A high-drag divergent Mach number laminar airfoil suitable for light-medium-sized high-speed business jets

Abstract

The invention provides a high-drag divergent Mach number laminar airfoil suitable for light-medium-sized high-speed business jets, wherein the airfoil is composed of a leading edge, a trailing edge, and an upper camber and a lower camber located between the leading edge and the trailing edge; the ratio of the leading edge radius r to the airfoil chord length c is r / c=1.47%, the ratio of the maximum thickness a to the airfoil chord length c is a / c=11.93%, the maximum thickness position is located at x / c=37.47%, the ratio of the maximum camber b to the airfoil chord length c is b / c=1.17%, the maximum camber position is The position is x / c=60.3%, the ratio of the trailing edge thickness w to the airfoil chord length c is w / c=0.146%; x is the distance from the leading edge to the trailing edge along the airfoil chord direction, and the values ​​of r / c, a / c, b / c, x / c and w / c have a maximum error of ±3% respectively; the lengths of the laminar flow areas on the upper and lower surfaces of the airfoil are not less than 40% of the chord length; when Ma=0.71, the airfoil drag divergence Mach number is not less than 0.73; when Ma=0.20, the airfoil maximum lift coefficient is not less than 1.75. The present invention is designed for laminar control in low-speed and high-speed cruising states, and has the characteristics of high lift, high lift-to-drag ratio, mild stall characteristics, and high drag divergence Mach number.

Description

Technical Field

[0001] The invention belongs to the field of airfoil design, and in particular to the field of laminar airfoil design in aerodynamic shape design of aircraft, and specifically is a high-drag divergent Mach number laminar airfoil suitable for light and medium-sized high-speed turbofan business jets. Background Art

[0002] Business jets refer to special aircraft used for administrative affairs or business activities, which can provide high-quality and personalized services for high-end customers. As a highly efficient long-distance transportation tool, business jets have many advantages such as advanced, flexible, fast, safe, comfortable, and strong privacy. With the rapid development of my country's economy and the gradual implementation of the reform policy of low-altitude airspace management, the business aviation market is becoming increasingly prosperous. As high-end civil aircraft products, the economic benefits created by light and medium-sized business jets are recognized by more and more entrepreneurs and business people. However, the current development of my country's business aviation market does not match the level of my country's economic development. In order to prevent foreign business aircraft manufacturers from seizing my country's huge business aviation market, it is necessary to focus on improving the technical performance of my country's business aircraft.

[0003] The airfoil is the basis of wing design, and the performance of the airfoil can greatly affect the performance of the entire aircraft. Generally speaking, light and medium-sized high-speed turbofan business jets have high flight speeds, and the cruise Mach number exceeds 0.8. Advanced supercritical wings must be used to meet aerodynamic characteristics. However, light and medium-sized high-speed business jets have high wing loading and small wing area. Under the performance index requirements of their higher range, the internal fuel volume acceptable to the engineering design and the absolute height of the internal structure of the wing must be guaranteed, which creates a higher practical constraint on the relative thickness of the airfoil. Summary of the invention

[0004] Technical issues to be solved

[0005] In response to the needs of the business jet project, the conditions based on the cruise Mach number of 0.82 for the whole aircraft and the wing sweep angle of 30° were proposed. The designed airfoil was required to meet the following design indicators under the conditions of the design state Reynolds number of 3.63e6 and the design Mach number of 0.71:

[0006] 1. The length of the laminar flow area on the upper and lower surfaces of the airfoil shall not be less than 40% of the chord length.

[0007] 2. Under high-speed conditions (Ma=0.71), the drag divergence Mach number is not less than 0.73.

[0008] 3. Taking into account the aerodynamic performance at low speed (Ma=0.20), the maximum lift coefficient shall not be less than 1.75.

[0009] 4. The maximum thickness shall not be less than 11.5% of the airfoil chord length.

[0010] However, there are few designs of laminar airfoils in China at present. Among them, the applicant unit has applied for the following patents in the early stage: Take the patent with publication number CN106828875A, which is named a laminar airfoil suitable for general aircraft with a heavy climbing characteristic, as an example. This patent is mainly designed for high-altitude, low-speed and multi-operating conditions. In addition, there is a patent with publication number CN104691739A, which is named a high-lift laminar airfoil with low drag and high drag divergence Mach number, and a patent with publication number CN101492090, which is named a high-lift and high-speed laminar airfoil with a trailing edge separation vortex. The above two patent applications are mainly designed for flows with a Mach number of about 0.6. The resulting airfoil will significantly increase the shock wave drag in high-speed flows with a Mach number of 0.71, and the drag divergence Mach number cannot meet the design index of not less than 0.73. In addition, since it does not take low-speed performance as a design index, the maximum lift coefficient and stall angle of attack cannot meet the design index requirements.

[0011] To this end, the present invention takes the RAE2822 airfoil as the basic airfoil and proposes a high-drag divergent Mach number laminar airfoil suitable for light and medium-sized high-speed business jets. The key parameters of the airfoil are given through calculation comparison and analysis design by parameterization method and CFD method, and the airfoil that meets the design indicators is further given in the form of airfoil parameterization formula and geometric coordinates.

[0012] The technical solution of the present invention is:

[0013] The invention discloses a high-drag divergent Mach number laminar airfoil suitable for light-medium-sized high-speed business jets. The airfoil is composed of a leading edge, a trailing edge, and an upper camber and a lower camber located between the leading edge and the trailing edge. The ratio of the leading edge radius r of the airfoil to the airfoil chord length c is r / c=1.47%, the ratio of the maximum thickness a to the airfoil chord length c is a / c=11.93%, the maximum thickness position is located at x / c=37.47%, the ratio of the maximum camber b to the airfoil chord length c is b / c=1.17%, the maximum camber position is Located at x / c=60.3%, the ratio of the trailing edge thickness w to the airfoil chord length c is w / c=0.146%; x is the distance from the leading edge to the trailing edge along the chord line of the airfoil, and the values ​​of r / c, a / c, b / c, x / c and w / c have a maximum error of ±3% respectively; the lengths of the laminar flow areas on the upper and lower surfaces of the airfoil are not less than 40% of the chord length; when Ma=0.71, the airfoil drag divergence Mach number is not less than 0.73; when Ma=0.20, the airfoil maximum lift coefficient is not less than 1.75.

[0014] Furthermore, the parameterization formula of the upper camber of the airfoil is as follows:

[0015] y(x)=a0+a1*cos(x*w)+b1*sin(x*w)+a2*cos(2*x*w)+b2*sin(2*x*w)+a3*cos(3*x*w)+b3*sin(3*x*w)+a4*cos(4*x*w)+b4*sin(4*x* w)+a5*cos(5*x*w)+b5*sin(5*x*w)+a6*cos(6*x*w)+b6*sin(6*x*w)+a7*cos(7*x*w)+b7*sin(7*x*w)+a8*cos(8*x*w)+b8*sin(8*x*w)

[0016] in

[0017] w=1.049*(1±0.03); a0=(-3.398e+09)*(1±0.03);

[0018] a1=(5.201e+09)*(1±0.03); b1=(3.123e+09)*(1±0.03);

[0019] a2=(-2.022e+09)*(1±0.03); b2=(-3.797e+09)*(1±0.03);

[0020] a3=(-1.23e+08)*(1±0.03); b3=(2.395e+09)*(1±0.03);

[0021] a4=(5.747e+08)*(1±0.03); b4=(-8.545e+08)*(1±0.03);

[0022] a5=(-2.984e+08)*(1±0.03); b5=(1.397e+08)*(1±0.03);

[0023] a6=(7.366e+07)*(1±0.03); b6=(7.616e+06)*(1±0.03);

[0024] a7=(-8.356e+06)*(1±0.03); b7=(-6.274e+06)*(1±0.03);

[0025] a8=(2.623e+05)*(1±0.03); b8=(6.462e+05)*(1±0.03).

[0026] Furthermore, the parameterization formula of the lower camber of the airfoil is as follows:

[0027] y(x)=A0+A1*cos(x*w)+B1*sin(x*w)+A2*cos(2*x*w)+B2*sin(2*x*w)+A3*cos(3*x*w)+B3*sin(3*x*w)+A4*cos(4*x*w)+B4*sin(4*x* w)+A5*cos(5*x*w)+B5*sin(5*x*w)+A6*cos(6*x*w)+B6*sin(6*x*w)+A7*cos(7*x*w)+B7*sin(7*x*w)+A8*cos(8*x*w)+B8*sin(8*x*w)

[0028] in

[0029] w=1.049*(1±0.03); A0=(3.295e+09)*(1±0.03);

[0030] A1=(-5.046e+09)*(1±0.03); B1=(-3.025e+09)*(1±0.03);

[0031] A2=(1.965e+09)*(1±0.03); B2=(3.68e+09)*(1±0.03);

[0032] A3=(1.155e+08)*(1±0.03); B3=(-2.322e+09)*(1±0.03);

[0033] A4=(-5.554e+08)*(1±0.03); B4=(8.297e+08)*(1±0.03);

[0034] A5=(2.889e+08)*(1±0.03); B5=(-1.362e+08)*(1±0.03);

[0035] A6=(-7.143e+07)*(1±0.03); B6=(-7.148e+06)*(1±0.03);

[0036] A7=(8.123e+06)*(1±0.03); B7=(6.05e+06)*(1±0.03);

[0037] A8=(-2.57e+05)*(1±0.03); B8=(-6.251e+05)*(1±0.03);

[0038] Furthermore, the geometric coordinate value pairs x / c and y of the camber line on the airfoil are u / c means:

[0039]

[0040]

[0041]

[0042] where y u It is the vertical distance between the coordinate point of the upper arc and the chord line. The maximum error of the geometric coordinate value pair is ±3%.

[0043] Furthermore, the geometric coordinate value pair x / c and y of the lower camber line of the airfoil is l / c means:

[0044]

[0045]

[0046]

[0047] where y l It is the vertical distance between the coordinate point of the lower arc and the chord line. The maximum error of the geometric coordinate value pair is ±3%.

[0048] Beneficial Effects

[0049] The high drag divergence Mach number laminar airfoil (KTR) provided by the present invention is based on the RAE2822 airfoil, and is designed for laminar control in low-speed and high-speed cruising states, and has the characteristics of high lift, high lift-to-drag ratio, mild stall characteristics, and high drag divergence Mach number. Among them, the maximum thickness of the airfoil is 11.93% of the unit chord length, which meets the index of not less than 11.5% of the unit chord length; the drag coefficient decreases slightly at the cruising point, the lift-to-drag ratio is improved to a certain extent, the cruising moment coefficient is reduced, the cruise trim resistance can be reduced, the drag divergence Mach number is 0.73, and it has the characteristics of high drag divergence Mach number. The low-speed performance is greatly improved, the maximum lift coefficient at low speed can reach 1.867, and the stall angle of attack is increased to 17 degrees, indicating that the airfoil has the characteristics of high lift and mild stall characteristics. It meets the design index requirements. In the cruising state, the laminar flow areas on the upper and lower surfaces are not less than 40% of the chord length.

[0050] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0052] Figure 1: A comparison of the geometrical shapes of the KTR airfoil designed by the present invention and the RAE2822 airfoil;

[0053] Figure 2 : Comparison of lift coefficient curves of the KTR airfoil designed by the present invention and the RAE2822 airfoil at low speed (Ma=0.20);

[0054] Figure 3 : The pressure coefficient distribution curve of the KTR airfoil designed by the present invention under the cruising state (0.71 Mach number, 1.125 degree angle of attack);

[0055] Figure 4 : The surface friction coefficient distribution curve of the KTR airfoil designed by the present invention under the cruising state (0.71 Mach number, 1.125 degree angle of attack);

[0056] Figure 5 : Comparison of lift coefficient curves of the KTR airfoil designed by the present invention and the RAE2822 airfoil at the design point 0.71 Mach state;

[0057] Figure 6 : Comparison of drag coefficient curves of the KTR airfoil designed by the present invention and the RAE2822 airfoil under cruise state;

[0058] Figure 7 : The drag creep curves of the KTR airfoil designed by the present invention are compared with those of the RAE2822 airfoil. DETAILED DESCRIPTION

[0059] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0060] The laminar airfoil proposed in this embodiment, which is suitable for light-medium-sized high-speed business jets, pays more attention to the cruising characteristics of the airfoil while meeting the design requirements for low-speed performance.

[0061] In view of the situation where the high-speed cruising state is dominated by laminar flow, the high-speed characteristics of the airfoil are improved on the premise of meeting the low-speed performance design requirements, and the airfoil design is carried out. The index requirements are:

[0062] 1. The length of the laminar flow area on the upper and lower surfaces of the airfoil shall not be less than 40% of the chord length.

[0063] 2. Under high-speed conditions (Ma=0.71), the drag divergence Mach number is not less than 0.73.

[0064] 3. Taking into account the aerodynamic performance at low speed (Ma=0.20), the maximum lift coefficient shall not be less than 1.75.

[0065] 4. The maximum thickness shall not be less than 11.5% of the airfoil chord length.

[0066] This embodiment uses advanced airfoil design and optimization technology and takes the RAE2822 airfoil as the basic airfoil to design a high drag divergence Mach number laminar airfoil (KTR), so that the airfoil can have a higher lift-to-drag ratio at a higher flight Mach number, thereby improving the cruise efficiency.

[0067] The KTR airfoil is composed of a leading edge, a trailing edge, and an upper camber and a lower camber located between the leading edge and the trailing edge; the ratio of the leading edge radius r of the airfoil to the chord length c of the airfoil is r / c=1.47%, the ratio of the maximum thickness a to the chord length c of the airfoil is a / c=11.93%, the maximum thickness position is located at x / c=37.47%, the ratio of the maximum camber b to the chord length c of the airfoil is b / c=1.17%, the maximum camber position is located at x / c=60.3%, the ratio of the trailing edge thickness w to the chord length c of the airfoil is w / c=0.146%; x is the distance from the leading edge to the trailing edge along the chord line direction of the airfoil, and the values ​​of r / c, a / c, b / c, x / c and w / c are respectively allowed to have a maximum error of ±3% of their own values.

[0068] If a parameterized formula is used for description, the parameterized formula of the upper camber of the airfoil is as follows:

[0069] y(x)=a0+a1*cos(x*w)+b1*sin(x*w)+a2*cos(2*x*w)+b2*sin(2*x*w)+a3*cos(3*x*w)+b3*sin(3*x*w)+a4*cos(4*x*w)+b4*sin(4*x* w)+a5*cos(5*x*w)+b5*sin(5*x*w)+a6*cos(6*x*w)+b6*sin(6*x*w)+a7*cos(7*x*w)+b7*sin(7*x*w)+a8*cos(8*x*w)+b8*sin(8*x*w)

[0070] in

[0071] w=1.049*(1±0.03); a0=(-3.398e+09)*(1±0.03);

[0072] a1=(5.201e+09)*(1±0.03); b1=(3.123e+09)*(1±0.03);

[0073] a2=(-2.022e+09)*(1±0.03); b2=(-3.797e+09)*(1±0.03);

[0074] a3=(-1.23e+08)*(1±0.03); b3=(2.395e+09)*(1±0.03);

[0075] a4=(5.747e+08)*(1±0.03); b4=(-8.545e+08)*(1±0.03);

[0076] a5=(-2.984e+08)*(1±0.03); b5=(1.397e+08)*(1±0.03);

[0077] a6=(7.366e+07)*(1±0.03); b6=(7.616e+06)*(1±0.03);

[0078] a7=(-8.356e+06)*(1±0.03); b7=(-6.274e+06)*(1±0.03);

[0079] a8=(2.623e+05)*(1±0.03); b8=(6.462e+05)*(1±0.03).

[0080] The parameterization formula of the lower camber of the airfoil is as follows:

[0081] y(x)=A0+A1*cos(x*w)+B1*sin(x*w)+A2*cos(2*x*w)+B2*sin(2*x*w)+A3*cos(3*x*w)+B3*sin(3*x*w)+A4*cos(4*x*w)+B4*sin(4*x* w)+A5*cos(5*x*w)+B5*sin(5*x*w)+A6*cos(6*x*w)+B6*sin(6*x*w)+A7*cos(7*x*w)+B7*sin(7*x*w)+A8*cos(8*x*w)+B8*sin(8*x*w)

[0082] in

[0083] w=1.049*(1±0.03); A0=(3.295e+09)*(1±0.03);

[0084] A1=(-5.046e+09)*(1±0.03); B1=(-3.025e+09)*(1±0.03);

[0085] A2=(1.965e+09)*(1±0.03); B2=(3.68e+09)*(1±0.03);

[0086] A3=(1.155e+08)*(1±0.03); B3=(-2.322e+09)*(1±0.03);

[0087] A4=(-5.554e+08)*(1±0.03); B4=(8.297e+08)*(1±0.03);

[0088] A5=(2.889e+08)*(1±0.03); B5=(-1.362e+08)*(1±0.03);

[0089] A6=(-7.143e+07)*(1±0.03); B6=(-7.148e+06)*(1±0.03);

[0090] A7=(8.123e+06)*(1±0.03); B7=(6.05e+06)*(1±0.03);

[0091] A8=(-2.57e+05)*(1±0.03); B8=(-6.251e+05)*(1±0.03);

[0092] If geometric data parameters are used, the geometric coordinate values ​​of the upper camber of the airfoil are x / c and y u / c means:

[0093]

[0094]

[0095]

[0096] where y u It is the vertical distance between the coordinate point of the upper arc and the chord line. The maximum error of the geometric coordinate value pair is ±3%.

[0097] The geometric coordinate value pair x / c and y of the lower camber line of the airfoil l / c means:

[0098]

[0099]

[0100]

[0101] where y l It is the vertical distance between the coordinate point of the lower arc and the chord line. The maximum error of the geometric coordinate value pair is ±3%.

[0102] Calculations show that the performance of the airfoil of the present invention meets the design requirements. Its low-speed maximum lift coefficient is 1.867, and the stall angle of attack is 17 degrees. The drag divergence Mach number is 0.73. In the cruising state, the length of the laminar flow area of ​​the airfoil reaches 40%-50%, meeting the requirements of the technical indicators.

[0103] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A high-drag divergent Mach number laminar airfoil suitable for light-medium-sized high-speed business jets, the airfoil comprising a leading edge, a trailing edge, and an upper camber and a lower camber located between the leading edge and the trailing edge; characterized in that: The ratio of the leading edge radius r of the airfoil to the chord length c of the airfoil is r / c=1.47%, the ratio of the maximum thickness a to the chord length c of the airfoil is a / c=11.93%, the maximum thickness position is located at x / c=37.47%, the ratio of the maximum camber b to the chord length c of the airfoil is b / c=1.17%, the maximum camber position is located at x / c=60.3%, the ratio of the trailing edge thickness w to the chord length c of the airfoil is w / c=0.146%; x is the distance along the wing The distances from the leading edge to the trailing edge in the direction of the chord line, r / c, a / c, b / c, x / c and w / c have a maximum error of ±3% respectively; the lengths of the laminar flow areas on the upper and lower surfaces of the airfoil are not less than 40% of the chord length; when the Reynolds number is 3.63e6 and Ma=0.71, the airfoil drag divergence Mach number is not less than 0.73; when the Reynolds number is 3.63e6 and Ma=0.20, the maximum lift coefficient of the airfoil is not less than 1.

75.

2. According to claim 1, a high-drag divergent Mach number laminar airfoil suitable for light-medium-sized high-speed business jets, characterized in that: The parameterization formula of the upper camber of the airfoil is as follows: y(x)=a0+a1*cos(x*w)+b1*sin(x*w)+a2*cos(2*x*w)+b2*sin(2*x*w)+a3*cos(3*x*w)+b3*sin(3*x*w)+a4*cos(4*x*w)+b4*sin(4*x* w)+a5*cos(5*x*w)+b5*sin(5*x*w)+a6*cos(6*x*w)+b6*sin(6*x*w)+a7*cos(7*x*w)+b7*sin(7*x*w)+a8*cos(8*x*w)+b8*sin(8*x*w) in w=1.049*(1±0.03); a0=(-3.398e+09)*(1±0.03); a1=(5.201e+09)*(1±0.03); b1=(3.123e+09)*(1±0.03); a2=(-2.022e+09)*(1±0.03); b2=(-3.797e+09)*(1±0.03); a3=(-1.23e+08)*(1±0.03); b3=(2.395e+09)*(1±0.03); a4=(5.747e+08)*(1±0.03); b4=(-8.545e+08)*(1±0.03); a5=(-2.984e+08)*(1±0.03); b5=(1.397e+08)*(1±0.03); a6=(7.366e+07)*(1±0.03); b6=(7.616e+06)*(1±0.03); a7=(-8.356e+06)*(1±0.03); b7=(-6.274e+06)*(1±0.03); a8=(2.623e+05)*(1±0.03); b8=(6.462e+05)*(1±0.03).

3. A high-drag divergent Mach number laminar airfoil suitable for light-medium-sized high-speed business jets according to claim 1 or 2, characterized in that: The parameterization formula of the lower camber of the airfoil is as follows: y(x) = A0 + A1*cos(x*w) + B1*sin(x*w) + A2*cos(2*x*w) + B2*sin(2*x*w) + A3*cos(3*x*w) + B3*sin(3*x*w) + A4*cos(4*x*w) + B4*sin(4*x*w) + A5*cos(5*x*w) + B5*sin(5*x*w) + A6*cos(6*x*w) + B6*sin(6*x*w) + A7*cos(7*x*w) + B7*sin(7*x*w) + A8*cos(8*x*w) + B8*sin(8*x*w) where w = 1.049*(1 ± 0.03); A0 = (3.295e+09)*(1 ± 0.03); A1 = (-5.046e+09)*(1 ± 0.03); B1 = (-3.025e+09)*(1 ± 0.03); A2 = (1.965e+09)*(1 ± 0.03); B2 = (3.68e+09)*(1 ± 0.03); A3 = (1.155e+08)*(1 ± 0.03); B3 = (-2.322e+09)*(1 ± 0.03); A4 = (-5.554e+08)*(1 ± 0.03); B4 = (8.297e+08)*(1 ± 0.03); A5 = (2.889e+08)*(1 ± 0.03); B5 = (-1.362e+08)*(1 ± 0.03); A6 = (-7.143e+07)*(1 ± 0.03); B6 = (-7.148e+06)*(1 ± 0.03); A7 = (8.123e+06)*(1 ± 0.03); B7 = (6.05e+06)*(1 ± 0.03); A8 = (-2.57e+05)*(1 ± 0.03); B8 = (-6.251e+05)*(1 ± 0.03).

4. According to claim 1, a high-drag divergent Mach number laminar airfoil suitable for light-medium-sized high-speed business jets, characterized in that: The geometric coordinates of the camber line on the airfoil are x / c and y u / c means: where y u It is the vertical distance between the coordinate point of the upper arc and the chord line. The maximum error of the geometric coordinate value pair is ±3%.

5. According to claim 1, a high-drag divergent Mach number laminar airfoil suitable for light-medium-sized high-speed business jets, characterized in that: The geometric coordinate value pair x / c and y of the lower camber line of the airfoil l / c means: where y l It is the vertical distance between the coordinate point of the lower arc and the chord line. The maximum error of the geometric coordinate value pair is ±3%.

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