A method of predicting aerodynamic derivatives of an aircraft

Abstract

The application relates to a method for predicting aerodynamic derivatives of an aircraft, and belongs to the technical field of the aircraft.The application establishes an aircraft wing model based on a vortex lattice method; a steady form of a state space equation is given based on the established aircraft wing model; then, derivatives of aircraft aerodynamic force and aerodynamic moment with respect to aircraft motion variables are obtained based on the steady form of the state space equation, and derivatives of the aircraft aerodynamic force and the aerodynamic moment with respect to aircraft rudder deflection are obtained.The aerodynamic derivative prediction method solves the problems of complex prediction process, high cost, long cycle and inaccurate prediction results of the existing aerodynamic derivative prediction method of the aircraft.

Description

Technical Field

[0001] This invention belongs to the field of aircraft technology, specifically relating to a method for predicting the aerodynamic derivative of an aircraft. Background Technology

[0002] In aircraft design, constructing aerodynamic models based on aerodynamic derivatives is a common method. Traditional methods for predicting aircraft aerodynamic derivatives mainly include flight testing, wind tunnel testing, engineering empirical methods, and CFD numerical calculation methods. Flight testing methods are based on aerodynamic data obtained during actual flight, solving for aerodynamic derivatives through interpolation, fitting, or parameter identification. This method is difficult, time-consuming, risky, and costly, making it difficult to obtain guiding data in the early stages of aircraft design. Wind tunnel testing methods are based on aerodynamic data obtained during wind tunnel tests, solving for aerodynamic derivatives through interpolation, fitting, or parameter identification. This method also suffers from high cost and long cycle time, making it difficult to apply in the early stages of aircraft design. Engineering empirical methods calculate aerodynamic derivatives using simple formulas combined with aircraft aerodynamic shape parameters, offering quick calculations but significantly limited accuracy. CFD numerical calculation methods offer higher accuracy than engineering empirical methods but are computationally expensive, requiring extensive simulations to obtain aerodynamic derivatives, thus limiting design analysis efficiency. Summary of the Invention

[0003] In view of the above analysis, the present invention provides a method for predicting the aerodynamic derivative of an aircraft, which solves the problems of existing methods for predicting the aerodynamic derivative of an aircraft being complex, costly, and time-consuming, and having inaccurate prediction results.

[0004] This invention provides a method for predicting the aerodynamic derivative of an aircraft, comprising the following steps:

[0005] S1. Establishing an aerodynamic model based on the vortex lattice method:

[0006] Multiple quadrilateral aerodynamic grids are divided along the chord and span of the curved surface of the aircraft wing. The aerodynamic grids include attached vortex grids attached to the wing surface and the first row of trailing vortex grids and other trailing vortex grids along the direction of the incoming flow at the trailing edge of the wing.

[0007] S2. Establish state-space aerodynamic equations for the aerodynamic grid obtained in step S1:

[0008] S2-1. Arrange vortex segments at the 1 / 4 chord of each aerodynamic grid. Connect two adjacent vortex segments of equal intensity to form a vortex ring. Select the midpoint of the 1 / 4 chord as the point of application of the aerodynamic force of the aerodynamic grid, and select the midpoint of the 3 / 4 chord as the control point of the aerodynamic grid.

[0009] S2-2. The attached vortex mesh, the first row of wake vortex mesh, and other wake vortex meshes in the aerodynamic model are mapped as follows: attached vortices on the wing surface, the first row of wake vortices on the wing trailing edge, and other wake vortices. Let the vortex intensity of the attached vortex on the wing surface be Γ. b The intensity of the first row of tail vortices on the trailing edge of the wing is Γ. w0 The intensity of other wake vortices is Γ. wl The aerodynamic control equations are:

[0010] K b Γ b +K w0 Γ w0 +K wl Γ wl =-w (29)

[0011] Where w is the induced velocity on the wing surface, w = (V ∞ +V g )·n;V ∞ V is the velocity vector of the incoming flow. g Let K be the velocity vector of the incoming flow disturbance, and n be the normal vector matrix at the control point. b ,K w0 ,K wl These are the induction coefficient matrices for the attached vortex, the first row of wake vortices, and other wake vortices, respectively.

[0012] S2-3. The first row of tail vortices on the wing trailing edge maintains vortex strength conservation during the detachment process, as expressed by:

[0013]

[0014] in, Let C1 be the time derivative of the intensity of the first row of trailing edge vortices, where Δt is the time step and C1 is the coefficient matrix that ensures the correct correspondence between the trailing edge vortices and the attached vortices, containing only 0 and 1 elements.

[0015] S2-4. It is stipulated that the vortex strength remains constant after other wake vortices are released, and the relationship is expressed as follows:

[0016]

[0017] in, C1 represents the derivative of the intensity of other wake vortices with respect to time. C2 and C3 are constant extraction matrices that characterize the correspondence between the positions of other vortices and the first row of wake vortices on the trailing edge of the wing, containing only 0 and 1 elements.

[0018] S2-5, Combining equations (1), (2), and (3), we obtain the state-space equation form of the vortex lattice method as follows:

[0019]

[0020] Among them, the intensity Γ of the wake vortex w =[Γ w0 Γ wl ] T A a B a The state-space coefficient matrix is ​​related to the geometry of the wing and tail vortex, as well as the division of the attached vortex on the wing surface, the first row of tail vortices on the wing trailing edge, and other tail vortices.

[0021]

[0022]

[0023] Where I is the identity matrix and O is a zero matrix containing only 0 elements.

[0024] S2-6. Give the aerodynamic force expression on the aerodynamic mesh. The aerodynamic force expression of the aerodynamic mesh is as follows:

[0025]

[0026] Among them, V ∞ e is the velocity vector of the incoming flow. Γ Here, ρ is the tangential vector of the leading-edge vortex, and ρ is the air density. The incoming flow unit vector, Γ is the unit vector of the leading-edge vortex tangentially, and A is the aerodynamic grid area; i The effective vorticity in the i-th aerodynamic grid is represented by the difference in vortex intensity between the front and rear positions of the aerodynamic grid along the flight direction of the aircraft. Let be the effective vorticity time derivative on the i-th aerodynamic grid, and let be the average value of the vortex intensity time derivative of the surface vortex of the aerodynamic grid at positions before and after the flight direction of the aircraft.

[0027] S2-7, combined with equations (2), (3), (4) and (7), yields the vector expression F of the aerodynamic force of the aerodynamic grid:

[0028]

[0029] Among them, D a , C a The coefficient matrix, Let w be the derivative of w with respect to time.

[0030] S3. Give the steady form of the aerodynamic equations for the state-space aerodynamic grid:

[0031] Based on equations (4) and (8) given in step S2, ignoring the unsteady terms regarding vortex intensity variation in the vortex lattice state-space form, the steady form of the aerodynamic equations for the state-space aerodynamic grid is:

[0032] A a Γ w +B a w = 0 (37)

[0033] F = C a Γ w +D a w (38)

[0034] Wherein, given the incoming flow conditions, the coefficient matrix A a B a C a D a It is related to the geometry of the wing and the tail vortex.

[0035] S4. Find the derivatives of the aerodynamic forces and aerodynamic moments of the entire aircraft with respect to the aircraft's motion variables:

[0036] S4-1. Considering only the rigid body motion of the aircraft, the velocity V of the aircraft is:

[0037] v=[V0+ω×r0] (39)

[0038] Where V0 is the level flight velocity vector of the aircraft, ω is the rotational angular velocity vector of the aircraft, and r0 is the distance vector of the aircraft from the center of gravity.

[0039] S4-2, Surface induced velocity w at the control point of the i-th aerodynamic grid i for:

[0040] w i =v i ·n 0i =(V 0i n 0i +(ω×r 0i )n 0i (40)

[0041] Among them, v i Let V be the velocity of the i-th aerodynamic grid. 0i Let n be the velocity of the i-th aerodynamic grid during level flight. 0i Let r be the normal vector of the i-th aerodynamic mesh. 0i Let be the position vector from the i-th aerodynamic grid to the center of gravity of the aircraft.

[0042] S4-3. From equations (11) and (12), the aerodynamic force of the aerodynamic grid can be obtained as follows:

[0043]

[0044] Where G is the interpolation matrix of the aerodynamic grid and the aircraft wing structure.

[0045] S4-4, the resultant external force F of the aircraft's overall aerodynamic forces. Ar With the resultant external torque M Ar The aerodynamic forces of all aerodynamic grids are summed to obtain:

[0046] F Ar =Φ t F (42)

[0047] M Ar =Φ r F (43)

[0048] Specifically, the summation matrix Φ t and Φ r for:

[0049]

[0050] Where, N s The total number of aerodynamic grids, i = 1, 2, 3, ..., N S , x is the tensor from the point of application of the aerodynamic force in the i-th aerodynamic grid to the point of moment taking; i Let y be the distance in the x-direction from the point of application of the aerodynamic force of the i-th aerodynamic grid to the point of taking the moment. i Let z be the distance in the y-direction from the point of application of the aerodynamic force of the i-th aerodynamic grid to the point of moment taking. i Let I be the distance from the point of application of the aerodynamic force of the i-th aerodynamic grid to the point of moment taking in the z-direction. 3×3 I is a 3-order identity matrix. 3×3 The value of 3×3 in the formula is consistent with the x-direction force, y-direction force and z-direction force of the aerodynamic force vector, ensuring that the force and torque multiplied by the summation matrix are the total resultant external force and resultant external torque.

[0051] Let V0 = [-V0 -V0β -V0α] T ω=[pqr] T Substituting into equation (15), the derivatives of the overall aerodynamic forces and aerodynamic moments with respect to the trim variables are obtained as follows:

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] Among them, c p ,c q ,c r n is a column vector; n0 is the column matrix of normal vectors for all aerodynamic meshes. n 0z Let n be the z-direction component of the normal vector n0. 0y Let n0 be the y-direction component of the normal vector, and its elements have the following form:

[0059]

[0060] Where, n 0ix ,n 0iy ,n 0iz The n-th aerodynamic mesh normal vectors are respectively 0i x, y, and z direction components; x i Let y be the distance in the x-direction from the aerodynamic force application point of the i-th aerodynamic grid to the moment point. i Let z be the distance in the y-direction from the aerodynamic force application point of the i-th aerodynamic grid to the moment point. i Let be the distance from the aerodynamic force application point of the i-th aerodynamic grid to the point of moment taking in the z-direction.

[0061] It is worth noting that in the expressions for the aerodynamic forces and aerodynamic moments of the entire machine (16) and (17), the coefficient matrix A a B a C a D a The variables are only related to the geometry of the wing and tail vortex; the variables related to the aircraft's speed are:

[0062] Angle of attack α, sideslip angle β, roll rate p, pitch rate q, and yaw rate r are all included in the expression for induced velocity w.

[0063] S5. Calculate the aerodynamic derivative of the rudder deflection:

[0064] When calculating the aerodynamic derivative of the overall aerodynamic forces with respect to the control surface deflection angle δ, we only consider the aerodynamic forces of the aerodynamic grid caused by the control surface deflection through the change of the normal vector. The aerodynamic grid corresponding to the control surface does not undergo physical deflection. Therefore, we change the normal vector n0 to n = n0 + cδ, where c is the control surface deflection axis vector. Let the direction of the control surface rotation axis be e. Then, the change in the normal vector caused by the rotation angle δ is:

[0065] Δn=sinδ(e×n0)+(1-cosδ)[e×(e×n0)] (52)

[0066] When δ is less than 5 degrees:

[0067]

[0068] Therefore, the derivative of the overall aerodynamic force with respect to the control surface deflection angle δ is:

[0069]

[0070]

[0071] Wherein, column vector c δ for:

[0072] c δi =V0·c+(ω×r 0i )·c (56)

[0073] S6. Obtain the aerodynamic derivative of the aircraft through equations (17), (18), (19), (20), (21), (26) and (27).

[0074] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0075] (1) The prediction method of the present invention can directly calculate the unsteady aerodynamic force under arbitrary motion without the simple harmonic motion assumption, and the prediction efficiency is high.

[0076] (2) The prediction method of the present invention realizes the prediction of the aerodynamic derivative of the aircraft wing (rigid body) based on the state-space form vortex lattice method. The prediction process is simple and improves the accuracy of the prediction results. Attached Figure Description

[0077] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0078] Figure 1 This is a flowchart of the aerodynamic derivative prediction method for aircraft of the present invention;

[0079] Figure 2 Example design model diagram of the aerodynamic derivative prediction method for aircraft of the present invention;

[0080] Figure 3 The aerodynamic mesh diagram of the entire wing and tail of the aircraft is an example model of the aerodynamic derivative prediction method of the aircraft of the present invention.

[0081] Figure 4 The spanwise lift calculation results are for an example model of the aerodynamic derivative prediction method for aircraft of the present invention. Detailed Implementation

[0082] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other.

[0083] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0084] This embodiment uses a winged unmanned aerial vehicle (UAV) model. The entire aircraft's wings include a left wing, a right wing, and a center wing. All three wings are rectangular and straight, with an equal span of approximately 1000mm. Ailerons are located on the trailing edges of both the left and right wings, extending through the left and right wings respectively. The control surface chord length accounts for one-third of the total wing chord length. The wings and tail are connected by a tail strut extending from the fuselage. The vertical distance between the tail and the wings is 1020mm. The tail includes a horizontal stabilizer and a vertical stabilizer. The horizontal stabilizer is an all-moving design with a span of 960mm and a chord length of 120mm, functioning as an elevator during flight control. The vertical stabilizer uses a dual all-moving vertical tail design with a span of 240mm and a chord length of 120mm, functioning as a rudder during flight control.

[0085] Some parameters of the winged drone model are shown in Table 1:

[0086] Table 1 Parameters of the Winged UAV Model

[0087] Parameter name Parameter value Overall wingspan / mm 3000 Aileron span / mm 1000 Vertical tail span / mm 240 Flat tail span length / mm 960 Vertical distance from tail fin to wing of the entire aircraft / mm 1020 Overall wing chord length / mm 270 Aileron chord length / mm 90 Tail chord length / mm 120 Flat tail chord length / mm 120 Total machine weight / kg 8

[0088] S1. Establishing an aerodynamic model:

[0089] On the wing of the wing model, the curved surface of the entire wing is divided into 8 grids along the chord direction and 90 grids along the span. The trailing vortex grid is divided into 160 grids along the chord direction and 90 grids along the span. On the tail, the curved surface is divided into 8 grids along the chord direction and 46 grids along the span. The trailing vortex grid is divided into 160 grids along the chord direction and 46 grids along the span. The grid division of the entire wing and tail is as follows: Figure 3 and 4 As shown.

[0090] S2. Establish state-space aerodynamic equations for the aerodynamic grid obtained in step S1:

[0091] The state-space equations of the vortex lattice method are:

[0092]

[0093] Among them, the vortex intensity Γ w =[Γ w0 Γ wl ] T A a B a Let w be the state-space coefficient matrix, and w be the induced velocity on the wing surface, including the disturbance.

[0094] The expression for the aerodynamic vector F is:

[0095]

[0096] Among them, D a , C a The coefficient matrix, The derivative of w with respect to time

[0097] S3. Give the steady form of the aerodynamic equations in state-space form:

[0098] Based on equations (4) and (8) given in step S2, the time-invariant form of the state-space equations is given as follows:

[0099] A a Γ w +B a w = 0 (59)

[0100] F = C a Γ w +D a w (60)

[0101] S4. Find the derivatives of the aerodynamic forces and aerodynamic moments with respect to the aircraft's motion variables:

[0102] Step S3 yields the steady form of the state-space equations. The derivatives of the aerodynamic forces and moments with respect to the aircraft's motion variables—angle of attack α, sideslip angle β, roll rate p, pitch rate q, and yaw rate r—are calculated. Their analytical expressions are given in equations (17), (18), (19), (20), and (21). The calculation conditions are: flight speed 20 m / s, trim angle of attack 1 degree, and atmospheric density 1.225 kg / m³. 3 The spanwise lift distribution of the entire aircraft is as follows: Figure 4 As shown, the aerodynamic derivative values ​​are calculated by substituting the flight speed, trim angle of attack, and atmospheric density into the analytical expression.

[0103] S5. Calculate the aerodynamic derivative of the rudder deflection:

[0104] Step S3 yields the steady form of the state-space equations. The derivatives of the aerodynamic forces and aerodynamic moments with respect to the aircraft rudder deflection δ are calculated, and their analytical expressions are given in equations (26) and (27). The calculation conditions are a flight speed of 20 m / s, a trim angle of attack of 1 degree, and an atmospheric density of 1.225 kg / m³. 3 The aerodynamic derivative values ​​are obtained by substituting the flight speed, trim angle of attack, and atmospheric density into the analytical expression.

[0105] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the aerodynamic derivative of an aircraft, characterized in that, Includes the following steps: S1. Establishing an aerodynamic model based on the vortex lattice method: Multiple quadrilateral aerodynamic grids are divided along the chord and span directions on the curved surface of the aircraft wing. The aerodynamic grids include attached vortex grids attached to the wing surface and the first row of trailing vortex grids and other trailing vortex grids along the direction of the incoming flow at the trailing edge of the wing. S2. Establish state-space aerodynamic equations for the aerodynamic grid obtained in step S1: S2-1. Arrange vortex segments at the 1 / 4 chord of each aerodynamic grid; select the midpoint of the 1 / 4 chord as the point of application of the aerodynamic force of the aerodynamic grid, and select the midpoint of the 3 / 4 chord as the control point of the aerodynamic grid; S2-2. The attached vortex mesh, the first row of wake vortex mesh, and other wake vortex meshes in the aerodynamic model are mapped as follows: attached vortices on the wing surface, the first row of wake vortices on the wing trailing edge, and other wake vortices. Let the vortex intensity of the attached vortex on the wing surface be... The intensity of the first row of tail vortices on the trailing edge of the wing is The intensity of other wake vortices is The aerodynamic control equations are: (1) Where w is the induced velocity on the wing surface. ; The velocity vector of the incoming flow. The velocity vector of the incoming flow disturbance. Let be the normal vector matrix at the control points; These are the induction coefficient matrices for the attached vortex, the first row of wake vortices, and other wake vortices, respectively. S2-3. The first row of tail vortices on the wing trailing edge maintains vortex strength conservation during the detachment process, as expressed by: (2) in, Let be the time derivative of the intensity of the first row of wake vortices on the trailing edge of the wing. For time step, To ensure the correct correspondence between the trailing vortex and the attached vortex in the first row of trailing edges, the coefficient matrix contains only 0 and 1 elements; S2-4. It is stipulated that the vortex strength remains constant after other wake vortices are released, and the relationship is expressed as follows: (3) in, Let be the derivative of the intensity of other wakes with respect to time. The constant extraction matrix, which characterizes the correspondence between the positions of other vortices and the first row of wake vortices on the trailing edge of the wing, contains only two elements: 0 and 1. For unit array; S2-5, Combining equations (1), (2) and (3), we obtain the state-space equation form of the vortex lattice method as follows: (4) in, The derivative of the wake intensity with respect to time; the intensity of the wake. , The state-space coefficient matrix is ​​related to the geometry of the wing and tail vortex, as well as the division of the attached vortex on the wing surface, the first row of tail vortices on the wing trailing edge, and other tail vortices. (5) (6) in, As a unit array, It is a zero matrix containing only 0 elements; S2-6. Give the aerodynamic force expression on the aerodynamic mesh. The aerodynamic force expression of the aerodynamic mesh is as follows: (7) in, The velocity vector of the incoming flow. The leading edge vortex tangential vector. air density, The incoming flow unit vector, The unit vector of the leading edge vortex tangential direction. The area of ​​the aerodynamic grid; For the first i The effective vorticity in an aerodynamic grid is the difference in vortex intensity of the surface vortex between the aerodynamic grids at positions before and after the aircraft's flight direction. For the first i The effective vorticity time derivative on each aerodynamic grid is the average value of the vortex intensity time derivative of the surface vortex of the aerodynamic grid at positions before and after the aircraft's flight direction. S2-7, combined with formulas (2), (3), (4) and (7), yields the vector of aerodynamic forces in the aerodynamic grid. The expression is: (8) in, The coefficient matrix, for The derivative with respect to time; S3. Give the steady form of the aerodynamic equations for the state-space aerodynamic grid: Based on equations (4) and (8) given in step S2, ignoring the unsteady terms concerning vortex intensity variation in the vortex lattice state-space form, the steady form of the aerodynamic equations for the state-space aerodynamic grid is: (9) (10) Wherein, given the incoming flow conditions, the coefficient matrix , , , It is related to the geometry of the wing and the tail vortex; S4. Find the derivatives of the aerodynamic forces and aerodynamic moments of the entire aircraft with respect to the aircraft's motion variables: S4-1, The velocity V of the aircraft is: (11) in, This is the level flight velocity vector of the aircraft. The angular velocity vector of the aircraft. This is the distance vector from the center of gravity of the aircraft; S4-2, No. Surface induced velocity at control points of a pneumatic grid for: (12) Among them, v i For the first The velocity of the aerodynamic grid, V 0i For the first i The aerodynamic grid level flight speed, For the first The normal vector of the aerodynamic mesh, r 0i For the first The position vector from the aerodynamic grid to the center of gravity of the aircraft; S4-3. From equations (11) and (12), the aerodynamic force of the aerodynamic grid can be obtained as follows: (13) in, This is the interpolation matrix for the aerodynamic forces of the aerodynamic grid and the wing structure of the aircraft; S4-4, the resultant external force of the aircraft's overall aerodynamic forces and the resultant external torque The following is obtained by summing the aerodynamic forces through the aerodynamic grid: (14) (15) Specifically, summation matrix for: (16) in, This represents the total number of aerodynamic grids. i= 1,2,3…, N S , For the first i The tensor from the point of application of the aerodynamic force of the aerodynamic grid to the point of taking moments; For the first i The distance in the x-direction from the point of application of the aerodynamic force of each aerodynamic grid to the point of taking the moment. For the first i The distance in the y-direction from the point of application of the aerodynamic force of each aerodynamic grid to the point of taking the moment. For the first i The distance in the z-direction from the point of application of the aerodynamic force of each aerodynamic grid to the point of taking the moment. It is a 3-order identity matrix. The value of 3×3 in the formula is consistent with the x-direction force, y-direction force and z-direction force of the aerodynamic force vector, ensuring that the force and torque multiplied by the summation matrix are the total resultant external force and resultant external torque. Will , Substituting into equation (15), the derivatives of the aircraft's overall aerodynamic forces and aerodynamic moments with respect to the trim variables are obtained as follows: (17) (18) (19) (20) (21) (22) in, , , , and These represent the aircraft's angle of attack, sideslip angle, roll rate, pitch rate, and yaw rate, respectively. is a column vector representing the force direction; n0 is the column matrix of normal vectors for all aerodynamic meshes. , For the normal vector n0 z Directional components, For the normal vector n0 y The directional component, whose elements are in the form of: (23) in, The first i aerodynamic mesh normal vector of x , y and z Directional components; For the first i The distance in the x-direction from the point of application of aerodynamic forces in each aerodynamic grid to the point of taking the moment. For the first i The distance in the y-direction from the point of application of aerodynamic forces in each aerodynamic grid to the point of moment taking. For the first i The distance from the point of application of aerodynamic forces in the aerodynamic grid to the point of taking the moment in the z-direction; , and Representing column vectors respectively The Middle i One component; S5. Calculate the aerodynamic derivative of the rudder deflection: Change the normal vector n0 to , Let the control surface deflection axis vector be and the direction of the control surface rotation axis be . Then the rotation angle The resulting change in the normal vector is: (24) When in When the temperature is less than 5 degrees: (25) Therefore, the aerodynamic forces of the entire aircraft affect the deflection angle of the control surfaces. The derivative is: (26) (27) Among them, column vectors Let be the column vector of rudder deflection influence coefficients, where the i-th component for: (28) S6. Obtain the aerodynamic derivative of the aircraft through equations (17), (18), (19), (20), (21), (26) and (27).

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