Three-dimensional profile rotor wing and multi-wake pneumatic analysis method thereof

Abstract

The invention provides a three-dimensional shape rotor wing and a multi-wake aerodynamic analysis method thereof. The method comprises the following steps: acquiring overall parameters, aerodynamic parameters, kinetic parameters, wake parameters and flight state parameters of the rotor wing; based on the rotor overall parameters, the aerodynamic parameters, the kinetic parameters, the wake parameters and the flight state parameters, rotor overall flow field distribution under the initial condition is obtained; updating the overall flow field distribution of the rotor wing under the initial condition to obtain final overall flow field distribution of the rotor wing; according to the method, the unsteady aerodynamic model, the multi-wake model and the structural dynamics model suitable for the complex three-dimensional shape rotor wing are established, and the aerodynamic analysis and aeroelastic dynamics analysis capabilities of the complex three-dimensional shape rotor wing are improved.

Description

Technical Field

[0001] The present application belongs to the technical field of helicopter rotor design and theoretical modeling, and in particular relates to a three-dimensional rotor and a multi-wake aerodynamic analysis method thereof. Background Art

[0002] The rotor system is the core component of the helicopter, and its performance directly determines the level of helicopter equipment. The current helicopter R&D and design must comprehensively consider and balance multiple target requirements such as rotor performance, noise, and vibration, forcing the rotor to adopt unconventional rotors.

[0003] However, compared with traditional straight blades, unconventional rotors pose new difficulties in aerodynamic analysis and aeroelastic analysis.

[0004] Therefore, it is necessary to establish an aerodynamic analysis method that can accurately predict unconventional rotors and process characteristics in order to effectively support the design and development of unconventional rotors. Summary of the invention

[0005] Purpose of the invention: To propose a multi-wake aerodynamic calculation method considering a three-dimensional rotor shape, which is applied to the aerodynamic noise analysis and aeroelastic dynamics analysis of rotors with complex three-dimensional aerodynamic layouts such as forward protrusion, backsweep and downward reversal.

[0006] In a first aspect, the present application provides a three-dimensional rotor, comprising:

[0007] The blade beam has a three-dimensional bending structure; wherein the elastic axis of the blade beam is a broken line or a curve.

[0008] Preferably, the three-dimensional bending structure is arranged at the middle part and / or the tip part of the blade beam.

[0009] In a second aspect, the present application also provides a method for aerodynamic analysis of a three-dimensional rotor with multiple wakes, the method comprising:

[0010] Step 1, obtaining rotor overall parameters, aerodynamic parameters, dynamic parameters, wake parameters and flight state parameters;

[0011] Step 2, calculating the rotor flow field under initial conditions based on the rotor overall parameters, aerodynamic parameters, dynamic parameters, wake parameters and flight state parameters;

[0012] Step 3, setting a time step and a time threshold; wherein the time step is negatively correlated with the rotor speed;

[0013] Step 4: Based on the rotor overall parameters, the aerodynamic parameters and the flight state parameters, an aerodynamic model is used to update the blade aerodynamic force under the initial conditions with the time step to obtain the blade aerodynamic force at the current moment;

[0014] Step 5: Based on the rotor overall parameters, the dynamic parameters and the blade aerodynamic force at the current moment, the blade elastic space displacement field is calculated using the rotor dynamics model;

[0015] Step 6: Based on the rotor overall parameters, the aerodynamic parameters, the wake parameters, the flight state parameters, the blade aerodynamic force at the current moment, and the blade elastic space displacement field, a multi-wake model is adopted to update the rotor initial wake with the step size to obtain the rotor wake at the current moment;

[0016] Step 7: Based on the blade aerodynamic force, blade elastic space displacement field and rotor wake at the current moment, an updated rotor flow field is obtained.

[0017] Preferably, the method further comprises:

[0018] Step 8: If the update time is greater than the time threshold, stop updating the rotor flow field; wherein the update time is the time obtained by accumulating the step length.

[0019] Preferably, the step 2 comprises:

[0020] Step 201, based on the rotor overall parameters, the aerodynamic parameters and the flight state parameters, an aerodynamic model is used to calculate the blade aerodynamic force under initial conditions;

[0021] Step 202: determining the blade spatial position under initial conditions based on the rotor overall parameters and the aerodynamic parameters;

[0022] Step 203, based on the rotor overall parameters, the aerodynamic parameters, the wake parameters, the flight state parameters, the blade aerodynamic force under the initial conditions and the blade spatial position under the initial conditions, a multi-wake model is used to calculate the rotor initial wake.

[0023] Preferably, the aerodynamic model is a Leishman-Beddoes two-dimensional unsteady aerodynamic model.

[0024] Preferably, the step 203 includes:

[0025] Based on the Lagrangian description of the flow field, the control equations of the rotor wake are constructed using the discrete vortex element and vortex line method;

[0026] Based on the control equations, the initial rotor wake is calculated.

[0027] Preferably, step 5 comprises:

[0028] The medium deformation beam hypothesis was adopted, and the blade strain energy, kinetic energy and virtual work terms were derived based on the Hamiltonian principle. The rotor dynamics equation was established, and the blade elastic space displacement field was obtained by solving the rotor dynamics equation.

[0029] Beneficial technical effects of this application:

[0030] The present invention establishes an unsteady aerodynamic model, a multi-wake model and a structural dynamics model suitable for a rotor with a complex three-dimensional shape. On the one hand, it can effectively reflect the trailing vortex released by the rotor with a complex three-dimensional shape in a working state and the wake formed by converging at the bend, and effectively reflects the rolling and convergence characteristics of the wake near the blade. On the other hand, it effectively reflects the three-dimensional layout characteristics such as protrusion / sweepback / downward reversal, accurately describes the movement of the blade with a complex three-dimensional shape in the spatial field, and improves the aerodynamic analysis and aeroelastic dynamics analysis capabilities of the rotor with a complex three-dimensional shape. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram of a complex three-dimensional rotor geometry model structure provided in an embodiment of the present application;

[0032] Figure 2 This is a schematic diagram of a blade multi-wake provided in an embodiment of the present application;

[0033] Figure 3 This is a schematic diagram of a rotor single blade tip vortex wake result provided in an embodiment of the present application;

[0034] Figure 4 It is a schematic diagram of the geometric result of multiple wakes of a straight blade in a hovering state provided by an embodiment of the present application;

[0035] Figure 5 It is a schematic diagram of the geometric result of a complex three-dimensional rotor with multiple wakes in a forward flight state provided by an embodiment of the present application;

[0036] Figure 6 It is a flow chart of an aerodynamic analysis method considering multiple wakes of a three-dimensional rotor provided in an embodiment of the present application. DETAILED DESCRIPTION

[0037] See also Figure 1-Figure 6 It should be noted that the rotor with unconventional forward sweep and downward reverse geometry (see Figure 1 ) Compared with traditional straight blades, the most direct and obvious feature is that the elastic axis of the blade beam is no longer a straight line, but a broken line or a curve. The aerodynamic layout and structural characteristics bring new difficulties to the aerodynamic analysis and aeroelastic analysis of the complex three-dimensional rotor.

[0038] On the one hand, the blades have three-dimensional bending structures such as forward protrusion, backward sweep and downward reversal, so that the trailing vortex released by the rotor will converge at the bend to form a vortex line, making the three-dimensional effect and flow field distribution of the rotor more complicated.

[0039] On the other hand, rotors with complex three-dimensional shapes have complex coupling effects including bending-torsion coupling, tension-torsion coupling, and tension-bending coupling. The elastic movement of the blades directly affects the aerodynamic distribution on the blades and the changes in the rotor wake.

[0040] Second, see Figure 2 For non-conventional straight blades, vortices will appear at the blade bends and blade tips such as blade flaps (trailing edge winglets), forward sweeps, etc., and converge into vortex lines to form wakes. Figure 4 The figure on the right is a schematic diagram of the wake geometry results of a single straight blade, and the figure on the left is a schematic diagram of the wake geometry results of the entire rotor.

[0041] In an embodiment of the present application, a multi-wake aerodynamic analysis method considering a three-dimensional rotor is provided, including:

[0042] Step 1: Initialization: Obtain the input information required by the calculation module, including rotor overall parameters, aerodynamic parameters, dynamic parameters, wake parameters, and flight state parameters.

[0043] Among them, the overall parameters of the rotor include rotor radius, rotor speed, rotation direction, and hub configuration; aerodynamic parameters include airfoil data, blade airfoil distribution, aerodynamic shape distribution, and aerodynamic unit settings; dynamic parameters include blade mass distribution, flapping / flapping / torsional stiffness distribution, center of gravity position distribution, polar moment of inertia distribution, hinge position, hub mass distribution, flapping / flapping / torsional stiffness distribution, and rotor structural unit settings; wake parameters include time step, total time, and number of wake circles; flight state parameters include forward flight speed, air density, and rotor attitude angle.

[0044] Step 2: Calculate the rotor flow field under the initial conditions, which includes calculating the aerodynamic force under the initial conditions of the blades, determining the spatial position of the blades under the initial conditions, and calculating the initial wake of the rotor, and then calculating the overall flow field of the rotor, including the velocities of each section of the blade.

[0045] Among them, the blade aerodynamic calculation adopts the Leishman-Beddoes two-dimensional unsteady aerodynamic model, and requires the input of overall parameters and aerodynamic parameters.

[0046] Among them, the blade elastic space displacement field calculation adopts the medium deformation beam assumption, and the blade strain energy, kinetic energy and virtual work terms are derived based on the Hamilton principle (the expression is as follows, where δU is the virtual potential energy, δT is the virtual kinetic energy, and δW is the virtual work of the external force) to establish the rotor dynamics equation, and finally the blade elastic space displacement field is obtained by solving the equation. The blade elastic space displacement field calculation requires the input of overall parameters, aerodynamic parameters, dynamic parameters, and flight state parameters.

[0047]

[0048] The expression of virtual potential energy δU is as follows, where ε is the strain matrix, σ is the material stress matrix, A is the cross-sectional area, and x is the radial position.

[0049] δU=∫∫(δε T σ)dAdx

[0050] The external virtual work δW is calculated using the above aerodynamic model. The virtual kinetic energy δT is expressed as follows, where ρ is the air density, V is the blade motion speed, including the blade flapping / swinging / torsion motion speed and rotation speed, A is the cross-sectional area, and x is the radius position.

[0051] δT=∫∫ρVδVdAdx

[0052] The rotor dynamics equation is expressed as follows, where M is the rotor system mass matrix, C is the rotor system damping matrix, K is the rotor system stiffness matrix, and F is the rotor system force column vector

[0053]

[0054] When calculating the virtual kinetic energy δT, it is necessary to accurately describe the spatial position of the control point of the blade circulation distribution and establish the position vector at any point on the blade. (The expression is as follows), where O is the hub center, k is the blade segment number, A is the node number, P is any point on the undeformed elastic axis of blade segment k, P1 is any point on the elastic axis of blade segment k after deformation, and Q is any point on the cross section of blade segment k P1 after deformation.

[0055]

[0056] In view of the forward / backward sweep and up / downward reverse characteristics, in order to maintain the continuity and consistency of the spatial positions of the two adjacent unit nodes at the blade bending, the transformation matrix T is introduced. Assuming that the forward swept section of the blade is at an angle of Λ1 relative to the main blade section unit, the down reverse section is at an angle of Λ2 relative to the main blade section unit, and the blade's own pre-twist is at an angle of Λ3 relative to the main blade section unit, the coordinate matrix relationship is as follows, [i, j, k] is the conjoined coordinate system of the blade unit, and the subscript represents the unit number.

[0057]

[0058] The transformation matrix T is as follows:

[0059]

[0060] In addition, the deformation compatibility principle of adjacent units at the inflection point of the blade should be established to maintain the deformation coordination between the units, that is, to describe the nonlinear transformation matrix between the deformation and the undeformed three-dimensional blade. The specific expression is as follows, where U represents the undeformed coordinate, D represents the deformed coordinate, and the subscript represents the number of the two adjacent unit segments at the inflection point. s It is the inter-node transformation matrix, and the deformation displacement between units must be coordinated and continuous, and the bending slope must also be continuous, that is, the translational freedom degree is continuous and the rotational freedom degree is continuous.

[0061] U2=T s U1

[0062] D2=T s D1

[0063] Among them, the multi-wake model is used to calculate the overall flow field distribution of the rotor, which requires the input of overall parameters, aerodynamic parameters, wake parameters and flight state parameters. The multi-wake model describes the flow field based on Lagrangian, and uses discrete vortex elements and vortex line methods to construct the control equation of the rotor wake. The transport equation of the wake motion is as follows, where r0 is the starting position vector of the vortex line, r is the vortex line wake vector; V is the local velocity at the location of the vortex line, and t is the time term.

[0064]

[0065] The blade generates aerodynamic force in the flow field, and a trailing vortex is released at the trailing edge of the blade, which converges behind the blade to form a near wake. The circulation of each trailing vortex is equal to the difference in the circulation of the adjacent blade aerodynamic sections as follows: n,j is the circulation of the jth trailing vortex; Γ b,j is the attached vortex ring of the jth blade unit, N s is the number of pneumatic units of the blade.

[0066] Γ n,j+1 =Γ b,j -Γ b,j+1 ,j=1,...,N s

[0067] The traditional free wake model assumes that the trailing vortices will distort each other, roll up, and converge to form a far wake after they are released, and that they will roll up to form a single blade tip vortex far wake within a certain time and azimuth. In the invention, however, any number of far wakes can be set, and they will be maintained during the subsequent wake movement and distortion process, and eventually form two far wakes of blade root vortex and blade tip vortex, thereby effectively improving the aerodynamic analysis and prediction capabilities of complex three-dimensional rotors.

[0068] The Biot-Osafal theorem is used to solve the induced velocity of the wake at any position in space. The Vatistas vortex core model is used in the process of movement, distortion and dissipation of the wake. The expression is as follows, where V θ is the induced velocity, Γ v is the vortex strength, n = 2, r c is the vortex core radius, and r is the position vector of the current wake.

[0069]

[0070] The position vector of the wake in the global coordinates is r(ψ,ζ), where ψ is the blade azimuth and ζ is the wake angle. It moves freely at the local speed. The control equation for a wake can be written as follows, where: Ω is the rotor rotation angular velocity, V ∞ Incoming flow velocity, V ind is the induced velocity at that point, and r is the vortex vector of the wake straight segment. Finally, the time-marching algorithm is used to solve the rotor wake geometry and blade aerodynamic distribution.

[0071]

[0072] The rotor wake under the initialization condition is obtained only by solving the rotation speed and the incoming flow speed, and is not affected by the mutual induction effect, and no distortion iterative calculation is performed on the wake. In the subsequent iterative cycle calculation, the distortion iterative solution of the wake will be performed.

[0073] Step 3: Set the current time T and the step size Δt, update the blade aerodynamic force distribution at the current time, and update the blade aerodynamic force distribution for one round under the fixed wake shape; the aerodynamic force model adopts the unsteady aerodynamic force model based on the second-order lift line theory (Leishman-Beddoes two-dimensional unsteady aerodynamic force model).

[0074] Step 4, calculate the elastic spatial displacement field of the blade, and adopt a rotor dynamics model that considers the complex three-dimensional blade layout design to obtain the elastic motion of the blade under the periodic state and the spatial displacement field of each blade of the entire rotor. Unlike the traditional rotor dynamics model that simplifies the blade elastic axis into a one-dimensional linear, the present invention adopts a rotor dynamics model that considers the complex three-dimensional blade shape. The blade elastic axis considers the three-dimensional characteristics in space, and introduces a conversion matrix at the blade bend. At the same time, the deformation compatibility principle of the adjacent bending units is established to maintain the continuity and coordination of the blade in the spatial displacement field, and accurately reflect the movement of any point of the blade under the three-dimensional layout and the flapping / swaying / torsion coupling effect.

[0075] Among them, the calculation of the blade elastic spatial displacement field requires an accurate description of the spatial position of the control points of the blade circulation distribution and the establishment of the position vector at any point on the blade. (The expression is as follows), where O is the hub center, k is the blade segment number, A is the node number, P is any point on the undeformed elastic axis of blade segment k, P1 is any point on the elastic axis of blade segment k after deformation, and Q is any point on the cross section of blade segment k P1 after deformation.

[0076]

[0077] In view of the forward / backward sweep and up / downward reverse characteristics, in order to maintain the continuity and consistency of the spatial positions of the two adjacent unit nodes at the blade bending, the transformation matrix T is introduced. Assuming that the forward swept section of the blade is at an angle of Λ1 relative to the main blade section unit, the down reverse section is at an angle of Λ2 relative to the main blade section unit, and the blade's own pre-twist is at an angle of Λ3 relative to the main blade section unit, the coordinate matrix relationship is as follows, [i, j, k] is the conjoined coordinate system of the blade unit, and the subscript represents the unit number.

[0078]

[0079] The transformation matrix T is as follows:

[0080]

[0081] In addition, the deformation compatibility principle of adjacent units at the inflection point of the blade should be established to maintain the deformation coordination between the units, that is, to describe the nonlinear transformation matrix between the deformation and the undeformed three-dimensional blade. The specific expression is as follows, where U represents the undeformed coordinate, D represents the deformed coordinate, and the subscript represents the number of the two adjacent unit segments at the inflection point. s It is the inter-node transformation matrix, and the deformation displacement between units must be coordinated and continuous, and the bending slope must also be continuous, that is, the translational freedom degree is continuous and the rotational freedom degree is continuous.

[0082] U2=T s U1

[0083] D2=T s D1

[0084] Step 5: Update the rotor wake and use a multi-wake model to update the rotor wake shape. Unlike the traditional free wake method that rolls up the near wake to form a single blade tip vortex, the present invention uses a multi-wake design method to set any far wake and participate in the subsequent wake distortion, merging and dissipation, further accurately simulating the induction effect of the flow wake near the blade on the blade, and improving the accuracy of the blade aerodynamic estimation.

[0085] Among them, the position vector of each wake in the global coordinate is r(ψ,ζ), where ψ is the blade azimuth and ζ is the wake angle. It moves freely at the local speed. The control equation for a wake can be written as follows, where: Ω is the rotor rotation angular velocity, V ∞ Incoming flow velocity, V ind is the induced velocity at that point, and r is the vortex vector of the wake straight segment. Finally, the time-marching algorithm is used to solve the rotor wake geometry and blade aerodynamics.

[0086]

[0087] Step 6: Update the rotor flow field distribution, including the velocity field distribution of each blade section. If the current time T is greater than the set time limit T max , then end the calculation, if it is less than T max Then continue to enter the aerodynamic calculation cycle at the next moment.

[0088] The aerodynamic model, multi-wake model and rotor dynamics model involved in the multi-wake aerodynamic calculation method considering the three-dimensional rotor are as follows:

[0089] (1) Rotor unsteady aerodynamic model

[0090] The unsteady aerodynamic model based on the second-order lift line theory (Leishman-Beddoes two-dimensional unsteady aerodynamic model) is adopted. The aerodynamic center is arranged at the 1 / 4 chord length position on the mid-arc of the blade profile, and the control point is arranged at the 3 / 4c chord length. The blade is divided into several aerodynamic segments along the span direction, which can effectively reflect the three-dimensional layout of the blade's protrusion, sweepback and downward reflection. The relationship between the blade aerodynamic force and the blade circulation distribution is established based on the Kutta-Joukowski theorem.

[0091] Where L is the blade segment aerodynamic force, ρ is the air density, U is the incoming flow velocity, c is the chord length, C lα is the slope of the lift line, α eff is the effective angle of attack, Γ the circulation.

[0092]

[0093] Each blade section will shed a trailing vortex at the trailing edge, and its strength is the difference in the circulation of adjacent blade sections. After the trailing vortex is shed, it will condense behind the blade to form a near wake, and continue to roll up and converge to eventually form a far wake.

[0094] (2) Multi-wake model

[0095] The multi-wake model is based on the Lagrangian description of the flow field, and the control equations of the rotor wake are constructed using the discrete vortex element and vortex line method. The transport equation of the wake motion is as follows, where r0 is the starting position vector of the vortex line, r is the vortex line wake vector; V is the local velocity at the location of the vortex line, and t is the time term.

[0096]

[0097] The blade generates aerodynamic force in the flow field, and a trailing vortex is released at the trailing edge of the blade, which converges behind the blade to form a near wake. The circulation of each trailing vortex is equal to the difference in the circulation of the adjacent blade aerodynamic sections as follows: n,j is the circulation of the jth trailing vortex; Γ b,j is the attached vortex ring of the jth blade unit, N s is the number of blade aerodynamic units

[0098] Γ n,j+1 =Γ b,j -Γ b,j+1 ,j=1,...,N s

[0099] The traditional free wake model assumes that the trailing vortices will distort each other, roll up, and converge to form a far wake after they are released, and that they will roll up to form a single blade tip vortex far wake within a certain time and azimuth. In the invention, however, any number of far wakes can be set, and they will be maintained during the subsequent wake movement and distortion process, and eventually form two far wakes of blade root vortex and blade tip vortex, thereby effectively improving the aerodynamic analysis and prediction capabilities of complex three-dimensional rotors.

[0100] The Biot-Osafal theorem is used to solve the induced velocity of the wake at any position in space. The Vatistas vortex core model is used in the process of movement, distortion and dissipation of the wake. The expression is as follows, where V θ is the induced velocity, Γ v is the vortex strength, n = 2, r c is the vortex core radius, and r is the position vector of the current wake.

[0101]

[0102] The position vector of the wake in the global coordinates is r(ψ,ζ), where ψ is the blade azimuth and ζ is the wake angle. It moves freely at the local speed. The control equation for a wake can be written as follows, where: Ω is the rotor rotation angular velocity, V ∞ Incoming flow velocity, V ind is the induced velocity at that point, and r is the vortex vector of the wake straight segment. Finally, the time-marching algorithm is used to solve the rotor wake geometry and blade aerodynamics.

[0103]

[0104] (3) Dynamic model of rotor blades with complex three-dimensional shapes;

[0105] It is necessary to accurately describe the spatial position of the control points of the blade circulation distribution, and it is necessary to be able to prepare a structural dynamics model that describes the motion of a complex three-dimensional rotor blade. The traditional rotor dynamics model simplifies the blade elastic axis into a one-dimensional linear, but the blade elastic axis of a complex three-dimensional blade with a forward / backward sweep and up / down reverse layout configuration also exhibits three-dimensional characteristics in space. Traditional rotor dynamics are no longer applicable, so this patent proposes a rotor dynamics model that takes into account complex three-dimensional blades. On the basis of the traditional dynamics model, a transformation matrix is ​​introduced at the blade bend, and at the same time, a deformation compatibility principle of adjacent bend units is established to maintain the continuity and coordination of the blade in the spatial displacement field, thereby effectively reflecting the three-dimensional layout characteristics such as forward protrusion / backward sweep / downward reverse, and accurately describing the motion of any point on the blade under the three-dimensional layout.

[0106] Establish the position vector at any point on the blade (The expression is as follows), where O is the hub center, k is the blade segment number, A is the node number, P is any point on the undeformed elastic axis of blade segment k, P1 is any point on the elastic axis of blade segment k after deformation, and Q is any point on the cross section of blade segment k P1 after deformation.

[0107]

[0108] The blades with complex three-dimensional shapes have layout configurations such as forward / backward sweep and up / down reverse, which makes the blade elastic axis no longer one-dimensional linear, but also shows three-dimensional characteristics in space. The blade is discretized into several units. In order to maintain the continuity and consistency of the spatial positions of the two adjacent unit nodes at the blade bending, the transformation matrix T is introduced. Assuming that the angle between the forward swept section of the blade and the main blade section unit is Λ1, the angle between the down reverse section and the main blade section unit is Λ2, and the angle between the blade's own pre-twist and the main blade section unit is Λ3, then the coordinate matrix relationship is as follows, [i, j, k] is the joint coordinate system of the blade unit, and the subscript represents the unit number.

[0109]

[0110] The transformation matrix T is as follows:

[0111]

[0112] The conversion relationship of blade elastic deformation is considered on the basis of the conversion relationship between blade units under undeformed conditions. Blade elastic motion includes stretching, flapping, swinging linear motion, and angular motion of flapping / swinging / torsion. In order to maintain the continuity of blade elastic deformation, the deformation compatibility principle of adjacent units at the blade inflection point must be established to maintain the deformation coordination between units, that is, to describe the nonlinear conversion matrix of three-dimensional blade deformation and undeformation. The specific expression is as follows, where U represents the undeformed coordinate, D represents the deformed coordinate, and the subscript represents the number of two adjacent unit segments at the inflection point. T s It is the inter-node transformation matrix, and the deformation displacement between units must be coordinated and continuous, and the bending slope must also be continuous, that is, the translational freedom degree is continuous and the rotational freedom degree is continuous.

[0113] U2=T s U1

[0114] D2=T s D1

[0115] Finally, based on the Hamilton principle (the expression is as follows), the blade strain energy, kinetic energy and virtual work terms are derived to establish the rotor dynamics equation, where δU is the virtual potential energy, δT is the virtual kinetic energy, and δW is the virtual work of the external force.

[0116]

[0117] The present invention proposes a multi-wake aerodynamic calculation method considering a three-dimensional rotor. Compared with the traditional straight blade, the present invention establishes an unsteady aerodynamic model, a multi-wake model and a structural dynamics model suitable for a complex three-dimensional rotor. On the one hand, it can effectively reflect the trailing vortex released by the complex three-dimensional rotor in the working state and the wake formed by converging at the bend ( Figure 5 ), and effectively reflects the rolling and convergence characteristics of the wake near the blades. On the other hand, it effectively reflects the three-dimensional layout characteristics such as forward projection / backward sweep / downward reflection, accurately describes the movement of complex three-dimensional shape blades in the space field, and improves the aerodynamic analysis and aeroelastic dynamics analysis capabilities of complex three-dimensional shape rotors.

[0118] In other embodiments of the present application, a multi-wake aerodynamic calculation method considering a three-dimensional rotor includes:

[0119] 1. Initialization: Input the input information required by the calculation module of the method of the present invention, including the overall parameters of the rotor, aerodynamic parameters, dynamic parameters, wake parameters, and flight state parameters.

[0120] 2. Calculate the rotor flow field distribution under initial conditions, which includes calculating the aerodynamic force distribution under the initial conditions of the blades, the elastic space displacement field of the blades under the initial conditions, and calculating the initial fixed wake shape based on the rigid body wake assumption, and then calculating the overall flow field distribution of the rotor, including the velocity field distribution of each blade section.

[0121] 3. Set the current time T and step size Δt, update the blade aerodynamic force at the current time, and update the aerodynamic force distribution of one round of blades under a fixed wake shape; the aerodynamic model adopts an unsteady aerodynamic model based on the second-order lift line theory.

[0122] 4. Calculate the elastic spatial displacement field of the blades, and adopt a rotor dynamics model that takes into account the complex three-dimensional blade layout design to obtain the elastic motion of the blades under the periodic state and the spatial displacement field of each blade of the entire rotor. Unlike the traditional rotor dynamics model that simplifies the blade elastic axis into a one-dimensional linear, the present invention adopts a rotor dynamics model that takes into account the complex three-dimensional shape of the blades. The three-dimensional characteristics of the blade elastic axis are considered in space, and a conversion matrix is ​​introduced at the blade bend. At the same time, the deformation compatibility principle of adjacent bending units is established to maintain the continuity and coordination of the blade in the spatial displacement field, and accurately reflect the movement of any point of the blade under the three-dimensional layout and the flapping / swing / torsion coupling effect.

[0123] 5. Update the rotor wake and use a multi-wake model to update the rotor wake shape. Unlike the traditional free wake method that rolls up the near wake to form a single blade tip vortex, the present invention uses a multi-wake design method to set any far wake and participate in the subsequent wake distortion, merging and dissipation, further accurately simulate the induction effect of the flow wake near the blade on the blade, and improve the accuracy of the blade aerodynamic estimation.

[0124] 6. Update the rotor flow field distribution, including the velocity field distribution of each blade section. If the current time T is greater than the set time limit T max , then end the calculation, if it is less than T max Then continue to enter the aerodynamic calculation cycle at the next moment.

[0125] The aerodynamic model, multi-wake model and rotor dynamics model involved in the multi-wake aerodynamic calculation method considering the three-dimensional rotor are as follows:

[0126] (1) Rotor unsteady aerodynamic model

[0127] The present invention adopts an unsteady aerodynamic model based on the second-order lift line theory. The aerodynamic center is arranged at the 1 / 4 chord length position on the mid-arc line of the blade profile, and the control point is arranged at the 3 / 4c chord length. The blade is divided into several aerodynamic segments along the span direction, which can effectively reflect the three-dimensional layout of the blade's forward protrusion, sweepback and downward reflection. The relationship between the blade aerodynamic force and the blade circulation distribution is established based on the Kutta-Joukowski theorem (where L is the blade segment aerodynamic force, ρ is the air density, U is the incoming flow velocity, c is the chord length, C lα is the slope of the lift line, α eff is the effective angle of attack, Γ is the circulation)

[0128]

[0129] Each blade section will shed a trailing vortex at the trailing edge, and its strength is the difference in the circulation of adjacent blade sections. After the trailing vortex is shed, it will condense behind the blade to form a near wake, and continue to roll up and converge to eventually form a far wake.

[0130] (2) Multi-wake model

[0131] The multi-wake model describes the flow field based on Lagrangian, and establishes the discrete vortex element and vortex line method to construct the control equation of the rotor wake moving in space. The transport equation of the wake motion is as follows, where r0 is the starting position vector of the vortex line, r is the vortex line wake vector; V is the local velocity at the location of the vortex line, and t is the time term.

[0132]

[0133] The blade generates aerodynamic force in the flow field, and a trailing vortex is released at the trailing edge of the blade, which converges behind the blade to form a near wake. The circulation of each trailing vortex is equal to the difference in the circulation of the adjacent blade aerodynamic sections as follows: n,j is the circulation of the jth trailing vortex; Γ b,j is the attached vortex ring of the jth blade unit, N s is the number of blade aerodynamic units

[0134] Γ n,j+1 =Γ b,j -Γ b,j+1 ,j=1,...,N s

[0135] The free wake model assumes that the trailing vortices will distort each other, roll up, and converge to form a far wake after they escape, and that they will roll up to form a single blade tip vortex far wake within a certain time and azimuth.

[0136] In the present invention, any number of far wakes can be set and maintained during the subsequent wake movement and distortion process, and eventually two far wakes of blade root vortex and blade tip vortex are formed, thereby effectively improving the aerodynamic analysis and prediction capabilities of complex three-dimensional rotors.

[0137] The Biot-Osafal theorem is used to solve the induced velocity of the wake at any position in space. The Vatistas vortex core model is used in the process of movement, distortion and dissipation of the wake. The expression is as follows, where V θ is the induced velocity, Γ v is the vortex strength, n = 2, r c is the vortex core radius, and r is the position vector of the current wake.

[0138]

[0139] The position vector of the wake separation point in the global coordinates is r(ψ,ζ), where ψ is the blade azimuth and ζ is the wake angle. It moves freely at the local speed. For a wake separation point, its control equation can be written as follows, where: Ω is the rotor rotation angular velocity, V ∞ Incoming flow velocity, V ind is the induced velocity at that point, and r is the vortex vector of the wake straight segment. Finally, the time-marching algorithm is used to solve the rotor wake geometry and blade aerodynamic distribution.

[0140]

[0141] (3) Dynamic model of rotor blades with complex three-dimensional shapes;

[0142] It is necessary to accurately describe the spatial position of the control points of the blade circulation distribution, and to be able to prepare a structural dynamics model that describes the motion of the rotor blades with complex three-dimensional shapes.

[0143] The rotor dynamics model simplifies the blade elastic axis into a one-dimensional linear, but the blade elastic axis of the complex three-dimensional blade with forward / backward sweep and up / down reverse layout configuration also exhibits three-dimensional characteristics in space. Traditional rotor dynamics is no longer applicable, so a rotor dynamics model considering complex three-dimensional blades is proposed. On the basis of the traditional dynamics model, a transformation matrix is ​​introduced at the blade bend, and the deformation compatibility principle of adjacent bending units is established to maintain the continuity and coordination of the blade in the spatial displacement field, thereby effectively reflecting the three-dimensional layout characteristics such as forward / backward sweep / downward reverse, and accurately describing the movement of any point on the blade under the three-dimensional layout.

[0144] Establish the position vector at any point on the blade (The expression is as follows), where O is the hub center, k is the blade segment number, A is the node number, P is any point on the undeformed elastic axis of blade segment k, P1 is any point on the elastic axis of blade segment k after deformation, and Q is any point on the cross section of blade segment k P1 after deformation.

[0145]

[0146] The blades with complex three-dimensional shapes have layout configurations such as forward / backward sweep and up / down reverse, which makes the blade elastic axis no longer one-dimensional linear, but also shows three-dimensional characteristics in space. The blade is discretized into several units. In order to maintain the continuity and consistency of the spatial positions of the two adjacent unit nodes at the blade bending, the transformation matrix T is introduced. Assuming that the angle between the forward swept section of the blade and the main blade section unit is Λ1, the angle between the down reverse section and the main blade section unit is Λ2, and the angle between the blade's own pre-twist and the main blade section unit is Λ3, then the coordinate matrix relationship is as follows, [i, j, k] is the joint coordinate system of the blade unit, and the subscript represents the unit number.

[0147]

[0148] The transformation matrix T is as follows:

[0149]

[0150] The conversion relationship of blade elastic deformation is considered on the basis of the conversion relationship between blade units under undeformed conditions. Blade elastic motion includes stretching, flapping, swinging linear motion, and angular motion of flapping / swinging / torsion. In order to maintain the continuity of blade elastic deformation, the deformation compatibility principle of adjacent units at the blade inflection point must be established to maintain the deformation coordination between units, that is, to describe the nonlinear conversion matrix of three-dimensional blade deformation and undeformation. The specific expression is as follows, where U represents the undeformed coordinate, D represents the deformed coordinate, and the subscript represents the number of two adjacent unit segments at the inflection point. T s It is the inter-node transformation matrix, and the deformation displacement between units must be coordinated and continuous, and the bending slope must also be continuous, that is, the translational freedom degree is continuous and the rotational freedom degree is continuous.

[0151] U2=T s U1

[0152] D2=T s D1

[0153] Finally, based on the Hamilton principle (expression as follows), the blade strain energy, kinetic energy and virtual work terms are derived to establish the blade dynamics equation, where δU is the virtual potential energy, δT is the virtual kinetic energy, and δW is the virtual work of the external force.

[0154]

[0155] The present invention establishes an unsteady aerodynamic model, a multi-wake model and a structural dynamics model suitable for complex three-dimensional rotors. On the one hand, it can effectively reflect the trailing vortex released by the complex three-dimensional rotor in the working state and the wake formed by the convergence at the bend ( Figure 5), and effectively reflects the rolling and convergence characteristics of the wake near the blades. On the other hand, it effectively reflects the three-dimensional layout characteristics such as forward projection / backward sweep / downward reflection, accurately describes the movement of complex three-dimensional shape blades in the space field, and improves the aerodynamic analysis and aeroelastic dynamics analysis capabilities of complex three-dimensional shape rotors.

Claims

1. A three-dimensional rotor, characterized in that: include: The blade beam has a three-dimensional bending structure; wherein the elastic axis of the blade beam is a broken line or a curve.

2. The three-dimensional rotor according to claim 1, characterized in that: The three-dimensional bending structure is arranged at the middle part and / or the tip part of the blade beam.

3. A three-dimensional rotor multi-wake aerodynamic analysis method, characterized in that: The method comprises: Step 1, obtaining rotor overall parameters, aerodynamic parameters, dynamic parameters, wake parameters and flight state parameters; Step 2, calculating the rotor flow field under initial conditions based on the rotor overall parameters, aerodynamic parameters, dynamic parameters, wake parameters and flight state parameters; Step 3, setting a time step and a time threshold; wherein the time step is negatively correlated with the rotor speed; Step 4: Based on the rotor overall parameters, the aerodynamic parameters and the flight state parameters, an aerodynamic model is used to update the blade aerodynamic force under the initial conditions with the time step to obtain the blade aerodynamic force at the current moment; Step 5: Based on the rotor overall parameters, the dynamic parameters and the blade aerodynamic force at the current moment, the blade elastic space displacement field is calculated using the rotor dynamics model; Step 6: Based on the rotor overall parameters, the aerodynamic parameters, the wake parameters, the flight state parameters, the blade aerodynamic force at the current moment, and the blade elastic space displacement field, a multi-wake model is adopted to update the rotor initial wake with the step size to obtain the rotor wake at the current moment; Step 7: Based on the blade aerodynamic force, blade elastic space displacement field and rotor wake at the current moment, an updated rotor flow field is obtained.

4. The method according to claim 3, characterized in that The method further comprises: Step 8: If the update time is greater than the time threshold, stop updating the rotor flow field; wherein the update time is the time obtained by accumulating the step length.

5. The method according to claim 3, characterized in that: The step 2 comprises: Step 201, based on the rotor overall parameters, the aerodynamic parameters and the flight state parameters, an aerodynamic model is used to calculate the blade aerodynamic force under initial conditions; Step 202: determining the blade spatial position under initial conditions based on the rotor overall parameters and the aerodynamic parameters; Step 203, based on the rotor overall parameters, the aerodynamic parameters, the wake parameters, the flight state parameters, the blade aerodynamic force under the initial conditions and the blade spatial position under the initial conditions, a multi-wake model is used to calculate the rotor initial wake.

6. The method according to claim 5, characterized in that The aerodynamic model is a Leishman-Beddoes two-dimensional unsteady aerodynamic model.

7. The method according to claim 6, characterized in that The step 203 includes: Based on the Lagrangian description of the flow field, the control equations of the rotor wake are constructed using the discrete vortex element and vortex line method; Based on the control equations, the initial rotor wake is calculated.

8. The method according to claim 3, characterized in that The step 5 comprises: The medium deformation beam hypothesis was adopted, and the blade strain energy, kinetic energy and virtual work terms were derived based on the Hamiltonian principle. The rotor dynamics equation was established, and the blade elastic space displacement field was obtained by solving the rotor dynamics equation.

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