CN111634408A

CN111634408A - Supersonic double-wing and design method thereof

Info

Publication number: CN111634408A
Application number: CN202010492378.3A
Authority: CN
Inventors: 翟建; 张伟伟; 张陈安; 王发民; 骆府庆
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2020-06-03
Filing date: 2020-06-03
Publication date: 2020-09-08

Abstract

A supersonic double wing and a design method thereof. The lower wing section in the supersonic double wing is an isosceles triangle, and the upper wing section is a rectangle. The vertical distance h between the wing airfoil leading edge vertex and the lower surface of the upper wing is determined by an oblique shock wave relational expression and a Prandtl-Meyer expansion wave relational expression₁The vertical distance h between the top of the upper wing surface of the lower wing profile and the lower wing surface of the upper wing profile₂The distance x between the foot from the vertex of the front edge of the lower wing profile to the lower surface of the upper wing and the front edge point of the upper wing profile and the distance L between the front edge point of the upper wing profile and the rear edge point of the upper wing profile effectively shorten the time for designing the supersonic speed double wings and improve the efficiency.

Description

Supersonic double-wing and design method thereof

Technical Field

The invention relates to the field of aircraft design, in particular to a low-resistance high-lift-drag-ratio pneumatic configuration of a civil supersonic/hypersonic transport plane.

Background

Since the retirement of "collaborative" supersonic aircraft in 2003, civil supersonic/hypersonic aircraft were designed with great interest. For a successful civil aircraft, high economic efficiency is a fundamental requirement. To improve economic efficiency, the aircraft should have a high lift-to-drag ratio. The lift-drag ratio is higher, the airplane flies farther, and more fuel is saved.

In fig. 1 of the academic paper "k.cui, g.l.li, y.xiao, y.z.xu, High-pressure capturing with regulations, AIAA Journal,55(2017) 1909-. This pneumatic configuration places a flat plate above the body for capturing the high pressure air stream generated by the body. This results in a much higher pressure on the lower wall of the plate than on the upper wall. Therefore, the flat plate has high lift. And the flat plate belongs to a thin wing structure, and the additional resistance is very small, so that the lift-drag ratio of the whole aircraft is improved. Patents CN210258809U and CN210258810U propose an air-breathing hypersonic flight vehicle based on high-pressure capturing wings. The leading edge line of the high pressure capture wings in both patents is a smooth curve and the trailing edge line is a dovetail curve. The high pressure capture foil thus designed can utilize as much of the high pressure zone as possible. However, the high-pressure trapping wing has a disadvantage that the shock resistance of the body is relatively large.

The academic paper, namely Liguangli, Cuyyyya, Xiaoyao, Xuoughhou, research on the position design method of the high-pressure capture wing, mechanical science report, 48(2016)576 + 584, proposes that the position of the high-pressure capture wing is difficult to be directly obtained by using a theoretical method. To solve this problem, the paper applies a uniform experimental design method to obtain sample points in the design space and obtains their design positions using computational fluid dynamics analysis and iteration. However, this method requires extensive computational fluid dynamics analysis, is time consuming and inefficient.

In fig. 8 of the academic paper "k.kusunose, k.matsushima, d.maruyama.supersonic biplane-areview, Progress in Aerospace Sciences,47(2011) 53-87", a Busemann doublewing for reducing shock resistance is shown. A typical Busemann doublet consists of two isosceles triangular airfoils. Under the design condition, the shock waves attached to the front edges of the upper wing and the lower wing are mutually counteracted. Therefore, the pressure acting on the front half and the rear half of the double wing internal passage is the same. Theoretically, under the design condition, the shock wave resistance and the lift force of the Busemann double wings are zero. Although the actual zero-lift shock resistance of the Busemann double wing is greater than zero due to the entropy of the shock between the upper and lower wings, it is still low. The main disadvantage of the Busemann twin-wing is that the shock resistance at off-design cruise mach numbers is high and difficult to start. Patent CN107421402B proposes a control device for reducing the shock resistance of the Busemann twin-wing at off-design cruise mach numbers. This device rotates the upper and lower wings of the Busemann double wing. The ratio of the throat area to the inlet area of the inner channel between the upper wing and the lower wing after rotation is increased, so that the shock resistance of the Busemann double wing is reduced when the Busemann double wing is at the non-design cruise Mach number. But the structure of such a device is relatively complex.

In the academic paper "D.Igra, E.Arad, A parametric study of the Busemann biplana, Shock Waves,16(2007) 269-273", designing Busemann biplanar using oblique Shock wave relation is proposed, but no specific design method is given, and only one possibility is proposed.

Disclosure of Invention

In order to overcome the defects of large shock resistance and complex structure of the engine body in the prior art, the invention provides a supersonic velocity double wing and a design method thereof.

The supersonic double-wing comprises a lower wing and an upper wing. The upper wing is positioned above the lower wing, so that an airflow inner channel is formed between the lower wing surface of the upper wing and the upper wing surface of the lower wing. The supersonic speed double wings are connected with the fuselage through the central wing box. The wing type of the lower wing is an isosceles triangle; the vertex of the front edge of the lower wing airfoil is A, the vertex of the rear edge of the lower wing airfoil is C, and the vertex of the upper wing surface of the lower wing airfoil is B. The upper wing is a flat plate; and the upper surface and the lower surface of the flat plate respectively form an upper wing surface and a lower wing surface of the upper wing. The leading edge point of the upper wing profile is D; the upper airfoil trailing edge point is E. And the distance from the upper wing section leading edge point D to the upper wing section trailing edge point E is L. The wing profile of the upper wing is rectangular.

The vertical distance between the top point A of the leading edge of the lower wing airfoil and the lower surface of the upper wingIs separated by h₁. The vertical foot from the vertex A of the front edge of the lower wing airfoil to the lower surface of the upper wing is F. The distance from the vertex A of the front edge of the lower wing airfoil section to the foot F of the lower surface of the upper wing and the point D of the front edge of the upper wing airfoil section is x. The vertical distance between the top B of the upper wing surface of the lower wing profile and the lower surface of the upper wing is h₂。

The bottom edge between the lower wing profile leading edge vertex A and the lower wing profile trailing edge vertex C is a plane, and a lower wing surface of the lower wing profile is formed. The length of the lower wing surface of the lower wing airfoil is c. The edge between the lower wing profile leading edge vertex A and the lower wing surface vertex B forms a leading edge upper wing surface of the lower wing profile; the edge between the lower airfoil surface apex B and the lower airfoil trailing edge apex C constitutes the lower airfoil trailing edge upper airfoil surface.

The upper wing surface and the lower wing surface of the upper wing are both planes; the included angle between the connecting line between the upper wing section trailing edge point E and the upper wing surface vertex B of the lower wing section and the upper wing surface of the trailing edge of the lower wing section is also an acute angle, and the included angle is the Mach angle mu of the Mach line of the lower wing section₁。

The design process of the supersonic speed double wings is as follows;

step 1, determining the shock angle β of the lower wing profile shock wave₁。

The included angle between the connecting line between the upper wing profile leading edge point D and the lower wing profile leading edge point A and the lower wing profile of the lower wing profile is the shock wave angle β of the shock wave of the lower wing profile₁。

Under supersonic conditions, the leading edge upper wing of the lower wing compresses the air and generates a lower wing profile shock wave. The airflow deflection angle of the lower wing profile shock wave is equal to the leading edge vertex angle theta of the lower wing profile₁. The pressure of the air is increased through the compression of the lower wing profile shock wave, and the Mach number of the air is M from the designed cruise Mach number₁Reduced to Mach number M of lower wing profile shock wave downstream₂。

The leading edge vertex angle theta of the lower wing airfoil₁The wing consists of a lower wing surface of a lower wing airfoil and a front edge upper wing surface of a lower wing; the leading edge vertex angle theta of the lower wing airfoil₁And trailing edge apex angle theta of lower wing airfoil₂Are all acute angles.

Design cruise Mach number M₁And the leading edge apex angle theta of the lower airfoil₁Respectively substituted into a seventh formula (7) of the oblique shock wave relational expression to determine the shock wave angle β of the lower wing airfoil shock wave₁。

Step 2, determining the shock angle β of the upper wing profile shock wave₂。

The included angle between the upper wing section auxiliary line 8 and the connecting line of the upper wing section leading edge point D and the upper wing surface vertex B of the lower wing section is the shock wave angle β of the shock wave of the upper wing section₂。

Deflection angle theta of airflow through upper wing profile shock wave₃And Mach number M of lower wing profile shock wave downstream₂Obtaining the shock wave angle β of the upper wing profile shock wave₂。

The deflection angle theta of the airflow of the upper wing profile shock wave₃Is the included angle between the auxiliary line of the upper wing profile and the lower surface of the upper wing. The included angle between the upper wing profile auxiliary line and the lower surface of the upper wing is the airflow deflection angle theta of the upper wing profile shock wave₃(ii) a The deflection angle theta of the air flow₃Equal to the leading edge apex angle theta of the lower wing profile₁. The starting point of the upper wing section auxiliary line is the front edge point D of the upper wing section, and the upper wing section auxiliary line is parallel to the front edge upper wing of the lower wing section.

1. Determining Mach number M of lower wing airfoil shock wave downstream₂The specific process comprises the following steps:

i will design cruise Mach number M₁And shock angle β of lower airfoil shock₁Respectively substituted into the first formula (1) of the oblique shock wave relational expression to determine the design cruise Mach number M₁Perpendicular to the component M of the lower-wing profile shock wave_n,1；

M_n，1＝M₁sinβ₁(1)

II design cruise Mach number M₁Perpendicular to the component M of the lower-wing profile shock wave_n,1Substituting into a second oblique shock relationIn the formula (2), determining the Mach number M of the lower wing profile downstream of the shock wave₂Component M perpendicular to lower wing profile shock wave_n,2；

III Mach number M of the downstream of the lower wing profile shock wave₂Perpendicular to the component M of the lower-wing profile shock wave_n,2The vertex angle theta of the front edge of the lower wing profile₁And shock angle β of lower airfoil shock₁Respectively substituting into a sixth formula (6) of the oblique shock wave relational expression to determine the Mach number M of the lower wing profile shock wave downstream₂。

2. Determining shock angle β of upper wing airfoil shock₂：

Mach number M of the lower wing airfoil shock wave downstream₂And the deflection angle theta of the air flow of the upper airfoil shock wave₃Respectively substituted into a seventh formula (7) of the oblique shock wave relational expression to determine the shock wave angle β of the upper wing airfoil shock wave₂。

And step 3: determining the vertical distance h between the top point of the lower wing profile leading edge and the lower surface of the upper wing₁。

Shock angle β of lower wing profile shock₁Shock angle β of top wing airfoil shock₂The vertex angle theta of the front edge of the lower wing profile₁Respectively substituting the length c of the lower wing surface of the lower wing profile into a formula (8) to determine the vertical distance h between the vertex of the leading edge of the lower wing profile and the lower surface of the upper wing₁。

And 4, step 4: upper wing for determining lower wing profileVertical distance h between surface vertex and lower wing surface of upper wing airfoil₂。

The vertical distance h between the top point of the front edge of the lower wing airfoil and the lower surface of the upper wing₁The vertex angle theta of the front edge of the lower wing profile₁Respectively substituting the length c of the lower wing surface of the lower wing airfoil into a formula (9) to determine the vertical distance h between the top of the lower wing surface of the lower wing and the lower surface of the upper wing₂。

h₂＝h₁-0.5c·tanθ₁(9)

And 5: and determining the distance x from the vertex of the front edge of the lower wing airfoil to the foot of the lower surface of the upper wing and the front edge point of the upper wing airfoil.

The vertical distance h between the top point of the front edge of the lower wing airfoil and the lower surface of the upper wing₁And shock angle β of lower airfoil shock₁And respectively substituting the distance x from the vertex of the front edge of the lower wing section to the vertical foot of the lower surface of the upper wing section and the front edge point of the upper wing section into the formula (10).

x＝h₁/tanβ₁(10)

Step 6: determining the Mach angle mu of the Mach line of the lower airfoil profile₁。

Passing the trailing edge apex angle theta of the lower wing profile₂And Mach number M downstream of Mach line of lower wing airfoil₄Determining the Mach angle mu of the Mach line of the lower airfoil profile₁。

Mach number M of the downstream Mach line of the lower wing airfoil₄Substituting into formula (12) to determine Mach angle μ of lower wing profile Mach line₁。

μ₁＝sin^-1(1/M₄) (12)

Determining Mach number M downstream of Mach line of lower wing airfoil₄The specific process comprises the following steps:

i Mach number M of lower wing profile shock wave downstream₂And shock angle β of upper airfoil shock₂Respectively substituted into the first formula (1) of the oblique shock wave relational expression to obtain the Mach number M of the lower wing profile shock wave downstream₂Perpendicular to the component M of the upper wing profile shock wave_n,3；

M_n，3＝M₂sinβ₂(1)

II, dividing the Mach number M of the lower wing airfoil shock wave downstream₂Perpendicular to the component M of the upper wing profile shock wave_n,3Substituting into the second formula (2) of the oblique shock wave relational expression to obtain the Mach number M of the upper wing profile shock wave downstream₃Perpendicular to the component M of the lower-wing profile shock wave_n,4；

III Mach number M of upper wing profile shock wave downstream₃Perpendicular to the component M of the lower-wing profile shock wave_n,4Deflection angle theta of air flow of upper wing type shock wave₃And shock angle β of upper airfoil shock₂Respectively substituting into a sixth formula (6) of the oblique shock wave relational expression to obtain the Mach number M of the lower reaches of the upper wing profile shock wave₃。

IV, adjusting the Mach number M of the downstream of the upper wing airfoil shock wave₃And trailing edge apex angle theta of lower wing airfoil₂Respectively substituted into Prandtl-Meyer expansion wave relational expression (11) to obtain Mach number M at the downstream of Mach line of lower wing profile₄。

And 7: the distance L from the upper airfoil leading edge point to the upper airfoil trailing edge point is determined.

The length c of the bottom edge of the lower wing profile, the distance x between the foot from the top point of the front edge of the lower wing profile to the lower surface of the upper wing and the front edge point of the upper wing profile, and the vertical distance h between the top point of the upper surface of the lower wing profile and the lower surface of the upper wing profile₂Mach angle mu of Mach line of lower wing airfoil₁And the leading edge apex angle theta of the lower airfoil₁And respectively substituting the distances L into the formula (13) to determine the distance L from the leading edge point of the upper wing airfoil to the trailing edge point of the upper wing airfoil.

L＝0.5c-x+h₂/tan(μ₁-θ₁) (13)

Thus, the design of the supersonic double wing is completed.

The invention aims to provide a supersonic speed double wing and a design method thereof.

The supersonic double-wing consists of a lower wing and an upper wing. The upper wing is positioned above the lower wing, so that an airflow inner channel is formed between the lower wing surface of the upper wing and the upper wing surface of the lower wing. The supersonic speed double wings are connected with the fuselage through the central wing box. The lower wing profile is an isosceles triangle. The vertex angle of the front edge of the lower wing airfoil and the vertex angle of the rear edge of the lower wing airfoil are acute angles. The upper wing is a flat plate with the upper surface and the lower surface being flat, and the upper surface and the lower surface of the flat plate respectively form an upper wing surface and a lower wing surface of the upper wing; the upper wing profile is rectangular. And an included angle between a connecting line between the upper wing profile leading edge point and the lower wing profile of the lower wing profile is an acute angle, and the included angle is a shock wave angle of the shock wave of the lower wing profile. The included angle between the connecting line between the upper wing section leading edge point and the lower wing section upper wing surface vertex and the lower wing section leading edge upper wing surface is also an acute angle, and the included angle is the shock wave angle of the upper wing section shock wave. The included angle between the connecting line between the trailing edge of the upper wing section and the vertex of the upper wing surface of the lower wing section and the upper wing surface of the trailing edge of the lower wing is also an acute angle, and the included angle is the Mach angle of the Mach line of the lower wing section.

Compared with the prior art, the total drag coefficient of the supersonic speed double wing is very low when the cruise Mach number is designed, as shown in figure 12. This is because the shock resistance coefficient and the frictional resistance coefficient of the supersonic twin wings are low, as shown in fig. 10 and 11. Since the total drag coefficient of the supersonic twin-wing is low, the lift-drag ratio of the supersonic twin-wing is high, as shown in fig. 14.

At off-design cruise Mach numbers, the shock resistance of the supersonic twin-wing is lower, as shown in FIG. 17. In addition, the supersonic dual wings are easier to activate, as shown in FIG. 18. This is because the ratio of the throat area to the inlet area of the supersonic twin-wing inner compression section is large.

The design formula derived by the oblique shock wave relational expression and the Prandtl-Meyer expansion wave relational expression can shorten the time for designing the supersonic speed double wings and improve the efficiency.

Drawings

FIG. 1 is a three-dimensional schematic of the present invention.

Fig. 2 is a schematic diagram of the design of the present invention.

FIG. 3 is a schematic diagram of the design parameters of the present invention.

Fig. 4 is a schematic diagram of an embodiment of the present invention.

FIG. 5 is a pressure cloud of an embodiment of the present invention in a design state.

Fig. 6 is a prior art Busemann double wing schematic.

FIG. 7 is a pressure cloud of a Busemann double wing in the prior art under design conditions.

FIG. 8 is a schematic view of a prior art high pressure trapping wing.

FIG. 9 is a pressure cloud of a prior art high pressure trapping airfoil in the design state.

FIG. 10 is a shock coefficient curve for an embodiment of the present invention, a prior art Busemann twin wing, and a prior art high pressure capture wing at a design cruise Mach number of 2.

FIG. 11 is a plot of the coefficient of friction for an embodiment of the present invention, a prior art Busemann twin wing, and a prior art high pressure capture wing at a design cruise Mach number of 2.

FIG. 12 is a plot of the total drag coefficient for an embodiment of the present invention, a prior art Busemann twin wing, and a prior art high pressure capture wing at a design cruise Mach number of 2.

FIG. 13 is a plot of lift coefficient for an embodiment of the present invention, a prior art Busemann twin wing, and a prior art high pressure capture wing at a design cruise Mach number of 2.

FIG. 14 is a plot of lift-to-drag ratio for an embodiment of the present invention, a prior art Busemann twin wing, and a prior art high pressure capture wing at a design cruise Mach number of 2.

FIG. 15 is a schematic diagram of an inner compression section of an embodiment of the present invention.

FIG. 16 is a schematic representation of the prior art internal compression section of a Busemann double wing

FIG. 17 is a shock resistance coefficient for Busemann doublets at off-design cruise Mach number for embodiments of the present invention and prior art.

FIG. 18 is a shock resistance coefficient for Busemann doublets during acceleration and deceleration according to embodiments of the present invention and prior art.

FIG. 19 is a flow chart of the present invention.

In the figure: 1. a lower wing; 2. an upper wing; 3. a lower wing profile; 4. an upper wing profile; 5. lower wing profile shock waves; 6. upper wing profile shock waves; 7. a lower airfoil profile mach line; 8. an upper wing profile auxiliary line; 9. the symmetry axis of the Busemann double wings in the prior art; 10. in the prior art, a shock wave resistance coefficient curve of a Busemann double wing is designed when the cruise Mach number is 2; 11. in the prior art, a shock wave resistance coefficient curve of a high-pressure capturing wing is designed when the cruise Mach number is 2; 12. in the embodiment of the invention, a shock wave resistance coefficient curve is designed when the cruise Mach number is 2; 13. in the prior art, a frictional resistance coefficient curve of Busemann double wings is designed when the cruise Mach number is 2; 14. in the prior art, a friction resistance coefficient curve of a high-pressure capturing wing is designed when the cruise Mach number is 2; 15. according to the embodiment of the invention, a friction resistance coefficient curve is designed when the cruise Mach number is 2; 16. in the prior art, a Busemann double-wing curve of the total resistance coefficient when the cruise Mach number is 2 is designed; 17. the total resistance coefficient curve of a high-pressure capturing wing in the prior art when the cruise Mach number is designed to be 2; 18. according to the embodiment of the invention, the total resistance coefficient curve when the cruise Mach number is 2 is designed; 19. in the prior art, a lift coefficient curve of a Busemann double wing is designed when the cruise Mach number is 2; 20. in the prior art, a lift coefficient curve of a high-pressure capturing wing when the cruise Mach number is designed to be 2; 21. according to the embodiment of the invention, a lift coefficient curve when the cruise Mach number is 2 is designed; 22. in the prior art, a lift-drag ratio curve of Busemann double wings when the cruise Mach number is 2 is designed; 23. in the prior art, a lift-drag ratio curve of a high-pressure capture wing is designed when the cruise Mach number is 2; 24. according to the embodiment of the invention, a lift-drag ratio curve is designed when the cruise Mach number is 2; 25. the total resistance coefficient curve of the Busemann double-wing in the prior art; 26. the total resistance coefficient curve of the embodiment of the invention; 27. the Busemann double-wing in the prior art accelerates from a low incoming flow Mach number to a resistance coefficient curve of a high incoming flow Mach number; 28. the Busemann double-wing in the prior art is a resistance coefficient curve for decelerating from a high incoming flow Mach number to a low incoming flow Mach number; 29. the resistance coefficient curve of the embodiment of the invention accelerates from low incoming flow Mach number to high incoming flow Mach number; 30. the embodiment of the invention provides a resistance coefficient curve for decelerating from a high incoming flow Mach number to a low incoming flow Mach number.

A. The lower wing profile leading edge vertex; B. the top of the upper wing surface of the lower wing profile; C. the trailing edge vertex of the lower wing profile; D. an upper airfoil leading edge point; E. an upper wing profile trailing edge point; F. the top point of the front edge of the lower wing profile is connected with the foot of the lower surface of the upper wing; m₁Designing a cruise Mach number; m₂Mach number downstream of the lower wing profile shock wave; m₃Mach number downstream of the upper airfoil shock wave; m₄Mach number downstream of the lower airfoil mach line; p₁The incoming flow pressure; p₂Pressure downstream of the lower airfoil shock; p₃Pressure downstream of the upper wing profile shock wave; p₄Pressure downstream of the lower airfoil mach line; p₅The pressure acting on the bottom plane of the lower wing profile of the high-pressure capture wing in the prior art; l, the distance from the front edge point of the upper wing profile to the rear edge point of the upper wing profile; c. length of lower airfoil surface of the lower airfoil profile; h is₁The vertical distance between the top of the lower wing profile leading edge and the lower surface of the upper wing; h is₂The vertical distance between the top of the upper wing surface of the lower wing profile and the lower surface of the upper wing; h is₃The inlet area of the contraction section in the embodiment of the present invention; h is₄The throat area of the Busemann double-wing internal contraction section in the prior art; h is₅Inlet area of the Busemann double-winged inner contraction section in the prior art; x, the distance from the vertex of the front edge of the lower wing airfoil to the foot of the lower surface of the upper wing and the front edge point of the upper wing airfoil; theta₁A leading edge apex angle of the lower airfoil profile; theta₂The trailing edge apex angle of the lower airfoil profile; theta₃Deflection angle of flow of upper wing airfoil shock wave β₁Shock angle of lower wing profile shock β₂The shock angle of the upper wing profile shock; mu.s₁Mach angle of lower airfoil mach line.

Detailed Description

The embodiment is a method for designing a supersonic double-wing, and the specific process is as follows:

the supersonic double wing comprises a lower wing 1 and an upper wing 2. The upper wing is positioned above the lower wing, so that an airflow inner channel is formed between the lower wing surface of the upper wing and the upper wing surface of the lower wing. The supersonic speed double wings are connected with the fuselage through the central wing box.

The wing profile of the lower wing 1 is an isosceles triangle. The vertex of the front edge of the lower wing airfoil is A, the vertex of the rear edge of the lower wing airfoil is C, and the vertex of the upper wing surface of the lower wing airfoil is B. The bottom edge between the lower wing profile leading edge vertex A and the lower wing profile trailing edge vertex C is a plane, and a lower wing surface of the lower wing profile is formed. The length of the lower wing surface of the lower wing airfoil is c. The edge between the lower wing profile leading edge vertex A and the lower wing surface vertex B forms a leading edge upper wing surface of the lower wing profile; the edge between the lower airfoil surface apex B and the lower airfoil trailing edge apex C constitutes the lower airfoil trailing edge upper airfoil surface. The lower wing surface of the lower wing airfoil and the front edge upper wing surface of the lower wing form a front edge vertex angle theta of the lower wing airfoil₁The lower wing surface of the lower wing profile and the trailing edge upper wing surface of the lower wing profile form a trailing edge vertex angle theta of the lower wing profile₂. The leading edge vertex angle theta of the lower wing airfoil₁And trailing edge apex angle theta of lower wing airfoil₂Are all acute angles.

The upper wing 2 is a flat plate; the upper surface and the lower surface of the flat plate are both planes, and the upper surface and the lower surface of the flat plate respectively form an upper wing surface and a lower wing surface of the upper wing. The wing profile of the upper wing is rectangular. The leading edge point of the upper wing profile is D; the upper airfoil trailing edge point is E. And the distance from the upper wing section leading edge point D to the upper wing section trailing edge point E is L. The included angle between the connecting line between the upper wing section trailing edge point E and the upper wing surface vertex B of the lower wing section and the upper wing surface of the trailing edge of the lower wing section is also an acute angle, and the included angle is the Mach angle mu of the Mach line of the lower wing section₁. Making an upper wing section auxiliary line 8, wherein the starting point of the upper wing section auxiliary line is an upper wing section leading edge point D, and the upper wing section leading edge point D is parallel to the upper wing section of the leading edge of the lower wing section. The upper wing profile auxiliary line 8 and the lower surface of the upper wing form an airflow deflection angle theta of the upper wing profile shock wave₃。

The vertical distance between the top point A of the lower wing airfoil leading edge and the lower surface of the upper wing is h₁. The vertical foot from the vertex A of the front edge of the lower wing airfoil to the lower surface of the upper wing is F. The distance from the vertex A of the front edge of the lower wing airfoil section to the foot F of the lower surface of the upper wing and the point D of the front edge of the upper wing airfoil section is x. The vertical distance between the top B of the upper wing surface of the lower wing profile and the lower surface of the upper wing is h₂。

The included angle between the connecting line between the upper wing profile leading edge point D and the lower wing profile leading edge point A and the lower wing profile of the lower wing profile is the shock wave angle β of the shock wave of the lower wing profile₁The included angle between the upper airfoil profile auxiliary line 8 and the connecting line of the upper airfoil profile leading edge point D and the upper airfoil surface vertex B of the lower airfoil profile is the shock wave angle β of the upper airfoil profile shock wave₂。

M in FIG. 3₁Designing a cruise Mach number; m₂The Mach number of the lower wing profile shock wave downstream is; m₃The Mach number of the downstream of the upper wing airfoil shock wave; m₄The mach number downstream of the lower airfoil mach line.

In this example, M₁＝2；M₂＝1.786；M₃＝1.579；M₄＝1.783；θ₁＝6°；θ₂＝6°；θ₃＝6°；β₁＝35.241°；β₂＝39.837°；μ₁＝34.115°；c＝1m；h₁＝0.199m；h₂＝0.147m；x＝0.282m；L＝0.493m。

In this embodiment, the shock angle β of the lower wing airfoil shock is determined by the oblique shock relation₁。

Each Oblique shock wave relationship is given in chapter 9, obblique shock relationships, section 2, of the monodamics-filfhedification, 2012, monograph "John d.anderson, jr., Fundamentals of Aerodynamics, including:

first formula of oblique shock wave relation

M_n，a＝M_asinβ (1)

Mach of shock wave upstream in equation (1)Number M_aMach number M upstream of shock wave_aThe component perpendicular to the shock wave being M_n,aThe shock angle of the shock wave is β.

Second formula of oblique shock wave relation

Mach number M of shock wave downstream in formula (2)_bThe component perpendicular to the shock wave being M_n,bThe specific heat ratio is γ, and γ is 1.4.

Third formula of oblique shock wave relation

The density of the shock wave upstream in the formula (3) is ρ_aDensity downstream of the shock wave is ρ_b。

Fourth formula of oblique shock wave relation

The pressure upstream of the shock wave in equation (4) is p_aDownstream of the shock wave, pressure p_b。

Fifth formula of oblique shock wave relation

The temperature upstream of the shock wave in the formula (5) is T_aTemperature downstream of shock wave is T_b。

Sixth formula of oblique shock wave relation

Mach number M downstream of shock wave in equation (6)_bThe deflection angle of the shock wave is θ.

Seventh formula of oblique shock wave relation

The specific process for designing the supersonic double-wing is provided by the embodiment;

Under supersonic conditions, the leading edge of the lower wing compresses the air against the upper wing surface and produces a lower wing profile shock wave 5. The airflow deflection angle of the lower wing profile shock wave 5 is equal to the leading edge vertex angle theta of the lower wing profile₁. The pressure of the air is increased through the compression of the lower wing profile shock wave 5, and the Mach number of the air is M from the designed cruise Mach number₁Reduced to Mach number M of lower wing profile shock wave downstream₂。

In this embodiment, the cruise Mach number M is designed₁And the leading edge apex angle theta of the lower airfoil₁Respectively substituted into a seventh formula (7) of the oblique shock wave relational expression to determine the shock wave angle β of the lower wing airfoil shock wave₁。

In the embodiment, the cruise Mach number M is designed₁2, leading edge vertex angle theta of lower wing profile₁Respectively substituting the angle of 6 degrees into a seventh formula (7) of the oblique shock wave relational expression to determine a shock wave angle β of the lower wing airfoil shock wave₁＝35.241°。

The air downstream of the lower airfoil shock 5 will be recompressed by the upper airfoil shock 6. The pressure of the air is increased again after the compression of the upper wing profile shock wave 6, and the Mach number of the air is M from the Mach number of the lower wing profile shock wave downstream₂Reducing the Mach number M of the upper wing profile shock wave downstream₃. Making an auxiliary wing line 8; the starting point of the upper wing section auxiliary line is the front edge point D of the upper wing section, and the upper wing section auxiliary line is parallel to the front edge of the lower wing sectionAn airfoil. The included angle between the upper wing profile auxiliary line 8 and the lower surface of the upper wing is the airflow deflection angle theta of the upper wing profile shock wave 6₃(ii) a The deflection angle theta of the air flow₃Equal to the leading edge apex angle theta of the lower wing profile₁。

Deflection angle theta of airflow through upper wing profile shock wave₃And Mach number M of lower wing profile shock wave downstream₂Obtaining the shock wave angle β of the upper wing profile shock wave₂. The deflection angle theta of the airflow of the upper wing profile shock wave₃Is the included angle between the upper wing profile auxiliary line 8 and the lower surface of the upper wing.

Determining Mach number M of lower wing airfoil shock wave downstream₂The specific process comprises the following steps:

M_n，1＝M₁sinβ₁(1)

In the embodiment, the cruise Mach number M is designed₁2, shock angle β of lower wing airfoil shock₁The Mach number M of the designed cruise is determined by substituting 35.241 degrees into the first formula (1) of the oblique shock wave relational expression respectively₁Perpendicular to the component M of the lower-wing profile shock wave_n,1＝1.154。

II will design cruise Mach number M₁Perpendicular to the component M of the lower-wing profile shock wave_n,1Substituting into the second formula (2) of the oblique shock wave relational expression to determine the Mach number M of the lower wing profile shock wave 5 downstream₂Component M perpendicular to lower wing profile shock wave_n,2；

In the embodiment, the cruise Mach number M is designed₁Perpendicular to the component M of the lower-wing profile shock wave_n,1Substituting 1.154 into the second formula (2) of the oblique shock wave relational expression to determine the lower wing airfoil shock waveMach number M downstream of 5₂Perpendicular to the component M of the lower-wing profile shock wave_n,2＝0.872；

III Mach number M of lower wing type shock wave 5 downstream₂Perpendicular to the component M of the lower-wing profile shock wave_n,2The vertex angle theta of the front edge of the lower wing profile₁And shock angle β of lower airfoil shock₁Respectively substituting into the sixth formula (6) of the oblique shock wave relational expression to determine the Mach number M of the lower wing profile shock wave downstream₂。

In this embodiment, the mach number M of the lower wing profile shock wave 5 downstream₂Perpendicular to the component M of the lower-wing profile shock wave_n,20.872, leading edge apex angle theta of lower wing profile ₁6 ° shock angle β of lower airfoil shock₁Respectively substituting the 35.241 degrees into a sixth formula (6) of the oblique shock wave relational expression to determine the Mach number M of the lower wing profile shock wave downstream₂＝1.786。

Determining shock angle β of upper wing airfoil shock₂：

In this embodiment, the mach number M of the lower wing profile downstream of the shock wave₂1.786, deflection angle θ of upper wing shock₃When the measured values are 6 °, they are respectively substituted into the seventh formula (7) of the oblique shock wave relational expression, and β is determined₂＝39.837°。

Shock angle β of lower wing profile shock₁Upper wingShock angle β of airfoil shock₂The vertex angle theta of the front edge of the lower wing profile₁Respectively substituting the length c of the lower wing surface of the lower wing profile into a formula (8) to determine the vertical distance h between the vertex of the leading edge of the lower wing profile and the lower surface of the upper wing₁。

In this embodiment, the shock angle β of the lower airfoil shock₁35.241 ° and shock angle β of upper wing profile shock₂39.837 DEG, leading edge apex angle theta of lower airfoil profile₁The length c of the lower wing surface of the lower wing section is 1m, the length c is substituted into the formula (8), and the vertical distance h between the top point of the leading edge of the lower wing section and the lower surface of the upper wing is determined₁＝0.199m。

And 4, step 4: determining the vertical distance h between the top of the upper airfoil surface of the lower airfoil and the lower airfoil surface of the upper airfoil₂。

h₂＝h₁-0.5c·tanθ₁(9)

In this embodiment, the vertical distance h between the top point of the leading edge of the lower wing airfoil and the lower surface of the upper wing₁0.199m, leading edge apex angle theta of lower wing profile₁The length c of the lower airfoil profile is 1m at 6 °, and these are respectively substituted into formula (9) to determine h₂＝0.147m。

The vertical distance h between the top point of the front edge of the lower wing airfoil and the lower surface of the upper wing₁And shock angle β of lower airfoil shock₁Respectively substituted into the formula (10) to determine the vertical foot and the upper part from the top point of the front edge of the lower wing profile to the lower surface of the upper wingDistance x of the leading edge point of the airfoil profile.

x＝h₁/tanβ₁(10)

In this embodiment, the vertical distance h between the top point of the leading edge of the lower wing airfoil and the lower surface of the upper wing₁0.199m shock angle β of lower wing airfoil shock₁When 35.241 ° is obtained, the values are respectively substituted into equation (10), and x is determined to be 0.282 m.

Since the rear half of the lower wing profile is thinned from thick, this results in a gradual expansion of the internal passage between the lower wing profile and the upper wing profile. Therefore, after the air passes through the upper airfoil vertex B of the lower airfoil, an expansion wave occurs in the downstream flow field. And an included angle between the lower surface of the upper wing and the upper wing surface of the trailing edge of the lower wing airfoil is an airflow deflection angle of the expansion wave. The deflection angle of the expansion wave is equal to the trailing edge vertex angle theta of the lower wing profile₂. The downstream boundary of the expansion wave is the lower airfoil mach line 7. After the expansion wave, the pressure of the air is reduced, and the Mach number of the air is lower than the Mach number M of the downstream of the upper wing type shock wave₃Mach number M increasing downstream of Mach line of lower wing airfoil₄。

For determining the Mach angle mu of the lower airfoil Mach line₁Determining the Mach number M of the lower wing profile downstream of the Mach line₄. And for determining the Mach number M downstream of the Mach line of the lower airfoil profile₄In addition to the deflection angle of the flow requiring an expansion wave, a Mach number M downstream of the upper airfoil shock wave is required₃。

Deflection angle theta of air flow through expansion wave₂And Mach number M of upper wing type shock wave downstream₃Determining the Mach angle mu of the Mach line of the lower airfoil profile₁. The method comprises the following steps:

i Mach number M of lower wing profile shock wave downstream₂And shock angle β of upper airfoil shock₂Respectively substituted into the first formula (1) of the oblique shock wave relational expression to determine the Mach number M of the lower wing profile shock wave downstream₂Perpendicular to the component M of the upper wing profile shock wave_n,3；

M_n，3＝M₂sinβ₂(1)

In this embodiment, the mach number M of the lower wing profile downstream of the shock wave₂1.786 shock angle β of top wing airfoil shock₂39.837 degrees, and respectively substituting the 39.837 degrees into the first formula (1) of the oblique shock wave relational expression to determine the Mach number M at the downstream of the lower wing profile shock wave₂Perpendicular to the component M of the upper wing profile shock wave_n,3＝1.144。

II, dividing the Mach number M of the lower wing airfoil shock wave downstream₂Perpendicular to the component M of the upper wing profile shock wave_n,3Substituting into a second formula (2) of the oblique shock wave relational expression to determine the Mach number M of the downstream of the shock wave of the upper wing airfoil₃Perpendicular to the component M of the lower-wing profile shock wave_n,4；

In this embodiment, the mach number M of the lower wing profile downstream of the shock wave₂Perpendicular to the component M of the upper wing profile shock wave_n,31.144, mixing said M_n,3Substituting into a second formula (2) of the oblique shock wave relational expression to determine the Mach number M of the downstream of the shock wave of the upper wing airfoil₃Perpendicular to the component M of the lower-wing profile shock wave_n,4＝0.879。

III Mach number M of upper wing profile shock wave downstream₃Perpendicular to the component M of the lower-wing profile shock wave_n,4Deflection angle theta of air flow of upper wing type shock wave₃And shock angle β of upper airfoil shock₂Respectively substituting into a sixth formula (6) of the oblique shock wave relational expression to determine the Mach number M of the upper wing profile shock wave downstream₃。

In this embodiment, the mach number M of the downstream of the upper wing profile shock wave₃Perpendicular to the component M of the lower-wing profile shock wave_n,4Deflection angle theta of air flow of upper wing airfoil shock wave of 0.879₃6 ° shock angle β of upper airfoil shock₂When they are 39.837 °, they are substituted into each otherIn the sixth formula (6) of the oblique shock wave relational expression, the Mach number M of the downstream of the upper wing airfoil shock wave is determined₃＝1.579。

Mach number M of upper wing profile shock wave downstream₃And trailing edge apex angle theta of lower wing airfoil₂Respectively substituted into Prandtl-Meyer expansion wave relational expression (11) to determine Mach number M of the downstream of the Mach line of the lower wing airfoil profile₄。

In this embodiment, the trailing edge apex angle θ of the lower wing airfoil₂Mach number M of 6 degree downstream of upper wing airfoil shock wave₃Respectively substituting the values into a Prandtl-Meyer expansion wave relation formula (11) to determine the Mach number M downstream of the Mach line of the lower wing airfoil profile₄＝1.783。

IV, adjusting the Mach number M of the downstream of the Mach line of the lower wing airfoil₄Substituting into formula (12) to determine Mach angle μ of lower wing profile Mach line₁。

μ₁＝sin^-1(1/M₄) (12)

In the embodiment, the Mach number M of the downstream of the Mach line of the lower wing airfoil₄(ii) 1.783, converting said M₄Substituting the equation (12) to determine the Mach angle mu of the Mach line of the lower wing airfoil₁＝34.115°。

L＝0.5c-x+h₂/tan(μ₁-θ₁) (13)

In the present embodiment, the length of the bottom edge of the lower wing airfoilThe distance x between the vertex of the front edge of the lower wing section and the vertical foot of the lower surface of the upper wing section and the front edge point of the upper wing section is 0.282m, and the vertical distance h between the vertex of the upper surface of the lower wing section and the lower surface of the upper wing section is 1m₂Mach angle μ of lower airfoil Mach line of 0.147m₁34.115 DEG, the leading edge apex angle theta of the lower wing profile₁The distance L from the leading edge point of the upper wing profile to the trailing edge point of the upper wing profile is 0.493m, respectively, by substituting 6 ° into equation (13).

Thus, the design of the supersonic double wing is completed.

Design cruise Mach number M of the embodiment₁2.0, the leading edge apex angle theta of the lower wing profile₁Is 6.0 deg., and the length c of the bottom edge of the lower wing profile is 1m, as shown in fig. 4.

The pressure cloud under the design condition of the present embodiment is shown in fig. 5. In the figure P₁Is the incoming flow pressure; p₂The pressure downstream of the lower wing profile shock wave; p₃The pressure downstream of the upper wing profile shock wave; p₄The pressure downstream of the lower airfoil mach line. The air is compressed by the shock wave 5 of the lower wing airfoil, and the pressure is from the outflow pressure P₁Pressure P rising downstream of lower airfoil shock₂. After the compression of the upper wing section shock wave 6, the pressure rises to the pressure P at the downstream of the upper wing section shock wave₃. After the high-pressure air passes through the Mach line 7 of the lower wing airfoil, the pressure is reduced to the pressure P at the downstream of the Mach line of the lower wing airfoil₄。

Incoming flow pressure P in FIG. 5₁7565 Pa; pressure P downstream of lower airfoil shock₂10615 Pa; pressure P downstream of upper airfoil shock wave₃14685 Pa; pressure P downstream of Mach line of lower airfoil profile₄10618 Pa. The pressure acting on the upper surface of the lower airfoil leading edge is equal to P₂And the pressure acting on 80% of the surface of the upper airfoil of the trailing edge of the lower airfoil is equal to P₄. Therefore, the force acting on the upper surface of the lower airfoil trailing edge cancels most of the force acting on the upper surface of the lower airfoil leading edge, so that the lower airfoil has low shock resistance. In the design state, the upper wing surface and the lower wing surface of the upper wing are both parallel to the incoming flow, so the shock wave resistance is alsoAre small. Therefore, the shock resistance of the present embodiment is low, and the shock resistance coefficient is 0.00141.

A schematic of a Busemann double wing of the prior art is shown in figure 6. The design cruise Mach number M of the Busemann double-wing₁2.0, the leading edge apex angle theta of the lower wing profile₁Is 6.0 degrees, and the length c of the bottom edge of the lower wing airfoil is 1 m. Unlike the embodiment of the present invention, the upper wing profile and the lower wing profile of the Busemann double wing are the same.

The pressure cloud of the Busemann twin wing in the prior art under the design condition is shown in fig. 7. Since the Busemann doublet is symmetrical about the axis of symmetry 9, only the shock and expansion waves in one half of the flow field are labeled in fig. 7. The positions of the shock wave and the expansion wave in the embodiment are the same as those in a half flow field of the Busemann double wing. The forces acting on the upper airfoil surface of the lower airfoil trailing edge also counteract a majority of the forces acting on the upper airfoil surface of the lower airfoil leading edge. Therefore, the shock resistance of the Busemann double wing is also low, and the shock resistance coefficient is 0.00181. This means that this embodiment has the same low shock resistance characteristics as the Busemann doublet of the prior art.

A schematic of a prior art high pressure capture foil is shown in fig. 8. The designed cruise Mach number M of the high-pressure capturing wing₁2.0, the leading edge apex angle theta of the lower wing profile₁Is 6.0 degrees, and the length of the lower surface of the lower wing airfoil is 0.5 m. Unlike the embodiment of the present invention, the lower wing profile of the high pressure capture wing in the prior art is a right triangle.

The pressure cloud of the prior art high pressure capture foil in the design state is shown in fig. 9. The vertical edge of the vertex B of the upper surface of the lower wing airfoil is the bottom plane of the lower wing airfoil. The pressure acting on the bottom plane of the lower wing airfoil is P₅. In FIG. 9, P₅1660 Pa. Because of the pressure P acting on the bottom plane of the lower wing airfoil₅Much less than the incoming flow pressure P₁Therefore, the shock resistance of the lower wing profile is very large, and the shock resistance coefficient is 0.02. Therefore, the shock resistance coefficient of the present embodiment is only 7% of that of the high pressure capture foil.

The shock resistance coefficient curves of the Busemann double wings in the prior art and the high-pressure capture wings in the prior art when the cruise Mach number is designed to be 2 are shown in FIG. 10. When the cruise mach number is designed to be 2.0, the shock resistance coefficient of the embodiment is slightly smaller than that of the Busemann double wing in the prior art, and is far smaller than that of the high-voltage capturing wing in the prior art.

The friction resistance coefficient curves of the Busemann twin-wing in the prior art and the high-pressure capture wing in the prior art at the design cruise mach number of 2 according to the embodiment of the present invention are shown in fig. 11. Because the surface area of the upper wing profile of the embodiment is smaller than that of the Busemann upper wing profile in the prior art, the coefficient of friction resistance of the embodiment is smaller than that of the Busemann double wing in the prior art; since the surface area of the lower wing profile of the present embodiment is larger than that of the high-pressure capture wing of the prior art, the coefficient of friction resistance of the present embodiment is larger than that of the high-pressure capture wing of the prior art.

The total drag coefficient of the aircraft is the sum of the shock wave drag coefficient and the friction drag coefficient. The total drag coefficient curves of the present embodiment, the Busemann twin-wing in the prior art, and the high-pressure trapping wing in the prior art at a design cruise mach number of 2 are shown in fig. 12. The overall drag coefficient of this embodiment is minimal. The reason why the total drag coefficient of this embodiment is smaller than that of the Busemann twin wings in the prior art is that the shock resistance coefficient and the frictional drag coefficient of this embodiment are both smaller than those of the Busemann twin wings in the prior art. The reason why the total drag coefficient of the present embodiment is smaller than that of the high pressure trapping wing in the related art is that although the frictional drag coefficient of the present embodiment is larger than that of the high pressure trapping wing in the related art, the shock drag coefficient thereof is much smaller than that of the high pressure trapping wing in the related art.

The lift coefficient curves of the Busemann twin-wing of the prior art and the high-pressure capture wing of the prior art at the design cruise Mach number of 2 according to the embodiment of the invention are shown in FIG. 13. The lift coefficient of the embodiment is smaller than that of the Busemann double-wing in the prior art; but also at small angles of attack it is smaller than the lift coefficient of the high pressure captivating wing of the prior art. However, since the total drag coefficient of the present embodiment is the smallest of the three, the maximum lift-drag ratio of the present embodiment is the largest, as shown in fig. 14. The lift-to-drag ratios for the Busemann twin wings of this example, the prior art, and the high pressure capture wings of the prior art were 8.45, 7.5, and 5.04, respectively, when the angle of attack was 3.5 °.

For the two-wing configuration of the present embodiment and the prior art Busemann two-wing with an inner compression section, the ratio of the throat area to the inlet area of the inner compression section determines their shock resistance and launch performance at off-design cruise Mach numbers. The larger the ratio of the throat area to the inlet area of the inner compression section is, the smaller the shock resistance at the non-designed cruise Mach number is, and the easier the starting is.

An inner compression section of an embodiment of the present invention is shown in fig. 15. The shaded portion in the figure is the inner compression section of the present embodiment. The throat area of the inner contraction section is equal to the vertical distance h between the top of the upper wing surface of the lower wing profile and the lower wing surface of the upper wing profile₂And the length of a vertical line section from the vertex of the front edge of the upper wing airfoil to the upper wing surface of the front edge of the lower wing airfoil is an inlet area of an inner contraction section h₃. The ratio of the inner compression section throat area to the inlet area is 0.869 for this embodiment.

The prior art internal contraction section of the Busemann twin wings is shown in fig. 16. The shaded portion in the figure is the inner contraction section of the Busemann double wing. The distance between the vertex of the leading edge of the Busemann double-wing upper wing airfoil profile and the vertex of the leading edge of the lower wing airfoil profile is the throat area h of the Busemann double-wing inner contraction section₄And the distance between the vertex of the lower wing surface of the Busemann double-wing upper wing airfoil section and the vertex of the upper wing surface of the lower wing airfoil section is the inlet area h of the Busemann double-wing inner contraction section₅. The Busemann double wing has an inner contraction section throat area to inlet area ratio of 0.736. This demonstrates that the ratio of throat area to inlet area of the compression section in the embodiments of the present invention is less than the ratio of throat area to inlet area of the Busemann double wing internal compression section of the prior art. Therefore, the embodiment of the invention is excited when the Mach number of the cruise is not designedThe wave resistance is smaller and the start is easier.

The shock resistance coefficients of Busemann double wings in the embodiment of the invention and the Busemann double wings in the prior art at the non-design cruise Mach number are shown in FIG. 17. The shock resistance coefficient of the present embodiment is smaller than that of the Busemann twin wings in the prior art. For example, when the incoming flow mach number is 1.2, the shock resistance coefficient of the present embodiment is 0.056, while the shock resistance coefficient of the Busemann twin vane in the prior art is 0.124; namely, the shock resistance coefficient of the embodiment is reduced by 55% compared with the shock resistance coefficient of the Busemann double wing in the prior art.

The shock resistance coefficients of the Busemann twin wings in the embodiment of the present invention and the prior art in the acceleration and deceleration processes are shown in fig. 18. For the dual-vane configuration with an inner compression section, such as the Busemann dual-vane of the present embodiment and the prior art, the dual-vane configuration is initially in an inactive state during acceleration from a low incoming flow mach number to a high incoming flow mach number. In the non-starting state, the shock resistance coefficient of the double-wing configuration is high. When the incoming flow mach number accelerates to the starting mach number, the shock resistance coefficient of the double-wing configuration is rapidly reduced to the shock resistance coefficient when the incoming flow mach number decelerates from a high incoming flow mach number to a low incoming flow mach number. The higher the starting mach number, the more difficult the twin wing configuration is to start. In fig. 18, the starting mach number of the Busemann twin vane in the prior art is 2.9, while the starting mach number of the present embodiment is 1.9. Thus, the present embodiment is easier to activate than the Busemann twin wings of the prior art.

The invention provides a method for determining the vertical distance h between the top point of the leading edge of a lower wing airfoil and the lower surface of an upper wing₁Equation (8) of (a), determining the vertical distance h between the top of the upper airfoil surface of the lower airfoil and the lower airfoil surface of the upper airfoil₂And (3) determining the distance x from the vertex of the front edge of the lower wing section to the foot of the lower surface of the upper wing section and the front edge point of the upper wing section. And (3) determining a distance L from the upper airfoil leading edge point to the upper airfoil trailing edge point. The equations need to use not only the oblique shock wave relation but also the Prandtl-Meyer expansion wave relation. The time for designing the supersonic speed double wings can be shortened through the formulas, and the efficiency is improved.

Claims

1. A supersonic double wing comprises a lower wing and an upper wing; the upper wing is positioned above the lower wing, so that an airflow inner channel is formed between the lower wing surface of the upper wing and the upper wing surface of the lower wing; the supersonic speed double wings are connected with the fuselage through a central wing box; the wing type of the lower wing is an isosceles triangle; the vertex of the front edge of the lower wing airfoil is A, the vertex of the rear edge of the lower wing airfoil is C, and the vertex of the upper wing surface of the lower wing airfoil is B; the upper wing is a flat plate; the upper surface and the lower surface of the flat plate respectively form an upper wing surface and a lower wing surface of the upper wing; the leading edge point of the upper wing profile is D; the trailing edge point of the upper wing profile is E; the distance from the upper wing profile leading edge point D to the upper wing profile trailing edge point E is L; the wing profile of the upper wing is rectangular;

the vertical distance between the top point A of the lower wing airfoil leading edge and the lower surface of the upper wing is h₁(ii) a The vertical foot from the vertex A of the front edge of the lower wing airfoil to the lower surface of the upper wing is F; the distance from the vertex A of the front edge of the lower wing airfoil section to the foot F of the lower surface of the upper wing and the front edge point D of the upper wing airfoil section is x; the vertical distance between the top B of the upper wing surface of the lower wing profile and the lower surface of the upper wing is h₂。

2. The supersonic speed double wing as set forth in claim 1, wherein the bottom side between the lower wing profile leading edge vertex a and the lower wing profile trailing edge vertex C is a plane, which constitutes the lower wing surface of the lower wing profile; the length of the lower wing surface of the lower wing airfoil is c; the edge between the lower wing profile leading edge vertex A and the lower wing surface vertex B forms a leading edge upper wing surface of the lower wing profile; the edge between the lower airfoil surface apex B and the lower airfoil trailing edge apex C constitutes the lower airfoil trailing edge upper airfoil surface.

3. The dual supersonic airfoil of claim 1 wherein the upper airfoil surface and the lower airfoil surface of the upper airfoil are both planar; the included angle between the connecting line between the upper wing section trailing edge point E and the upper wing surface vertex B of the lower wing section and the upper wing surface of the trailing edge of the lower wing section is also an acute angle, and the included angle is equal to the Mach angle of the Mach line of the lower wing sectionμ₁。

4. A design method of the supersonic speed double wings as claimed in claim 1, wherein the specific process is;

step 1, determining the shock angle β of the lower wing profile shock wave₁：

Under supersonic conditions, the leading edge upper wing surface of the lower wing compresses air and generates lower wing profile shock waves; the airflow deflection angle of the lower wing profile shock wave is equal to the leading edge vertex angle theta of the lower wing profile₁(ii) a The pressure of the air is increased through the compression of the lower wing profile shock wave, and the Mach number of the air is M from the designed cruise Mach number₁Reduced to Mach number M of lower wing profile shock wave downstream₂；

Design cruise Mach number M₁And the leading edge apex angle theta of the lower airfoil₁Respectively substituted into a seventh formula (7) of the oblique shock wave relational expression to determine the shock wave angle β of the lower wing airfoil shock wave₁；

Step 2, determining the shock angle β of the upper wing profile shock wave₂：

Deflection angle theta of airflow through upper wing profile shock wave₃And Mach number M of lower wing profile shock wave downstream₂Obtaining the shock wave angle β of the upper wing profile shock wave₂；

M_n，1＝M₁sinβ₁(1)

II design cruise Mach number M₁Perpendicular to the component M of the lower-wing profile shock wave_n,1Substitution intoIn a second formula (2) of the oblique shock wave relational expression, the Mach number M of the lower wing profile shock wave downstream is determined₂Component M perpendicular to lower wing profile shock wave_n,2；

III Mach number M of the downstream of the lower wing profile shock wave₂Perpendicular to the component M of the lower-wing profile shock wave_n,2The vertex angle theta of the front edge of the lower wing profile₁And shock angle β of lower airfoil shock₁Respectively substituting into a sixth formula (6) of the oblique shock wave relational expression to determine the Mach number M of the lower wing profile shock wave downstream₂；

2. Determining shock angle β of upper wing airfoil shock₂：

Mach number M of the lower wing airfoil shock wave downstream₂And the deflection angle theta of the air flow of the upper airfoil shock wave₃Respectively substituted into a seventh formula (7) of the oblique shock wave relational expression to determine the shock wave angle β of the upper wing airfoil shock wave₂；

And step 3: determining the vertical distance h between the top point of the lower wing profile leading edge and the lower surface of the upper wing₁；

Shock angle β of lower wing profile shock₁Shock angle β of top wing airfoil shock₂The vertex angle theta of the front edge of the lower wing profile₁Respectively substituting the length c of the lower wing surface of the lower wing profile into a formula (8) to determine the vertical distance h between the vertex of the leading edge of the lower wing profile and the lower surface of the upper wing₁；

And 4, step 4: determining the vertical distance h between the top of the upper airfoil surface of the lower airfoil and the lower airfoil surface of the upper airfoil₂：

The vertical distance h between the top point of the front edge of the lower wing airfoil and the lower surface of the upper wing₁The vertex angle theta of the front edge of the lower wing profile₁Respectively substituting the length c of the lower wing surface of the lower wing airfoil into a formula (9) to determine the vertical distance h between the top of the lower wing surface of the lower wing and the lower surface of the upper wing₂；

h₂＝h₁-0.5c·tanθ₁(9)

And 5: determining the distance x from the vertex of the front edge of the lower wing airfoil to the vertical foot of the lower surface of the upper wing and the front edge point of the upper wing airfoil: the vertical distance h between the top point of the front edge of the lower wing airfoil and the lower surface of the upper wing₁And shock angle β of lower airfoil shock₁Respectively substituting the distance x between the vertex of the front edge of the lower wing airfoil and the vertical foot of the lower surface of the upper wing and the front edge point of the upper wing airfoil into a formula (10);

x＝h₁/tanβ₁(10)

step 6: determining the Mach angle mu of the Mach line of the lower airfoil profile₁：

Passing the trailing edge apex angle theta of the lower wing profile₂And Mach number M downstream of Mach line of lower wing airfoil₄Determining the Mach angle mu of the Mach line of the lower airfoil profile₁；

Mach number M of the downstream Mach line of the lower wing airfoil₄Substituting into formula (12) to determine Mach angle μ of lower wing profile Mach line₁；

μ₁＝sin^-1(1/M₄) (12)

And 7: determining the distance L from the leading edge point of the upper wing section to the trailing edge point of the upper wing section:

the length c of the bottom edge of the lower wing profile, the distance x between the foot from the top point of the front edge of the lower wing profile to the lower surface of the upper wing and the front edge point of the upper wing profile, and the vertical distance h between the top point of the upper surface of the lower wing profile and the lower surface of the upper wing profile₂Mach angle mu of Mach line of lower wing airfoil₁And the leading edge apex angle theta of the lower airfoil₁Respectively substitute into the formulas (13) Determining the distance L from the front edge point of the upper wing profile to the rear edge point of the upper wing profile;

L＝0.5c-x+h₂/tan(μ₁-θ₁) (13)

thus, the design of the supersonic double wing is completed.

5. The method for designing a supersonic double-wing structure as defined in claim 4, wherein the deflection angle θ of the flow of the shock wave of the upper wing profile is₃Is an included angle between the upper wing profile auxiliary line and the lower surface of the upper wing; the included angle between the upper wing profile auxiliary line and the lower surface of the upper wing is the airflow deflection angle theta of the upper wing profile shock wave₃(ii) a The deflection angle theta of the air flow₃Equal to the leading edge apex angle theta of the lower wing profile₁。

6. The method of claim 5, wherein the starting point of the auxiliary line of the upper wing section is a leading edge point D of the wing section, and the leading edge point D of the upper wing section is parallel to the leading edge upper wing section of the lower wing section.

7. The method for designing a supersonic double wing as defined in claim 4, wherein the lower wing surface of the lower wing profile and the leading edge upper wing surface of the lower wing form a leading edge apex angle θ of the lower wing profile₁(ii) a The leading edge vertex angle theta of the lower wing airfoil₁And trailing edge apex angle theta of lower wing airfoil₂Are all acute angles.

8. The supersonic double wing of claim 4, wherein the angle between the line between the upper wing profile leading edge point D and the lower wing profile leading edge point A and the lower wing profile is the shock angle β of the lower wing profile shock wave₁The included angle between the upper wing profile auxiliary line and the connecting line of the upper wing profile leading edge point D and the upper wing surface vertex B of the lower wing profile is the shock wave angle β of the shock wave of the upper wing profile₂。

9. Supersonic velocity according to claim 4Double wing, characterised in that the Mach number M downstream of the Mach line of the lower wing profile is determined₄The specific process comprises the following steps:

M_n，3＝M₂sinβ₂(1)

III Mach number M of upper wing profile shock wave downstream₃Perpendicular to the component M of the lower-wing profile shock wave_n,4Deflection angle theta of air flow of upper wing type shock wave₃And shock angle β of upper airfoil shock₂Respectively substituting into a sixth formula (6) of the oblique shock wave relational expression to obtain the Mach number M of the lower reaches of the upper wing profile shock wave₃；

IV, adjusting the Mach number M of the downstream of the upper wing airfoil shock wave₃And trailing edge apex angle theta of lower wing airfoil₂Respectively substituted into Prandtl-Meyer expansion wave relational expression (11) to obtain Mach number M at the downstream of Mach line of lower wing profile₄；