CN109250144B - Method for designing osculating cone waverider with directly controllable sweepback angle and upper/lower dihedral angles - Google Patents

Method for designing osculating cone waverider with directly controllable sweepback angle and upper/lower dihedral angles Download PDF

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CN109250144B
CN109250144B CN201811155643.8A CN201811155643A CN109250144B CN 109250144 B CN109250144 B CN 109250144B CN 201811155643 A CN201811155643 A CN 201811155643A CN 109250144 B CN109250144 B CN 109250144B
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waverider
equation
shock wave
angle
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CN109250144A (en
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陈韶华
柳军
丁峰
刘珍
王晓燕
罗仕超
蒋浩
张文浩
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National University of Defense Technology
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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
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C30/00—Supersonic type aircraft

Abstract

The invention provides a method for designing osculating cone waverider with directly controllable sweepback angle and upper/lower dihedral, which comprises the steps of firstly, giving reference flow field parameters, giving a sweepback angle change rule of a horizontal projection molded line of a front edge line of the waverider along the z direction of a coordinate system of a machine body, namely giving a sweepback angle equation, and solving the horizontal projection molded line of the front edge line of the waverider; then, a shock wave bottom section molded line is designed and solved, a front edge point on a wave multiplication body front edge line is solved, then, a flow line forming the lower surface of the wave multiplication body is generated by starting from the front edge point and adopting a forward flow line tracking method, and finally, the wave multiplication body is generated by geometric lofting. Based on the design method, the final target that the swertive cone-waverider leading edge line sweepback angle and the dihedral angle are controllable is achieved.

Description

Method for designing osculating cone waverider with directly controllable sweepback angle and upper/lower dihedral angles
Technical Field
The invention belongs to the technical field of aerodynamic shape design of hypersonic aircrafts, and particularly relates to a method for designing a osculating cone waverider with a directly controllable sweepback angle and upper/lower dihedral angles of the waverider.
Background
The hypersonic aerocraft is an aerocraft with the speed exceeding Mach 5, and comprises an air-breathing hypersonic aerocraft, a rocket power hypersonic aerocraft and an unpowered gliding aerocraft, and the specific application forms comprise various aerocrafts such as a hypersonic cruise missile, a hypersonic manned/unmanned airplane, an aerospace plane and the like.
In order to pursue good cruise and percussion performance, hypersonic aircraft must have a high lift-to-drag ratio and a large available space to increase the proportion of payload in the total volume.
The aerodynamic shape of the hypersonic flight vehicle mainly comprises three major types, namely an axisymmetric configuration, a lifting body configuration and a waverider configuration, wherein the waverider configuration utilizes a shock wave compression principle (waverider principle) to realize the aerodynamic requirement of high lift-drag ratio under the hypersonic flight condition.
The current commonly used wave rider design methods include a cone guided wave rider design method and a osculating cone wave rider design method. Compared with a cone guide wave rider, the osculating cone wave rider design method has the advantage that the quality of the outlet compressed air flow is higher. Meanwhile, the bottom section molded line of the osculating cone waverider shock wave is not limited to the circular arc, and the degree of freedom of the design of the waverider is effectively improved.
Sobieczky et al propose a generation method of Osculating Cone Waverider (OCW), and have conducted a great deal of research, and the basic idea is to use a Cone-shaped flow field to approximate an arbitrary three-dimensional flow field, thereby greatly simplifying the calculation. Specifically, a complete shock wave is designed by a given shock wave bottom section molded line, then a series of kiss sections are cut from the molded line, and a series of conical flow fields are constructed in each kiss section, wherein the series of conical flow fields are the reference flow fields designed by a wave multiplier. Determining the leading edge of a waverider through the intersection line of the osculating cone shock wave and the flow capturing pipe, and finally carrying out streamline tracing from the leading edge in the osculating cone flow field to obtain a waverider configuration.
Taking fig. 1 and 2 as examples, fig. 1 is a horizontal projection profile of a leading edge line of a waverider, and an input profile in a general osculating pyramid waverider design method is a shock bottom section profile 8 plus a waverider upper surface bottom section profile 9 or a waverider lower surface bottom section profile 10. In order to realize the controllability of the dihedral angle of the waverider, the control can be completed by adjusting the position of the B point of the section molded line 9 at the bottom of the upper surface of the waverider. However, in the scheme, the dihedral angle of the waverider is not used as a design input parameter of the waverider, so that the dihedral angle of the waverider cannot be directly controlled, and the final shape is obtained after several iterations through the steps of design, generation of the waverider, measurement of the dihedral angle and the like. In addition, in a general design method, the horizontal projection profile of the leading edge line of the waverider is an indirectly controlled curve, and the controllable design of the sweepback angle cannot be realized.
Disclosure of Invention
Aiming at the defect that the back sweep angle and the upper dihedral angle of a front edge line are mutually coupled and cannot be directly controlled in a general osculating cone waverider design method, the invention provides a method for designing an osculating cone waverider with directly controllable back sweep angle and upper/lower dihedral angles based on a horizontal projection type line waverider design method.
The sweep angle and the dihedral angle are defined in the present invention as shown in FIG. 1. The coordinate system in fig. 1 is a body coordinate system, the origin of the body coordinate system is the midpoint of the shock wave bottom section line 8, and the vertical axis (x axis), the horizontal axis (z axis) and the vertical axis (y axis) of the body coordinate system are established with reference to the 3.1.4 body coordinate system in GV/T14410.1-93.
The sweep definition described in this invention is referred to as 3.1.19 wing sweep in GB/T16638.3-1996. In FIG. 1, 1 is the horizontal projection profile of the leading edge line of the waverider, PlThe transverse coordinate z of any point on the profile 1 of the horizontal projection of the leading edge line of the waverider is equal to zl。PtThe point is the intersection point of the horizontal projection molded line of the wave rider leading edge line and the y-z plane, and is also the transverse widest part of the horizontal projection molded line of the wave rider leading edge line. And 2 is the incoming flow direction of the airflow.
3 is P on the horizontal projection type line of the leading edge line of the waveriderlSweepback angle of points, i.e. P on horizontal projection profile across leading edge line of waveriderlPoint tangent line and over waverider leading edge line horizontal projection type line PlThe angle of the reference line of the point perpendicular to the direction of airflow, i.e. the line of the wave-multiplier leading edge, where z is equal to zlPoint sweep (definition reference GB/T16638.3-1996 wing 3.1.18 substantially local sweep). The sweep angle therefore has different values at different lateral (z-coordinate) positions. The invention designs the sweepback angle edgeAnd a change equation in the z direction of the coordinate is solved, and the horizontal projection molded line of the leading edge line of the waverider is solved, so that the target that the sweepback angle of the leading edge line of the waverider is directly controllable is realized.
4 is P on the horizontal projection type line of the leading edge line of the over-waveriderlThe vertical airflow direction reference line of the point, the vertical airflow direction reference line 4 crosses P on the horizontal projection type line of the wave rider leading edge linelPoint and parallel to the coordinate horizontal axis (z-axis).
5 is P on the horizontal projection type line of the leading edge line of the over-waveriderlTangent to the point.
The dihedral angle of the present invention is defined in GB/T16638.3-1996 with reference to 3.5.21 wing dihedral angle. Since the projected profile of the waverider on the bottom section is different from that of the wing described in the GB/T16638.3-1996 standard, the chord point is not determined, so that the up-and-down characteristic of the waverider cannot be evaluated through the concept of a chord line. According to the principle of the dihedral angle on the transverse stability of the aircraft (refer to the influence of the dihedral angle of the missile wing in sections 1-7 of missile flight mechanics, compiled by Qianxiang and the like), the transverse speed generated during sideslip flight acts on the wing, so that the rolling moment of the aircraft changes, and the transverse stability of the aircraft during flight is finally influenced. The geometric characteristics of the wave multiplier in different longitudinal (x coordinate) section shapes are similar, and the invention adopts the dihedral characteristic of the lower surface of the bottom section of the wave multiplier to represent the inverse characteristic of the wave multiplier. The specific definition is shown in fig. 2, where: pcThe point is the intersection point of the outlet section profile of the lower surface of the waverider and the x-y plane. 6 is per PtHorizontal line of points and PtPoint sum PcThe angle between the connecting lines between the two points. P in FIG. 2tPoint sum PcThe line between two points is located at PtAbove the horizontal line of points, passing PtHorizontal line of points and PtPoint sum PcThe included angle between the connecting lines between the two points is also called as the dihedral angle; if PtPoint sum PcThe line between two points is located at PtBelow the horizontal line of points, passing PtHorizontal line of points and PtPoint sum PcThe angle between the connecting lines between two points is called the dihedral angle. 7 is per PtHorizontal line of points, passing PtThe horizontal line of points is parallel to the z-axis; the 8 is the profile line of the bottom section of the shock wave,it consists of a straight line segment and a power curve segment. And 9 is the profile of the bottom section of the upper surface of the wave rider. And 10 is the bottom section profile of the lower surface of the wave rider. 11 is PtPoint sum PcThe connecting line between the two points.
In order to realize the purpose of the invention, the following technical scheme is adopted for realizing the purpose:
the osculating pyramid waverider design method with directly controllable sweepback angle and upper/lower dihedral angle includes the following steps:
and S1, giving reference flow field parameters, wherein the reference flow field parameters comprise an incoming flow Mach number Ma and a shock wave angle β.
S2: designing a sweepback angle equation and solving a horizontal projection molded line of a leading edge line of the waverider;
based on the symmetry of the waverider, half curve equation x of the horizontal projection profile of the leading edge line of the waverider, namely f (z), z ∈ [0, W/2], is discussed, and the other half curve equation can be obtained according to symmetric transformation.
Assuming that the sweep angle of the horizontal projection profile of the leading edge line of the waverider along the z direction of the coordinate system of the airframe is χ (z), any point P on the horizontal projection profile of the leading edge line of the waverider is assumed to belThe value of the corresponding sweep angle is chil(ii) a P on horizontal projection type line of wave rider leading edge linelPoint corresponding sweep angle χlThe following relation exists with the wave multiplier leading edge line horizontal projection type line equation, see formula (1):
Figure GDA0002497814240000041
the wave multiplier leading edge line horizontal projection type line equation is x ═ f (z), z ∈ [0, W/2], wherein W is the wave multiplier width.
For solving the sweepback angle equation χ (z), the invention gives the following A, B two solutions:
scheme A:
the given sweep angle equation is shown in formula (2), wherein χA1,χA2Are all constant, xA1And chiA2Respectively being sweepback angle squareSweep back angles of different sections;
Figure GDA0002497814240000042
in the scheme a, the sweep angle equation is assumed to be χ (z) ═ χcIn the form of (1). The formula (2) adopts a piecewise function form, and the sweep angle equation is designed in a piecewise mode, so that the obtained aircraft has piecewise characteristics, namely different sections have different sweep angles.
By substituting equation (2) into (1), we can see that:
Figure GDA0002497814240000051
it can further be assumed that the front edge line horizontal projection type line equation in the scheme a is shown in equation (4):
Figure GDA0002497814240000052
wherein k isA1,bA1,kA2,bA2,z1Are all parameters to be solved.
The known condition is the sweep angle equation χ ═ χA(z) and the length L and width W of the waverider, the parameters to be solved in the front edge line horizontal projection type line equation (4) can be given by the following equations (5) and (6):
Figure GDA0002497814240000053
Figure GDA0002497814240000054
χ in equation (6)AbIs a reference sweep angle. Due to the fact that
Figure GDA0002497814240000055
f(z1) ∈ (0, L), sweep Angle χ in sweep Angle equation (2)A1,χA2The requirement of formula (7) needs to be satisfied at the same time:
min(tan(χA1),tan(χA2))＜tan(χAb)＜max(tan(χA1),tan(χA2)) (7)
the equation x of a half curve of the horizontal projection type line of the leading edge line of the waverider is f (z), z ∈ [0, W/2] is solved, and based on the symmetry of the waverider, the other half curve of the horizontal projection type line of the leading edge line of the waverider can be obtained through symmetrical transformation according to the half curve obtained through solving.
Scheme B:
to pair
Figure GDA0002497814240000061
And integrating, substituting the sweepback angle equation χ (z) into χ (z), and simplifying by an element-changing integration method to obtain a formula (8):
Figure GDA0002497814240000062
substituting the formula (1) into the formula (8), and further simplifying to obtain the formula (9). Equation (9) is a relationship between the front edge line horizontal projection type equation x ═ f (z) and the sweep angle equation χ ═ χ (z).
Figure GDA0002497814240000063
Wherein the sweep angle equation chi (z) needs to satisfy the following conditions:
i. when z ∈ [0, W/2], the χ '═ χ' (z) equation is continuous;
ii, wherein the coordinate value χ (0) χ of the end point of the sweep angle equation1,χ(W/2)＝χ2And when z ∈ [0, W/2]]When it is, chi (z) ∈ [ chi [)1,χ2]。
The sweep angle equation is assumed to vary linearly along the z-coordinate in the B scheme, i.e. as shown in equation (10):
Figure GDA0002497814240000064
and substituting the formula (10) into the formula (9) to obtain a formula (11), which is the front edge line horizontal projection type line equation of the scheme B.
Figure GDA0002497814240000071
The parameter to be solved in the formula (11) is mB、dB、CBThe specific solution is shown in formula (12). The known parameter in equation (12) is χBn、χBt、W。χBn、χBtRespectively, P on the front edge line horizontal projection type linen、PtThe sweepback angle corresponding to the two points, W, is the width of the waverider.
Figure GDA0002497814240000072
The length L of the waverider is a parameter to be solved, and is shown in a formula (13):
Figure GDA0002497814240000073
as shown in the formula (12), the scheme B horizontally projects the head end and the tail end of the molded line through the front edge line, namely Pn、PtSweepback angle chi corresponding to two pointsBn、χBtAnd a passenger width W, the change rate chi of the sweepback angle of the front edge line is controlled'B(z)＝mBAnd finally, the goal that the sweepback angle of the front edge line is directly controllable is achieved.
The equation x of a half curve of the horizontal projection type line of the leading edge line of the waverider is f (z), z ∈ [0, W/2] is solved, and based on the symmetry of the waverider, the other half curve of the horizontal projection type line of the leading edge line of the waverider can be obtained through symmetrical transformation according to the half curve obtained through solving.
The two schemes are combined and compared, and the input conditions in the scheme A comprise the length and width (L, W) of the wave multiplier and the sweepback angle equation. The input conditions in the scheme B comprise the width W of the wave multiplier and a sweepback angle equation, and the length L of the wave multiplier is obtained by the sweepback angle equation and the width W.
S3: and solving the profile of the bottom section of the shock wave.
The profile of the bottom section of the shock wave to be solved is a combined profile of a straight line and a power curve.
And (3) obtaining the bottom section profile of the shock wave of the waverider by giving an upper dihedral angle psi, the length of a straight line segment in the bottom section profile of the shock wave of 2 x Ls, the width W of the waverider and the power curve power n and combining the thickness H of the symmetrical surface of the waverider obtained by solving. The specific method comprises the following steps:
s3.1, setting an upper inverted angle psi of a waverider, the length of a straight line segment in a section profile at the bottom of the shock wave is 2 x Ls, the width W of the waverider and the power of a power curve n;
s3.2, designing a bottom section profile equation of the wave multiplier shock wave;
the shock wave bottom section profile equation is a straight line plus power curve, and is shown in the formula (14):
Figure GDA0002497814240000081
wherein the bottom section of the waverider is on the y-z plane, and α is the coefficient of the power curve, which is the coefficient of the quantity to be calculated.
S3.3, solving the thickness H of the symmetrical surface of the waverider;
the method comprises the steps of knowing a shock wave angle β and a waverider length L, solving a reference flow field and a flow line in a osculating plane where a symmetrical plane of the waverider is located by utilizing a Taylor-Maccoll control equation and a flow line tracking method (the specific solving method refers to a T-peak hypersonic glide-cruise two-stage waverider design method for researching a 4.2-section conical flow field solving method in Changsha university of national defense science and technology (Master) 2012), and obtaining the thickness H of the symmetrical plane of the waverider according to the length of the flow line projected on the bottom surface of the waverider.
S3.4, solving a shock wave bottom section profile equation;
Ptthe coordinates of the point are (0, W/2, h)1). Wherein
Figure GDA0002497814240000091
h0Providing Ltan (β); adding PtSubstituting the point coordinates into formula (14) to obtain formula (15):
Figure GDA0002497814240000092
the power curve coefficient α is obtained by substituting equation (15) with the design shock angle β, the multiplier length L, and the dihedral angle ψ (see fig. 5).
S4: solving a front edge point on a wave-multiplying body front edge line;
in fig. 3, a point 18 on a leading edge line 16 of the waverider is a to-be-solved leading edge point on the leading edge line, and the following specific steps are described by taking solving the leading edge point 18 as an example:
and S4.1, dispersing the molded line of the bottom section of the shock wave obtained by solving in the S3 to obtain a series of discrete points.
The discrete scheme adopts an equidistant discrete method, firstly, the number of discrete points is given, so that the discrete points are distributed equidistantly in the transverse direction, and then, the coordinates of all the discrete points are solved.
And S4.2, determining the kiss section corresponding to each discrete point on the section line of the bottom of the shock wave.
The definition and solving of the kiss section are referred to [ T peak, hypersonic glide-cruise two-stage waverider design method research [ D ]. Changsha: section 6.1 of the university of defense science and technology (major) · 2012 ].
For any discrete point on the profile line of the bottom section of the shock wave, the discrete point is marked as an A discrete point.
Firstly, the coordinates of the curvature center point of the shock wave bottom section molded line at the A discrete point are obtained, and the curvature center point is simultaneously the projection of the reference cone vertex in the osculating plane corresponding to the A discrete point on the bottom section of the waverider.
The vertex of the reference cone in the osculating plane corresponding to the discrete point A is positioned on the locus line of the vertex of the reference cone of the osculating cone waverider; and the reference cone vertex in the osculating plane corresponding to any point on the section line of the bottom of the shock wave is positioned on the locus line of the reference cone vertex of the osculating cone-wave body.
And the connecting line of the curve center point of the shock wave bottom section molded line at the discrete point A and the reference cone vertex in the osculating plane corresponding to the discrete point A is collinear on the reference cone axis of the reference cone in the osculating plane corresponding to the discrete point A.
The line between the discrete point A and the reference cone vertex in the osculating plane corresponding to the discrete point A is the shock wave profile in the osculating plane corresponding to the discrete point A, the included angle between the shock wave profile in the osculating plane corresponding to the discrete point A and the reference cone axis of the reference cone in the osculating plane corresponding to the discrete point A is the design shock wave angle β given in S1, and the plane where the shock wave profile in the osculating plane corresponding to the discrete point A and the reference cone axis of the reference cone in the osculating plane corresponding to the discrete point A are located is the osculating plane corresponding to the discrete point A.
And S4.3, solving a shock wave profile equation in the osculating section corresponding to each discrete point on the profile of the bottom section of the shock wave.
And the connecting line of the discrete point A and the reference cone vertex in the osculating plane corresponding to the discrete point A is the shock wave molded line in the osculating plane corresponding to the discrete point A. Because the shock wave molded lines in the osculating plane are all straight lines, the shock wave molded lines in the osculating plane corresponding to the A discrete points can be obtained through the coordinates of two points, namely a reference cone vertex and the A discrete points in the osculating plane corresponding to the A discrete points.
And S4.4, solving the coordinates of the front edge points in the osculating plane corresponding to each discrete point on the section line of the bottom of the shock wave.
And combining the equation of the shock wave molded line in the osculating plane corresponding to the discrete point A with the equation of the horizontal projection molded line of the leading edge line of the waverider to obtain the coordinates of the leading edge point in the osculating plane corresponding to the discrete point A, wherein the leading edge point in the osculating plane corresponding to the discrete point A is the leading edge point on the leading edge line of the waverider.
By adopting the same method, the kiss-cut surface corresponding to all discrete points on the profile of the bottom section of the shock wave and the shock wave profile in the kiss-cut surface corresponding to each discrete point can be obtained, and then the coordinates of the leading edge point in the kiss-cut surface corresponding to each discrete point can be obtained through solving.
S5: solving the streamline of the lower surface of the waverider;
s5.1, solving a reference flow field in the osculating plane corresponding to each discrete point on the section line of the bottom of the shock wave.
According to the Mach number Ma of incoming flow and the shock angle β given in S1, a Taylor-Macoll control equation is solved to obtain a reference flow field in a osculating plane corresponding to each discrete point on a section line at the bottom of a shock wave, and the reference flow field in the osculating plane corresponding to each discrete point on the section line at the bottom of the shock wave is a conical flow field.
S5.2 solving the streamline.
In the osculating plane corresponding to each discrete point on the section line at the bottom of the shock wave, starting from the leading edge point in each osculating plane obtained in S4, in the reference flow field in the osculating plane corresponding to each discrete point on the section line at the bottom of the shock wave obtained in S5.1, the streamline corresponding to the leading edge point in each osculating plane, i.e. the streamline of the lower surface of the waverider, is solved by a forward streamline tracing method, and the concrete solving method is shown in the study on the design method of [ butyl peak, hypersonic glide-cruise two-stage waverider [ D ]. Changsha: 4.3 sections of streamline solving method in the university of defense science and technology (Master) · 2012 ].
S6: geometric lofting generates a waverider.
And (3) performing combined lofting on streamlines (the same as a streamline solving method, see S5.2) on the lower surfaces of all waverider bodies to obtain the lower surfaces of the waverider bodies, and generating the upper surfaces of the waverider bodies by adopting a free streamline method (see section 4.1 in [ Tpeak, hypersonic glide-cruise two-stage waverider design method research [ D ]. Changsha: national defense science and technology university (Master): 2012 ].
Compared with the prior art, the invention has the following beneficial technical effects:
different from the design scheme proposed by Sobieczky et al, the invention determines the leading edge line of the waverider by a method of kissing the intersection line of the cone shock wave and the leading edge line horizontal projection molded line. The advantage of the wave rider design method based on the horizontal projection profile is obvious.
Firstly, the aerodynamic characteristics of the waverider are closely related to the aerodynamic layout and related parameters thereof, and the horizontal projection profile of the front edge line and the bottom profile (the bottom profile is the projection of the lower surface profile of the waverider on the bottom section) are the key. The horizontal projection shape (the horizontal projection shape is the horizontal projection shape of the front edge line) determines the lift distribution of the waverider, and the relationship between the lift distribution and the pressure center position (the pressure center is characterized in that the total aerodynamic force is zero relative to the aerodynamic moment of the point, and the lift distribution determines the pressure center position, and the relative positions of the pressure center and the mass point determine the longitudinal static stability of the waverider) indirectly determines the influence of the horizontal projection shape on the longitudinal static stability of the aircraft; the lateral stability of the rider can also be adjusted by the sweepback angle and the dihedral angle of the leading edge line (see sections 1-7 of missile aeromechanics, Qianxingfang, etc.), and the two shape parameters are related to the horizontal projection and the bottom shape of the rider.
And the pneumatic layout of certain horizontal projection shapes can effectively improve the lift-drag ratio performance of the waverider. For example, when the wide-speed-range hypersonic aircraft flies in a subsonic stage, extra vortex lift force can be obtained through the design of the distribution rule of the sweepback angle extension direction of the leading edge line.
Drawings
Figure 1 is a top view of a conceptual illustration of the sweep back and dihedral angles of the leading edge line,
FIG. 2 is a right side view of a conceptual illustration of the sweep back and dihedral angles of the leading edge line;
in fig. 1 and 2: x, y and z are longitudinal, normal and transverse coordinate axes of a coordinate system of the body where the waverider is located;
o is the origin of the coordinate system of the body where the waverider is located; plThe point is any point on the horizontal projection line of the leading edge line of the waverider, and the transverse coordinate z is equal to zl；PtThe point is the intersection point of the horizontal projection molded line of the wave rider leading edge line and the y-z plane and is also the transverse widest part of the horizontal projection molded line of the wave rider leading edge line; pcThe point is the intersection point of the outlet section molded line on the lower surface of the waverider and the x-y plane;
1 is a horizontal projection profile of a wave multiplier leading edge line; 2 is the incoming flow direction of the airflow; 3 is P on the horizontal projection type line of the leading edge line of the waveriderlSweepback angle of points, i.e. P on horizontal projection profile across leading edge line of waveriderlPoint tangent line and over waverider leading edge line horizontal projection type line PlThe included angle of the reference line of the point perpendicular to the airflow direction; 4 is P on the horizontal projection type line of the leading edge line of the over-waveriderlA vertical airflow direction reference line of points; 5 is P on the horizontal projection type line of the leading edge line of the over-waveriderlTangent to the point; 6 is per PtHorizontal line of points and PtPoint sum PcThe included angle between the connecting lines between the two points; p in FIG. 2tPoint sum PcThe line between two points is located at PtAbove the horizontal line of points, passing PtHorizontal line of points and PtPoint sum PcThe included angle between the connecting lines between the two points is also called as the dihedral angle; if PtPoint sum PcThe line between two points is located at PtBelow the horizontal line of points, passing PtHorizontal line of points and PtPoint sum PcThe included angle between the connecting lines of the two points is called as a dihedral angle; 7 is per PtHorizontal line of points, wherein P is passedtThe horizontal line of points is parallel to the z-axis; the shock wave bottom section molded line 8 is composed of a straight line section and a power curve section; 9 is the profile of the bottom section of the upper surface of the waverider; 10 is the bottom section profile of the lower surface of the waverider; 11 is PtPoint sum PcThe connecting line between the two points.
Fig. 3 is a schematic design diagram of the present invention.
12 is an incoming current Mach number Ma, 13 is a shock wave angle β, 14 is a vertex trajectory line of a reference cone of a osculating cone multiplied by a wave body, 15 is a reference cone axis of the reference cone in the osculating plane corresponding to an A discrete point 19, 16 is a wave body leading edge line which is a projection of a horizontal projection molded line 1 of the wave body leading edge line on the shock wave plane, 17 is a discrete point on the horizontal projection molded line 1 of the wave body leading edge line, the discrete point 17 corresponds to a leading edge point 18 on the wave body leading edge line 16, 18 is a leading edge point in the osculating plane corresponding to the A discrete point 19, 18 is a projection point of the discrete point 17 on the horizontal projection molded line of the wave body leading edge line on the shock wave plane, 18 is a projection point of the shock wave line 22 in the osculating plane corresponding to the A discrete point 19, 19 is a discrete point on the shock wave plane, 18 is a discrete point 20 on the shock wave body leading edge line, a discrete point 21-21 is a discrete point in the shock wave surface, and a curvature of the shock wave body leading edge point is obtained from a discrete point 21-21.
FIG. 4 is a schematic diagram of a sectional design of a sweep angle equation in the scheme A;
in fig. 4: 24. the sweep angle is chiA1A line segment of (a); 25. the sweep angle is chiA2A line segment of (a); pnThe point is the intersection of the horizontal projection profile 1 of the wave multiplier leading edge line and the x-y plane.
FIG. 5 is a schematic diagram of solving for the shock bottom section profile 8;
in fig. 5: the shock wave bottom section molded line 8 is composed of a straight line section and a power curve section, wherein the length of the straight line section is Ls. Psi is the dihedral angle of the waverider, and W/2 is the half width of the waverider. h is0Is defined as PnThe length of the projection of the connecting line between the point and the o point on the bottom section of the wave rider. H is defined as PnPoint and PcThe length of the projection of the connecting line between the two points on the bottom section of the waverider, and H is the thickness of the symmetrical plane of the waverider. h is1Is defined as PtThe difference in height of the point from the o point in the normal direction (y-axis).
FIG. 6 is a schematic diagram of linear variation of the horizontal projection profile sweep angle of the leading edge line of the waverider along the transverse coordinate (z axis) in the solution B; χ in fig. 6BnHexix-BtAre respectively PnPoint sum PtCorresponding sweepback angles; in fig. 6, the width W of the waverider is given, and the length L of the waverider is a parameter to be obtained;
fig. 7 and 8 are a top view and a right side view of caseA1, respectively.
Fig. 9 and 10 are a top view and a right side view of caseA2, respectively.
Fig. 11 and 12 are a top view and a right side view of caseA3, respectively.
Fig. 13 is a pressure contour cloud of the bottom section of the caseA1 profile compared to the shock bottom section profile line discrete points.
Fig. 14 and 15 are a top view and a right side view of caseB1, respectively.
Fig. 16 and 17 are a top view and a right side view of caseB2, respectively.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the drawings of the embodiments of the present invention, and further detailed description will be given without limiting the scope of the present invention.
The osculating pyramid waverider design method with directly controllable sweepback angle and upper/lower dihedral angle includes the following steps:
and S1, giving reference flow field parameters, wherein the reference flow field parameters comprise an incoming flow Mach number Ma and a shock wave angle β.
S2: designing a sweepback angle equation and solving a horizontal projection molded line of a leading edge line of the waverider;
based on the symmetry of the waverider, half curve equation x of the horizontal projection profile of the leading edge line of the waverider, namely f (z), z ∈ [0, W/2], is discussed, and the other half curve equation can be obtained according to symmetric transformation.
As shown in fig. 1 and 2, assuming that the sweep angle of the horizontal projection profile of the leading edge line of the waverider along the z direction of the coordinate system of the airframe is χ (z), any point P on the horizontal projection profile 1 of the leading edge line of the waverider is assumed to be χ (z)lThe value of the corresponding sweep angle is chil(ii) a P on horizontal projection type line of wave rider leading edge linelPoint corresponding sweep angle χlThe following relation exists with the wave multiplier leading edge line horizontal projection type line equation, see formula (1):
Figure GDA0002497814240000161
the wave multiplier leading edge line horizontal projection type line equation is x ═ f (z), z ∈ [0, W/2], wherein W is the wave multiplier width.
For solving the sweepback angle equation χ (z), the invention provides the following two schemes:
scheme A:
referring to FIG. 4, FIG. 4 is a schematic diagram of the sectional design of the sweep angle equation, where the given sweep angle equation is shown in formula (2), where χA1,χA2Are all constant, xA1And chiA2Respectively the sweep angles of different sections of the sweep angle equation. As shown in fig. 4, the sweep angles are χA1 Line segment 24 and sweep angle are xA2The line segment 25 forms a horizontal projection molded line of a front edge line of the waverider, and the sweepback angle of the horizontal projection molded lines of the two front edge lines is kept unchanged along the direction of a z coordinate; ptThe point is the intersection point of the horizontal projection molded line of the wave rider leading edge line and the y-z plane and is also the water of the wave rider leading edge lineThe transverse widest part of the flat projection type line; pnThe point is the intersection point of the horizontal projection molded line of the wave multiplier leading edge line and the x-y plane and is also the peak of the wave multiplier; chi shapeAbIs a reference sweep angle of PnAnd PtAnd the backswept angle corresponding to the connecting line between the two points.
Figure GDA0002497814240000171
Referring to fig. 4, in the scheme a, the sweep angle equation is assumed to be χ (z) ═ χcIn the form of (1). The formula (2) adopts a piecewise function form, and the sweep angle equation is designed in a piecewise mode, so that the obtained aircraft has piecewise characteristics, namely different sections have different sweep angles.
By substituting equation (2) into (1), we can see that:
Figure GDA0002497814240000172
it can further be assumed that the front edge line horizontal projection type line equation in the scheme a is shown in equation (4):
Figure GDA0002497814240000173
wherein k isA1,bA1,kA2,bA2,z1Are all parameters to be solved.
The known condition is the sweep angle equation χ ═ χA(z) and the length L and width W of the waverider, the parameters to be solved in the front edge line horizontal projection type line equation (4) can be given by the following equations (5) and (6):
Figure GDA0002497814240000181
Figure GDA0002497814240000182
further, by
Figure GDA0002497814240000183
f(z1) ∈ (0, L), sweep Angle χ in sweep Angle equation (2)A1,χA2The requirement of formula (7) needs to be satisfied at the same time:
min(tan(χA1),tan(χA2))＜tan(χAb)＜max(tan(χA1),tan(χA2)) (7)
the equation x of a half curve of the horizontal projection type line of the leading edge line of the waverider is f (z), z ∈ [0, W/2] is solved, and based on the symmetry of the waverider, the other half curve of the horizontal projection type line of the leading edge line of the waverider can be obtained through symmetrical transformation according to the half curve obtained through solving.
Scheme B:
to pair
Figure GDA0002497814240000184
And integrating, substituting the sweepback angle equation χ (z) into χ (z), and simplifying by an element-changing integration method to obtain a formula (8):
Figure GDA0002497814240000185
substituting the relation formula (1) of the horizontal projection type line equation of the sweepback angle and the leading edge line into a formula (8), and further simplifying to obtain a formula (9). Equation (9) is a relationship between the front edge line horizontal projection type equation x ═ f (z) and the sweep angle equation χ ═ χ (z).
Figure GDA0002497814240000186
Wherein the sweep angle equation chi (z) needs to satisfy the following conditions:
when z ∈ [0, W/2], the χ '═ χ' (z) equation continues;
iv, wherein the coordinate value χ (0) of the end point of the sweep angle equation is χ1,χ(W/2)＝χ2And when z ∈ [0, W/2]]When it is, chi (z) ∈ [ chi [)1,χ2]
Referring to fig. 6, the sweep angle equation is assumed to vary linearly along the z-coordinate in the B scheme, which is shown in equation (10):
Figure GDA0002497814240000191
and substituting the formula (10) into the formula (9) to obtain a formula (11), which is the front edge line horizontal projection type line equation of the scheme B.
Figure GDA0002497814240000192
The parameter to be solved in the formula (11) is mB、dB、CBThe specific solution is shown in formula (12). The known parameter in equation (12) is χBn、χBt、W。χBn、χBtRespectively, P on the front edge line horizontal projection type linen、PtThe sweepback angle corresponding to the two points, W, is the width of the waverider.
Figure GDA0002497814240000193
The length L of the waverider is a parameter to be solved, and is shown in a formula (13):
Figure GDA0002497814240000194
as shown in the formula (12), the scheme B horizontally projects the head end and the tail end of the molded line through the front edge line, namely Pn、PtSweepback angle chi corresponding to two pointsBn、χBtAnd a passenger width W, the change rate chi of the sweepback angle of the front edge line is controlled'B(z)＝mBAnd finally, the goal that the sweepback angle of the front edge line is directly controllable is achieved.
The equation x of a half curve of the horizontal projection type line of the leading edge line of the waverider is f (z), z ∈ [0, W/2] is solved, and based on the symmetry of the waverider, the other half curve of the horizontal projection type line of the leading edge line of the waverider can be obtained through symmetrical transformation according to the half curve obtained through solving.
The two schemes are combined and compared, and the input conditions in the scheme A comprise the length and width (L, W) of the wave multiplier and the sweepback angle equation. The input conditions in the scheme B comprise the width W of the wave multiplier and a sweepback angle equation, and the length L of the wave multiplier is obtained by the sweepback angle equation and the width W.
S3: and solving the profile of the bottom section of the shock wave.
The profile of the bottom section of the shock wave to be solved is a combined profile of a straight line and a power curve.
As shown in fig. 5, the bottom section profile of the shock wave of the waverider is obtained by giving an upper dihedral angle ψ, a straight line segment length 2 × Ls in the bottom section profile of the shock wave, a waverider width W and a power curve power n, and combining the thickness H at the symmetrical plane of the waverider obtained by solving. The specific method comprises the following steps:
s3.1, as shown in figure 5, giving a dihedral angle psi of the waverider, the length of a straight line segment in a section profile at the bottom of the shock wave, 2 x Ls, the width W of the waverider and the power of a power curve n;
s3.2 design wave multiplier shock wave bottom section profile equation
The shock wave bottom section profile equation is a straight line plus power curve, and is shown in the formula (14):
Figure GDA0002497814240000201
wherein the bottom section of the waverider is on the y-z plane, and α is the coefficient of the power curve, which is the coefficient of the quantity to be calculated.
S3.3, solving the thickness H of the symmetrical surface of the waverider;
the method comprises the steps of knowing a shock wave angle β and a waverider length L, solving a reference flow field and a flow line in a osculating plane where a symmetrical plane of the waverider is located by utilizing a Taylor-Maccoll control equation and a flow line tracking method (the specific solving method refers to a T-peak hypersonic glide-cruise two-stage waverider design method for researching a 4.2-section cone flow field solving method in Changsha university of national defense science and technology (Master) 2012), and obtaining the thickness H of the symmetrical plane of the waverider according to the projection length of the flow line on the bottom surface of the waverider.
S3.4, solving a shock wave bottom section profile equation;
specifically, P in FIG. 5tThe coordinates of the point are (0, W/2, h)1). In FIG. 5
Figure GDA0002497814240000211
h0Ltan (β); P in FIG. 5tSubstituting the point coordinates into formula (14) to obtain formula (15):
Figure GDA0002497814240000212
the power curve coefficients α are obtained by substituting equation (15) with known design shock angle β, multiplier length L (given in S2, see fig. 4), and dihedral angle ψ (see fig. 5).
S4: solving a front edge point on a wave-multiplying body front edge line;
in fig. 3, the leading edge point 18 on the leading edge line 16 of the wave multiplier is a to-be-solved leading edge point on the leading edge line of the wave multiplier, and the following specific steps are described by taking solving the leading edge point 18 as an example:
and S4.1, dispersing the shock wave bottom section molded line 8 obtained by solving in the S3 to obtain a series of discrete points.
The discrete scheme adopts an equidistant discrete method, firstly, the number of discrete points is given, so that the discrete points are distributed equidistantly in the transverse direction, and then, the coordinates of all the discrete points are solved.
And S4.2, determining the kiss section corresponding to each discrete point on the section line of the bottom of the shock wave.
The definition and solving of the kiss section are referred to [ T peak, hypersonic glide-cruise two-stage waverider design method research [ D ]. Changsha: section 6.1 of the university of defense science and technology (major) · 2012 ].
As shown in fig. 3, the step of defining the anastomosis section by taking any discrete point on the bottom section profile 8 of the shock wave as an example is to set any discrete point as a discrete point 19.
First, the coordinates of the center point 20 of curvature of the shock bottom section molded line 8 at the discrete point a are obtained, and the center point 20 of curvature is also the projection of the reference cone vertex 23 in the osculating plane corresponding to the discrete point a on the bottom section of the waverider.
The reference cone vertex 23 in the osculating plane corresponding to the discrete point a is located on the osculating cone-waverider reference cone vertex trajectory line 14. The reference cone vertex in the osculating plane corresponding to any point on the shock wave bottom section molded line 8 is positioned on the osculating cone wave-multiplying body reference cone vertex trajectory line 14.
The connecting line of the shock wave bottom section molded line 8 between the curvature center point 20 of the discrete point A and the reference cone vertex 23 in the osculating plane corresponding to the discrete point A is on the reference cone axis 15 of the reference cone in the osculating plane corresponding to the discrete point A, and the two are collinear.
The connecting line between the A discrete point 19 and the reference cone vertex 23 in the osculating plane corresponding to the A discrete point is the shock wave profile 22 in the osculating plane corresponding to the A discrete point, the included angle between the shock wave profile 22 in the osculating plane corresponding to the A discrete point and the reference cone axis 15 of the reference cone in the osculating plane corresponding to the A discrete point is the design shock wave angle β given in S1, the shock wave profile 22 in the osculating plane corresponding to the A discrete point and the reference cone axis 15 of the reference cone in the osculating plane corresponding to the A discrete point are located on the osculating plane corresponding to the A discrete point, namely the osculating plane corresponding to the A discrete point 19.
S4.3, solving a shock wave type line equation in the osculating tangent plane corresponding to the A discrete point 19.
The solution of the shock wave profile 22 in the osculating plane corresponding to the discrete point a in step S4.2 will be described as an example.
As shown in fig. 3, a connection line of the discrete point a 19 and a reference cone vertex 23 in the osculating plane corresponding to the discrete point a is the shock wave profile 22 in the osculating plane corresponding to the discrete point a. The shock wave molded lines in the osculating plane are all straight lines, and the shock wave molded line 22 in the osculating plane corresponding to the A discrete point can be obtained through the coordinates of two points, namely a reference cone vertex 23 and the A discrete point 19, in the osculating plane corresponding to the A discrete point.
And S4.4, solving the coordinates of the leading edge point in the osculating plane corresponding to the discrete point A19.
As shown in fig. 3, the coordinates of the leading edge point 18 in the osculating plane corresponding to the discrete point a can be obtained by combining the equation of the shock wave profile 22 in the osculating plane corresponding to the discrete point a with the equation of the horizontal projection profile 1 of the leading edge line of the waver. The leading edge point 18 in the osculating plane corresponding to the a discrete point is a leading edge point on the leading edge line of the waverider.
S4.5, by adopting the methods from S4.2 to S4.4, the kiss section corresponding to all the discrete points on the shock wave bottom section molded line in S4.1 and the shock wave molded line in the kiss section corresponding to each discrete point can be obtained, and then the coordinates of the leading edge point in the kiss section corresponding to each discrete point can be obtained through solving.
S5: solving the streamline of the lower surface of the waverider;
s5.1, solving a reference flow field in the osculating plane corresponding to each discrete point on the section line of the bottom of the shock wave.
According to the Mach number Ma of incoming flow and the shock angle β given in S1, a Taylor-Macoll control equation is solved to obtain a reference flow field in a osculating plane corresponding to each discrete point on a section line at the bottom of a shock wave, and the reference flow field in the osculating plane corresponding to each discrete point on the section line at the bottom of the shock wave is a conical flow field.
S5.2 solving the streamline.
In the osculating plane corresponding to each discrete point on the section line at the bottom of the shock wave, starting from the leading edge point in each osculating plane obtained in S4, solving the streamline corresponding to the leading edge point in each osculating plane in the reference flow field in the osculating plane corresponding to each discrete point on the section line at the bottom of the shock wave obtained in S5.1 by adopting a forward streamline tracing method, namely the streamline of the lower surface of the waverider, and the specific solving method is shown in the design method of [ butyl peak, hypersonic glide-cruise two-stage waverider: 4.3 sections of streamline solving method in the university of defense science and technology (Master) · 2012 ].
As shown in FIG. 3, in the reference flow field of the osculating plane corresponding to the discrete point A, from the front edge point 18 in the osculating plane corresponding to the discrete point A, the streamline 18-21 in the osculating plane corresponding to the discrete point A can be obtained by the forward streamline tracing method. The starting point of the streamline 18-21 in the osculating plane corresponding to the discrete point A is the front edge point 18 in the osculating plane corresponding to the discrete point A, and the tail end point 21 is positioned on the bottom section of the waverider.
And for other discrete points on the shock wave bottom section molded line 8, solving by adopting the same method as the discrete points A to obtain the osculating plane internal streamline corresponding to each discrete point.
S6: geometric lofting generates a waverider.
And (3) performing combined lofting on streamlines (the same as a streamline solving method, see S5.2) on the lower surfaces of all waverider bodies to obtain the lower surfaces of the waverider bodies, and generating the upper surfaces of the waverider bodies by adopting a free streamline method (see section 4.1 in [ Tpeak, hypersonic glide-cruise two-stage waverider design method research [ D ]. Changsha: national defense science and technology university (Master): 2012 ].
If the sweep angle equation is given according to the scheme A and the horizontal projection profile of the leading edge line of the waverider is solved in S2, the known parameters are divided into reference flow field parameters (Ma, β) and geometric shape parameters (L, psi, n, W, Ls, chi)A1、χA2) Two, collectively referred to as input conditions for the waverider design. Thickness (H) of waverider obtained in S3 and reference sweep angle (χ) in S2Ab) The thickness (H) of the waverider is determined by the length L of the waverider and the reference flow field (Ma, β), and the sweep angle (χ) is intermediateAb) Represented by the formula tan (χ)Bb) Determined at 2L/W.
An embodiment of the present invention is provided below, wherein in S2, a sweep angle equation is given according to the scheme a and a horizontal projection profile of a leading edge line of a waverider is solved, specifically as follows:
setting reference flow field parameters of Ma 6 and β 12 degrees;
giving the parameters of the profile of the bottom section of the shock wave: l is 6m, W is 4.37m, n is 3, Ls is 0.01W.
According to the constraint of formula, the horizontal projection profile line sweep angle parameter (chi)A1、χA2) The values are as follows: a first group: chi shapeA1＝75°,χA265 °; second group: chi shapeA1＝80°,χA2＝65°。
The waverider up/down dihedral ψ takes two sets, the first: psi-7 °; the second set ψ is 10 °.
The sweep angle combination scheme is matched with the up/down dihedral scheme to obtain three appearance schemes shown in table 1.
TABLE 1
Figure GDA0002497814240000251
Fig. 7 to 12 are a top view and a right side view of three profiles. In the top view and the right view, the sweep angle and the up/down dihedral angle of the appearance of the design scheme both meet the design requirements.
The osculating pyramid waverider obtained by design meets the requirement through calculation of the non-viscous numerical value. As shown in fig. 13, the pressure contour cloud chart of the bottom section of the medium flow field in the diagram shows that the high-pressure airflows are all located on the lower surface of the waverider, and the designed shock wave bottom section profile discrete points are consistent with the calculation results.
If the sweep angle equation is given according to the scheme B and the horizontal projection profile of the leading edge line of the waverider is solved in S2, the known parameters in S1 to S3 are divided into reference flow field parameters (Ma, β) and geometric shape parameters (psi, n, W, Ls, chi)Bn、χBt) The multiplier length L is determined in S2, and the multiplier thickness (H) is determined from the multiplier length L and the reference flow field (Ma, β).
Another embodiment of the present invention is provided below, wherein in S2, the sweep angle equation is given according to scheme B and the horizontal projection profile of the leading edge line of the waverider is solved, as follows:
setting reference flow field parameters of Ma 6 and β 16 degrees;
giving the parameters of the profile of the bottom section of the shock wave: w is 4.32m, n is 3, Ls is 0.01W.
The values of the sweep angle equation parameters and the values of the dihedral angles of the leading edge lines of the two appearance schemes are shown in Table 2.
TABLE 2
Figure GDA0002497814240000261
Fig. 14 to 17 are a plan view and a right side view of the outer shape. The sweep angle and the up/down dihedral angle of the designed shape both meet the design requirements.
In summary, although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes and modifications can be made by those skilled in the art without departing from the spirit and scope of the invention.

Claims (7)

1. A method for designing osculating cone waverider with directly controllable sweepback angle and upper/lower dihedral angle is characterized by comprising the following steps:
s1, giving reference flow field parameters, wherein the reference flow field parameters comprise an incoming flow Mach number Ma and a shock wave angle β;
s2: giving a sweepback angle equation and solving a horizontal projection profile of a leading edge line of the waverider;
assuming that the sweep angle of the horizontal projection profile of the leading edge line of the waverider along the z direction of the coordinate system of the airframe is χ (z), any point P on the horizontal projection profile of the leading edge line of the waverider is assumed to belThe value of the corresponding sweep angle is chil(ii) a P on horizontal projection type line of wave rider leading edge linelPoint corresponding sweep angle χlThe following relation exists with the wave multiplier leading edge line horizontal projection type line equation, see formula (1):
Figure FDA0002497814230000011
the wave multiplier leading edge line horizontal projection type line equation is x ═ f (z), z ∈ [0, W/2], wherein W is the wave multiplier width;
the horizontal projection molded line of the leading edge line of the waverider can be solved by giving a sweepback angle equation and known parameters of the waverider;
s3: solving the profile of the bottom section of the shock wave;
setting the bottom section profile of the shock wave to be solved as a combined profile of a straight line and a power curve; the method comprises the steps of obtaining the bottom section profile of the shock wave of the waverider by giving an upper dihedral angle psi, the length of a straight line segment in the bottom section profile of the shock wave of 2 x Ls, the width W of the waverider and the power curve power n and combining the thickness H of the symmetrical surface of the waverider obtained by solving;
s4: solving a front edge point on a wave-multiplying body front edge line;
s5: solving the streamline of the lower surface of the waverider;
s6: geometric lofting is carried out to generate a waverider;
and (4) performing combined lofting on the streamlines of the lower surfaces of all waverider bodies to obtain the lower surfaces of the waverider bodies, wherein the upper surfaces of the waverider bodies are generated by adopting an own streamline method.
2. The osculating cone waverider design method with directly controllable sweepback angle and upper/lower dihedral according to claim 1, wherein the solving process of S2 is as follows:
the given sweep angle equation is shown in formula (2), wherein χA1,χA2Are all constant, xA1And chiA2Respectively representing the sweepback angles of different sections of the sweepback angle equation;
Figure FDA0002497814230000021
by substituting equation (2) into (1), we can see that:
Figure FDA0002497814230000022
assuming that the leading edge line horizontal projection type line equation is shown in equation (4):
Figure FDA0002497814230000023
wherein k isA1,bA1,kA2,bA2,z1All are parameters to be solved;
the known condition is the sweep angle equation χ ═ χA(z), the length L and the width W of the waverider, the parameters to be solved in the front edge line horizontal projection type line equation (4) can be given by the following equations (5) and (6):
Figure FDA0002497814230000024
Figure FDA0002497814230000025
χ in equation (6)AbIs a reference sweep angle; due to the fact that
Figure FDA0002497814230000026
Sweep Angle χ in sweep Angle equation (2)A1,χA2The requirement of formula (7) needs to be satisfied at the same time:
min(tan(χA1),tan(χA2))＜tan(χAb)＜max(tan(χA1),tan(χA2)) (7)
the equation x of a half curve of the horizontal projection type line of the leading edge line of the waverider is f (z), z ∈ [0, W/2] is solved, and based on the symmetry of the waverider, the other half curve of the horizontal projection type line of the leading edge line of the waverider can be obtained through symmetrical transformation according to the half curve obtained through solving.
3. The osculating cone waverider design method with directly controllable sweepback angle and upper/lower dihedral according to claim 1, wherein the solving process of S2 is as follows:
to pair
Figure FDA0002497814230000031
And integrating, substituting the sweepback angle equation χ (z) into χ (z), and simplifying by an element-changing integration method to obtain a formula (8):
Figure FDA0002497814230000032
substituting the formula (1) into a formula (8), and further simplifying to obtain a formula (9); equation (9) is a relationship between the front edge line horizontal projection type equation x ═ f (z) and the sweep angle equation χ ═ χ (z):
Figure FDA0002497814230000033
wherein the sweep angle equation chi (z) needs to satisfy the following conditions:
i. when z ∈ [0, W/2], the χ '═ χ' (z) equation is continuous;
ii, wherein the coordinate value χ (0) χ of the end point of the sweep angle equation1,χ(W/2)＝χ2And when z ∈ [0, W/2]]When it is, chi (z) ∈ [ chi [)1,χ2]；
Let the sweep angle equation vary linearly along the z-coordinate, i.e., as shown in equation (10):
Figure FDA0002497814230000034
substituting the formula (10) into the formula (9) to obtain a formula (11), which is a front edge line horizontal projection type line equation;
Figure FDA0002497814230000035
the parameter to be solved in the formula (11) is mB、dB、CBSolving the solution shown in formula (12); the known parameter in equation (12) is χBn、χBt、W，χBn、χBtRespectively, P on the front edge line horizontal projection type linen、PtThe sweepback angle corresponding to the two points, W is the width of the wave rider,
Figure FDA0002497814230000041
the length L of the waverider is a parameter to be solved, and is shown in a formula (13):
Figure FDA0002497814230000042
from the formula (12), the front and the tail end points, i.e. P, on the line projected horizontally through the front edge linen、PtSweepback angle chi corresponding to two pointsBn、χBtAnd passenger width W, the sweep angle change rate χ'B(z)＝mBFinally, the goal that the sweepback angle of the front edge line is directly controllable is reached;
the equation x of a half curve of the horizontal projection type line of the leading edge line of the waverider is f (z), z ∈ [0, W/2] is solved, and based on the symmetry of the waverider, the other half curve of the horizontal projection type line of the leading edge line of the waverider can be obtained through symmetrical transformation according to the half curve obtained through solving.
4. The osculating cone waverider design method with directly controllable sweepback angle and upper/lower dihedral according to claim 2 or 3, characterized in that the solving method of S3 is as follows:
s3.1, setting an upper inverted angle psi of a waverider, the length of a straight line segment in a section profile at the bottom of the shock wave is 2 x Ls, the width W of the waverider and the power of a power curve n;
s3.2, designing a bottom section profile equation of the wave multiplier shock wave;
the shock wave bottom section profile equation is a straight line plus power curve, and is shown in the formula (14):
Figure FDA0002497814230000043
wherein the cross section of the bottom of the waverider is on a y-z plane, and α is a power curve coefficient which is a coefficient of a quantity to be solved;
s3.3, solving the thickness H of the symmetrical surface of the waverider;
knowing a shock wave angle β and the length L of the waverider, solving a reference flow field and a flow line in a osculating plane where the symmetrical surface of the waverider is located by using a Taylor-Maccoll control equation and a flow line tracking method;
s3.4, solving a bottom section profile equation of the wave multiplier shock wave;
Ptthe coordinates of the point are (0, W/2, h)1) Wherein
Figure FDA0002497814230000051
h0Providing Ltan (β); adding PtSubstituting the point coordinates into formula (14) to obtain formula (15):
Figure FDA0002497814230000052
the power curve coefficient α is obtained by substituting the design shock angle β, the multiplier length L, and the dihedral angle ψ into equation (15).
5. The osculating cone waverider design method with directly controllable sweepback angle and upper/lower dihedral according to claim 4, wherein the solving method of S4 is as follows:
s4.1, dispersing the molded line of the bottom section of the shock wave obtained by solving in the S3 to obtain a series of discrete points;
s4.2, determining an anastomosis section corresponding to each discrete point on a section line at the bottom of the shock wave;
s4.3, solving a shock wave profile equation in the osculating plane corresponding to each discrete point on the profile of the bottom section of the shock wave;
and S4.4, solving the coordinates of the front edge points in the osculating plane corresponding to each discrete point on the section line of the bottom of the shock wave.
6. The method for designing the osculating cone waverider with the directly controllable sweep angle and upper/lower dihedral according to claim 5, wherein in S4.2, for any discrete point on the profile line of the bottom section of the shock wave, the discrete point is marked as A discrete point;
firstly, the coordinates of the curvature center point of the shock wave bottom section molded line at the A discrete point are solved, and the curvature center point is simultaneously the projection of the reference cone vertex in the osculating plane corresponding to the A discrete point on the bottom section of the waverider;
the vertex of the reference cone in the osculating plane corresponding to the discrete point A is positioned on the locus line of the vertex of the reference cone of the osculating cone waverider; the reference cone vertex in the osculating plane corresponding to any point on the section line of the bottom of the shock wave is positioned on the locus line of the reference cone vertex of the osculating cone-wave body;
the connecting line of the curve center point of the shock wave bottom section molded line at the discrete point A and the reference cone vertex in the osculating plane corresponding to the discrete point A is on the reference cone axis of the reference cone in the osculating plane corresponding to the discrete point A, and the two connecting lines are collinear;
the included angle between the shock wave molded line in the osculating plane corresponding to the A discrete point and the reference cone axis of the reference cone in the osculating plane corresponding to the A discrete point is the design shock wave angle β given in S1;
s4.3, a connecting line of the discrete point A and a reference cone vertex in the osculating plane corresponding to the discrete point A is a shock wave molded line in the osculating plane corresponding to the discrete point A; because the shock wave molded lines in the osculating plane are all straight lines, the shock wave molded lines in the osculating plane corresponding to the A discrete points can be obtained through the coordinates of two points, namely a reference cone vertex and the A discrete points in the osculating plane corresponding to the A discrete points;
in S4.4, the equation of the shock wave molded line in the osculating plane corresponding to the discrete point A and the equation of the horizontal projection molded line of the leading edge line of the waverider are combined to obtain the coordinates of the leading edge point in the osculating plane corresponding to the discrete point A, wherein the leading edge point in the osculating plane corresponding to the discrete point A is the leading edge point on the leading edge line of the waverider.
7. The osculating cone waverider design method with directly controllable sweepback angle and upper/lower dihedral according to claim 6, wherein the implementation method of S5 is as follows:
s5.1, solving a reference flow field in a osculating plane corresponding to each discrete point on a section line at the bottom of the shock wave;
according to the incoming flow Mach number Ma and the shock wave angle β given in S1, a reference flow field in the osculating plane corresponding to each discrete point on the shock wave bottom section line is obtained by solving a Taylor-Maccoll control equation, and the reference flow field in the osculating plane corresponding to each discrete point on the shock wave bottom section line is a conical flow field;
s5.2, solving a streamline;
in the osculating plane corresponding to each discrete point on the shock wave bottom section line, starting from the leading edge point in each osculating plane obtained in S4, a forward streamline tracing method is adopted in the reference flow field in the osculating plane corresponding to each discrete point on the shock wave bottom section line obtained in S5.1, and the streamline corresponding to the leading edge point in each osculating plane, that is, the streamline of the lower surface of the waverider is solved.
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