Wave rider windward side parameterization design method without solving partial differential equation

Abstract

According to the waverider windward side parameterization design method without solving a partial differential equation, the windward side profile and the leading edge curve are designed in the form of explicit functions, the waverider design process of the windward side is remarkably simplified on the basis of keeping waverider characteristics, and the waverider design efficiency of the windward side is further improved. By optimizing the waverider design process, the design efficiency of the front edge shape and the curved surface shape of the waverider windward face, the intuition of shape adjustment and the shape adjustment efficiency are further improved.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic layout, specifically relating to a parametric design method for wave-riding windward surfaces that does not require solving partial differential equations. Background Technology

[0002] Lift-to-drag ratio is a crucial parameter for evaluating the performance of high-speed aircraft, and waverider design of the frontal surface is a common measure to improve the lift-to-drag ratio. Classical waverider design theories, such as conical waverider design, kissing conical waverider design, and kissing flow field waverider design, all involve three steps. First, a characteristic line mesh is constructed according to the pre-defined shock surface, and partial differential equations are solved to complete the baseline flow field design. Second, the given two-dimensional leading edge profile is projected onto the shock surface to obtain the final three-dimensional leading edge profile. Finally, the complete frontal surface shape is obtained by starting from points on the three-dimensional leading edge profile and using the streamline tracing method.

[0003] The complex windward wave-riding design process limits the efficiency of windward surface generation; the projection-based leading edge design process results in a lack of direct means to adjust the shape of the leading edge line, requiring a large number of iterations to complete the adjustment; the streamline-based windward surface construction method results in the windward surface being composed of thousands of discrete points, making it difficult to manually adjust the surface shape in 3D modeling software. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes a parametric design method for the windward face of a waverider that eliminates the need to solve partial differential equations. The method designs the windward face profile and leading edge curve using explicit functions, significantly simplifying the waverider design process while preserving the waverider characteristics and further improving its efficiency. By optimizing the waverider design process, the design efficiency of the leading edge shape and surface shape of the windward face is further improved, along with the intuitiveness and efficiency of shape adjustment.

[0005] A parameterized design method for wave-riding windward surfaces that does not require solving partial differential equations includes the following steps: (1) Design and parametric description of the leading edge of the wave-riding windward side; (2) Design and parametric description of the windward surface of the wave-riding surface.

[0006] In step (1), the shape of the leading edge curve is expressed by a Bézier curve. Taking a six-control-point Bézier curve as an example, the parametric expression of the leading edge curve is: in, , The three-dimensional coordinates of the six control points can be freely set as needed.

[0007] Furthermore, in step (2), based on the fact that any point on the leading edge curve corresponds to a flow-direction cross-sectional curve, The parametric expression for the flow section curve at the location is: in, , The deflection angle of the cross section. The length of the waverider. The parameters of the flow section curve The shape function.

[0008] Furthermore, the shape function in the flow section curve is a bivariate function that satisfies the following three equations: in, The deflection angle at the starting point of the flow profile curve. The deflection angle at the endpoint of the flow-direction section curve.

[0009] Furthermore, a feasible solution for the shape function is: in, is the length of the waverider.

[0010] The beneficial effects of this invention are as follows: (1) The shape of the front edge of the windward side is adjusted in the form of an explicit function, which solves the problems of poor efficiency and low design freedom caused by the previous projection method; (2) While maintaining the basic wave multiplication characteristics, the shape of the windward surface is directly solved by multiple explicit functions, and the surface shape is generated by only a dozen parameters, which improves the design efficiency and the convenience of surface shape adjustment. Attached Figure Description

[0011] Figure 1 This is a flowchart of a parameterized design method for wave-riding windward surfaces that does not require solving partial differential equations; Figure 2 This is a schematic diagram of the waverider leading edge curve designed using this invention, where L is the length of the waverider and W is the half-span of the waverider. This curve is parametrically represented by a Bézier curve, and point O on the curve corresponds to... Location, point A corresponds to Location; Figure 3 This is a schematic diagram of the flow profile curve corresponding to a point on the wave-riding leading edge designed using this invention. OA is the leading edge curve, B is any point on the leading edge line, BC is the corresponding flow profile curve, and BD is a reference line parallel to the X-axis. The angle between the tangent to curve BC at point B and BD corresponds to the angle in formula (4). The angle between the tangent to curve BC at point C and BD corresponds to formula (4). ; Figure 4 This is a schematic diagram of the windward surface designed using the present invention. Detailed Implementation

[0012] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection claimed by the present invention.

[0013] A parameterized design method for wave-riding windward surfaces that does not require solving partial differential equations is as follows: (1) Design and parametric description of the leading edge of the wave-riding windward side The shape of the leading edge curve is expressed by a Bézier curve. Taking a six-control-point Bézier curve as an example, the parametric expression of the leading edge curve is: in, , The three-dimensional coordinates of the six control points can be freely set as needed.

[0014] (2) Design and parametric description of the windward surface of the wave-riding surface Leading edge curve based on design Regarding his previous position The parametric expression for the flow profile curve at that point is: in, , The length of the waverider. The deflection angle of the cross section. The parameters of the flow section curve The shape function.

[0015] The cross section deflection angle in formula (2) It can be calculated using the following formula: in, h These are geometric adjustment parameters, and , For formula (1) The y-coordinate of the point corresponds to the leading edge curve. Location, and In formula (1) The y and z coordinates at the location.

[0016] In formula (2), the shape function is a bivariate function that satisfies the following three equations: In formula (4), This parameter represents the deflection angle of the flow profile curve at the endpoint. A fixed value needs to be pre-defined for this parameter, within a reference range. , The flow profile curve at the leading edge position ( The deflection angle is given by the design conditions of the waverider, where the Mach number is Ma and the angle of attack of the incoming flow is... α The shock angle of the conical shock wave is β It can be calculated using formulas (5) and (6).

[0017] A feasible solution for the shape function in formula (2) to satisfy formula (4) is: in, is the length of the waverider.

[0018] The parametric design of the windward side of the wave-riding surface can be completed by formulas (1) to (7). All of the above formulas are explicit expressions and do not involve solving differential equations or complex iterative calculations.

[0019] The waverider leading edge curve designed in this invention is as follows: Figure 2 As shown, the contour line corresponding to a point on the wave-riding leading edge is shown below. Figure 3 A schematic diagram of the design results can be found in [the diagram]. Figure 4 In the diagram, L represents the length of the wave-riding windward surface, and W represents the half-width of the wave-riding windward surface.

[0020] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A parameterized design method for wave-riding windward surfaces that does not require solving partial differential equations, characterized in that, Includes the following steps: (1) Design and parametric description of the leading edge of the wave-riding windward side; (2) Design and parametric description of the windward surface of the wave-riding surface.

2. The method for parameterized design of a wave-riding windward surface without the need to solve partial differential equations as described in claim 1, characterized in that, In step (1), the shape of the leading edge curve is expressed by a Bézier curve. Taking a six-control-point Bézier curve as an example, the parametric expression of the leading edge curve is: in, , The three-dimensional coordinates of the six control points can be freely set as needed.

3. The method for parameterized design of the windward face of a wave-riding surface without the need to solve partial differential equations, as described in claim 2, is characterized in that... In step (2), based on the fact that any point on the leading edge curve corresponds to a flow cross-section curve, The parametric expression for the flow section curve at the location is: in, , The deflection angle of the cross section. The length of the waverider. The parameters of the flow section curve The shape function.

4. The method for parameterized design of the windward face of a wave-riding surface without the need to solve partial differential equations, as described in claim 3, is characterized in that... The shape function in the flow profile curve is a bivariate function that satisfies the following three equations: in, The deflection angle at the starting point of the flow profile curve. The deflection angle at the endpoint of the flow-direction section curve.

5. The method for parameterized design of the windward face of a wave-riding surface without the need to solve partial differential equations as described in claim 4, characterized in that, A feasible solution to the shape function is: in, is the length of the waverider.

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