Method for correcting operating condition parameters of cascade wind tunnel experiment based on ensemble Kalman filter

Abstract

The present invention relates to a method for correcting the working condition parameters of a cascade wind tunnel by using the ensemble-averaged Kalman filter, belonging to the field of aerospace experimental measurement. The main steps of the method for correcting the working condition parameters of the cascade wind tunnel based on the numerical simulation of the flow field and the ensemble-averaged Kalman filter include: floating the incoming flow Mach number and the angle of attack of the experimental working condition to be corrected, constructing multiple groups of incoming flow parameter samples and performing numerical calculations on the cascade flow field; using the ensemble-averaged Kalman filter method to correct the incoming flow Mach number and the incoming flow angle of attack during the experimental measurement. The present invention can effectively correct the incoming flow boundary conditions of the cascade wind tunnel experiment, can effectively overcome the prediction deviation of the separation zone generated by the turbulence model, has strong correction ability, does not require a specific selection of the turbulence model, has a small amount of calculation, and does not require iteration, and is particularly suitable for the rapid correction of the experimental parameters of the cascade wind tunnel.

Description

Technical Field

[0001] The invention belongs to the field of aerospace experimental measurement, and relates to a method for correcting the working condition parameters of a cascade wind tunnel experiment based on flow field numerical simulation and ensemble-averaged Kalman filter. Background Art

[0002] The cascade wind tunnel experiment is a common method for measuring the performance of impeller blade profiles. Its working condition parameters mainly refer to the incoming flow angle of attack and the incoming flow Mach number. Generally, the incoming flow angle of attack is obtained by rotating the cascade installation turntable to the corresponding angle; the incoming flow Mach number is adjusted by adjusting the valve of the wind tunnel air source or the fan speed so that the Mach number sensor in front of the test piece shows the given Mach number. However, in the actual wind tunnel experiment process, the airflow in the wind tunnel is affected by the wind tunnel wall surface, and there are losses and deflections after the airflow passes through the Mach number sensor. The actual Mach number and angle of attack of the airflow blowing onto the cascade area are not the given working condition parameters. At large angles of attack and high Mach numbers, the working condition deviation is generally more obvious, seriously affecting the effect of the cascade wind tunnel experiment.

[0003] The existing methods for correcting the working condition parameters of cascade wind tunnel experiments use flow field numerical simulation and utilize all the measurement data on the blade surface. However, flow separation generally occurs in the 50% area behind the blade suction surface, and the prediction accuracy of the separation area by the common turbulence models is relatively poor. The correction results will be contaminated by the prediction deviation of the separation area, affecting the accuracy of the working condition parameter correction results.

[0004] Therefore, there is currently a lack of an accurate and reliable method for correcting working condition parameters in the field of cascade wind tunnel experiments. Summary of the Invention

[0005] The technical problem to be solved by the present invention is:

[0006] In order to avoid the problem of correction errors caused by flow separation in the sample data of the existing correction method, the present invention provides a method for correcting the working condition parameters of a cascade wind tunnel experiment based on flow field numerical simulation and ensemble-averaged Kalman filter.

[0007] In order to solve the above technical problem, the technical solution adopted by the present invention is:

[0008] A method for correcting the working condition parameters of a cascade wind tunnel experiment based on flow field numerical simulation and ensemble-averaged Kalman filter, characterized by comprising:

[0009] Step 1: Floating the working condition parameters, constructing multiple groups of incoming flow working condition parameter samples, and performing flow field numerical simulation on each group of working condition parameters;

[0010] Step 2: Composing a state vector from the floating working condition parameters and the corresponding physical quantities at the measuring point positions in the 50% area in front of the blade chord length of the numerical flow field;

[0011] Step 3: Calculate the sample covariance matrix, generate the sub-sample noise vector and the noise covariance matrix;

[0012] Step 4: Calculate the Kalman filter matrix of the sub-sample;

[0013] Step 5: Perform Kalman filtering on each sub-sample;

[0014] Step 6: Average the state vectors of the sub-samples of all samples, and extract the corrected operating conditions parameters from the averaged state vectors.

[0015] Further technical solution of the present invention: Step 1 is specifically as follows: Set the floating range according to the regulation accuracy of the incoming flow parameters, use the Latin hypercube method for random sampling, construct the samples of the incoming flow parameters, and perform numerical calculation of the cascade flow field for each sample in the turbulence model.

[0016] Further technical solution of the present invention: It is characterized in that Step 2 is specifically as follows:

[0017] Construct the sample state vector x with the floating incoming flow parameters and their numerical flow field results f,i :

[0018]

[0019] where Ma in,i and α i are respectively the incoming flow Mach number and the incoming flow attack angle of the i-th sample after the incoming flow parameters float, represents the corresponding measured physical quantity at the j-th measurement point position in the first 50% blade chord length region of the i-th sample's flow field during the experiment, j = 1, 2,..., M, and M represents the number of measurement points in the first 50% blade chord length region during the experiment.

[0020] Further technical solution of the present invention: The measured physical quantities include surface isentropic Mach number, static pressure coefficient, and static pressure.

[0021] Further technical solution of the present invention: Step 3 is specifically as follows:

[0022] Step 3-1: Calculate the average value of the sample state vector

[0023]

[0024] Step 3-2: Calculate the sample covariance matrix P:

[0025]

[0026]

[0027] Step 3-3: Generate the noise vector wi,l and the noise matrix W l : where l = 1, …, L, representing the l-th subsample, L is the number of subsamples, and the length of the noise vector is the same as the number of measurement points, i.e., is a set of random numbers following a Gaussian distribution with zero mean, and its distribution variance can refer to the measurement error. The noise vectors are combined into a noise matrix:

[0028] W l = [w 1,l , w 2,l , …, w N,l

[0029] Step 3 - 4: Calculate the noise covariance matrix of the subsamples:

[0030]

[0031] A further technical solution of the present invention: The calculation formula of the Kalman filter matrix in Step 4 is as follows:

[0032] K l = PH T (HPH T + R l ) -1

[0033] In the formula, H is the observation matrix:

[0034] H = [0 M×2 , I M×M

[0035] which is used to map the state vector to the corresponding experimental measurement value, where 0 M×2 represents an M×2-dimensional zero matrix, and I M×M represents an M×M-dimensional identity matrix.

[0036] A further technical solution of the present invention: Step 5 is specifically as follows:

[0037] Perform Kalman filtering on the subsamples of the set of samples to obtain the corrected result x a,i,l for each subsample:

[0038] x a,i,l = x f,i + K l (y exp - Hx f,i + w i,l )

[0039] In the formula, y exp is a column vector composed of the surface isentropic Mach numbers measured in the first 50% blade chord length region in the cascade wind tunnel experiment.

[0040] ​​A further technical solution of the present invention: Step 6 is specifically as follows:

[0041] Average all the filtered samples to obtain the averaged state vector

[0042]

[0043] vector The first two data are the corrected oncoming Mach number and the oncoming angle of attack.

[0044] A computer system, characterized in that it includes: one or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors are caused to implement the above method.

[0045] A computer-readable storage medium, characterized in that it stores computer-executable instructions, and the instructions are used to implement the above method when executed.

[0046] The beneficial effects of the present invention are as follows:

[0047] A method for correcting the working condition parameters of a cascade wind tunnel based on flow field numerical simulation and ensemble-averaged Kalman filter provided by the present invention corrects the oncoming Mach number and the angle of attack of the cascade wind tunnel by using flow field numerical simulation and ensemble-averaged Kalman filter method. The correction result has high accuracy, and even for parameters with large deviations, it can be corrected well with small computational load; the ensemble-averaged Kalman filter method proposed by the present invention is simpler than the existing ensemble Kalman filter method, does not require iteration, and has better robustness. Specifically as follows:

[0048] 1. Since flow separation generally occurs in the 50% region behind the blade, and the current turbulence models are not very accurate in predicting flow separation, the data in the latter 50% are contaminated by the prediction deviation of the turbulence model, which will lead to correction errors. Therefore, the present invention uses the data in the first 50% chord length region instead of all the data, and the first 50% region is attached flow without flow separation, and the turbulence model can generally predict it very accurately.

[0049] 2. The present invention uses the ensemble-averaged Kalman filter method for data assimilation, and proposes the concept of sub-samples, that is, when generating synthetic noise, several noise vectors are generated for each sample, several sub-samples are formed for each sample, and filtering operations are performed on each sub-sample, and then overall averaging is performed. It has better robustness than the ensemble Kalman filter method in the prior art.

[0050] 3. The average ensemble Kalman filtering method is adopted. The calculation result is stable, with little randomness, good robustness, accurate results, and requires fewer samples and less computational effort. There are two parts of randomness in the ensemble Kalman filtering method. One is the generation of samples, and the other is random noise. The traditional method only performs averaging once and cannot completely eliminate randomness. In order to obtain stable results, only a large number of samples can be used. The average ensemble Kalman filtering uses subsamples and performs averaging on two scales, better eliminating the randomness of the results. Therefore, it has better stability and can obtain stable results with fewer samples. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The drawings are only for the purpose of showing specific embodiments and are not considered as limitations of the present invention. Throughout the drawings, the same reference signs denote the same components.

[0052] Figure 1 It is a flow chart of the method for correcting the operating condition parameters of the cascade wind tunnel based on the numerical simulation of the flow field and the average ensemble Kalman filtering of the present invention;

[0053] Figure 2 It is a comparison chart of the flow field calculation results and the experimental measurement results before and after the correction of the oncoming flow parameters. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0055] As Figure 1 shown, a method for correcting the operating condition parameters of the cascade wind tunnel based on the numerical simulation of the flow field and the average ensemble Kalman filtering provided by the present invention includes the following steps:

[0056] Step 1: Floating the operating condition parameters. The specific floating amplitude depends on the regulation accuracy of the oncoming flow parameters. A typical floating range can be set as follows: floating the oncoming flow Mach number by ±0.05, and floating the oncoming flow angle of attack by ±1°. Methods such as Latin hypercube can be used for random sampling to construct samples of the oncoming flow parameters, and numerical calculations of the cascade flow field are performed for each sample. The present invention is not sensitive to the turbulence model during the numerical calculation of the flow field, and a suitable turbulence model can be selected;

[0057] Step 2: Construct a sample state vector x from the floating oncoming flow parameters and their numerical flow field results f,i :

[0058]

[0059] In the formula, Ma in,i and α i are respectively the incoming flow Mach number and the incoming flow angle of attack of the i-th sample after the incoming flow parameters fluctuate. represents the corresponding measured physical quantity at the j-th measurement point in the flow field of the i-th sample located in the first 50% blade chord length region in the experiment, where j = 1, 2, …, M, and M represents the number of measurement points in the first 50% blade chord length region in the experiment. The measured physical quantity can generally be the surface isentropic Mach number, the static pressure coefficient, the static pressure, etc. Here, the data in the first 50% chord length region is used instead of all the data because flow separation generally occurs in the last 50% region of the blade. Currently, the prediction of flow separation by the turbulence model is not very accurate. Therefore, the predicted data of the flow field in the last 50% region will be contaminated by the prediction deviation of the turbulence model, which will bring about correction errors. While the first 50% region is attached flow without flow separation, and the turbulence model can generally predict it very accurately.

[0060] Step 3: Calculate the sample covariance matrix P and generate the sub-sample noise vector w i,l and the noise covariance matrix R l , and the specific steps are as follows:

[0061] Step 3-1: Calculate the average value of the sample state vector

[0062]

[0063] Step 3-2: Calculate the sample covariance matrix P:

[0064]

[0065]

[0066] Step 3-3: Generate the noise vector w i,l and the noise matrix W l : where l = 1, …, L, representing the l-th sub-sample, and L is the number of sub-samples. The length of the noise vector is the same as the number of measurement points, that is is a group of random numbers with a Gaussian distribution of zero mean, and its distribution variance can refer to the measurement error. Combine the noise vectors into a noise matrix:

[0067] W l = [w 1,l , w 2,l , …, w N,l (5)

[0068] Step 3-4: Calculate the noise covariance matrix of the sub-samples:

[0069]

[0070] Step 4: Calculate the Kalman gain matrix K of the sub-sample l :

[0071] K l = PH T (HPH T + R l ) -1 (7)

[0072] In the formula, H is the observation matrix, which represents mapping the state vector to the corresponding experimental measurement value;

[0073] H = [0 M×2 , I M×M (8)

[0074] where 0 M×2 represents an M×2-dimensional zero matrix, and I M×M represents an M×M-dimensional identity matrix;

[0075] Step 5: Perform Kalman filtering on the sub-samples of the set sample to obtain the corrected result x of each sub-sample a,i,l :

[0076] x a,i,l = x f,i + K l (y exp - Hx f,i + w i,l ) (9)

[0077] y exp is a column vector composed of the surface isentropic Mach numbers measured in the first 50% blade chord length region in the experiment;

[0078] Step 6: Average all the filtered samples to obtain the averaged state vector

[0079]

[0080] vector The first two data of the vector are the corrected oncoming flow Mach number and the oncoming flow angle of attack.

[0081] Example 1:

[0082] Taking the MAN GHH 1-S1 compressor cascade as an example, its designed Mach number is 0.62, the designed angle of attack is 0°, the surface isentropic Mach number distributions at 10 measurement points on the pressure surface and the suction surface of the blade are experimentally measured, and the working condition parameters of the oncoming flow Mach number of 0.62 and the oncoming flow angle of attack of 4° are corrected. The numerical simulation and experimental measurement results of the surface isentropic Mach number of the blade before correcting the parameters are as shown in the appendix Figure 2 shown, and the specific implementation steps of this example are as follows:

[0083] Step 1: Floating condition parameters. The specific floating amplitude depends on the regulation accuracy of the oncoming flow parameters. A typical floating range can be set as follows: The floating oncoming flow Mach number Ma in,i = 0.62 ± 0.05, and the floating angle of attack of the oncoming flow α i = 4° ± 1°. Methods such as Latin hypercube can be used for random sampling, where i = 1, 2, …, N, and N is the number of samples. In this example, N = 16. For each sample, numerical calculations of the cascade flow field are performed. The present invention is not sensitive to the turbulence model during the numerical calculation of the flow field, and a suitable turbulence model can be selected. In this example, the SST turbulence model is selected;

[0084] Step 2: Construct the sample state vector x from the floating oncoming flow parameters and their numerical flow field results f,i :

[0085] x f,i = [Ma in,i , α i , Ma is,i,1 , Ma is,i,2 , …, Ma is,i,M T (1)

[0086] In the formula, Ma in,i and α i are respectively the oncoming flow Mach number and the oncoming flow angle of attack of the i-th sample after the floating of the oncoming flow parameters. Ma is,i,j represents the isentropic Mach number on the blade surface at the j-th measurement point position in the region of the first 50% of the blade chord length in the flow field of the i-th sample, where j = 1, 2, …, M, and M represents the number of measurement points in the region of the first 50% of the blade chord length in the experiment. In this example, M = 12;

[0087] Step 3: Calculate the sample covariance matrix P, generate the sub-sample noise vector w i,l and the noise covariance matrix R l , and the specific steps are as follows:

[0088] Step 3-1: Calculate the average value of the sample state vector

[0089]

[0090] Step 3-2: Calculate the sample covariance matrix P:

[0091]

[0092]

[0093] Step 3-3: Generate the noise vector w i,l and this noise matrix W​l : where \(l = 1,\ldots,L\) represents the \(l\)-th subsample, and \(L\) is the number of subsamples. For this example, \(L = 300\). The length of the noise vector is the same as the number of measurement points, i.e., is a set of random numbers following a Gaussian distribution with zero mean. Its distribution variance can refer to the measurement error. For this example, it can be taken as 0.01. Combine the noise vectors into a noise matrix:

[0094] W l = [w 1,l , w 2,l , \ldots, w N,l (5)

[0095] Step 3 - 4: Calculate the noise covariance matrix of the subsamples:

[0096]

[0097] Step 4: Calculate the Kalman gain matrix \(K\) of the subsamples l :

[0098] K l = PH T (HPH T + R l ) -1 (7)

[0099] In the formula, \(H\) is the observation matrix, which represents mapping the state vector to the experimental measurement values. For this example:

[0100] H = [0 M×2 , I M×M (8)

[0101] where \(0 M×2 represents a \(M\times2\) zero matrix, and \(I M×M represents a \(M\times M\) identity matrix;

[0102] Step 5: Perform Kalman filtering on the subsamples of the set of samples to obtain the corrected result \(x\) for each subsample a,i,l :

[0103] x a,i,l = x f,i + K l (y exp - Hx f,i + w i,l ) (9)

[0104] y exp is the column vector composed of the surface isentropic Mach numbers measured in the first 50% blade chord length region in the experiment;

[0105] Step 6: Average all the filtered samples to obtain the averaged state vector

[0106]

[0107] vector The first two data are the corrected oncoming flow Mach number and the oncoming flow angle of attack. In this example, the corrected operating conditions are: the oncoming flow Mach number is 0.6349, and the oncoming flow angle of attack is 2.3394°.

[0108] The comparison diagram of the isentropic Mach number curve of the corrected prediction result and the experimental result is shown in the appendix Figure 2 , it can be seen that after correcting the oncoming flow parameters, except for the trailing edge region, the numerical simulation results of the flow field are in good agreement with the experimental results. The deviation in the trailing edge region is because the turbulence model itself has limited prediction ability for the separation region, but the turbulence model has high prediction accuracy for attached flows. In the parameter correction of the present invention, the experimental measurement data in the first 50% chord length region are used, and this region is an attached flow, thus avoiding the influence of the prediction deviation of the turbulence model. It can be seen that the correction amplitude of the angle of attack in this operating condition is relatively large, and proxy model correction methods such as neural networks cannot extrapolate the space outside the training data range. The present invention has more advantages in correcting the problem of large deviation of operating conditions parameters.

[0109] As described above, it is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should be covered within the protection scope of the present invention.

Claims

1. A method for correcting the experimental working condition parameters of a cascade wind tunnel based on numerical simulation of flow field and ensemble-averaged Kalman filter, characterized in that, Including: Step 1: Fluctuate the experimental working condition parameters, construct multiple sets of incoming flow working condition parameter samples, and perform numerical simulations of the flow field for each set of working condition parameters; Step 2: Compose a state vector from the fluctuating working condition parameters and the corresponding physical quantities at the measuring point positions in the 50% area in front of the blade chord length of the numerical flow field; specifically as follows: Construct a sample state vector from the floating incoming flow parameters and their numerical flow field results : In the formula, and are respectively the incoming flow Mach number and the incoming flow angle of attack of the i-th sample after the incoming flow parameters fluctuate, represents the corresponding physical quantity to be measured at the j-th measuring point position in the flow field of the i-th sample in the region of the first 50% of the blade chord length in the experiment, , and M represents the number of measuring points in the region of the first 50% of the blade chord length in the experiment; Step 3: Calculate the sample covariance matrix, generate the sub-sample noise vector and the noise covariance matrix; specifically as follows: Step 3-1: Calculate the average value of the sample state vector : Step 3-2: Calculate the sample covariance matrix P: Step 3-3: Generate the noise vector w i,l and the noise matrix W l : where l = 1, …, L, representing the l-th subsample, L being the number of subsamples, the length of the noise vector is the same as the number of measurement points, i.e., , which is a set of random numbers following a Gaussian distribution with zero mean, and its distribution variance can refer to the measurement error. Combine the noise vectors into the noise matrix: Step 3-4: Calculate the noise covariance matrix of the sub-sample: Step 4: Calculate the Kalman filter matrix of the sub-sample; Step 5: Perform Kalman filtering on each sub-sample; Step 6: Average the state vectors of the sub-samples of all samples, and extract the corrected working condition parameters from the averaged state vectors.

2. A method for correcting the experimental condition parameters of a cascade wind tunnel based on numerical simulation of flow field and ensemble-averaged Kalman filter, characterized in that Step 1 is specifically as follows: Set the fluctuation range according to the regulation accuracy of the incoming flow parameters, use the Latin hypercube method for random sampling to construct samples of the incoming flow parameters, and perform numerical calculations of the cascade flow field for each sample in the turbulence model.

3. A method for correcting the experimental condition parameters of a cascade wind tunnel based on numerical simulation of fluid flow and ensemble Kalman filter according to claim 1, characterized in that, The measured physical quantities include the surface isentropic Mach number, static pressure coefficient, and static pressure.

4. A method for correcting the experimental working condition parameters of a cascade wind tunnel based on numerical simulation of flow field and ensemble Kalman filter, characterized in that, The calculation formula of the Kalman filter matrix described in Step 4 is as follows: In the formula, H is the observation matrix: For mapping a state vector to a corresponding experimental measurement value, where represents an M×2 dimensional zero matrix, represents an M×M dimensional identity matrix.

5. A method for correcting the operating condition parameters of a cascade wind tunnel experiment based on flow field numerical simulation and ensemble-averaged Kalman filter, characterized in that, Step 5 is specifically as follows: Perform Kalman filtering on the subsamples of the set of samples to obtain the corrected results for each subsample : where y exp is a column vector composed of the surface isentropic Mach numbers measured in the first 50% blade chord length region in the cascade wind tunnel experiment.

6. A method for correcting the experimental condition parameters of a cascade wind tunnel based on numerical simulation of flow field and ensemble-averaged Kalman filter according to claim 5, characterized in that Step 6 is specifically as follows: Average all the filtered samples to obtain the averaged state vector : (9) vector The first two data are the corrected incoming flow Mach number and the incoming flow angle of attack respectively.

7. A computer system, characterized in that Including: One or more processors, a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method described in claim 1.

8. A computer-readable storage medium, characterized in that Stored with computer-executable instructions, the instructions are used to implement the method described in claim 1 when executed.

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