Propeller aerodynamic noise prediction method based on data assimilation

Abstract

The invention discloses an aviation propeller aerodynamic noise prediction method based on data assimilation, and belongs to the field of aviation aerodynamic acoustics. The method comprises the following steps: firstly, establishing a propeller flow field numerical simulation model and finishing initial simulation; quantifying the parameter uncertainty of the turbulence model through Latin hypercube sampling and a non-interference polynomial chaos proxy model, and determining key sensitive parameters in combination with global sensitivity analysis; then collecting wake flow velocity field and far field noise data of the wind tunnel experiment; and finally, assimilating experimental data and a CFD prediction result by using an ensemble Kalman filtering method, correcting key sensitive parameters of the turbulence model, and performing simulation again. The ensemble Kalman filtering data assimilation technology is applied to propeller turbulence model parameter correction, prediction errors of transonic velocity and a complex vortex structure area are reduced, the prediction precision of a propeller flow field and aerodynamic noise is improved, the method has the advantages of being high in precision and adaptability, the efficient and low-noise design requirements of modern aviation are met, and the method is suitable for popularization and application. The method has important engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of aeroacoustics and relates to prediction techniques for aerodynamic noise of aircraft propellers. Specifically, it relates to a method for improving the prediction accuracy of propeller flow field and far-field noise by correcting turbulence model parameters based on data assimilation techniques. Background Technology

[0002] Propeller propulsion systems are widely used in turboprop aircraft due to their high efficiency and economy. However, propellers generate strong aerodynamic noise during operation, which adversely affects passenger comfort, crew safety, and the surrounding environment. Noise issues have become a significant bottleneck restricting the development of turboprop aircraft. Currently, propeller aerodynamic noise prediction methods generally combine CFD numerical simulation with acoustic analogy equations (such as the FW-H equations). The accuracy of the turbulence model directly determines the accuracy of aerodynamic noise prediction. However, in existing numerical simulation techniques, the turbulence model parameters are mostly empirically determined constants, failing to consider the variation of turbulence parameters at different Reynolds numbers. This leads to large prediction errors, especially in transonic flows and regions with complex three-dimensional vortex structures at the propeller tip. This problem of insufficient prediction accuracy urgently needs to be addressed. Summary of the Invention

[0003] To address the aforementioned problems, this invention provides a propeller aerodynamic noise prediction method based on data assimilation technology. It quantifies the uncertainty of turbulence model parameters using a non-interfering polynomial chaotic method, and then assimilates experimental data using an ensemble Kalman filter (EnKF) method. By quantifying the uncertainty of turbulence model parameters and optimizing and correcting them using experimental data, the turbulence model parameters can be adapted to specific operating conditions. This significantly improves the accuracy of propeller flow field and aerodynamic noise prediction, offering advantages such as high accuracy and strong adaptability, and possessing significant engineering application value.

[0004] This invention relates to a propeller aerodynamic noise prediction method based on data assimilation technology, the steps of which include:

[0005] Step 1: Establish a numerical simulation model of the propeller flow field and perform mesh generation; select a turbulence model to perform actual numerical simulation and obtain the initial calculation results of the propeller flow field.

[0006] Step 2: Quantify the uncertainty of turbulence model parameters.

[0007] (1) Determine the parameters of the turbulence model to be evaluated and their range of variation.

[0008] (2) The Latin hypercube sampling method is used to generate a sample set of turbulence model parameters.

[0009] (3) A non-interference polynomial chaotic proxy model is constructed using numerical simulation to realize the propagation of parameter uncertainty and obtain the statistical characteristics of propeller thrust, torque and flow field velocity.

[0010] Step 3: Use global sensitivity analysis based on variance decomposition to calculate the Sobol sensitivity index of each parameter and determine the key sensitivity index.

[0011] Step 4: In a wind tunnel environment, for the propeller operating conditions corresponding to the numerical simulation in Step 1, perform multi-point synchronous measurements of the propeller wake velocity field and far-field noise to obtain multi-point experimental measurement data. This is used for subsequent data assimilation to correct turbulence model parameters.

[0012] Step 5: By fusing CFD flow field prediction results and wind tunnel experimental data using the ensemble Kalman filter data assimilation method, the key sensitive parameters of the turbulence model are corrected.

[0013] 1) Using the key sensitive parameters obtained in step 3 as the correction targets, random uniform sampling is performed using the Latin hypercube sampling method to generate a parameter sample set. .

[0014] 2) Set the parameter samples Each set of parameters Substituting the values ​​into the SST k-ω turbulence model and solving it using AnsysFluent, we obtain a set of predicted flow field values. Furthermore, we calculate the mean of the parameter sample set and, based on the deviation of the members of the parameter sample set from the mean, obtain the error-covariance matrix P of the parameter sample set.

[0015] 3) The prediction results are fused with the experimental measurement data obtained in step 4 using the EnKF method.

[0016] ① Introduce wind tunnel experimental data and, based on sensor accuracy, introduce experimental noise. , thus obtaining the experimental value set Y.

[0017] ② Use ensemble Kalman filtering to correct the parameters.

[0018] Calculate the error-covariance matrix R of the experimental values, determine the Kalman gain matrix K, and update each member of the experimental value set to obtain the state analysis value set; further, take the mean of the state analysis value set to obtain the optimal state estimate and correction parameters.

[0019] 4) Substitute the corrected parameters back into the propeller flow field numerical simulation model established in step 1, and conduct a new round of numerical simulation to finally obtain propeller flow field and far-field noise results with significantly improved prediction accuracy.

[0020] The advantages of this invention are:

[0021] 1. The present invention is a propeller aerodynamic noise prediction method based on data assimilation technology. It innovatively applies the Kalman filter data assimilation technology to the parameter correction of the three-dimensional rotating flow field turbulence model of the propeller for the first time, which effectively reduces the prediction error in transonic and complex vortex structure regions.

[0022] 2. The propeller aerodynamic noise prediction method based on data assimilation technology of the present invention adopts non-interference polynomial chaos method to accurately quantify the uncertainty of turbulence model parameters, which greatly improves the robustness and generalization ability of the data assimilation method.

[0023] 3. The propeller aerodynamic noise prediction method based on data assimilation technology in this invention improves the accuracy of propeller flow field and noise numerical prediction, meeting the urgent needs of efficient and low-noise design in the modern aviation field. Attached Figure Description

[0024] Figure 1 This is a flowchart of the propeller aerodynamic noise prediction method based on data assimilation technology of the present invention;

[0025] Figure 2 Flowchart of a method for quantifying the uncertainty of turbulence model parameters;

[0026] Figure 3 Flowchart of the method for correcting parameters for ensemble Kalman filter data assimilation.

[0027] Figure 4 A roadmap for ensemble Kalman filter-corrected turbulence models;

[0028] Figure 5 The graph shows the change in relative velocity at 140mm below the propeller disk as a function of the dimensionless radius before and after correction (comparison of CFD calculated values ​​and experimental values).

[0029] Figure 6 A comparison of the relative error before and after correction at 140mm below the propeller disk with the dimensionless radius using CFD and experimental values.

[0030] Figure 7 A comparison of calculated and experimental values ​​of the directivity of 1 BPF noise sound pressure level before and after CFD correction. Detailed Implementation

[0031] Based on the D5 wind tunnel experimental platform of Beijing University of Aeronautics and Astronautics, the method of the present invention is further described in detail with the following figures, using the propeller operating speed of 10000 RPM, the tip Mach number of 0.928, the incoming flow velocity of 30m / s, and the blade installation angle of 14° as the operating conditions.

[0032] This invention relates to a propeller aerodynamic noise prediction method based on data assimilation technology, such as... Figure 1As shown, the specific steps are as follows:

[0033] Step 1: Establish a numerical simulation model of the propeller flow field.

[0034] Based on the propeller geometry and operating conditions, a numerical simulation model of the propeller flow field was established, and mesh generation was performed. After initial mesh generation, mesh independence verification was conducted, and an 8 million mesh size was ultimately chosen to ensure that the mesh's influence on the calculation results was within 1%. After determining a suitable mesh, the SST turbulence model and Ansys Fluent were selected for actual numerical simulation to obtain the initial calculation results of the propeller flow field.

[0035] Meanwhile, by using periodic symmetric structure mesh modeling, wake region structure refinement, and dynamic and static domain interface boundary conditions, the computational efficiency and accuracy of propeller flow field and noise prediction are significantly improved.

[0036] Step 2: Quantify the uncertainty of turbulence model parameters.

[0037] (1) Determine the parameters of the turbulence model to be evaluated and their range of variation;

[0038] SST k-ω turbulence model parameters are as follows Figure 2 As shown in Table 1.

[0039] Table 1 Parameters of SST k-ω turbulence model

[0040]

[0041] The uncertainty range (range of variation) of the turbulence model parameters is set as follows: the lower limit of the range is 70% of the standard value, and the upper limit is 130% of the standard value.

[0042] (2) The Latin hypercube sampling (LHS) method is used to generate N=500 sets of SST k-ω turbulence model parameter samples to form a parameter sample set, wherein the i-th set of parameter vectors corresponds to a set of values ​​of the 9 coefficients in Table 1.

[0043] (3) A non-interference polynomial chaos (NIPC) proxy model is constructed using numerical simulation to realize the propagation of parameter uncertainty and obtain the statistical characteristics of propeller thrust, torque and flow field velocity.

[0044] The non-interventional polynomial chaotic proxy model is as follows:

[0045]

[0046]

[0047] In the formula, These are the parameters for the SST k-ω model; for

[0048] A multivariable orthogonal polynomial with SST k-ω turbulence model parameters as independent variables. Let be the coefficients of the proxy model to be determined. The output of the proxy model system corresponds to the CFD output value; m represents the number of orthogonal polynomial terms.

[0049] Based on the parameter sample set generated in sub-step (2) and the corresponding CFD simulation results, the linear equation system is solved using the least squares method to obtain the surrogate model coefficients. .

[0050] Step 3: Sensitivity analysis of SST k-ω model parameters.

[0051] The Sobol sensitivity index of each parameter was calculated using global sensitivity analysis based on variance decomposition. To identify the key parameters that contribute most to the uncertainty of the propeller flow field output (thrust, torque, and flow velocity), the Sobol sensitivity index of each SST k-ω model parameter in Table 1 was calculated using the global sensitivity analysis method based on variance decomposition. The output variance can be decomposed into the following form:

[0052]

[0053]

[0054] in, For all variables that are determined by and only by the independent variable The variance provided by the polynomial is decomposed into terms that characterize the contribution of different individual inputs and their interactions to the variance of the output response. The coefficients of the proxy model to be determined; It is a multivariate orthogonal polynomial with parameters as independent variables.

[0055] The Sobol sensitivity index is used to assess the relative contribution of variables to uncertainty. It is expressed as the proportion of the variance of each random variable to the total variance, and satisfies the following relationship.

[0056]

[0057]

[0058] In the formula, It represents all variables that are determined by and only by the independent variable. The variance provided by the polynomial is decomposed into terms that characterize the contribution of different individual inputs and their interactions to the variance of the output response. The contribution of the i-th variable as a single entity to the total variance; Let be the contribution of the interaction between the i-th and j-th parameters to the total variance.

[0059] To describe the total contribution of a parameter, a parameter is defined. Sobol index It includes all parameters The sum of the Sobol exponents characterizes the total contribution of a single input and its interaction with other inputs to the response variance, as shown below:

[0060]

[0061] in, For including parameters The variance; C is the included parameter. The parameter set.

[0062] Ultimately, this embodiment shows that the Sobol exponent of parameter a1 has the largest proportion and its distribution changes significantly, making it a key sensitive parameter. Analyzing the distribution of the Sobol exponent of parameter a1 separately reveals a clear correlation between the variation patterns of the Sobol exponent along the blade radial direction and the turbulent kinetic energy of the blade element.

[0063] Step 4: Wind tunnel experiment data acquisition

[0064] In the D5 wind tunnel environment, for the propeller operating conditions corresponding to the numerical simulation in step 1, multi-point synchronous measurements of the propeller wake velocity field and far-field noise were performed to obtain multi-point experimental measurement data. This is used for subsequent data assimilation to correct turbulence model parameters.

[0065] Step 5: Fuse CFD flow field prediction results with wind tunnel experimental data using the ensemble Kalman filter (EnKF) data assimilation method to correct key sensitive parameters of the turbulence model, such as... Figure 3 As shown.

[0066] (1) Using the key sensitive parameters obtained in step 3 as the correction objects, random uniform sampling is performed using the Latin hypercube sampling method, with a sampling number of N, to generate a parameter sample set. ;

[0067] (2) Set the parameter sample set Each set of parameters Substituting these values ​​into the SST k-ω turbulence model and solving it using AnsysFluent, we obtain the set of predicted flow field values ​​X:

[0068]

[0069] Each parameter sample set member consists of numerical simulation output values ​​at n grid points. and corresponding turbulence model parameters composition.

[0070] Furthermore, the mean of the parameter sample set is calculated. And based on the deviation of the members of the parameter sample set from the mean, the error-covariance matrix P of the parameter sample set is obtained:

[0071] .

[0072] (3) The prediction results are fused with the experimental measurement data obtained in step 4 using the EnKF method, such as... Figure 4 As shown.

[0073] ① Introduce wind tunnel experimental data and, based on sensor accuracy, introduce experimental noise. , thus obtaining the experimental value set Y.

[0074]

[0075]

[0076]

[0077] In the formula, This is the experimental observation vector, which includes the true values ​​of wake velocity, pressure, noise, etc., measured in the wind tunnel.

[0078] ② Use ensemble Kalman filtering to correct the parameters.

[0079] Calculate the error-covariance matrix R of the experimental values:

[0080]

[0081] Determine the Kalman gain matrix K:

[0082]

[0083] In the formula, P is the error-covariance matrix of the parameter sample set; H is the observation matrix;

[0084] Then, each member of the experimental value set is updated to obtain the state analysis value set. :

[0085]

[0086] Further analysis of the set of state analysis values Take the average. We obtain the optimal state estimate and the corrected parameters (the corrected parameter sample set). ).

[0087] In strongly nonlinear systems, a single analysis step is insufficient to optimally estimate the state variables. Therefore, this invention employs an iteratively updated EnKF method; and to prevent overestimation of the parameters, a relaxation factor β is introduced and set to 0.1. When the experimental observation vector... When the variance of the state variables exceeds the variance of the experimental variables, the relaxation factor will take effect. The optimal state variables can then be obtained after multiple iterations, at which point the iteration converges or reaches the maximum number of iterations. The iteration process is as follows: the set of state analysis values ​​obtained from the previous EnKF update is used as input, and then substituted back into the CFD model from step 1 to generate a new set of flow field predictions. This set is then merged and updated with the experimental value set Y, and this process is repeated until the convergence criterion is met or the maximum number of iterations is reached.

[0088]

[0089]

[0090] In the formula, Represents the set of state analysis values ​​after the j-th iteration; This represents the Kalman gain after the j-th iteration; This indicates the difference rate.

[0091] The maximum number of iterations is set to 30 to prevent overfitting, and the convergence criterion for the iteration is defined in the formula, which states that the iteration of the confirmation step continues until the rate of difference between the experimental data and the analytical state variables decreases to below 2%.

[0092] (4) Substitute the optimal correction parameters obtained after iterative convergence back into the propeller flow field numerical simulation model established in step 1, and perform a new round of numerical simulation to finally obtain propeller flow field and far-field noise results with significantly improved prediction accuracy.

[0093] The propeller aerodynamic characteristics, flow field velocity, and far-field noise predicted by the turbulence model corrected by ensemble Kalman filtering are closer to the experimental values, and the prediction error is significantly reduced. Moreover, after verification under different operating conditions, the corrected turbulence model has stronger generalization ability and significantly improved calculation accuracy.

[0094] The results indicate that:

[0095] like Figure 5 , Figure 6 , Figure 7 As shown in the figure, the improvement in prediction accuracy is demonstrated by comparing numerical simulation and experimental data. It can be seen from the figure that the prediction results of the optimized turbulence model significantly improve the prediction accuracy of the transonic flow region, the complex vortex structure at the blade tip, and aerodynamic noise. The agreement with the experimental data is significantly improved, which proves the effectiveness and superiority of the method of the present invention.

[0096] This embodiment verifies the feasibility of the method of the present invention, and demonstrates the great potential of data assimilation to correct turbulence model parameters to improve the prediction accuracy of propeller aerodynamic noise, with clear prospects for engineering applications.

Claims

1. A method for predicting aerodynamic noise of aircraft propellers based on data assimilation, characterized in that: The specific steps are as follows: Step 1: Establish a numerical simulation model of the propeller flow field and perform mesh generation; select a turbulence model to perform actual numerical simulation and obtain the initial calculation results of the propeller flow field; Step 2: Quantify the uncertainty of turbulence model parameters; (1) Determine the parameters of the turbulence model to be evaluated and their range of variation; (2) The Latin hypercube sampling method is used to generate a sample set of turbulence model parameters; (3) A non-interference polynomial chaotic proxy model is constructed using numerical simulation to realize the propagation of parameter uncertainty and obtain the statistical characteristics of propeller thrust, torque and flow field velocity; Step 3: Calculate the Sobol sensitivity index of each parameter using global sensitivity analysis based on variance decomposition, and determine the key sensitivity indices; Step 4: In a wind tunnel environment, for the propeller operating conditions corresponding to the numerical simulation in Step 1, perform multi-point synchronous measurements of the propeller wake velocity field and far-field noise to obtain multi-point experimental measurement data. This is used for subsequent data assimilation to correct turbulence model parameters; Step 5: By fusing CFD flow field prediction results and wind tunnel experimental data using the ensemble Kalman filter data assimilation method, the key sensitive parameters of the turbulence model are corrected; 1) Using the key sensitive parameters obtained in step 3 as the correction targets, random uniform sampling is performed using the Latin hypercube sampling method to generate a parameter sample set. ; 2) Set the parameter samples Each set of parameters Substituting the values ​​into the turbulence model, the set of predicted flow field values ​​is obtained; further, the mean of the parameter sample set is calculated, and based on the deviation of the members of the parameter sample set from the mean, the error-covariance matrix P of the parameter sample set is obtained. 3) The prediction results are fused with the experimental measurement data obtained in step 4 using the EnKF method; ① Introduce wind tunnel experimental data and, based on sensor accuracy, introduce experimental noise. The experimental value set Y is obtained; ② Calculate the error-covariance matrix R of the experimental values, determine the Kalman gain matrix K, and update each member of the experimental value set to obtain the state analysis value set; further, take the mean of the state analysis value set to obtain the optimal state estimate and correction parameters. 4) Substitute the corrected parameters back into the propeller flow field numerical simulation model established in step 1, and conduct a new round of numerical simulation to finally obtain propeller flow field and far-field noise results with significantly improved prediction accuracy.

2. The aerodynamic noise prediction method for aircraft propellers based on data assimilation as described in claim 1, characterized in that: In step 1, the computational efficiency and accuracy of propeller flow field and noise prediction are improved by using periodic symmetric structure mesh modeling, wake region structure refinement, and dynamic and static domain interface boundary conditions.

3. The aerodynamic noise prediction method for aircraft propellers based on data assimilation as described in claim 1, characterized in that: In step 2, the non-interference polynomial chaotic proxy model is: In the formula, These are the parameters for the SST k-ω turbulence model; It is a multivariable orthogonal polynomial with the parameters of the SST k-ω turbulence model as independent variables. Let be the coefficients of the proxy model to be determined. The output of the proxy model system corresponds to the CFD output value; m represents the number of orthogonal polynomial terms. Based on the parameter sample set generated in sub-step (2) and the corresponding CFD simulation results, the linear equation system is solved using the least squares method to obtain the surrogate model coefficients. .

4. The aerodynamic noise prediction method for aircraft propellers based on data assimilation as described in claim 1, characterized in that: In step 3, a global sensitivity analysis method based on variance decomposition is used to calculate the Sobol sensitivity index of the turbulence model parameters, and the variance decomposition is output in the form of the following formula: in, For all variables that are determined by and only by the independent variable The variance provided by the polynomial is decomposed into terms that characterize the contribution of different individual inputs and their interactions to the variance of the output response. The coefficients of the proxy model to be determined; It is a multivariable orthogonal polynomial with parameters as independent variables; The Sobol sensitivity index is expressed as the proportion of the variance of each random variable to the total variance, and satisfies the following relationship: In the formula, It represents all variables that are determined by and only by the independent variable. The variance provided by the polynomial is decomposed into terms that characterize the contribution of different individual inputs and their interactions to the variance of the output response. The contribution of the i-th variable as a single entity to the total variance; The contribution of the interaction between the i-th and j-th parameters to the total variance; Define a parameter Sobol index It includes all parameters The sum of the Sobol exponents characterizes the total contribution of a single input and its interaction with other inputs to the response variance, as shown below: in, For including parameters The variance; C is the included parameter. The set of parameters; Ultimately, the parameters with the largest Sobol index and significant changes in distribution were identified as key sensitive parameters.

5. The aerodynamic noise prediction method for aircraft propellers based on data assimilation as described in claim 1, characterized in that: Step 5 also employs the iterative update EnKF method. The iterative process is as follows: the set of state analysis values ​​obtained from the previous round of EnKF update is used as input, and then substituted back into the CFD model of step 1 to generate a new set of flow field predictions. This set is then merged and updated with the experimental value set Y, and the process is repeated until the convergence criterion is met or the maximum number of iterations is reached.

6. The aerodynamic noise prediction method for aircraft propellers based on data assimilation as described in claim 5, characterized in that: Introduce a relaxation factor β and set it to 0.1.

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