CN111460580B - Method for expanding waverider volume by using cubic polynomial - Google Patents
Method for expanding waverider volume by using cubic polynomial Download PDFInfo
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- CN111460580B CN111460580B CN202010224363.9A CN202010224363A CN111460580B CN 111460580 B CN111460580 B CN 111460580B CN 202010224363 A CN202010224363 A CN 202010224363A CN 111460580 B CN111460580 B CN 111460580B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64C—AEROPLANES; HELICOPTERS
- B64C30/00—Supersonic type aircraft
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64F—GROUND OR AIRCRAFT-CARRIER-DECK INSTALLATIONS SPECIALLY ADAPTED FOR USE IN CONNECTION WITH AIRCRAFT; DESIGNING, MANUFACTURING, ASSEMBLING, CLEANING, MAINTAINING OR REPAIRING AIRCRAFT, NOT OTHERWISE PROVIDED FOR; HANDLING, TRANSPORTING, TESTING OR INSPECTING AIRCRAFT COMPONENTS, NOT OTHERWISE PROVIDED FOR
- B64F5/00—Designing, manufacturing, assembling, cleaning, maintaining or repairing aircraft, not otherwise provided for; Handling, transporting, testing or inspecting aircraft components, not otherwise provided for
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/15—Correlation function computation including computation of convolution operations
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
A method for expanding the volume of waverider using cubic polynomial features that the lower surface of waverider is unchanged, and the cubic polynomial is used to construct convex upper surface instead of the upper surface traced in free flow for increasing volume. The modeling contour line of the upper surface is set to comprise a central part keel line and a cross section line, which are expressed by using a third-order polynomial, and the coefficients of the polynomial are determined by the positions and the slopes of the first and the last two points. In combination with the leading edge contour, the expression form of the upper surface can be obtained. On the basis of ensuring the smooth and continuous upper surface, the extractable design parameters comprise the thickness of the rear edge, the inclination angle of the head and the inclination angle of the side edge, and wave-taking body shapes with different volumes can be generated by changing the design parameters. This method of expanding the upper surface results in less loss of lift-drag ratio of the profile than generating a waverider lower surface of greater thickness.
Description
Technical Field
The invention relates to the field of hypersonic pneumatic design, in particular to a waverider layout form.
Background
The aircraft can generate stronger shock waves during hypersonic flight, and in general, the existence of the shock waves causes wave drag, so that the resistance during hypersonic flight is increased; on the other hand, the pressure of the wave back flow field is increased, the reasonable utilization of the characteristic can improve the lift force, and the waverider is a typical appearance utilizing the characteristic. The leakage of high-pressure gas on the lower surface to the upper surface is prevented by attaching shock waves, so that the flow field is divided into two independent problems along the front edge: the lower surface is a wave-multiplying surface and is a main provider of lift; the upper surface can be generated along a free flow tracking streamline, and a scholars can also generate Mach expansion surfaces, so that the lift force is further improved.
Waverider has been widely concerned at home and abroad due to the high lift-drag ratio characteristic, but the smaller volume always limits the engineering application. The method for expanding the volume of the waverider in most researches is to design the lower surface, and increase the thickness of the lower surface of the waverider by increasing the shock angle of a reference flow field or modifying the shock outlet molded line, but the treatment can greatly increase the resistance and have adverse effects on the installation of the air inlet.
Disclosure of Invention
The technical solution of the invention is as follows: the upper surface is rebuilt through a cubic polynomial, the loading space of the waverider is improved, and the lift-drag ratio loss is reduced.
The technical scheme of the invention is as follows: a method for expanding the volume of a waverider using a cubic polynomial, the lower surface waverider being kept unchanged, the upper surface of the 'convex' being constructed using a cubic polynomial to replace the upper surface free flow surface of the waverider.
Preferably, the upper surface is constructed by:
from the lower surface leading edge discrete points, the position expression in the direction of the spreading direction and the height direction is obtained through fittingRepresenting a fitted leading edge line;
constructing an upper surface keel line, namely a longitudinal section line at the central symmetry plane of the waverider, by using a cubic polynomial; determining coefficients of a cubic polynomial according to the positions and slopes of the first and last points and ensuring smoothness of the trailing edge;
and constructing a cross section line by using a cubic polynomial, determining the positions and the slopes of the first and the last points of the cross section line according to the fitted front edge line, and determining the coefficients of the cubic polynomial according to the positions and the slopes of the first and the last points and ensuring the smooth symmetry plane.
Preferably, the coefficients of the cross-sectional trigonometric polynomials at each location are the same.
Further, the expression of the upper surface curved surface is:
x, y is the longitudinal and radial positions of the waverider and is limited in the interval surrounded by the front edge line le (x) and the keel line k (x); coefficient a 0 ,b 0 ,c 0 ,d 0 Coefficients of the keel line cubic polynomial and a 1 ,b 1 ,c 1 ,d 1 Coefficients of the cross-sectional truncated cubic polynomial.
Further, the trailing edge thickness, the head inclination angle and the side edge inclination angle are used as control parameters, and different waverider volumes are obtained by changing the control parameters.
The invention is suitable for the wave carrier layout of hypersonic aircrafts.
Compared with the prior art, the invention has the beneficial effects that:
according to the thought that the maximum lift-drag ratio of a plurality of wavelets is not obtained at an attack angle of 0 degree in a design state, but is between about 2 degrees and about 6 degrees, at the moment, the upper surface is a leeward surface, airflow is shielded, the influence of the expansion of the upper surface on the aerodynamic performance of the appearance is small, a method for constructing the upper surface by adopting a cubic polynomial is provided, and design parameters are extracted to generate a convex curved surface so as to improve the volume. CFD verification shows that this method of changing the expansion of the upper surface has less lift-drag ratio loss on the basis of increasing the equivalent volume as compared to the method of expanding the lower surface. Specifically:
(1) By replacing the upper surface, the influence on the waverider performance of the lower surface is reduced to the minimum when the waverider flies at a positive attack angle.
(2) Ensuring the smoothness and continuity of the constructed curved surface, extracting design parameters including trailing edge thickness, head inclination angle and side edge inclination angle, and conveniently generating different volume shapes.
(3) Compared with the method for expanding the lower surface, the method for changing the expansion of the upper surface has smaller lift-drag ratio loss on the basis of improving the equivalent volume.
Drawings
FIG. 1 is a schematic diagram of modeling the upper surface of a waverider in the present invention;
fig. 2 shows the pressure distribution (h=30km, ma=8, α=3°);
FIG. 3 is a view of the invention with the upper and lower surfaces extended respectively;
fig. 4 shows the expansion of the change in the lift-drag ratio of the upper and lower surface profiles (h=30 km, ma=8, no bottom resistance) according to the present invention.
Detailed Description
The lower surface is a waverider surface obtained by streamline tracking in a shock wave flow field.
The upper surface was constructed using a cubic polynomial to increase the volume, a modeling diagram and a coordinate system are shown in fig. 1 (half-mode), with the waverider vertices as the origin of coordinates, and the longitudinal, spanwise and height-wise coordinates are denoted by x, y and z, respectively.
First, a Leading Edge curve (Edge) is determined, which is also the Edge line of the lower surface, and is composed of discrete points, and the three-dimensional Leading Edge curve can be used as a functionFitting the spanwise and height-wise positional expressions, respectively.
Next, the upper surface Keel Line (Keel Line), i.e., the longitudinal cross-section at the central symmetry plane, is constructed. As shown, a cubic polynomial k (x) =a is used 0 +b 0 x+c 0 x 2 +d 0 x 3 And (5) expression. In general, the expression of the third-order polynomial is not very visual, and the invention determines the coefficient of k (x) through the position and the slope of the first and the last two points, so that the control parameter has more physical significance. As shown in formula (1):
z 0 ,z l for the z coordinate of k (x) at the first and last two points, θ 0 And theta l The local tilt angle of the first and last two points, i is the length of the waverider, known as z 0 ,z l ,θ 0 ,θ l I.e. the coefficient a of k (x) can be determined 0 ,b 0 ,c 0 ,d 0 . Considering the vertex, i.e. the origin of coordinates, z 0 =0; to ensure smoothness at the trailing edge, a given trailing edge cut of 0 is required, so equation (2) can be written as:
the cubic polynomial expression is also used in the cross-sectional direction. Similar to the keel line expression, the coefficients are also determined based on the position and slope of the first and last points. Where a coordinate transformation is performed to transform each of the stub positions of the upper surface to [0,1 ]]And (3) calculating the domain of the interval, determining the coefficient, and then converting the coefficient into a physical domain according to the leading edge curve and the keel line. The computational domain cubic polynomial can be expressed as: c (ζ) =a 1 +b 1 ξ+c 1 ξ 2 +d 1 ξ 3 ξ∈[0,1]
For simplicity, the polynomial coefficients are the same for each cross section. Using the first and last two point positions and slope, expressed as:
wherein the 0 position is the edge of the cross section, i.e. the intersection with the leading edge line, taking 0 ensures that the height is also 0, delta 0 Is the side edge inclination angle; the position of the 1 is a central symmetrical plane, and the slope is 0 to ensure smooth connection at the symmetrical plane. The expression of the upper surface curved surface is that the calculation domain is transformed into the physical domain by combining the expression forms of the keel line and the front edge line:
x, y is defined in the interval enclosed by the leading edge line le (x) and the keel line k (x), coefficient a 0 ,b 0 ,c 0 ,d 0 And a 1 ,b 1 ,c 1 ,d 1 Determined by equations (2) and (3), respectively.
According to the modeling method and the smooth condition to be satisfied, the control parameters of the extended upper surface are 3: upper surface trailing edge thickness z l Head inclination angle theta 0 Side edge inclination delta 0 . By varying these three parameters, one canThe upper surfaces with different volumes and different shapes are obtained, and meanwhile, the smoothness of the curved surface at the symmetrical surface and the rear edge is ensured.
FIG. 2 shows a single swept multiplier body with varying upper surface trailing edge thickness z l The pressure distribution of the upper surface and the lower surface can be seen that under the same state, the flow fields of the lower surface are identical, the upper surface is changed, the upper surface and the lower surface are not interfered with each other, and the upper surface and the lower surface can be designed separately.
The method for expanding the upper surface provided by the invention has smaller lift-drag ratio loss compared with the expansion of the wave surface of the lower surface. Fig. 3 is a schematic view of the external shapes of the extended upper and lower surfaces, wherein the external shapes comp-1 and comp-3 are waverider bodies in the traditional sense, and the external shapes with different thickness and different volume are obtained by setting different flow field shock wave angles, and the upper surfaces are free flow surfaces. By setting different z l ，θ 0 ，δ 0 And upper surface profile comp-1 and profile z l The planar shape of =1 is the same, the volume is the same; comp-3 and z l =3 planar shape and volume are the same.
FIG. 4 shows the lift-to-drag ratio as a function of angle of attack for the design state, as can be seen relative to z l Maximum lift-drag ratio of =1 profile 5.13, maximum lift-drag ratio of extended lower surface profile comp-1 of equal volume is 4.81; z l =3 profile maximum lift-drag ratio is 4.25, while comp-3 maximum lift-drag ratio is 4.09. Fig. 4 illustrates that increasing the upper surface is better than increasing the lift-drag ratio of the lower surface to achieve the same expansion volume.
Therefore, the waverider capacity expansion method provided by the invention can bring less lift-drag ratio loss while the capacity is increased.
The invention is not described in detail in the field of technical personnel common knowledge.
Claims (3)
1. A method for expanding the volume of a waverider using a cubic polynomial, comprising: the wave-taking surface of the lower surface of the wave-taking body is kept unchanged, and the upper surface of the convex part is constructed by using a cubic polynomial to replace the free flow surface of the upper surface of the wave-taking body, so that the method is applicable to the layout of the wave-taking body of the hypersonic aircraft;
the upper surface is constructed by:
from the lower surface leading edge discrete points, the position expression in the direction of the spreading direction and the height direction is obtained through fittingRepresenting a fitted leading edge line;
constructing an upper surface keel line, namely a longitudinal section line at the central symmetry plane of the upper surface of the waverider, by using a cubic polynomial; determining coefficients of a cubic polynomial according to the positions and slopes of the first and last points and ensuring smoothness of the trailing edge;
constructing a cross section line by using a cubic polynomial, determining the positions and slopes of the first and last points of the cross section line according to the fitted front edge line, and determining coefficients of the cubic polynomial according to the positions and slopes of the first and last points and combining the symmetry plane smooth condition;
the expression of the upper surface curved surface is:
x, y is the longitudinal and radial positions of the waverider and is limited in the interval surrounded by the front edge line le (x) and the keel line k (x); coefficient a 0 ,b 0 ,c 0 ,d 0 Coefficients of the keel line cubic polynomial and a 1 ,b 1 ,c 1 ,d 1 Coefficients of the cross-sectional truncated cubic polynomial.
2. The method according to claim 1, characterized in that: the coefficients of the cross-sectional cubic polynomials at each location are the same.
3. The method according to claim 1, characterized in that: the thickness of the trailing edge, the inclination angle of the head and the inclination angle of the side edge are used as control parameters, and the wave-taking body shapes with different volumes can be obtained by changing the control parameters.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103770935A (en) * | 2013-12-13 | 2014-05-07 | 中国航天空气动力技术研究院 | Wave rider appearance designing method |
| CN110589010A (en) * | 2019-09-09 | 2019-12-20 | 南京航空航天大学 | Hypersonic large-loading-space waverider design method |
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| US11325700B2 (en) * | 2017-07-21 | 2022-05-10 | The Government Of The United States Of America, As Represented By The Secretary Of The Navy | Hypersonic waverider stream surface actuation for variable design point operation |
| CN107963236B (en) * | 2017-11-09 | 2020-11-10 | 中国航天空气动力技术研究院 | Fixed-plane wave-rider design method based on osculating cone theory |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103770935A (en) * | 2013-12-13 | 2014-05-07 | 中国航天空气动力技术研究院 | Wave rider appearance designing method |
| CN110589010A (en) * | 2019-09-09 | 2019-12-20 | 南京航空航天大学 | Hypersonic large-loading-space waverider design method |
Non-Patent Citations (3)
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| 刘传振 等.三维流场乘波体快速设计方法及多目标优化.宇航学报.2016,37(05),41-49. * |
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