Distributed multi-rotor aerodynamic interference analysis method

Abstract

The invention provides a distributed multi-rotor aerodynamic interference analysis method. The method comprises the following steps: establishing a rotor flow field model; establishing a wing flow field model; based on the rotor wing flow field model and the wing flow field model, establishing a rotor wing and wing aerodynamic interference model; wherein the rotor wing and wing aerodynamic interference model is a distributed rotor wing aerodynamic interference model considering three-dimensional elastic deformation; analyzing the aerodynamic interference of the distributed multi-rotor aircraft according to the rotor and wing aerodynamic interference model; according to the method, the unsteady surface element method is adopted to replace the two-dimensional leaf element theory, the free wake model is adopted to replace the inflow model, and the influence of three-dimensional deformation is considered, so that the aerodynamic interference analysis precision of the distributed multi-rotor wing and the wing is effectively improved.

Description

Technical Field

[0001] The present application belongs to the technical field of distributed multi-rotor aircraft design and theoretical modeling, and in particular relates to a distributed multi-rotor aerodynamic interference analysis method. Background Art

[0002] To overcome speed limitations, various high-speed rotorcraft concepts have been researched and tested. Distributed multi-rotor aircraft are currently the most successful rotorcraft configuration. Compared to traditional helicopters, these aircraft offer advantages such as longer range and higher speed. However, their rotors are connected to the wings, creating strong aerodynamic interference between the rotors and between the rotors and wings during flight. This interference significantly affects the magnitude and distribution of aerodynamic forces between the rotors and wings, directly impacting aircraft performance and flight safety.

[0003] At the same time, the rotors and wings of distributed multi-rotor aircraft will produce large elastic deformations after being subjected to aerodynamic loads, and due to the structural coupling between the wings and the rotors, the wings will produce large multi-directional three-dimensional elastic deformations. These three-dimensional elastic deformations will significantly change the shape of the rotors and wings and thus change the overall aerodynamic interference environment. Therefore, it is very important to consider three-dimensional elastic deformations when analyzing aerodynamic interference.

[0004] Comparatively speaking, aerodynamic interference analysis models for distributed multi-rotor aircraft often use simplified two-dimensional blade element theory combined with an inflow model or computational fluid dynamics (CFD) analysis. This simplified two-dimensional blade element theory combined with an inflow model assumes rigid cross-sections and cannot fully account for arbitrary three-dimensional elastic deformation. Summary of the Invention

[0005] Purpose of the invention: Compared with the CFD analysis method in the technology, which currently only considers rigid body motion and does not consider elastic deformation, and has low computational efficiency, in order to effectively solve the above problems, a new aerodynamic interference analysis method of distributed multi-rotor rotors and wings that considers three-dimensional elastic deformation is needed.

[0006] The present application provides a distributed multi-rotor aerodynamic interference analysis method, the method comprising:

[0007] Step 101: Establish a rotor flow field model;

[0008] Step 201: Establish a wing flow field model;

[0009] Step 301: Establishing a rotor and wing aerodynamic interference model based on the rotor flow field model and the wing flow field model; wherein the rotor and wing aerodynamic interference model is a distributed rotor aerodynamic interference model that considers three-dimensional elastic deformation;

[0010] Step 401: Analyze the aerodynamic interference of the distributed multi-rotor aircraft according to the rotor and wing aerodynamic interference model.

[0011] Preferably, step 101 includes:

[0012] The rotor flow field model is established by using the aerodynamic modeling method of quasi-steady aerodynamics combined with a predetermined modified free wake.

[0013] Preferably, the aerodynamic modeling method using quasi-steady aerodynamic forces combined with a predetermined modified free wake to establish a rotor flow field model includes:

[0014] The predetermined modified free wake is based on the incompressible assumption and simplifies the rotor wake vortex into a straight vortex line;

[0015] The rotor vorticity field is described by the three-dimensional incompressible viscous NS equations and expressed as velocity-vorticity (u, ω);

[0016] The wake vortex line moves freely at the local speed in the rotor flow field, and the intensity remains unchanged. The speed of the wake position movement is expressed as follows:

[0017]

[0018] Where r is the position vector of the wake point, V is the local velocity of the wake point, and the position vector r can be expressed as the tail angle ξ and the blade azimuth angle function, so formula (1) can be expressed as the following partial differential equation:

[0019]

[0020] The term on the right side of Equation (2) is the vortex line's moving velocity V. The finite difference format is used to discretize Equation (2) in time and space to obtain the difference equation. The difference equation is solved using the predictor-corrector method.

[0021] The boundary conditions are

[0022] Preferably, the step 201 includes:

[0023] Since the distributed multi-rotor aircraft is in a subsonic state in forward flight, the wing aerodynamic force is analyzed using the unsteady panel method to establish the wing flow field model.

[0024] Preferably, since the distributed multi-rotor aircraft is in a subsonic forward flight state, the wing aerodynamic force adopts the unsteady panel method to establish a wing flow field model, including:

[0025] Except for the vicinity of the object surface and the wake region, the wing flow field can be assumed to be inviscid, irrotational, and incompressible. In the inertial coordinate system, the continuity equation can be expressed as a function of the velocity potential φ, that is,

[0026]

[0027] The solution of Equation (3) can be composed of a series of sinks σ and dipoles μ on the object surface and the wake vortex surface, that is,

[0028]

[0029] Where S B With S W are the wing object surface and the wing trailing vortex surface, n is the unit vector of the outer normal of the object surface, and r = (x, y, z) is the position of the spatial point;

[0030] The potential function φ can satisfy the object surface boundary conditions and far-field boundary conditions to determine the surface element σ and dipole μ strength.

[0031] Preferably, step 301 includes:

[0032] The relationships between rotors, between rotors and wings, and between elastic deformation and aerodynamic grid motion are established to form a distributed multi-rotor rotor and wing aerodynamic interference model.

[0033] Preferably, the establishing of the relationship between rotors, between rotors and wings, and between elastic deformation and aerodynamic grid motion to form a distributed multi-rotor rotor and wing aerodynamic interference model includes:

[0034] The rotor flow field model and the wing flow field model are coupled through the induced velocities between the rotors and between the rotor and the wing. Based on the interpolation relationship between the aerodynamic grid motion and the three-dimensional deformation motion of the rotor and fuselage, an aerodynamic interference model of the rotor and wing that can consider the three-dimensional elastic deformation is established.

[0035] Preferably, step 401 includes:

[0036] According to the Kutta-Joukowski theorem, the rotor aerodynamic force is determined, and according to the unsteady Bernoulli equation, the wing aerodynamic force is determined, and the aerodynamic interference analysis of the distributed multi-rotor rotor and wing is completed.

[0037] Beneficial technical effects of this application:

[0038] The distributed multi-rotor aerodynamic interference analysis method provided in this application, which can consider three-dimensional elastic deformation, is different from the traditional aerodynamic interference analysis method based on simplified two-dimensional blade element theory and inflow model. It adopts the unsteady panel method to replace the two-dimensional blade element theory, and adopts the free wake model to replace the inflow model, and considers the influence of three-dimensional deformation, thereby effectively improving the accuracy of aerodynamic interference analysis of distributed multi-rotor rotors and wings. At the same time, it is different from the distributed multi-rotor aerodynamic interference analysis method that can consider three-dimensional elastic deformation of the CFD analysis method. It can consider elastic deformation, thereby effectively improving the efficiency and accuracy of aerodynamic interference calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a schematic diagram of the aerodynamic grid of a distributed multi-rotor aircraft provided in an embodiment of the present application;

[0040] Figure 2 This is a schematic diagram of the wing cross-sectional pressure distribution under the aerodynamic interference of the rotor and wing provided in an embodiment of the present application. DETAILED DESCRIPTION

[0041] The present invention proposes a distributed multi-rotor aircraft aerodynamic interference analysis method that can consider three-dimensional elastic deformation. The aerodynamic interference analysis between the rotors and between the rotors and wings of the distributed multi-rotor aircraft needs to consider the three-dimensional deformation of the rotors and wings. The free wake method is combined with the lifting surface theory to establish a rotor aerodynamic model, and the unsteady panel method that can take into account the three-dimensional deformation motion of any point on the wing is used to model the wing aerodynamic force. Finally, the transmission relationship between the rotor and wing structure motion and the aerodynamic grid motion is established. The above methods are combined to establish a distributed multi-rotor aircraft aerodynamic interference analysis method between the rotors and between the rotors and wings that can consider three-dimensional elastic deformation. This is of great significance for accurately analyzing the aerodynamic interference, aeroelastic response and stability of the rotors and wings of the distributed multi-rotor aircraft.

[0042] In an embodiment of the present application, a free wake method based on a predetermined correction format is used to simulate the rotor flow field. The rotor blades are discretized into multiple aerodynamic grids using the lifting surface method, and each aerodynamic grid satisfies the object surface and far-field boundary conditions. An aerodynamic model of the fuselage is established based on the unsteady panel method. The wing is discretized into multiple aerodynamic grids using unsteady panel elements. The continuity equation can be expressed as a function of the velocity potential. The solution of the velocity potential function can be composed of a series of sinks σ and dipoles μ on the object surface and the wake vortex surface. The potential function satisfies the object surface boundary conditions and the far-field boundary conditions, and the panel element and dipole strengths are determined.

[0043] By establishing coupling relationships between the induced velocities between the rotors and between the rotors and wings, and to account for 3D elastic deformation, the aerodynamic mesh motion term caused by the deformation of the rotor and wing structures is added to the surface boundary conditions. The aerodynamic mesh motion term is derived by interpolation of the structural motion. Based on this, an aerodynamic interference model for a distributed multirotor aircraft is established. The rotor aerodynamic forces are then determined using the Kutta-Joukowski theorem, and the wing aerodynamic forces are determined using the unsteady Bernoulli equations. This completes the aerodynamic interference analysis of the rotors and wings of a distributed multirotor aircraft, considering 3D elastic deformation.

[0044] In the present invention, a free wake is used to simulate the rotor flow field, and an unsteady panel method is used to establish a wing aerodynamic model. In order to take into account three-dimensional elastic deformation, thin plate spline interpolation, which is commonly used in fixed-wing flutter analysis, is introduced into the wing aerodynamic model. Shape function interpolation is introduced into the rotor aerodynamic model. A coupling relationship is established through the induced velocity between the rotors and between the rotor and the wing. Finally, an aerodynamic force equation is used to establish an aerodynamic interference analysis model for a distributed multi-rotor aircraft.

[0045] Different from traditional aerodynamic interference analysis methods for distributed multi-rotor aircraft based on simplified two-dimensional blade element theory and inflow models, this new method can account for three-dimensional elastic deformation. It replaces the two-dimensional blade element theory with an unsteady panel method and the inflow model with a free wake model. It also considers the effects of three-dimensional deformation, effectively improving the accuracy of aerodynamic interference analysis of distributed multi-rotor rotors and wings. Furthermore, unlike CFD analysis methods that can account for three-dimensional elastic deformation, this method can account for elastic deformation and has higher computational efficiency, making it more suitable for engineering calculation analysis.

[0046] See also Figure 1 and Figure 2 In other embodiments of the present application, a method for analyzing aerodynamic interference between a distributed multi-rotor rotor and a wing taking into account three-dimensional elastic deformation includes:

[0047] (1) Establishing a rotor flow field model based on a predetermined modified free wake and lifting surface model;

[0048] (2) Establish a wing flow field model based on the unsteady panel method;

[0049] (3) Establish the relationship between rotors, between rotors and wings, and between elastic deformation and aerodynamic grid motion to form a distributed multi-rotor rotor and wing aerodynamic interference model;

[0050] (4) Determine the rotor aerodynamic force based on the Kutta-Joukowski theorem, determine the wing aerodynamic force based on the unsteady Bernoulli equation, and complete the aerodynamic interference analysis of the distributed multi-rotor rotor and wing;

[0051] In a feasible implementation, the following is included:

[0052] Step 1: Establish the rotor flow field model.

[0053] The rotor aerodynamic analysis uses a quasi-steady aerodynamic analysis method combined with a pre-determined modified free wake. The pre-determined modified free wake is based on the incompressible assumption and simplifies the rotor wake vortices into straight vortex lines. The rotor vorticity field can be described by the three-dimensional incompressible viscous Navier-Stokes equations, expressed as velocity-vorticity (u, ω). In many practical applications, it is reasonable to assume that the viscosity term has little effect on the rotor flow field. Therefore, the wake vortex lines move freely at the local velocity in the rotor flow field, and their intensity remains unchanged. The wake position movement speed is expressed as follows:

[0054]

[0055] Where r is the position vector of the wake point and V is the local velocity of the wake point. The position vector r can be expressed as the tail angle ξ and the blade azimuth angle function, so formula (1) can be expressed as the following partial differential equation:

[0056]

[0057] The right-hand side of Equation (2) is the velocity V of the vortex line. The finite difference scheme is used to discretize Equation (2) in time and space to obtain the difference equation. The difference equation is solved by the predictor-corrector method (PIPC)

[0058] The boundary conditions are

[0059] Step 2: Establish the wing flow field model.

[0060] Since the distributed multi-rotor aircraft flies forward at subsonic speed, the wing aerodynamic force is analyzed using the unsteady panel method. Except for the vicinity of the object surface and the wake region, the wing flow field can be assumed to be inviscid, irrotational, and incompressible. In the inertial coordinate system, the continuity equation can be expressed as a function of the velocity potential φ, that is,

[0061]

[0062] The solution of Equation (3) can be composed of a series of sinks σ and dipoles μ on the object surface and the wake vortex surface, that is,

[0063]

[0064] Where S B With S W are the wing object surface and the wing trailing vortex surface respectively, n is the unit vector of the outer normal of the object surface, and r = (x, y, z) is the position of the spatial point.

[0065] The potential function φ can be used to satisfy the object surface boundary conditions and far-field boundary conditions to determine the strength of the surface element σ and the dipole μ. Step 3: Establish an aerodynamic interference model of the distributed multi-rotor rotor and wing considering elastic deformation.

[0066] In the process of solving the rotor wake, the coupling between rotors and wing to rotor is realized through the velocity term V in formula (2). The formula of the velocity term V is as follows:

[0067] V=V b∞ +V fb +V bb +V sb +V wb +V db (5)

[0068] Among them, V b∞ is the free flow velocity of the blade, V db is the blade speed, V fb is the unsteady surface element induced velocity of the fuselage, V bb is the vortex induced speed of each rotor, V sb is the trailing vortex induced velocity of each rotor, V wb is the far wake induced speed of each rotor.

[0069] The coupling between the rotors is given by Equation (5): The vortex induced velocity V of each rotor blade is bb , the induced speed V of each rotor trailing vortex sb and each rotor blade tip vortex induced velocity V wb The induced velocity is obtained by calculation using the Biot-Savart law.

[0070] The induced velocity V of the wing relative to the rotor fb Based on the Hess theorem, the induced velocity u of a dipole element with strength μ at any point in space is μ Calculated by the following formula:

[0071]

[0072] Where r is the position vector, γ is the equivalent surface vortex, μ is the line vortex, l is the wake linear vortex unit vector, and C represents the wake surface element boundary line.

[0073] Blade movement speed V db Finite element mesh motion of blade three-dimensional structure The motion of any position of the blade is obtained by shape function interpolation. The specific formula is as follows:

[0074]

[0075] Where H(s) is the structural finite element shape function, and s is any position on the blade.

[0076] In solving the wing flow field, the boundary conditions of the object surface are as follows:

[0077]

[0078] Among them, n is the external normal direction, V f is the velocity of any point on the surface. To consider the influence of the rotor on the wing and the three-dimensional elastic deformation of the wing, V f The calculation formula is as follows:

[0079]

[0080] Where, is the induced velocity of each rotor attachment vortex on the wing aerodynamic grid, is the induced velocity of each rotor trailing vortex on the wing aerodynamic grid, is the induced velocity of each rotor tip vortex on the wing aerodynamic grid, V df is the wing aerodynamic grid movement speed. The above induced speed can be obtained according to the Biot-Savart law. The wing aerodynamic grid movement speed V df By structural deformation get.

[0081] In order to obtain the wing aerodynamic grid motion speed, it is necessary to calculate the speed of the wing structure grid point displacement meter using the thin plate spline interpolation method. The three-dimensional structure finite element grid point motion and aerodynamic grid point motion V df The conversion relationship is as follows

[0082]

[0083] Where G as is the thin plate spline interpolation matrix.

[0084] The rotor flow field model and the wing flow field model are coupled through the induced velocities between the rotors and between the rotors and wings. Based on the interpolation relationship between the aerodynamic grid motion and the three-dimensional deformation motion of the rotor and fuselage, an aerodynamic interference analysis model of a distributed multi-rotor aircraft that can consider three-dimensional elastic deformation is established.

[0085] Step 4: Aerodynamic interference analysis of distributed multi-rotor aircraft

[0086] After establishing the flow field of the distributed multi-rotor, the Kutta-Joukowski theorem is used to determine the rotor aerodynamic force. The specific analysis formula is as follows

[0087]

[0088] Where L iis the blade aerodynamic force, ρ is the air density, c is the rotor chord length, is the lift line slope, α ei is the effective angle of attack. ei The sum of the angle of attack caused by the blade section twist angle, free flow and induced velocity.

[0089] According to the unsteady Bernoulli equation, the aerodynamic force of the wing is calculated by the velocity potential and the surface velocity. The specific formula is as follows:

[0090]

[0091] The dimensionless pressure can be expressed as follows:

[0092]

[0093] where v, p, and ρ d 、p ref 、v ref are local fluid velocity, pressure, density, reference pressure and reference velocity respectively. The partial derivative of the potential function with respect to time is It can be calculated from the surface velocity potential of the object.

[0094] The unsteady aerodynamic force ΔF of the kth grid of the wing k It can be calculated through the equation, the specific formula is as follows:

[0095]

[0096] Where C pk , ΔS k and n k are the dimensionless pressure, grid area and normal vector of the kth grid respectively.

[0097] Through the above theory, the aerodynamic solution of the rotor and wing can be completed to complete the aerodynamic interference analysis of the distributed multi-rotor aircraft.

[0098] This application is different from the traditional aerodynamic interference analysis method based on simplified two-dimensional blade element theory and inflow model. It adopts the unsteady panel method to replace the two-dimensional blade element theory, and the free wake model to replace the inflow model, and considers the influence of three-dimensional deformation, effectively improving the accuracy of aerodynamic interference analysis of distributed multi-rotor rotors and wings. At the same time, it is different from the CFD analysis method of the distributed multi-rotor aerodynamic interference analysis method that can consider three-dimensional elastic deformation. It can consider elastic deformation, effectively improving the efficiency and accuracy of aerodynamic interference calculation.

Claims

1. A distributed multi-rotor aerodynamic interference analysis method, characterized in that: The method comprises: Step 101: Establish a rotor flow field model; Step 201: Establish a wing flow field model; Step 301: Establishing a rotor and wing aerodynamic interference model based on the rotor flow field model and the wing flow field model; wherein the rotor and wing aerodynamic interference model is a distributed rotor aerodynamic interference model that considers three-dimensional elastic deformation; Step 401: Analyze the aerodynamic interference of the distributed multi-rotor aircraft according to the rotor and wing aerodynamic interference model.

2. The method according to claim 1, characterized in that The step 101 includes: The rotor flow field model is established by using the aerodynamic modeling method of quasi-steady aerodynamics combined with a predetermined corrected free wake.

3. The method according to claim 2, characterized in that The aerodynamic modeling method using quasi-steady aerodynamic forces combined with a predetermined corrected free wake to establish a rotor flow field model includes: The predetermined modified free wake is based on the incompressible assumption and simplifies the rotor wake vortex into a straight vortex line; The rotor vorticity field is described by the three-dimensional incompressible viscous NS equations and expressed as velocity-vorticity (u, ω); The wake vortex line moves freely at the local speed in the rotor flow field, and the intensity remains unchanged. The speed of the wake position movement is expressed as follows: Where r is the position vector of the wake point, V is the local velocity of the wake point, and the position vector r can be expressed as the tail angle ξ and the blade azimuth angle function, so formula (1) can be expressed as the following partial differential equation: The term on the right side of Equation (2) is the vortex line's moving velocity V. The finite difference format is used to discretize Equation (2) in time and space to obtain the difference equation. The difference equation is solved using the predictor-corrector method. The boundary conditions are 4. The method according to claim 3, characterized in that The step 201 includes: Since the distributed multi-rotor aircraft is in a subsonic state in forward flight, the wing aerodynamic force is analyzed using the unsteady panel method to establish the wing flow field model.

5. The method according to claim 4, characterized in that Since the distributed multi-rotor aircraft is in a subsonic forward flight state, the wing aerodynamic force adopts the unsteady panel method to establish a wing flow field model, including: Except for the vicinity of the object surface and the wake region, the wing flow field can be assumed to be inviscid, irrotational, and incompressible. In the inertial coordinate system, the continuity equation can be expressed as a function of the velocity potential φ, that is, The solution of Equation (3) can be composed of a series of sinks σ and dipoles μ on the object surface and the wake vortex surface, that is, Where S B With S W are the wing object surface and the wing trailing vortex surface, n is the unit vector of the outer normal of the object surface, and r = (x, y, z) is the position of the spatial point; The potential function φ can satisfy the object surface boundary conditions and far-field boundary conditions to determine the surface element σ and dipole μ strength.

6. The method according to claim 5, characterized in that The step 301 includes: The relationships between rotors, between rotors and wings, and between elastic deformation and aerodynamic grid motion are established to form a distributed multi-rotor rotor and wing aerodynamic interference model.

7. The method according to claim 6, characterized in that The relationship between rotors, between rotors and wings, and between elastic deformation and aerodynamic grid motion is established to form a distributed multi-rotor rotor and wing aerodynamic interference model, including: The rotor flow field model and the wing flow field model are coupled through the induced velocities between the rotors and between the rotor and the wing. Based on the interpolation relationship between the aerodynamic grid motion and the three-dimensional deformation motion of the rotor and fuselage, an aerodynamic interference model of the rotor and wing that can consider the three-dimensional elastic deformation is established.

8. The method according to claim 7, characterized in that The step 401 includes: According to the Kutta-Joukowski theorem, the rotor aerodynamic force is determined, and according to the unsteady Bernoulli equation, the wing aerodynamic force is determined, and the aerodynamic interference analysis of the distributed multi-rotor rotor and wing is completed.

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