A method for time-domain calculation of gust loads for flight simulation

Abstract

This invention discloses a time-domain calculation method for gust loads in flight simulation, applicable to aircraft simulation. The method first divides the aircraft into planar aerodynamic meshes, then further divides them into aerodynamic strips along the spanwise direction, calculating the generalized aerodynamic coefficients of each strip. A calibration condition is selected, and the aerodynamic forces of each strip are calculated using traditional frequency domain methods and transformed to the time domain. A gust aerodynamic force fitting formula is proposed, and the amplitude and time delay coefficients of the aerodynamic forces are determined using the calculation results under the calibration condition. For the calculation condition, gust parameters are determined, and the time-domain gust aerodynamic forces of the aircraft are obtained by substituting them into the gust aerodynamic force formula. These are then used to calculate the time-domain gust load by substituting them into the state-space equations of the aircraft structure for flight simulation calculations. This invention avoids the problem of excessively large errors caused by the highly spiraled fitting curves in traditional time-domain solutions. Compared with CFD / CSD solutions, it significantly reduces computation time while ensuring computational accuracy, and can be widely applied in flight simulation.

Description

Technical Field

[0001] This invention relates to aircraft, specifically to the field of gust load calculation, and more specifically to a time-domain calculation method for gust load in flight simulation. Background Technology

[0002] Since the invention of the airplane, aircraft designers have paid close attention to atmospheric disturbances during flight, with gusts being a crucial form. Aircraft are inevitably affected by gusts during flight, generating additional aerodynamic forces and moments that cause vibrations and turbulence, affecting maneuverability, stability, and even leading to structural damage that threatens flight safety. With the pursuit of higher flight performance, aircraft are increasingly evolving towards higher aspect ratios and greater flexibility, making them more sensitive to the additional aerodynamic disturbances caused by gusts. Therefore, the impact of gust loads must be considered during the design process.

[0003] The most famous accident was the crash of the solar-powered drone "Helios" into the Pacific Ocean after being hit by a gust. Furthermore, turbulence experienced by commercial airliners during flight is also caused by gusts. Therefore, gust loads need to be considered and mitigated during aircraft design to improve aircraft performance and enhance the passenger experience. Gusts are generally classified into two types: discrete gusts, commonly 1-cos gusts, and continuous turbulence, characterized by pulsating turbulent velocity around its average value. To quantitatively represent this stochastic process, the power spectral density of the turbulent velocity needs to be expressed as a function; commonly used models include the Dryden model and the von Karman model.

[0004] In aircraft design, flight simulation is typically required for safety and flight performance evaluation. Because gusts are crucial during flight, time-domain gust aerodynamics simulation is necessary. While computational fluid dynamics (CFD) / computational solid mechanics (CSD) coupled methods are relatively accurate for calculating time-domain aerodynamics, they consume significant computational resources and time. Therefore, in engineering practice, the element-based method, such as the dipole lattice method (DLM), is primarily used for calculating time-domain aerodynamics. However, the element-based method is a frequency-domain aerodynamic calculation method, requiring conversion from the frequency domain to the time domain. The current mainstream approach is to use rational function fitting (RFA), which is crucial in the process. However, in engineering calculations, it has been found that for models where the gust reference point is far from the wing, such as large aircraft where the gust reference point is chosen at the nose, the curve of the wing's gust aerodynamic influence coefficient with respect to the reduction frequency k exhibits a highly spiral shape, making effective fitting impossible. This leads to excessively large calculation errors, sometimes exceeding 50%, failing to meet engineering requirements.

[0005] With the increasing demand for aircraft flight simulation, most engineering projects now require obtaining time-domain gust aerodynamic forces, which are then used to calculate the aircraft response using structural models, followed by control law design to mitigate gust loads. However, solving time-domain aerodynamic forces using CFD / CSD is currently too computationally expensive and unsuitable for large-scale calculations. While RFA can produce highly spiral fitting curves for some models, failing to yield accurate and effective results, it limits the computational scope of flight simulation.

[0006] Therefore, there is an urgent need for an efficient and accurate time-domain calculation method for gust loads that can be applied to flight simulation. Summary of the Invention

[0007] To address the need for time-domain gust aerodynamics calculations in aircraft flight simulations, and to solve the problem of inaccurate calculations caused by the highly spiraled fitting curves resulting from the use of RFA to convert aerodynamic forces from the frequency domain to the time domain in traditional gust load time-domain solutions, this invention provides a time-domain calculation method for gust loads in flight simulation based on sheet theory. This method enables accurate and rapid calculation of gust aerodynamic forces in the time domain and can be widely applied in the design phase of aircraft and control laws.

[0008] This invention provides a method for calculating gust loads in the time domain for flight simulation, which is implemented as a computer program and can be executed by a processor. The method includes the following steps:

[0009] Step 1: Draw a planar aerodynamic mesh for the calculation object, divide the mesh in the same wing into strips along the spanwise direction (y direction), and obtain the generalized aerodynamic influence coefficient (AIC) corresponding to each strip.

[0010] Step 2: Select the calibration condition, calculate the sudden gust aerodynamic force corresponding to each strip using the traditional frequency domain method, and convert it to the time domain sudden gust aerodynamic force; let the sudden gust velocity under the calibration condition be expressed as w. g (t), the time-domain aerodynamic force of strip i is calculated as follows:

[0011] Step 3: Fit the aerodynamic amplitude coefficient and time delay of each strip;

[0012] For each pneumatic strip, based on the results obtained in step 2 and w g (t), find the maximum values ​​corresponding to the sudden wind aerodynamic force and sudden wind disturbance velocity for each strip. and w gmax Calculate the aerodynamic amplitude coefficient B corresponding to strip i. i g, as follows:

[0013] Where ρ is atmospheric density and V is flight speed.

[0014] set up for The corresponding time, For w gmax At the corresponding moment, the aerodynamic time delay τ corresponding to slice i is... i Depend on and The time difference is obtained, that is

[0015] Step 4: Substitute the aerodynamic amplitude coefficient and aerodynamic time delay obtained in Step 3 into the aerodynamic fitting formula for sudden gusts proposed in this invention to fit the time-domain aerodynamic force of each aerodynamic strip.

[0016] Fitting the time-domain aerodynamic dynamics of strip i Represented as:

[0017] Step 5: Based on the current calculation conditions of the aircraft, calculate the time-domain gust aerodynamic force of each segment according to the fitting formula; superimpose the time-domain gust aerodynamic force calculation results of each segment to obtain the gust aerodynamic force f of the aircraft. g (t). The time-domain sudden wind dynamics f g (t) is substituted into the state-space model of the elastic aircraft dynamics to obtain the time-domain gust load.

[0018] The advantages of this invention are as follows: This invention provides a time-domain calculation method for gust loads suitable for flight simulation. It proposes a novel time-domain calculation method for gust aerodynamic forces, which are only related to the current and previous moments. The calculation speed is fast and it can be used for real-time flight simulation. This invention eliminates the need for rational function fitting, avoiding excessive fitting errors and accurately determining gust aerodynamic forces. Compared to the more accurate CFD / CSD methods, it significantly reduces computation time. The invention has been validated for discrete gusts and Dryden turbulence, and comparisons with existing mature methods demonstrate its effectiveness. This invention balances solution accuracy and computation time when calculating time-domain gust aerodynamic forces and can be widely applied in flight simulation. Attached Figure Description

[0019] Figure 1 This is a schematic diagram illustrating the implementation principle of the time-domain calculation of gust loads for flight simulation according to the present invention.

[0020] Figure 2 This is a schematic diagram of the aerodynamic grid and strip division according to an embodiment of the present invention;

[0021] Figure 3 This is a schematic diagram of a discrete 1-cos airflow.

[0022] Figure 4 Flowchart for solving the aircraft response;

[0023] Figure 5 This is a comparison chart of the calculation results of the method of the present invention and the traditional frequency domain method under discrete gust conditions in this embodiment;

[0024] Figure 6 This is a comparison chart of the calculation results of the method of the present invention and the traditional frequency domain method under continuous gust wind conditions in this embodiment. Detailed Implementation

[0025] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail and in depth below with reference to the accompanying drawings.

[0026] To address the needs of aircraft and gust mitigation control law design, and to solve the problems of traditional gust load time-domain simulation methods where the fitted curve becomes highly spiraled during rational function fitting, leading to distorted calculation results, and frequency domain algorithms being unable to solve for continuous turbulent time-domain gust loads, this invention proposes a gust load time-domain calculation method for flight simulation. This method employs sheet theory to simulate the gust load time domain of various aircraft layouts, enabling accurate calculation of both discrete and continuous gust loads on aircraft. This method is widely applied in the aircraft and gust mitigation control law design phase.

[0027] The present invention provides a time-domain calculation method for gust loads in flight simulation, such as... Figure 1 As shown, the specific steps include the following:

[0028] Step 1: Simplify the aircraft into a two-dimensional planar model, draw the aircraft's planar aerodynamic mesh, divide the mesh in the same wing into strips along the spanwise direction (y-direction), and use DLM to calculate the generalized aerodynamic effects corresponding to the aerodynamic strips.

[0029] First, a planar aerodynamic mesh for the dipole lattice method is drawn for the computational object. In this embodiment, a scaled-down model of a conventional layout passenger aircraft is used as an example, simplifying the aircraft into two parts: the wing and the fuselage. The wing has a half-span of 1m, a root chord length of 0.4m, and a tip chord length of 0.07m. The wing is divided into 24 meshes along its span. The chordal meshing is slightly denser at the root direction, with 15 meshes, while the other chordal directions are divided into 10 meshes each. Figure 2 As shown. Because the fuselage is less affected by gusts, the fuselage is not considered in the subsequent segmentation and calculation of gust aerodynamic forces.

[0030] After mesh generation, the reduction frequency k is determined to range from 0.05 to 2. The generalized aerodynamic influence coefficient AIC matrix A for each mesh is calculated using DLM.g (k). Where the reduction frequency k = ωb / V, V is the flight velocity, b is the reference half-chord length, and ω is the angular frequency of the simple harmonic oscillation. The generalized aerodynamic influence coefficient matrix A corresponding to each grid is calculated using the dipole lattice method. g (k) is as follows:

[0031]

[0032] in, S represents the mode shape matrix at the aerodynamic point of the grid. D represents the aerodynamic influence coefficient matrix obtained by DLM. S = diag(ΔS1,…,ΔS) n ) is an area-weighted matrix, with the diagonal terms representing the area of ​​each aerodynamic grid, ΔS i Let be the area of ​​aerodynamic grid i, and n be the number of aerodynamic grids, i = 1, 2, ..., n. d = [d1 ... dn] n ] T For the sudden wind vibration mode array, the i-th column x0 is the selected reference point for the sudden wind, x j Let be the control point of the j-th aerodynamic grid. The superscript T denotes matrix transpose, and the superscript -1 denotes the inverse matrix.

[0033] Finally, based on the calculated A g (k) According to the divided strips, the grids with the same spanwise coordinates in the wing are divided into strips, and the generalized aerodynamic influence coefficients corresponding to each grid in the same strip are added together to obtain the generalized aerodynamic influence coefficient corresponding to the strip. Let the generalized aerodynamic coefficient of the i-th strip be... Here, 'i' represents the wing strip number; in this embodiment of the invention, there are 24 wing strips.

[0034] In this embodiment of the invention, it is not necessary to draw the mesh again for the strip model. The mesh can be directly divided on the DLM aerodynamic mesh, which saves time and facilitates the subsequent solution of the correlation coefficients in the gust aerodynamic formula.

[0035] Step 2: Select the calibration condition, use the traditional frequency domain method to calculate the sudden wind force corresponding to each strip, and convert it to the time domain.

[0036] Select a suitable discrete inrush calculation case as the calibration case. The inrush is selected as a discrete inrush of the form of 1-cos, such as... Figure 3 As shown, the expression is as shown in equation (2).

[0037]

[0038] Determine relevant parameters such as discrete gusts, with a gust size L = 80m and a maximum gust velocity W. g=3.32 m / s, atmospheric density ρ = 0.8412 kg / m³ 3 Flight speed V = 271 m / s, reference half-chord length b = 0.27 m, frequency step size d f =0.122Hz, time step dt=0.001s and number of time points nt=8192.

[0039] For discrete gust velocity w g First, perform a Fourier transform on (t) to obtain the frequency domain form of the discrete gust velocity. here This represents the Fourier transform. Next, it is multiplied by the aerodynamic influence coefficient of the i-th strip. The frequency domain form of the sudden aerodynamic force of the i-th strip is obtained. Right now

[0040]

[0041] Finally, let's talk about... Performing an inverse Fourier transform yields the time-domain form of the sudden wind dynamics. Right now

[0042]

[0043] in, This represents the inverse Fourier transform.

[0044] By superimposing the time-domain gust dynamics corresponding to the 24 winglets, the total gust dynamics f of the entire aircraft can be obtained. gfft (t), that is

[0045]

[0046] The above In this context, ω represents frequency, and f gfft In (t), t represents time.

[0047] Step 3: Fit the aerodynamic amplitude coefficient of the strip.

[0048] For each pre-divided aerodynamic strip i, the present invention proposes a sudden wind aerodynamic formula (6) to fit the aerodynamic force.

[0049]

[0050] Where, τ i The time delay of the aerodynamic force of the i-th strip is given by... is the aerodynamic amplitude coefficient corresponding to the i-th strip.

[0051] According to step two and w g(t), find the sudden wind aerodynamic force for each strip. and gust disturbance speed w g The maximum value corresponding to (t) and w gmax Substitute this into the following equation to obtain the aerodynamic amplitude coefficient corresponding to the i-th strip.

[0052]

[0053] Step 4: Time delay τ of fitting the aerodynamic force of the strip i .

[0054] The time-domain expression for the sudden wind aerodynamics proposed in this invention is shown in equation (6), and the amplitude coefficient has been determined in step three. set up for The corresponding time, For w gmax The corresponding time is τ i Depend on and The time difference was calculated as follows:

[0055]

[0056] Step 5: Calculate the time-domain aerodynamic forces of the sudden wind for the calculation conditions corresponding to discrete sudden wind and continuous turbulence.

[0057] Substituting the aerodynamic amplitude coefficients and aerodynamic time delays calculated in steps 3 and 4 into formula (6), we obtain the aerodynamic fitting formula for each gust corresponding to each segment. For the current calculation conditions of the aircraft, we determine the atmospheric density, the aircraft's flight speed, and gust-related parameters. If it is a discrete gust, we determine the discrete gust scale and the maximum gust velocity; if it is continuous turbulence, we determine the discrete gust scale and the root mean square of the gust. Based on the aerodynamic fitting formula for each segment, we calculate the time-domain aerodynamic force of each segment under the current conditions, and sum the time-domain aerodynamic forces of all segments to obtain the total aerodynamic force f of the aircraft. g (t).

[0058] To demonstrate the effectiveness of the method for the required gust conditions, verification calculations were performed under both discrete gust and continuous turbulence conditions. The relevant parameters for discrete gusts, including the gust scale L, were set. dis =13.57m and maximum gust velocity W gdis = 3.32 m / s. For continuous turbulence, the Dryden model is chosen, which represents the power spectral density function of the gust velocity as follows:

[0059]

[0060] A Dryden gust satisfying this power spectral density distribution can be achieved as follows: a power spectral density of Φ W (f)=2σ g Gaussian white noise is passed through a Dryden gust-shaped filter to obtain a root mean square value of σ. g The time-domain signal of the sudden wind. The representation of this Dryden sudden wind shaping filter in the Laplace domain, Gg(s), is:

[0061]

[0062] Here, τ is an intermediate variable introduced for simplification, τ = L / V. Here, f is the frequency, a parameter in the frequency domain, and s is the complex frequency, a parameter in the Laplace domain.

[0063] Set the relevant parameters for continuous turbulence, and the discrete gust scale L. con =760m and root mean square σ of sudden wind gcon = 3.32 m / s. A discrete gust of wind w is generated. gdis (t) and continuous turbulence w gcon (t), then the results calculated in steps 3 and 4 and τ i Substituting the time-domain aerodynamic dynamics into the solution for each strip of the aerodynamic dynamics of the sudden wind, let's assume the discrete aerodynamic wind w gdis (t) and continuous turbulence w gcon Under the calculation condition of (t), the sudden aerodynamic forces corresponding to the i-th strip are respectively and

[0064] By superimposing the time-domain aerodynamic force calculation results of each segment, the total gust aerodynamic force of the aircraft under the two calculation conditions is obtained. and as follows:

[0065]

[0066]

[0067] Step 6: Calculate the time-domain gust aerodynamic force f of the aircraft. g (t) is substituted into the state-space model of elastic aircraft dynamics, and then the aircraft response is calculated and compared with the results calculated by the traditional wind-driven aerodynamic frequency domain algorithm.

[0068] like Figure 4 As shown, the aerodynamic force f at time t, which was calculated previously, is... g(t) is input into the state space solution module of the elastic aircraft flight simulation, and the time-domain gust load at time t is obtained after calculation. The response of the aircraft is then calculated for subsequent use by the aircraft and control law to complete the flight simulation calculation.

[0069] This invention's method is applicable not only to discrete gust calculations but also to continuous gust calculations. While maintaining the accuracy of time-domain gust aerodynamic calculations, it offers a fast solution speed, balancing accuracy and computation time, and can be widely applied to simulation studies of various aircraft. For continuous gust calculations, traditional frequency-domain methods cannot calculate the time-domain response, requiring the use of CFD / CSD methods, which are very slow. Experiments show that, for the same aircraft calculation scenario on an 8-core computer, using both this invention's method and the CFD / CSD method, the method calculates the time-domain gust aerodynamics in just 4-5 seconds, while the CFD / CSD method takes 10 hours.

[0070] like Figure 5 and Figure 6 The diagram shows a comparison of the technical effects of the method of this invention with traditional frequency domain calculation methods. For the calculation case of 1-cos discrete sudden wind, the time domain response can be directly plotted and compared with the traditional frequency domain calculation results after Fourier transform. Figure 5 The acceleration response of an aircraft under discrete 1-cos discrete gusts is presented. A comparison of the calculation results from the proposed method with those from traditional frequency domain methods shows that the results are largely consistent. For calculations involving continuous turbulence, since traditional frequency domain methods can only calculate the frequency domain response, the calculation results from the proposed method need to be converted to the frequency domain through power spectral density analysis. Figure 6 The power spectral density (PSD) of the aircraft acceleration response under Dryden continuous turbulence is presented. The figure shows the calculation results of the traditional frequency domain method and the calculation results of the method of this invention, and it can be seen that the results of the two are basically consistent. Therefore, it can be seen that the method of this invention ensures the accuracy of time-domain gust aerodynamic calculations under different calculation conditions. This proves that the method of this invention can accurately and effectively calculate time-domain gust loads under various gust conditions and can be applied to control law design.

[0071] The present invention proposes a new formula for solving gust aerodynamic forces, as shown in formula (6). The formula shows that the aerodynamic forces are only related to the previous and current moments, making the calculation simple and fast. The solution accuracy meets engineering requirements, and a time-domain calculation framework for gust loads in flight simulation is established. The present invention skips the rational function fitting step in the traditional time-domain method for solving gust loads, thus avoiding the distortion of results caused by highly spiraled fitting curves. Compared to CFD / CSD solutions, it significantly reduces computation time, ensuring computational accuracy without requiring a large amount of computation time. Furthermore, the present invention is applicable to some aircraft configurations where traditional frequency-domain calculation methods are not suitable. Therefore, the present invention can be widely applied to flight simulation and has certain engineering significance.

[0072] Except for the technical features described in the specification, all other technologies are known to those skilled in the art. Descriptions of well-known components and technologies are omitted in this invention to avoid redundancy and unnecessary limitation. The embodiments described above do not represent all embodiments consistent with this application. Various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this invention are still within the protection scope of this invention.

Claims

1. A method for time-domain calculation of gust loads in flight simulation, characterized in that, Includes the following steps: Step 1: Draw a planar aerodynamic mesh for the aircraft to be calculated, divide the mesh in the same wing into strips along the spanwise direction, and obtain the generalized aerodynamic influence coefficient corresponding to each strip; Step 2: Select the calibration condition, calculate the sudden wind aerodynamic force corresponding to each strip, and convert it into time-domain sudden wind aerodynamic force; Step 3: Fit the aerodynamic amplitude coefficient and time delay of each strip; For each strip i, the time-domain aerodynamic force and aerodynamic velocity under the calibration conditions are obtained from step 2, and the maximum aerodynamic force of strip i is found from them. and maximum gust speed w g max The aerodynamic amplitude coefficient of strip i is obtained. ρ is atmospheric density, V is flight speed; let ρ be the atmospheric density, V be the flight speed. for At the corresponding time, For w g max The time delay of obtaining the aerodynamic force of slice i at the corresponding moment. Step 4: Determine the fitting form of the sudden wind aerodynamic force for each strip; Fitting the time-domain aerodynamic dynamics of strip i Represented as: w g (t) represents the gust speed at time t; Step 5: Determine the current calculation conditions of the aircraft, calculate the time-domain gust aerodynamic force of each segment using the fitting form of the gust aerodynamic force of each segment, and superimpose the time-domain gust aerodynamic forces of each segment to obtain the gust aerodynamic force f of the aircraft. g (t), f g (t) Substitute the state-space equation of the aircraft structure to obtain the time-domain gust load.

2. The method according to claim 1, characterized in that, In step 1, the generalized aerodynamic influence coefficient for each strip is calculated as follows: Determine the reduction frequency k = ωb / V, where V is the flight speed, b is the reference half-chord length, and ω is the angular frequency of the simple harmonic oscillation. The generalized aerodynamic influence coefficient matrix A for each grid is calculated using the dipole lattice method. g (k) is as follows: in, Let S be the mode shape matrix at the aerodynamic point of the grid, D represent the aerodynamic influence coefficient matrix obtained by DLM; S is the area-weighted matrix, with the diagonal terms being the area of ​​each aerodynamic grid; d is the gust mode shape array, with the i-th column... x0 is the selected reference point for the sudden wind, x j Let j be the control point of the j-th aerodynamic grid; The generalized aerodynamic coefficients of strip i are obtained by summing the generalized aerodynamic coefficients of all grids in strip i.

3. The method according to claim 1, characterized in that, In step 2, a discrete gust calculation condition is selected as the calibration condition, and the gust aerodynamic force corresponding to each strip is calculated using the traditional frequency domain method.

Images