A multi-constrained refined aerodynamic optimization design method for tailless flying wing layout

Abstract

The present application belongs to the field of aerospace technology, and particularly relates to a multi-constraint refined aerodynamic optimization design method for a tailless flying wing layout. The multi-constraint refined aerodynamic optimization design method for a tailless flying wing layout of the present application adopts a unified objective function to achieve the optimization of design goals under multiple design constraints, adopts a flow field solution method based on the N‑S equation to obtain accurate aerodynamic performance, and adopts a gradient solution method based on adjoint theory to quickly and efficiently obtain the gradient information of multiple design variables, effectively realizing the unification of multiple design constraints, refined design, and efficient optimization design of the tailless layout, meeting the detailed design requirements of the aircraft scheme in the project, and being able to quickly obtain the optimized design results.

Description

Technical Field

[0001] The present application belongs to the field of aerospace technology, and in particular relates to a multi-constraint refined aerodynamic optimization design method for a tailless flying wing layout. Background Art

[0002] The tailless flying wing layout has been widely used in military aircraft due to its good aerodynamic efficiency and stealth characteristics. At the same time, the flying wing layout has typical problems such as low control efficiency and trim loss. Generally speaking, the aircraft is required to have a high lift-to-drag ratio in cruising state and a small nose-down moment so as not to cause a large trim loss. These two requirements are often contradictory, especially in the flying wing layout, that is, improving the cruise lift-to-drag ratio will bring a large nose-down moment, so that the final lift-to-drag ratio of the whole aircraft is not improved. The aerodynamic design parameters of the tailless flying wing layout are seriously coupled. It is a comprehensive design problem involving professional constraints such as aerodynamics, stability control, overall, stealth, and structure. It is also a typical multi-objective and multi-constraint design problem in aerodynamic optimization design.

[0003] At present, the design of flying wing layout in China mainly adopts the "trial and error method" based on artificial experience. This method can meet the requirements in conceptual design and preliminary design. However, with the deepening of the development stage, the design constraints of various disciplines are increasing, and the space for aerodynamic shape optimization is further reduced. It is difficult to find a reasonable optimization result based on artificial experience. At the same time, the aerodynamic shape is required to be quickly frozen, and the aerodynamic shape design cycle is further compressed. Therefore, the refined aerodynamic design of the tailless flying wing layout has become a difficult problem for designers. The optimization methods based on CFD are divided into random methods and gradient methods. The random method tracks the information related to the value of the objective function, has good globality, and does not require the continuous distribution of design variables and the existence of derivatives. The advantages of assumptions such as genetic algorithms and surrogate model methods, but its disadvantage is that in the refined aerodynamic shape design of multiple design variables, the optimization efficiency is low and the accuracy is reduced; while the gradient method is the most widely used, and the optimization method based on the adjoint theory has a gradient calculation amount that is independent of the numerical model of the design variables, and has good applicability in the refined design stage of the aircraft.

[0004] Therefore, it is desired to have a technical solution to overcome or at least alleviate at least one of the above-mentioned defects of the prior art. Summary of the invention

[0005] The purpose of this application is to provide a multi-constraint refined aerodynamic optimization design method for a tailless flying wing layout to solve at least one problem existing in the prior art.

[0006] The technical solution of this application is:

[0007] A multi-constrained refined aerodynamic optimization design method for a tailless flying wing layout, comprising:

[0008] Step 1: Determine the baseline shape, design state, design goal and design constraints of the design to be optimized;

[0009] Step 2: Construct the objective function and determine the weights of the design objectives and design constraints respectively;

[0010] Step 3: derive the boundary conditions of the adjoint equation and the gradient solution formula according to the objective function;

[0011] Step 4: using the baseline shape as input, parameterizing the shape by bending and twisting using the Hicks-Henne shape function to obtain design variables;

[0012] Step 5: Generate a baseline shape flow field calculation grid using a wireless interpolation method;

[0013] Step 6: Calculate the aerodynamic performance parameters of the baseline shape using a CFD solution method based on the NS equation according to the baseline shape flow field calculation grid;

[0014] Step 7: Solve the adjoint equation according to the aerodynamic performance parameters to obtain the numerical solution of the adjoint variable;

[0015] Step 8: Calculate the gradient of the objective function with respect to the design variable according to the gradient solution formula, the aerodynamic performance parameter and the numerical solution of the adjoint variable;

[0016] Step 9: Use the steepest descent method to perform gradient search to obtain the optimal solution, and generate an optimized shape based on the optimal solution;

[0017] Step 10. Use the CFD solution method based on the NS equation to calculate the aerodynamic performance parameters of the optimized shape, compare the aerodynamic performance parameters of the optimized shape with the aerodynamic performance parameters of the previous round of shape, and check whether the optimized design results meet the requirements. If so, stop the optimization, otherwise, return to step 5 until the number of iterations exceeds the preset maximum value.

[0018] In at least one embodiment of the present application, in step 1, determining the baseline shape, design state, design goal, and design constraint of the design to be optimized includes:

[0019] The baseline shape is a high aspect ratio flying wing layout;

[0020] The design state is that the flight Mach number Ma=0.75 and the angle of attack α=4°;

[0021] The design goal is resistance optimization;

[0022] The design constraints are that lift, moment and area are not reduced.

[0023] In at least one embodiment of the present application, in step 2, constructing an objective function and determining the weights of the design objectives and design constraints respectively include:

[0024] The objective function is:

[0025]

[0026] Among them, C D Drag coefficient, C L is the lift coefficient, C m is the pitch moment coefficient, A(IS) is the area of ​​the IS-th control section, C L0 is the initial value of the lift coefficient of the baseline shape under design conditions, C m0 is the initial value of the pitching moment coefficient of the baseline shape in the design state, A0(IS) is the initial value of the area of ​​the IS-th control section of the baseline shape in the design state, ISECTION is the number of control sections, and the weights of each section are: Ω1 = 50, Ω2 = 2, Ω3 = 0.001, Ω4 = 0.5;

[0027] Weight of design goal: drag coefficient C D The absolute value decreases;

[0028] Weights of design constraints:

[0029] Lift coefficient C L The change does not exceed 5%;

[0030] Pitch moment coefficient -0.004≤C m ≤0.008;

[0031] The area A(IS) of the control section does not vary by more than 6%.

[0032] In at least one embodiment of the present application, in step three, deriving the adjoint equation boundary conditions and the gradient solution formula according to the objective function includes:

[0033] According to the objective function, the corresponding adjoint equation boundary conditions are derived as follows:

[0034]

[0035]

[0036]

[0037]

[0038] ψ=(ψ1,φ1,φ2,φ3,θ) T

[0039] Among them, M ∞ is the free stream Mach number, P ∞ is the pressure, S ref is the reference area, α is the angle of attack, (x ref ,y ref ) is the coordinate of the moment reference point, ψ=(ψ1,φ1,φ2,φ3,θ) T is the accompanying variable;

[0040] The corresponding gradient solution formula is:

[0041]

[0042] (i,j=1,2,3)

[0043] F i =S ij f j

[0044] F vi =S ij f vj

[0045]

[0046] Among them, n i is the direction vector of the computational domain, f i is the inviscid vector term of the three-dimensional NS equation, f vi is the three-viscosity vector term of the three-dimensional NS equation, J is the modulus of the transformation matrix from the physical domain (x1, x2, x3) to the computational domain (ξ1, ξ2, ξ3), S ij To calculate the spatial matrix, dB ξ 、dD ξ They are the surface and space integration units in the calculation space respectively.

[0047] In at least one embodiment of the present application, in step 4, the design variables are 108, including 26 design variables for each of the four control sections and four section torsion angles.

[0048] In at least one embodiment of the present application, in step six, the aerodynamic performance parameters of the baseline shape include: drag coefficient, lift coefficient, pitch moment coefficient and area of ​​the control section.

[0049] The invention has at least the following beneficial technical effects:

[0050] The multi-constraint refined aerodynamic optimization design method for the tailless flying wing layout of the present application adopts a unified objective function to achieve the optimization of design goals under multiple design constraints, adopts a flow field solution method based on the NS equations to obtain accurate aerodynamic performance, and adopts a gradient solution method based on the adjoint theory to quickly and efficiently obtain the gradient information of multiple design variables, effectively realizing the unification of multiple design constraints, refined design, and efficient optimization design of the tailless layout, and meeting the detailed design requirements of the aircraft scheme in the engineering project. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is a schematic diagram of a flow field calculation grid according to an embodiment of the present application;

[0052] Figure 2 It is a surface pressure cloud diagram of the optimized front and rear flying wing layout according to one embodiment of the present application;

[0053] Figure 3 It is a schematic diagram comparing the pressure coefficient and appearance of the control section of the optimized front and rear flying wing layout according to one embodiment of the present application. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical scheme and advantages of the implementation of this application clearer, the technical scheme in the embodiment of this application will be described in more detail below in conjunction with the drawings in the embodiment of this application. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described embodiments are part of the embodiments of this application, not all of them. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain this application, and should not be construed as limitations on this application. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. The embodiments of this application are described in detail below in conjunction with the drawings.

[0055] In the description of the present application, it should be understood that the terms "center", "longitudinal", "lateral", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the scope of protection of the present application.

[0056] The following is combined with Figures 1 to 3 This application is described in further detail.

[0057] The present application provides a multi-constraint refined aerodynamic optimization design method for a tailless flying wing layout, comprising the following steps:

[0058] Step 1: Determine the baseline shape, design state, design goal and design constraints of the design to be optimized;

[0059] Step 2: Construct the objective function and determine the weights of the design objectives and design constraints respectively;

[0060] Step 3: Derive the boundary conditions of the adjoint equation and the gradient solution formula according to the objective function;

[0061] Step 4: Taking the baseline shape as input, the Hicks-Henne shape function is used to parameterize the shape by bending and twisting to obtain the design variables;

[0062] Step 5: Generate a baseline shape flow field calculation grid using a wireless interpolation method;

[0063] Step 6: Calculate the aerodynamic performance parameters of the baseline shape using a CFD solution method based on the NS equation according to the baseline shape flow field calculation grid;

[0064] Step 7: Solve the adjoint equation according to the aerodynamic performance parameters to obtain the numerical solution of the adjoint variable;

[0065] Step 8: Calculate the gradient of the objective function with respect to the design variables according to the gradient solution formula, the aerodynamic performance parameters and the numerical solution of the adjoint variables;

[0066] Step 9: Use the steepest descent method to perform gradient search to obtain the optimal solution, and generate an optimized shape based on the optimal solution;

[0067] Step 10. Use the CFD solution method based on the NS equation to calculate the aerodynamic performance parameters of the optimized shape, compare the aerodynamic performance parameters of the optimized shape with the aerodynamic performance parameters of the previous round of shape, and check whether the optimized design results meet the requirements. If so, stop the optimization, otherwise, return to step 5 until the number of iterations exceeds the preset maximum value.

[0068] The multi-constrained refined aerodynamic optimization design method for the tailless flying wing layout of the present application first gives the design object and goal. In one embodiment of the present application, in step 1, determining the baseline shape, design state, design goal and design constraint of the design to be optimized includes:

[0069] The baseline shape is a high aspect ratio flying wing layout;

[0070] The design state is flight Mach number Ma = 0.75, angle of attack α = 4° (speed, angle of attack);

[0071] The design goal is resistance optimization;

[0072] The design constraints are lift, moment and area not reduced.

[0073] The multi-constrained refined aerodynamic optimization design method for the tailless flying wing layout of the present application, secondly, needs to construct a unified objective function and determine the weights of the design objectives and design constraints respectively. In this embodiment, in step 2, the following objective function, design objectives and design constraint weights are defined:

[0074]

[0075] Among them, C D Drag coefficient, C L is the lift coefficient, C m is the pitch moment coefficient, A(IS) is the area of ​​the IS-th control section, C L0 is the initial value of the lift coefficient of the baseline shape under design conditions, C m0 is the initial value of the pitching moment coefficient of the baseline shape in the design state, A0(IS) is the initial value of the area of ​​the IS-th control section of the baseline shape in the design state, ISECTION is the number of control sections, and the weights of each section are: Ω1 = 50, Ω2 = 2, Ω3 = 0.001, Ω4 = 0.5;

[0076] Weight of design goal: drag coefficient C D The absolute value decreases;

[0077] Weights of design constraints:

[0078] Lift coefficient C L The change does not exceed 5%;

[0079] Pitch moment coefficient -0.004≤C m ≤0.008;

[0080] The area A(IS) of the control section does not vary by more than 6%.

[0081] In addition, in this embodiment, the number of control sections ISECTION=4.

[0082] Furthermore, in step 3, the boundary conditions of the adjoint equation and the gradient solution formula are derived according to the objective function, including:

[0083] According to the objective function, the corresponding adjoint equation boundary conditions are derived as follows:

[0084]

[0085]

[0086]

[0087]

[0088] ψ=(ψ1,φ1,φ2,φ3,θ) T

[0089] Among them, M ∞ is the free stream Mach number, P ∞ is the pressure, S ref is the reference area, α is the angle of attack, (x ref ,y ref ) is the coordinate of the moment reference point, ψ=(ψ1,φ1,φ2,φ3,θ) T is the accompanying variable;

[0090] The corresponding gradient solution formula is:

[0091]

[0092] (i,j=1,2,3)

[0093] F i =S ij f j

[0094] F vi =S ij f vj

[0095]

[0096] Among them, n i is the direction vector of the computational domain, f i is the inviscid vector term of the three-dimensional NS equation, f vi is the three-viscosity vector term of the three-dimensional NS equation, J is the modulus of the transformation matrix from the physical domain (x1, x2, x3) to the computational domain (ξ1, ξ2, ξ3), S ij To calculate the spatial matrix, dB ξ 、dD ξ They are the surface and space integration units in the calculation space respectively.

[0097] Then, in step 4, the baseline shape is used as input, and the Hicks-Henne shape function is used to parameterize the shape by bending and twisting to obtain design variables. In this embodiment, the control section is the profile of 4 wings, each section has 26 design variables, plus 4 section twist angles, a total of 108 design variables.

[0098] In the preferred embodiment of the present application, in step 5, a wireless interpolation method is used to generate a baseline shape flow field calculation grid, such as Figure 1 According to the baseline shape flow field calculation grid, the aerodynamic performance parameters of the baseline shape are calculated using the CFD solution method based on the NS equation, including the drag coefficient, lift coefficient, pitch moment coefficient and the area of ​​the control section.

[0099] The multi-constraint refined aerodynamic optimization design method for the tailless flying wing layout of the present application requires optimization design of the baseline shape, mainly including: solving the adjoint equation according to the aerodynamic performance parameters to obtain the numerical solution of the adjoint variable; calculating the gradient of the objective function to the design variable according to the gradient solution formula, the aerodynamic performance parameters and the numerical solution of the adjoint variable; using the steepest descent method to perform gradient search to obtain the optimal solution, and generating an optimized shape according to the optimal solution; finally, using the CFD solution method based on the NS equation to calculate the aerodynamic performance parameters of the optimized shape, comparing the aerodynamic performance parameters of the optimized shape with the aerodynamic performance parameters of the previous round of shape, and checking whether the optimization design result meets the requirements. If so, stop the optimization, otherwise, return to step five until the number of iteration steps exceeds the preset maximum value.

[0100] In a preferred embodiment of the present application, Table 1 shows the specific numerical changes of aerodynamic coefficients and control section areas before and after optimization. The optimization iterations were 8 steps, which took about 18 hours. The drag coefficient was reduced from the initial 0.01665 to 0.01506, a decrease of about 9.55%; the lift coefficient was changed from 0.361 to 0.355, a decrease of 1.66%, satisfying the constraint conditions; the pitch moment coefficient was changed from the initial 0.0062 to 0.0036, satisfying the constraint conditions; and the changes in the control section areas also met the constraint indicators.

[0101] Table 1

[0102]

[0103] In a preferred embodiment of the present application, Figure 2 The comparison of surface pressure distribution between the initial shape and the designed shape is given. Figure 3 The corresponding wing profile pressure distribution and shape comparison at different positions in the span are given. It can be seen that the negative pressure peak area of ​​the design surface pressure is reduced, the adverse pressure gradient is reduced, and the shock wave intensity at different positions in the span is weakened to varying degrees, especially in the 60%-70% range in the span. The main change trend of the corresponding profile shape is that the maximum thickness is slightly reduced, and the chord position is slightly moved back; the torsion angle is mainly that the profile close to the symmetry plane has a smaller positive torsion angle, and the other profiles do not change much.

[0104] The multi-constraint refined aerodynamic optimization design method for the tailless flying wing layout of this application adopts a unified objective function to achieve the optimization of design goals under multiple design constraints, adopts a flow field solution method based on the NS equation to obtain accurate aerodynamic performance, and adopts a gradient solution method based on adjoint theory to quickly and efficiently obtain the gradient information of multiple design variables, effectively realizing the unification of multiple design constraints, refined design, and efficient optimization design of the tailless layout, meeting the detailed design requirements of the aircraft scheme in the project, and being able to quickly obtain the optimized design results. This application takes transonic drag reduction as the design goal, comprehensively considers design constraints such as lift, balancing loss, and structural volume, and carries out a multi-constraint aerodynamic optimization design of a large aspect ratio flying wing layout, obtains a drag-optimized aerodynamic shape that meets the design constraints, and verifies the effectiveness of the optimization method.

[0105] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A multi-constrained refined aerodynamic optimization design method for a tailless flying wing layout. It is characterized in that include: Step 1: Determine the baseline shape, design state, design goal and design constraints of the design to be optimized; Step 2: Construct the objective function and determine the weights of the design objectives and design constraints respectively; Step 3: derive the boundary conditions of the adjoint equation and the gradient solution formula according to the objective function; Step 4: using the baseline shape as input, parameterizing the shape by bending and twisting using the Hicks-Henne shape function to obtain design variables; Step 5: Generate a baseline shape flow field calculation grid using a wireless interpolation method; Step 6: Calculate the aerodynamic performance parameters of the baseline shape using a CFD solution method based on the NS equation according to the baseline shape flow field calculation grid; Step 7: Solve the adjoint equation according to the aerodynamic performance parameters to obtain the numerical solution of the adjoint variable; Step 8: Calculate the gradient of the objective function with respect to the design variable according to the gradient solution formula, the aerodynamic performance parameter and the numerical solution of the adjoint variable; Step 9: Use the steepest descent method to perform gradient search to obtain the optimal solution, and generate an optimized shape based on the optimal solution; Step 10: Calculate the aerodynamic performance parameters of the optimized shape using the CFD solution method based on the NS equation, compare the aerodynamic performance parameters of the optimized shape with the aerodynamic performance parameters of the previous round of shape, and check whether the optimized design results meet the requirements. If so, stop the optimization, otherwise, return to step 5 until the number of iteration steps exceeds the preset maximum value; In step 1, determining the baseline shape, design state, design goal and design constraints of the design to be optimized includes: The baseline shape is a high aspect ratio flying wing layout; The design state is that the flight Mach number Ma=0.75 and the angle of attack α=4°; The design goal is resistance optimization; The design constraints are that lift, moment and area are not reduced; In step 2, the objective function is constructed, and the weights of the design objectives and design constraints are determined respectively, including: The objective function is: Among them, C D Drag coefficient, C L is the lift coefficient, C m is the pitch moment coefficient, A(IS) is the area of ​​the IS-th control section, C L0 is the initial value of the lift coefficient of the baseline shape under design conditions, C m0 is the initial value of the pitching moment coefficient of the baseline shape in the design state, A 0 (IS) is the initial value of the area of ​​the IS-th control section of the baseline shape under the design state, ISECTION is the number of control sections, and the weights of each part are: Ω 1 =50,Ω 2 =2,Ω 3 =0.001,Ω 4 =0.5; Weight of design goal: drag coefficient C D The absolute value decreases; Weights of design constraints: Lift coefficient C L The change does not exceed 5%; Pitch moment coefficient -0.004≤C m ≤0.008; The area A(IS) of the control section shall not change by more than 6%; In step three, the derivation of the adjoint equation boundary conditions and the gradient solution formula according to the objective function includes: According to the objective function, the corresponding adjoint equation boundary conditions are derived as follows: ψ=(ψ 1 ,f 1 ,f 2 ,f 3 ,i) T Among them, M ∞ is the free stream Mach number, P ∞ is the pressure, S ref is the reference area, α is the angle of attack, (x ref ,y ref ) is the coordinate of the moment reference point, ψ=(ψ 1 ,φ 1 ,φ 2 ,φ 3 ,θ) T is the accompanying variable; The corresponding gradient solution formula is: (i,j=1,2,3) F i =S ij f j F vi =S ij f vj Among them, n i is the direction vector of the computational domain, f i is the inviscid vector term of the three-dimensional NS equation, f vi is the three-viscosity vector term of the three-dimensional NS equation, J is the physical domain (x 1 ,x 2 ,x 3 ) to the computational domain (ξ 1 ,ξ 2 ,ξ 3 ) The modulus of the transformation matrix, S ij To calculate the spatial matrix, dB ξ 、dD ξ They are the surface and space integration units in the calculation space respectively.

2. The multi-constrained refined aerodynamic optimization design method for the tailless flying wing layout according to claim 1, It is characterized in that In step 4, the design variables are 108, including 26 design variables for each of the four control sections and four section torsion angles.

3. The multi-constrained refined aerodynamic optimization design method for the tailless flying wing layout according to claim 2, It is characterized in that In step six, the aerodynamic performance parameters of the baseline shape include: drag coefficient, lift coefficient, pitch moment coefficient and area of ​​the control section.

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