CN110531619B - Method for realizing flow control - Google Patents

Method for realizing flow control Download PDF

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CN110531619B
CN110531619B CN201910804157.2A CN201910804157A CN110531619B CN 110531619 B CN110531619 B CN 110531619B CN 201910804157 A CN201910804157 A CN 201910804157A CN 110531619 B CN110531619 B CN 110531619B
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刘雪玲
汪健生
焦钰
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Tianjin University
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Abstract

The invention relates to a method for realizing flow control, which comprises a plurality of miniature wing-shaped turbulence controllers with self-adaptive deformation characteristics and an arrangement mode on the surface of a channel, wherein the miniature wing-shaped turbulence controllers are made of self-adaptive deformation, namely flexible materials, the bottom surfaces of the miniature wing-shaped turbulence controllers are fixed on the surface of the channel, are vertical to the flow direction of fluid in the channel and are arranged in a plurality of arrays, and the space between the miniature wing-shaped turbulence controllers is the statistical average width of a velocity band in a turbulence program simulating structure.

Description

Method for realizing flow control
Technical Field
The invention relates to a novel flow control technology and an implementation method thereof, wherein a miniature wing-shaped turbulence controller with self-adaptive deformation characteristics is arranged on the surface of a channel according to a certain requirement, and the reduction of flow resistance is realized by controlling a turbulence flow structure, so that the flow control technology can be widely applied to the fields of heat energy engineering, aerospace engineering and the like.
Background
The existing drag reduction technologies are many, and can be specifically divided into:
1. the method of adding other substances to the wall surface, such as surface polymer coating, micro-bubble and other drag reduction methods;
2. boundary layer control method: trying to delay or make the transition of the wall surface boundary layer larger, and adopting an elastic wall surface method, an air suction method and the like;
3. non-smooth surface method: such as a trench method, etc.
On the basis of this, methods of rib drag reduction (groove method), polymer additive method, compliant wall method, microbubble method, biomimetic drag reduction, wall vibration drag reduction, and the like have been developed.
In the existing drag reduction technology, there is a technology for reducing drag reduction by delaying transition of a boundary layer, which reduces flow resistance by fluidizing a turbulent layer, but does not directly control a quasi-sequence structure in the boundary layer in turbulence, thereby realizing the situation of flow drag reduction.
Disclosure of Invention
In order to solve the problems, overcome the defects of the prior art and combine with the bionics principle, the invention designs a novel flow control technology and an implementation method thereof, a miniature wing-shaped turbulence controller with self-adaptive deformation characteristics is arranged on the surface of a channel according to certain requirements, and the reduction of flow resistance can be realized by controlling the flow structure in a turbulence boundary layer. In order to achieve the purpose, the invention adopts the following technical scheme:
a method for realizing flow control comprises a plurality of miniature wing-shaped turbulence controllers with self-adaptive deformation characteristics and an arrangement mode on the surface of a channel, wherein the miniature wing-shaped turbulence controllers are made of self-adaptive deformation flexible materials, the bottom surfaces of the miniature wing-shaped turbulence controllers are fixed on the surface of the channel and are vertical to the flow direction of fluid in the channel, and a plurality of miniature wing-shaped turbulence controllers are arranged in an array mode, the distance between the miniature wing-shaped turbulence controllers is the statistical average width of a velocity band in a turbulence program simulating structure, and the method comprises the following steps:
the method comprises the following steps: measuring the characteristic length L (m) of the channel, the flow direction section A (m) of the channel2) Length L of the channel0(m)Width of channel Z0(m) average flow velocity Um(m/s) according to the formula of mass flow in the channel Q ═ UmA(m3S) estimated or measured density ρ (m) of the fluid3Kg) and the kinematic viscosity of the fluid, i.e., the kinematic viscosity of the fluid, i.
Figure BDA0002183147020000021
Can be calculated to determine
Figure BDA0002183147020000022
Step two: an abstract physical model of the channel is built and gridded ANSYS ICEM: using empirical formulas
Figure BDA0002183147020000023
L (m) is a characteristic length, let y+Determining the height delta y (m) of a first layer of grid on the boundary of the channel model, and obtaining a computational grid required by numerical calculation according to a grid division method on the basis of determining the first layer of grid on the boundary of the channel model;
step three:introducing the calculation grid obtained in the step two into an ANSYS Fluent, calculating by using a large-vortex numerical simulation method, keeping constant mass flow by adopting periodic boundary conditions for the boundary conditions of the inlet and the outlet of the channel, and obtaining the shear stress tau on the surface of the channel model according to the numerical simulation resultw(N/m2) The surface of the channel model is an object needing enhanced heat transfer;
step four: using shear stress tau of channel model surface in numerical simulation resultsw(N/m2) The fluid density ρ (kg/m) is known3) Calculating the frictional velocity of the surface of the channel model
Figure BDA0002183147020000024
Step five: height without dimension
Figure BDA0002183147020000025
From the kinematic viscosity v (m) of the fluid2S) and the friction speed uτ(m/s) is calculated, y (m) is the actual height, ρ (kg/m)3) Is the fluid density; y is+When 1 denotes a unit dimensionless height, use
Figure BDA0002183147020000026
To express a unit dimensionless height of 1, y1(m) to represent a unit dimensionless height
Figure BDA0002183147020000027
A corresponding actual height;
step six: and (3) designing the space between the miniature wing-shaped turbulence controllers: the motion center of the velocity bands is located in a turbulent flow near-wall region, the distance between every two adjacent spanwise velocity bands is 60-180, a lognormal probability distribution is presented, and the average spanwise distance of the bands is 100 wall surface wall units. The dimensionless distance between two adjacent wing shapes is 100, and under the distance, the two adjacent wing shapes can control a turbulence quasi-sequence structure such as a flow direction vortex, so that the flow resistance can be effectively reduced; the front ends of the wing shapes are fixed on the bottom surface along the incoming flow direction; several wing-shaped bodies are arranged along the spanwise direction, and the spanwise dimensionless distance between the adjacent wing-shaped bodies is
Figure BDA0002183147020000028
Let y+When the dimensionless distance is 100, the corresponding actual distance Δ G is y100=100y1(m) the actual spacing being the pitch of the arrangement of adjacent micro-foil turbulence controllers;
step seven: the front end of a self-adaptive deformation miniature wing-shaped turbulence controller is fixed on the bottom surface of a channel, and the front end of the self-adaptive deformation miniature wing-shaped turbulence controller is arranged in an array form along the incoming flow direction, and the distance is set to be delta G (y)100=100y1(m) arranged on the actual channel surface; the preferred wing shape is a rectangular parallelepiped sheet with a thickness of 0.2 times the unit dimensionless distance
Figure BDA0002183147020000031
Actual thickness Δ z is 0.2y1(m); length 4 times unit dimensionless distance
Figure BDA0002183147020000032
Actual length Δ x is 4y1(m); unit dimensionless distance of 23 times height
Figure BDA0002183147020000033
Actual height Δ h 23y1(m)。
Due to the adoption of the technical scheme, the invention has the following advantages:
(1) from material analysis, most of the conventional turbulence control devices are made of rigid materials and cannot generate deformation according to fluid movement, and the micro wing-shaped turbulence controller with the self-adaptive deformation characteristic can generate self-adaptive deformation along with the flow of the fluid, so that the resistance of the fluid flowing through can be reduced;
(2) from material analysis, the wing-shaped turbulence controller made of flexible materials can generate self-adaptive bending deformation phenomena aiming at different flow velocities, can adapt to variable working condition, and enables the turbulence controller to be automatically optimized and adapted to the minimum flow resistance;
(3) from the analysis of the arrangement mode, the arrangement mode of a turbulence control device for controlling turbulence has no certain basis, and certain guidance and inspiration are lacked for industrial production and scientific research; the spanwise dimensionless spacing between adjacent airfoils is 100, at which the array type micro airfoil turbulence controllers can control the flow structure and reduce the surface flow resistance;
(4) at present, some technologies for reducing resistance by delaying transition of a boundary layer exist, flow resistance is reduced by fluidizing a turbulent layer, and the flow resistance is reduced by controlling movement of a turbulent structure in a small range according to different principles.
The invention comprises two types of drag reduction types of controlling the drag reduction of a turbulent structure and reducing the flow resistance by the flexible material, thereby realizing the superposition of two drag reduction effects, and the drag reduction effect is better than that of one of the two drag reduction types which are used independently.
According to the novel flow control technology and the implementation method thereof provided by the invention, the array type self-adaptive deformation miniature wing-shaped turbulence controller with the dimensionless spacing of 100 is designed. The self-adaptive deformation can be generated along with the flow of the fluid, the turbulence sequence simulating structure can be better controlled, the surface resistance is further better reduced, and the excellent flow drag reduction effect is realized.
Drawings
FIG. 1 shows the application of adaptive shape-changing micro-airfoil turbulence controllers in a matrix arrangement in a channel flow under the recommended conditions
Figure 2 shows an enlarged view of an adaptively deformable miniature airfoil-shaped turbulence controller arranged in a preferred situation in a channel.
Fig. 3 is a deformation diagram of adaptive deformation micro wing-shaped turbulence controllers arranged in an array, and (a) - (f) are various deformation modes.
Detailed Description
The present invention will be further described with reference to specific embodiments for the purpose of facilitating an understanding of technical means, characteristics of creation, objectives and functions realized by the present invention, but the following embodiments are only preferred embodiments of the present invention, and are not intended to be exhaustive. Based on the embodiments in the implementation, other embodiments obtained by those skilled in the art without any creative efforts belong to the protection scope of the present invention. The experimental methods in the following examples are conventional methods unless otherwise specified, and materials, reagents and the like used in the following examples are commercially available unless otherwise specified.
The invention comprises a miniature wing-shaped turbulence controller body with self-adaptive deformation characteristics and an arrangement mode on the surface of a channel. The miniature wing-shaped turbulence controllers are made of self-adaptive deformation (flexible) materials, and the bottom surfaces of the miniature wing-shaped turbulence controllers are fixed on the surface of the channel, are vertical to the flow direction of fluid in the channel, and are arranged in an array manner. The micro-foil turbulence controller pitch in the present invention is the statistical average width of the velocity bands in the turbulence program structure, i.e., a unit dimensionless length of 100.
The size design and the arrangement mode of the wing-shaped turbulence controller based on the self-adaptive deformation (flexibility) comprise the following steps
The method comprises the following steps: measuring the characteristic length L (m) of the channel, the flow direction section A (m) of the channel2) Length L of the channel0(m) channel width Z0(m) average flow velocity Um(m/s) according to the formula of mass flow in the channel Q ═ UmA(m3S) estimated or measured density ρ (m) of the fluid3Kg) and the kinematic viscosity of the fluid, i.e., the kinematic viscosity of the fluid, i.
Figure BDA0002183147020000041
Can be calculated to determine
Figure BDA0002183147020000042
Step two: an abstract physical model of the channel is built and gridded ANSYS ICEM: using empirical formulas
Figure BDA0002183147020000043
L (m) is a characteristic length, let y+Determining the height delta y (m) of a first layer of grid on the boundary of the channel model, and obtaining a computational grid required by numerical calculation according to a grid division method on the basis of determining the first layer of grid on the boundary of the channel model;
step three: introducing the calculation grid obtained in the step two into an ANSYS Fluent, calculating by using a large-vortex numerical simulation method, keeping constant mass flow by adopting periodic boundary conditions for the boundary conditions of the inlet and the outlet of the channel, and obtaining the shear stress tau on the surface of the channel model according to the numerical simulation resultw(N/m2) The surface of the channel model is an object needing enhanced heat transfer;
step four: using shear stress tau of channel model surface in numerical simulation resultsw(N/m2) The fluid density ρ (kg/m) is known3) Calculating the frictional velocity of the surface of the channel model
Figure BDA0002183147020000051
Step five: height without dimension
Figure BDA0002183147020000052
From the kinematic viscosity v (m) of the fluid2S) and the friction speed uτ(m/s) is calculated, y (m) is the actual height, ρ (kg/m)3) Is the fluid density; y is+When 1 denotes a unit dimensionless height, use
Figure BDA0002183147020000053
To express a unit dimensionless height of 1, y1(m) to represent a unit dimensionless height
Figure BDA0002183147020000054
A corresponding actual height;
step six: the pitch of the miniature wing-shaped turbulence controller in the invention is the statistical average width of the velocity bands in the turbulence program structure, namely 100 times of the unit dimensionless length. The center of motion of the velocity fringes is located in the turbulent near-wall region. The spacing between the spanwise adjacent speed strips is 60-180, a lognormal probability distribution is presented, and the average spanwise spacing of the strips is 100 wall surface wall units. Through research, the dimensionless distance between two adjacent wing-shaped bodies is 100, and at the distance, the two adjacent wing-shaped bodies can control the turbulence quasi-sequence structure such as flow direction vortexTherefore, the flow resistance can be effectively reduced; the front ends of the wing shapes are fixed on the bottom surface along the incoming flow direction; several wing-shaped bodies are arranged along the spanwise direction, the spanwise direction is very thin, and the spanwise dimensionless distance between every two adjacent wing-shaped bodies is
Figure BDA0002183147020000055
Let y+When the dimensionless distance is 100, the corresponding actual distance Δ G is y100=100y1(m) the actual spacing being the pitch of the arrangement of adjacent micro-foil turbulence controllers;
step seven: the front end of a self-adaptive deformation miniature wing-shaped turbulence controller is fixed on the bottom surface of a channel, and the front end of the self-adaptive deformation miniature wing-shaped turbulence controller is arranged in an array form along the incoming flow direction, and the distance is set to be delta G (y)100=100y1(m) arranged on the actual channel surface; the preferred wing shape is a rectangular parallelepiped sheet with a thickness of 0.2 times the unit dimensionless distance
Figure BDA0002183147020000056
Actual thickness Δ z is 0.2y1(m); length 4 times unit dimensionless distance
Figure BDA0002183147020000057
Actual length Δ x is 4y1(m); unit dimensionless distance of 23 times height
Figure BDA0002183147020000058
Actual height Δ h 23y1(m)。
The invention is described in detail below with reference to the figures and examples.
The present invention provides the use of adaptive shape changing micro aerofoil turbulence controllers in a matrix arrangement in a channel flow as shown in the preferred embodiments of figures 1-2. The array type self-adaptive deformation micro wing-shaped turbulence controller arranged on the surface of a channel is used for controlling a flow structure and comprises the channel 1 and a channel fluid inlet 2, wherein the front end 3 of the self-adaptive deformation micro wing-shaped turbulence controller is fixed on the surface of the channel, the parts 4 of the self-adaptive deformation micro wing-shaped turbulence controller except the front end are not fixed, the self-adaptive deformation micro wing-shaped turbulence controller is arranged in an array type and at equal intervals, and the channel fluid outlet 5 is arranged. Figure 3 shows a deformed diagram of an array of equally spaced adaptively deformed miniature aerofoil turbulence controllers arranged on the surface of a channel.
Specifically, the method comprises the following steps:
average flow rate U as flow ratemWith reference to 0.547(m/s) of air flowing through the channel, the channel half height (as a characteristic length) is L0.1 (m), and the channel length is L01.256(m), channel width Z00.628(m), air density ρ 1.225 (m)3Kg), aerodynamic viscosity μ 1.7894e-05(kg/(m · s)), the kinematic viscosity of air
Figure BDA0002183147020000061
The method comprises the following steps: characteristic length L of measuring channel is 0.1(m), average flow speed Um0.547(m/s) depending on the kinematic viscosity of the fluid
Figure BDA0002183147020000062
Determining
Figure BDA0002183147020000063
Step two: an abstract physical model of the channel is built at ANSYS ICEM, using
Figure BDA0002183147020000064
(this empirical formula was proposed by Schlichting in 1979), the characteristic length L is 0.1(m), let y+Determining that the height of a first layer grid on the boundary of the channel model is delta y approximately equal to 0.00035(m) so as to establish a calculation grid;
step three: introducing a calculation grid into ANSYS Fluent, and calculating by using a large-vortex numerical simulation method to obtain the shear stress tau of the surface of the channel modelw≈0.00145(N/m2);
Step four: the shear stress tau of the channel surface (the object needing enhanced heat transfer) in the numerical simulation result is utilizedw≈0.00145(N/m2) The known air density ρ is 1.225 (kg/m)3) Calculating the frictional velocity of the surface of the passage
Figure BDA0002183147020000065
Step five: height without dimension
Figure BDA0002183147020000066
y (m) is the actual height, and the air density ρ is 1.225 (m)3Kg), aerodynamic viscosity μ 1.7894e-05(kg/(m · s)), kinematic viscosity of air
Figure BDA0002183147020000067
Frictional velocity uτ≈0.0344(m/s);y+When 1 denotes a unit dimensionless height, use
Figure BDA0002183147020000068
To express a unit dimensionless height of 1, y1(m) to represent an actual height corresponding to a unit dimensionless height; let y+1, obtaining unit dimensionless height
Figure BDA0002183147020000069
Corresponding actual height y1≈0.00042(m);
Step six: the pitch of the miniature wing-shaped turbulence controller in the invention is the statistical average width of the velocity bands in the turbulence program structure, namely 100 times of the unit dimensionless length. The center of motion of the velocity fringes is located in the turbulent near-wall region. The spacing between the spanwise adjacent speed strips is 60-180, a lognormal probability distribution is presented, and the average spanwise spacing of the strips is 100 wall surface wall units. Through research, the dimensionless distance between adjacent wing-shaped bodies is 100, and under the distance, the two adjacent wing-shaped bodies can control a turbulence quasi-sequence structure such as a flow direction vortex, so that the flow resistance can be effectively reduced; the front ends of the wing shapes are fixed on the bottom surface along the incoming flow direction; several wing-shaped bodies are arranged along the spanwise direction, the spanwise direction is very thin, and the spanwise dimensionless distance between every two adjacent wing-shaped bodies is
Figure BDA0002183147020000071
Let y+=100,Obtaining the corresponding actual distance delta G ═ y when the dimensionless distance is 100100=100y10.042(m), this actual pitch being the arrangement pitch of adjacent micro-foil turbulence controllers;
step seven: as shown in fig. 2, the front end of the adaptive deformation miniature wing-shaped turbulence controller is fixed on the bottom surface of the channel, and the front end is arranged in an array form along the incoming flow direction, and the distance is set to 100y10.042(m) is arranged on the surface of the actual channel; y is1Approximately equal to 0.00042, the preferred wing shape is a rectangular parallelepiped sheet, very thin in the spanwise direction (z-axis direction), with a thickness of 0.2 times the unit dimensionless distance
Figure BDA0002183147020000072
Actual thickness Δ z is 0.2y10.000084 (m); length 4 times unit dimensionless distance
Figure BDA0002183147020000073
Actual length Δ x is 4y10.00168 (m); unit dimensionless distance of 23 times height
Figure BDA0002183147020000074
Actual height Δ h 23y10.00966 (m). As shown in fig. 1 and 2
Step eight: the micro-airfoil turbulence controller, which is fixed to the surface of the fluid channel, is adaptively deformed, as shown in fig. 3, indicating the good adaptive characteristics of the micro-airfoil turbulence controller.
The invention is inspired by bionics, through observing the movement law of fish and finding, the fish body has very strong flexibility, under the motion state, the skin and wavelike scale of fish can reduce the external resistance in the swimming process effectively, its flexible viscous bottom layer thickens, reduce the speed gradient of the boundary layer of epidermis effectively. Meanwhile, dynamic change can be generated according to the change of external load (stress), so that the velocity gradient and the shearing force on the surface boundary layer are reduced, the power consumption caused by the shearing force is finally reduced, and the effect of reducing the frictional resistance is achieved. Therefore, the flexible wall can reduce energy consumption more than the traditional rigid wall, and the flexible wall material can play a role in effectively saving energy when being applied to the turbulence drag reduction process.
By utilizing the phenomena and the statistical characteristics in the turbulent boundary layer, the invention controls the turbulent structure, thereby realizing the flow drag reduction. The flow structure of a turbulent boundary layer includes several features: generating and evolving a speed band in the boundary layer; the low-speed fluid in the near-wall surface area is affected and bursts; the generation and development of span-wise vortices, flow-wise vortices, etc. Wherein the streamwise vortex structure induces eruption of low velocity fluid in the near wall region (Ejection), Sweep down of the high velocity fluid strip (Sweep), and creates additional reynolds stresses. The center of motion of the velocity fringes is located in the turbulent near-wall region. The spacing between the spanwise adjacent speed strips is 60-180, a lognormal probability distribution is presented, and the average spanwise spacing of the strips is 100 wall surface wall units. Through research, the dimensionless distance between two adjacent wing-shaped bodies is 100, and at the distance, the two adjacent wing-shaped bodies can control a turbulence quasi-sequence structure such as a flow direction vortex, so that the flow resistance can be effectively reduced.

Claims (1)

1. A method for realizing flow control comprises a plurality of miniature wing-shaped turbulence controllers with self-adaptive deformation characteristics and an arrangement mode on the surface of a channel, wherein the miniature wing-shaped turbulence controllers are made of self-adaptive deformation flexible materials, the bottom surfaces of the miniature wing-shaped turbulence controllers are fixed on the surface of the channel and are vertical to the flow direction of fluid in the channel, and a plurality of miniature wing-shaped turbulence controllers are arranged in an array mode, the distance between the miniature wing-shaped turbulence controllers is the statistical average width of a velocity band in a turbulence program simulating structure, and the method comprises the following steps:
the method comprises the following steps: measuring the characteristic length L (m) of the channel, the flow direction section A (m) of the channel2) Length L of the channel0(m) channel width Z0(m) average flow velocity Um(m/s) according to the formula of mass flow in the channel Q ═ UmA(m3S) estimated or measured density ρ (m) of the fluid3Kg) and the kinematic viscosity of the fluid, i.e., the kinematic viscosity of the fluid, i.
Figure FDA0003375818980000011
Can be calculated to determine
Figure FDA0003375818980000012
Step two: an abstract physical model of the channel is built and gridded ANSYS ICEM: using empirical formulas
Figure FDA0003375818980000013
L (m) is a characteristic length, let y+Determining the height delta y (m) of a first layer of grid on the boundary of the channel model, and obtaining a computational grid required by numerical calculation according to a grid division method on the basis of determining the first layer of grid on the boundary of the channel model;
step three: introducing the calculation grid obtained in the step two into an ANSYS Fluent, calculating by using a large-vortex numerical simulation method, keeping constant mass flow by adopting periodic boundary conditions for the boundary conditions of the inlet and the outlet of the channel, and obtaining the shear stress tau on the surface of the channel model according to the numerical simulation resultw(N/m2) The surface of the channel model is an object needing enhanced heat transfer;
step four: using shear stress tau of channel model surface in numerical simulation resultsw(N/m2) The fluid density ρ (kg/m) is known3) Calculating the frictional velocity of the surface of the channel model
Figure FDA0003375818980000014
Step five: height without dimension
Figure FDA0003375818980000015
From the kinematic viscosity v (m) of the fluid2S) and the friction speed uτ(m/s) is calculated, y (m) is the actual height, ρ (kg/m)3) Is the fluid density; y is+When 1 denotes a unit dimensionless height, use
Figure FDA0003375818980000016
To express a sheetBit dimensionless height 1, y1(m) to represent a unit dimensionless height
Figure FDA0003375818980000017
A corresponding actual height;
step six: and (3) designing the space between the miniature wing-shaped turbulence controllers: the motion center of the velocity bands is located in a turbulent flow near-wall area, the distance between every two adjacent velocity bands in the spanwise direction is 60-180, a lognormal probability distribution is presented, and the average spanwise distance of the bands is 100 wall surface wall units; the dimensionless distance between two adjacent wing shapes is 100, and under the distance, the two adjacent wing shapes can control a turbulence quasi-sequence structure such as a flow direction vortex, so that the flow resistance can be effectively reduced; the front ends of the wing shapes are fixed on the bottom surface along the incoming flow direction; several wing-shaped bodies are arranged along the spanwise direction, and the spanwise dimensionless distance between the adjacent wing-shaped bodies is
Figure FDA0003375818980000021
Let y+When the dimensionless distance is 100, the corresponding actual distance Δ G is y100=100y1(m) the actual spacing being the pitch of the arrangement of adjacent micro-foil turbulence controllers;
step seven: the front end of a self-adaptive deformation miniature wing-shaped turbulence controller is fixed on the bottom surface of a channel, and the front end of the self-adaptive deformation miniature wing-shaped turbulence controller is arranged in an array form along the incoming flow direction, and the distance is set to be delta G (y)100=100y1(m) arranged on the actual channel surface; the preferred wing shape is a rectangular parallelepiped sheet with a thickness of 0.2 times the unit dimensionless distance
Figure FDA0003375818980000022
Actual thickness Δ z is 0.2y1(m); length 4 times unit dimensionless distance
Figure FDA0003375818980000023
Actual length Δ x is 4y1(m); unit dimensionless distance of 23 times height
Figure FDA0003375818980000024
Actual height Δ h 23y1(m)。
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