A Design Method for a Wide-Field Waverider-Body Fusion Configuration

Abstract

The present invention discloses a design method for a wide - domain waverider - body blended configuration, including: determining the planar geometric parameters of the wide - domain waverider - body blended configuration: generating the lower surface of the waverider forebody according to the design parameters kw, φ, η, and λ of the leading - edge line of the waverider forebody and the length LF of the waverider forebody; generating the upper surface of the waverider forebody: performing leading - edge blunting on the waverider forebody; generating the wing surface: determining the upper and lower surfaces of the fuselage: based on known data points, determining the upper and lower surfaces of the fuselage through the CST surface parameterization method; obtaining the blended - body segment surface with a smooth transition between the fuselage and the wing: generating the leading - edge surface of the blended - body segment: connecting the leading - edge of the waverider forebody and the leading - edge of the wing through a number of smooth curves, and generating the leading - edge surface of the blended - body segment on the basis of the fitted curve; The present invention parameterizes the waverider - body blended configuration by using the CST parameterization curve and surface method, providing an effective design method for the engineering application of wide - domain waverider - type aircraft.

Description

Technical Field

[0001] The present invention belongs to the technical field of wide - domain aircraft, and particularly relates to a design method for a wide - domain waverider - body blended configuration. Background Art

[0002] The aerodynamic layout of a wide - domain aircraft needs to be matched and designed considering the entire flight speed range from sub - sonic, transonic, supersonic to hypersonic. However, the optimal layout characteristics of the aircraft under different speed conditions are often contradictory: To meet the requirements of high lift - to - drag ratio at sub - sonic speed and low - speed landing, traditional aircraft often exhibit characteristics such as a small sweep angle and a large wing area. However, these characteristics will lead to excessive drag under hypersonic conditions, rapid energy loss, and inability to cruise for a long time. For example, fighter jets often use components such as canards and leading - edge and trailing - edge flaps to increase low - speed lift. However, at the hypersonic stage, too many aerodynamic components will lead to a complex wave system of the whole aircraft, mutual interference, and is not conducive to thermal protection. In addition, during the wide - domain flight process, the handling and stability characteristics of the aircraft, such as the center of pressure, focus, and rudder effectiveness, will change violently, bringing problems such as large trim losses, reduced available lift - to - drag ratio, and even difficulty in control, which have an important impact on the overall performance. Therefore, how to obtain the optimal shape that meets the aerodynamic performance in different speed ranges under the condition of meeting complex engineering constraints is the key problem that urgently needs to be solved in the aerodynamic layout design.

[0003] Under different speed ranges, the optimal layout characteristics of the aircraft are often contradictory. The high lift - to - drag ratio advantage of the waverider has great application value at hypersonic speed. However, traditional waveriders are difficult to meet the aerodynamic characteristic requirements at low speed. The full - trajectory aerodynamic characteristics of the waverider layout show that the lift during the landing stage is seriously insufficient, and due to the violent changes in the center of pressure and focus in the wide speed range, the control surfaces designed based on the hypersonic state are difficult to meet the trim requirements at sub - sonic speed.

[0004] The wing is the core component of traditional low - speed aircraft to generate aerodynamic force. Through the reasonable design of the airfoil and wing planform, efficient circulation lift and vortex lift can be generated.

[0005] However, existing technical research is all for the design and performance evaluation of waveriders or other layouts, and cannot simultaneously meet the requirements of high lift - to - drag ratio in the supersonic - hypersonic case and the aerodynamic characteristics requirements at sub - sonic speed. Moreover, existing research is all for the performance evaluation of a single scheme, mainly relying on empirical design during the scheme design process, without a clear and mature design method for reference, and it is even more difficult to directly carry out aerodynamic layout optimization. Summary of the Invention

[0006] In view of the problems existing in the prior art, the present invention proposes a design method for a wide-domain waverider body fusion configuration, aiming to solve the problem that the existing aircraft design methods cannot meet the aerodynamic performance requirements within a wide speed range. In order to conduct an optimized design study on the wide-domain waverider body fusion configuration, this patent proposes a parameterization method for the waverider body fusion configuration, realizing the full-parameter description of the baseline layout.

[0007] The present invention proposes the following technical solutions to solve the problems existing in the prior art;

[0008] A design method for a wide-domain waverider body fusion configuration, characterized by comprising the following steps:

[0009] Step 1: Determine the planar geometric parameters of the wide-domain waverider body fusion configuration: LT represents the total length of the configuration; LF represents the length of the waverider forebody; b F represents the width of the waverider forebody; b / 2 represents the semi-span of the configuration; L1 represents the longitudinal distance from the foremost end of the wing to the bottom of the waverider forebody; L2 represents the length of the fusion section in the spanwise direction; Λ represents the sweep angle of the wing leading edge; Ltip represents the chord length of the wing tip; D is the blunt diameter of the waverider forebody; θ is the angle between the symmetric surface profile line on the upper surface of the waverider forebody and the x-axis at the head; H1 is the height of the bottom cross-section of the waverider forebody; H2 is the maximum height constraint of the fuselage; H3 is the height constraint of the tail of the configuration; after the lower surface of the waverider forebody is given, the forebody width is a known quantity, and the wing span and the trailing edge sweep angle can be determined according to b / 2 and L2;

[0010] Step 2: Generate the lower surface of the waverider forebody according to the design parameters kw, η and λ of the leading edge line of the waverider forebody, and the length LF of the waverider forebody;

[0011] Step 3: Generate the upper surface of the waverider forebody: Determine the symmetric surface profile line l1 of the upper surface according to the design parameter θ of the upper surface of the waverider forebody and the height constraint H1, and represent the spanwise cross-section profile line l2 of the upper surface by a CST curve, and then generate the upper surface of the waverider forebody;

[0012] Step 4: Conduct leading edge blunting on the waverider forebody;

[0013] Step 5: Generate the wing surface: According to the planar geometric parameters of the wide-domain waverider body fusion configuration, determine the wing shape, and obtain the airfoils of each longitudinal cross-section through the airfoil design parameter bw i to generate the wing surface; the planar geometric parameters include the layout semi-width b / 2, the width b of the waverider forebody F , and the width L2 of the wing-body fusion section; the wing shape includes the wing root length, the wing tip length, and the wing sweep angle;

[0014] Step 6. Determine the upper and lower surfaces of the fuselage: Based on the known data points of the waverider forebody, as shown by the dashed line in 8 and the defined data points of the fuselage cross-section profile, as Figure 8 shown by the double-dot dash line in, determine the upper and lower surfaces of the fuselage through the CST surface parameterization method;

[0015] Step 7. Obtain the wing-body fairing section surface with smooth transition between the fuselage and the wing: According to the generated fuselage and wing, determine several (generally 10 - 15 are sufficient) curves with smooth transition between the fuselage and the wing, and then, with the fuselage, wing and smooth curves as constraints, obtain the wing-body fairing section surface with smooth transition between the fuselage and the wing through CST surface fitting;

[0016] Step 8. Generate the leading-edge surface of the wing-body fairing section: Describe the blunt leading-edge curve of the fairing section through a cubic polynomial, and generate the leading-edge surface of the wing-body fairing section through the mesh surface method;

[0017] Step 9. Parametric result: Obtain the wide-domain waverider wing-body fairing configuration with smooth surface transition.

[0018] Furthermore, the specific steps for generating the lower surface of the waverider forebody in Step 2 are as follows:

[0019] ① Generate the leading-edge line according to the conical waverider

[0020] The generation process is as Figure 1 shown: Given the incoming flow Mach number Ma and the shock wave angle β of the conical shock wave s obtain the three-dimensional shock wave surface, define an arbitrary-form reference curve on the bottom YZ plane of the shock wave surface. Here, a cubic polynomial in the following form is used to define the reference curve on the bottom surface:

[0021]

[0022] To describe this curve more clearly and intuitively, let the radius of the shock wave circle be R s , the Z intercept of the reference curve be R0, and the azimuth angle be Let the angle between the tangent of the curve at the intersection position with the shock wave circle and the Y axis be η, and the angle between the tangent of the curve at the intersection position with the Z axis and the Y axis be λ, and let the parameter kw = R0 / R s , after simplification, we can get:

[0023]

[0024] In this way, given the design parameters kw, η and λ, the form of the reference curve in Equation (1) can be completely determined; then project this curve along the X-axis direction onto the shock wave surface to obtain an intersection line, which is the leading-edge line of the waverider.

[0025] ② Solve the reference flow field

[0026] Due to the axisymmetric characteristics of the reference flow field, the flow characteristics on each streamline starting from the vertex are constant. Its governing equation in the axisymmetric coordinate system is the Taylor-Maccoll equation, as shown in Equation (3). This governing equation is derived from the continuity equation, Euler equation of conical flow, and combined with the irrotational condition.

[0027]

[0028] Where r and θ represent the independent variables in the radial and normal directions respectively, and V max represents the maximum theoretical velocity at zero temperature, V r represents the radial velocity component, and γ represents the specific heat ratio. Assuming the oncoming flow is a calorically perfect gas, then γ = 1.4. The normal velocity component in the axisymmetric conical flow field can be calculated using Equation (4):

[0029]

[0030] By numerically solving the Taylor-Maccoll equation, the reference flow field can be obtained.

[0031] ③ Generate the lower surface of the waverider

[0032] Select several points (usually 20 - 30 are sufficient) on the leading edge line of the waverider. In the reference flow field, streamline tracing is performed along the downstream direction for each point, and the lower surface can be generated as shown in Figure 2 ; The streamline is determined by the following equation:

[0033]

[0034] Where u, v, and w represent the velocity components along the corresponding coordinate axes;

[0035] ④ Scale the lower surface of the waverider proportionally to the required length L F .

[0036] Furthermore, the specific steps for generating the upper surface of the waverider forebody in step three are as follows:

[0037] ① Define the symmetric profile line l1 using a cubic polynomial

[0038] Determine the upper surface symmetric profile line according to the design parameters θ and height constraint H1 of the waverider forebody upper surface. Use a cubic polynomial in the following form to define the symmetric profile line l1, as shown in Figure 5 :

[0039] y = ax + bx 2 + cx 3 (6)

[0040] The polynomial coefficients a, b, and c can be determined based on the geometric constraint θ and the height constraint H1. According to the geometric constraint, the upper surface profile of the waverider needs to satisfy the following constraints:

[0041]

[0042] Substituting the above constraints into the above equation (6), the solution is:

[0043]

[0044] ② Represent the upper surface spanwise sectional profile l2 through the CST curve

[0045] Specifically as follows:

[0046] The z - sectional profile l2 at any x position is represented by CST, as in Figure 5 l2 in, and the expression is:

[0047]

[0048] The class function in formula (8) is defined as:

[0049]

[0050] where N1 and N2 are the exponents of the class function respectively, ψ is the independent variable, representing the dimensionless z - coordinate,

[0051] The definition of the shape function in formula (8) is:

[0052]

[0053] In formula (10), b i , i = 0, 1, 2, …, n are the weight factors of the polynomial; is the term of the n - th order Bernstein polynomial, and ψ is the independent variable, representing the dimensionless z - coordinate.

[0054] The values of A and B in formula (8) are:

[0055]

[0056] where y1 is the y - coordinate of the leading - edge point 1, and y2 is the y - coordinate of the point 2 on the symmetric - plane profile.

[0057] ③ Generate the upper surface of the waverider considering the volume constraint

[0058] Select several points on the leading - edge line of the waverider. By the above method, several spanwise sectional profiles are determined, and then the upper surface of the waverider considering the volume constraint can be generated, as shown in Figure 6 shown.

[0059] Furthermore, the specific steps for generating the wing surface in Step Five are as follows:

[0060] A. Obtain the planar geometric parameters of the wing

[0061] ① Calculate the root length of the wing: Based on the total length L of the waverider-body blended configuration T , the length L of the waverider forebody F and the length L1 of the blended section, the root length of the wing can be calculated;

[0062] ② Calculate the span of the wing: Based on the half-width b / 2 of the configuration, the length L2 of the blended section, and the width b of the waverider forebody F , the span of the wing can be calculated;

[0063] ③ Calculate the tip length of the wing and the sweep angle of the leading edge of the wing;

[0064] B. The airfoil parametric equation is shown in Equation (12):

[0065]

[0066] In the formula where bw i , i = 0, 1, …, n are airfoil design parameters, and ζ T is the trailing edge thickness.

[0067] By determining the design parameter bw i , the airfoil curve can be determined; for simplicity here, the same airfoil is used for each cross-section of the wing, and different airfoils can also be used for each cross-section in the actual design process;

[0068] C. Generate the upper and lower surfaces of the wing: After the airfoil is determined, scale the airfoil according to the chord length of each cross-section to obtain each airfoil cross-section of the wing as shown in Figure 7 , and then generate the upper and lower surfaces of the wing.

[0069] Furthermore, the specific steps for determining the upper and lower surfaces of the fuselage in Step Six are as follows:

[0070] A. Select some points on the waverider forebody surface as known data points, as shown by the dashed line in Figure 8 , define the fuselage cross-section profile according to the fuselage geometric constraints, as shown by the double-dot dash line in Figure 8 , and use it as the known data point;

[0071] B. To achieve a smooth transition between the waverider forebody and the fuselage, the CST reverse fitting technology is used here to realize the integrated characterization of the waverider forebody and the fuselage, specifically as follows:

[0072] For the CST parametric modeling of surfaces with arbitrary planar shapes, the surface can be normalized in two directions in the z-x plane through coordinate transformation. The Bernstein polynomial is used to describe the surface, and class functions are added in the characteristic directions of the surface. The CST method representation of the surface is obtained as follows:

[0073]

[0074] where ψ is the dimensionless z coordinate, η is the dimensionless x coordinate, and ζ is the dimensionless surface y coordinate. is the class function, Sx j (η) and Sz i (ψ) are the Bernstein polynomial functions in two directions, and B i,j is the surface control parameter. The expression of the coordinate transformation is:

[0075]

[0076] where x U , x D are the boundaries of the surface in the x direction in the z-x plane, and z U , z D are the boundaries of the surface in the z direction in the z-x plane; the relationship between ζ in Equation (13) and the change of the surface y coordinate is:

[0077] ζ = y / b (15)

[0078] C. Using the above CST method, fit the known points of the waverider forebody and fuselage. During the fitting process, the solution of the CST surface coefficient B i,j can be obtained by the Newton method or by solving the overdetermined equations.

[0079] D. After obtaining the coefficient B i,j , generate the fuselage surface. As Figure 9 shown.

[0080] Furthermore, the specific steps to obtain the wing-body fairing surface with a smooth transition between the fuselage and the wing in Step 7 are as follows:

[0081] ① According to the generated fuselage and wing, determine the spanwise profile of the wing-body fairing, as shown by the double-dashed line in Figure 10 . Here, the spanwise sectional profile is defined by a cubic polynomial as in Equation (16); the coefficients a, b, c, and d can be solved by substituting the coordinates and slopes at the endpoints of the curve into Equation (16), and then the points on the curve can be solved.

[0082] y = a + bx + cx 2 + dx 3 (16)

[0083] Similarly, a cubic polynomial is used to define the leading edge line of the blending section. As shown in Figure 10 , the coefficients a, b, c, and d can be determined from the coordinates at the curve endpoints and the tangent slopes at the endpoints, and then the curve can be solved.

[0084] ② Select some known points on the fuselage surface and the wing surface, as shown by the dashed lines in Figure 10 , and the sectional profile line in the spanwise direction of the blending section. A smooth transition wing-body blending section surface between the fuselage and the wing is obtained through the above CST surface fitting method;

[0085] Furthermore, the specific steps for generating the leading edge surface of the wing-body blending section in step eight are as follows:

[0086] Select several points on the leading edge line of the blending section. Define the blunt leading edge curve of the blending section using a cubic polynomial curve in Equation (16), as shown in Figure 11 . Since the endpoint coordinates of this curve are known, the slope at this point can be obtained from the upper and lower surface profiles of the blending section, such as the slope at the dashed line endpoints in Figure 11 . The coefficients a, b, c, and d in the equation can be calculated, and the blunt leading edge curve can be obtained; according to the leading edge line of the blending section and the arcs of each section, the blunt leading edge surface of the blending section is generated through the mesh surface method.

[0087] Advantages and effects of the present invention

[0088] The present invention parameterizes the waverider wing-body blended configuration using CST parametric curves and surfaces, achieving smooth transitions between the waverider forebody and the fuselage, the fuselage and the wing, etc. It not only solves the problem of difficult smooth transition between surfaces but also takes into account the requirements of waverider forebody leading edge blunting and fuselage volume constraints, providing an effective design method for the engineering application of wide-domain waverider aircraft. Description of the drawings

[0089] Figure 1 Schematic diagram for generating a conical waverider;

[0090] Figure 2 Schematic diagram for generating the lower surface of the waverider;

[0091] Figure 3 Schematic diagram for the leading edge blunting process;

[0092] Figure 4 Schematic diagram for the planar geometric constraints of the wide-domain waverider wing-body blended configuration;

[0093] Figure 5 One of the schematic diagrams for generating the upper surface of the waverider forebody;

[0094] Figure 6 Another schematic diagram for generating the upper surface of the waverider forebody;

[0095] Figure 7 Schematic diagram of the upper surface of the afterbody wing

[0096] Figure 8 Schematic diagram of known data points of the waverider forebody and data points of the fuselage cross-section profile

[0097] Figure 9 Schematic diagram of the generation of the fuselage surface

[0098] Figure 10 Schematic diagram of the fitting data of the wing-body fusion section

[0099] Figure 11 Schematic diagram of the leading edge line of the wing-body fusion section

[0100] Figure 12 Effect picture of the waverider wing-body fusion configuration

[0101] Figure 13 Flow chart of the design of the wide-domain waverider wing-body fusion configuration

[0102] Figure 14 Lift-to-drag ratio of the waverider wing-body fusion configuration Detailed implementation mode

[0103] Design principle of the present invention

[0104] One of the innovation points: Combined design of the traditional waverider configuration and the wing provides a feasible idea for the design of wide-speed-domain aircraft. The wide-domain flight includes subsonic, supersonic and hypersonic flights. The waverider has the advantage of high lift-to-drag ratio at hypersonic speed, but its subsonic performance is poor and it is difficult to meet the aerodynamic characteristics requirements at low speed. In the design of traditional low-speed aircraft, the wing is the core component for generating aerodynamic force. Through the reasonable design of the airfoil and the wing planform, efficient circulation lift and vortex lift can be generated, and then the lift required for subsonic flight can be provided. Therefore, in order to improve the subsonic performance of the waverider, combining the traditional waverider configuration and the wing design is a feasible idea to achieve the efficient integration of different design principles at high and low speeds.

[0105] The second innovation point: A parametric method for the wide-domain waverider wing-body fusion layout is proposed. This method can realize the smooth fusion of the waverider forebody, wing and fuselage, and at the same time realize the parametric description of the waverider wing-body fusion layout. The method is as follows: the lower surface of the forebody adopts the cone-guided waverider configuration, the two sides of the afterbody adopt wing design, and the middle fuselage is wing-body fused through the CST surface to obtain a fully parametric reference layout, where the upper surface is not limited to the free-stream surface to consider the volume requirement. Based on this, local engineering modification is carried out at the tail to provide a certain space for the power system, RCS nozzle layout and vertical tail assembly, etc., to obtain an engineered layout.

[0106] Based on the above design principle, the present invention designs a design method for a wide - domain waverider - body fusion configuration, as Figure 13 shown, including the following steps:

[0107] Step 1: Determine the planar geometric parameters of the wide - domain waverider - body fusion configuration: LT represents the total length of the configuration; LF represents the length of the waverider forebody; b F represents the width of the waverider forebody; b / 2 represents the semi - span of the configuration; L1 represents the longitudinal distance from the foremost end of the wing to the bottom of the waverider forebody; L2 represents the span - wise length of the fusion section; Λ represents the sweep angle of the wing leading edge; Ltip represents the chord length of the wing tip; D is the blunt - nose diameter of the waverider forebody; θ is the angle between the symmetric profile line on the upper surface of the waverider forebody and the x - axis at the head; H1 is the height of the bottom cross - section of the waverider forebody; H2 is the maximum height constraint of the fuselage; H3 is the height constraint at the tail of the configuration; after the lower surface of the waverider forebody is given, the forebody width is a known quantity, and the wing span and the trailing - edge sweep angle can be determined according to b / 2 and L2;

[0108] Step 2: Generate the lower surface of the waverider forebody according to the design parameters kw, η and λ of the leading - edge line of the waverider forebody, and the length LF of the waverider forebody;

[0109] Step 3: Generate the upper surface of the waverider forebody: Determine the symmetric profile line l1 of the upper surface according to the design parameter θ of the upper surface of the waverider forebody and the height constraint H1, and represent the span - wise cross - section profile line l2 of the upper surface by a CST curve, and then generate the upper surface of the waverider forebody;

[0110] Step 4: Blunt the leading edge of the waverider forebody;

[0111] Supplementary description

[0112] The leading edge of the waverider forebody is blunted as Figure 3 shown, and the "material addition" method is used for leading edge blunting. Specifically The process includes the following 5 steps:

[0113] ① For any given original sharp leading-edge waverider forebody, assume the leading-edge blunt radius is R;

[0114] ② Move the upper surface of the waverider up by a distance of D = 2*R;

[0115] ③ Select a certain number of cross-sections along the flow direction, find the intersection points of each cross-section with the leading-edge lines of the upper and lower surfaces, and make a semi-circular arc with a radius of R at the current cross-section according to the upper and lower two intersection points;

[0116] ④ Generate a blunt leading-edge through the mesh surface method according to the leading-edge lines of the upper and lower surfaces and the arcs of each cross-section;

[0117] ⑤ Regenerate the bottom surface, and then a solid of the blunt waverider can be generated according to the upper surface, the lower surface, the blunt leading-edge and the bottom surface body.

[0118] Step 5: Generate the wing surface: Determine the wing shape according to the planar geometric parameters of the wide - domain waverider - body fusion configuration, and through the airfoil design parameter bw iObtain the airfoils of each longitudinal section, and then generate the wing surface; the plane geometric parameters include the layout semi-width b / 2 and the waverider forebody width b F , the wing-body fairing width L2; the wing shape includes the wing root length, the wing tip length, and the wing sweep angle;

[0119] Step Six: Determine the upper and lower surfaces of the fuselage: Based on the known data points of the waverider forebody, as shown by the dotted line in 8 and the defined data points of the fuselage cross-section profile, as shown by the double-dotted line in Figure 8 , determine the upper and lower surfaces of the fuselage through the CST surface parameterization method;

[0120] Step Seven: Obtain the wing-body fairing surface with smooth transition between the fuselage and the wing: According to the generated fuselage and wing, determine several (usually 10 - 15 are sufficient) curves with smooth transition between the fuselage and the wing, and then use the fuselage, wing, and smooth curves as constraints to obtain the wing-body fairing surface with smooth transition between the fuselage and the wing through CST surface fitting;

[0121] Step Eight: Generate the leading edge surface of the wing-body fairing: Describe the blunt leading edge curve of the fairing through a cubic polynomial, and generate the leading edge surface of the wing-body fairing through the mesh surface method;

[0122] Step Nine: Parametric result: Obtain the wide-domain waverider wing-body fairing configuration with smooth surface transition.

[0123] Furthermore, the specific steps for generating the lower surface of the waverider forebody in Step Two are as follows:

[0124] ① Generate the leading edge line according to the conical waverider

[0125] The generation process is as shown in Figure 1 : Given the incoming flow Mach number Ma and the shock wave angle β of the conical shock wave s Obtain the three-dimensional shock wave surface, and define an arbitrary form of reference curve on the bottom YZ plane of the shock wave surface. Here, a cubic polynomial in the following form is used to define the reference curve on the bottom surface:

[0126]

[0127] To describe this curve more clearly and intuitively, let the shock wave circle radius be R s , the Z intercept of the reference curve be R0, and the azimuth angle be Let the angle between the tangent of the curve at the intersection position with the shock wave circle and the Y axis be η, the angle between the tangent of the curve at the intersection position with the Z axis and the Y axis be λ, and let the parameter kw = R0 / R s , after simplification, we can get:

[0128]

[0129] Thus, given the design parameters kw, η and λ, the form of the reference curve in Equation (1) can be completely determined; then project this curve along the X-axis direction onto the shock wave surface to obtain an intersection line, which is the leading edge line of the waverider.

[0130] ② Solve the reference flow field

[0131] Due to the axisymmetric characteristics of the reference flow field, the flow characteristics on each streamline starting from the vertex are constant. Its governing equation in the axisymmetric coordinate system is the Taylor-Maccoll equation, as shown in Equation (3). This governing equation is derived from the continuity equation, Euler equation of conical flow, and combined with the irrotational condition.

[0132]

[0133] In the formula, r and θ represent the independent variables in the radial and normal directions respectively, V max represents the maximum theoretical velocity at zero temperature, V r represents the radial velocity component, and γ represents the specific heat ratio. Assuming the oncoming flow is a calorically perfect gas, then γ = 1.4. The normal velocity component in the axisymmetric conical flow field can be calculated using Equation (4):

[0134]

[0135] By numerically solving the Taylor-Maccoll equation, the reference flow field can be obtained.

[0136] ③ Generate the lower surface of the waverider

[0137] Select several points (usually 20 - 30 are sufficient) on the leading edge line of the waverider, and perform streamline tracing downstream for each point in the reference flow field to generate the lower surface as Figure 2 shown; the streamline is determined by the following equation:

[0138]

[0139] In the formula, u, v, and w represent the velocity components along the corresponding coordinate axes;

[0140] ④ Scale the lower surface of the waverider proportionally to the required length L F .

[0141] Furthermore, the specific steps for generating the upper surface of the waverider forebody in Step 3 are as follows:

[0142] ① Define the symmetric profile line l1 using a cubic polynomial

[0143] The upper surface symmetric profile curve is determined according to the design parameter θ of the upper surface of the waverider forebody and the height constraint H1. A cubic polynomial in the following form is used to define the symmetric profile curve l1, as Figure 5 shown below:

[0144] y = ax + bx 2 + cx 3 (6)

[0145] The polynomial coefficients a, b, and c can be determined based on the geometric constraint θ and the height constraint H1. According to the geometric constraints, the upper surface profile curve of the waverider forebody needs to satisfy the following constraints:

[0146]

[0147] Substituting the above constraints into the above equation (6), we can solve for:

[0148]

[0149] ② Represent the upper surface spanwise sectional profile curve l2 through the CST curve

[0150] Specifically as follows:

[0151] The z-direction sectional profile curve l2 at any x position is represented by the CST, as shown in Figure 5 l2 in, and the expression is:

[0152]

[0153] The definition of the class function in formula (8) is:

[0154]

[0155] where N1 and N2 are the exponents of the class function respectively, and ψ is the independent variable, representing the dimensionless z coordinate,

[0156] The definition of the shape function in formula (8) is:

[0157]

[0158] In formula (10), b i , i = 0, 1, 2, …, n are the weight factors of the polynomial; is the term of the nth-order Bernstein polynomial, and ψ is the independent variable, representing the dimensionless z coordinate.

[0159] The values of A and B in formula (8) are:

[0160]

[0161] Where y1 is the y - coordinate of the leading - edge point 1, and y2 is the y - coordinate of the point 2 on the symmetric airfoil curve.

[0162] ③ Generate the upper surface of the waverider forebody considering volume constraints

[0163] Select several points on the leading - edge line of the waverider forebody, and determine several span - wise sectional curves through the above - mentioned method, then the upper surface of the waverider forebody considering volume constraints can be generated, as Figure 6 shown.

[0164] Furthermore, the specific steps of generating the wing surface in step five are as follows:

[0165] A. Obtain the planar geometric parameters of the wing

[0166] ① Calculate the root length of the wing: According to the total length L of the waverider wing - body fusion configuration T , the length L of the waverider forebody F and the length L1 of the fusion section, the root length of the wing can be calculated;

[0167] ② Calculate the span of the wing: According to the half - width b / 2 of the configuration, the length L2 of the fusion section and the width b of the waverider forebody F , the span of the wing can be calculated;

[0168] ③ Calculate the tip length of the wing and the leading - edge sweep angle of the wing;

[0169] B. The airfoil parametric equation is shown in Equation (12):

[0170]

[0171] In the formula where bw i , i = 0, 1, …, n are airfoil design parameters, and ζ T is the trailing - edge thickness.

[0172] By determining the design parameter bw i , the airfoil curve can be determined; here, for simplicity, the same airfoil is used for each cross - section of the wing, and different airfoils can also be used for each cross - section in the actual design process;

[0173] C. Generate the upper and lower surfaces of the wing: After the airfoil is determined, scale the airfoil according to the chord length of each cross - section to obtain each airfoil cross - section of the wing as Figure 7 shown, and then generate the upper and lower surfaces of the wing.

[0174] Furthermore, the specific steps of determining the upper and lower surfaces of the fuselage in step six are as follows:

[0175] A. Select some points on the waverider forebody surface as known data points, as Figure 8As shown by the dashed line, the fuselage cross-section is defined according to the fuselage geometric constraints, such as Figure 8 As shown by the double-dashed line, and use it as the known data points;

[0176] B. To achieve a smooth transition between the waverider forebody and the fuselage, the CST inverse fitting technique is adopted here to realize the integrated characterization of the waverider forebody and the fuselage, as follows:

[0177] For the CST parametric modeling of the surface with any planar shape, the surface can be normalized in two directions in the z-x plane through coordinate transformation, and the Bernstein polynomial is used to describe the surface. At the same time, class functions are added in the characteristic direction of the surface, and the CST method representation form of the surface is obtained as:

[0178]

[0179] where ψ is the dimensionless z coordinate, η is the dimensionless x coordinate, and ζ is the dimensionless surface y coordinate, is the class function, Sx j (η) and Sz i (ψ) are the Bernstein polynomial functions in two directions, and B i,j is the surface control parameter. The expression of the coordinate transformation is:

[0180]

[0181] where x U , x D is the boundary of the surface in the x direction in the z-x plane, and z U , z D is the boundary of the surface in the z direction in the z-x plane; the relationship between ζ in Equation (13) and the change of the surface y coordinate is:

[0182] ζ = y / b (15)

[0183] C. Using the above CST method, fit the known points of the above waverider forebody and fuselage. In the fitting process, the solution of the CST surface coefficient B i,j can be obtained by Newton's method or by solving an overdetermined system of equations;

[0184] D. After obtaining the coefficient B i,j , generate the fuselage surface. As Figure 9 shown.

[0185] Furthermore, the specific steps for obtaining the wing-body fairing section surface with a smooth transition between the fuselage and the wing in step seven are as follows:

[0186] ① According to the generated fuselage and wing, determine the spanwise profile of the wing-body fairing section, such as Figure 10As shown by the double-dashed line, a cubic polynomial as in Equation (16) is used to define the spanwise sectional profile; the coefficients a, b, c, and d can be solved by substituting the coordinates and slopes at the curve endpoints into Equation (16), and then the points on the curve can be solved for.

[0187] y = a + bx + cx 2 + dx 3 (16)

[0188] Similarly, a cubic polynomial is used to define the leading edge line of the blending section, as Figure 10 shown, and the coefficients a, b, c, and d can be determined from the coordinates at the curve endpoints and the tangent slope at the endpoints, and then the curve can be solved for.

[0189] ② Select some known points on the fuselage surface and the wing surface, as Figure 10 shown by the dashed line, and the spanwise sectional profile of the blending section. Through the above CST surface fitting method, a smoothly transitioning wing-fuselage blending section surface between the fuselage and the wing is obtained;

[0190] Furthermore, the specific steps for generating the leading edge surface of the wing-fuselage blending section in Step Eight are as follows:

[0191] Select several points on the leading edge line of the blending section, and define the blunt leading edge curve of the blending section by a cubic polynomial curve of Equation (16), as Figure 11 shown. Since the endpoint coordinates of this curve are known, the slope at this point can be obtained from the upper and lower surface profiles of the blending section, as Figure 11 the slope at the dashed line endpoints shown, and the coefficients a, b, c, and d in the equation can be calculated, and the blunt leading edge curve can be calculated; according to the leading edge line of the blending section and the arcs of each section, a blunt leading edge surface of the blending section is generated by the mesh surface method.

[0192] Example 1

[0193] Wave-rider forebody design condition: Mach number 12

[0194] Shock wave angle: 7.0°

[0195] Wave-rider forebody design parameters:

[0196] kw = 0.750, φ = 32.763, η = 34.576, λ = 11.597

[0197] <![CDATA[L T > <![CDATA[L F > b / 2 <![CDATA[L1]]> <![CDATA[L2]]> Λ <![CDATA[L tip > D θ (deg) <![CDATA[H1]]> <![CDATA[H2]]> <![CDATA[H3]]> 37.0 18.5 11.5 3.0 1.25 60 7.882 0.1 11 3.0 3.4 2.6

[0198] Flight condition: Mach number 12.0, flight altitude 40 km

[0199] Aircraft length: 37.0 m,

[0200] Aircraft width: 23.0 m

[0201] Based on the above parameters, the generated waverider blended wing body configuration has an outer shape as Figure 12 shown in Figure 14 The lift-drag ratio of this outer shape at an altitude of 40 km and Mach 12 is given. The lift-drag ratio of this configuration is the largest at an angle of attack of 6°, which is 4.54.

[0202] The above content is only an example and explanation of the concept of the present invention. Those skilled in the art of this technology can make various modifications or supplements to the described specific embodiments or use similar methods for substitution, as long as they do not deviate from the concept of the invention or exceed the scope defined by this claims, they should all fall within the protection scope of the present invention.

Claims

1. A design method for a wide-range waverider wing-body fusion configuration, characterized by: The following steps are involved: Step 1: Determine the plane geometric parameters of the wide-band waverider wing-body fusion configuration: LT represents the total length of the configuration; LF represents the length of the waverider forebody; b F represents the width of the waverider forebody; b / 2 represents the half span of the configuration; L1 represents the longitudinal distance between the front end of the wing and the bottom of the waverider forebody; L2 represents the length of the fusion section along the span direction; Λ represents the sweep angle of the leading edge of the wing; Ltip represents the chord length of the wing tip; D is the blunt diameter of the waverider forebody; θ is the angle between the symmetry surface line of the upper surface of the waverider forebody at the head and the x-axis; H1 is the height of the bottom section of the waverider forebody; H2 is the maximum height constraint of the fuselage; H3 is the height constraint of the tail of the configuration; after the lower surface of the waverider forebody is given, the width of the forebody is a known quantity, and the wing span and the sweep angle of the trailing edge can be determined according to b / 2 and L2; Step 2: Design parameters kw according to the leading edge line of the waverider front body. η and λ, as well as the waverider front length LF generate the lower surface of the waverider front; kw = R0 / Rs, Rs is the shock circle radius, R0 is the Z intercept of the reference curve, is the azimuth angle, η is the angle between the tangent line at the intersection of the curve and the shock circle and the Y axis; λ is the angle between the tangent line at the intersection of the curve and the Z axis and the Y axis; Step 3, generating the upper surface of the waverider precursor: determining the upper surface symmetry surface line l1 according to the upper surface design parameter θ of the waverider precursor and the height constraint H1, and representing the upper surface spanwise cross-sectional line l2 by the CST curve, thereby generating the upper surface of the waverider precursor; Step 4, passivating the leading edge of the waverider precursor; Step 5: Generate wing surface: Determine the wing shape according to the plane geometric parameters of the wide-band waverider wing-body fusion configuration, and use the airfoil design parameters bw i The airfoil of each longitudinal section is obtained, and then the wing surface is generated; the plane geometric parameters include the half span b / 2 of the configuration, the width of the waverider front body b F , the wing-body fusion section width L2; the wing shape includes the wing root length, wing tip length and wing sweep angle; Step 6: Determine the upper and lower surfaces of the fuselage: Based on the known data points of the waverider forebody and the defined fuselage cross-section line data points, determine the upper and lower surfaces of the fuselage by using the CST surface parameterization method; Step 7: Obtain a wing-body blending section surface with a smooth transition between the fuselage and the wing: According to the generated fuselage and wing, determine 10 to 15 curves with a smooth transition between the fuselage and the wing, and then use the fuselage, wing and smooth curves as constraints to obtain a wing-body blending section surface with a smooth transition between the fuselage and the wing through CST surface fitting; Step 8, generating the leading edge surface of the wing-body fusion section: describing the blunt leading edge curve of the fusion section by a cubic polynomial, and generating the leading edge surface of the wing-body fusion section by a mesh surface method; Step 9. Parameterization results: A wide-area waverider wing-body fusion configuration with smooth surface transition is obtained.

2. According to claim 1, a wide-range waverider wing-body fusion configuration design method is characterized by: The specific steps of generating the lower surface of the waverider precursor in step 2 are as follows: ① Generate the leading edge line based on the cone-guided waverider The generation process is as follows: given the incoming flow Mach number Ma and the shock wave angle β of the conical shock wave s A three-dimensional shock wave surface is obtained, and an arbitrary reference curve is defined on the YZ plane at the bottom of the shock wave surface. Here, the following cubic polynomial is used to define the reference curve on the bottom surface: In order to describe the curve more clearly and intuitively, let the radius of the shock wave circle be R s , the Z intercept of the reference curve is R0, and the azimuth is Let the angle between the tangent line at the intersection of the curve and the shock circle and the Y axis be η, the angle between the tangent line at the intersection of the curve and the Z axis and the Y axis be λ, and let the parameter kw = R0 / R s , after simplification, we can get: Thus, given the design parameters kw, η and λ, the reference curve form of equation (1) can be completely determined; then the curve is projected along the X-axis direction toward the shock wave surface to obtain an intersection line, which is the leading edge line of the waverider; ② Solving the benchmark flow field Due to the axisymmetric characteristics of the reference flow field, the flow characteristics on each streamline starting from the vertex are constant. Its governing equation in the axisymmetric coordinate system is the Taylor-Maccoll equation, as shown in equation (3). This governing equation is derived from the continuity equation of conical flow, the Euler equation, and the irrotational condition. Where r and θ represent the independent variables in radial and normal directions respectively, V max Indicates the maximum theoretical speed when the temperature is zero, V r represents the radial velocity component, and γ represents the specific heat ratio; assuming that the incoming flow is a calorimetric perfect gas, γ = 1.4; the normal velocity component in the axisymmetric conical flow field can be calculated using formula (4): By numerically solving the Taylor-Maccoll equation, the benchmark flow field can be obtained; ③ Generate the lower surface of the waverider Select 20 to 30 points on the leading edge of the waverider and trace the streamlines downstream of each point in the reference flow field to generate the lower surface. The streamlines are determined by the following equation: Where u, v and w represent the velocity components along the corresponding coordinate axes; ④ Scale the lower surface of the waverider proportionally to the required length L F .

3. According to claim 1, a wide-range waverider wing-body fusion configuration design method is characterized by: The specific steps of generating the upper surface of the waverider precursor in step 3 are as follows: ①Use cubic polynomial to define the symmetry surface line l1 The upper surface symmetry line is determined based on the upper surface design parameter θ and the height constraint H1 of the waverider precursor, and the symmetry line l1 is defined by a cubic polynomial of the following form: y=ax+bx 2 +cx 3 (6) The polynomial coefficients a, b, c are determined according to the geometric constraint θ and the height constraint H1. According to the geometric constraint, the upper surface profile of the waverider precursor needs to satisfy the following constraints: Substituting the above constraints into equation (6), we can obtain: ② The CST curve is used to represent the cross-sectional profile line l2 on the upper surface The details are as follows: The z-direction cross-sectional profile l2 at any x position is represented by CST, and the expression is: The class function in formula (8) is defined as: Where N1 and N2 are the exponents of the class function, ψ is the independent variable, representing the dimensionless z coordinate, The shape function in formula (8) is defined as: In formula (10), b i ,i=0,1,2,…,n is the weight factor of the polynomial; is the term of the nth-order Bernstein polynomial, ψ is the independent variable, representing the dimensionless z coordinate; The values ​​of A and B in formula (8) are: Where y1 is the y coordinate of the leading edge point 1, and y2 is the y coordinate of the point 2 on the symmetry surface line; ③ Generate the upper surface of the waverider precursor considering volume constraints By selecting several points on the leading edge line of the waverider forerunner and determining several spanwise cross-sectional profile lines using the above method, the upper surface of the waverider forerunner considering the volume constraint can be generated.

4. According to claim 1, a wide-range waverider wing-body fusion configuration design method is characterized by: The specific steps of generating the wing surface in step 5 are as follows: A. Obtain the plane geometric parameters of the wing ① Calculate the wing root length: According to the total length L of the waverider wing-body fusion configuration T , waverider front length L F The wing root length of the wing is calculated by the fusion section length L1; ② Calculate the span of the wing: Based on the half span b / 2 of the configuration, the length of the fusion section L2, and the width of the waverider front body b F , calculate the span of the wing; ③ Calculate the wing tip length and the wing leading edge sweep angle; B. The airfoil parameterization equation is shown in formula (12): In the formula where bw i , i=0,1,…,n are airfoil design parameters, ζ T is the trailing edge thickness; By determining the design parameter bw i , the airfoil curve can be determined; for simplicity, all sections of the wing adopt the same airfoil, but in the actual design process, different airfoils can be used for each section; C. Generate the upper and lower surfaces of the wing: After the airfoil is determined, scale the airfoil according to the chord length of each section to obtain the airfoil sections of the wing, and then generate the upper and lower surfaces of the wing.

5. According to claim 1, a wide-range waverider wing-body fusion configuration design method is characterized by: The specific steps of determining the upper and lower surfaces of the fuselage in step 6 are as follows: A. Select some points from the waverider front surface as known data points, define the fuselage cross-section according to the fuselage geometric constraints, and use them as known data points; B. In order to achieve a smooth transition between the waverider forebody and the fuselage, the CST reverse fitting technology is used here to achieve the integrated characterization of the waverider forebody and the fuselage, as follows: For surfaces of arbitrary plane shapes, CST parametric modeling is performed. The surfaces are normalized in two directions of the zx plane by coordinate changes. The surfaces are described by Bernstein polynomials. At the same time, class functions are added in the characteristic directions of the surfaces. The CST method representation of the surfaces is obtained as follows: Where ψ is the dimensionless z-coordinate, η is the dimensionless x-coordinate, and ζ is the dimensionless y-coordinate of the surface. is a class function, Sx j (η) and Sz i (ψ) is the Bernstein polynomial function in two directions, B i,j is the surface control parameter; the coordinate transformation expression is: where x U ,x D is the boundary of the surface in the x direction on the zx plane, z U ,z D is the boundary of the surface in the z direction on the zx plane; the relationship between ζ in formula (13) and the y coordinate of the surface is: ζ=y / b (15) C. Use the above CST method to fit the known points of the waverider forebody and fuselage. During the fitting process, the CST surface coefficient B i,j The solution is obtained by Newton's method or by solving an overdetermined system of equations; D. After getting coefficient B i,j After that, the fuselage surface is generated.

6. According to claim 1, a wide-range waverider wing-body fusion configuration design method is characterized by: The specific steps of obtaining a wing-body fusion section curved surface with a smooth transition between the fuselage and the wing in step 7 are as follows: ① According to the generated fuselage and wing, determine the spanwise profile of the wing-body fusion section. Here, a cubic polynomial such as formula (16) is used to define the spanwise section profile. Substitute the coordinates and slope of the curve endpoints into formula (16) to obtain the coefficients a, b, c and d, and then solve for each point on the curve. y=a+bx+cx 2 +dx 3 (16) Similarly, a cubic polynomial is used to define the leading edge of the fusion segment, and the coefficients a, b, c and d are determined by the coordinates at the end points of the curve and the slope of the tangent line at the end points, and then the curve is solved; ② Select some known points on the fuselage surface and the wing surface, as well as the span-wise cross-sectional profile of the fusion section, and obtain the wing-body fusion section surface with a smooth transition between the fuselage and the wing through the above-mentioned CST surface fitting method.

7. The method for designing a wide-range waverider wing-body fusion configuration according to claim 1, characterized in that: The specific steps of generating the leading edge surface of the wing-body fusion section in step eight are as follows: Select several points on the leading edge line of the fusion segment, and define the blunt leading edge curve of the fusion segment through the cubic polynomial curve of formula (16). Since the coordinates of the endpoints of the curve are known, the slope at the point is obtained from the upper and lower surface profiles of the fusion segment, and the coefficients a, b, c and d in the formula are calculated to obtain the blunt leading edge curve; according to the leading edge line of the fusion segment and the arcs of each section, the blunt leading edge surface of the fusion segment is generated by the mesh surface method.

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