A cfd simulation method for rotor blade corner

Abstract

The application relates to the technical field of rotor aerodynamics and computational fluid dynamics, and discloses a CFD simulation method for rotor disc chamfering, which comprises the following steps: obtaining a damped flapping dynamics equation according to a flapping dynamics equation of a blade; converting the damped flapping dynamics equation into a second-order ordinary differential equation; obtaining a flapping dynamics response under ideal simple harmonic vibration excitation according to the second-order ordinary differential equation; converting the second-order ordinary differential equation into a first-order ordinary differential equation group; solving the first-order ordinary differential equation group to obtain a flapping angle of the blade and a first time derivative of the flapping angle; performing fast Fourier transform on the flapping angle to obtain a periodic flapping solution; obtaining an aerodynamic moment of the blade on a flapping hinge through flow field calculation; substituting the aerodynamic moment into the second-order ordinary differential equation; solving the second-order ordinary differential equation to obtain a new flapping angle; and obtaining a final flapping angle according to harmonic components of the flapping angle in each rotation period. The application improves the simulation precision of rotor disc chamfering.

Description

Technical Field

[0001] This application relates to the fields of rotor aerodynamics and computational fluid dynamics, and in particular to a CFD simulation method for rotor disk chamfering. Background Technology

[0002] The rotor system is the main lifting and control surface of rotorcraft (such as helicopters, tiltrotor aircraft, and multi-rotor UAVs), and is the core component for achieving flight control. There are two main types of rotor control: collective pitch control, which refers to controlling the angle of attack of all blades to change simultaneously and equally; and cyclic pitch control, which refers to controlling the angle of attack of the blades to change periodically with changes in their azimuth. Cyclic pitch control is generally achieved through a swashplate (also known as an automatic swashplate), which converts the pilot's non-rotating control input into periodic control of the rotating blades. By periodically changing the angle of attack of the rotating blades, two things can be done: first, to compensate for the asymmetry of lift between the advancing and retreating sides of the rotor, maintaining balance forward, backward, and left, right; and second, to actively and purposefully create a lift difference, tilting the rotor tip trajectory plane in the desired direction, thereby changing the direction of the total lift and generating a horizontal component that propels the aircraft in a certain direction.

[0003] Rotor cyclic pitch control relies on the flapping motion of the blades, which is an elastic motion under aerodynamic excitation, influenced by multiple factors such as centrifugal force, inertial force, gravity, flapping hinge constraints, and flapping pitch coupling. Measuring the control effectiveness of rotor cyclic pitch control through wind tunnel testing presents several challenges: first, ensuring geometric similarity of the rotor hub at scale is difficult; second, fully satisfying dynamic similarity conditions (such as blade lock number, flapping constraint stiffness, and flapping pitch coupling coefficient) is challenging; and third, limitations imposed by motor power and vibration constraints make it difficult to conduct tests under certain high-load conditions. In CFD simulation, rotor cyclic pitch control involves the coupled solution of the blade flapping dynamics model and the dynamic boundary flow control equations. Blade aerodynamics drives the flapping, which in turn adjusts the aerodynamic forces. Through iterative calculations, an "automatic balance" is established, yielding the blade flapping response and rotor aerodynamic forces under stable flight conditions. Numerical methods offer the advantage of being unrestricted by physical conditions, serving as a verification and supplement to scaled-down model wind tunnel tests. Summary of the Invention

[0004] In view of this, this application provides a CFD simulation method for rotor disk chamfering.

[0005] This application discloses a CFD simulation method for rotor disk chamfering, which includes:

[0006] Step 1: Based on the flapping dynamics equation of the blade, obtain the damped flapping dynamics equation, convert the damped flapping dynamics equation into a second-order ordinary differential equation, and obtain the flapping dynamics response under ideal simple harmonic vibration excitation based on the second-order ordinary differential equation.

[0007] Step 2: Convert the second-order ordinary differential equation into a system of first-order ordinary differential equations, solve the system of first-order ordinary differential equations to obtain the flapping angle of the blade and the first time derivative of the flapping angle, perform a fast Fourier transform on the flapping angle to obtain the periodic flapping solution; the periodic flapping solution includes the taper angle of the flapping motion, the longitudinal blade chamfer, and the transverse blade chamfer.

[0008] Step 3: Under known periodic pitch control conditions, the aerodynamic torque of the blade about the flapping hinge is obtained through flow field calculation. The aerodynamic torque of the blade about the flapping hinge is substituted into the second-order ordinary differential equation, and the second-order ordinary differential equation is solved to obtain the new flapping angle. This process is repeated to statistically determine the harmonic components of the flapping angle in each rotation cycle. Based on the harmonic components of the flapping angle in each rotation cycle, it is determined whether the blade flapping motion meets the convergence condition. If the convergence condition is met, the final flapping angle is output. Otherwise, the new periodic flapping solution is substituted into the next rotation cycle until the convergence condition is met.

[0009] Furthermore, prior to step 1, the procedure also includes:

[0010] Based on the fact that the sum of the torques of all forces acting on the blade in the flapping plane about the flapping hinge is 0, the flapping dynamics equation of the blade is obtained; all forces include aerodynamic force T, gravity G, centrifugal force C, flapping inertial force F, and flapping hinge support reaction force.

[0011] Further, step 1 includes:

[0012] The expression for the blade flapping dynamics equation is:

[0013] (1)

[0014] in, Let the static moment of the blade about the flapping hinge be . Let be the linear density of the blade. R is the distance between the blade segment and the center of rotation, and R is the rotor radius. For the blade flapping hinge extension, Let the moment of inertia of the blade about the flapping hinge be denoted as . For the second derivative of the waving angle with respect to time, The swing hinge stiffness coefficient is... For aerodynamic torque, It is the acceleration due to gravity. For rotational speed, The flapping angle of the propeller at any given moment.

[0015] Further, step 2 includes:

[0016] Step 21: Substitute the design parameters of the rotor system, such as blade overhang, flapping stiffness, and flapping pitch coupling coefficient, into the flapping dynamics equation of the blade to obtain the undamped flapping dynamics equation.

[0017] Step 22: Decompose the aerodynamic torque in the undamped swing dynamics equation into aerodynamic damping torque and aerodynamic external torque to obtain the damped swing dynamics equation.

[0018] Step 23: Convert the damped flapping dynamics equation into a second-order ordinary differential equation, convert the second-order ordinary differential equation into the standard form of damped one-dimensional vibration, solve the standard form of damped one-dimensional vibration, and obtain the natural frequency and damping ratio of the blade flapping elastic system.

[0019] Step 24: Based on the second-order differential equation and the natural frequency and damping ratio of the blade flapping elastic system, obtain the flapping dynamic response. From the flapping dynamic response, obtain the blade amplitude response and phase lag angle. The phase lag angle is equivalent to the rotor's aerodynamic advance control angle.

[0020] Further, step 21 includes:

[0021] The distance between the pitch control rocker arm node and the flapping hinge axis of the propeller blade is The distance between the pitch rocker arm node and the pitch hinge axis is Changes in the flapping angle of the propeller blades Move the variable pitch rocker arm node by a certain distance The movement of the pitch control arm node simultaneously causes the blade to rotate about the pitch control hinge in the negative direction. Assume the rotation angle of the pitch control hinge is... ,but Therefore, the flapping motion of the blades causes an additional blade pitch angle. change :

[0022] (2)

[0023]

[0024] in, Let be the angle between the line connecting the variable pitch rocker arm node and the swing hinge and the axis of the swing hinge. It is the taper angle. The flapping angle of the blades at any given moment. and These are the longitudinal propeller disk chamfer and the transverse propeller disk chamfer, respectively. It is the azimuth angle. The flapping pitch coupling coefficient; flapping pitch coupling causes the pitch angle to decrease during upward flapping and increase during downward flapping; The pre-cone angle refers to the angle at which the blade is tilted upward relative to the rotor shaft plane when it is not rotating.

[0025] Pitch angle of the blade The expression is:

[0026] (3)

[0027] in, For collective pitch control, and These are the lateral periodic pitch control amount and the longitudinal periodic pitch control amount, respectively.

[0028] Calculation of blade flapping pitch coupling torque using the blade element method:

[0029] (4)

[0030] in, To swing the variable-pitch coupling torque, air density, The slope of the lift line, For the blade chord length, For rotational speed, The distance between the blade segment and the center of rotation. R is the rotor number, and R is the rotor radius. Let be the moment of inertia of the blade about the flapping hinge;

[0031] Substituting equation (4) into the flapping dynamics equation of the blade, we obtain the undamped flapping dynamics equation:

[0032] (5)

[0033] in, For the second derivative of the waving angle with respect to time, For the blade flapping hinge extension, Let the static moment of the blade about the flapping hinge be . For aerodynamic torque, It is the acceleration due to gravity. is the stiffness coefficient of the swing hinge.

[0034] Further, step 22 includes:

[0035] Based on the change in the angle of attack of the airflow generated by the blade flapping, the aerodynamic damping torque generated by the blade flapping is obtained:

[0036] (6)

[0037] in, This is the aerodynamic damping torque. The first derivative of the swing angle with respect to time;

[0038] In the undamped swing dynamics equations, the aerodynamic torque is... Decomposed into aerodynamic damping torque and aerodynamic external torque aerodynamic damping torque Substituting into the equations for undamped wave dynamics, we obtain the equations for damped wave dynamics:

[0039] (7)

[0040] in, For inertia, The ratio of the coefficient of the damping term to the coefficient of the inertia term is the Locke number. The higher the Lock number, the greater the aerodynamic damping, the faster the oscillation decays, and the shorter the time it takes for the blade to reach a steady state.

[0041] Further, step 23 includes:

[0042] The dynamic equations of damped flapping can be expressed in the form of dynamic equations including inertial terms, damping terms, stiffness terms, and external force terms, i.e., second-order ordinary differential equations:

[0043] (8)

[0044] in, ; An external torque independent of the swing angle; The damping coefficient of the system; The total equivalent swing stiffness coefficient includes the additional stiffness generated by centrifugal force. , swinging variable pitch coupling stiffness and swing hinge stiffness ;

[0045] The second-order ordinary differential equation can be written in the standard form of damped one-dimensional vibration. Under the condition of free vibration without external force, the expression is:

[0046] (9)

[0047] Among them, natural frequency Damping ratio They are represented as follows:

[0048]

[0049] (10).

[0050] Further, step 24 includes:

[0051] Under the action of a periodic external torque, the flapping dynamic response of the blade is a damped forced vibration. Assume that the aerodynamic external torque excites the blade elastic system, and expresses it as the amplitude. ,frequency simple harmonic function , where t is a time variable;

[0052] Ignoring the gravitational torque in formula (8), we obtain the following expression:

[0053] (11)

[0054] The solution to equation (11) is the waving dynamic response under simple harmonic excitation. :

[0055] (12)

[0056] Among them, amplitude response and phase lag angle They are respectively:

[0057] (13)

[0058] (14)

[0059] in, The ratio of the excitation frequency to the natural frequency:

[0060] (15).

[0061] Further, step 2 includes:

[0062] make , The second-order ordinary differential equation shown in equation (8) is transformed into a system of first-order ordinary differential equations as shown in equation (16):

[0063] (16)

[0064] in, , They are respectively and The first derivative with respect to time; The damping coefficients of the system in the second-order ordinary differential equation;

[0065] Formula (16) can be simplified as follows:

[0066]

[0067] in, , The right-hand side of formula (16) is equal to... The fourth-order Runge-Kutta method is used to solve this problem.

[0068] (17)

[0069] in, For variables The value at time n+1 For variables The value at time n, To be and Substituting into the right-hand side of formula (16), To be and Substituting into the right-hand side of formula (16), To be and Substituting into the right-hand side of formula (16), To be and Substitute into the right-hand side of formula (16); For time step, , , , All are temporary variables;

[0070] Solving the system of first-order ordinary differential equations shown in equation (16), we obtain the variables. The solution consists of transient and steady-state solutions, taking the swing angle as an example. The steady-state solution is subjected to a fast Fourier transform to obtain the values ​​of each harmonic component of the waving angle.

[0071] Further, step 3 includes:

[0072] Import the mesh and flow field calculation parameters; the flow field calculation parameters include the incoming flow velocity, direction, rotor speed, and rotor control parameters;

[0073] Based on the rotor speed and control input, the unsteady flow Navier-Stokes equations are solved using time-stepping. Assuming the rotor blades are Nb, one rotation cycle contains Ncyc time steps. Within each time step, under known periodic pitch control conditions, the aerodynamic torque of the blades about the flapping hinge is obtained through overlapping mesh assembly and flow field calculations with a preset number of steps, ensuring convergence of the aerodynamic torque within that time step. After completing the flow field calculation for one rotation cycle, each blade sweeps across the rotor in the final Ncyc / Nb steps. The Nb blades together form a single unit. The process of aerodynamic torque variation during the rotation period;

[0074] Substituting the aerodynamic torque of the blade about the flapping hinge into the second-order ordinary differential equation, and solving it using the Runge-Kutta explicit time-propagation method, the blade flapping angle is obtained. The course of time changes, taking the waving angle The steady-state solution is subjected to a Fast Fourier Transform (FFT) to obtain the harmonic components of the flapping angle. Only the 0th and 1st harmonic components are retained, which represent the periodic flapping solution of the blade. The periodic flapping solution includes the taper angle of the flapping motion. Longitudinal propeller chamfer and transverse propeller chamfer ;

[0075] Based on the harmonic components of the flapping angle in each rotation cycle, determine whether the blade flapping motion meets the convergence condition. If the convergence condition is met, output the final flapping angle; otherwise, substitute the new cycle flapping solution into the calculation of the next rotation cycle until the convergence condition is met.

[0076] Due to the adoption of the above technical solution, this application has the following advantages:

[0077] 1. This application applies to both individual rotors and entire rotorcraft. The invention is based on the coupled solution of the flapping dynamics equations and the flow control Navier-Stokes equations for rotor blades. The flapping is driven by blade aerodynamic forces, which in turn adjust the aerodynamic forces. Through iterative calculations, an "automatic balance" is ultimately established, yielding the blade flapping response and rotor aerodynamic forces under stable flight conditions. The method employed is based on first principles of physics, accurately reflecting blade motion and unsteady flow around it, and fully considering the nonlinear interaction between blade flapping motion and aerodynamic loads. The computational accuracy is significantly improved compared to traditional blade element engineering analysis methods. Standard model examples show that the blade disk chamfer obtained using this method agrees well with experimental values, verifying the correctness of the method.

[0078] 2. This application can serve as a verification and supplement to the wind tunnel test of the scaled-down model. It has the advantages of short test cycle and low cost, and the test conditions are not limited by objective conditions. It has important application value for the evaluation of the control effectiveness of rotorcraft and the design of dynamic parameters. Attached Figure Description

[0079] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings.

[0080] Figure 1This is a schematic diagram of the forces acting on the blade flapping motion according to an embodiment of this application;

[0081] Figure 2 This is a schematic diagram of blade flapping pitch coupling in an embodiment of this application;

[0082] Figure 3 This is a schematic diagram illustrating the coupled solution of the flow control equations and the flapping dynamics equations in an embodiment of this application.

[0083] Figure 4 This is a schematic diagram illustrating the convergence process of the rotor thrust coefficient with the longitudinal and transverse disk chamfers in an embodiment of this application.

[0084] Figure 5 This is a schematic diagram illustrating the variation of the longitudinal propeller chamfer angle with the advance ratio in an embodiment of this application;

[0085] Figure 6 This is a schematic diagram illustrating the change of the transverse propeller chamfer angle with the advance ratio in an embodiment of this application. Detailed Implementation

[0086] The present application will be further described in conjunction with the accompanying drawings and embodiments. The described embodiments are only some, not all, of the embodiments of the present application. All other embodiments obtained by those skilled in the art should fall within the protection scope of the embodiments of the present application.

[0087] Explanation of technical terms:

[0088] ① Rotorcraft: A type of aircraft that generates lift and thrust through rotating rotors, possessing vertical takeoff and landing, hovering, and low-speed maneuverability. Typical types include helicopters, tiltrotor aircraft, and multi-rotor drones. Its core principle is to generate lift by creating a pressure difference between the upper and lower surfaces of the rotor blades through the relative motion between the rotor and the air, while simultaneously achieving attitude control through cyclic pitch control.

[0089] ② Blade tip trajectory plane: When the helicopter rotor rotates, all the blade tips move in space to form a virtual plane. Its shape is approximately circular. The normal of this plane directly determines the direction of the rotor's thrust and is the core reference plane for measuring the rotor's working state.

[0090] ③ Periodic pitch control: This is a method in which the blades periodically change the pitch during rotation. The pilot tilts the rotor cone by periodically changing the pitch to control the direction of the rotor's aerodynamic force, thereby controlling the aircraft's speed or attitude.

[0091] ④ Rotor disc chamfer: refers to the angle at which the rotor cone tilts during flapping motion, including the rear chamfer and the side chamfer. The rear chamfer refers to the angle at which the rotor blades... Phase droop, in Phase elevation refers to the angle at which the rotor cone tilts backward; side chamfer refers to the angle at which the blades... Phase droop, in The phase is raised, causing the rotor cone to tilt forward at an angle.

[0092] See Figure 1 This application provides an embodiment of a CFD simulation method for rotor disk chamfering, which includes:

[0093] Step 1: Based on the flapping dynamics equation of the blade, obtain the damped flapping dynamics equation, convert the damped flapping dynamics equation into a second-order ordinary differential equation, and obtain the flapping dynamics response under ideal simple harmonic vibration excitation based on the second-order ordinary differential equation.

[0094] Step 2: Convert the second-order ordinary differential equation into a system of first-order ordinary differential equations, solve the system of first-order ordinary differential equations to obtain the flapping angle of the blade and the first time derivative of the flapping angle, perform a fast Fourier transform on the flapping angle to obtain the periodic flapping solution; the periodic flapping solution includes the taper angle of the flapping motion, the longitudinal blade chamfer, and the transverse blade chamfer.

[0095] Step 3: Under known periodic pitch control conditions, the aerodynamic torque of the blade about the flapping hinge is obtained through flow field calculation. The aerodynamic torque of the blade about the flapping hinge is substituted into the second-order ordinary differential equation, and the second-order ordinary differential equation is solved to obtain the new flapping angle. This process is repeated to statistically determine the harmonic components of the flapping angle in each rotation cycle. Based on the harmonic components of the flapping angle in each rotation cycle, it is determined whether the blade flapping motion meets the convergence condition. If the convergence condition is met, the final flapping angle is output. Otherwise, the new periodic flapping solution is substituted into the next rotation cycle until the convergence condition is met.

[0096] Optionally, before step 1, the method further includes:

[0097] Based on the fact that the sum of the moments of all forces acting on the blade in the flapping plane about the flapping hinge is zero, the flapping dynamics equation of the blade is obtained; all forces include aerodynamic force T, gravity G, centrifugal force C, flapping inertial force F, and the reaction force of the flapping hinge support, such as... Figure 1 As shown.

[0098] Optionally, step 1 includes:

[0099] The expression for the blade flapping dynamics equation is:

[0100] (1)

[0101] in, Let the static moment of the blade about the flapping hinge be . Let be the linear density of the blade. R is the distance between the blade segment and the center of rotation, and R is the rotor radius. For the blade flapping hinge extension, Let the moment of inertia of the blade about the flapping hinge be denoted as . For the second derivative of the waving angle with respect to time, The swing hinge stiffness coefficient is... For aerodynamic torque, It is the acceleration due to gravity. For rotational speed, The flapping angle of the blade at any given moment (the angle between the blade axis and the hub plane).

[0102] Optionally, step 2 includes:

[0103] Step 21: Substitute the design parameters of the rotor system, such as blade overhang, flapping stiffness, and flapping pitch coupling coefficient, into the flapping dynamics equation of the blade to obtain the undamped flapping dynamics equation.

[0104] Step 22: Decompose the aerodynamic torque in the undamped swing dynamics equation into aerodynamic damping torque and aerodynamic external torque to obtain the damped swing dynamics equation.

[0105] Step 23: Convert the damped flapping dynamics equation into a second-order ordinary differential equation, convert the second-order ordinary differential equation into the standard form of damped one-dimensional vibration, solve the standard form of damped one-dimensional vibration, and obtain the natural frequency and damping ratio of the blade flapping elastic system.

[0106] Step 24: Based on the second-order differential equation and the natural frequency and damping ratio of the blade flapping elastic system, obtain the flapping dynamic response. From the flapping dynamic response, obtain the blade amplitude response and phase lag angle. The phase lag angle is equivalent to the rotor's aerodynamic advance control angle.

[0107] Optionally, step 21 includes:

[0108] See Figure 2 The distance between the pitch control rocker arm node and the flapping hinge axis of the propeller is The distance between the pitch rocker arm node and the pitch hinge axis is Changes in the flapping angle of the propeller blades Move the variable pitch rocker arm node by a certain distance The movement of the pitch control arm node simultaneously causes the blade to rotate about the pitch control hinge in the negative direction. Assume the rotation angle of the pitch control hinge is... ,but Therefore, the flapping motion of the blades causes an additional blade pitch angle. change :

[0109] (2)

[0110]

[0111] in, Let be the angle between the line connecting the variable pitch rocker arm node and the swing hinge and the axis of the swing hinge. It is the taper angle. The flapping angle of the blades at any given moment. and These are the longitudinal propeller disk chamfer and the transverse propeller disk chamfer, respectively. It is the azimuth angle. The flapping pitch coupling coefficient; flapping pitch coupling causes the pitch angle to decrease during upward flapping and increase during downward flapping; The pre-cone angle refers to the angle at which the blade is tilted upward relative to the rotor shaft plane when it is not rotating.

[0112] Pitch angle of the blade The expression is:

[0113] (3)

[0114] in, For collective pitch control, and These are the lateral periodic pitch control amount and the longitudinal periodic pitch control amount, respectively.

[0115] Calculation of blade flapping pitch coupling torque using the blade element method:

[0116] (4)

[0117] in, To swing the variable-pitch coupling torque, air density, The slope of the lift line, For the blade chord length, For rotational speed, The distance between the blade segment and the center of rotation. R is the rotor number, and R is the rotor radius. Let be the moment of inertia of the blade about the flapping hinge;

[0118] Substituting equation (4) into the flapping dynamics equation of the blade, we obtain the undamped flapping dynamics equation:

[0119] (5)

[0120] in, For the second derivative of the waving angle with respect to time, For the blade flapping hinge extension, Let the static moment of the blade about the flapping hinge be . For aerodynamic torque, It is the acceleration due to gravity. is the stiffness coefficient of the swing hinge.

[0121] Optionally, step 22 includes:

[0122] Based on the change in the angle of attack of the airflow generated by the blade flapping, the aerodynamic damping torque generated by the blade flapping is obtained:

[0123] (6)

[0124] in, This is the aerodynamic damping torque. The first derivative of the swing angle with respect to time;

[0125] In the undamped swing dynamics equations, the aerodynamic torque is... Decomposed into aerodynamic damping torque and aerodynamic external torque aerodynamic damping torque Substituting into the equations for undamped wave dynamics, we obtain the equations for damped wave dynamics:

[0126] (7)

[0127] in, For inertia, The ratio of the coefficient of the damping term to the coefficient of the inertia term is the Locke number. The higher the Lock number, the greater the aerodynamic damping, the faster the oscillation decays, and the shorter the time it takes for the blade to reach a steady state.

[0128] Optionally, step 23 includes:

[0129] The dynamic equations of damped flapping can be expressed in the form of dynamic equations including inertial terms, damping terms, stiffness terms, and external force terms, i.e., second-order ordinary differential equations:

[0130] (8)

[0131] in, ; An external torque independent of the swing angle; The damping coefficient of the system; The total equivalent swing stiffness coefficient includes the additional stiffness generated by centrifugal force. , swinging variable pitch coupling stiffness and swing hinge stiffness ;

[0132] The second-order ordinary differential equation can be written in the standard form of damped one-dimensional vibration. Under the condition of free vibration without external force, the expression is:

[0133] (9)

[0134] Among them, natural frequency Damping ratio They are represented as follows:

[0135]

[0136] (10).

[0137] Optionally, step 24 includes:

[0138] Under the action of periodic external torque, the blade flapping dynamic response is a damped forced vibration. Here, we are mainly concerned with the steady-state response, including the amplitude response and the phase response.

[0139] Suppose there is an aerodynamic external torque that excites the blade elastic system, and it can be expressed as the amplitude. ,frequency simple harmonic function Where t is the time variable, in formula (8) since the gravitational torque is small compared with the aerodynamic torque, it is ignored here, and the following expression is obtained:

[0140] (11)

[0141] The solution to equation (11) is the waving dynamic response under simple harmonic excitation. :

[0142] (12)

[0143] Among them, amplitude response and phase lag angle They are respectively:

[0144] (13)

[0145] (14)

[0146] in, The ratio of the excitation frequency to the natural frequency:

[0147] (15)

[0148] From the steady-state solution (Equation 13), it can be seen that under simple harmonic vibration excitation, the response is also simple harmonic, and the response frequency is the same as the excitation frequency; the amplitude response of the forced vibration under simple harmonic excitation... and phase lag angle The phase lag angle is determined by the physical characteristics of the system itself and the magnitude and frequency of the excitation force, and is independent of the initial conditions. Also known as the aerodynamic advance control angle of the blade, it represents the angle by which the control is performed before the flapping response. Formula (12) is the solution to the flapping dynamics equation under ideal simple harmonic vibration excitation. In engineering applications, the aerodynamic torque on the blade is a non-ideal external torque similar to simple harmonic vibration, which cannot be obtained analytically and must be obtained by numerical calculation. The specific process is shown in steps 6 and 7.

[0149] Optionally, step 2 includes:

[0150] make , The second-order ordinary differential equation shown in equation (8) is transformed into a system of first-order ordinary differential equations as shown in equation (16):

[0151] (16)

[0152] in, , They are respectively and The first derivative with respect to time; The damping coefficients of the system in the second-order ordinary differential equation;

[0153] Formula (16) is simplified as in , Let be the right-hand side of formula (16), and the right-hand side is... The fourth-order Runge-Kutta method is used to solve this problem.

[0154] (17)

[0155] in, For variables The value at time n+1 For variables The value at time n, To be and Substituting into the right-hand side of formula (16), To be and Substituting into the right-hand side of formula (16), To be and Substituting into the right-hand side of formula (16), To be and Substitute into the right-hand side of formula (16); For time step, , , , All are temporary variables;

[0156] Solving the system of first-order ordinary differential equations shown in equation (16), we obtain the variables. The solution consists of transient and steady-state solutions, taking the swing angle as an example. The steady-state solution is subjected to a fast Fourier transform to obtain the values ​​of each harmonic component of the waving angle.

[0157] Optionally, step 3 includes:

[0158] See Figure 3 The grid and flow field calculation parameters are read in; the flow field calculation parameters include the incoming flow velocity, direction, rotor speed, and rotor control parameters.

[0159] Based on the rotor speed and control input, the unsteady flow Navier-Stokes equations are solved using time-stepping. Assuming the rotor blades are Nb, one rotation cycle contains Ncyc time steps. Within each time step, under known periodic pitch control conditions, the aerodynamic torque of the blades about the flapping hinge is obtained through overlapping mesh assembly and flow field calculations with a preset number of steps, ensuring convergence of the aerodynamic torque within that time step. After completing the flow field calculation for one rotation cycle, each blade sweeps across the rotor in the final Ncyc / Nb steps. The Nb blades together form a single unit. The process of aerodynamic torque variation during the rotation period;

[0160] Substituting the aerodynamic torque of the blade about the flapping hinge into the second-order ordinary differential equation, and solving it using the Runge-Kutta explicit time-propagation method, the blade flapping angle is obtained. The course of time changes, taking the waving angle The steady-state solution is subjected to a Fast Fourier Transform (FFT) to obtain the harmonic components of the flapping angle. Only the 0th and 1st harmonic components are retained, which represent the periodic flapping solution of the blade. The periodic flapping solution includes the taper angle of the flapping motion. Longitudinal propeller chamfer and transverse propeller chamfer ;

[0161] Based on the harmonic components of the flapping angle in each rotation cycle, determine whether the blade flapping motion meets the convergence condition. If the convergence condition is met, output the final flapping angle; otherwise, substitute the new cycle flapping solution into the calculation of the next rotation cycle until the convergence condition is met.

[0162] For ease of understanding, this application provides a more specific embodiment:

[0163] The following uses the CH-47 model rotor as an example to illustrate how to calculate the rotor disk chamfer through numerical simulation under variable forward speed conditions. The calculation process is carried out in the following five steps.

[0164] (1) Prepare the rotor CFD calculation mesh. Construct the three-dimensional geometric shape according to the rotor geometric parameters shown in Table 1, and further generate the surface mesh and spatial mesh. When constructing the blade geometric model, the spanwise position of the blade root section is taken as 0.16m, and the airfoil installation angle is... , The spanwise position of the cross section is 0.6237m, and the airfoil installation angle is... The spanwise position of the blade tip section is 0.8316m, and the airfoil installation angle is... The mesh employs a dynamic overlapping mesh structure, comprising a blade mesh and a spatial background mesh. The blade mesh moves with the blades, undergoing rotation, pitch changes, and flapping, while the spatial background mesh remains constant. At each time step, as the blades move to a new orientation, the blade mesh and the background mesh re-establish an overlapping interpolation relationship, exchanging flow field information between sub-regions through this overlapping interpolation. Flow field calculations utilize a domain decomposition MPI (message passing) parallel algorithm. This requires the mesh to be partitioned to satisfy parallel load balancing, with each sub-domain computation performed on different CPU cores.

[0165] (2) Prepare the parameters for the blade flapping dynamics model. The parameters for the blade flapping dynamics model include the moment of inertia of the blade about the flapping hinge. The static moment of mass of the blades about the flapping hinge , swing hinge stiffness coefficient Gravitational acceleration Locke number Rotation speed Blade flapping hinge extension , swing pitch coupling coefficient For the CH-47 model rotor, the flapping hinge adopts a mechanical hinge structure, and the flapping hinge stiffness coefficient... The variable pitch rocker arm node is located on the swing hinge axis, and the swing variable pitch coupling coefficient is... Other dynamic parameters are shown in Table 1.

[0166] Table 1. Rotor geometry and mass parameters

[0167]

[0168] (3) Simulation state parameter settings. The rotor disk chamfer was simulated at different forward flight speeds. The simulation state was consistent with the wind tunnel test state of the CH47 model rotor shown in Table 2, where the rotor tip speed was fixed at [value missing]. , moving forward is more than in Variation within range, step size Maintain rotor thrust coefficient under all conditions The lateral periodic pitch control amount is constant. The longitudinal periodic pitch control amount is constant. In the CFD simulation, the rotor thrust coefficient was trimmed to the experimental value in each state. During the trimming process, only the collective pitch of the rotor was adjusted, and the values ​​of the longitudinal and lateral cyclic pitch control were kept consistent with the experimental values. Table 2 shows the taper angles obtained from the experiments. Horizontal propeller chamfer Longitudinal propeller chamfer and Then the taper angle Horizontal propeller chamfer Longitudinal propeller chamfer The correctness of the CFD calculation method is verified by comparing it with CFD simulation data.

[0169] Table 2. Wind tunnel test data for CH47 standard rotor

[0170]

[0171] In Table 2, Indicates the serial number. This indicates the forward tilt angle of the rotor shaft.

[0172] (4) CFD simulation convergence process. Figure 4 The display shows the rotor thrust coefficient. and transverse propeller chamfer Longitudinal propeller chamfer The CFD calculation convergence process is shown. The calculation consisted of seven rotation cycles. The first two cycles were for initial flow field calculations. From the third cycle onwards, periodic pitch trimming was performed based on the target rotor thrust coefficient, and the rotor blade flapping response was calculated simultaneously. As can be seen from the figure, after completing the first six cycles, the rotor thrust exhibited a periodic variation, with the average thrust coefficient closely resembling the target value. =0.08, and the transverse and longitudinal blade chamfers are also basically converging, which means that through coupled calculation, a stable convergent solution of the blade flapping response has been obtained, achieving the expected calculation purpose.

[0173] (5) Comparison of simulation and experimental data

[0174] The experimental data includes two sets of wind tunnel test data. The first set of test data is from a fuselage rotor model, and the data is relatively complete, but it can only approximate the flow state of an isolated rotor. The second set of data is from an isolated rotor, and the data points are sparse. The rotor disk chamfer in the experiment was measured using a rotary variable displacement sensor, and the data error is approximately [missing information]. °. Figure 5 The given value is the longitudinal propeller chamfer. Comparing the calculated and experimental values, it can be seen from the figure that as the advance ratio increases, the rotor's back chamfer increases. At that time, the rotor back chamfer is approximately Comparison between CFD simulations and wind tunnel test values ​​shows that the two are in good agreement in terms of trends and magnitudes, reflecting the rationality of the current calculation method. Figure 6 The figure shows a comparison between the calculated and experimental values ​​of the rotor's lateral flapping. As can be seen from the figure, the lateral disk chamfer first increases and then decreases with the advance ratio. The location of the maximum disk chamfer in the CFD simulation is consistent with the experimental value. After reaching the maximum disk chamfer, the CFD simulation value is close to the single rotor experimental value, but there is a certain difference from the rotor fuselage model experimental value. Preliminary analysis suggests that this difference is caused by fuselage interference.

[0175] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.

Claims

1. A method of CFD simulation of a rotor disc chamfer, characterized in that, include: Step 1: Based on the flapping dynamics equation of the blade, obtain the damped flapping dynamics equation, convert the damped flapping dynamics equation into a second-order ordinary differential equation, and obtain the flapping dynamics response under ideal simple harmonic vibration excitation based on the second-order ordinary differential equation. Step 2: Convert the second-order ordinary differential equation into a system of first-order ordinary differential equations, solve the system of first-order ordinary differential equations to obtain the flapping angle of the blade and the first time derivative of the flapping angle, perform a fast Fourier transform on the flapping angle to obtain the periodic flapping solution; the periodic flapping solution includes the taper angle of the flapping motion, the longitudinal blade chamfer, and the transverse blade chamfer. Step 3: Under known periodic pitch control conditions, the aerodynamic torque of the blade about the flapping hinge is obtained through flow field calculation. The aerodynamic torque of the blade about the flapping hinge is substituted into the second-order ordinary differential equation, and the second-order ordinary differential equation is solved to obtain the new flapping angle. Based on the harmonic components of the flapping angle in each rotation cycle, it is determined whether the blade flapping motion meets the convergence condition. If the convergence condition is met, the final flapping angle is output. Otherwise, the new periodic flapping solution is substituted into the next rotation cycle until the convergence condition is met. Before step 1, the following are also included: Based on the fact that the sum of the moments of all forces acting on the blade in the flapping plane about the flapping hinge is 0, the flapping dynamics equation of the blade is obtained; all forces include aerodynamic force T, gravity G, centrifugal force C, flapping inertial force F, and flapping hinge support reaction force; Step 1 includes: The expression for the blade flapping dynamics equation is: (1) in, Let the static moment of the blade about the flapping hinge be . Let be the linear density of the blade. R is the distance between the blade segment and the center of rotation, and R is the rotor radius. For the blade flapping hinge extension, Let the moment of inertia of the blade about the flapping hinge be . For the second derivative of the waving angle with respect to time, The swing hinge stiffness coefficient is... For aerodynamic torque, It is the acceleration due to gravity. For rotational speed, The flapping angle of the propeller at any given moment.

2. The method of claim 1, wherein, Step 2 includes: Step 21: Substitute the characteristic parameters representing the flapping motion of the rotor into the flapping dynamics equation of the blade to obtain the undamped flapping dynamics equation; the characteristic parameters include the blade overhang, flapping stiffness, and flapping pitch coupling coefficient of the rotor system. Step 22: Decompose the aerodynamic torque in the undamped swing dynamics equation into aerodynamic damping torque and aerodynamic external torque to obtain the damped swing dynamics equation. Step 23: Convert the damped flapping dynamics equation into a second-order ordinary differential equation, convert the second-order ordinary differential equation into the standard form of damped one-dimensional vibration, solve the standard form of damped one-dimensional vibration, and obtain the natural frequency and damping ratio of the blade flapping elastic system. Step 24: Based on the second-order differential equation and the natural frequency and damping ratio of the blade flapping elastic system, obtain the flapping dynamic response. From the flapping dynamic response, obtain the blade amplitude response and phase lag angle. The phase lag angle is equivalent to the rotor's aerodynamic advance control angle.

3. The method of claim 2, wherein, Step 21 includes: The distance between the pitch control rocker arm node and the flapping hinge axis of the propeller blade is The distance between the pitch rocker arm node and the pitch hinge axis is Changes in the flapping angle of the propeller blades Move the variable pitch rocker arm node by a certain distance The movement of the pitch control arm node simultaneously causes the blade to rotate about the pitch control hinge in the negative direction. Assume the rotation angle of the pitch control hinge is... ,but Therefore, the flapping motion of the blades causes an additional blade pitch angle. change : (2) in, Let be the angle between the line connecting the variable pitch rocker arm node and the swing hinge and the axis of the swing hinge. It is the taper angle. The flapping angle of the blades at any given moment. and These are the longitudinal propeller disk chamfer and the transverse propeller disk chamfer, respectively. It is the azimuth angle. The flapping pitch coupling coefficient; flapping pitch coupling causes the pitch angle to decrease during upward flapping and increase during downward flapping; The pre-cone angle refers to the angle at which the blade is tilted upward relative to the rotor shaft plane when it is not rotating. Paddle angle of the paddle The expression for the paddle angle of the paddle (3) in, For collective pitch control, and These are the lateral periodic pitch control amount and the longitudinal periodic pitch control amount, respectively. Calculation of blade flapping pitch coupling torque using the blade element method: (4) in, To swing the variable-pitch coupling torque, air density, The slope of the lift line, For the blade chord length, For rotational speed, The distance between the blade segment and the center of rotation. R is the rotor number, and R is the rotor radius. Let be the moment of inertia of the blade about the flapping hinge; Substituting equation (4) into the flapping dynamics equation of the blade, we obtain the undamped flapping dynamics equation: (5) in, For the second derivative of the waving angle with respect to time, For the blade flapping hinge extension, Let the static moment of the blade about the flapping hinge be . For aerodynamic torque, It is the acceleration due to gravity. is the stiffness coefficient of the swing hinge.

4. The method of claim 3, wherein, Step 22 includes: Based on the change in the angle of attack of the airflow generated by the blade flapping, the aerodynamic damping torque generated by the blade flapping is obtained: (6) wherein is the aerodynamic damping moment, is the first derivative of the flap angle with respect to time; In the undamped edgewise dynamic equation, the aerodynamic moment is decomposed into an aerodynamic damping moment and an aerodynamic out-of-plane moment The aerodynamic damping moment is substituted into the undamped edgewise dynamic equation to obtain the damped edgewise dynamic equation: (7) in, For inertia, The ratio of the coefficient of the damping term to the coefficient of the inertia term is the Locke number. The higher the Lock number, the greater the aerodynamic damping, the faster the oscillation decays, and the shorter the time it takes for the blade to reach a steady state.

5. The method of claim 4, wherein, Step 23 includes: The dynamic equations of damped flapping can be expressed in the form of dynamic equations including inertial terms, damping terms, stiffness terms, and external force terms, i.e., second-order ordinary differential equations: (8) in, ; An external torque independent of the swing angle; The damping coefficient of the system; The total equivalent swing stiffness coefficient includes the additional stiffness generated by centrifugal force. , swinging variable pitch coupling stiffness and swing hinge stiffness ; The second-order ordinary differential equation can be written in the standard form of damped one-dimensional vibration. Under the condition of free vibration without external force, the expression is: (9) where the natural frequency and the damping ratio are given by (10)。 6. The method according to claim 5, characterized in that, Step 24 includes: Under the action of a periodic external torque, the flapping dynamic response of the blade is a damped forced vibration. Assume that the aerodynamic external torque excites the blade elastic system, and expresses it as the amplitude. ,frequency simple harmonic function , where t is a time variable; Ignoring the gravitational torque in formula (8), we obtain the following expression: (11) The solution of equation (11) is the response of the flapwise dynamics under a harmonic excitation : (12) Among them, amplitude response and phase lag angle They are respectively: (13) (14) wherein is the ratio of the excitation frequency to the natural frequency: (15)。 7. The method of claim 6, wherein, Step 2 includes: Let , , transform the second order ordinary differential equation shown in equation (8) into a system of first order ordinary differential equations as shown in equation (16): (16) in, , They are respectively and The first derivative with respect to time; The damping coefficients of the system in the second-order ordinary differential equation; Formula (16) can be simplified as follows: in, , The right-hand side of formula (16) is equal to... The fourth-order Runge-Kutta method is used to solve this problem. (17) in, For variables The value at time n+1 For variables The value at time n, To be and Substituting into the right-hand side of formula (16), To be and Substituting into the right-hand side of formula (16), To be and Substituting into the right-hand side of formula (16), To be and Substitute into the right-hand side of formula (16); For time step, , , , All are temporary variables; Solving the system of first-order ordinary differential equations shown in equation (16), we obtain the variables. The solution consists of transient and steady-state solutions, taking the swing angle as an example. The steady-state solution is subjected to a fast Fourier transform to obtain the values ​​of each harmonic component of the waving angle.

8. The method of claim 7, wherein, Step 3 includes: Import the mesh and flow field calculation parameters; the flow field calculation parameters include the incoming flow velocity, direction, rotor speed, and rotor control parameters; Based on the rotor speed and control input, the unsteady flow Navier-Stokes equations are solved using time-stepping. Assuming the rotor blades are Nb, one rotation cycle contains Ncyc time steps. Within each time step, under known periodic pitch control conditions, the aerodynamic torque of the blades about the flapping hinge is obtained through overlapping mesh assembly and flow field calculations with a preset number of steps, ensuring convergence of the aerodynamic torque within that time step. After completing the flow field calculation for one rotation cycle, each blade sweeps across the rotor in the final Ncyc / Nb steps. The Nb blades together form a single unit. The process of aerodynamic torque variation during the rotation cycle; Substituting the aerodynamic torque of the blade about the flapping hinge into the second-order ordinary differential equation, and solving it using the Runge-Kutta explicit time-propagation method, the blade flapping angle is obtained. The course of time changes, taking the waving angle The steady-state solution is subjected to a Fast Fourier Transform (FFT) to obtain the harmonic components of the flapping angle. Only the 0th and 1st harmonic components are retained, which represent the periodic flapping solution of the blade. The periodic flapping solution includes the taper angle of the flapping motion. Longitudinal propeller chamfer chamfering of the transverse propeller disk ; Based on the harmonic components of the flapping angle in each rotation cycle, determine whether the blade flapping motion meets the convergence condition. If the convergence condition is met, output the final flapping angle; otherwise, substitute the new cycle flapping solution into the calculation of the next rotation cycle until the convergence condition is met.

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