An iterative algorithm and device for evaluating the aerodynamic performance of coaxial rotors of eVTOL aircraft

Abstract

The present invention discloses an iterative algorithm and device for evaluating the aerodynamic performance of the coaxial rotor of an eVTOL aircraft, which belongs to the field of aircraft design and can effectively improve the accuracy and stability of the aerodynamic performance evaluation of the coaxial rotor. The method is as follows: the aerodynamic performance and wake contraction of the upper rotor are mapped to the lower rotor, the inflow ratio of the lower rotor is calculated, and the aerodynamic performance of the lower rotor is mapped to the upper rotor. At the same time, the upper and lower rotor influencing factors are introduced to calculate the inflow ratio of the upper rotor. The above process is cross-iterated until the convergence standard is met to obtain the final aerodynamic performance of the coaxial rotor. The present invention can effectively consider the influence of the spacing between the upper and lower rotors, and at the same time consider the mutual interference of the upper and lower rotors through iterative calculation.

Description

Technical Field

[0001] The present invention belongs to the field of aircraft design, and in particular relates to an iterative algorithm and device for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft. Background Art

[0002] With advances in electric energy storage and motor technologies, as well as the application of distributed electric drive systems, electric vertical take-off and landing (eVTOL) aircraft are playing a vital role in urban air mobility (UAM). As a key rotor configuration for eVTOL aircraft, accurate evaluation of aerodynamic performance during the design phase is crucial. Due to the involvement of multiple blades and the aerodynamic interference between the upper and lower rotors, aerodynamic performance evaluation techniques based on CFD and vortex methods are often not suitable for the preliminary design of coaxial rotors. The momentum blade element theory (BEMT) is one of the simplest numerical methods for analyzing the aerodynamic performance of rotors in hover and vertical climb flight. However, the BEMT for coaxial rotors faces two challenges that need to be addressed: first, the method must be able to account for the mutual interference between the upper and lower rotors; second, the method must be able to account for the influence of the spacing between the upper and lower rotors. Currently proposed BEMTs for coaxial rotors have failed to effectively address these issues. Summary of the Invention

[0003] To address the problem that the prior art does not consider the mutual interference between the upper and lower rotors and the spacing between the upper and lower rotors, the present invention provides the following solution: an iterative algorithm for evaluating the aerodynamic performance of the coaxial rotors of an eVTOL aircraft, comprising the following steps:

[0004] Step 1: Use the classic BEMT to obtain the induced velocity inflow ratio, thrust coefficient, and torque coefficient of the upper rotor;

[0005] Step 2: Use the Landgrebe predetermined wake model to obtain the wake contraction radius of the upper rotor;

[0006] Step 3: Interpolate the induced velocity inflow ratio and the drag coefficient of the upper rotor to the lower rotor, correct the blade tip loss, and calculate the induced velocity inflow ratio, drag coefficient, and torque coefficient of the lower rotor based on the wake contraction radius;

[0007] Step 4: Interpolate the induced velocity inflow ratio and the drag coefficient of the lower rotor to the upper rotor, correct the blade tip loss, and calculate the drag coefficient and torque coefficient after the upper rotor interaction correction;

[0008] Step 5: Based on the convergence criteria, determine whether the corrected thrust coefficient and torque coefficient of the upper rotor converge with the thrust coefficient and torque coefficient of the lower rotor. If so, the calculation ends; if not, return to step 2.

[0009] Furthermore, in step one, the classic BEMT calculation is specifically as follows: the blades of the rotor to be evaluated are divided into multiple infinitely thin blade units, namely blade elements, along the radial direction. A control volume is established on each blade element, and the law of conservation of momentum is applied to the control volume, considering the momentum change of the airflow before and after the blade element acts.

[0010] Furthermore, in step 1, the tension coefficient is obtained by:

[0011]

[0012] Obtain, where σ is the solidity, C l is the lift coefficient of the blade element, and r is the dimensionless blade element position.

[0013] Furthermore, in step 1, the torque coefficient is calculated by:

[0014]

[0015] Obtained, where λ is the inflow ratio, C d is the drag coefficient of the blade element.

[0016] Furthermore, in step 2, the landgrebe predetermined trail model is:

[0017]

[0018] k1=-0.25(C T / σ+0.001θ tw )

[0019]

[0020] Among them, ψ ω is the vortex age angle, z tip is the distance between the upper and lower rotors, N b is the number of blades, R is the rotor radius, θ tw is the torsion angle;

[0021] Furthermore, in step 2, the tail shrinkage radius of the upper rotor is calculated by:

[0022] r tip =A+(1-A)exp(-Λψ ω )

[0023] Obtained, where A = 0.78, Λ = 0.145 + 27C T .

[0024] Furthermore, in steps 3 and 4, the tip loss is calculated by:

[0025]

[0026] Correction, where F is the correction factor and φ is the relative inflow angle.

[0027] Furthermore, in step 5, the convergence criterion is

[0028]

[0029] Among them, ε is the error control parameter, which is selected as 0.001.

[0030] The present invention also provides a computer device, which includes a memory and a processor, wherein a computer program is stored in the memory, and when the processor runs the computer program stored in the memory, the processor executes the above algorithm.

[0031] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and the computer program implements the above algorithm when executed by a processor.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] (1) It can quickly and robustly analyze the aerodynamic performance of coaxial rotors in hover and axial flight states, and can serve as the core solution algorithm in the preliminary design and optimization design stages of coaxial rotors;

[0034] (2) The influence of the distance between the upper and lower rotors can be effectively considered, and the mutual interference between the upper and lower rotors can be considered through iterative calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A flowchart of an iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft;

[0036] Figure 2 is the rotor blade unit (blade element) assumed in the present invention;

[0037] Figure 3 The flow environment around the rotor blade element assumed in the present invention;

[0038] Figure 4 The flow environment around the coaxial rotor assumed in the present invention;

[0039] Figure 5 Comparison of calculated and tested results for the Harrington 2 full-scale coaxial rotor. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of the implementation of the present invention clearer, the technical solutions of the present invention will be described in detail below with reference to the accompanying drawings. In the accompanying drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. It should be understood here that the described embodiments are partial embodiments of the present invention, not all embodiments. The following embodiments are exemplary and are intended to be used to explain the present invention, and should not be understood as limitations on the present invention. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without making creative work are all within the scope of protection of the present invention.

[0041] Example 1, combined Figure 1-4 This embodiment describes an iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft. The steps are as follows:

[0042] Step 1: Use the classic BEMT to obtain the induced velocity inflow ratio, thrust coefficient, and torque coefficient of the upper rotor;

[0043] Step 2: Use the Landgrebe predetermined wake model to obtain the wake contraction radius of the upper rotor;

[0044] Step 3: Interpolate the induced velocity inflow ratio and the drag coefficient of the upper rotor to the lower rotor, correct the blade tip loss, and calculate the induced velocity inflow ratio, drag coefficient, and torque coefficient of the lower rotor based on the wake contraction radius;

[0045] Step 4: Interpolate the induced velocity inflow ratio and the drag coefficient of the lower rotor to the upper rotor, correct the blade tip loss, and calculate the drag coefficient and torque coefficient after the upper rotor interaction correction;

[0046] Step 5: Based on the convergence criteria, determine whether the corrected thrust coefficient and torque coefficient of the upper rotor converge with the thrust coefficient and torque coefficient of the lower rotor. If so, the calculation ends; if not, return to step 2.

[0047] Specifically, the cross calculation of the upper and lower rotor performance is the core step of the iterative process. For the coaxial rotor in the vertical climb state, the surrounding flow is as follows Figure 4 As shown, the Bernoulli equation governing the flow is:

[0048]

[0049] Among them, V c is the vertical climbing speed, V1=V2, V3=V4, P0=P ∞V is velocity, P is pressure, ρ is density, subscript c represents climb, subscript 0 represents the upstream far field, subscript 1 represents the upper side of the upper rotor disc, subscript 2 represents the lower side of the upper rotor disc, subscript 3 represents the upper side of the lower rotor disc, subscript 4 represents the lower side of the lower rotor disc, and subscript ∞ represents the downstream far field.

[0050] The rotor force balance equation is:

[0051]

[0052] Where T is the thrust, A is the disc area, subscript u represents the upper rotor, and subscript l represents the lower rotor.

[0053] Therefore, the thrust of the coaxial rotor is:

[0054]

[0055] Among them, v i,u is the induced speed of the upper rotor, v i,l is the induced speed of the lower rotor, K t K is the wake contraction ratio from the upper rotor to the downstream far field, l is the wake contraction ratio from the lower rotor to the downstream far field.

[0056] At the same time, due to:

[0057]

[0058] Among them, C T is the tension coefficient, Ω is the angular velocity of rotation. y is the distance from the center of the blade element to the rotation axis. K u is the tail contraction ratio from the upper rotor to the lower rotor.

[0059] Therefore, the upper rotor induced speed is:

[0060]

[0061] Using ΩR to make the induced velocity dimensionless, the induced velocity inflow ratio of the upper rotor is:

[0062]

[0063] in, λ represents the inflow ratio.

[0064] Similarly, the induced velocity inflow ratio of the lower rotor is

[0065]

[0066] because,

[0067] λ u =λ c+λ i,u

[0068]

[0069] r u,tip is the dimensionless upper rotor tip radius.

[0070] Then, the upper rotor inflow ratio is calculated by:

[0071]

[0072] Obtained, where, due to wind tunnel test data verification, B u is 0.55, B l is 0.115.

[0073] The lower rotor inflow ratio is:

[0074]

[0075] get.

[0076] In step one, the classic BEMT calculation involves dividing the rotor blade to be evaluated into multiple infinitely thin blade units, or blade elements, along the radial direction. A control volume is established on each blade element, and the law of conservation of momentum is applied to the control volume, taking into account the momentum change of the airflow before and after the blade element acts.

[0077] Specifically, the leaf element is defined as Figure 2 As shown, the flow around the blade is as follows Figure 3 As shown. The effective angle of attack of the blade element is:

[0078]

[0079] Among them, U P is the velocity component perpendicular to the blade element, U P =V c +v i ;U T is the velocity component parallel to the blade element, U T =Ωy.

[0080] The lift force of a blade element is:

[0081]

[0082] in, C l is the lift coefficient of the airfoil.

[0083] The resistance of the blade element is:

[0084]

[0085] Among them, Cd is the airfoil drag coefficient.

[0086] The blade tension of all blades is:

[0087] dT=N b (dLcosφ-dDsinφ)

[0088] Among them, N b is the number of blades.

[0089] The blade element torque of all blades is:

[0090] dQ=N b (dLsinφ+dDcosφ)y

[0091] For the coaxial rotor of the eVTOL aircraft, the thrust and torque can be simplified to

[0092] dT=N b dL

[0093] dQ=N b (φdL+dD)y

[0094] The blade tension coefficient and torque coefficient are

[0095]

[0096] in, In step 1, the tension coefficient is calculated by:

[0097]

[0098] Obtain, where σ is the solidity, C l is the lift coefficient of the blade element, and r is the dimensionless blade element position. Specifically, the rotor thrust coefficient can be obtained by integrating along the span direction of the blade.

[0099] In step 1, the torque coefficient is calculated by:

[0100]

[0101] Obtained, where λ is the inflow ratio, C d is the drag coefficient of the blade element.

[0102] Specifically, the torque coefficient of the rotor can be obtained by integrating along the span direction of the blade.

[0103]

[0104] in,

[0105] Lift coefficient C of the airfoil l =C l(α, Re, M), drag coefficient C d =C d (α, Re, M) is a function of the angle of attack, Reynolds number and Mach number, and can be calculated using empirical formulas or CFD methods.

[0106] In step 2, the landgrebe predetermined trail model is:

[0107]

[0108] k1=-0.25(C T / σ+0.001θ tw )

[0109]

[0110] Among them, ψ ω is the vortex age angle, z tip is the distance between the upper and lower rotors, N b is the number of blades, R is the rotor radius, θ tw is the torsion angle;

[0111] In step 2, the tail shrink radius of the upper rotor is calculated by:

[0112] r tip =A+(1-A)exp(-Λψ ω )

[0113] Obtained, where A = 0.78, Λ = 0.145 + 27C T .

[0114] In steps 3 and 4, the tip loss is calculated by:

[0115]

[0116] Correction, where F is the correction factor and φ is the relative inflow angle.

[0117] In step 5, the convergence criterion is

[0118]

[0119] Among them, ε is the error control parameter, which is selected as 0.001.

[0120] Example 2

[0121] Take the calculation of the thrust coefficient and torque coefficient of the Harrington 2 full-scale coaxial rotor as an example. The upper and lower rotors of the Harrington 2 full-scale coaxial rotor each contain two rectangular blades, no twist, a rotor radius of 3.81 meters, a solidity of 0.076, a pitch of 16%R between the upper and lower rotors, and a blade airfoil of NACA0012. The calculation results of Example 2 are compared with the test results. Figure 5 As shown in Figure 3, the calculated results are in good agreement with the experimental measurement data of the coaxial rotor.

[0122] The above is only one specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or modifications within the technical concept disclosed by the present invention and any simple substitutions or modifications based on the technical solution of the present invention shall fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be based on the scope of protection of the claims.

Claims

1. An iterative algorithm for evaluating the aerodynamic performance of coaxial rotors of eVTOL aircraft, characterized by: Here are the steps: Step 1: Use the classic BEMT to obtain the induced velocity inflow ratio, thrust coefficient, and torque coefficient of the upper rotor; Step 2: Use the Landgrebe predetermined wake model to obtain the wake contraction radius of the upper rotor; Step 3: Interpolate the induced velocity inflow ratio and the drag coefficient of the upper rotor to the lower rotor, correct the blade tip loss, and calculate the induced velocity inflow ratio, drag coefficient, and torque coefficient of the lower rotor based on the wake contraction radius; Step 4: Interpolate the induced velocity inflow ratio and the drag coefficient of the lower rotor to the upper rotor, correct the blade tip loss, and calculate the drag coefficient and torque coefficient after the upper rotor interaction correction; Step 5: Based on the convergence criteria, determine whether the corrected thrust coefficient and torque coefficient of the upper rotor converge with the thrust coefficient and torque coefficient of the lower rotor. If so, the calculation ends. If it does not converge, go back to step 2.

2. The iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft according to claim 1, characterized in that: In step one, the classic BEMT calculation involves dividing the rotor blade to be evaluated into multiple infinitely thin blade units, or blade elements, along the radial direction. A control volume is established on each blade element, and the law of conservation of momentum is applied to the control volume, taking into account the momentum change of the airflow before and after the blade element acts.

3. The iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft according to claim 1, characterized in that: In step 1, the tension coefficient is calculated by: Obtain, where σ is the solidity, C l is the lift coefficient of the blade element, and r is the dimensionless blade element position.

4. The iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft according to claim 3, characterized in that: In step 1, the torque coefficient is calculated by: Obtained, where λ is the inflow ratio, C d is the drag coefficient of the blade element.

5. The iterative algorithm for evaluating the aerodynamic performance of the coaxial rotor of an eVTOL aircraft according to claim 4, characterized in that: In step 2, the landgrebe predetermined trail model is: k1=-0.25(C T / σ+0.001θ tw ) Among them, ψ ω is the vortex age angle, z tip is the distance between the upper and lower rotors, N b is the number of blades, R is the rotor radius, θ tw is the torsion angle.

6. The iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft according to claim 5, characterized in that: In step 2, the tail shrink radius of the upper rotor is calculated by: r tip =A+(1-A)exp(-Λψ ω ) Obtained, where A = 0.78, Λ = 0.145 + 27C T .

7. The iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft according to claim 6, characterized in that: In steps 3 and 4, the tip loss is calculated by: Correction, where F is the correction factor and φ is the relative inflow angle.

8. The iterative algorithm for evaluating the aerodynamic performance of the coaxial rotor of an eVTOL aircraft according to claim 7, characterized in that: In step 5, the convergence criterion is Among them, ε is the error control parameter, which is selected as 0.

001.

9. A computer device comprising a memory and a processor, characterized in that A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes the iterative algorithm for evaluating the aerodynamic performance of the coaxial rotor of an eVTOL aircraft according to any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which, when executed by a processor, implements an iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft according to any one of claims 1 to 8.

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