Coaxial contra-rotating propeller design method and system based on rapid pneumatic calculation method

Abstract

The invention discloses a coaxial contra-rotating propeller design method and system based on a rapid pneumatic calculation method, and relates to the technical field of aircraft design, and the method comprises the steps: obtaining the layout and parameter design of a coaxial contra-rotating propeller, and determining the blade load distribution in a cruising state through a Goldstein theory; calculating the thickness distribution and chord length distribution of the blades according to the dimensionless spanwise positions of the blades and the diameter of the propeller disc; an airfoil lift coefficient and an airfoil distribution are determined based on these data. The torsion distribution of the blades is calculated through the blade element theory, and the sweepback / sweepback distribution is determined according to pneumatic and structural requirements. A rapid momentum source pneumatic calculation method is used for evaluating whether the pneumatic performance meets the cruise and take-off states or not, and when the pneumatic performance meets the cruise and take-off states, coaxial contra-rotating propeller design is completed; and if not, updating chord length distribution, airfoil profile distribution and torsion distribution of the blades until the design requirements of the cruise and take-off states are met. According to the method, rapid design of the coaxial contra-rotating propeller can be achieved.

Description

Technical Field

[0001] The present application relates to the technical field of aircraft design, and in particular to a design method and system for coaxial counter-rotating propellers based on a rapid aerodynamic calculation method. Background Art

[0002] Propeller efficiency is the main factor that determines the cruising speed, range and endurance of aircraft with propellers as the main propulsion device. Coaxial counter-rotating propellers help control the geometric dimensions of the propeller and improve propulsion efficiency. This configuration of propellers consists of two coaxial reverse-rotating identical or similar propellers. Compared with conventional propellers, the presence of the rear propeller in its propulsion system can recover part of the circulation in the front propeller slipstream, so the propulsion efficiency is higher. Under a given size, counter-rotating propellers can provide more power than single propellers and have lower fuel consumption.

[0003] Due to the advantages of coaxial counter-rotating propellers in aerodynamics and other aspects, domestic and foreign researchers have conducted many studies on them, such as the study of the interference flow field characteristics of the front and rear propellers, the study of aerodynamic and noise characteristics, etc. However, in terms of propeller design, most of the research focuses on single-row propellers, and there is less research on the design process of coaxial counter-rotating propellers. In the preliminary design process of the propeller, it is necessary to use engineering methods to quickly evaluate its aerodynamic performance for iterative design. The aerodynamic theory used for single-row propellers is difficult to consider the mutual influence of the two propellers. Some scholars have developed some aerodynamic theories suitable for coaxial counter-rotating propellers based on the aerodynamic theory of single-row propellers based on the airflow model obtained by experiments or experience, such as the strip theory, but the value of the empirical coefficient is related to parameters such as aerodynamic layout and incoming flow conditions.

[0004] The momentum source method can be used to simulate the interference effect of propellers on the flow field. This method has the advantages of less computing resources and short computing cycle while meeting engineering accuracy. Since it was proposed by Rajagopalan and Chaffin in the 20th century, it has been widely used in engineering design. The basic idea of ​​the momentum source method is to use an action disk to replace the propeller, and add a momentum source term to the control equation in the area of ​​the action disk, so that the airflow momentum around the propeller disk changes to replace the effect of the blade on the surrounding air. Since this method can consider the influence of two propellers close to each other from the perspective of flow field momentum, and the unsteady aerodynamic characteristics of the coaxial counter-rotating propeller in the axial flow state within a rotation cycle have strong regularity, it is suitable for the aerodynamic characteristics analysis and downwash flow field characteristics simulation of the coaxial counter-rotating propeller in the axial flow state to a certain extent.

[0005] Although some research has been carried out on the aerodynamic, acoustic and structural characteristics of coaxial counter-rotating propellers at home and abroad, the existing coaxial counter-rotating propeller design process is not clear and systematic, and there are few calculation methods suitable for quickly evaluating its aerodynamic performance and it is affected by its aerodynamic layout and changes in incoming flow parameters. Therefore, the present invention proposes a set of reference coaxial counter-rotating propeller design processes, and uses the momentum source method as a rapid aerodynamic evaluation tool therein. The purpose of rapid design of coaxial counter-rotating propellers is achieved through the design process and the aerodynamic evaluation tool. Summary of the invention

[0006] The purpose of this application is to provide a coaxial counter-rotating propeller design method and system based on a rapid aerodynamic calculation method, which can realize the rapid design of the coaxial counter-rotating propeller.

[0007] To achieve the above objectives, this application provides the following solutions:

[0008] In a first aspect, the present application provides a design method for a coaxial counter-rotating propeller based on a fast aerodynamic calculation method, comprising:

[0009] Step 1: Obtain the layout design and working parameter design of the coaxial counter-rotating propeller; the layout includes propeller diameter, number of blades, spacing, rear propeller diameter cutting ratio, rotation speed and load distribution ratio; the working parameters include the incoming flow velocity and cruising state of the airfoil section in the spanwise position; the cruising state is the state of an aircraft equipped with a coaxial counter-rotating propeller.

[0010] Step 2: Based on the layout design and working parameter design, the Goldstein theory is used to determine the spanwise load distribution of the blades under cruising conditions.

[0011] Step 3: Calculate the thickness distribution and chord length distribution of the blade based on the dimensionless spanwise position of the blade and the disk diameter.

[0012] Step 4: Determine the blade spanwise airfoil lift coefficient according to the blade spanwise load distribution, blade thickness distribution and blade chord length distribution, and determine the blade airfoil distribution based on the blade spanwise airfoil lift coefficient.

[0013] Step 5: According to the incoming flow velocity of the airfoil section at the spanwise position and based on the blade element theory, determine the torsion distribution of the blade.

[0014] Step 6: Based on the aerodynamic performance and structural strength requirements, determine the forward / backward sweep distribution of the blade; the aerodynamic performance refers to ensuring that the local Mach number of each airfoil section in the direction perpendicular to the quarter chord line of the blade does not exceed the drag divergence Mach number corresponding to the cruise design point; the structural strength requirement refers to the moment of the blade around the pitch rotation axis under stress is not greater than the upper limit of the structural strength.

[0015] Step 7: Based on the rapid momentum source aerodynamic calculation method, determine whether the aerodynamic performance of the blades meets the design requirements for cruise and take-off states.

[0016] When the design requirements for cruising and take-off states are met, the coaxial counter-rotating propeller design is completed.

[0017] When the cruise and take-off state design requirements are not met, the chord length distribution, airfoil distribution and twist distribution of the blade are updated, and based on the updated chord length distribution, airfoil distribution and twist distribution, steps 5 to 7 are executed until the cruise and take-off state design requirements are met.

[0018] In a second aspect, the present application provides a coaxial counter-rotating propeller design system based on a fast aerodynamic calculation method, comprising:

[0019] A design parameter acquisition module is used to acquire the layout design and working parameter design of the coaxial counter-rotating propeller; the layout includes propeller diameter, number of blades, spacing, rear propeller diameter cutting ratio, rotation speed and load distribution ratio; the working parameters include the incoming flow velocity and cruising state of the spanwise position airfoil section; the cruising state is the state of an aircraft equipped with a coaxial counter-rotating propeller.

[0020] The blade spanwise load distribution determination module is used to determine the blade spanwise load distribution under cruising conditions based on layout design and working parameter design using the Goldstein theory.

[0021] The thickness distribution and chord length distribution calculation module is used to calculate the thickness distribution and chord length distribution of the blade according to the dimensionless spanwise position of the blade and the propeller disk diameter.

[0022] The airfoil distribution determination module is used to determine the blade spanwise airfoil lift coefficient according to the blade spanwise load distribution, blade thickness distribution and blade chord length distribution, and determine the blade airfoil distribution based on the blade spanwise airfoil lift coefficient.

[0023] The twist distribution calculation module is used to determine the twist distribution of the blade according to the incoming flow velocity of the airfoil section at the spanwise position based on the blade element theory.

[0024] The forward / backward sweep distribution determination module is used to determine the forward / backward sweep distribution of the blade based on aerodynamic performance and structural strength requirements; the aerodynamic performance refers to ensuring that the local Mach number of each airfoil section of the blade in the direction perpendicular to the quarter chord line does not exceed the drag divergence Mach number corresponding to the cruise design point; the structural strength requirement refers to the moment of the blade around the pitch rotation axis under stress state is not greater than the upper limit of the structural strength.

[0025] The evaluation module is used to determine whether the aerodynamic performance of the blades meets the design requirements for cruise and take-off states based on the fast momentum source aerodynamic calculation method.

[0026] When the design requirements for cruising and take-off states are met, the coaxial counter-rotating propeller design is completed.

[0027] When the design requirements for the cruise and take-off states are not met, the chord length distribution, airfoil distribution and torsion distribution of the blade are updated, and calculations are performed based on the updated chord length distribution, airfoil distribution and torsion distribution until the design requirements for the cruise and take-off states are met.

[0028] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0029] The present application provides a design method and system for coaxial counter-rotating propellers based on a rapid aerodynamic calculation method, step one: obtain the layout design and working parameter design information of the coaxial counter-rotating propeller. The layout design covers key elements such as propeller diameter, number of blades, spacing, rear propeller diameter cutting ratio, speed and load distribution ratio; the working parameters include the incoming flow velocity of the airfoil section at the spanwise position and the state of the aircraft carrying the propeller in the cruising state. Step two: Based on the layout design and working parameter design, the Goldstein theory is used to determine the spanwise load distribution of the blade in the cruising state. Step three: Combine the dimensionless spanwise position and propeller disk diameter data of the blade to accurately calculate the thickness distribution and chord length distribution of the blade. Step four: Based on the spanwise load distribution, thickness distribution and chord length distribution of the blade, determine the spanwise airfoil lift coefficient of the blade, and further determine the airfoil distribution of the blade accordingly. Step five: Based on the incoming flow velocity of the airfoil section at the spanwise position, combined with the blade element theory, accurately determine the torsion distribution of the blade. Step 6: Consider the aerodynamic performance and structural strength requirements comprehensively, and determine the forward / backward sweep distribution of the blade. Among them, the aerodynamic performance needs to ensure that the local Mach number of each airfoil section of the blade in the vertical direction of the quarter chord does not exceed the drag divergence Mach number corresponding to the cruise design point; the structural strength requirement means that the moment generated around the rotation axis of the blade under stress must exceed the structural standard. The moment around the pitch rotation axis is not greater than the upper limit of the structural strength. Step 7: Use the fast momentum source aerodynamic calculation method to evaluate whether the aerodynamic performance of the blade meets the design requirements of the cruise and take-off states. If it does, the design of the coaxial counter-rotating propeller is completed; when it does not meet the design requirements of the cruise and take-off states, the chord length distribution, airfoil distribution and torsion distribution of the blade are updated, and based on the updated data, steps five to seven are repeated until the design requirements of the cruise and take-off states are met. The method involved in this application is suitable for evaluating the aerodynamic performance of coaxial counter-rotating propellers under any aerodynamic layout. This method can take into account the interaction between the two propellers, and there is no need to rely on test data or empirical coefficients to adjust the inflow model. In order to further improve the computational efficiency of the momentum source method, the calculation speed is significantly improved by applying periodic boundary conditions, which greatly shortens the calculation time to 1 / n of the original time, thereby promoting the rapid design process of coaxial counter-rotating propellers. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0031] Figure 1 It is a flow chart of a method for designing coaxial counter-rotating propellers based on a rapid aerodynamic calculation method in one embodiment of the present application.

[0032] Figure 2 A design flow chart of a coaxial counter-rotating propeller provided in one embodiment of the present application.

[0033] Figure 3 A flow chart of a momentum source method suitable for coaxial counter-rotating propellers provided in one embodiment of the present application.

[0034] Figure 4 A grid diagram of a momentum source method for an isolated coaxial counter-rotating propeller provided in one embodiment of the present application; the left side of the diagram is a side view, and the right side is a longitudinal cross-sectional view.

[0035] Figure 5 A momentum source method grid for isolated coaxial counter-rotating propellers after applying periodic boundary conditions is provided in one embodiment of the present application.

[0036] Figure 6 A schematic diagram of an area for adding a momentum source term to a coaxial counter-rotating propeller provided in one embodiment of the present application.

[0037] Figure 7 A flow chart for solving a momentum source term is provided in one embodiment of the present application.

[0038] Figure 8 A schematic diagram of a periodic boundary condition provided for an embodiment of the present application.

[0039] Fig. 9 A comparison diagram of calculation results and test results when the incoming flow Mach number Ma=0.35 is provided for one embodiment of the present application; wherein (a) is a curve diagram of the total pull coefficient and the total power coefficient changing with the forward ratio; and (b) is a curve diagram of the comprehensive efficiency changing with the forward ratio.

[0040] Fig.10 This is a structural schematic diagram of a coaxial counter-rotating propeller design system based on a rapid aerodynamic calculation method in one embodiment of the present application. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0042] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0043] Embodiment 1

[0044] like Figure 1 As shown, this embodiment provides a design method for coaxial counter-rotating propellers based on a fast aerodynamic calculation method, including:

[0045] Step 1: Obtain the layout design and working parameter design of the coaxial counter-rotating propeller; the layout includes propeller diameter, number of blades, spacing, rear propeller diameter cutting ratio, rotation speed and load distribution ratio; the working parameters include the incoming flow velocity and cruising state of the airfoil section in the spanwise position; the cruising state is the state of an aircraft equipped with a coaxial counter-rotating propeller.

[0046] Step 2: Based on the layout design and working parameter design, the Goldstein theory is used to determine the spanwise load distribution of the blades under cruising conditions.

[0047] Step 3: Calculate the thickness distribution and chord length distribution of the blade based on the dimensionless spanwise position of the blade and the disk diameter.

[0048] Step 4: Determine the blade spanwise airfoil lift coefficient according to the blade spanwise load distribution, blade thickness distribution and blade chord length distribution, and determine the blade airfoil distribution based on the blade spanwise airfoil lift coefficient.

[0049] Step 5: According to the incoming flow velocity of the airfoil section at the spanwise position and based on the blade element theory, determine the torsion distribution of the blade.

[0050] Step 6: Based on the aerodynamic performance and structural strength requirements, determine the forward / backward sweep distribution of the blade; the aerodynamic performance refers to ensuring that the local Mach number of each airfoil section in the direction perpendicular to the quarter chord line of the blade does not exceed the drag divergence Mach number corresponding to the cruise design point; the structural strength requirement refers to the moment of the blade around the pitch rotation axis under stress is not greater than the upper limit of the structural strength.

[0051] Step 7: Based on the rapid momentum source aerodynamic calculation method, determine whether the aerodynamic performance of the blades meets the design requirements for cruise and take-off states.

[0052] When the design requirements for cruising and take-off states are met, the coaxial counter-rotating propeller design is completed.

[0053] When the cruise and take-off state design requirements are not met, the chord length distribution, airfoil distribution and twist distribution of the blade are updated, and based on the updated chord length distribution, airfoil distribution and twist distribution, steps 5 to 7 are executed until the cruise and take-off state design requirements are met.

[0054] Among them, in this embodiment, the steps of coaxial counter-rotating propeller design can be divided into: the first part is the layout and working parameter design, the second part is the blade shape design, both of which aim to obtain a coaxial counter-rotating propeller with better comprehensive performance, and the third part is the evaluation of the aerodynamic performance of the coaxial counter-rotating propeller. When carrying out the second part of the design, the aerodynamic performance of the coaxial counter-rotating propeller is evaluated and the propeller blade design is completed based on the layout and working parameters of the coaxial counter-rotating propeller determined in the first part.

[0055] Among them, Figure 2 As shown, in this embodiment, when executing step 101, the specific steps may be as follows:

[0056] Determine the layout and working parameter design of the coaxial counter-rotating propeller, such as propeller diameter, number of blades, pitch, rear propeller diameter cutting ratio, speed, load distribution ratio and other parameters.

[0057] Specifically, when selecting the propeller diameter, factors such as its structure, weight and space layout must be considered comprehensively. The selected diameter should ensure that the maximum thrust requirements for cruise performance and take-off are met, while ensuring that the noise level meets the specified standards. The cruise efficiency of the propeller is closely related to the disc load; reducing the disc load (i.e. increasing the propeller diameter) can improve efficiency because it reduces the induced speed and thus reduces the induced loss. Under the same disc load conditions, the counter-rotating propeller has higher efficiency than the single propeller. However, the efficiency of the counter-rotating propeller is less sensitive to changes in the disc load, and it can operate at higher disc loads without significantly reducing efficiency. However, a larger propeller diameter will have a negative impact on the weight of the propulsion system, because larger propellers are heavier and require heavier gearboxes to reduce their rotational speed to ensure that the tip speed remains within an appropriate range. Therefore, it is crucial to select the propeller diameter reasonably.

[0058] For example, when designing a small drone, engineers need to choose the right propeller diameter to meet its performance requirements. Considering the compact structure and weight limit of the drone, engineers may choose a propeller with a smaller diameter to reduce the overall weight. For example, if the take-off weight of the drone is 5 kg, engineers may choose a carbon fiber propeller with a diameter of 30 cm to ensure sufficient thrust and low noise levels. Although a smaller propeller diameter may result in a higher propeller disc load, thereby reducing cruising efficiency, this is acceptable considering the size and mission requirements of the drone. At the same time, in order to keep the propeller speed within a safe range, engineers will design a lightweight gearbox to ensure that the propeller operates efficiently without affecting the drone's endurance too much.

[0059] Specifically, the number of propeller blades has a significant impact on aerodynamics, acoustic properties and structural strength. In terms of aerodynamics, in order to maintain constant thrust, increasing the number of blades to increase the aspect ratio of the blades helps reduce tip losses and thus improve aerodynamic efficiency. From an acoustic point of view, increasing the total number of blades and ensuring that the number of front and rear blades does not have a common multiple can help reduce noise levels. In terms of structural design, in order to minimize blade stress and reduce the risk of flutter, a smaller number of blades and a larger chord length are better options. It is recommended that the total number of blades for coaxial counter-rotating propellers be between 14 and 20, with a difference of 2 to 3 blades between the front and rear blades. Considering the impact of load distribution on aerodynamic performance and the maximum acceptable stress of the blades on the structure, if the difference in the number of blades exceeds 3, it may have an adverse effect on the aerodynamic efficiency of the propeller.

[0060] Specifically, the parameter of the distance between the two propellers of the rotor has a relatively limited effect on aerodynamic efficiency, but it has a more significant impact on the noise level and structural weight. In this case, setting the distance between the two propellers to 0.2 to 0.3 times the diameter of the front propeller is a more reasonable range of values.

[0061] Specifically, the diameter of the rear propeller of the rotating propeller is trimmed: by reducing the diameter of the rear propeller, the interference of the front propeller tip vortex on the rear propeller can be reduced, thereby reducing the noise level generated by the rotating propeller. However, excessive trimming of the rear propeller diameter will have a significant negative impact on cruise efficiency. Typically, a 10-15% trimming ratio of the rear propeller diameter may cause a 0.5%-2% decrease in cruise efficiency. Therefore, when trimming the rear propeller diameter, a balance must be found between meeting aerodynamic performance and reducing noise.

[0062] Propeller speed: This parameter has a significant impact on aerodynamic performance and noise characteristics. Normally, under the premise of keeping the propeller thrust unchanged, the aerodynamic performance will improve with the increase of the speed. This is because the increase in speed causes the thrust component of the blade perpendicular to the propeller disc plane to increase, while the drag component in the propeller disc plane decreases, thereby improving the aerodynamic efficiency of the propeller. However, when the blade tip Mach number approaches 1, the aerodynamic and noise performance of the propeller will drop sharply due to the compressibility of the air and the generation of shock waves. Modern high-speed propeller design uses thin airfoils and swept technology to keep the blade tip Mach number between 0.9-1.0 in the cruising state and the blade tip Mach number between 0.6-0.7 in the take-off state, which is a relatively suitable parameter selection.

[0063] Load distribution between the two propellers of a counter-rotating propeller: This parameter mainly affects the aerodynamic performance of the counter-rotating propeller. Compared with a single propeller, the rear propeller of a coaxial counter-rotating propeller can recover the energy consumed by the front propeller to distort the air, so that under the same thrust and size conditions, the overall efficiency of the counter-rotating propeller is higher. Therefore, the comprehensive aerodynamic efficiency of the counter-rotating propeller is affected by the degree to which the rear propeller recovers the energy of the front propeller. When the torque generated or the power consumed by the two propellers of the counter-rotating propeller is evenly distributed, the aerodynamic efficiency is the highest. At this time, the circumferential distortion of the air behind the counter-rotating propeller is the smallest, and the circumferential induced loss is also the smallest. Under the same thrust conditions, the aerodynamic efficiency of the counter-rotating propeller is insensitive to small changes near the average load distribution. When the diameter of the rear propeller decreases, a load distribution slightly tilted toward the front propeller helps reduce the circumferential induced losses of the counter-rotating propeller.

[0064] Among them, when designing the blade shape of the second part, if Figure 2 As shown, steps 2 to 6 may be specifically as follows:

[0065] Specifically, when executing step 2, the spanwise load distribution of the blades in the cruising state is determined. From the perspective of optimal aerodynamic efficiency, the spanwise load distribution of the blades can be determined by the Goldstein theory.

[0066] Specifically, when executing step 3, the thickness distribution and chord length distribution of the blade are determined. This can be given based on the design experience of modern high-speed propellers. For example, the thickness and chord length distribution of a certain high-speed propeller are given by the following formula:

[0067]

[0068]

[0069] in, is the airfoil thickness, c is the airfoil chord length, D is the disc diameter and x is the dimensionless spanwise position of the blade.

[0070] Specifically, when executing step 4, the specific steps may be as follows:

[0071] The lift coefficient distribution of the blade spanwise airfoil is determined according to the thickness distribution and chord length distribution of the blade, the incoming flow conditions and the working parameters in the cruising state; the incoming flow conditions are determined according to the incoming flow velocity.

[0072] Based on the spanwise airfoil lift coefficient distribution of the blade, the airfoil distribution of the blade is determined; the spanwise airfoil lift coefficient distribution of the blade is such that when the blade is at a spanwise position of 0.75R, the lift coefficient ranges from 0.4 to 0.6.

[0073] Specifically, steps 4-5 need to clarify the airfoil distribution and torsion distribution of the blade. Based on the spanwise load distribution of the blade obtained in step 2, the blade thickness distribution and chord length distribution determined in step 3, and the incoming flow conditions and working parameters under the cruise state, the spanwise airfoil lift coefficient distribution of the blade can be preliminarily determined. Subsequently, the airfoil distribution and torsion distribution of the blade are determined based on this information. When selecting an airfoil, priority should be given to airfoils with a better lift-to-drag ratio under high-speed conditions to ensure efficiency under the cruise state; at the same time, an airfoil with a higher maximum lift coefficient should be selected to ensure sufficient pulling force during takeoff. Taking into account aerodynamic performance and acoustic effects, the lift coefficient at the spanwise position of the blade 0.75R should be maintained between 0.4 and 0.6. The determination of the torsion distribution can be achieved by analyzing the incoming flow velocity of the airfoil section at each spanwise position and applying the blade element theory.

[0074] When executing step 6, the forward sweep and backward sweep distribution of the blades must be accurately determined. By configuring the forward sweep and backward sweep distribution of the blades, it can be ensured that the local Mach number of each airfoil section in the direction perpendicular to the quarter chord is lower than the drag divergence Mach number of the cruise design point, thereby optimizing the aerodynamic performance and improving the acoustic characteristics. When configuring the forward sweep and backward sweep distribution of the blades, the relationship with the variable pitch rotation axis should also be considered to ensure that the torque around the rotation axis can meet the structural requirements when subjected to force. When performing CAD modeling of blades with forward sweep and backward sweep distribution, the airfoils at each spanwise position should be moved along the chord direction of the airfoil after the installation angle is arranged.

[0075] In this embodiment, the step of evaluating the aerodynamic performance of the coaxial counter-rotating propellers in the third part is step 7. When executing step 7, if Figure 3 As shown, the specific details can be as follows:

[0076] Based on the spacing between the two blades, a grid is generated for momentum source calculation of the coaxial counter-rotating propeller.

[0077] According to the diameters of the two blades, the mesh cells in the disk plane where the source term is applied are determined.

[0078] According to the rotation speed of the two blades and the number of blades, the size of the source term on the grid unit in the propeller disk plane is determined.

[0079] The source items on the grid cells in the disk plane of the two blades are substituted into the RANS equation, and the flow field is solved by iterative advancement to obtain a stable flow field considering the mutual influence of the two blades.

[0080] The aerodynamic performance of the blades is evaluated based on the stable flow field considering the interaction between the two propellers.

[0081] Among them, when generating a grid for momentum source calculation of a coaxial counter-rotating propeller according to the spacing between the two blades, the specific method can be as follows:

[0082] According to the spacing between the two blades, a cylindrical structured momentum source grid is generated for the coaxial counter-rotating propeller to carry out momentum source calculation; the cylindrical structured momentum source grid is used to make the two propeller disk planes located on both sides of the 1 / 2 height plane of the cylindrical momentum source grid, and the distances to the 1 / 2 height plane are equal.

[0083] Specifically, when the momentum source method is used to simulate the aerodynamic characteristics of an isolated coaxial counter-rotating propeller, a cylindrical structured momentum source grid is generated according to the spacing between the two propellers, so that the two propeller disk planes are located on both sides of the 1 / 2 height plane of the cylindrical momentum source grid, and the distances to the plane are equal, and the grids near the two propeller disks are encrypted. The generated grid is as follows: Figure 4 In addition, record the grid numbers corresponding to the height positions of the two propeller disk planes so that the source terms can be applied later.

[0084] This embodiment also introduces periodic boundary conditions in the momentum source method of coaxial counter-rotating propellers. Since the steady momentum source method allows the effect of the propeller on the flow field to be expressed in the form of time averaging, the flow field information in the propeller disk plane obtained by the solution is periodic. Therefore, the periodic flow field area can be artificially intercepted and the entire flow field can be simulated by assigning periodic boundary conditions, thereby reducing the amount of grids and improving the calculation efficiency. The grid of the momentum source method of isolated coaxial counter-rotating propellers after applying periodic boundary conditions is as follows: Figure 5 As shown in Figure 1, the parameter settings during mesh generation are basically consistent with the parameter settings of the complete momentum source mesh, except that only a few meshes are retained around the propeller disk.

[0085] Among them, when determining the grid cells in the disk plane where the source term is applied according to the diameters of the two blades, the specific method can be as follows:

[0086] The size of the propeller disk plane is determined according to the diameters of the two propeller blades, and the grid area in the propeller disk plane where the source term needs to be applied is determined; the source term is applied to the grid unit by a marking method; and the grid area includes a plurality of grid units.

[0087] Specifically, the basic idea of ​​the momentum source method is to use an action disk to replace the propeller, and add a momentum source term to the control equation in the area of ​​the action disk, so that the airflow momentum around the propeller disk changes to replace the effect of the blade on the surrounding air. The calculation process of the momentum source term mainly uses the blade element theory and Newton's third law (the law of action and reaction).

[0088] When using the momentum source method, we first need to determine the propeller disk position, that is, the momentum source term addition area. The two propeller disks of the coaxial counter-rotating propeller in the axial flow state are perpendicular to the incoming flow direction. The schematic diagram of the momentum source term addition area of ​​the coaxial counter-rotating propeller is shown in Figure 6 shown.

[0089] The area where the momentum source term is added is determined by the height position of the two propeller disc planes and the grid units in the propeller disc plane. In the first step, the corresponding height positions of the two propeller disc planes in the momentum source grid are determined. The grid units in the propeller disc plane can be determined by the diameters of the two propellers. When the distance from the grid point in the propeller disc plane to the center of the propeller disc plane is less than the propeller disc diameter, the grid point is considered to be a grid point in the propeller disc plane. The grid unit composed of all the grid points in the propeller disc plane is the grid unit in the propeller disc plane to which the source term needs to be applied.

[0090] Among them, when determining the upper source limit size of the grid unit in the propeller disk plane according to the rotation speed of the two propeller blades and the number of propeller blades, the specific method can be as follows:

[0091] According to the relevant parameters such as the rotation speed of the two propellers and the number of propeller blades, the source item size on the grid unit in the propeller disk plane is determined. Among them, it is necessary to clarify the momentum source item size on the grid unit in the propeller disk plane. Figure 7 The flowchart of the momentum source term solution is shown. Finally, the flow field information is solved by iterative advancement in combination with the CFD method. This part is consistent with the traditional momentum source term solution method, so it will not be elaborated here.

[0092] Compared with the traditional momentum source method, the momentum source method of coaxial counter-rotating propellers requires special attention to the following matters: According to the calculation theory of momentum source terms, source terms need to be added at the corresponding positions of the front and rear propeller disks, and the grid units in the propeller disk plane where the source terms are applied are determined based on the results of the second step; when applying the source terms, the size of the source terms on the grid units in the propeller disk plane needs to be determined based on the conditions such as the rotation speed of the two propellers and the number of propeller blades, and the size of the momentum source terms and their distribution forms in the two propeller disk planes may be different; in addition, since the front and rear propellers rotate in opposite directions, the tangential velocity calculation method of the airfoils in the two propeller disks is different, and the circumferential induction effect on the airflow is also in opposite directions. This is a key issue in correctly applying the momentum source method to the aerodynamic calculation of coaxial counter-rotating propellers.

[0093] Among them, when substituting the source item size on the grid unit in the disk plane of the two blades into the RANS equation, iteratively advancing the solution of the flow field, and obtaining a stable flow field considering the mutual influence of the two blades, the specific method can be as follows:

[0094] The source items on the grid cells in the disk plane of the two blades are substituted into the RANS equations, and the flow field is iteratively solved by using an improved CFD iterative propulsion method to obtain a stable flow field that takes into account the mutual influence of the two blades. The improved CFD iterative propulsion method is a CFD iterative propulsion method that introduces momentum source items into the control equations in each iterative step according to the local incoming flow conditions at the position of the coaxial counter-rotating propellers.

[0095] Specifically, the determined source item size on the grid unit in the two propeller disk planes is substituted into the RANS equation, and the flow field is iteratively advanced to solve. This part is the same as the traditional CFD iterative advancement method and will not be repeated here. During the calculation process, each iteration step will add a momentum source item to the control equation according to the local flow conditions of the coaxial counter-rotating propeller, and finally a stable flow field that takes into account the mutual influence of the two propellers is obtained.

[0096] In order to improve the calculation speed of the momentum source method of coaxial counter-rotating propellers, this embodiment uses periodic boundary conditions, and its schematic diagram is shown as follows: Figure 8 As shown, it needs to be used in conjunction with the momentum source method grid of an isolated coaxial counter-rotating propeller after applying periodic boundary conditions.

[0097] Assuming the symmetry plane is in the direction I, then the symmetry boundary i = i max The physical quantity at and i=1 is as follows:

[0098]

[0099]

[0100]

[0101] Where p is the pressure of the grid unit, ρ is the density of the grid unit, and subscript i is max / 1 means i=i max or the grid cell on i=1, 2 / i max -1 means i=2 or i=i max-1 The grid cells on the disc, u, v, and w are the velocity components of the grid cells in the three axes of the coordinate system. The relevant data such as the thrust, power consumption, and spanwise load distribution of the two propellers are obtained. After the calculated flow field reaches a stable state, the force exerted by each grid cell on the air in the disc plane can be calculated based on the application of the momentum source term, and then the thrust, power consumption, and spanwise load distribution of the two propellers can be derived.

[0102] Finally, determine whether the aerodynamic performance of the coaxial counter-rotating propeller meets the requirements.

[0103] That is, analyze whether the blade load distribution and aerodynamic performance in the cruise state meet expectations; analyze whether the aerodynamic performance in the take-off state meets the needs; if it does not meet the requirements, it is necessary to iteratively adjust the chord length distribution of the blade in step 3 and the airfoil distribution and torsion distribution of the blade in step 4.

[0104] This embodiment also provides a specific example for verification, which is as follows:

[0105] 1) In order to ensure that the established numerical simulation method can effectively analyze the aerodynamic characteristics of the coaxial counter-rotating propeller, the test data of the eight-blade coaxial counter-rotating propeller NACA3-(3)(05)-05 is used to verify the calculation method used in this embodiment. The diameters of the front and rear propellers of the counter-rotating propeller are both 0.91m, the distance between the two propellers is 0.1524m, both have 4 blades and the root cutting ratio is 0.36. The blades are composed of NACA-16 series airfoils and have similar geometric shapes, the same chord length distribution, different linear negative torsion slopes, and no forward and backward sweep distribution. The test fixed the blade angle and changed the rotation speed of the two propellers at multiple speeds in the incoming flow Mach number range of 0.35-0.925 to measure the aerodynamic performance of the coaxial counter-rotating propeller.

[0106] Verification and comparison of the coaxial counter-rotating propeller forward propulsion ratio J of each front propeller at the incoming flow Mach number of 0.53 F The corresponding total tension coefficient C T , total power coefficient C P , comprehensive efficiency η, such as Fig. 9 As shown in (a) and (b) in . When the forward propeller ratio is relatively large, the calculated results of the total thrust coefficient and the total power coefficient are basically consistent with the test results. When the forward propeller ratio is relatively small, the aerodynamic angle of attack of multiple blade sections of the front and rear propellers is large. At this time, these sections are in a stall state, and the momentum source method cannot make reliability predictions. Within the test range, the calculated results of the comprehensive efficiency changing with the forward propeller ratio are basically consistent with the test results. In summary, this shows that this calculation method has a certain reliability in evaluating the comprehensive aerodynamic performance of coaxial counter-rotating propellers, and can be used for preliminary engineering design or theoretical analysis of aerodynamic aspects of coaxial counter-rotating propellers within an appropriate range.

[0107] 2) Comparison of calculation results and calculation efficiency before and after applying periodic boundary by momentum source method:

[0108] In the comparison of this embodiment, the impeller disk of the complete cylindrical momentum source grid is evenly distributed with 90 grids, and the total number of grids is about 900,000. After applying the periodic boundary conditions, the impeller disk of the momentum source grid used retains only 3 grids, and the total number of grids is about 30,000. The calculation amount of using this grid is 1 / 30 of the calculation amount of using the complete cylindrical momentum source grid.

[0109] Table 1 Comparison of calculation results

[0110]

[0111] Among them, for the comparison of computational efficiency, the computational time consumed before applying the periodic boundary conditions is 16606.3 s, and the computational time consumed after applying the periodic boundary conditions is 643.3 s.

[0112] In summary, the application of periodic boundary conditions does not have much impact on the calculation results of the aerodynamic performance of the coaxial counter-rotating propeller, but the single calculation time is greatly reduced, which is shortened to 1 / 26 of the original calculation time, that is, the calculation time of this method is approximately shortened to 1 / n of the original calculation time, where n is equal to "the amount of grid before applying the periodic boundary conditions / the amount of grid after applying the periodic boundary conditions".

[0113] 3) Applicability of the momentum source method:

[0114] This method can be used to calculate the aerodynamic performance of coaxial counter-rotating propellers with arbitrary aerodynamic layouts, such as arbitrary pitch, combination of two-propeller disk diameters, combination of two-propeller blade numbers and combination of two-propeller speeds. The mutual influence of the two propellers can be considered and there is no need to correct and adjust the inflow models of the two propellers through experiments or empirical coefficients.

[0115] Embodiment 2

[0116] like Fig.10 As shown, this embodiment provides a coaxial counter-rotating propeller design system based on a fast aerodynamic calculation method, including:

[0117] The design parameter acquisition module 1001 is used to obtain the layout design and working parameter design of the coaxial counter-rotating propeller; the layout includes the propeller diameter, the number of blades, the spacing, the rear propeller diameter cutting ratio, the rotation speed and the load distribution ratio; the working parameters include the incoming flow velocity and the cruising state of the airfoil section in the spanwise position; the cruising state is the state of the aircraft equipped with the coaxial counter-rotating propeller.

[0118] The blade spanwise load distribution determination module 1002 is used to determine the blade spanwise load distribution in a cruising state by using the Goldstein theory based on the layout design and the working parameter design.

[0119] The thickness distribution and chord length distribution calculation module 1003 is used to calculate the thickness distribution and chord length distribution of the blade according to the dimensionless spanwise position of the blade and the diameter of the propeller disk.

[0120] The airfoil distribution determination module 1004 is used to determine the blade spanwise airfoil lift coefficient according to the blade spanwise load distribution, the blade thickness distribution and the blade chord length distribution, and determine the blade airfoil distribution based on the blade spanwise airfoil lift coefficient.

[0121] The twist distribution calculation module 1005 is used to determine the twist distribution of the blade according to the incoming flow velocity of the airfoil section at the spanwise position based on the blade element theory.

[0122] The forward / backward sweep distribution determination module 1006 is used to determine the forward / backward sweep distribution of the blade based on the aerodynamic performance and structural strength requirements; the aerodynamic performance refers to ensuring that the local Mach number of each airfoil section of the blade in the direction perpendicular to the quarter chord line does not exceed the drag divergence Mach number corresponding to the cruise design point; the structural strength requirement refers to the moment of the blade around the pitch rotation axis under the force state is not greater than the upper limit of the structural strength.

[0123] The evaluation module 1007 is used to determine whether the aerodynamic performance of the blade meets the design requirements of the cruise and take-off states based on the fast momentum source aerodynamic calculation method.

[0124] When the design requirements for cruising and take-off states are met, the coaxial counter-rotating propeller design is completed.

[0125] When the design requirements for the cruise and take-off states are not met, the chord length distribution, airfoil distribution and torsion distribution of the blade are updated, and calculations are performed based on the updated chord length distribution, airfoil distribution and torsion distribution until the design requirements for the cruise and take-off states are met.

[0126] The airfoil distribution determination module 1004 specifically includes:

[0127] The blade spanwise airfoil lift coefficient distribution determination submodule is used to determine the blade spanwise airfoil lift coefficient distribution according to the blade thickness distribution and chord length distribution as well as the incoming flow conditions and working parameters in the cruise state; the incoming flow conditions are determined according to the incoming flow velocity.

[0128] The airfoil distribution determination submodule is used to determine the airfoil distribution of the blade based on the spanwise airfoil lift coefficient distribution of the blade; the spanwise airfoil lift coefficient distribution of the blade is such that when the blade is at the spanwise position of 0.75R, the lift coefficient ranges from 0.4 to 0.6.

[0129] In summary, this application has the following technical effects:

[0130] The present application proposes a set of reference coaxial counter-rotating propeller design processes based on the aerodynamic, acoustic and structural characteristics of coaxial counter-rotating propellers, which can be used to guide the design of coaxial counter-rotating propellers with better aerodynamic efficiency, less aerodynamic noise and better structural characteristics; since the CFD high-precision aerodynamic calculation method has a large amount of calculation, in order to be able to evaluate the aerodynamic characteristics of the coaxial counter-rotating propellers and iteratively design them more quickly during the preliminary design process, the present application proposes a momentum source method suitable for evaluating the aerodynamic performance of coaxial counter-rotating propellers. This method can be used to calculate the aerodynamic performance of coaxial counter-rotating propellers with any aerodynamic layout, and can consider the mutual influence of the two propellers without the need to correct and adjust the inflow models of the two propellers through experiments or empirical coefficients; in order to further improve the calculation speed of the momentum source method, the calculation speed of this method is greatly improved by applying periodic boundary conditions, so that its calculation time is approximately shortened to 1 / n of the original calculation time, where n is equal to "grid volume before applying periodic boundary conditions / grid volume after applying periodic boundary conditions".

[0131] The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0132] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A design method for coaxial counter-rotating propellers based on a fast aerodynamic calculation method, characterized in that: The coaxial counter-rotating propeller design method comprises: Step 1: Obtain the layout design and working parameter design of the coaxial counter-rotating propeller; the layout includes propeller diameter, number of blades, pitch, rear propeller diameter cutting ratio, rotation speed and load distribution ratio; the working parameters include the incoming flow velocity of the airfoil section at the spanwise position and the cruising state; the cruising state is the state of the aircraft equipped with the coaxial counter-rotating propeller; Step 2: Based on the layout design and working parameter design, the Goldstein theory is used to determine the spanwise load distribution of the blades under cruising conditions. Step 3: Calculate the thickness distribution and chord length distribution of the blade according to the dimensionless spanwise position of the blade and the diameter of the propeller disk; Step 4: Determine the blade spanwise airfoil lift coefficient according to the blade spanwise load distribution, the blade thickness distribution, and the blade chord length distribution, and determine the blade airfoil distribution based on the blade spanwise airfoil lift coefficient; Step 5: According to the incoming flow velocity of the airfoil section at the spanwise position, based on the blade element theory, determine the torsion distribution of the blade; Step 6: Based on the aerodynamic performance and structural strength requirements, determine the forward / backward sweep distribution of the blade; the aerodynamic performance refers to ensuring that the local Mach number of each airfoil section in the direction perpendicular to the quarter chord line of the blade does not exceed the drag divergence Mach number corresponding to the cruise design point; the structural strength requirement refers to that the moment of the blade around the pitch rotation axis under the force state is not greater than the upper limit of the structural strength; Step 7: Based on the rapid momentum source aerodynamic calculation method, determine whether the aerodynamic performance of the blades meets the design requirements for cruise and take-off states; When the design requirements for cruising and take-off states are met, the coaxial counter-rotating propeller design is completed; When the cruise and take-off state design requirements are not met, the chord length distribution, airfoil distribution and twist distribution of the blade are updated, and based on the updated chord length distribution, airfoil distribution and twist distribution, steps 5 to 7 are executed until the cruise and take-off state design requirements are met.

2. A method for designing coaxial counter-rotating propellers based on a rapid aerodynamic calculation method according to claim 1, characterized in that: The step 3 specifically includes: According to the formula Calculate the thickness distribution of the blade; According to the formula Calculate the chord length distribution of the blade; in, is the airfoil thickness, c is the airfoil chord, D is the disk diameter, and x is the dimensionless spanwise position of the blade.

3. The design method of coaxial counter-rotating propellers based on a fast aerodynamic calculation method according to claim 1, characterized in that: The step 4 specifically includes: Determine the lift coefficient distribution of the blade spanwise airfoil according to the thickness distribution and chord length distribution of the blade and the incoming flow conditions and working parameters in the cruise state; the incoming flow conditions are determined according to the incoming flow velocity; Based on the spanwise airfoil lift coefficient distribution of the blade, the airfoil distribution of the blade is determined; the spanwise airfoil lift coefficient distribution of the blade is such that when the blade is at a spanwise position of 0.75R, the lift coefficient ranges from 0.4 to 0.

6.

4. The method for designing coaxial counter-rotating propellers based on a rapid aerodynamic calculation method according to claim 1, characterized in that: The step 5 specifically includes: According to the formula Calculate the installation angle of the profile of the blade at different spanwise positions; where: is the profile airfoil installation angle, V y is the axial flow velocity, V yi is the induced speed, ω is the rotational angular velocity, and α0 is the aerodynamic angle of attack corresponding to the lift coefficient of the profile airfoil; The installation angle of the cross-section airfoil at each spanwise position of the blade is calculated to determine the torsion distribution of the blade.

5. The method for designing coaxial counter-rotating propellers based on a rapid aerodynamic calculation method according to claim 1, characterized in that: Based on the rapid momentum source aerodynamic calculation method, determine whether the aerodynamic performance of the blades meets the design requirements for cruise and take-off states, including: Generate a grid for momentum source calculation of the coaxial counter-rotating propeller according to the spacing between the two blades; According to the diameters of the two blades, determine the grid cells in the disk plane where the source term is applied; According to the rotation speed of the two blades and the number of blades, the source item size on the grid unit in the propeller disk plane is determined; Substitute the source items on the grid cells in the disk plane of the two blades into the RANS equation, solve the flow field iteratively, and obtain the stable flow field considering the mutual influence of the two blades. The aerodynamic performance of the blades is evaluated based on the stable flow field considering the interaction between the two propellers.

6. A method for designing coaxial counter-rotating propellers based on a rapid aerodynamic calculation method according to claim 5, characterized in that: According to the spacing between the two blades, a grid is generated for the momentum source calculation of the coaxial counter-rotating propeller, including: According to the spacing between the two blades, a cylindrical structured momentum source grid is generated for the coaxial counter-rotating propeller to carry out momentum source calculation; the cylindrical structured momentum source grid is used to make the two propeller disk planes located on both sides of the 1 / 2 height plane of the cylindrical momentum source grid, and the distances to the 1 / 2 height plane are equal.

7. The method for designing coaxial counter-rotating propellers based on a rapid aerodynamic calculation method according to claim 5, characterized in that: According to the diameters of the two blades, the grid cells in the disk plane where the source term is applied are determined, including: The size of the propeller disk plane is determined according to the diameters of the two propeller blades, and the grid area in the propeller disk plane where the source term needs to be applied is determined; the source term is applied to the grid unit by a marking method; and the grid area includes a plurality of grid units.

8. The method for designing coaxial counter-rotating propellers based on a rapid aerodynamic calculation method according to claim 5, characterized in that: Substitute the source items on the grid cells in the disk plane of the two blades into the RANS equation, iteratively advance the solution of the flow field, and obtain the stable flow field considering the mutual influence of the two blades, including: The source items on the grid cells in the disk plane of the two blades are substituted into the RANS equations, and the flow field is iteratively solved by using an improved CFD iterative propulsion method to obtain a stable flow field that takes into account the mutual influence of the two blades. The improved CFD iterative propulsion method is a CFD iterative propulsion method that introduces momentum source items into the control equations in each iterative step according to the local incoming flow conditions at the position of the coaxial counter-rotating propellers.

9. A coaxial counter-rotating propeller design system based on a fast aerodynamic calculation method, characterized in that: include: A design parameter acquisition module is used to obtain the layout design and working parameter design of the coaxial counter-rotating propeller; the layout includes the propeller diameter, the number of blades, the pitch, the rear propeller diameter cutting ratio, the rotation speed and the load distribution ratio; The working parameters include the incoming flow velocity of the airfoil section at the spanwise position and the cruising state; the cruising state is the state of the aircraft equipped with coaxial counter-rotating propellers; The blade spanwise load distribution determination module is used to determine the blade spanwise load distribution under cruising conditions based on the layout design and working parameter design using the Goldstein theory; Thickness distribution and chord length distribution calculation module, used to calculate the thickness distribution and chord length distribution of the blade according to the dimensionless spanwise position of the blade and the diameter of the propeller disk; An airfoil distribution determination module is used to determine the blade spanwise airfoil lift coefficient according to the blade spanwise load distribution, the blade thickness distribution and the blade chord length distribution, and determine the blade airfoil distribution based on the blade spanwise airfoil lift coefficient; The twist distribution calculation module is used to determine the twist distribution of the blade according to the incoming flow velocity of the airfoil section at the spanwise position based on the blade element theory; A forward / backward sweep distribution determination module is used to determine the forward / backward sweep distribution of the blade based on aerodynamic performance and structural strength requirements; the aerodynamic performance refers to ensuring that the local Mach number of each airfoil section in the direction perpendicular to the quarter chord line of the blade does not exceed the drag divergence Mach number corresponding to the cruise design point; the structural strength requirement refers to that the moment of the blade around the pitch rotation axis under the force state is not greater than the upper limit of the structural strength; An evaluation module is used to determine whether the aerodynamic performance of the blades meets the design requirements for cruise and take-off states based on a fast momentum source aerodynamic calculation method; When the design requirements for cruising and take-off states are met, the coaxial counter-rotating propeller design is completed; When the design requirements for the cruise and take-off states are not met, the chord length distribution, airfoil distribution and torsion distribution of the blade are updated, and calculations are performed based on the updated chord length distribution, airfoil distribution and torsion distribution until the design requirements for the cruise and take-off states are met.

10. A coaxial counter-rotating propeller design system based on a fast aerodynamic calculation method according to claim 9, characterized in that: The airfoil distribution determination module specifically includes: The blade spanwise airfoil lift coefficient distribution determination submodule is used to determine the blade spanwise airfoil lift coefficient distribution according to the blade thickness distribution and chord length distribution as well as the incoming flow conditions and working parameters in the cruise state; the incoming flow conditions are determined according to the incoming flow velocity; The airfoil distribution determination submodule is used to determine the airfoil distribution of the blade based on the spanwise airfoil lift coefficient distribution of the blade; the spanwise airfoil lift coefficient distribution of the blade is such that when the blade is at the spanwise position of 0.75R, the lift coefficient ranges from 0.4 to 0.6.

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