Iterative algorithm and equipment for evaluating aerodynamic performance of coaxial rotor of eVTOL aircraft

Abstract

The invention discloses an iterative algorithm and equipment for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft, and belongs to the field of aircraft design, and can effectively improve the precision and stability of the aerodynamic performance evaluation of the coaxial rotor, the method comprises the following steps: mapping the aerodynamic performance and wake contraction of an upper rotor to a lower rotor, calculating the inflow ratio of the lower rotor, and calculating the aerodynamic performance of the lower rotor; the method comprises the steps that the aerodynamic performance of a lower rotor wing is mapped to an upper rotor wing, meanwhile, influence factors of the upper rotor wing and the lower rotor wing are introduced, the inflow ratio of the upper rotor wing is calculated, the process is conducted in a crossed iteration mode till the convergence standard is met, and the final aerodynamic performance of the coaxial rotor wings is obtained. Meanwhile, mutual interference of upper and lower rotors is considered 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 the advancement of electric energy storage technology and motor technology and the application of distributed electric drive systems, electric Vertical Take-off and Landing (eVTOL) aircraft plays an important role in urban air mobility (UAM). As a key rotor layout of eVTOL aircraft, the coaxial rotor is crucial for the accurate evaluation of aerodynamic performance in its design stage. Due to the involvement of multiple blades and aerodynamic interference between the upper and lower rotors, aerodynamic performance evaluation techniques based on CFD methods and vortex methods are often not applicable to the preliminary design stage of coaxial rotors. The momentum blade element theory (BEMT) is one of the simplest numerical methods for analyzing the aerodynamic performance of rotors in hovering and vertical climb flight states. However, there are two problems to be solved in the momentum blade element theory for coaxial rotors: one is that the method can consider the mutual interference between the upper and lower rotors; the other is that the method can consider the influence of the spacing between the upper and lower rotors. The momentum blade element theory of coaxial rotors proposed so far has failed to effectively solve the above problems. Summary of the invention

[0003] In order to solve the problem that the prior art does not consider the mutual interference between the upper and lower rotors and the distance between the upper and lower rotors, the present invention provides the following solution: an iterative algorithm for evaluating the aerodynamic performance of the coaxial rotor of an eVTOL aircraft, the steps are as follows:

[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 speed inflow ratio and the thrust coefficient of the upper rotor to the lower rotor, correct the blade tip loss, and calculate the induced speed inflow ratio, thrust coefficient and torque coefficient of the lower rotor in combination with the wake contraction radius;

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

[0008] Step 5: According to the convergence standard, determine whether the thrust coefficient and torque coefficient after the interaction correction of the upper rotor converge with the thrust coefficient and torque coefficient of the lower rotor. If converged, the calculation ends; if not, return to step 2.

[0009] Furthermore, in step one, the classical 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 body is established on each blade element, the law of conservation of momentum is applied to the control body, and the momentum change of the airflow before and after the action of the blade element is considered.

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

[0011]

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

[0013] Further, in step 1, the torque coefficient is obtained 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 step 3 and step 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, on which a computer program is stored, 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 the coaxial rotor in hover and axial flight states, and can be used as the core solution algorithm in the preliminary design and optimization design stages of the coaxial rotor;

[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 It is a flowchart of an iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft;

[0036] Figure 2 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 scheme and advantages of the implementation of the present invention clearer, the technical scheme of the present invention will be described in detail in conjunction with 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, rather than all embodiments. The following embodiments are exemplary and are intended to be used to explain the present invention, and should not be construed 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] Embodiment 1, combination Figure 1-4 This embodiment describes an iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft, and 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 speed inflow ratio and the thrust coefficient of the upper rotor to the lower rotor, correct the blade tip loss, and calculate the induced speed inflow ratio, thrust coefficient and torque coefficient of the lower rotor in combination with the wake contraction radius;

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

[0046] Step 5: According to the convergence standard, determine whether the thrust coefficient and torque coefficient after the interaction correction of the upper rotor converge with the thrust coefficient and torque coefficient of the lower rotor. If converged, 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 climbing 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 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 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 speed dimensionless, the induced speed 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 is 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 body is established on each blade element, the law of conservation of momentum is applied to the control body, and the momentum change of the airflow before and after the action of the blade element is considered.

[0077] Specifically, the leaf element is defined as Figure 2 As shown, the flow around the blade element is 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 the 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 propeller 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 as

[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] Obtained, 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] The lift coefficient of the airfoil is C 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-size coaxial rotor as an example. The upper and lower rotors of the Harrington 2 full-size coaxial rotor each contain two rectangular blades, no twist, a rotor radius of 3.81 meters, a solidity of 0.076, an upper and lower rotor spacing of 16%R, and a blade airfoil of NACA0012. Compare the calculation results of Example 2 with the test results, as shown in FIG. 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 a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any simple replacement or change within the technical idea disclosed by the present invention and the technical solution of the present invention should be within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. An iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft, characterized in that: 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 speed inflow ratio and the thrust coefficient of the upper rotor to the lower rotor, correct the blade tip loss, and calculate the induced speed inflow ratio, thrust coefficient and torque coefficient of the lower rotor in combination with the wake contraction radius; Step 4: interpolate the induced speed inflow ratio and the thrust coefficient of the lower rotor to the upper rotor, correct the blade tip loss, and calculate the thrust coefficient and torque coefficient after the upper rotor interaction correction; Step 5: According to the convergence standard, determine whether the thrust coefficient and torque coefficient after the interaction correction of the upper rotor converge with the thrust coefficient and torque coefficient of the lower rotor. If converged, the calculation ends; If it does not converge, go back to step 2.

2. The iterative algorithm for evaluating the aerodynamic performance of the coaxial rotor of an eVTOL aircraft according to claim 1, characterized in that: In step one, the classic BEMT calculation is 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 body is established on each blade element, the law of conservation of momentum is applied to the control body, and the momentum change of the airflow before and after the action of the blade element is considered.

3. The iterative algorithm for evaluating the aerodynamic performance of the coaxial rotor of an eVTOL aircraft according to claim 1, characterized in that: In step 1, the tension coefficient is calculated by: Obtained, 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 the coaxial rotor of an eVTOL aircraft according to claim 1, 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 1, 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 twist angle.

6. The iterative algorithm for evaluating the aerodynamic performance of the coaxial rotor of an eVTOL aircraft according to claim 1, 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 the coaxial rotor of an eVTOL aircraft according to claim 1, 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 1, 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 an iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft as described in claims 1-8.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, an iterative algorithm for evaluating the aerodynamic performance of a coaxial rotor of an eVTOL aircraft as described in claims 1-8 is implemented.

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