A leading edge combined protrusion structure for controlling airfoil attachment flow and a flow control method thereof

Abstract

The present invention discloses a leading edge combined protrusion structure for controlling the attached flow of an airfoil and a flow control method thereof. The leading edge combined protrusion structure comprises a basic airfoil (1) and a leading edge combined protrusion, the basic airfoil (1) is provided with a leading edge combined protrusion, the leading edge combined protrusion comprises a protrusion I (1) and a protrusion II (2), the protrusion I (1) and the protrusion II (2) are arranged adjacent to each other, the front end contour lines of the protrusion I (1) and the protrusion II (2) are sinusoidal, and the periodic chord length of the protrusion I (1) and the protrusion II (2) is 25%. The present invention fixes the strong side and the weak side by adding a small protrusion while ensuring that the flow pattern is basically similar.

Description

Technical Field

[0001] The invention belongs to the technical field of passive control in airfoil stall control, and specifically relates to a leading edge combined protrusion structure for controlling airfoil attachment flow and a flow control method thereof. Background Art

[0002] In recent years, reducing wing drag or increasing its lift and improving the stall process have become hot issues in the field of fluid mechanics. According to research, fluid and wall separation often occur in the boundary layer, causing the lift of the wing section to decrease rapidly, leading to blade vibration and, in severe cases, fracture.

[0003] There are several methods to solve the above problems in the existing research results. At present, a large number of civil aircraft wings use flaps to ensure the performance of the aircraft during take-off and landing. In addition to adding flaps to the surface of the wing section, there are two other types of control methods, including active control and passive control. The method of active control is to introduce energy from the outside to enhance the kinetic energy of the fluid on the surface of the wing section, ensure that flow separation is more difficult to occur, and improve the external characteristics of the airfoil. Common active control methods mainly include synthetic jets, plasma disturbances, blowing and suction flow control and other methods. The method of controlling flow separation without externally supplementing kinetic energy for the fluid is called passive control. Wing blades, vortex generators, leading edge protrusion structures and spoilers are common passive control methods.

[0004] The leading edge bulge structure has the characteristics of simple structure and low manufacturing cost, but it has certain limitations in the fields of aviation, wind energy utilization, etc. There are several difficulties in promoting its use on a large scale: (1) The control effect is limited, and the leading edge bulge structure belongs to passive control; (2) There is no need to control the performance reduction in the stage, and the leading edge bulge structure changes the flow structure, causing the performance of the airfoil to be slightly reduced at a small angle of attack. Summary of the invention

[0005] The present invention provides a leading edge combined protrusion structure for controlling the attached flow of the airfoil and a flow control method thereof. The leading edge large and small protrusions of the present invention function to change the flow direction vorticity distribution of the fluid flowing around the airfoil. In the prior art, the asymmetric vorticity distribution of the single protrusion airfoil at a small angle of attack is not significant. When approaching the stall angle of attack, the vorticity on both sides of the protrusion is obviously strong and weak, and the strong side behind the protrusion is deflected to the weak side to form a deflected flow, which replenishes energy for the weak side fluid to achieve the weak side entering a large separation state later than the basic airfoil stall angle of attack, while the strong side enters a complete separation state one step earlier. Since the strong and weak sides have obvious randomness, the step-type stall process found in the prior art has great instability. The present invention further optimizes the design here, and fixes the strong side and the weak side by adding small protrusions while ensuring that the flow state is basically similar.

[0006] The present invention is achieved through the following technical solutions:

[0007] A leading edge combined protrusion structure for controlling airfoil attachment flow, the leading edge combined protrusion structure comprising a basic airfoil 3 and a leading edge combined protrusion, the basic airfoil 3 is provided with a leading edge combined protrusion, the leading edge combined protrusion comprises a protrusion I2-1 and a protrusion II2-2, the protrusion I2-1 and the protrusion II2-2 are arranged adjacent to each other, the front end contour lines of the protrusion I2-1 and the protrusion II2-2 are sinusoidal, and the periodic chord length of the protrusion I2-1 and the protrusion II2-2 is 25%.

[0008] Furthermore, the amplitude of the protrusion Ⅰ2-1 is 15% of the chord length, and the amplitude of the protrusion Ⅱ2-2 is 5% of the chord length.

[0009] A method for controlling airfoil attachment flow of a leading edge combined protrusion structure, the flow control method specifically comprising the following steps:

[0010] Step 1: Enter various parameters and edit various conditions;

[0011] Step 2: Perform geometric modeling according to the editing conditions and determine the airfoil model used for calculation;

[0012] Step 3: Mesh the airfoil model according to step 2;

[0013] Step 4: Calculate the basic control equations of the fluid according to the grid division in step 3;

[0014] Step 5: Select and modify the turbulence model for the basic control equation of the fluid;

[0015] Step 6: Select boundary conditions and use the discretization numerical method based on the basic fluid control equation in step 4;

[0016] Step 7: Determine the leading edge combined protrusion structure according to the influence of the change in amplitude of the single protrusion;

[0017] Step 8: Determine the attachment area and the separation area according to the random flow under the working condition of the leading edge combined convex structure control;

[0018] Step 9: Verify the feasibility of the leading edge combined protrusion structure.

[0019] Furthermore, the geometric modeling in step 2 is specifically as follows: UG software is used to draw the basic airfoil contour line, the wing section chord length is 200 mm, the span width is 3.25 times the chord length, the maximum thickness is 21% of the chord length and is located at 34% of the chord length, the leading edge modified protrusion adopts a sinusoidal modified wing section with a wavelength of 0.25 times the chord length and an amplitude of 0.1 times the chord length. The peak section is generated by an outward expansion method, and the coordinate point generation method is determined by Formula 1 and the airfoil contour line is modeled in the same way.

[0020]

[0021] In the formula, (x′ i ,y′ i ) is the coordinate point of the convex peak section after modification, (x i ,y i ) is the reference wing section coordinate point, x m is the horizontal coordinate of the maximum thickness point of the wing section, A is the bulge amplitude, where i = 1, 2, ..., k, the subscript i is the i-th point constituting the two-dimensional contour line of the airfoil, and the subscript m is the m-th point corresponding to the maximum thickness point of the airfoil;

[0022] In order to ensure that the flow at the leading edge of the airfoil and the flow at the exit of the calculation domain are fully developed, appropriate extension is performed in the flow direction. Finally, the inlet of the calculation domain is 3000mm away from the leading edge of the airfoil, the outlet is 5000mm away from the trailing edge of the airfoil, and the span width is 650mm.

[0023] Furthermore, the step 3 is specifically to set 70 layers of boundary layer grids, the first layer height of the wing surface grid is 0.01mm, and the growth rate is about 1.1 to meet the calculation model for y + value requirements; finally, the mesh quality of each airfoil flow area is higher than 0.6, and the mesh is updated to achieve faster convergence and optimize the flow field calculation results, mainly for the rear part of the bulge.

[0024] Furthermore, the step 4 is specifically to use air as the calculation working fluid, and its inlet flow velocity is 13.1 m / s. At this time, the flow is simplified to a constant temperature incompressible motion, which satisfies the control equation in fluid mechanics; the continuity equation:

[0025]

[0026] Momentum equation:

[0027]

[0028] Where: u i is the speed (m / s), i=1,2,3; p is the pressure (Pa); x i is the coordinate (m); f i is the mass force (N / kg); t is the time (s); v is the kinematic viscosity (Pa·s);

[0029] At present, scholars widely adopt the idea of ​​turbulent average motion proposed by Reynolds, which expresses the instantaneous value as the sum of the average value and the pulsation value, that is:

[0030]

[0031] Where D' is the pulsation value, is the average value, and D is the instantaneous value;

[0032] At this time, the above two equations will become:

[0033] Conservation of mass:

[0034]

[0035] Conservation of momentum (Reynolds equation):

[0036]

[0037] Where: is the Reynolds stress.

[0038] However, after the introduction of Reynolds stress, the number of equations is insufficient to be solved; therefore, it is necessary to select appropriate turbulence model equations to link the pulsation term and the time-averaged term in order to solve the equation.

[0039] Furthermore, the step 5 is specifically that the eddy viscosity model assumes:

[0040]

[0041] Where: μ t is the turbulent viscosity (Pa·s); k is the turbulent kinetic energy (m2 / s2); δ ij is the Kronecker symbol;

[0042] The SST k-ω model considering transition is adopted, and the model equations are shown in formulas (8) to (11);

[0043]

[0044]

[0045]

[0046]

[0047] Where: γ is the intermittent factor, P γ1 and E γ1 is the transition source term, P γ2 and E γ2 is the laminar source term, Re θt is the transition momentum thickness Reynolds number, μ t is the turbulent viscosity, σ θt is the diffusion coefficient, P θt is the source term, Γ k is the effective diffusion rate of turbulent kinetic energy k, Γ ω , G ω , Y ω , D ωare the effective diffusivity, generation term, dissipation term and cross-diffusion term of ω, respectively. is the product of the effective intermittent factor and the generated term of the original k equation in the SSTk-ω model, It is the product of the modified intermittency factor compared with 0.1 and 1 and the dissipation term of the original k equation.

[0048] Furthermore, the step 6 is specifically as follows: the fluid control equation is a nonlinear partial differential equation group which is difficult to solve directly and needs to be discretized; the finite volume method is used for discretization, and the pressure and velocity are solved by the SIMPLEC algorithm;

[0049] The variable Φ discretizes the control equation using the finite volume method:

[0050]

[0051] Where: Γ is the generalized diffusion coefficient of Φ; ρ is the fluid density; u i is the fluid velocity;

[0052] Integrating the above equation on the control volume yields:

[0053]

[0054] Using the Gauss-Green formula to simplify:

[0055]

[0056] Further, the step 7 is specifically that the leading edge bulge amplitude parameter will not affect whether the step-type stall process will occur, but will affect the critical angle of attack that occurs and the value of the lift-drag coefficient when approaching the stall;

[0057] As the angle of attack increases, the area of ​​the separation zone gradually increases, and the pressure on the trailing edge of the wing drops rapidly. When the flow field is separated or the final angle of attack increases to the point where both sides enter a separated state, a rapid increase in leading edge pressure can be seen. Therefore, there is a direct connection between the rapid increase in leading edge pressure and the decrease in lift coefficient.

[0058] Furthermore, the step 8 is specifically as follows: the amplitudes of the protrusions I (1) and II (2) are 0.15c and 0.05c respectively. Since the deformation near the protrusions is large, the first layer height of the airfoil must still be about 0.01mm to meet the requirements of the turbulence model. Finally, the lowest mesh quality is reduced to 0.45; after understanding that the airfoil with no spacing always has a trend of changing from an expansion type to a contraction type, and understanding the influence of the amplitude of the protrusion on the airfoil flow, a double-protrusion airfoil with large and small protrusions is used to achieve further control of flow separation and attachment;

[0059] By studying the vorticity distribution in the flow section closest to the leading edge, it was found that the larger the bulge amplitude, the stronger the intensity of the vortex caused by the flow, resulting in the formation of an overall asymmetric vortex structure at the leading edge, causing flow deflection, and ensuring that the small-amplitude side maintains the attached flow during a sufficiently large range of attack angle changes.

[0060] The beneficial effects of the present invention are:

[0061] The present invention arranges a small sinusoidal protrusion with the same period and amplitude only one-third of the original protrusion on the right side of the original single-protrusion airfoil protrusion. When the angle of attack gradually increases, due to the induction effect of the large and small protrusions on the leading edge, the attachment flow caused by the protrusion is fixedly converged from the two protrusions to the middle valley section and deflected to the side of the small protrusion.

[0062] The high-energy attachment flow formed at the convex peak of the airfoil suction surface ensures that the airfoil can maintain a certain attachment flow when working at a large angle of attack, thereby optimizing the performance.

[0063] The random deflection phenomenon becomes controllable and predictable through the combination of large and small protrusions. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a schematic diagram comparing the basic airfoil and the convex peak cross-section contour lines of the present invention.

[0065] Figure 2 It is a schematic diagram comparing the cross-sectional contour lines of two airfoils and their modified airfoils of the present invention.

[0066] Figure 3 It is a schematic diagram of the three-dimensional calculation domain of the leading edge combined protrusion that controls the airfoil attachment flow in an embodiment of the present invention.

[0067] Figure 4 Schematic diagram of the computational grid of the present invention, wherein (a) is a schematic diagram of the overall grid, (b) is a schematic diagram of the multi-convex airfoil grid, (c) is a schematic diagram of the overall airfoil grid, and (d) is a schematic diagram of the boundary layer grid.

[0068] Figure 5 It is a schematic diagram of the raised local grid after improvement of the present invention.

[0069] Figure 6 It is a comparison chart of the settlement results of various turbulence models of the present invention.

[0070] Figure 7 It is a comparison chart between the calculated value and the experimental value of the lift coefficient of the basic wing section of the uncorrected turbulence model of the present invention.

[0071] Figure 8 1 is a comparison diagram of the calculated lift and drag coefficients of the modified basic wing section of the present invention and the experimental results, wherein (a) is a schematic diagram of the lift coefficient and (b) is a schematic diagram of the drag coefficient.

[0072] Fig. 9 It is the y+ value cloud diagram of the airfoil of the present invention.

[0073] Fig.10 It is a comparison diagram of the raised contour lines of different amplitudes of the present invention.

[0074] Fig.11 Schematic diagrams of the external characteristics of protrusions of different amplitudes of the present invention, wherein (a) is a schematic diagram of the lift coefficient curve, and (b) is a schematic diagram of the drag coefficient curve.

[0075] Fig.12 It is a schematic diagram comparing the limiting streamlines of the S and B working conditions of the present invention.

[0076] Fig.13 It is a schematic diagram of the double-protrusion large-small amplitude combination model of the present invention.

[0077] Fig.14 The single convex airfoil of the prior art has a Re of 1.8×10 5 and schematic diagram of the suction surface separation area at an attack angle of 16°.

[0078] Fig.15 The single convex airfoil of the prior art has a Re of 1.8×10 5 and schematic diagram of the suction surface separation area at an attack angle of 18°.

[0079] Fig.16 The leading edge combined convex structure airfoil of the control airfoil attachment flow in the embodiment of the present invention is at Re = 1.8 × 10 5 and schematic diagram of the suction surface separation area at an attack angle of 12°.

[0080] Fig.17 The leading edge combined convex structure airfoil of the control airfoil attachment flow in the embodiment of the present invention is at Re = 1.8 × 10 5 and schematic diagram of the suction surface separation area at an attack angle of 14°.

[0081] Fig.18 The leading edge combined convex structure airfoil of the control airfoil attachment flow in the embodiment of the present invention is at Re = 1.8 × 10 5 and schematic diagram of the suction surface separation area at an attack angle of 16°.

[0082] Fig.19 The leading edge combined convex structure airfoil of the control airfoil attachment flow in the embodiment of the present invention is at Re = 1.8 × 10 5 and the suction surface V at 16° attack angle 2 Cloud map. DETAILED DESCRIPTION

[0083] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0084] Example 1

[0085] A leading edge combined protrusion structure for controlling airfoil attachment flow, the leading edge combined protrusion structure comprising a basic airfoil 3 and a leading edge combined protrusion, the basic airfoil 3 is provided with a leading edge combined protrusion, the leading edge combined protrusion comprises a protrusion I1 and a protrusion II2, the protrusion I1 and the protrusion II2 are arranged adjacent to each other, the front end contour lines of the protrusions I1 and II2 are sinusoidal, the periodic chord length of the protrusions I1 and II2 is 25%, the transition between the protrusions I1 and II2 and the basic airfoil starts from the maximum thickness point of the airfoil, thereby ensuring that the whole has a good streamline shape; the wingspan width is 325% of the chord length.

[0086] Furthermore, the amplitude of the protrusion Ⅰ1 is 15% of the chord length; the amplitude of the protrusion Ⅱ2 is 5% of the chord length.

[0087] Furthermore, the flow control method specifically comprises the following steps:

[0088] Step 1: Enter various parameters and edit various conditions;

[0089] Step 2: Perform geometric modeling according to the editing conditions and determine the airfoil model used for calculation;

[0090] Step 3: Mesh the airfoil model according to step 2;

[0091] Step 4: Calculate the basic control equations of the fluid according to the grid division in step 3;

[0092] Step 5: Select and modify the turbulence model for the basic control equation of the fluid;

[0093] Step 6: Select boundary conditions and use the discretization numerical method based on the basic fluid control equation in step 4;

[0094] Step 7: Determine the leading edge combined protrusion structure according to the influence of the change in amplitude of the single protrusion;

[0095] Step 8: Determine the attachment area and the separation area according to the random flow under the working condition of the leading edge combined convex structure control;

[0096] Step 9: Verify the feasibility of the leading edge combined protrusion structure.

[0097] Furthermore, the geometric modeling in step 2 is specifically as follows: UG software is used to draw the basic airfoil contour line, the wing section chord length is 200 mm, the span width is 3.25 times the chord length, the maximum thickness is 21% of the chord length and is located at 34% of the chord length, the leading edge modified protrusion adopts a sinusoidal modified wing section with a wavelength of 0.25 times the chord length and an amplitude of 0.1 times the chord length. The convex peak section of the modified wing section is generated by an outward expansion method, and the coordinate point generation method is determined by formula 1 and the airfoil contour line is modeled in the same way. The profile of the convex peak section of the reference type and the modified wing section is compared. Figure 1 Comparison of two wing types and their modified wing types Figure 2 .

[0098]

[0099] In the formula, (x′ i ,y′ i ) is the coordinate point of the convex peak section after modification, (x i ,y i ) is the reference wing section coordinate point, x m is the horizontal coordinate of the maximum thickness point of the wing section, A is the bulge amplitude, where i = 1, 2, ..., k, the subscript i is the i-th point constituting the two-dimensional contour line of the airfoil, and the subscript m is the m-th point corresponding to the maximum thickness point of the airfoil;

[0100] In order to ensure that the flow at the leading edge of the airfoil and the flow at the exit of the calculation domain are fully developed, the flow direction is appropriately extended. Finally, the entrance of the calculation domain is 3000mm away from the leading edge of the airfoil, the exit is 5000mm away from the trailing edge of the airfoil, and the span width is 650mm. Figure 3 shown.

[0101] Furthermore, the step 3 is specifically that the structured grid has the advantages of fast convergence speed and saving computational grids for a simple computational model. Therefore, this paper adopts the structured grid division method to divide the fluid domain into grids. When dividing the grid, there are some requirements for the grid near the wing surface. In order to fully solve the boundary layer flow and the influence of the leading edge bulge, the boundary layer and the bulge are mainly encrypted; 70 layers of boundary layer grids are set, the first layer height of the wing surface grid is 0.01mm, and the growth ratio is about 1.1 to meet the computational model for y + Value requirements; Finally, the mesh quality of each airfoil flow area is higher than 0.6, and the mesh structure is as follows Figure 4 ; The grid is updated to achieve faster convergence and optimize the flow field calculation results, such as Figure 5 ; Mainly optimize the rear mesh of the bulge.

[0102] Furthermore, the step 4 is specifically to use air as the calculation working fluid, and its inlet flow velocity is 13.1 m / s. At this time, the flow is simplified to a constant temperature incompressible motion, which satisfies the control equation in fluid mechanics; the continuity equation:

[0103]

[0104] Momentum equation:

[0105]

[0106] Where: u i is the speed (m / s), i=1,2,3; p is the pressure (Pa); x i is the coordinate (m); f i is the mass force (N / kg); t is the time (s); v is the kinematic viscosity (Pa·s);

[0107] At present, scholars widely adopt the idea of ​​turbulent average motion proposed by Reynolds, which expresses the instantaneous value as the sum of the average value and the pulsation value, that is:

[0108]

[0109] Where D' is the pulsation value, is the average value, and D is the instantaneous value;

[0110] At this time, the above two equations will become:

[0111] Conservation of mass:

[0112]

[0113] Conservation of momentum (Reynolds equation):

[0114]

[0115] Where: is the Reynolds stress.

[0116] However, after the introduction of Reynolds stress, the number of equations is insufficient to be solved; therefore, it is necessary to select appropriate turbulence model equations to link the pulsation term and the time-averaged term in order to solve the equation.

[0117] Furthermore, the step 5 is specifically that the eddy viscosity model assumes:

[0118]

[0119] Where: μ t is the turbulent viscosity (Pa·s); k is the turbulent kinetic energy (m2 / s2); δ ij is the Kronecker symbol;

[0120] Considering that this calculation is a problem of aerodynamic flow near the wing surface, the SA model, Transition SST and DES models suitable for solving the flow field around the airfoil are used to calculate the lift coefficient curve of the NACA 0012 original airfoil. The results are shown in Figure 6 As shown. The survey found that the maximum lift coefficient of NACA 0012 at the stall angle of 9° under this Reynolds number is about 0.9. By comparing the calculation time and the external characteristics of the near-wing section, in terms of calculation time: the DES model takes the longest time to calculate, the transition model takes less time to complete the calculation than the DES model, the SA model is the fastest to complete the calculation, and the DES model does not have an advantage in large-scale calculations; in terms of calculation results: the three calculation models all perform well when the wing surface is in an attached flow state at a small angle of attack. When approaching the stall point, the calculated value of the SA model deviates seriously, and the other two values ​​have a stall point lag. At a large angle of attack, the Transition SST calculation result is closer to the stall point and the maximum lift coefficient value, and there are certain differences between the other two models. Therefore, from the perspective of external characteristics, it is more reliable to use the Transition SST model as a calculation model.

[0121] The SST k-ω model considering transition is adopted, and the model equations are shown in formulas (8) to (11);

[0122]

[0123]

[0124]

[0125]

[0126] Where: γ is the intermittent factor, P γ1 and E γ1 is the transition source term, P γ2 and E γ2 is the laminar source term, Re θt is the transition momentum thickness Reynolds number, μ t is the turbulent viscosity, σ θt is the diffusion coefficient, P θt is the source term, Γ k is the effective diffusion rate of turbulent kinetic energy k, Γ ω , G ω , Y ω , D ω are the effective diffusivity, generation term, dissipation term and cross-diffusion term of ω, respectively. is the product of the effective intermittent factor and the generated term of the original k equation in the SSTk-ω model, It is the product of the modified intermittency factor compared with 0.1 and 1 and the dissipation term of the original k equation.

[0127] Although the model has good calculation results at small and large angles of attack, the turbulent kinetic energy dissipation is overestimated at medium angles of attack, resulting in the separation point moving forward, the laminar separation bubble size being slightly larger, and the lift coefficient being smaller; the turbulent kinetic energy dissipation is underestimated at large angles of attack, resulting in a larger lift coefficient. Adjust the parameter α1 to 0.335 before stalling and adjust the parameter to 0.335 after stalling. is 0.11, and the surface roughness height of the wing surface is changed to 0.01 mm. The numerical simulation of the original wing section has achieved good results, such as Figure 8 .

[0128] Furthermore, the step 6 is specifically as follows: the fluid control equation is a nonlinear partial differential equation group which is difficult to solve directly and needs to be discretized; the finite volume method is used for discretization, and the pressure and velocity are solved by the SIMPLEC algorithm;

[0129] The variable Φ discretizes the control equation using the finite volume method:

[0130]

[0131] Where: Γ is the generalized diffusion coefficient of Φ; ρ is the fluid density; u i is the fluid velocity;

[0132] Integrating the above equation on the control volume yields:

[0133]

[0134] Using the Gauss-Green formula to simplify:

[0135]

[0136] The time step is 0.002s, and each iteration step is repeated 40 times. The convergence standard is that the residual error is less than 10 -4 The inlet of the computational domain is set as a velocity inlet with a velocity of 13.1 m / s and a turbulence intensity of 0.2%; the planes where the two ends of the airfoil are located are set as symmetry conditions; the boundary condition of the wing section surface is selected as a no-slip wall; and the pressure outlet is selected at the rear of the computational domain.

[0137] Since the grid density has a great influence on the accuracy of numerical simulation, when the grid density is not large, the larger the grid density, the more accurate the flow field information that can be obtained. However, the problem that follows is that as the grid density gradually increases, the cost is longer calculation time and higher computer performance. Therefore, it is necessary to first perform preliminary calculations on grids with different node densities to find the appropriate number and density of grids for further calculations.

[0138] Incoming flow velocity 13.1m / s, Re=1.8×10 5 , the original wing section with an angle of attack of 8°, the single-convex airfoil, the double-convex airfoil, the triple-convex airfoil and the thirteen-convex airfoil, and the Richard extrapolation method were used to verify the independence of three sets of grids with different numbers. The following is a brief introduction to the formulas needed for the Richard extrapolation method:

[0139] (1) Define the grid height h, for a three-dimensional object:

[0140]

[0141] Where V is the volume and N is the total number of grid cells used for calculation.

[0142] (2) Three groups of grids with significantly different coarseness and fineness were selected for verification, and the grid refinement factor r = h coarse / h fine Should be greater than 1.3.

[0143] (3) Take three sets of different grid heights h1<h2<h3 and define r 21 =h2 / h1, r 32 =h3 / h2 Use the above defined variables to calculate the surface order p.

[0144]

[0145]

[0146] s=1.sign(ε 32 / ε 21 ) (18)

[0147] Where: ε 32 =φ3-φ2,ε 21 =φ2-φ1; if 0<ε 32 / ε 21 <1, the grid convergence condition is monotonic convergence; ε 32 / ε 21 <0 means oscillation convergence; 1 < ε 32 / ε 21 To diverge.

[0148] (4) Calculate the extrapolated value φ ext ,

[0149]

[0150]

[0151] (5) Calculate and report the following error estimates and surface accuracy p,

[0152] Approximate relative error:

[0153]

[0154] Extrapolation relative error:

[0155]

[0156] Fine mesh convergence index:

[0157]

[0158] When using the above method, in order to obtain high credibility, it is necessary to pay attention to several application criteria: ensure that the iterative calculation of each grid converges well, otherwise it will lead to large numerical calculation discrepancies; the results of the coarse grid should be close to the exact solution, or at least ensure that the results of the coarsest grid are qualitatively correct; if a low Reynolds number turbulence model is used, the coarsest grid should be able to ensure that the turbulence model is accurate to y + The selected turbulence model requires the first layer of grid y on the wing wall to be + Less than 1. + The value can be adjusted by controlling the height of the first-layer grid, and its definition is:

[0159]

[0160] Where: τ ω is the wall shear stress, N / m 2 ; ρ is the fluid density, kg / m 3 ; Δn is the height of the first layer of the wall grid, m; ν is the kinematic viscosity, m 2 / s.

[0161] Taking the original wing section as an example, it can be seen from the results of numerical simulation that y + Less than 1, such as Fig. 9 ,y + The maximum value is 0.859109, which meets the requirements of the turbulence model.

[0162] Furthermore, the step 7 is specifically as follows: lift-drag coefficient curves of three different amplitude conditions are as follows: Fig.11From the two figures, we can see that the lift-drag coefficient curves after 16° angle of attack are relatively similar. The obvious difference is that the larger the amplitude of the 14° angle of attack condition, the smaller the lift coefficient and the larger the drag coefficient. Combined with the lift coefficient curve of its basic airfoil, it can be found that the external characteristics of the S condition under this condition are closer to the values ​​of its basic wing section. The B condition has a very small lift coefficient under this condition, indicating that a large separation area has been produced on the wing surface at this time, causing the lift coefficient to drop rapidly. Overall, the step-type stall process can still be seen, and it can be concluded that the leading edge bulge amplitude parameter will not affect whether the step-type stall process will occur, but it will affect the critical angle of attack that occurs, as well as the value of the lift-drag coefficient when approaching the stall.

[0163] For five typical working conditions, namely, the incoming flow angles are 14°, 16°, 18°, 20° and 22°, the airfoil limit streamlines are extracted. Fig.12 , is a comparison of the extreme streamlines of the airfoil in the S condition and the B condition. It can be found that the leading edge bulges with three different bulge amplitudes can all cause the airfoil to produce a unilateral stall phenomenon. At an angle of attack of 14°, the separation zone formed on the trailing edge of the airfoil in the S condition is a certain distance away from the leading edge, and the separation zones in the other two conditions have moved to the leading edge of the airfoil; the distribution of the separation zones from the 16° to 18° angles of attack is basically the same; there is a big difference at the 20° angle of attack, and it can be clearly found that the right side of the bulge in the S condition is already in a completely separated state, while there is still an area near the wing tip that has not yet entered the separation state on the large separation side of the M condition and the B condition; at an angle of attack of 22°, the airfoils in the three conditions are all in a large separation state. The range of the attachment flow caused by the leading edge in the three conditions is closely related to the amplitude, indicating that the leading edge bulge of the airfoil does play a role in separating the flow field, regardless of the bulge amplitude. The bulge amplitude affects the degree of influence on the flow field. The larger the amplitude, the more significant the impact on the flow field. The unilateral stall phenomenon occurs earlier at the angle of attack, and the range of the attached flow increases at a large angle of attack.

[0164] From the perspective of pressure distribution, the low pressure area at the leading edge of the S condition is more obvious, so it contributes more to the lift coefficient of the airfoil at 14°. At the same time, it is found that as the angle of attack increases, the area of ​​the separation zone gradually increases, and the pressure at the trailing edge of the airfoil drops rapidly. When the flow field is separated or the final angle of attack increases to both sides entering the separation state, the leading edge pressure can be seen to rise rapidly. Therefore, there is a direct connection between the rapid increase in leading edge pressure and the decrease in lift coefficient.

[0165] Based on the above analysis of the impact of three different amplitudes on the flow field, the small amplitude ensures that the airfoil has a step-type stall process, and the first stall process occurs slightly later than other amplitude conditions. At the same time, the impact on the external characteristics of the airfoil after a unilateral stall occurs is basically the same as that of other amplitudes. In practical applications, it can solve the problem that the airfoil deviates from the designed angle of attack range when an emergency occurs during use. When the wing section with a single protrusion is increased to the critical angle of attack, a unilateral stall phenomenon occurs first. It ensures that the airfoil still has a good lift acquisition capability at this time. At the same time, the airfoil enters a complete stall angle greater than the stall angle of the basic airfoil, which increases the critical safety range of the airfoil.

[0166] Further, the step 8 is specifically that the amplitudes of the protrusions Ⅰ1 and Ⅱ2 are 0.15c and 0.05c respectively. Due to the large deformation near the protrusions, the first layer height of the airfoil must still be about 0.01mm to meet the requirements of the turbulence model. The lowest mesh quality is reduced to 0.45 at the end. After understanding that the airfoil with no spacing always has a trend of changing from an expansion type to a contraction type, and understanding the influence of the amplitude of the protrusion on the airfoil flow, a double-protrusion airfoil with large and small protrusions is used to achieve further control of flow separation and attachment.

[0167] The high-energy flow always deflects from the leading edge bulge to the side with smaller bulge amplitude. At the same time, the calculation results of multiple calculations for a single working condition are consistent, which eliminates the problem of randomness of unilateral stall in the calculation process of single and double bulges. The reason why the symmetrical flow field is obtained in the calculation of the double-bulge airfoil with no spacing is that the high-energy flow behind the two bulges has the same kinetic energy distribution, so when converging to the rear of the valley, the spanwise velocities cancel each other out and become 0, so that the flow presents two-dimensional characteristics in the valley section. For different bulge amplitudes, the kinetic energy of the rear of the large-amplitude bulge is higher, resulting in the convergence of the two flows, which manifests as the large-amplitude attachment flow "entraining" the small-amplitude attachment flow to the side with small amplitude. At the same time, it can be observed that the deflection becomes increasingly intense with the increase of the angle of attack. When the angle of attack increases to 18°, the high-energy flow dissipates rapidly in the deflection and cannot reach the trailing edge of the airfoil.

[0168] By studying the vorticity distribution in the flow section closest to the leading edge, it was found that the larger the bulge amplitude, the stronger the intensity of the vortex caused by the flow, resulting in the formation of an overall asymmetric vortex structure at the leading edge, causing flow deflection, and ensuring that the small-amplitude side maintains the attached flow during a sufficiently large range of attack angle changes.

[0169] Example 2

[0170] The small protrusion is protrusion II2, and the large protrusion is protrusion I1.

[0171] Figure 3 3D schematic diagram of the leading edge combined convex structure airfoil for controlling the airfoil attachment flow in an embodiment of the present invention. Figure 3As shown, in the implementation process of this example, the focus is on the leading edge protrusion structure and the transition between it and the basic airfoil. Through the analysis of the existing technology, the airfoil with a single leading edge protrusion will cause a step-type stall process in the stall process of the airfoil when the protrusion amplitude is 5%, 10% and 15% of the chord length, accompanied by a unilateral stall phenomenon, and random deflection phenomena exist. In this example, the protrusion amplitude of 5% and 15% of the chord length is selected as the small and large protrusion amplitudes of the airfoil, respectively, and the convex peak section of the airfoil is generated from the maximum thickness point of the airfoil, that is, 34% of the chord length, and the rear part remains consistent with the basic airfoil.

[0172] Fig.13 The single convex airfoil of the prior art has a Re of 1.8×10 5 and schematic diagram of the suction surface separation area at an attack angle of 16°; Figure 4 The single convex airfoil of the prior art has a Re of 1.8×10 5 and schematic diagram of the suction surface separation area at an attack angle of 18°.

[0173] like Fig.14 and Fig.15 As shown, in the prior art, it is analyzed that at an angle of attack of 16°, the airfoil separation zone is first mainly distributed on the right side of the protrusion, and the deflected attachment flow is biased to the left side of the protrusion; at an angle of attack of 18°, the airfoil separation zone is first mainly distributed on the left side of the protrusion, and the deflected attachment flow is biased to the right side of the protrusion. The first-step stall angle of attack is smaller than the stall angle of attack of the basic airfoil, and the second-step stall angle of attack is larger than the stall angle of attack of the basic airfoil, which effectively extends the use angle of attack of the airfoil. The problem is that the separation zone appears on which side of the protrusion randomly, making the flow difficult to control.

[0174] The present invention optimizes the above problems by utilizing numerical simulation. Fig.16 The leading edge combined convex structure airfoil of the control airfoil attachment flow in the embodiment of the present invention is at Re = 1.8 × 10 5 and schematic diagram of the suction surface separation area at an attack angle of 12°; Fig.17 The leading edge combined convex structure airfoil of the control airfoil attachment flow in the embodiment of the present invention is at Re = 1.8 × 10 5 and schematic diagram of the suction surface separation area at an attack angle of 14°; Fig.18 The leading edge combined convex structure airfoil of the control airfoil attachment flow in the embodiment of the present invention is at Re = 1.8 × 10 5 and schematic diagram of the suction surface separation area at an attack angle of 16°.

[0175] Fig.15 , Fig.16 and Fig.17 From the calculation results, it can be found that the control of the separation zone and the deflected attachment flow is achieved by adding small protrusions. Figure 7 , V 2It can be found in the cloud map that the high-energy flow beam always deflects from the leading edge bulge to the side with a smaller bulge amplitude. At the same time, the calculation results of multiple calculations for a single working condition are consistent, which eliminates the problem of randomness of unilateral stall in the calculation process of single and double bulges. The large-amplitude bulge has higher kinetic energy at the rear, resulting in the convergence of the two flows, which manifests as the large-amplitude attachment flow "entraining" the small-amplitude attachment flow to the side with a small amplitude. At the same time, it can be observed that as the angle of attack increases, the deflection becomes increasingly intense. When the angle of attack increases to 18°, the high-energy flow beam dissipates rapidly during the deflection and cannot reach the trailing edge of the airfoil. A study of the vorticity distribution in the flow section closest to the leading edge found that the larger the bulge amplitude, the stronger the intensity of the vortex caused by the flow, resulting in the formation of an overall asymmetric vortex structure at the leading edge, resulting in flow deflection, ensuring that the small-amplitude side maintains the attachment flow over a sufficiently large range of angle changes.

[0176] The invention also describes the flow control principle of the leading edge combined protrusion structure for controlling the airfoil attachment flow.

[0177] Fig.15 , Fig.16 and Fig.17 V x =0 isosurface and streamwise vorticity cloud diagram, in which the convex section and the root section are defined as the spanwise section of the airfoil. Extract the streamwise vorticity distribution on the streamwise section, analyze it using the right-hand system, and use the positive and negative values ​​of the vorticity to determine the direction of vortex rotation. It can be seen that the leading edge vortex of the airfoil has alternating positive and negative values, that is, the vortex rotation direction is alternating. Simplify and analyze the two typical combinations, analyze the vortex pair located between the two root sections, the left side of the convex section is a clockwise rotating vortex, and the right side of the convex section is a counterclockwise rotating vortex. The two vortices form a vortex pair that adds a downward velocity to the fluid in the convex section, producing a strong downwash effect; on the contrary, analyze the vortex pair located on both sides of the two root sections, the left side of the root section is a counterclockwise rotating vortex, and the right side of the root section is a clockwise rotating vortex. The two vortices form a vortex pair that adds an upward velocity to the fluid in the root section, producing a strong upwash effect. During the installation and use of the airfoil, the angle between the airfoil chord direction and the actual incoming flow direction is the actual angle of attack or the incoming flow angle of attack. Due to the downwash effect, the airfoil feels the fluid flow not only as an incoming flow velocity but also as a downward downwash velocity. The two velocity vectors are synthesized to form the relative motion between the airfoil section and the fluid. Therefore, the effective incoming flow angle of attack felt by the airfoil is the angle between the relative incoming flow and the airfoil chord, which is the difference between the actual angle of attack and the downwash angle. Similarly, it can be analyzed that due to the upwash effect, the airfoil feels the fluid flow not only as an incoming flow velocity but also as an upward upwash velocity. The two velocities are synthesized to form the relative motion between our airfoil section and the fluid. Therefore, the effective incoming flow angle of attack felt by the airfoil is the angle between the relative incoming flow and the airfoil chord, which is the sum of the actual angle of attack and the upwash angle. After the above analysis, it can be concluded that the downwash effect reduces the effective angle of attack, while the upwash effect increases the effective angle of attack.

Claims

1. A method for controlling the airfoil attachment flow of a leading edge combined convex structure, characterized in that: The flow control method uses a leading edge combined convex structure to control the airfoil attachment flow, and the flow control method specifically comprises the following steps: Step 1: Enter various parameters and edit various conditions; Step 2: Perform geometric modeling according to the editing conditions and determine the airfoil model used for calculation; Step 3: Mesh the airfoil model according to step 2; Step 4: Calculate the basic control equations of the fluid according to the grid division in step 3; Step 5: Select and modify the turbulence model for the basic control equation of the fluid; Step 6: Select boundary conditions and use the discretization numerical method based on the basic fluid control equation in step 4; Step 7: Determine the leading edge combined protrusion structure according to the influence of the change in amplitude of the single protrusion; Step 8: Determine the attachment area and the separation area according to the random flow under the working condition of the leading edge combined convex structure control; Step 9: Verify the feasibility of the leading edge combined protrusion structure; The leading edge combined protrusion structure comprises a basic airfoil (3) and a leading edge combined protrusion, the basic airfoil (3) is provided with a leading edge combined protrusion, the leading edge combined protrusion comprises a protrusion I (1) and a protrusion II (2), the protrusion I (1) and the protrusion II (2) are arranged adjacent to each other, the front end contour lines of the protrusion I (1) and the protrusion II (2) are sinusoidal, and the period of the protrusion I (1) and the protrusion II (2) is 25% of the chord length; The amplitude of the protrusion I (1) is 15% of the chord length; the amplitude of the protrusion II (2) is 5% of the chord length.

2. The airfoil attachment flow control method according to claim 1, characterized in that: The geometric modeling in step 2 is specifically as follows: the basic airfoil contour line is drawn using UG software, the wing section chord length is 200 mm, the span width is 3.25 times the chord length, the maximum thickness is 21% of the chord length and is located at 34% of the chord length, the leading edge modified protrusion adopts a sinusoidal modified wing section peak section with a wavelength of 0.25 times the chord length and an amplitude of 0.1 times the chord length, and is generated by an outward expansion method. The coordinate point generation method is determined by formula (1) and the airfoil contour line is modeled in the same way: In the formula, (x i ′,y i ′) is the coordinate point of the convex peak section after modification, (x i ,y i ) is the reference wing section coordinate point, x m is the horizontal coordinate of the maximum thickness point of the wing section, A is the bulge amplitude, where i = 1, 2, ..., k, the subscript i is the i-th point constituting the two-dimensional contour line of the airfoil, and the subscript m is the m-th point corresponding to the maximum thickness point of the airfoil; In order to ensure that the flow at the leading edge of the airfoil and the flow at the exit of the calculation domain are fully developed, appropriate extension is performed in the flow direction. Finally, the inlet of the calculation domain is 3000mm away from the leading edge of the airfoil, the outlet is 5000mm away from the trailing edge of the airfoil, and the span width is 650mm.

3. The airfoil attachment flow control method according to claim 1, characterized in that: Specifically, step 3 is to set 70 layers of boundary layer grids, the first layer height of the wing surface grid is 0.01 mm, and the growth rate is 1.1 to meet the calculation model for y + value requirements; finally, the mesh quality of each airfoil flow area is higher than 0.6, and the mesh is updated to achieve faster convergence and optimize the flow field calculation results, mainly for the rear mesh of the bulge.

4. The airfoil attachment flow control method according to claim 1, characterized in that: Specifically, step 4 uses air as the calculation working fluid, and its inlet flow velocity is 13.1 m / s. At this time, the flow is simplified to a constant temperature incompressible motion, which satisfies the control equation in fluid mechanics; Continuity equation: Momentum equation: Where: u i is the velocity, i=1,2,3; p is the pressure; x i is the coordinate; f i is the mass force; t is the time; v is the kinematic viscosity; The idea of ​​turbulent average motion is adopted, and the instantaneous value is expressed as the sum of the average value and the pulsation value, that is: Where D' is the pulsation value, is the average value, and D is the instantaneous value; At this time, the above two equations will become: Conservation of mass: Conservation of momentum is the Reynolds equation: Where: is the Reynolds stress; However, after the introduction of Reynolds stress, the number of equations is insufficient to be solved; therefore, it is necessary to select appropriate turbulence model equations to link the pulsation term and the time-averaged term in order to solve the equation.

5. The airfoil attachment flow control method according to claim 1, characterized in that: Specifically, the step 5 is that the eddy viscosity model assumes: Where: μ t is the turbulent viscosity; k is the turbulent kinetic energy; δ ij is the Kronecker symbol; The SSTk-ω model considering transition is adopted, and the model equations are shown in formulas (8) to (11); Where: γ is the intermittent factor, P γ1 and E γ1 is the transition source term, P γ2 and E γ2 is the laminar source term, Re θt is the transition momentum thickness Reynolds number, μ t is the turbulent viscosity, σ θt is the diffusion coefficient, P θt is the source term, Γ k is the effective diffusion rate of turbulent kinetic energy k, Γ ω , G ω , Y ω , D ω are the effective diffusivity, generation term, dissipation term and cross-diffusion term of ω, is the product of the effective intermittent factor and the generated term of the original k equation in the SSTk-ω model, It is the product of the modified intermittency factor compared with 0.1 and 1 and the dissipation term of the original k equation.

6. The airfoil attachment flow control method according to claim 1, characterized in that: Specifically, the step 6 is as follows: the fluid control equation is a nonlinear partial differential equation group which is difficult to solve directly and needs to be discretized; the finite volume method is used for discretization, and the pressure and velocity are solved by the SIMPLEC algorithm; The variable Φ discretizes the control equation using the finite volume method: Where: Γ is the generalized diffusion coefficient of Φ; ρ is the fluid density; u i is the fluid velocity; Integrating the above equation on the control volume yields: Using the Gauss-Green formula to simplify:

7. The airfoil attachment flow control method according to claim 2, characterized in that: Specifically, the parameter of the leading edge bulge amplitude will not affect whether the step-type stall process will occur, but will affect the critical angle of attack that will occur and the value of the lift-drag coefficient when approaching the stall; As the angle of attack increases, the area of ​​the separation zone gradually increases, and the pressure on the trailing edge of the wing drops rapidly. When the flow field is separated or the final angle of attack increases to the point where both sides enter a separated state, a rapid increase in leading edge pressure can be seen. Therefore, there is a direct connection between the rapid increase in leading edge pressure and the decrease in lift coefficient.

8. The airfoil attachment flow control method according to claim 2, characterized in that: Specifically, the amplitudes of protrusions I (1) and II (2) are 0.15c and 0.05c, respectively. Due to the large deformation near the protrusions, the first layer height of the airfoil must still be 0.01mm to meet the requirements of the turbulence model. The lowest mesh quality is reduced to 0.

45. After understanding that the airfoil with no spacing always has a trend of changing from an expansion type to a contraction type, and understanding the influence of the protrusion amplitude on the airfoil flow, a double-protrusion airfoil with large and small protrusions is used to achieve further control of flow separation and attachment. By studying the vorticity distribution in the flow section closest to the leading edge, it was found that the larger the bulge amplitude, the stronger the intensity of the vortex caused by the flow, resulting in the formation of an overall asymmetric vortex structure at the leading edge, causing flow deflection, and ensuring that the small-amplitude side maintains the attached flow during a sufficiently large range of attack angle changes.

Images