Method for acquiring numerical value of pitching dynamic derivative of rotary aircraft

Abstract

The invention belongs to the technical field of aerodynamics of aircrafts, and particularly relates to a method for acquiring a numerical value of a pitching dynamic derivative of a rotating aircraft. The method comprises the following steps: generating a set of spherical multi-domain structured grids based on aircraft configuration, firstly performing steady state aircraft flow field surrounding calculation according to flight conditions, and taking a converged steady state result as an initial flow field of unsteady calculation; carrying out rotation-pitching coupling motion and rotation-coning coupling motion modeling aiming at the inner domain grid, and representing position coordinates of the aircraft at different moments through coordinate transformation according to initial position coordinates; on the basis of the coupling motion model, in combination with a grid dynamic motion technology, a complex motion form of the aircraft is realized, an unsteady flow control equation is further solved, and flow field simulation of the aircraft during rotation-pitching coupling and rotation-cone motion coupling motion is realized; and when a simulation termination condition is reached, the calculation is terminated, a transient pitching moment coefficient is obtained according to numerical simulation, and a pitching dynamic derivative can be obtained about a time integral.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of aircraft aerodynamics, and particularly relates to a numerical acquisition method of a pitching dynamic derivative of a rotary aircraft. BACKGROUND

[0002] Prediction of dynamic stability derivatives (also known as dynamic derivatives) is essential for aircraft design. Dynamic derivatives are used to measure the degree of change in forces and moments acting on the aircraft when the flight state of the aircraft (including angle of attack, speed) changes. The main dynamic derivatives include pitching damping force, pitching damping moment, rolling damping moment, and Magnus force / moment coefficients. These dynamic stability derivatives are used to analyze the flight stability of the aircraft when it experiences complex pitching-rolling-yaw coupling motion. Therefore, dynamic derivatives, among which the pitching damping moment coefficient is the most commonly used dynamic derivative (hereinafter referred to as the pitching dynamic derivative), are key parameters in the design of aircraft flight stability. The pitching dynamic derivative has received extensive attention in numerical research and wind tunnel research.

[0003] In the study of the pitching dynamic derivative, in addition to the wind tunnel test method, computational fluid dynamics method is considered as an efficient means, and is usually used as a supplement to flight tests, wind tunnel tests and semi-empirical theoretical evaluations. Current numerical calculation or wind tunnel test research is basically carried out for the case where the aircraft only exists in pitching oscillation. By numerically simulating the flow field around the aircraft during pitching oscillation, the variation of the pitching moment coefficient with time within one oscillation period is directly obtained, and the pitching dynamic derivative can be calculated by integrating the pitching moment coefficient with respect to time. However, the related research does not involve the calculation of the pitching dynamic derivative when the aircraft exists in rotary motion or rotary-cone motion coupling, which has a certain gap with the dynamic derivative characteristics in the actual flight process.

[0004] The motion form of the aircraft in actual flight can be complex, involving pitching-rolling-yaw coupling motion, rather than ideal harmonic oscillation. How to obtain accurate pitching dynamic derivatives under real flight conditions is a difficulty to be overcome in the development of related research. At present, numerical calculation and wind tunnel test are mostly carried out for the case of only pitching oscillation, and the precision is limited; the calculation of the pitching dynamic derivative in rotary motion or rotary-cone motion coupling process is still of high difficulty. SUMMARY

[0005] (1) Technical problem to be solved

[0006] The technical problem to be solved by the present application is how to provide a numerical calculation method suitable for the pitching dynamic derivative of a rotary aircraft, to solve the difficulties in the simulation of rotary-pitching coupling motion flow around the aircraft, the calculation of the pitching dynamic derivative, and other problems, and to sort out the numerical calculation process of the pitching dynamic derivative of the rotary aircraft, for the convenience of engineering application.

[0007] (2) Technical scheme

[0008] To solve the above technical problems, the application provides a numerical acquisition method for a pitch dynamic derivative of a rotary aircraft, which comprises the following steps:

[0009] Step 1: Based on the configuration of the rotary aircraft, a set of spherical hexahedral structured calculation grids composed of an inner domain and an outer domain is generated, the interface between the inner domain and the outer domain is connected through the interpolation transmission of the sliding grid technology, and the converged steady-state flow field is taken as the initial flow field of the unsteady simulation according to the flight conditions.

[0010] Step 2: The rotary-pitch coupling motion and the rotary-coning coupling motion are modeled for the inner domain grid, and the coupling motion form is characterized by a mathematical expression, that is, the aircraft attitude coordinates at different motion times are obtained through coordinate transformation according to the initial flight attitude coordinates.

[0011] Step 3: The complex coupling motion of the aircraft is realized according to the coupling motion model combined with the grid dynamic motion technology, and the unsteady flow control equation is further solved to realize the flow field simulation of the aircraft in the rotary-pitch and rotary-coning coupling motion, and the pitch moment coefficient at each time is collected.

[0012] Step 4: The simulation termination condition is reached, the calculation is terminated, and the pitch dynamic derivative is obtained based on the time integral of the pitch moment coefficient obtained in step 3.

[0013] In step 1, the grid division form of the interface between the inner domain and the outer domain is consistent with the grid size.

[0014] In step 1, the grid division tool of the interface between the inner domain and the outer domain includes ICEM or Pointwise.

[0015] In step 1, the fluid control equation is the Reynolds-averaged N-S equation, the steady flow field of different flight conditions is obtained, and the solver used includes Fluent, CFD++ or CFX.

[0016] In step 2, the aircraft attitude coordinates at any motion time are characterized by coordinate transformation according to the initial flight attitude, and the rotary-pitch coupling motion and rotary-coning coupling motion models are formed, which include the complex transformation process between the inertial coordinate system, the body coordinate system and the quasi-body coordinate system.

[0017] In step 2, the establishment process of the rotary-pitch coupling motion model is as follows:

[0018] Firstly, the coordinate transformation relationship between the inertial system and the quasi-elastic system is established to describe the attitude change caused by the initial attack angle a, and the coordinate transformation matrix is

[0019] Secondly, the coordinate transformation relationship between the quasi-elastic system and the elastic system is established to describe the attitude change caused by the spinning of the vehicle around the longitudinal axis, and the coordinate transformation matrix is T s , wherein the spinning rotation angle is θ s = ω s t; ω s is the spinning angular velocity;

[0020] Thirdly, the coordinate transformation relationship between the elastic system and the inertial system is established to describe the attitude change caused by the change of the pitch angle, and the coordinate transformation matrix is T θp , the pitch rotation angle is θ p = ω p t; ω p is the pitch angular velocity;

[0021] Finally, the vehicle attitude coordinates at different times, i.e. the grid node coordinates at different times, are obtained by the coordinate initial value, and the mathematical expression of the rotation-pitch coupling motion is obtained.

[0022] In the step two, the process of establishing the rotation-coning coupling motion model is:

[0023] The first two steps and the process of establishing the rotation-pitch coupling motion model are the same, and the grid node coordinate initial value in the inertial system is transformed into the result in the elastic system to describe the attitude change caused by the attack angle and the spinning motion, and the coordinate transformation matrix is and T s ;

[0024] Secondly, the grid node coordinates in the elastic system are converted into the inertial system, which involves the coning transformation matrix T α and the coning rotation angle transformation T θc , the coning rotation angle is θ c = ω c t; ω c is the coning angular velocity;

[0025] Finally, the vehicle attitude coordinates at different times, i.e. the grid node coordinates at different times, are obtained by the coordinate initial value, and the mathematical expression of the rotation-coning coupling motion is obtained.

[0026] In the step three, the motion function is determined according to the mathematical model of the rotation-pitch coupling and the rotation-coning coupling motion, the complex motion of the vehicle is realized by combining the grid dynamic motion technology, and the complex motion flow field is simulated by further combining the unsteady Reynolds average N-S equation to obtain the instantaneous pitch moment coefficient about the center of mass, and the reference length is the diameter of the vehicle.

[0027] (III) Beneficial Effects

[0028] Compared with the prior art, the beneficial effects of the present application are:

[0029] (1) Compared with the traditional method of using engineering algorithm or only pitch oscillation to calculate the pitch dynamic derivative, the present application innovatively establishes a rotation-pitch, rotation-coning coupling motion model, i.e. establishing a coordinate transformation relationship between the attitude at different times of complex motion of the aircraft and the initial attitude, which can more truly reflect the motion characteristics of the aircraft.

[0030] (2) In the simulation calculation of the coupling motion of the rotating aircraft, the motion function needs to be determined according to the coupling motion mathematical model, and the simulation of the aircraft motion is realized by means of the calculation grid motion, and further integration is performed to obtain more accurate pitch dynamic derivative. The difficulties in modeling, complex motion implementation, and complex motion flow simulation of rotation-pitch coupling and rotation-coning coupling motion are solved, and the numerical calculation process of the pitch dynamic derivative of the rotating aircraft is sorted out, which provides a reference for engineering application. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 The flow chart for calculating the pitch dynamic derivative of the rotating aircraft;

[0032] Figure 2 The space grid of the flow field and the division of the calculation domain;

[0033] Figures 3a-3c The mathematical model diagram of different motion forms;

[0034] Figure 3a The traditional only pitch oscillation model diagram;

[0035] Figure 3b The rotation-pitch coupling motion model diagram;

[0036] Figure 3c The rotation-coning coupling motion model diagram;

[0037] Figure 4 The curve diagram of the transient pitch moment coefficient changing with time;

[0038] Figure 5 The pitch dynamic derivative changing with the angle of attack under different motion forms. DETAILED DESCRIPTION

[0039] In order to make the purpose, content, and advantages of the present application more clear, the specific embodiments of the present application are further described in detail below in combination with the drawings and examples.

[0040] To solve the above technical problems, the application provides a numerical acquisition method for a pitch dynamic derivative of a rotary aircraft, and the numerical acquisition method comprises the following steps:

[0041] Step 1: Based on the configuration of the rotary aircraft, a set of spherical hexahedral structured calculation grids composed of an inner domain and an outer domain are generated, the interface between the inner domain and the outer domain is connected through the interpolation transmission of the sliding grid technology, and first, the steady-state flow field calculation is performed according to the flight conditions, and the converged steady-state result is used as the initial flow field for the unsteady simulation.

[0042] Step 2: The rotary-pitch coupling motion and the rotary-coning coupling motion are modeled for the inner domain grid, the coupling motion form is represented by a mathematical expression, and specifically, the aircraft attitude coordinates at different motion moments are obtained through coordinate transformation according to the initial flight attitude coordinates.

[0043] Step 3: The complex coupling motion of the aircraft needs to be realized according to the coupling motion model in combination with the grid dynamic motion technology, and the unsteady flow control equation is further solved to realize the flow field simulation of the aircraft in the rotary-pitch and rotary-coning coupling motion, and the pitch moment coefficient at each moment is collected.

[0044] Step 4: The simulation termination condition is reached, the calculation is terminated, and the pitch dynamic derivative is obtained based on the time integration of the pitch moment coefficient obtained in step 3.

[0045] In step 1, the grid division form and the grid size of the interface between the inner domain and the outer domain are consistent.

[0046] In step 1, the grid division tool of the interface between the inner domain and the outer domain comprises ICEM or Pointwise.

[0047] In step 1, the fluid control equation is the Reynolds-averaged N-S equation, the steady flow field of different flight conditions is obtained, and the solver used comprises Fluent, CFD++ or CFX.

[0048] In step 2, the aircraft attitude coordinates at any motion moment are represented by coordinate transformation according to the initial flight attitude, the rotary-pitch coupling motion and the rotary-coning coupling motion model are formed, and the process comprises the complex transformation process between the inertial coordinate system, the body coordinate system and the quasi-body coordinate system.

[0049] In step 2, the establishment process of the rotary-pitch coupling motion model is as follows:

[0050] First, the coordinate transformation relationship between the inertial system and the quasi-body system is established to describe the attitude change caused by the initial angle of attack α, and the coordinate transformation matrix is

[0051] Secondly, the coordinate transformation relationship between the quasi-elastic system and the elastic system is established, and the attitude change caused by the spinning of the aircraft around the longitudinal axis is described, and the coordinate transformation matrix is T s , wherein the spinning rotation angle is θ s = ω s t; ω s is the spinning angular velocity;

[0052] Thirdly, the coordinate transformation relationship between the elastic system and the inertial system is established, and the attitude change caused by the pitching angle change is described, and the coordinate transformation matrix is T θp , the pitching rotation angle is θ p = ω p t; ω p is the pitching angular velocity;

[0053] Finally, the aircraft attitude coordinates at different times, i.e. the grid node coordinates at different times, are obtained by the coordinate initial value, and the mathematical expression of the spin-pitch coupling motion is obtained.

[0054] In the step two, the process of establishing the spin-pitch coupling motion model is:

[0055] The first two steps and the process of establishing the spin-pitch coupling motion model are the same, and the grid node coordinate initial value in the inertial system is transformed into the result in the elastic system, and the attitude change caused by the attack angle and the spinning motion is described, and the coordinate transformation matrix is and T s ;

[0056] Secondly, the grid node coordinates in the elastic system are converted into the inertial system, which involves the cone angle transformation matrix T α and the cone rotation angle transformation T θc , the cone rotation angle is θ c = ω c t; ω c is the cone angular velocity;

[0057] Finally, the aircraft attitude coordinates at different times, i.e. the grid node coordinates at different times, are obtained by the coordinate initial value, and the mathematical expression of the spin-pitch coupling motion is obtained.

[0058] In the step three, the motion function is determined according to the mathematical model of the spin-pitch coupling and the spin-cone coupling motion, the complex motion of the aircraft is realized by combining the grid dynamic motion technology, and the complex motion flow field is simulated by further combining the unsteady Reynolds average N-S equation, and the instantaneous pitching moment coefficient about the center of mass is obtained, and the reference length is the diameter of the aircraft.

[0059] Embodiment 1

[0060] The numerical calculation method of the pitch dynamic derivative of the rotating aircraft of the embodiment comprises the following steps: based on the configuration of the rotating aircraft, a set of structured calculation grid composed of spherical inner domain and spherical outer domain is generated, and according to the flight condition, the steady-state flow field calculation is first performed to obtain the converged steady-state result as the initial flow field for the non-steady-state simulation;

[0061] The rotating-pitch coupling motion and rotating-coning coupling motion modeling are performed on the inner domain grid, and the aircraft attitude coordinates at different times are obtained through initial attitude coordinate transformation;

[0062] The grid motion function is written and debugged according to the coupling motion model, the complex motion of the aircraft is realized by combining the grid dynamic motion technology, and the flow field simulation of the aircraft in the rotating-pitch and rotating-coning coupling motion is realized by further solving the non-steady-state flow control equation.

[0063] When the simulation termination condition is reached, the calculation is terminated, the transient pitch moment coefficient in a motion period is obtained according to the numerical simulation, and the pitch dynamic derivative is obtained by integrating with respect to time.

[0064] Further details include that the interface grid partition form of the inner domain and the outer domain grid is consistent with the grid size, and the grid partition tool used can be ICEM or Pointwise; the steady-state calculation fluid control equation is the Reynolds average N-S equation, and the solver used can be Fluent, CFD++ or CFX. The rotating-pitch coupling motion and rotating-coning coupling motion modeling are performed on the inner domain grid, which involves the composite transformation between the inertial coordinate system, the body coordinate system and the quasi-body coordinate system to obtain the aircraft attitude coordinates at different times; the grid motion program is written according to the coupling motion mathematical model, the complex motion of the aircraft is realized by combining the grid dynamic motion technology, and the complex motion flow field is simulated by further combining the non-steady-state Reynolds average N-S equation to obtain the transient pitch moment coefficient with respect to the center of mass, and the reference length is the diameter of the aircraft.

[0065] Embodiment 2

[0066] The numerical calculation method of the pitch dynamic derivative of the rotating aircraft of the embodiment will be further described in combination with the drawings and examples. The numerical calculation method of the pitch dynamic derivative of the rotating aircraft comprises the following steps, referring to Figure 1 :

[0067] Based on the configuration of the rotating aircraft, the spherical space calculation domain is divided, and the whole spherical domain is divided into inner domain and outer domain, and the interface grid partition form of the inner domain and the outer domain is consistent with the grid size, referring to Figure 2 When the inner domain moves, the data transmission between the inner domain and the outer domain is realized by interpolation through the sliding technology of the interface grid. The height of the first layer of grid near the body wall needs to meet the dimensionless wall distance y+ The meshing tool used can be ICEM or Pointwise, and the mesh is a hexahedral structured mesh.

[0068] According to the flight conditions, the steady-state flow field is calculated using the entire computational domain. After the flow field converges, the converged flow field is used as the initial flow field for the unsteady simulation. The fluid control equations are the Reynolds-averaged NS equations in steady and unsteady forms:

[0069]

[0070] Where Γ is the preprocessing matrix, Q is the original variable matrix, W is the conserved variable, F is the inviscid flux, G is the viscous flux, and H is the source term. Ω is the control volume unit, dV represents the volume integral, Indicates the normal direction outside the boundary. The solver used can be Fluent, CFD++ or CFX.

[0071] The traditional pitch oscillation model is that the aircraft in the inertial coordinate system OXYZ (OX axis coincides with the aircraft longitudinal axis, OY axis is perpendicular to OX axis in the plumb plane, and OZ axis is determined by the right-hand rule), its longitudinal axis does a small pitch oscillation around the OZ axis, see Figure 3a By simulating the flow field during this motion, the pitching moment coefficient can be integrated with time to obtain the pitching derivative. Further work can be carried out on this basis.

[0072] Carry out rotation-pitch coupled motion modeling, that is, the aircraft rotates around its own longitudinal axis while oscillating slightly around the OZ axis, see Figure 3b In order to realize the coupled motion form, it is necessary to give the coordinates of the aircraft surface grid nodes in the inertial coordinate system at different times, involving the inertial coordinate system OXYZ, the missile body coordinate system OX B Y B Z B (The elastic axis is OX B Axis, OYB axis is perpendicular to OX in the plumb line B Axially, OZ B The axis is determined by the right-hand rule and is fixed to the projectile), the quasi-projectile coordinate system (the initial state is the same as OX B Y B Z B First, the coordinate transformation relationship between the inertial system and the quasi-projectile system is established to describe the attitude change caused by the initial attack angle α. The coordinate transformation matrix is: Secondly, the coordinate transformation relationship between the quasi-missile system and the missile system is established to describe the attitude change caused by the aircraft spinning around the longitudinal axis. The coordinate transformation matrix is ​​T s (The rotation angle is θ s =ω st); again, the coordinate transformation relationship between the elastic body and the inertial system elastic body is established to describe the attitude change caused by the change in the pitch angle, and the coordinate transformation matrix is T θp (the pitch rotation angle is θ p = ω p t); finally, the grid node coordinates at different times (subscript new) can be obtained from the coordinate initial value (subscript initial), and thus the mathematical expression of the roll-pitch coupling motion is obtained.

[0073]

[0074] The roll-coning coupling motion is modeled. The roll-pitch coupling motion can be regarded as the coupling of roll motion and in-plane pitch oscillation, while the roll-coning coupling motion can be regarded as the coupling of roll motion, in-plane pitch oscillation, and in-plane yaw oscillation, as shown in Figure 3c To realize the coupling motion form, the grid node coordinates of the aircraft surface at different times in the inertial coordinate system need to be given, and the coordinate transformation involves the inertial system, the elastic body, and the quasi-elastic body. The first two steps are the same as the roll-pitch coupling motion, and the grid node coordinate initial value in the inertial system is transformed into the result in the elastic body to describe the attitude change caused by the change in the attack angle and the spin motion, and the coordinate transformation matrix is and T s ; secondly, the grid node coordinates in the elastic body are converted into the inertial system, which involves the coning angle transformation matrix T α and the coning rotation angle transformation T θc (the coning rotation angle is θ c = ω c t); finally, the grid node coordinates at different times (subscript new) can be obtained from the coordinate initial value (subscript initial), and thus the mathematical expression of the roll-coning coupling motion is obtained.

[0075]

[0076]

[0077] Further motion is applied to the inner domain grid to realize the complex motion form of the aircraft. This process needs to use the grid dynamic motion technology, that is, a user-defined motion function needs to be written according to the coupling motion mathematical model, and further combined with the unsteady Reynolds average N-S equation to simulate the complex motion flow field. When the simulation termination condition is reached, the calculation is terminated, and the instantaneous pitch moment coefficient about the center of mass is obtained based on the numerical simulation, wherein the reference length is the diameter of the elastic body, and the pitch combined dynamic derivative is obtained based on time integration, as shown in the following formula:

[0078]

[0079] where A is the amplitude of the pitch oscillation, d is the diameter of the projectile, C mz (t) is the transient pitch moment coefficient, V ∞ is the flight velocity, k d = ω p d / 2V ∞ is the reduced frequency.

[0080] The calculation process of the pitch dynamic derivatives of the rotating projectile is proposed in this paper. The pitch dynamic derivatives of the projectile in the pitch oscillation, the coupled rotation-pitch oscillation, and the coupled rotation-coning motion are compared and studied. The calculation and test conditions are as follows: Ma=0.4, α=-5°, 0°, 5°, 10°, P=89198 Pa, T=280.69 K, ρ=1.1073 kg / m 3 , V ∞ =134.4 m / s, L ref =0.055 m, S ref =0.0023758 m 2 , the distance between the moment reference point and the top of the projectile is 5.5d. The amplitude of the pitch oscillation A=1°, the frequency of the pitch oscillation / coning ω p = ω c =20π, the spin ω s =16π, the pitch period T=0.1 s, the time step dt=0.0001 s, and the physical time step N=1000. The calculation is stopped after one complete pitch period.

[0081] The transient pitch moment coefficient curves in one motion period are cosine type fluctuations in different motion forms, as shown in Figure 4 , and the equilibrium angle of attack α=0°. The amplitude and variation of the pitch moment coefficient are similar, but there are some differences in the specific values and phases. The pitch dynamic derivatives can be obtained by integrating the time. The numerical calculation and wind tunnel test can effectively and reliably predict the pitch dynamic derivatives of the projectile in different motion forms. The pitch dynamic derivatives in the pitch oscillation are smaller than those in the coupled rotation-pitch oscillation, and smaller than those in the coupled rotation-coning motion. The pitch dynamic derivatives in the coupled motion are at least 30% larger than those in the pitch oscillation. The spin motion of the projectile increases the pitch dynamic derivatives, which is beneficial to stable flight, as shown in Figure 5 .

[0082] In summary, the present application belongs to the field of aircraft aerodynamics, and particularly relates to a numerical acquisition method of a pitch dynamic derivative of a rotary aircraft. Based on the aircraft configuration, a set of spherical multi-domain structured grids is generated, and according to the flight conditions, the flow field calculation of the aircraft in a steady state is performed first, so as to take the converged steady state result as the initial flow field of the unsteady calculation; the rotary-pitch coupling motion and the rotary-coning coupling motion modeling are carried out for the inner domain grid, the position coordinates of the aircraft at different times of the coupling motion are represented through coordinate transformation according to the initial position coordinates; based on the coupling motion model, the complex motion form of the aircraft is realized by combining the grid dynamic motion technology, the unsteady flow control equation is further solved, the flow field simulation of the aircraft in the rotary-pitch coupling and the rotary-coning coupling motion is realized; the calculation is terminated when the simulation termination condition is reached, the transient pitch moment coefficient is obtained according to the numerical simulation, and the pitch dynamic derivative can be obtained by integrating with respect to time. The present application solves the problems of the flow field numerical simulation of the rotary aircraft in the coupling motion and the pitch dynamic derivative calculation in the complex motion state, and combs the numerical calculation process of the pitch dynamic derivative of the rotary aircraft, so as to provide a reference for engineering application.

[0083] The above only describes the preferred embodiments of the present application, and it should be noted that those skilled in the art can make several improvements and modifications without departing from the technical principles of the present application, and these improvements and modifications should also be considered as the protection scope of the present application.

Claims

1. A method for numerically obtaining pitch derivatives of a rotating aircraft, characterized in that: The method for obtaining the numerical value of the pitch derivative of the rotating aircraft comprises the following steps: Step 1: Based on the rotating aircraft configuration, a spherical hexahedral structured computational grid consisting of an inner domain and an outer domain is generated. The interface between the inner and outer domains of the grid is calculated, and data is interpolated and transferred using the sliding mesh technique. First, the steady-state flow field is calculated according to the flight conditions, and the converged steady-state results are used as the initial flow field for the unsteady simulation. Step 2: Model the rotation-pitch coupled motion and rotation-cone coupled motion for the inner domain grid, and characterize the coupled motion form using mathematical expressions. Specifically, based on the initial flight attitude coordinates, the aircraft attitude coordinates at different motion moments are obtained through coordinate transformation; Step 3: The complex coupled motion of the aircraft needs to be realized based on the coupled motion model combined with grid dynamic motion technology. The unsteady flow control equations are further solved to simulate the flow field around the aircraft during the rotation-pitch and rotation-cone coupled motions, and the pitch moment coefficient is collected at each moment. Step 4: When the simulation termination condition is reached, terminate the calculation and obtain the pitching moment coefficient obtained in step 3 based on the time integration to obtain the pitching dynamic derivative.

2. The method for obtaining the numerical value of the pitch derivative of a rotating aircraft according to claim 1, wherein: In the step 1, the grid division form of the interface between the inner domain and the outer domain is consistent with the grid size.

3. The method for obtaining the numerical value of the pitch derivative of a rotating aircraft according to claim 1, wherein: In the step 1, the meshing tools for the interface between the inner domain and the outer domain include ICEM or Pointwise.

4. The method for obtaining the numerical value of the pitch derivative of a rotating aircraft according to claim 1, wherein: In step 1, the fluid control equation is the Reynolds-averaged NS equation, and the steady flow field under different flight conditions is obtained. The solvers used include Fluent, CFD++ or CFX.

5. The method for obtaining the numerical value of the pitch derivative of a rotating aircraft according to claim 1, wherein: In the second step, the coordinates of the aircraft attitude at any moment of movement are represented by coordinate transformation according to the initial flight attitude to form a rotation-pitch coupled motion and a rotation-cone coupled motion model. This process includes a composite transformation process of motion between the inertial coordinate system, the projectile coordinate system, and the quasi-projectile coordinate system.

6. The method for obtaining the numerical value of the pitch derivative of a rotating aircraft according to claim 5, wherein: In step 2, the process of establishing the rotation-pitch coupled motion model is as follows: First, the coordinate transformation relationship between the inertial system and the quasi-projectile system is established to describe the attitude change caused by the initial attack angle α. The coordinate transformation matrix is: Secondly, the coordinate transformation relationship between the quasi-missile system and the missile system is established to describe the attitude change caused by the aircraft spinning around the longitudinal axis. The coordinate transformation matrix is ​​T s , where the rotation angle is θ s =ω s t;ω s is the spin angular velocity; Next, establish the coordinate transformation relationship between the missile system and the inertial system to describe the attitude change caused by the pitch angle change. The coordinate transformation matrix is ​​T θp , the pitch angle is θ p =ω p t;ω p is the pitch angular velocity; Finally, the attitude coordinates of the aircraft at different times, that is, the coordinates of the grid nodes at different times, are obtained through the initial coordinate values, thereby obtaining the mathematical expression of the rotation-pitch coupled motion.

7. The method for obtaining the numerical value of the pitch derivative of a rotating aircraft according to claim 6, wherein: In step 2, the process of establishing the rotation-cone coupling motion model is as follows: The first two steps are the same as the process of establishing the rotation-pitch coupled motion model. The initial values ​​of the grid node coordinates in the inertial system are transformed into the results in the missile system to describe the attitude changes caused by the angle of attack and spin motion. The coordinate transformation matrix is and T s ; Again, the grid node coordinates in the projectile system are converted to the inertial system, which involves the cone angle transformation matrix T α and cone rotation transformation T θc , the cone rotation angle is θ c =ω c t;ω c is the cone angular velocity; Finally, the attitude coordinates of the aircraft at different times, that is, the coordinates of the grid nodes at different times, are obtained through the initial coordinate values, thereby obtaining the mathematical expression of the rotation-cone coupling motion.

8. The method for obtaining the numerical value of the pitch derivative of a rotating aircraft according to claim 7, wherein: In step three, the motion function is determined based on the mathematical model of rotation-pitch coupling and rotation-cone coupling motion, and the complex motion of the aircraft is realized by combining the grid dynamic motion technology. The complex motion flow field is further simulated by combining the unsteady Reynolds-averaged NS equations to obtain the transient pitch moment coefficient about the center of mass, and the reference length is the aircraft diameter.

9. The method for obtaining the numerical value of the pitch derivative of a rotating aircraft according to claim 8, wherein: Compared with the traditional method of using engineering algorithms or only pitch oscillation to calculate pitch derivatives, the method innovatively establishes a rotation-pitch and rotation-cone coupled motion model, that is, establishing a coordinate transformation relationship between the posture of the aircraft at different moments of complex motion and the initial posture. This coupled motion model can more realistically reflect the motion characteristics of the aircraft.

10. The method for obtaining the numerical value of the pitch derivative of a rotating aircraft according to claim 8, wherein: In the coupled motion simulation calculation of a rotating aircraft, the method needs to determine the motion function according to the coupled motion mathematical model, simulate the aircraft motion with the help of the computational grid motion, and further integrate to obtain a more accurate pitch derivative. The method solves the difficult problems of rotation-pitch coupling and rotation-cone coupling motion modeling, complex motion realization, and complex motion flow simulation, and sorts out the numerical calculation process of the pitch derivative of the rotating aircraft, providing a reference for engineering applications.

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