An Efficient and High-Precision Prediction Method for Stall Flutter Based on Energy Maps and Deep Neural Operator Networks

Abstract

The present invention discloses a method for efficiently and accurately predicting stall flutter based on an energy graph and a deep neural operator network, and belongs to the technical field of aeroelastic analysis. The present invention constructs and trains a data-driven model for rapid prediction of unsteady aerodynamic torque of a dynamic stall cycle taking into account changes in wind speed, amplitude, and frequency based on a deep neural operator network, and implements efficient and accurate prediction of stall flutter response by rapidly calculating an energy graph based on a data-driven model and iteratively correcting stall flutter response taking into account aerodynamic stiffness correction. The present invention can predict stall flutter response under different incoming flow velocities, different structural natural frequencies, and damping coefficients with high accuracy, while greatly reducing the calculation time required for response prediction.

Description

Technical Field

[0001] The present invention belongs to the technical field of aeroelastic analysis, and relates to a method for efficiently and accurately predicting aeroelastic response, and specifically to a method for efficiently and accurately predicting stall flutter based on an energy graph and a deep neural operator network. Background Art

[0002] Stall flutter is an aeroelastic instability phenomenon closely related to flow separation, which manifests as a large pitch single-degree-of-freedom limit cycle oscillation of the airfoil. It is widely present in large flexible wings of high-altitude and long-endurance aircraft, helicopter rotors, and wind turbine blades. Stall flutter is highly destructive and seriously affects the performance and structural safety of related equipment. Obtaining the stall flutter response characteristics under different operating parameters is crucial for the anti-stall flutter design of related equipment.

[0003] Due to the large-scale flow separation in the stall flutter flow field, the stall flutter aerodynamic characteristics are highly nonlinear, and traditional high-efficiency unsteady aerodynamic engineering analysis methods such as the panel method and dipole grid generation are difficult to effectively predict. Therefore, the current analysis and calculation of stall flutter response characteristics mainly rely on the CFD (computational fluid dynamics) / CSD (computational structural dynamics) coupling method, which is very computationally intensive and extremely inefficient, making it difficult to meet the needs of anti-stall flutter design.

[0004] With the continuous development of deep learning technology, relevant scholars (Yuting Dai, Haoran Rong, You Wu, et al. Stall flutter prediction based on multi-layer GRU neural network [J]. Chinese Journal of Aeronautics, 2023, 36 (1): 75-90) use deep neural networks to construct an unsteady aerodynamic reduction model containing velocity information, and couple it with the structural dynamics equation to quickly obtain the response characteristics of stall flutter. However, the input of the unsteady aerodynamic reduction model in this method depends on the calculation results of the previous moment, and there is a certain error between the reduced-order model and the CFD calculation results. This method of coupling the reduced-order model with the structural dynamics equation for iterative solution is very easy to cause error accumulation, affecting the stability and convergence of the fluid-solid coupling calculation.

[0005] At the same time, relevant scholars proposed the concept of energy diagram (Menon K, Mittal R. Flow physics and dynamics of flow-induced pitch oscillations of an airfoil [J]. Journal of Fluid Mechanics, 2019, 877: 582-613). The energy diagram can be used to establish the connection between the aerodynamic characteristics of a given motion and the limit cycle oscillation characteristics of fluid-solid coupling, avoiding complex fluid-solid coupling iterative calculations. However, in order to obtain the energy diagram, hundreds of CFD calculations are required to obtain the periodic work of the aerodynamic torque under different given motion parameters, and the calculation cost is equivalent to the fluid-solid coupling calculation. At the same time, the energy diagram can only obtain the potential limit cycle oscillation branches under the current operating parameters, and cannot accurately obtain the stall flutter response characteristics under the current operating parameters, and cannot be used to predict the stall flutter response characteristics.

[0006] In summary, the current stall flutter prediction methods have the following main problems:

[0007] 1. The traditional high-efficiency engineering aerodynamic analysis method cannot effectively consider the aerodynamic nonlinearity caused by large-scale flow separation, which makes it difficult to effectively predict the stall flutter response characteristics; the high-precision fluid-solid coupling calculation method based on CFD / CSD coupling has high calculation accuracy, but due to the high calculation cost and low calculation efficiency, it cannot meet the design requirements of the anti-stall flutter design of related equipment;

[0008] 2. The stall flutter response characteristic calculation method that couples the unsteady aerodynamic reduced-order model based on deep neural network with the structural dynamics equation for iterative solution has the defects of easy error accumulation, poor calculation convergence and stability;

[0009] 3. The energy diagram method can only obtain the potential limit cycle oscillation branches under the current operating parameters, and cannot accurately obtain the stall flutter response characteristics under the current operating parameters; at the same time, the calculation cost of the energy diagram is equivalent to the fluid-solid coupling calculation, and it is difficult to effectively improve the calculation efficiency. Summary of the invention

[0010] In view of the above problems, the present invention proposes a method for predicting stall flutter with high efficiency and accuracy based on energy graph and deep neural operator network. The method realizes high efficiency and high accuracy prediction of stall flutter response by constructing and training a data-driven model for rapid prediction of unsteady aerodynamic torque of dynamic stall cycle considering wind speed, amplitude and frequency changes based on deep neural operator network, and rapidly calculating energy graph based on data-driven model and iterative correction of stall flutter response considering aerodynamic stiffness correction. The method can also be extended to predict the response of single-degree-of-freedom limit cycle oscillation with aerodynamic nonlinearity, such as laminar separation flutter and transonic buffeting and other aeroelastic problems. The prediction method can predict the stall flutter response with high accuracy under different incoming flow velocities, different structural natural frequencies and damping coefficients, and greatly reduces the calculation time required for response prediction.

[0011] The present invention provides a high-efficiency and high-precision stall flutter prediction method based on energy graph and deep neural operator network, and the specific steps are as follows:

[0012] Step 1: When performing CFD calculations for different incoming flow velocities and Reynolds numbers, the airfoil is driven to perform a given pitch motion according to the angle of attack signal of the airfoil pitch motion, and multiple sets of unsteady aerodynamic moment time domain data are obtained.

[0013] Step 2: Construct a deep neural operator network with angle of attack sequence, Reynolds number, incoming flow velocity, airfoil oscillation amplitude and frequency as input and unsteady aerodynamic torque time domain data as output; and use the input and output data obtained in step 1 to train the deep neural operator network to obtain an unsteady aerodynamic rapid prediction model for airfoil dynamic stall.

[0014] Step 3: Using the unsteady aerodynamic rapid prediction model of airfoil dynamic stall, given the incoming flow velocity and Reynolds number, calculate the time domain data of the unsteady aerodynamic moment of the pitch oscillation motion period corresponding to each amplitude and frequency combination within the given amplitude and frequency range.

[0015] Furthermore, the net work done by the fluid-solid coupling system in a single pitch oscillation period is calculated. Then, the net work cloud diagram of the period is drawn with the pitch oscillation frequency as the horizontal coordinate and the pitch oscillation amplitude as the vertical coordinate to obtain the limit cycle oscillation branch.

[0016] Step 4: After obtaining the limit cycle oscillation branch of the energy diagram, the stall flutter response characteristics under the current operating conditions are obtained through iterative calculation.

[0017] The advantages of the present invention are:

[0018] 1. The present invention is based on an energy graph and a deep neural operator network. The present invention provides an efficient and high-precision stall flutter prediction method. The deep neural operator network is used to quickly predict the time domain data of the unsteady aerodynamic moment of the pitch motion cycle and calculate the work done during the aerodynamic moment cycle to obtain an energy graph. The energy graph and a frequency correction method based on aerodynamic stiffness are then used to predict the response characteristics of the stall flutter. The deep neural operator network is directly run once to output the unsteady aerodynamic moment data within a pitch oscillation cycle. It does not need to rely on the solution results of the structural dynamics equations. While improving the computational efficiency, it solves the defects of poor computational convergence and stability caused by directly coupling and iteratively solving the unsteady aerodynamic reduced-order model based on the deep neural network with the structural dynamics equations.

[0019] 2. The present invention is based on an energy graph and a deep neural operator network to predict stall flutter with high efficiency and accuracy. The energy graph's limit cycle oscillation branch is combined with a structural natural frequency correction method based on aerodynamic stiffness. An energy graph-based stall flutter response iterative calculation method is proposed to solve the defect that the energy graph method can only obtain the limit cycle oscillation branch and cannot accurately calculate the stall flutter response characteristics.

[0020] 3. The present invention is a highly efficient and high-precision stall flutter prediction method based on energy graphs and deep neural operator networks. The deep neural operator network is used to quickly predict the time-domain data of the unsteady aerodynamic torque of the pitch motion cycle. The deep neural operator network is trained with high-precision CFD data. The trained deep neural operator network has the same calculation accuracy as CFD. While meeting high precision, the calculation efficiency is greatly improved. The invention can achieve efficient and high-precision prediction of stall flutter response for different incoming flow velocities, different structural natural frequencies and damping coefficients. At the same time, the method can also be extended to the efficient and high-precision prediction of other single-degree-of-freedom limit cycle oscillation responses with aerodynamic nonlinearity, such as laminar separation flutter and transonic buffeting. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a flow chart of the efficient and high-precision stall flutter prediction method based on energy graph and deep neural operator network of the present invention;

[0022] Figure 2 Provides a given signal for the airfoil pitch motion and the corresponding high-precision aerodynamic moment data;

[0023] Figure 3 This is the architecture diagram of the deep neural operator network DeepONet;

[0024] Figure 4 It is the cloud diagram of net work done in the period;

[0025] Figure 5 It is a flow chart of the iterative calculation method of stall flutter response based on energy diagram;

[0026] Figure 6 This is the result evolution diagram of the iterative calculation method of stall flutter response based on energy diagram.

[0027] Figure 7 Schematic diagram of aerodynamic stiffness calculation. DETAILED DESCRIPTION

[0028] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0029] The invention provides a high-efficiency and high-precision stall flutter prediction method based on energy graph and deep neural operator network, such as Figure 1 As shown, the following steps are included:

[0030] Step 1: Design an amplitude A α and frequency f α The time-varying time-domain frequency sweep signal is used as the angle of attack signal α(t) of the airfoil pitching motion, and is in the following form:

[0031] α(t)=A α sin(2πf α t),A α =0.5sin(0.1πt),f α =0.05t+2.5

[0032] In the formula, A α is the amplitude of the pitch oscillation, f α is the frequency of pitch oscillation, and t is the time.

[0033] Then, for different incoming flow velocities and Reynolds numbers, the UDF function in the commercial CFD software Fluent is used to drive the airfoil to perform a given pitch motion according to the above-mentioned angle of attack signal α(t) during CFD calculation, and multiple sets of unsteady aerodynamic moment time domain data are obtained, such as Figure 2 shown.

[0034] Step 2: Construct a deep neural operator network (DeepONet) with angle of attack sequence, Reynolds number, incoming flow velocity, airfoil oscillation amplitude and frequency as input and unsteady aerodynamic moment time domain data as output, such as Figure 3 As shown, the angle of attack sequence, Reynolds number, incoming flow velocity, airfoil oscillation amplitude and frequency are used as inputs of the deep neural operator network, wherein the angle of attack sequence is used as the input of the branch network (Branch net), and the Reynolds number, incoming flow velocity, oscillation amplitude and frequency are used as the input of the trunk network (Trunk net).

[0035] By training the deep neural operator network using multiple sets of input and output data calculated in step 1, a fast prediction model of unsteady aerodynamics of airfoil dynamic stall considering the incoming flow velocity, oscillation amplitude and frequency can be obtained. The input and output data of the prediction model are consistent with the CFD software, but the prediction model can quickly output the time domain data of unsteady aerodynamic moment of the pitch oscillation motion period by inputting the required data.

[0036] Step 3: Using the unsteady aerodynamic rapid prediction model of airfoil dynamic stall trained in step 2, given the incoming flow velocity and Reynolds number, quickly calculate the unsteady aerodynamic moment time domain data M of the pitch oscillation motion period corresponding to each amplitude and frequency combination within the given amplitude and frequency range. a (t).

[0037] Further combined with the pitch oscillation angle of attack change, the aerodynamic moment period work E corresponding to different amplitude frequency combinations can be calculated according to the following formula: f :

[0038]

[0039] In the formula, is the angular acceleration at the angle of attack, T is the period of the pitch oscillation;

[0040] At the same time, by giving the pitch oscillation damping coefficient of the structure (airfoil), the corresponding structural damping period work E can be quickly calculated by the following formula: d :

[0041]

[0042] In the formula, C d is the pitch oscillation damping coefficient of the structure.

[0043] The above-obtained aerodynamic moment period work minus the structural damping period work is the net work of the fluid-structure interaction system in a single pitch oscillation period, that is, E net =E f -E d .

[0044] Therefore, with the pitch oscillation frequency as the horizontal axis and the pitch oscillation amplitude as the vertical axis, a periodic net work cloud diagram is drawn, as shown in Figure 4 As shown, the cloud diagram satisfies dE net / dA α <0 is the zero contour, which is the potential limit cycle oscillation branch, that is, Figure 4 The dashed line is located in the upper right corner.

[0045] Step 4: After obtaining the limit cycle oscillation branch of the energy diagram, the stall flutter response characteristics under the current working condition are accurately obtained through iterative calculation, such as Figure 5 shown.

[0046] 401. According to the given structural stiffness K d and the moment of inertia of the structure about the pitch axis I d , determine the pitch oscillation natural frequency f of the structure d :

[0047]

[0048] 402. Determine the natural frequency f according to the limit cycle oscillation branch d The corresponding oscillation amplitude is Figure 6 As shown in FIG. 1 ; the natural frequency and the corresponding oscillation branch amplitude are used as the input of the unsteady aerodynamic fast prediction model of airfoil dynamic stall obtained in step 2, and then the periodic unsteady aerodynamic moment time domain data M corresponding to the amplitude and frequency are obtained. a (t);

[0049] 403. With the pitch angle α as the horizontal coordinate, the aerodynamic moment M a The hysteresis curve of the aerodynamic torque is plotted with y as the ordinate, and the slope of the hysteresis curve is obtained by the least square method. The slope is the aerodynamic stiffness K. a ,like Figure 7 As shown, the aerodynamic stiffness and structural stiffness are superimposed according to the following formula to calculate the corrected pitch oscillation natural frequency f i ;

[0050]

[0051] According to the corrected pitch oscillation natural frequency f i , the process may return to execute steps 402 to 403 to perform the next iteration.

[0052] 404. Repeat steps 402 to 403 until the relative error between two adjacent pitch oscillation natural frequencies is less than 5%, and then terminate the iteration. At this time, the pitch oscillation natural frequency and the oscillation amplitude corresponding to the natural frequency on the limit cycle oscillation branch are the response amplitude and frequency of the stall flutter. Otherwise, continue to the next iteration until the iteration termination condition is met.

[0053] For a Reynolds number of 1000, an incoming flow velocity of 1 m / s, and a structural stiffness K d is 2.04Nm, and the moment of inertia of the airfoil relative to the pitch axis is d 2.25kg.m 2 , structural pitch oscillation damping coefficient C d 0.13kg.m 2 / s working condition, the stall flutter amplitude calculated by the high-precision fluid-solid coupling calculation method based on CFD / CSD coupling is 24.4 degrees, the stall flutter amplitude calculated by the present invention is 24.5, and the relative error is 0.4%; the calculation time of the high-precision fluid-solid coupling calculation method based on CFD / CSD coupling is 75 hours, and the calculation time of the present invention is 4 minutes, which is reduced by 3 orders of magnitude.

Claims

1. An efficient and high-precision stall flutter prediction method based on energy graph and deep neural operator network, characterized by: The specific steps are designed as follows: Step 1: When performing CFD calculations for different incoming flow velocities and Reynolds numbers, the airfoil is driven to perform a given pitch motion according to the angle of attack signal of the airfoil pitch motion, and multiple sets of unsteady aerodynamic moment time domain data are obtained; Step 2: Construct a deep neural operator network with angle of attack sequence, Reynolds number, incoming flow velocity, airfoil oscillation amplitude and frequency as input and unsteady aerodynamic moment time domain data as output; and use the input and output data obtained in step 1 to train the deep neural operator network to obtain an unsteady aerodynamic rapid prediction model for dynamic stall of airfoil; Step 3: Using the unsteady aerodynamic fast prediction model of airfoil dynamic stall, given the incoming flow velocity and Reynolds number, calculate the unsteady aerodynamic moment time domain data M of the pitch oscillation motion period corresponding to each amplitude and frequency combination within the given amplitude and frequency range. a (t); Further combined with the pitch oscillation angle of attack change, the aerodynamic torque period work E corresponding to different amplitude-frequency combinations is calculated according to the following formula: f : In the formula, is the angular acceleration at the angle of attack, T is the period of the pitch oscillation; At the same time, by giving the damping coefficient of the airfoil pitch oscillation motion, the corresponding structural damping period work E can be quickly calculated by the following formula: d : In the formula, C d A is the pitch oscillation damping coefficient of the structure; α is the amplitude of pitch oscillation; The aerodynamic moment periodic work obtained above minus the structural damping periodic work is the net work of the fluid-structure interaction system in a single pitch oscillation period. Thus, a periodic net work cloud diagram is drawn with the pitch oscillation frequency as the abscissa and the pitch oscillation amplitude as the ordinate; Step 4: After obtaining the limit cycle oscillation branch of the energy diagram, the stall flutter response characteristics under the current working condition are obtained through iterative calculation; 401. According to the given structural stiffness K d and the moment of inertia of the structure about the pitch axis I d , determine the pitch oscillation natural frequency f of the structure d :

402. Determine the natural frequency f according to the limit cycle oscillation branch d The corresponding oscillation amplitude; the natural frequency and the corresponding oscillation branch amplitude are used as the input of the unsteady aerodynamic fast prediction model of airfoil dynamic stall obtained in step 2, and then the periodic unsteady aerodynamic moment time domain data M corresponding to the amplitude and frequency are obtained. a (t); 403. With the pitch angle α as the horizontal coordinate, the aerodynamic moment M a The hysteresis curve of the aerodynamic torque is plotted with y as the ordinate, and the slope of the hysteresis curve is obtained by the least square method. The slope is the aerodynamic stiffness K. a , and the aerodynamic stiffness and structural stiffness are superimposed according to the following formula to calculate the corrected pitch oscillation natural frequency f i ; According to the corrected pitch oscillation natural frequency f i , return to execute steps 402 to 403 and proceed to the next iteration; 404. Repeat steps 402 to 403 until the relative error between two adjacent pitch oscillation natural frequencies is less than 5%, and then terminate the iteration; at this time, the pitch oscillation natural frequency and the oscillation amplitude corresponding to the natural frequency on the limit cycle oscillation branch are the response amplitude and frequency of the stall flutter; otherwise, continue to the next iteration until the iteration termination condition is met.

2. The method for predicting stall flutter with high efficiency and accuracy based on energy graph and deep neural operator network as claimed in claim 1, characterized in that: In step 1, the angle of attack signal α(t) of the airfoil pitching motion is: α(t)=A α sin(2πf α t),A α =0.5sin(0.1πt),f α =0.05t+2.5 In the formula, A α is the amplitude of the pitch oscillation, f α is the frequency of pitch oscillation, and t is the time.

3. The method for predicting stall flutter with high efficiency and accuracy based on energy graph and deep neural operator network as claimed in claim 1, characterized in that: In step 2, the angle of attack sequence is used as the input of the branch network, and the Reynolds number, incoming flow velocity, oscillation amplitude and frequency are used as the input of the trunk network.

4. The method for predicting stall flutter with high efficiency and accuracy based on energy graph and deep neural operator network as claimed in claim 1, characterized in that: In step 3, the net work done by the fluid-structure interaction system in a single pitch oscillation cycle is E net =E f -E d ; Among them, E f The work done by the aerodynamic torque cycle corresponding to different amplitude-frequency combinations; E d is the work done during the structural damping cycle.

5. The method for predicting stall flutter with high efficiency and accuracy based on energy graph and deep neural operator network as claimed in claim 1, characterized in that: In step 3, the net work cloud diagram of the cycle satisfies dE net / dA α <0 is the zero contour line, which is the limit cycle oscillation branch; where E net A is the net work done by the fluid-structure interaction system in a single pitch oscillation cycle; α is the amplitude of the pitch oscillation.

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