and Convection current in the direction: , and They are respectively , and Viscous flux in the direction: , And the stress constitutive equation for the viscous fluid surrounding the aircraft is: , in, The viscosity coefficient, The second viscosity coefficient, The normal stress is in the x-direction. For the shear stress in the x and y planes, For the shear stress in the x and z planes, The normal stress is in the y-direction. For the shear stress in the y and z planes, The stress is normal in the z-direction. The fluid flowing around the aircraft generally satisfies the Stokes barotropic fluid assumption: , It is easy to obtain the second viscosity coefficient. .

[0027] The energy density flux of viscous flux is: , in It is the thermal conductivity coefficient of the fluid surrounding the aircraft.

[0028] Step 4: Calculation of wall friction.

[0029] Step 4.1: First, calculate the unit normal vector of the wall mesh.

[0030] For ease of description, the embodiments of the present invention use the area vector of a grid at a certain point on the solid wall of the aircraft. Abbreviated as ,in , and Cartesian coordinate system The unit coordinate basis vector, , and They are area vectors respectively exist , and Projected area in the direction, such as Figure 1 As shown. For the area vector After normalization, the unit normal vector of the wall mesh can be obtained. for: , in, Area vector The absolute value, , , for exist , and The directional component.

[0031] Step 4.2: Calculate the velocity vectors of the wall mesh in the normal and tangential directions.

[0032] According to the definition of friction, friction is the force generated when a fluid flows over a solid surface of an aircraft. Tangential velocity on the wall Along the wall normal The gradient determines the flow of Newtonian fluid around the aircraft as follows: , Based on this Figure 1 Velocity vector near the wall grid of the mid-aircraft Along the wall normal With tangential decomposition, it is easy to obtain the normal direction of the mesh along the aircraft wall. normal velocity vector of the wall mesh for: , in, , , for exist , and directional components, It is the normal velocity of the aircraft wall mesh, i.e., the normal velocity vector of the wall mesh. The projection component along the direction of the unit normal vector n on the wall.

[0033] The velocity along the tangential direction of the spacecraft wall grid for Its components are: , in, for exist , and The directional component.

[0034] Step 4.3: Calculate the gradient of the wall mesh normal velocity along the wall normal. Based on the velocity gradient calculated in Step 3, further decompose it according to the wall direction.

[0035] aircraft wall friction The components are: , According to the mathematical definition of the directional derivative: , by For example, we can get: , Continuing with the mathematical definition of the directional derivative, the normal velocity of the aircraft wall mesh can be obtained. Along the wall normal The gradient is: , Step 4.4: Based on the calculated gradient of the wall normal velocity along the wall normal direction. The frictional force of the solid wall of the aircraft was calculated. Each portion.

[0036] This invention provides embodiments of solid wall friction for aircraft. The precise calculation formulas for each component are: , It is easy to verify that the frictional force calculated based on the above expression is completely perpendicular to the normal to the aircraft wall, that is: , Step 5: Aerodynamic integration. Output the aircraft solid wall friction data calculated in the above steps according to the post-processing requirements to facilitate the extraction and application of flow field characteristic data in the post-processing process.

[0037] The present invention has the following technical effects: (1) Since the calculation method of the aircraft wall friction force proposed in this invention is strictly based on the definition of friction force, it theoretically ensures that the direction of the wall friction force vector is strictly perpendicular to the wall normal vector, and can be applied to steady or unsteady adhesion or separation flow problems. (2) The velocity gradient is a variable that is directly solved in the process of solving the flow field of the aircraft. The friction force is calculated directly based on the velocity gradient value of the solid wall of the aircraft. Compared with the method of reconstructing the velocity gradient on the aircraft wall, the friction force calculation is more direct, can better maintain the accuracy of numerical discretization, and is more accurate.

[0038] It should be noted that, for those skilled in the art, the technical features in the above embodiments can be freely combined, and the resulting technical solutions also belong to the embodiments disclosed in this invention.

[0039] Furthermore, without departing from the principles of this invention, several improvements and modifications can be made to this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for calculating friction force on any flowing wall surface of an aircraft, characterized in that, Includes the following steps: Step 1: Calculate the generation of the computational mesh. Generate a full-area mesh around the outer wall of the aircraft to be simulated. The full-area mesh is bounded by the solid wall of the aircraft and covers all key flow areas. The full-area mesh can be a structured mesh, an unstructured mesh, or a combination of structured and unstructured meshes. Step 2: Calculation of mesh feature information. For structured meshes in the whole-region mesh, calculate their mesh transformation derivative and mesh transformation Jacobian. For unstructured meshes in the whole-region mesh, directly calculate their area and volume. Step 3: Solve the flow field, solve for the conserved variables in the Navier-Stokes equations, including velocity vector, pressure, density, temperature, energy, and viscosity coefficient, and calculate the velocity gradient. Interpolate the velocity gradient values ​​stored at the center of the computational grid cells to the solid wall grid of the aircraft to obtain the velocity gradient of the wall grid. Step 4: Calculate the wall friction force. Calculate the unit normal vector of the wall mesh, as well as the velocity vectors of the wall mesh normal and tangential directions. Calculate the wall mesh normal velocity gradient along the wall mesh normal direction based on the wall mesh velocity gradient. Calculate the solid wall friction force of the aircraft based on the wall mesh normal gradient. Step 5: Aerodynamic integration, outputting the frictional force data of the solid wall of the aircraft according to the post-processing requirements for the extraction and application of flow field characteristic data.

2. The friction calculation method applicable to any flowing wall of an aircraft according to claim 1, characterized in that, Step 4: Calculation of wall friction force. This involves calculating the unit normal vector of the wall mesh, as well as the velocity vectors of the wall mesh in the normal and tangential directions. Based on the wall mesh velocity gradient, the gradient of the wall mesh normal velocity along the wall mesh normal direction is calculated. The solid wall friction force of the aircraft is then calculated based on this gradient. The specific calculation process is as follows: 4.1: Calculate the unit normal vector of the wall mesh and the area vector of the solid wall mesh of the aircraft in Cartesian coordinates. for: ,in, , and Cartesian coordinate system The unit coordinate basis vector, , and They are area vectors respectively exist , and The projected area of ​​the direction, the area vector of the wall mesh. Normalization yields the unit normal vector of the wall mesh. for: ， in, The area vector of the wall mesh The absolute value, , , for exist , and Component of direction; 4.2: Calculate the velocity vectors of the wall mesh in the normal and tangential directions, and the velocity vectors of the aircraft wall mesh. ,Will Along the wall mesh normal And tangential decomposition, to obtain the mesh normal along the aircraft wall. normal velocity vector of the wall mesh for: ， in, for exist , and Components of direction, It is the normal velocity of the aircraft wall mesh, i.e., the normal velocity vector of the wall mesh. The projection component along the direction of the unit normal vector n on the wall. velocity along the tangential direction of the spacecraft wall grid for , its in , and The directional components are: ， in, for exist , and Component of direction; 4.3: Based on the wall mesh velocity gradient, calculate the gradient of the wall mesh normal velocity along the wall mesh normal direction. , ， 4.4: Based on the calculated normal gradient of the wall mesh, the frictional force of the solid wall of the aircraft is calculated. Each component: ， satisfy That is, the frictional force of the solid wall of the aircraft. Completely perpendicular to the normal of the aircraft wall, wherein, They are respectively exist , and The directional component.

3. The friction calculation method applicable to any flowing wall of an aircraft according to claim 1, characterized in that, The NS equation in step 3 is: ， in, Let the flow field variables be those to be determined. ， and They are respectively , and Convection current in the direction: ， and They are respectively , and Viscous flux in the direction: ， in, Represents time, Represents the density of the fluid. and They represent the fluid along , and velocity components in the direction, It is more than always , For specific heat ratio, The hydrostatic pressure is given by the fluid's equation of state. For a calorimetrically perfect gas, it has: , For temperature, The gas constant is The normal stress is in the x-direction. For the shear stress in the x and y planes, For the shear stress in the x and z planes, The normal stress is in the y-direction. For the shear stress in the y and z planes, The normal stress is in the z-direction. , , for , and Energy density flux of viscous flux in a given direction.

4. The friction calculation method applicable to any flowing wall of an aircraft according to claim 1, characterized in that, The flow field solution in step 3 further includes the following steps: for the structured mesh in the whole region mesh, the flow field is solved using a structured mesh solver based on the finite difference method or the finite volume method; for the unstructured mesh in the whole region mesh, the flow field is solved using an unstructured mesh solver based on the finite volume method.

5. The friction calculation method applicable to any flowing wall of an aircraft according to claim 1 or 4, characterized in that, In step 3, the calculated velocity gradient values ​​are interpolated to the solid wall mesh of the aircraft to obtain the wall mesh velocity gradient. This includes: for structured mesh solvers based on the finite difference method, if the calculated velocity gradients are all stored at the center of the computational grid cells, the velocity gradient values ​​are interpolated to the wall mesh to obtain the wall mesh velocity gradient; for unstructured mesh solvers based on the finite volume method, the calculated velocity gradients are all stored at the center of the computational grid cells, and the velocity gradient values ​​are interpolated to the solid wall mesh to obtain the wall mesh velocity gradient.

6. The friction calculation method applicable to any flowing wall of an aircraft according to claim 1, characterized in that, The key flow regions in step 1 include: the wall boundary layer region, the wing-body blending area of ​​the aircraft, the trailing edge of the wing, the tail, and the engine nacelle, where there are abrupt changes in aerodynamic shape or curvature.

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