A method for predicting the aerodynamic performance of a coaxial twin-bladed rotor

Abstract

The application belongs to the field of aircraft aerodynamic performance analysis, and discloses a coaxial double-blade aerodynamic performance prediction method, which comprises the following steps: S1: formulating a calculation state and a target, determining that the flight state for calculation and analysis is a hovering state, and the calculation target is hovering efficiency and drag coefficient; S2: selecting a reference model and setting coaxial blade aerodynamic calculation basic parameters; S3: after the blade basic parameters are determined, based on the set blade spacing or blade spacing range, total thrust coefficient or total thrust coefficient range, rotating speed, lower blade wake contraction ratio and upper and lower blade pitch angle sum, the thrust coefficient, drag coefficient and hovering efficiency of the upper and lower blades of the coaxial double blades under each total thrust coefficient and each blade spacing are obtained through BEMT inner layer iteration, BEMT middle layer iteration and BEMT outer layer iteration. The interference physical mechanism between the coaxial blades is determined through the application, and the influence of the double-blade interference can be accurately taken into account in the performance calculation of the coaxial blades.

Description

Technical Field

[0001] This application belongs to the field of aircraft aerodynamic performance analysis, and in particular relates to a method for predicting the aerodynamic performance of a coaxial twin-bladed propeller. Background Technology

[0002] Coaxial rotorcraft represent a significant future trend in aircraft design. Compared to traditional single-bladed rotors, coaxial rotors utilize the self-balancing of rolling torque and anti-torque by the opposing upper and lower blades. They offer advantages such as compact structure, high aerodynamic efficiency, and superior maneuverability and handling. With the same rotor disk area, coaxial rotors can carry a greater payload, playing a crucial role in high-altitude heavy-duty operations or other hazardous missions. Therefore, they are widely used in helicopters, particularly multi-bladed aircraft, such as the DJI T50 agricultural drone and the EHang eVTOL manned aircraft EH216-S, both employing a coaxial rotor configuration.

[0003] The flowchart and wake diagram of the traditional BEMT calculation method are as follows: Figure 1 and Figure 2 As shown. The traditional BEMT (Blade Element Momentum Theory) is based on the momentum blade element theory, a simplified momentum balance equation, only upper blade disturbances, a fixed wake contraction ratio, and neglects thrust torque balancing and uniform induced velocity to perform separate calculations for coaxial dual blades.

[0004] Although the influence of axial spacing was considered, wake contraction was introduced. However, it used an ideal fixed value. Furthermore, it neglects the influence of the lower blade on the upper blade, essentially treating the twin blades as two independent single blades. Adding a unidirectional disturbance (upper blade → lower blade) using empirical formulas and employing a uniform inflow velocity also fails to predict the impact of blade spacing on aerodynamic performance. This results in significant errors in the calculations.

[0005] To quickly and accurately predict the performance of coaxial dual-blade propellers and reduce computational costs, improving and optimizing the aerodynamic performance calculation of coaxial blades is crucial. Since the aerodynamic principles of coaxial blades differ significantly from those of conventional blades, the application of momentum blade element theory should also be modified accordingly to better fit the aerodynamic performance of coaxial dual-blade propellers.

[0006] Previous experiments have shown that the flow field characteristics of coaxial blades differ significantly from those of traditional single blades, such as... Figure 3 and Figure 4As shown, due to the counter-rotating and close proximity of the upper and lower blades, there is significant aerodynamic interference between them. Most of the lower blade is within the strong downwash flow of the upper blade, while the upper blade is also affected by the aerodynamic interference from the lower blade. The interference losses experienced by both affect the aerodynamic performance of the coaxial dual-blade propeller and cannot be ignored.

[0007] The most significant characteristic of coaxial rotorcraft is its use of coaxial blades for flight. Coaxial rotorcraft exhibits aerodynamic interference between the upper and lower blades, resulting in significant differences in the airflow environment between them. This leads to substantial changes in the flow field and aerodynamic forces between the upper and lower blades compared to a single-blade rotor, making the aerodynamic characteristics analysis of coaxial rotorcraft crucial. However, existing research often uses traditional momentum-blade element thrust when calculating coaxial rotorcraft problems, only considering the influence of the upper blade on the lower blade, and lacking research on the influence of the lower blade on the upper blade.

[0008] Therefore, this invention innovatively proposes a method for predicting the aerodynamic performance of coaxial twin blades based on this problem. While considering the inter-blade interference factor, it introduces the wake contraction ratio to more accurately and comprehensively calculate the aerodynamic performance of coaxial twin blades. Summary of the Invention

[0009] The purpose of this application is to disclose a method for predicting the aerodynamic performance of a coaxial dual-blade propeller, addressing the differences in airflow environment and aerodynamic interference phenomena between the upper and lower blades of a coaxial dual-blade propeller. This method determines the physical mechanism of interference between the coaxial dual blades and is of great significance for the design and development of future aircraft.

[0010] The objective of this application is achieved through the following technical solution: A method for predicting the aerodynamic performance of a coaxial twin-bladed propeller, the method comprising: S1: Define the calculation state and objectives, determine that the flight state to be analyzed is the hovering state, and the calculation objectives are hovering efficiency and thrust coefficient; S2: Select the reference model and set the basic parameters for coaxial blade aerodynamic calculation; S3: After determining the basic blade parameters, based on the set blade spacing or blade spacing range, total thrust coefficient or total thrust coefficient range, rotational speed, and lower blade wake contraction ratio. and the pitch angle of the upper and lower blades and , Through BEMT inner layer iteration, BEMT middle layer iteration, and BEMT outer layer iteration, the thrust coefficient, pull coefficient, and hovering efficiency of the upper and lower blades of the coaxial twin blades under various total thrust coefficients and blade spacings are obtained.

[0011] According to a preferred embodiment, step S2 includes: selecting a two-dimensional airfoil based on the xfoil airfoil database, and obtaining the lift coefficient of the corresponding airfoil at different angles of attack. and drag coefficient Based on the blade condition and design parameters of the coaxial blade, set the basic parameters for coaxial blade aerodynamic calculation.

[0012] According to a preferred embodiment, in step S3, the induced velocity of the inner layer is induced through an iterative convergence process by initially assigning values ​​to the basic parameters. After the corresponding induced velocity converges, the wake contraction ratio from the upper blade to the lower blade in the middle layer... Iteration; Wake contraction ratio After iterative convergence, the outer loop is entered. Using the values ​​obtained from iterative convergence, the thrust and torque are balanced by changing the upper and lower blade pitch angles to meet the corresponding operating conditions. Finally, the thrust coefficient, thrust coefficient, and hovering efficiency of the upper and lower blades of the coaxial twin blades are output under various total thrust coefficients and blade pitches.

[0013] According to a preferred embodiment, the BEMT inner layer iteration includes: An expression for the thrust coefficient infinitesimal element is obtained based on the blade element momentum theory, and the initial dimensionless induced velocity of the upper blade is used. The inflow angle and angle of attack at the upper blade radius position are obtained from the pitch angle. Interpolation is then used to select the corresponding angle of attack. , And calculate the current , This represents the infinitesimal element of the upper blade thrust coefficient; Initialize the wake contraction ratio Under these conditions, the initial lower blade thrust coefficient infinitesimal element is introduced. Dimensionless induced velocity of the lower blade Dimensionless induced velocity of the upper blade Iterative calculations were performed on the induced velocity of the upper blade, and the calculated thrust coefficient of the upper blade was then calculated using a micro-element. The updated upper blade induced velocity is obtained. ; according to The calculated induced velocity and thrust coefficient of the upper blade are combined with the initial thrust coefficient of the lower blade. The induced velocity of the lower blade is calculated based on its radial position, and then the new lower blade thrust coefficient micro-element is calculated. ; After the inner loop ends, that is, after the induced velocity converges, the upper blade thrust coefficient is obtained by integration. Upper blade torque coefficient Lower blade thrust coefficient and lower blade torque coefficient .

[0014] According to a preferred embodiment, a reasonable wake shrinkage ratio is obtained through BEMT mid-layer iteration. The possible values ​​of ; The wake contraction ratio is calculated using the Landgrebe model and the following formula. Value:

[0015]

[0016] in, It is the axial position of the wake. Indicates the blade radius, The age of the tail current This is the thrust coefficient of the upper blade. It is the blade solidity. It is the wake radius. It is the number of leaves. The limiting contraction ratio of the far-field flow. and This is an empirical coefficient. It is the contraction rate coefficient.

[0017] According to a preferred embodiment, the empirical coefficient and They are obtained respectively through the following formulas:

[0018]

[0019] in, It is the blade torque; Shrinkage rate coefficient Obtained through the following formula: .

[0020] According to a preferred embodiment, the wake contraction ratio is determined. During the iteration process, Firstly, based on the thrust coefficient of the upper blade... and blade torque Solving for the results and Then calculate the critical wake age. ,and By comparing different formulas, a suitable formula can be chosen to calculate the wake age. ; Finally, based on the obtained intermediate values, we input them into the corresponding expression of the Landgrebe model to obtain a new... The value of , when Once convergence is achieved, the loop is exited, and the intermediate iteration convergence is completed.

[0021] According to a preferred embodiment, the wake contraction ratio During the iteration process, to ensure its convergence performance, the unrelaxed instantaneous values ​​calculated based on the corresponding expression of the Landgrebe model will be used. Recorded as and to Make corrections to obtain the actual data for the iterative process. The value and correction process are shown below.

[0022] in, This represents the wake contraction ratio in the k-th iteration. This represents the wake contraction ratio in the k-th iteration. .

[0023] According to a preferred embodiment, the outer BEMT iteration is an iterative cycle of the upper and lower blade pitch angles based on torque balance and thrust balancing, and the torque and thrust dual constraints are satisfied by adjusting the pitch angles.

[0024] According to a preferred embodiment, the specific process of the BEMT outer layer iteration includes: Based on the upper blade torque coefficient Lower blade torque coefficient and the thrust coefficient of the upper blade Lower blade thrust coefficient The residual matrix is ​​calculated. The reference point at the initial pitch angle, i.e., the initial residual matrix, is calculated using the finite difference method. Let Jacobi matrix for: ,in Represents torque balance. Represents thrust balancing. Indicates the upper blade pitch angle. This represents the lower blade pitch angle. The iteration process is completed using the BEMT method via pitch perturbation, and the result is obtained using the finite difference method. and Corresponding to and The partial derivatives are used to obtain the initial Jacobian matrix. The values ​​in the table; Meanwhile, the Jacobian matrix is ​​updated using the Broyden method. and residual matrix And the upper and lower propeller pitch angles, until the residual matrix Once the torque approaches zero and the thrust is balanced, the cycle ends. The final performance parameters of the dual blades are output, and the hovering efficiency and power coefficients of the upper and lower blades under a given thrust coefficient are obtained using the coaxial dual blade calculation formula.

[0025] The aforementioned main solution and its various further alternative solutions can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed in this application. Those skilled in the art, after understanding the solution of this application, will realize that there are many combinations based on the prior art and common general knowledge, all of which are technical solutions to be protected in this application, and will not be exhaustively listed here.

[0026] The beneficial effects of this application are: This application addresses the differences in airflow environment and aerodynamic interference between the upper and lower blades of a coaxial rotor blade, proposing for the first time a calculation formula and prediction method for the mutual interference between the upper and lower blades. A fully bidirectional coupled iterative solution framework for the thrust and induced velocity of the upper and lower blades is established. It innovatively integrates Landgrebe's pre-defined wake model into the BEMT iteration process, enabling real-time calculation and updating of the contraction ratio as a function of axial spacing and upper blade thrust. The BEMT system successfully and systematically predicts with high accuracy the changes in thrust distribution, power, and efficiency (FM) of the coaxial rotor blades with axial spacing, achieving high-precision and high-efficiency prediction of coaxial rotor blade spacing-dependent performance. The results calculated using this dual-blade performance iterative solution framework show a high degree of agreement with experimental values, enabling faster, more efficient, and more accurate prediction of the aerodynamic performance of coaxial dual rotor blades under different operating conditions. Attached Figure Description

[0027] Figure 1 This is a flowchart of the traditional BEMT calculation method; Figure 2 It is a traditional BEMT wake diagram; Figure 3 This is a schematic diagram of the flow field of a single blade. Figure 4 This is a schematic diagram of the flow field of a two-bladed propeller; Figure 5 This is a schematic diagram of the calculation process corresponding to the coaxial twin-bladed aerodynamic performance prediction method of this application; Figure 6 This is a diagram illustrating the wake of a coaxial twin-bladed propeller. Figure 7 It is a fitting graph of power coefficient and hovering efficiency under thrust coefficient. Detailed Implementation

[0028] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.

[0029] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of this application, it should also be noted that, unless otherwise expressly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0030] Furthermore, it should be noted that unless otherwise specified in this application, the specific structures, connections, positions, power sources, etc. involved are all things that a person skilled in the art can know without creative effort based on the prior art.

[0031] Example refer to Figure 5 As shown, this application discloses a method for predicting the aerodynamic performance of a coaxial twin-bladed propeller, which includes the following steps.

[0032] Step S1: Define the calculation state and objectives. The flight state for the calculation and analysis is determined to be hovering, and the calculation objectives are hovering efficiency and the power coefficients of the upper and lower blades. This further improves the accuracy of predicting the aerodynamic performance of coaxial blades.

[0033] Step S2: Select a reference model and set the basic parameters for coaxial blade aerodynamic calculations. This includes: selecting a two-dimensional airfoil based on the xfoil airfoil database and obtaining the corresponding airfoil at different angles of attack. and To perform aerodynamic performance calculations for the twin-bladed propeller.

[0034] Based on the blade condition and design parameters of the coaxial blade, the basic aerodynamic calculation parameters for the coaxial blade are set. Taking the NACA 0012 airfoil as an example, the reference blade parameters are defined as shown in Table 1. Both the upper and lower blades use the same reference blade shape.

[0035] Table 1. Aerodynamic shape parameters of the reference blade

[0036] Step S3: After determining the basic blade parameters, based on the set blade spacing... Or the blade spacing range, total thrust coefficient Or the range of total thrust coefficient, rotational speed, and lower blade wake contraction ratio. and the pitch angle of the upper and lower blades and By sequentially iterating through the inner, middle, and outer layers of BEMT, the power coefficients and hovering efficiencies of the upper and lower blades of the coaxial dual-blade propeller under various total thrust coefficients and blade spacings are obtained.

[0037] Specifically, in step S3, the induced velocity of the inner layer is iteratively converged by initially assigning values ​​to the basic parameters; after the corresponding induced velocity converges, the wake contraction ratio from the upper blade to the lower blade in the middle layer is determined. The iteration layer correlates the blade spacing with the performance of the upper and lower blades, resulting in more realistic calculations of the dual-blade performance.

[0038] Wake contraction ratio After iterative convergence, the outer loop is entered. Using the values ​​obtained from the iterative convergence, the thrust and torque are balanced by changing the upper and lower propeller pitch angles to meet the requirements of the corresponding operating conditions. Finally, the total thrust coefficients of the coaxial twin-bladed propeller are output. and the spacing between each blade The power coefficient and hovering efficiency of the upper and lower blades. Among them, The distance between the upper and lower blades is represented by , and D represents the blade diameter.

[0039] In this application, the inner iteration of BEMT is the most crucial part, and the outer iterations in BEMT will all converge based on the results of this part.

[0040] Furthermore, the inner iteration of BEMT includes: (a) Based on the blade element momentum theory, the following information about the thrust coefficient infinitesimal element is obtained. The expression is based on the initial dimensionless induced velocity of the upper blade. The inflow angle and angle of attack at the upper blade radius position are obtained from the pitch angle. Interpolation is then used to select the corresponding angle of attack. and And calculate the current , This represents the infinitesimal element of the upper blade thrust coefficient.

[0041] Formula 1:

[0042] in, As the local entry point, and This is the value at the corresponding angle of attack. For dimensionless radial position, For blade solidity, The expression is shown in Equation 2.

[0043] Formula 2:

[0044] in, Indicates the number of propeller blades. Indicates the chord length at point r. This indicates the blade radius.

[0045] The inner iteration is an iteration to induce the velocity. To obtain the objective equation, we will start with the Bernoulli equation. For example... Figure 6 As shown, it contains two control volumes. For the sake of generalization, the climb rate is included. Divide this flow section into three segments by the blades and formulate its Bernoulli equation.

[0046] Formula 3:

[0047] Formula 4:

[0048] Formula 5:

[0049] in, , , , , , These represent the static pressure at the inlet plane, the static pressure at the top of the upper propeller disk, the static pressure at the bottom of the upper propeller disk, the static pressure at the top of the lower propeller disk, the static pressure at the bottom of the lower propeller disk, and the static pressure at the lower outer flow field plane, respectively. Indicates air density, , , , , , Let $\mathbf$ represent the airflow velocity at the incoming plane, the airflow velocity at the top of the upper propeller disk, the airflow velocity at the bottom of the upper propeller disk, the airflow velocity at the top of the lower propeller disk, the airflow velocity at the bottom of the lower propeller disk, and the airflow velocity at the lower far-field plane, respectively. The velocities on the upper and lower surfaces of the propeller blades are the same, and the pressures in the far-field planes at both ends are the same. Therefore, the thrust element of the upper rotor section can be obtained through... and The pressure difference is expressed as [the pressure difference], and these two can be obtained by subtracting equation 3 from equation 4: Formula 6:

[0050] in, Indicates the tension of the upper blade. This indicates the area of ​​the upper propeller disk. Similarly, the thrust of the lower propeller blade can also be expressed through... and The pressure difference can be obtained from this. The expression, and then using Equation 5 to... You can get it by replacing it. expression.

[0051] Formula 7:

[0052] in, Indicates the tension of the lower blade. This represents the area of ​​the upper propeller disk. Combining equations 6 and 7 will eliminate the [variable / objective]. and Thrust from the blade section: Formula 8:

[0053] After permutation and combination, we can obtain: Formula 9:

[0054] As can be seen from the formula, the total force per unit area exerted by the rotor on the flow tube is equal to the dynamic pressure difference between the entire outlet and inlet.

[0055] To study the contraction ratio, the wake radius of each section is defined using... express, and These represent the induced velocities of the upper and lower blades on their respective blade planes. When the lower rotor exists, from 1 to The shrinkage ratio, This is the shrinkage ratio from the upper rotor to the lower rotor. For 3 to The shrinkage ratio.

[0056] Based on the induced velocity of the blade plane Partial conservation of mass It can be deduced The value of .

[0057] Formula 10:

[0058] Substituting into equation 6 yields: Formula 11:

[0059] in, Indicates the thrust of the upper blade. Indicates the thrust of the lower blade. Indicates the area of ​​the upper propeller disk. The area of ​​the lower propeller disk is represented by [the area of ​​the lower propeller disk]. After rearranging it and loading it into the area formula, the induced velocity of the upper propeller blade can be obtained. .

[0060] Formula 12:

[0061] in, This indicates the radial position of the leaf element in the upper pteris vittata. Indicates the thrust coefficient of the upper blade. This represents the thrust coefficient of the lower blade. It is then converted into dimensionless induced velocity or inflow ratio. We can then conclude that: Formula 13:

[0062] In the formula, The inflow ratio represents the climb rate. This represents the dimensionless radius of the upper blade. It is the dimensionless radial distance Similarly, the dimensionless induced velocity of the lower rotor can also be obtained. expression.

[0063] Formula 14:

[0064] in, This represents the dimensionless radius of the lower blade. Since the lower blade portion is within the downwash flow of the upper blade, the total inflow ratio of the upper blade is... The total inflow ratio of the lower blade and the upper blade They are respectively: Formula 15:

[0065] Formula 16:

[0066] In the formula, Indicates the induced velocity inflow ratio. The dimensionless blade tip radius of the upper rotor. This indicates the wake radius from the upper blade wake to the lower blade position.

[0067] Finally, the Prandtl tip loss effect is added. function and two empirical constants and Then the complete formula for induced velocity can be obtained: Equation 17:

[0068] Formula 18:

[0069] in, This represents the tip loss factor, calculated based on the Prandtl tip loss model. To determine the number of leaves, The dimensionless radial position, Given the local inflow angle, the tip loss factor is... The calculation formula is as follows: Formula 19:

[0070] in, This represents the interference factor of the lower blade on the upper blade. This represents the interference factor of the upper blade on the lower blade, and an empirical constant can be obtained by matching experimental data. empirical constants .

[0071] (b) Initializing the wake contraction ratio Under these conditions, the initial lower blade thrust coefficient infinitesimal element is introduced. Dimensionless induced velocity of the lower blade Dimensionless induced velocity of the upper blade Iterative calculations were performed on the induced velocity of the upper blade, and the calculated thrust coefficient of the upper blade was then calculated using a micro-element. Substituting into Equation 17, the new upper blade induced velocity is obtained. .

[0072] (c) Due to the influence of the downwash flow, the induced velocity of the lower blade is calculated in two regions, and cannot be calculated using Equation 1 first. It should be based on and the calculated induced velocity of the upper blade and thrust coefficient infinitesimal element And combined with the initial lower blade thrust coefficient micro-element The induced velocity of the lower blade is calculated based on Equation 18 of the radial position, and then the new lower blade thrust coefficient micro-element is calculated using Equation 1. .

[0073] (d) If the two induced velocity iterations do not converge, the value obtained in the kth iteration is used to enter the next loop until both induced velocity iterations converge, and then the loop is exited.

[0074] After the inner loop ends, that is, after the induced velocity converges, the upper blade thrust coefficient is obtained by integration. Upper blade torque coefficient Lower blade thrust coefficient and lower blade torque coefficient .

[0075] Furthermore, in the inner iterations, the initial value is used. This is used as the wake contraction ratio from the upper blade to the lower blade, but in reality... The influence of axial spacing needs to be considered, and its value needs to be determined in conjunction with the blade thrust. The calculations were performed using coupling. The intermediate iterations in BEMT primarily aim to obtain a reasonable wake contraction ratio. The value of .

[0076] After the induced velocity converges, the thrust coefficient of the upper blade can be obtained by integration. The value of . In calculating At that time, the focus is on the arrival of the upper blade wake at the lower blade, that is, the axial position. The contraction ratio at that point. The wake contraction ratio can be calculated using the Landgrebe model. The value of .

[0077] Formula 20:

[0078] Equation 21:

[0079] in, It is the axial position of the wake. Indicates the blade radius, The age of the tail current This is the thrust coefficient of the upper blade. It is the blade solidity. It is the wake radius. It is the number of leaves. The limiting contraction ratio of the far-field flow is, in other words, the ratio of... The value is consistently 0.78. and This is an empirical coefficient. It is the contraction rate coefficient.

[0080] empirical coefficient and They are obtained respectively through the following formulas: Equation 22:

[0081] Equation 23:

[0082] in, It is the blade twist (assuming the blade is a linear twist angle, its value is the total change in twist angle from the root to the tip).

[0083] Shrinkage rate coefficient Obtained through the following formula: Formula 24: .

[0084] Perform wake contraction ratio During the iterative process, the thrust coefficient of the upper blade is first determined. and blade torque Solving for the results and Then calculate the critical wake age. ,and By comparing different formulas, a suitable formula can be chosen to calculate the wake age. Finally, based on the obtained intermediate values, we substitute them into equation 21 to obtain the new... The value of , when Once convergence is achieved, the loop is exited, and the intermediate iteration convergence is completed.

[0085] Wake contraction ratio During the iteration process, to ensure its convergence performance, range requirements and relaxation factors need to be added. By fixing its value range within a reasonable interval, the unrelaxed instantaneous calculated value obtained from Equation 21 is... Recorded as and to Make corrections to obtain the actual data for the iterative process. The value and correction process are shown below. Formula 25:

[0086] in, Indicates the k-th iteration value, Represents the (k-1)th iteration value, .

[0087] Furthermore, the outer iteration of BEMT is an iterative cycle of the upper and lower blade pitch angles based on torque balance and thrust balancing. After the inner cycle is completed, the pitch angle is adjusted to satisfy the dual constraints of torque and thrust.

[0088] Furthermore, the specific process of the outer iteration of BEMT includes: Based on the upper blade torque coefficient Lower blade torque coefficient and the thrust coefficient of the upper blade Lower blade thrust coefficient The residual matrix is ​​calculated. Torque balance Thrust balance The goal of the iteration is to transform the matrix into a zero vector. Therefore: Torque residual:

[0089] Thrust residual:

[0090] Residual function:

[0091] The finite difference method is used to calculate the reference point at the initial pitch angle, i.e., the initial residual matrix. .

[0092] Jacobian matrix for: , Indicates the upper blade pitch angle and This represents the lower blade pitch angle. A Jacobian matrix is ​​used. After completing the first iteration using the pitch perturbation method, the BEMT solver is called to calculate the new residuals. First, the lower pitch angle is kept constant, and then a small increment is applied to the upper pitch angle. The inner iteration is then called to calculate the new coefficients, and the new residuals are obtained. Then, the upper pitch angle is fixed again, and the above steps are repeated (note that both perturbation methods are based on the initial pitch angle). This allows the finite difference method to obtain... and Corresponding to and The partial derivatives are used to obtain the initial Jacobian matrix. The values ​​in the table.

[0093] Based on the obtained upper and lower propeller pitch angles, the matrix and residual Then proceed to subsequent iterations. The Broyden method is used to update the matrix approximation, which means using the changes in the residuals and control variables from the current iteration to update the matrix, thereby avoiding the complex calculation of partial derivatives and saving computational resources.

[0094] Using Equation 26, the change in pitch angle is obtained, and adding it to the initial value yields the pitch angle for the next iteration.

[0095] Equation 26:

[0096] in, Let Jacobian matrix be the value of the k-th iteration. This represents the change in pitch angle. This represents the residual matrix of the k-th iteration. Therefore, after obtaining the new pitch angle, the next large loop can be entered to obtain the new performance parameters at that pitch angle. In the next loop, when updating the pitch angle, a new residual matrix is ​​also needed. And Jacobi matrix At this point, new performance parameters (thrust and torque) will be obtained, a new F matrix will be constructed, and then the old and new parameters will be combined. The difference between matrices yields the change in the residual matrix. Using Equation 27, a new... matrix: Equation 27:

[0097] in, The correction matrix, where the numerator represents the difference between the actual residuals and the residual changes predicted by the old Jacobian, corrects the old matrix to a new matrix that satisfies the secant criterion. This allows for step-by-step completion of the outer iteration.

[0098] Until the residual matrix The cycle ends when the torque approaches zero, meaning the torque is balanced and the thrust is balanced. This outputs the final performance parameters of the two blades. Then, using the traditional coaxial two-blade calculation formula, the hovering efficiency and the power coefficients of the upper and lower blades under a given thrust coefficient are obtained.

[0099] Optimize BEMT test case verification The following are the calculated and predicted results based on the initially given parameters of a three-bladed coaxial double propeller, with a fixed spacing of 0.093, a thrust coefficient ranging from 0.002 to 0.012, and a rotational speed of 800 rpm, compared with the experimental results. and The fitting situation, such as Figure 7 As shown.

[0100] This application addresses the differences in airflow environment and aerodynamic interference between the upper and lower blades of a coaxial rotor blade, proposing for the first time a calculation formula and prediction method for the mutual interference between the upper and lower blades. A fully bidirectional coupled iterative solution framework for the thrust and induced velocity of the upper and lower blades is established. It innovatively integrates Landgrebe's pre-defined wake model into the BEMT iteration process, enabling real-time calculation and updating of the contraction ratio as a function of axial spacing and upper blade thrust. The BEMT system successfully and systematically predicts with high accuracy the changes in thrust distribution, power, and efficiency (FM) of the coaxial rotor blades with axial spacing, achieving high-precision and high-efficiency prediction of coaxial rotor blade spacing-dependent performance. The results calculated using this dual-blade performance iterative solution framework show a high degree of agreement with experimental values, enabling faster, more efficient, and more accurate prediction of the aerodynamic performance of coaxial dual rotor blades under different operating conditions.

[0101] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for predicting the aerodynamic performance of a coaxial twin-bladed propeller, characterized in that, The method for predicting the aerodynamic performance of the coaxial twin-bladed propeller includes: S1: Define the calculation state and objectives, determine that the flight state to be analyzed is the hovering state, and the calculation objectives are hovering efficiency and thrust coefficient; S2: Select the reference model and set the basic parameters for coaxial blade aerodynamic calculation; S3: After determining the basic blade parameters, based on the set blade spacing or blade spacing range, total thrust coefficient or total thrust coefficient range, rotational speed, and lower blade wake contraction ratio. and the pitch angle of the upper and lower blades and , Through BEMT inner layer iteration, BEMT middle layer iteration, and BEMT outer layer iteration, the thrust coefficient, pull coefficient, and hovering efficiency of the upper and lower blades of the coaxial twin blades under various total thrust coefficients and blade spacings are obtained.

2. The method for predicting the aerodynamic performance of a coaxial twin-bladed propeller as described in claim 1, characterized in that, Step S2 includes: selecting a two-dimensional airfoil based on the xfoil airfoil database, and obtaining the lift coefficient of the corresponding airfoil at different angles of attack. and drag coefficient Based on the blade condition and design parameters of the coaxial blade, set the basic parameters for coaxial blade aerodynamic calculation.

3. The method for predicting the aerodynamic performance of a coaxial twin-bladed propeller as described in claim 2, characterized in that, In step S3, the basic parameters are initially assigned values, and the induced velocity of the inner layer is induced through an iterative convergence process. After the corresponding induced velocity converges, the wake contraction ratio from the upper blade to the lower blade in the middle layer... Iteration; Wake contraction ratio After iterative convergence, the outer loop is entered. Using the values ​​obtained from iterative convergence, the thrust and torque are balanced by changing the upper and lower blade pitch angles to meet the corresponding operating conditions. Finally, the thrust coefficient, thrust coefficient, and hovering efficiency of the upper and lower blades of the coaxial twin blades are output under various total thrust coefficients and blade pitches.

4. The method for predicting the aerodynamic performance of a coaxial twin-bladed propeller as described in claim 3, characterized in that, The inner iteration of BEMT includes: An expression for the thrust coefficient infinitesimal element is obtained based on the blade element momentum theory, and the initial dimensionless induced velocity of the upper blade is used. The inflow angle and angle of attack at the upper blade radius position are obtained from the pitch angle. Interpolation is then used to select the corresponding angle of attack. , And calculate the current , This represents the infinitesimal element of the upper blade thrust coefficient; Initialize the wake contraction ratio Under these conditions, the initial lower blade thrust coefficient infinitesimal element is introduced. Dimensionless induced velocity of the lower blade Dimensionless induced velocity of the upper blade Iterative calculations were performed on the induced velocity of the upper blade, and the calculated thrust coefficient of the upper blade was then calculated. The updated upper blade induced velocity is obtained. ; according to The calculated induced velocity and thrust coefficient of the upper blade are combined with the initial thrust coefficient of the lower blade. The induced velocity of the lower blade is calculated based on its radial position, and then the new lower blade thrust coefficient micro-element is calculated. ; After the inner loop ends, that is, after the induced velocity converges, the upper blade thrust coefficient is obtained by integration. Upper blade torque coefficient Lower blade thrust coefficient and lower blade torque coefficient .

5. The method for predicting the aerodynamic performance of a coaxial twin-bladed propeller as described in claim 4, characterized in that, A reasonable wake contraction ratio is obtained through mid-layer iteration of BEMT. The value of ; The wake contraction ratio is calculated using the Landgrebe model and the following formula. Value: in, It is the axial position of the wake. Indicates the blade radius. The age of the tail current It is the wake radius. It is the number of leaves. The limiting contraction ratio of the far-field flow. and This is an empirical coefficient. It is the contraction rate coefficient.

6. The method for predicting the aerodynamic performance of a coaxial twin-bladed propeller as described in claim 5, characterized in that, empirical coefficient and They are obtained respectively through the following formulas: in, It is the blade torque; Shrinkage rate coefficient Obtained through the following formula: 。 7. The method for predicting the aerodynamic performance of a coaxial twin-bladed propeller as described in claim 6, characterized in that, Perform wake contraction ratio During the iteration process, Firstly, based on the thrust coefficient of the upper blade... and blade torque Solving for the results and Then calculate the critical wake age. ,and By comparing different formulas, a suitable formula can be chosen to calculate the wake age. ; Finally, based on the obtained intermediate values, we input them into the corresponding expression of the Landgrebe model to obtain a new... The value of , when Once convergence is achieved, the loop is exited, and the intermediate iteration convergence is completed.

8. The method for predicting the aerodynamic performance of a coaxial twin-bladed propeller as described in claim 7, characterized in that, Wake contraction ratio During the iteration process, to ensure its convergence performance, the unrelaxed instantaneous values ​​calculated based on the corresponding expression of the Landgrebe model will be used. Recorded as and to Make corrections to obtain the actual data for the iterative process. The value and correction process are shown below. in, This represents the wake contraction ratio in the k-th iteration. This represents the wake contraction ratio in the (k-1)th iteration. .

9. The method for predicting the aerodynamic performance of a coaxial twin-bladed propeller as described in claim 7, characterized in that, The outer layer iteration of BEMT is an iterative cycle of the upper and lower blade pitch angles based on torque balance and thrust balancing, which satisfies the dual constraints of torque and thrust by adjusting the pitch angle.

10. The method for predicting the aerodynamic performance of a coaxial twin-bladed propeller as described in claim 9, characterized in that, The specific process of the outer layer iteration of BEMT includes: Based on the upper blade torque coefficient Lower blade torque coefficient and the thrust coefficient of the upper blade Lower blade thrust coefficient The residual matrix is ​​calculated. The reference point at the initial pitch angle, i.e., the initial residual matrix, is calculated using the finite difference method. Let Jacobi matrix for: ,in Represents torque balance. Represents thrust balancing. Indicates the upper blade pitch angle. This represents the lower blade pitch angle. The iteration process is completed using the BEMT method via pitch perturbation, and the result is obtained using the finite difference method. and Corresponding to and The partial derivatives are used to obtain the initial Jacobian matrix. The values ​​in the table; Meanwhile, the Jacobian matrix is ​​updated using the Broyden method. and residual matrix And the upper and lower propeller pitch angles, until the residual matrix Once the torque approaches zero and the thrust is balanced, the cycle ends. The final performance parameters of the dual blades are output, and the hovering efficiency and power coefficients of the upper and lower blades under a given thrust coefficient are obtained using the coaxial dual blade calculation formula.

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