A method for airfoil design considering dynamic effects

Abstract

This invention proposes an airfoil design method considering dynamic effects, comprising the following steps: Step 1: Given the initial shape of the airfoil to be optimized, generate a CFD mesh for the initial shape; Step 2: Parameterize the airfoil considering dynamic effects, determining design variables and design space; Step 3: Determine design objectives and constraints, and establish a mathematical model for the optimization problem; Step 4: Generate the velocity distribution at the front and rear interfaces of the ducted fan based on momentum theory and boundary layer theory to simulate dynamic effects, and establish a CFD method based on the RANS equations to solve for the aerodynamic performance of the airfoil considering dynamic effects, thereby obtaining the design objective value; Step 5: Use an intelligent optimization algorithm and the flow field numerical simulation method established in Step 4 to optimize and solve the optimization problem in Step 3, obtaining the optimized airfoil considering dynamic effects. The optimization design method for airfoils considering dynamic effects established in this invention can significantly improve the aerodynamic performance of ducted fan-wing coupled configuration airfoils.

Description

Technical Field

[0001] This invention belongs to the field of airfoil design methods, specifically relating to an airfoil design method that takes into account dynamic effects. Background Technology

[0002] Green aviation has become a trend and focus of development both domestically and internationally. Low carbon and environmental protection have become a consensus, requirement, and goal of the global aviation industry. Against this backdrop, electrification is a major trend in aircraft development. Electric ducted fans are power units that use electricity to drive fans arranged within ducts. Compared to open-type electric propellers, they have advantages such as compact structure, low noise level, high safety, and ease of internal embedding. In recent years, the electric distributed ducted fan-wing coupled layout has gradually become a key development direction for various research institutions. Conducting aerodynamic design research on such aircraft has significant engineering practical significance and application value. The characteristic of this type of aircraft layout is that multiple ducted fans are arranged on the wing. The suction effect of the fans affects the pressure distribution and aerodynamic performance on the wing surface. Since the aerodynamic performance of the wing directly determines the aerodynamic performance of the entire aircraft, improving the aerodynamic performance of the wing is of great importance.

[0003] Currently, traditional airfoil design and optimization methods have matured after decades of development. However, for distributed ducted fan-wing coupled layouts, where multiple ducted fans are arranged on or under the wing, this novel aerodynamic configuration deeply couples the wing and the engine. Due to the suction and exhaust of the fans, the pressure distribution on the wing surface and the intake and exhaust duct surfaces will change significantly compared to unpowered configurations. Since traditional airfoil design methods cannot consider the influence of the engine, the airfoil designed using unpowered design methods will deviate from the optimal design point under the influence of the engine, thus failing to achieve the optimal performance of the ducted fan-equipped wing. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides an airfoil design method that considers dynamic influences. By constructing an airfoil optimization design framework that considers dynamic influences, the airfoil under dynamic influences can be optimized, effectively improving the aerodynamic performance of the distributed ducted fan-wing coupled layout and providing technical support for the further application of the distributed ducted fan-wing coupled layout.

[0005] The technical solution of this invention is as follows:

[0006] An airfoil design method considering dynamic effects includes the following steps:

[0007] Step 1: Given the initial shape of the airfoil that needs to be optimized considering dynamics, generate the CFD mesh of the initial shape;

[0008] Step 2: Parametricize the airfoil considering dynamics to determine the design variables and design space;

[0009] Step 3: Determine the design objectives and constraints, and establish a mathematical model for the optimization problem;

[0010] Step 4: Generate the velocity distribution at the front and rear interfaces of the ducted fan based on momentum theory and boundary layer theory to simulate dynamic effects. Establish a CFD method for airfoils considering dynamic effects based on RANS equations, solve for the aerodynamic performance of the airfoil considering dynamic effects, and then obtain the design target value.

[0011] Step 5: The optimization problem in Step 3 is solved by using intelligent optimization algorithm and flow field numerical simulation method established in Step 4 to obtain optimized airfoil considering dynamics.

[0012] Furthermore, in step 1, the power refers to a ducted fan arranged on or under the wing.

[0013] Furthermore, in step 1, when generating the CFD mesh, the region inside the duct surrounding the blades is set as a solid domain and does not participate in the flow field calculation, while the interface between the front and rear of the duct fan is used as a velocity boundary condition to participate in the flow field calculation.

[0014] Furthermore, the parameterization method in step 2 is the FFD method.

[0015] Furthermore, the design target in step 3 is the drag coefficient C. D Minimum, constrained by the airfoil lift coefficient C L Keeping the set value unchanged, the thickness t does not decrease, and the pitching moment coefficient C... m The specific optimization model mathematical expression is as follows: (No increase)

[0016]

[0017] Among them, C Lset For the set lift coefficient values, t0 and C m0 These represent the initial airfoil thickness and pitching moment coefficient, respectively. The airfoil thickness is taken as the thickness value at one-quarter chord length.

[0018] Furthermore, step 4 includes the following sub-steps:

[0019] Step 4.1: Use momentum theory to solve for the average velocity at the interface between the front and rear of the ducted fan, and calculate the flow rate through the duct;

[0020] Specifically, the thrust T is obtained based on the parameters of the ducted fan, and then the average velocity V1 at the front and rear interfaces, the duct mass flow rate Q0, and the mass flow rate Q1 corresponding to the duct airflow inlet height are calculated using the following formula:

[0021] T = ρAV1(V1 - V0)

[0022] Q0 = ρAV1

[0023]

[0024] Where ρ is the air density, A is the area of ​​the front and rear interfaces, V0 is the incoming flow velocity, h is the inlet height of the duct airflow, h = D1 - D2, where D1 is the diameter of the inner wall of the duct and D2 is the diameter of the rotor hub.

[0025] Step 4.2: Use boundary layer theory to solve for the boundary layer thickness and velocity distribution near the object surface at the interface between the front and rear of the ducted fan. Specifically:

[0026] ① The thickness of the boundary layer near the object surface at the front and rear interfaces of the airfoil ducted fan is calculated using the following formula:

[0027]

[0028]

[0029] Where δ is the boundary layer thickness, Re is the local Reynolds number, ρ is the density, V0 is the incoming flow velocity, l is the horizontal distance from the leading edge to the local point, and μ is the viscosity coefficient;

[0030] For the front interface of the ducted fan, the boundary layer thickness δ1 near the wing region, the boundary layer thickness δ2 near the duct lip region, and the boundary layer thickness δ3 near the duct hub region are calculated using the above formula.

[0031] For the rear interface of the ducted fan, the boundary layer thickness δ4 near the duct hub region is calculated using the above formula.

[0032] ②Based on the obtained boundary layer thicknesses δ1, δ2, δ3, and δ4, the velocity distribution at the front and rear interfaces of the airfoil ducted fan is calculated, specifically as follows:

[0033] For the front interface of the ducted fan, the velocity on the outer side of the boundary layer is set to a value of V2. For the inner side of the boundary layer, the velocity distribution V3 within the boundary layer thickness δ1 near the wing region, the velocity distribution V4 within the boundary layer δ2 near the duct lip region, and the velocity distribution V5 within the boundary layer δ3 near the duct hub region are obtained by using the empirical formula for the velocity distribution of the flat plate turbulent boundary layer.

[0034] For the rear interface of the ducted fan, the velocity distribution is divided into two parts: the first part is the boundary layer region near the hub, where the velocity distribution V6 is calculated using the empirical formula for turbulent boundary layer velocity distribution in a flat plate; the second part is the other regions excluding the first part, where the velocity distribution V7 is calculated using the empirical formula for turbulent velocity distribution in a circular tube in boundary layer theory. Assuming the velocity is the same at the same radial position, the velocity distribution V7 at different radial positions is calculated using the empirical formula for the power function of turbulent velocity distribution in a circular tube, as shown in the following expression:

[0035]

[0036] Among them, V max The maximum flow velocity at the duct cross-section is given by y, where y is the radial position from the duct centerline, and r0 is the duct radius minus the hub radius; the exponents n and V... max It is obtained through the following calculation method:

[0037] The exponent n is a function of the Reynolds number, and is calculated as follows:

[0038] First, calculate the Reynolds number Re2 based on the average velocity:

[0039]

[0040] Where V1 is the average flow velocity of the culvert cross section, and D1 is the inner diameter of the culvert;

[0041] Then, based on the power exponent and Reynolds number data shown in Table 1, the n value corresponding to the current Reynolds number Re2 is obtained by interpolation calculation;

[0042] Table 1. Data corresponding to power exponents and Reynolds numbers.

[0043] Reynolds number Re n value <![CDATA[4×10 3 ]]> 6.0 <![CDATA[2.3×10 4 ]]> 6.6 <![CDATA[1.1×10 5 ]]> 7.0 <![CDATA[1.1×10 6 ]]> 8.8 <![CDATA[2.0×10 6 ]]> 10.0 <![CDATA[3.2×10 6 ]]> 10.0

[0044] V max V is a function of the exponent n. After obtaining the value of n, max The calculation method is as follows:

[0045]

[0046] ③ Integrate and calculate the current velocity distribution at the duct front interface Q2 and duct rear interface Q3, and compare it with the duct flow rate Q1 obtained in step 4.1. If the convergence criterion is not met, update the velocity V2 outside the boundary layer, calculate the velocity distribution inside the corresponding boundary layer based on the new velocity outside the boundary layer, and recalculate the duct flow rate Q until the convergence criterion is met, and obtain the velocity distribution at the duct fan front and rear interfaces.

[0047] For the ducted fan front interface, the duct flow rate Q2 under the current velocity distribution is calculated using the following formula:

[0048]

[0049] For the ducted fan rear interface, the duct flow rate Q3 under the current velocity distribution is calculated using the following formula:

[0050]

[0051] Step 4.3: Based on the CFD mesh and the velocity distribution obtained in Step 4.2, perform RANS solution on the airfoil flow field to obtain the flow field and aerodynamic coefficients of the airfoil considering dynamics. The key boundary condition treatment is as follows:

[0052] The velocity distribution on the front interface of the ducted fan is assigned to the front interface of the ducted fan and set as the outlet boundary; the velocity distribution on the rear interface of the ducted fan is assigned to the rear interface of the ducted fan and set as the inlet boundary; the influence of dynamics on the flow field is simulated through the above outlet boundary and inlet boundary.

[0053] Furthermore, step 5 employs a genetic algorithm for optimization. Specifically, the aerodynamic characteristics of the current optimized iterative shape are calculated using the CFD method established in step 4 to obtain the design target value, which is then fed back to the genetic optimization algorithm to determine whether the aerodynamic performance of the airfoil meets the design requirements, i.e., whether it has converged. If it has converged, the optimization design ends and a new shape is output. If it has not converged, the design variables are updated, and the process returns to step 4 until the end, thus obtaining the optimized shape.

[0054] Beneficial effects

[0055] This invention addresses the problem that traditional airfoil design methods cannot consider the influence of dynamics on the airfoil. It proposes an airfoil design method that takes into account the dynamics of the airfoil. The method calculates the average velocity at the interface between the front and rear of the ducted fan using momentum theory and calculates the boundary layer thickness and velocity distribution near the object surface at the interface using boundary layer theory. The velocity distributions of the two methods are superimposed and applied to the corresponding positions at the interface between the front and rear of the ducted fan. The method introduces exit and inlet boundaries to simulate the effect of the ducted fan on the flow field. This method can efficiently and accurately calculate the aerodynamic coefficients of airfoils that consider the dynamics of the ducted fan, thereby enabling aerodynamic optimization design of airfoils that consider dynamics and improving the aerodynamic performance of ducted fan-wing coupled configurations. Attached Figure Description

[0056] Figure 1 This is a model of a wing section with a ducted fan on the trailing edge of the upper surface of the wing, according to an embodiment of the present invention.

[0057] Figure 2 This is a schematic flowchart of the airfoil design method according to an embodiment of the present invention;

[0058] Figure 3This is a schematic diagram of a two-dimensional airfoil considering the dynamic effects according to an embodiment of the present invention;

[0059] Figure 4 This is a schematic diagram of a two-dimensional airfoil CFD mesh considering the dynamic effects according to an embodiment of the present invention;

[0060] Figure 5 This is a schematic diagram of the control point arrangement of the FFD parameterization method according to an embodiment of the present invention;

[0061] Figure 6 This is a schematic diagram illustrating the reliability verification of the CFD method according to an embodiment of the present invention;

[0062] Figure 7 This is a comparison of the initial airfoil, the optimized airfoil without considering the dynamic influence, and the optimized airfoil with considering the dynamic influence in the embodiments of the present invention;

[0063] Figure 8 These are the lift coefficient curves of the initial airfoil, the optimized airfoil without considering the dynamic influence, and the optimized airfoil considering the dynamic influence, as a function of angle of attack according to embodiments of the present invention.

[0064] Figure 9 These are the drag coefficient curves of the initial airfoil, the optimized airfoil without considering the dynamic influence, and the optimized airfoil considering the dynamic influence, as a function of angle of attack in embodiments of the present invention.

[0065] Figure 10 These are the lift-drag ratio curves of the initial airfoil, the optimized airfoil without considering the dynamic influence, and the optimized airfoil considering the dynamic influence, as a function of the lift coefficient in this invention embodiment.

[0066] In the diagram: 1-Ductwork; 2-Propeller hub; 3-Ductwork fan front interface; 4-Ductwork fan rear interface; 5-Solid domain; 6-Main airfoil; 7-Moving blade; 8-Stationary blade. Detailed Implementation

[0067] To make the technical problems solved, the technical solutions, and the beneficial effects of this invention clearer and to enable those skilled in the art to better understand the invention, the invention will be further described in detail and in full below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0068] This embodiment employs an airfoil aerodynamic optimization design method considering dynamic effects provided by the present invention. Taking an airfoil with a ducted fan on the trailing edge of the upper surface of the wing as an example, aerodynamic optimization design is performed. The airfoil segment model with the ducted fan on the trailing edge of the upper surface of the wing is shown below. Figure 1 As shown in Table 2, the design status and reference values ​​are as follows.

[0069] Table 2 Optimized Design Status and Reference Quantities for Airfoils with Ducted Fans

[0070] physical quantity numerical values Mach number 0.1238476 Flight speed 150km / h Flight altitude 1km Lift coefficient 0.5 Reference chord length 0.61434m Torque reference point -0.150887m Duct inner wall diameter 150mm Hub diameter 60mm

[0071] Optimize the design process, such as Figure 2 As shown, the specific steps include the following:

[0072] Step 1: Given the initial shape of the airfoil that needs to be optimized considering dynamics, generate the CFD mesh of the initial shape;

[0073] In this embodiment, the power source considered is an overwing dorsal ducted fan. A two-dimensional model of the ducted fan-wing coupled layout is selected as the initial shape, such as... Figure 3 As shown, the CFD mesh is generated as follows. Figure 4 As shown, when generating the CFD mesh, the region inside the duct surrounding the blades is set as a solid domain and does not participate in the flow field calculation, while the interface between the front and rear of the duct fan is used as a velocity boundary condition to participate in the flow field calculation.

[0074] Step 2: Parametricize the airfoil considering dynamics to determine the design variables and design space;

[0075] In this embodiment, the airfoil considering the upper surface dynamics is parameterized using the FFD method, and the control points are as follows: Figure 5 As shown in the figure, the black solid circles are control points, and the design variables are the vertical coordinate values ​​of these circles. Among them, the design variables of the two points in the leftmost column vary in the range of [-0.03, 0.03], and the design variables of the remaining points vary in the range of [-0.05, 0.05].

[0076] Step 3: Determine the design objectives and constraints, and establish a mathematical model for the optimization problem;

[0077] In this embodiment, the design objective is the drag coefficient C. D Minimum, constrained by the airfoil lift coefficient C L Keeping the set value of 0.5, the thickness t does not decrease, and the pitching moment coefficient C... m The specific optimization model mathematical expression is as follows: (No increase)

[0078]

[0079] Among them, t0 and C m0 These represent the initial airfoil thickness and pitching moment, respectively. The airfoil thickness is taken as the thickness value at one-quarter chord length.

[0080] Step 4: Generate the velocity distribution at the front and rear interfaces of the ducted fan based on momentum theory and boundary layer theory to simulate dynamic effects. Establish a CFD method for the airfoil considering dynamic effects based on the RANS equations, solve for the aerodynamic performance of the airfoil considering dynamic effects, and then obtain the design target value; specifically including the following sub-steps:

[0081] Step 4.1: Use momentum theory to solve for the average velocity at the interface between the front and rear of the ducted fan, and calculate the flow rate through the duct;

[0082] Specifically, based on the parameters of the ducted fan, the thrust T = 12.21 N is obtained. Then, the average velocity at the front and rear interfaces, V1 = 59.46 m / s, the duct mass flow rate Q0 = 0.9641 kg / s, and the mass flow rate Q1 corresponding to the duct airflow inlet height are calculated using the following formula:

[0083] T = ρAV1(V1 - V0)

[0084] Q0 = ρAV1

[0085]

[0086] Where ρ is the air density, A is the area of ​​the interface between the front and rear ends, V0 is the incoming flow velocity, h is the inlet height of the duct airflow, and h = D1 - D2, where D1 is the diameter of the inner wall of the duct and D2 is the diameter of the rotor hub.

[0087] Step 4.2: Use boundary layer theory to solve for the boundary layer thickness and velocity distribution near the object surface at the interface between the front and rear of the ducted fan. Specifically:

[0088] ① The thickness of the boundary layer near the object surface at the front and rear interfaces of the airfoil ducted fan is calculated using the following formula:

[0089]

[0090]

[0091] Where δ is the boundary layer thickness, Re is the local Reynolds number, ρ is the density, V0 is the incoming flow velocity, l is the horizontal distance from the leading edge to the local point, and μ is the viscosity coefficient;

[0092] For the ducted fan front interface, the boundary layer thickness δ1 = 26 mm near the wing region, the boundary layer thickness δ2 = 2.5 mm near the duct lip region, and the boundary layer thickness δ3 = 0.5 mm near the duct hub region are calculated using the above formula.

[0093] For the rear interface of the ducted fan, the boundary layer thickness δ4 = 2.8 mm is calculated using the above formula in the region near the duct hub.

[0094] ②Based on the obtained boundary layer thicknesses δ1, δ2, δ3, and δ4, the velocity distribution at the front and rear interfaces of the airfoil ducted fan is calculated, specifically as follows:

[0095] For the ducted fan front interface, the velocity on the outer side of the boundary layer is set to a value of V2. For the inner side of the boundary layer, the empirical formula for the velocity distribution of the turbulent boundary layer of a flat plate (refer to "Viscous Fluid Mechanics", 2nd edition, edited by Zhang Zixiong and Dong Zengnan) is used to obtain the velocity distribution V3 within the boundary layer thickness δ1 near the wing region, the velocity distribution V4 within the boundary layer δ2 near the duct lip region, and the velocity distribution V5 within the boundary layer δ3 near the duct hub region.

[0096] For the rear interface of the ducted fan, the velocity distribution is divided into two parts: the first part is the boundary layer region near the hub, where the velocity distribution V6 is calculated using the empirical formula for the velocity distribution of a flat plate turbulent boundary layer (refer to "Viscous Fluid Mechanics," 2nd edition, edited by Zhang Zixiong and Dong Zengnan); the second part is the other regions excluding the first region, where the velocity distribution V7 is calculated using the turbulent velocity distribution formula for a circular tube in boundary layer theory (refer to "Fluid Mechanics," edited by Jing Sirui and Zhang Mingyuan). Assuming the velocity is the same at the same radial position, the velocity distribution V7 at different radial positions is calculated according to the empirical formula for the power function of the turbulent velocity distribution in a circular tube, as shown in the following expression:

[0097]

[0098] Among them, V max The maximum flow velocity at the duct cross-section is given by y, where y is the radial position from the duct centerline, and r0 is the duct radius minus the hub radius; the exponents n and V... max It is obtained through the following calculation method:

[0099] The exponent n is a function of the Reynolds number, and is calculated as follows:

[0100] First, calculate the Reynolds number Re2 based on the average velocity.

[0101]

[0102] Where V1 is the average flow velocity of the culvert cross section, and D1 is the inner diameter of the culvert;

[0103] Then, based on the power exponent and Reynolds number data shown in Table 1, the n value corresponding to the current Reynolds number Re2 is obtained by interpolation calculation; the data in Table 1 is referenced from Fluid Mechanics, edited by Jing Sirui and Zhang Mingyuan, p169.

[0104] V max V is a function of the exponent n. After obtaining the value of n, max The calculation method is as follows:

[0105]

[0106] ③ Integrate and calculate the current velocity distribution at the duct front interface flow rate Q2 and the duct rear interface flow rate Q3, and compare them with the duct flow rate Q1 obtained in step 41. If the convergence criterion is not met, update the velocity V2 outside the boundary layer, calculate the velocity distribution inside the corresponding boundary layer based on the new velocity outside the boundary layer, and recalculate the duct flow rate Q until the convergence criterion is met, and obtain the velocity distribution at the duct fan front and rear interfaces.

[0107] For the ducted fan front interface, the duct flow rate Q under the current velocity distribution is calculated using the following formula:

[0108]

[0109] For the ducted fan rear interface, the duct flow rate Q3 under the current velocity distribution is calculated using the following formula:

[0110]

[0111] Step 4.3: Based on the CFD mesh and the velocity distribution obtained in Step 4.2, perform RANS solution on the airfoil flow field to obtain the flow field and aerodynamic coefficients of the airfoil considering dynamics. The key boundary condition treatment is as follows:

[0112] The velocity distribution on the front interface of the ducted fan is assigned to the front interface of the ducted fan and set as the outlet boundary; the velocity distribution on the rear interface of the ducted fan is assigned to the rear interface of the ducted fan and set as the inlet boundary; the influence of dynamics on the flow field is simulated through the above outlet boundary and inlet boundary.

[0113] In this embodiment, the RANS equations are solved using the k-ωSST turbulence model closed-loop equations, the spatial discretization scheme is the Roe scheme, and the time-progression method is the LU-SGS method. To verify the reliability of the CFD method for powered airfoils, the initial airfoil is calculated using the CFD method of this invention, and the control group is assembled with the initial airfoil. Figure 1 The three-dimensional airfoil model with a ducted fan at the trailing edge is shown. CFD calculations are performed on the obtained three-dimensional airfoil model based on the multi-reference coordinate system method and RANS equations. Then, the airfoil surface pressure coefficients obtained by the two methods are compared, such as... Figure 6 As shown, the CFD method established by this invention is accurate and reliable, and can be used for airfoil design that takes into account dynamic effects.

[0114] Step 5: The optimization problem in Step 3 is solved by using intelligent optimization algorithm and flow field numerical simulation method established in Step 4 to obtain optimized airfoil considering dynamics.

[0115] In this embodiment, the genetic group algorithm is used for optimization. Specifically, the aerodynamic characteristics of the current optimized shape are calculated using the CFD method established in step 4 to obtain the value of the design target. This value is then fed back to the genetic group optimization algorithm to determine whether the aerodynamic performance of the airfoil meets the design requirements, i.e., whether it has converged. If it has converged, the optimization design ends and a new shape is output. If it has not converged, the design variables are updated and the process returns to step 4 until the end, thus obtaining the optimized shape.

[0116] To visually demonstrate the effect of the design method of this invention on improving the aerodynamic performance of the airfoil by considering trailing edge dynamics, this embodiment uses a traditional airfoil optimization method to optimize the airfoil without considering dynamic effects as a control; that is, the airfoil design is performed after removing the dynamic effects of the upper airfoil. A comparison is made between the initial airfoil, the airfoil obtained using the traditional optimization design method without considering dynamic effects, and the airfoil obtained using the optimization design method proposed in this invention. Figure 7 As shown. The two optimized airfoils are assembled as follows. Figure 1 The three-dimensional airfoil model with a ducted fan at the trailing edge is shown. CFD calculations are performed on the obtained three-dimensional airfoil model based on the multi-reference coordinate system method and RANS equations. The calculated lift coefficient of the airfoil as a function of angle of attack is as follows: Figure 8 As shown, the drag coefficient varies with the angle of attack as follows: Figure 9 As shown, the lift-to-drag ratio varies with the lift coefficient as follows: Figure 10 As shown. By Figure 8 It is evident that, at the same angle of attack, the lift coefficient of the airfoil section assembling the optimized airfoil considering dynamic effects is greater than that of the airfoil section assembling the optimized airfoil without considering dynamic effects and the initial configuration; from Figure 9 It is evident that when the angle of attack is less than 6.5°, the drag coefficient of the airfoil section assembling the optimized airfoil considering dynamic effects is lower than that of the airfoil section assembling the optimized airfoil without considering dynamic effects and the initial configuration; Figure 10 It is evident that, within the lift coefficient range of less than 1.4, the lift-to-drag ratio of the airfoil section assembling the optimized airfoil considering dynamic influence is greater than that of the airfoil section assembling the optimized airfoil section assembling the initial configuration without considering dynamic influence. Compared to the traditional design method that does not consider trailing edge dynamics, the airfoil section assembling the optimized design method considering dynamic influence proposed in this invention achieves better performance at the design point (C). L The drag coefficient of (=0.5) decreased by 0.00142, and the lift-to-drag ratio increased by 6.218, as shown in Table 3.

[0117] Table 3 Comparison of aerodynamic performance (Ma=0.12385, Re=1618792, C L =0.5)

[0118] <![CDATA[C L ]]> <![CDATA[C D ]]> L / D Initial configuration 0.5 0.01328 36.361 Design without considering dynamic effects 0.5 0.01142 42.381 Design considering dynamic effects 0.5 0.01000 48.599 △ 0 24.7％ 33.7％

[0119] In summary, the optimization design method that considers the dynamic effects proposed in this invention can significantly improve the aerodynamic performance of ducted fan-wing coupled airfoil configurations compared to traditional optimization design methods that do not consider the dynamic effects.

[0120] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. An airfoil design method considering dynamic effects, characterized in that, Includes the following steps: Step 1: Given the initial shape of the airfoil that needs to be optimized considering dynamics, generate the CFD mesh of the initial shape; Step 2: Parametricize the airfoil considering dynamics to determine the design variables and design space; Step 3: Determine the design objectives and constraints, and establish a mathematical model for the optimization problem; Step 4: Generate the velocity distribution at the front and rear interfaces of the ducted fan based on momentum theory and boundary layer theory to simulate dynamic effects. Establish a CFD method for the airfoil considering dynamic effects based on the RANS equations, solve for the aerodynamic performance of the airfoil considering dynamic effects, and then obtain the design target value; specifically including the following sub-steps: Step 4.1: Use momentum theory to solve for the average velocity at the interface between the front and rear of the ducted fan, and calculate the flow rate through the duct; Step 4.2: Use boundary layer theory to solve for the boundary layer thickness and velocity distribution near the surface of the object at the front and rear interfaces of the ducted fan; Step 4.3: Based on the CFD mesh and the velocity distribution obtained in Step 4.2, perform RANS solution on the flow field of the airfoil to obtain the flow field and aerodynamic coefficients of the airfoil considering the dynamics; Step 5: The optimization problem in Step 3 is solved by using intelligent optimization algorithm and flow field numerical simulation method established in Step 4 to obtain optimized airfoil considering dynamics.

2. The airfoil design method considering dynamic effects according to claim 1, characterized in that, In step 1, the power source refers to the ducted fan located on or under the wing.

3. The airfoil design method considering dynamic effects according to claim 2, characterized in that, In step 1, when generating the CFD mesh, the region inside the ducted fan surrounding the blades is set as a solid domain and does not participate in the flow field calculation, while the front and rear interfaces of the ducted fan are used as velocity boundary conditions to participate in the flow field calculation.

4. The airfoil design method considering dynamic effects according to claim 1, characterized in that, The parameterization method in step 2 is the FFD method.

5. The airfoil design method considering dynamic effects according to claim 1, characterized in that, The design objective in step 3 is the drag coefficient C. D Minimum, constrained by the airfoil lift coefficient Keeping the set value unchanged, the thickness t does not decrease, and the pitching moment coefficient remains constant. The specific optimization model mathematical expression is as follows: (No increase) in, The set lift coefficient value, and These represent the initial airfoil thickness and pitching moment coefficient, respectively.

6. The airfoil design method considering dynamic effects according to claim 1, characterized in that, Step 4 includes the following sub-steps: Step 4.1: Use momentum theory to solve for the average velocity at the interface between the front and rear of the ducted fan, and calculate the flow rate through the duct; Specifically, the thrust T is obtained based on the parameters of the ducted fan, and then the average velocity V1 at the front and rear interfaces and the duct mass flow rate are calculated using the following formula. and the mass flow rate corresponding to the inlet height of the duct airflow : in, Let be the air density, A be the area of ​​the interface between the front and rear sections, V0 be the incoming flow velocity, and h be the inlet height of the duct. ,in, The diameter of the inner wall of the culvert. The diameter of the propeller hub; Step 4.2: Use boundary layer theory to solve for the boundary layer thickness and velocity distribution near the object surface at the interface between the front and rear of the ducted fan. Specifically: ① The thickness of the boundary layer near the object surface at the front and rear interfaces of the airfoil ducted fan is calculated using the following formula: in, Boundary layer thickness, For the local Reynolds number, Let V be the density and V0 be the incoming flow velocity. The horizontal distance from the leading edge to the local point. The viscosity coefficient; For the ducted fan front interface, the boundary layer thickness near the wing region is calculated using the above formula. Boundary layer thickness near the duct lip region and the boundary layer thickness near the duct hub region ; For the rear interface of the ducted fan, the boundary layer thickness near the duct hub region can be calculated using the above formula. ; ②Based on the obtained boundary layer thickness , , , The velocity distribution at the front and rear interfaces of the airfoil ducted fan is calculated separately, as follows: For the ducted fan front interface, the velocities on the outer side of the boundary layer are all set values. For the inner side of the boundary layer, the boundary layer thickness near the wing region is obtained using an empirical formula for the velocity distribution of a flat plate turbulent boundary layer. velocity distribution within Boundary layer near the duct lip region velocity distribution within Boundary layer near the duct hub region velocity distribution within ; For the rear interface of the ducted fan, the velocity distribution is divided into two parts: the first part is the boundary layer region near the hub, and the velocity distribution within the boundary layer is calculated using the empirical formula for the velocity distribution of a flat plate turbulent boundary layer. The second part, excluding the first region, calculates the velocity distribution of other regions using the empirical formula for turbulent velocity distribution inside a circular pipe in boundary layer theory. Assuming the velocity is the same at the same radial position, the velocity distribution at different radial positions is... The calculation is based on the empirical formula of the power function of the turbulent velocity distribution inside a circular pipe, and the specific expression is as follows: in, y represents the maximum flow velocity at the culvert cross-section, and y represents the radial position from the culvert centerline. The duct radius minus the hub radius; the exponent n and It is obtained through the following calculation method: The exponent n is a function of the Reynolds number, and is calculated as follows: First, calculate the Reynolds number based on the average velocity. in, The average flow velocity across the culvert cross section is... The inner diameter of the culvert; Then, based on the power exponent and Reynolds number data shown in Table 1, the current Reynolds number is obtained through interpolation. The corresponding value of n; Table 1. Data corresponding to power exponents and Reynolds numbers It is a function of the exponent n. After obtaining the value of n, The calculation method is as follows: ； ③ Integral calculation of the flow rate at the interface in front of the duct for the current velocity distribution Flow rate at the interface with the duct , compared with the duct flow rate obtained in step 4.1 The comparison is performed; if the convergence criterion is not met, the velocity outside the boundary layer is updated. The velocity distribution within the corresponding boundary layer is calculated based on the velocity outside the new boundary layer, and the duct flow rate is recalculated. Continue until the convergence criterion is met to obtain the velocity distribution at the front and rear interfaces of the ducted fan. For the ducted fan front interface, the duct flow rate at the current velocity distribution The calculation formula is as follows: For the ducted fan rear interface, the duct flow rate at the current velocity distribution The calculation formula is as follows: ； Step 4.3: Based on the CFD mesh and the velocity distribution obtained in Step 4.2, perform RANS solution on the airfoil flow field to obtain the flow field and aerodynamic coefficients of the airfoil considering dynamics. The key boundary condition treatment is as follows: The velocity distribution on the front interface of the ducted fan is assigned to the front interface of the ducted fan and set as the outlet boundary; the velocity distribution on the rear interface of the ducted fan is assigned to the rear interface of the ducted fan and set as the inlet boundary; the influence of dynamics on the flow field is simulated through the above outlet boundary and inlet boundary.

7. The airfoil design method considering dynamic effects according to claim 1, characterized in that, Step 5 uses a genetic algorithm for optimization. Specifically, the aerodynamic characteristics of the current optimized iterative shape are calculated using the CFD method established in step 4 to obtain the value of the design target. This value is then fed back to the genetic optimization algorithm to determine whether the aerodynamic performance of the airfoil meets the design requirements, i.e. whether it has converged. If it has converged, the optimization design ends and a new shape is output. If convergence is not achieved, update the design variables and return to step 4 until the end, obtaining the optimized shape.

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