Method for predicting unsteady flow field of turbine under unknown working condition

Abstract

The invention belongs to the technical field of gas turbine modeling and simulation, and particularly relates to a method for predicting an unsteady flow field of a turbine under an unknown working condition, which can realize accurate prediction of the unsteady flow field of the turbine under the unknown working condition, and comprises the following steps: establishing a snapshot matrix of the unsteady flow field of the turbine under the known working condition and performing modal decomposition; an objective function is established according to the flow field snapshot matrix and the reconstruction matrix, an optimal modal subset used for predicting unknown working conditions is obtained based on the objective function, and the modal number in the subset is the optimal modal number used for prediction; establishing a flow field reconstruction model based on the optimal modal number and a flow field snapshot matrix modal decomposition form; carrying out model training by utilizing the characteristic value and the amplitude of the unsteady flow field of the turbine under the known working condition, and carrying out characteristic value and amplitude prediction under the unknown working condition based on the trained model; and substituting the predicted characteristic value and amplitude under the unknown working condition into the flow field reconstruction model, and calculating a turbine unsteady flow field prediction value under the unknown working condition.

Description

Technical Field

[0001] The present invention belongs to the technical field of gas turbine turbine modeling and simulation, and specifically relates to a method for predicting the unsteady flow field of a turbine under unknown working conditions. Background Art

[0002] Gas turbines are one of the basic and key supporting facilities in China's modern steam turbine industry and are widely used in industrial fields such as power generation and propulsion. The turbine is a key component in a gas turbine that converts internal energy into mechanical energy. Studying the interaction mechanism between the internal flow structures of the turbine is of great significance for reducing energy loss, improving working efficiency, and turbine design. When studying the flow field, it is often necessary to obtain data inside the flow field. The Computational Fluid Dynamics (CFD) method can capture fine unsteady flow characteristics in the flow field and is currently the main means of obtaining high-precision aerodynamic data in the turbine flow field. However, in fluid mechanics research, high-precision numerical calculation methods capture the macroscopic characteristics and microscopic details of the flow field more accurately, but are limited by the grid scale and calculation step size, requiring a large amount of computing time and computing cost, and in some cases, the use of high-precision numerical simulations is restricted, making it difficult to be widely used in the industrial field. Currently, establishing an unsteady flow field prediction model to obtain unknown flow field data is an effective method to improve the calculation efficiency.

[0003] For the problem of predicting the unsteady flow field under unknown working conditions, it is necessary to obtain the common modes between different working conditions. The Proper Orthogonal Decomposition (POD) mode is restricted by spatial orthogonality and it is difficult to obtain the common modes between different working conditions; while the Dynamic Mode Decomposition (DMD) can decouple the spatio-temporal coherent structures in a complex system and obtain modes with a single oscillation frequency, but it does not have spatial orthogonality and it is difficult to identify the subset of modes that have the greatest impact on the flow field. In addition, the existing prediction methods currently only predict the parameters at individual spatial points and have not been applied to the entire flow field, which has limitations. Therefore, there is an urgent need for a method for predicting the unsteady flow field of a turbine under unknown working conditions to predict the flow field parameters and thus quickly obtain the flow field data under unknown working conditions. Summary of the Invention

[0004] In view of this, the present invention provides a method for predicting the unsteady flow field of a turbine under unknown working conditions, which can accurately predict the unsteady flow field of a turbine under unknown working conditions.

[0005] The technical solution of the present invention is implemented as follows: A method for predicting the unsteady flow field of a turbine under unknown working conditions, the specific process is as follows: Establish a snapshot matrix of the turbine unsteady flow field under known operating conditions and perform modal decomposition, decomposing the flow field snapshot matrix into modal, eigenvalue, and amplitude matrices; Establish an objective function based on the flow field snapshot matrix and the reconstruction matrix, and obtain an optimal modal subset for predicting unknown operating conditions based on the objective function. The number of modes in the subset is the optimal number of modes for prediction; Based on the optimal number of modes and the modal decomposition form of the flow field snapshot matrix, establish a flow field reconstruction model; Use the eigenvalues and amplitudes of the turbine unsteady flow field under known operating conditions for model training, and predict the eigenvalues and amplitudes under unknown operating conditions based on the trained model; Substitute the predicted eigenvalues and amplitudes under unknown operating conditions into the flow field reconstruction model to calculate the predicted value of the turbine unsteady flow field under unknown operating conditions.

[0006] Optionally, the flow field reconstruction model of the present invention is:

[0007] where, is the flow field snapshot matrix at time, is the optimal number of modes, is the th order mode, is the amplitude of the th order mode, is the eigenvalue corresponding to the th order mode at time. corresponding to time

[0008] Optionally, the present invention gives the following flow field prediction assumptions: Assumption 1: For the flow fields of different operating conditions, their dominant modes remain unchanged or approximately unchanged; Assumption 2: Under different inlet conditions, there is a functional relationship between the characteristic parameters corresponding to the dominant mode.

[0009] Optionally, based on the flow field prediction assumptions, the specific process of predicting eigenvalues and amplitudes under unknown operating conditions using a parametric regression model in the present invention is: Select the flow field modal subset under known operating conditions as the basis function for flow field prediction, and train the parametric regression model so that the parametric regression model represents the functional relationship; Use the trained parametric regression model to predict the eigenvalues and amplitudes under unknown operating conditions.

[0010] Optionally, the parametric regression model of the present invention is: Gaussian Process Regression (GPR) model. ​

[0011] Optionally, the present invention establishes the Frobenius norm of the difference between the objective function and the penalty function based on the flow field snapshot matrix and the reconstruction matrix, and constructs the objective function.

[0012] Optionally, the objective function of the present invention is:

[0013]

[0014] where represents the flow field snapshot matrix, represents the reconstruction matrix; is the penalty function, represents the hyperparameter, which is used to balance the data loss term and the penalty function; represents the set of amplitude values of each selected order mode; is the introduced parameter, which is used to decouple the objective function part and the penalty function part in the optimization problem; The reconstruction matrix is: the flow field snapshot is approximately projected onto the low-dimensional vector through the spatial structure information of the original flow field to obtain.

[0015] Optionally, the penalty function of the present invention is:

[0016] where represents the number of selected modes, represents the th order mode amplitude value.

[0017] Optionally, the present invention introduces the Lagrange function to solve the objective function, and when solving, each variable adopts the alternating optimization method.

[0018] Optionally, the present invention uses the Sparse-Promoting Dynamic Mode Decomposition (SPDMD) method for modal decomposition, and decomposes the process snapshot matrix into modal, eigenvalue, and amplitude matrices.

[0019] Optionally, the present invention uses the Dynamic Mode Decomposition (DMD) method to establish the turbine unsteady flow field snapshot matrix under known working conditions.

[0020] Beneficial effects: First, the present invention obtains a reduced-order flow field reconstruction model, and then uses Gaussian process regression to construct a surrogate model, realizing the prediction of unsteady flow fields under unknown working conditions directly based on numerical calculation results and experimental data, without relying on control equations. Therefore, accurate prediction of the unsteady flow field of turbines under unknown working conditions can be achieved.

[0021] Second, the results of flow field calculation examples under the action of periodic wakes using the method of the present invention show that the method has a high prediction accuracy for most regions of the velocity field and pressure field. The distribution of large-scale vortices such as passage vortices and leakage vortices in the prediction results is in good agreement with the numerical calculation results, laying a foundation for the popularization of CFD methods in the field of gas turbine turbine modeling and simulation technology. Description of the Drawings

[0022] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0023] Figure 1 It is the algorithm flow chart of the present invention; Figure 2 It is the geometric structure of the blade used in the illustrated embodiment; Figure 3 It is the average pressure coefficient of the numerical calculation results and experimental results of the present invention used in the illustrated embodiment Comparison; Figure 4 It is the friction coefficient of the numerical calculation results and experimental results of the present invention used in the illustrated embodiment Comparison; Figure 5 It is the real and imaginary parts of the eigenvalues of the first 11 modes and all calculated modes for flow field prediction using the present invention in the illustrated embodiment, as well as the corresponding energy distribution; Figure 6 It is the fitting curve of the amplitude modulus length of each order mode using the present invention in the illustrated embodiment; Figure 7 It is the trend result of the average residual MRE of the velocity field and pressure field prediction and calculation results using the present invention in the illustrated embodiment changing with time. Detailed Embodiments

[0024] The embodiments of the present invention will be described in detail below with reference to the drawings.

[0025] It should be noted that, without conflict, the following embodiments and the features in the embodiments may be combined with each other; and, based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present disclosure.

[0026] It should be noted that the following describes various aspects of embodiments within the scope of the appended claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is illustrative only. Based on the present disclosure, those skilled in the art should understand that one aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement an apparatus and / or practice a method. Additionally, this apparatus and / or method may be implemented using other structures and / or functionality in addition to one or more of the aspects described herein.

[0027] A method for predicting the unsteady flow field of a turbine under unknown working conditions in an embodiment of the present application has the following specific process: First, establish a snapshot matrix of the unsteady flow field of the turbine under known working conditions and perform modal decomposition, decomposing the flow field snapshot matrix into modal, eigenvalue, and amplitude matrices; second, establish an objective function based on the flow field snapshot matrix and the reconstruction matrix, and obtain an optimal modal subset for predicting unknown working conditions based on the objective function, where the number of modes in the subset is the optimal number of modes for prediction; third, establish a flow field reconstruction model based on the optimal number of modes and the modal decomposition form of the flow field snapshot matrix; then, use the eigenvalues and amplitudes of the unsteady flow field of the turbine under known working conditions for model training, and predict the eigenvalues and amplitudes under unknown working conditions based on the trained model; finally, substitute the predicted eigenvalues and amplitudes under unknown working conditions into the flow field reconstruction model to calculate the predicted value of the unsteady flow field of the turbine under unknown working conditions.

[0028] The flow chart of the method in this embodiment is as Figure 1 shown, and the specific steps are as follows: Step 1: Use the DMD algorithm to establish a snapshot matrix of the unsteady flow field of the turbine under known working conditions; specifically: In the DMD algorithm, the transient flow field data obtained from experiments or numerical simulations can be written in the following vector matrix form: (1) (2) where represents the flow field snapshot storing the flow parameters (such as pressure, velocity, entropy, etc.) at the th moment. The flow field data is sampled at equal time intervals, and the total number of sampling moments is , the sampling time interval is . In the above definition, the subscripts 0 and represent the first moment and the last moment in the flow field sequence respectively. is the product of the number of grid nodes and the number of variables.

[0029] Step 2: Perform modal decomposition based on SPDMD to decompose the flow field snapshot matrix into modal, eigenvalue, and amplitude matrices; the specific process is as follows: Assume that there is a certain linear relationship in any flow field, that is , then the flow field at the later moment can be approximately linearly represented by the flow field at the previous moment. Through the linear mapping it can be expressed as: (3) According to the assumption, the linear relationship contains the dynamic characteristics of this group of flow field snapshot sequences, such as: The eigenvalues of reflect the frequency and time growth rate of the corresponding mode, and identifying these characteristics is the purpose of this application. In order to obtain parameters such as eigenvalues, the matrix is decomposed into singular values as: (4) Among them, is order matrix, representing the original flow field. is order matrix, containing the spatial structure information of the original flow field. is order matrix, The singular values in represent the energy distribution in the original flow field. is order matrix, containing the time structure information of the original flow field.

[0030] Then there is , obviously and have the same eigenvalues. Solve the eigenvalues and eigenvectors of the matrix as follows: (5) Among them, is the eigenvalue matrix of the matrix , and is also 's eigenvalue matrix. is the eigenvector of the matrix . The mode of DMD can be obtained by calculation as: (6) To measure the importance of different modes in the flow field, they are sorted according to the energy magnitude of each order mode. The energy of a mode can be represented by the norm as follows. By projecting onto the mode shown in Equation (6), the energy value can be obtained, that is: (7) (8) where the energy can be regarded as the coefficient obtained by projecting the flow field snapshot onto the DMD mode. The rows of this matrix correspond to the DMD mode order, and the columns correspond to different moments. Therefore, the row norm of the matrix can be used as the energy ratio of different orders of DMD modes.

[0031] The flow field snapshot is approximately projected onto the low-dimensional vector through the matrix . The low-dimensional flow field snapshot can also be expressed as the product of the eigenvector , the eigenvalue and the amplitude . Therefore, the original flow field snapshot matrix can be expressed as the product of the mode matrix , the amplitude matrix and the Vandermonde matrix of eigenvalues , which is also the flow field reconstruction expression.

[0032] (9) (10) (11) Step 3: Identify the key modes and determine the optimal mode subset for flow field reconstruction. The number of modes in the subset is the optimal number of modes for prediction; After calculating the mode matrix of the flow field through the dynamic mode decomposition method, it is necessary to screen the modes to obtain the optimal mode subset for flow field reconstruction. The optimal mode subset for flow field reconstruction should not only reflect the main flow characteristics of the flow field to ensure the accuracy of the reduced-order model, but also minimize the number of modes in the subset to ensure the generalization ability of the reduced-order model. The specific process of determining the mode subset is as follows: First, use the Frobenius norm of the difference between the original matrix and the reconstructed matrix to measure the accuracy of the reduced-order model, that is, the truncation error: (12) where is the mode matrix, is the amplitude matrix, is the Vandermonde matrix of eigenvalues, is the energy distribution in the original flow field, is the time structure information of the original flow field, is the spatial structure information of the original flow field.

[0033] To improve the generalization ability of the model, when reconstructing the flow field, it is necessary to balance the computational cost and computational accuracy, that is, under the condition of allowing errors, reduce the computational cost as much as possible. Therefore, a penalty function is added to the objective function, and the optimization problem can be defined as: (13) where reflects the sparsity required by this problem. This is a typical convex optimization problem, which can be solved by the Alternating Direction Multiplier method (ADMM). Then the above problem is transformed into: (14) where .

[0034] Introduce the Lagrangian function (or use the gradient projection method, genetic algorithm, particle swarm optimization algorithm, etc.) to solve: (15) Since in Equation (15), and are coupled, which means it is very difficult to optimize the three variables simultaneously. Therefore, in the optimization process, the three variables are not optimized simultaneously, but two of them are alternately fixed and the other is optimized, that is, the following iterative format: (16) where the calculation convergence condition is: (17) Therefore, the truncation error when minimizing the objective function can be expressed as , and the number of modes at this time is the optimal number of modes for prediction.

[0035] Step 4: Set the flow field prediction hypothesis, and based on the number of modes in the optimal mode subset (equivalent to the predicted value of the flow field order reduction parameter) and the modal decomposition form of the flow field snapshot matrix, establish a flow field reconstruction model; specifically: The prediction of the flow field can be understood as reconstructing the flow field using the predicted characteristic parameters and modes, which is equivalent to performing the inverse process of the flow field decomposition process using the predicted characteristic parameters. The flow field reconstruction formula can be expressed as: (18) where is the number of modes used for prediction, is the -th order mode, and are the eigenvalue and amplitude corresponding to the -th order mode, respectively.

[0036] To obtain all the above parameters, this method proposes two assumptions: Assumption 1: For the flow fields under different working conditions, their dominant modes remain unchanged or approximately unchanged; Assumption 2: Under different inlet conditions, there is a certain functional relationship between the characteristic parameters corresponding to the dominant mode.

[0037] Based on Assumption 1, if the mode that controls the flow field remains unchanged or approximately unchanged, then a subset of the flow field modes under any working condition can be selected as the basis function for flow field prediction, that is: (19) Based on Assumption 2, the eigenvalue and amplitude corresponding to each order mode have a certain functional relationship with the inlet conditions, that is: (20) (21) Step Five: Predict the flow field parameters based on the regression algorithm, including the prediction of eigenvalues and amplitudes; specifically: First, to find the above function relationship, a regression model is used to model the characteristic parameters under known working conditions. Common parameter regression methods include: kernel ridge regression method, polynomial regression method, neural network, etc. Compared with the polynomial regression model, Gaussian Process Regression (GPR), as a non-parametric machine learning model, has better prediction effect for the non-linear characteristics of a small number of samples. While predicting non-linear problems, it can also provide a measure of the uncertainty of the prediction solution, increasing the interpretability of the model. Moreover, compared with the method based on neural network, this method has lower data requirements and will not have the problem of overfitting. Therefore, it is the preferred method for dataset training. In Gaussian process regression, different kernel functions can be used to capture different statistical characteristics. In this method, the Squared Exponential (SE) kernel model is used: (22) (23) where, is the true value function; is the kernel function; μ is the mean function; and are the hyperparameters of the kernel function; is the training set, which contains sample data of eigenvalue / modal amplitude under known different working conditions and can be obtained by solving the transient flow field data obtained in experiments or numerical simulations.

[0038] Use GPR to train the parameter curves of eigenvalue and modal amplitude and , then the predicted values of eigenvalue and amplitude under unknown working conditions can be solved from the trained curves.

[0039] Step 6: Obtain the predicted value of the flow field under unknown working conditions through the selected mode, the predicted eigenvalue and amplitude; specifically: (24) For the problem of unsteady flow field prediction under unknown working conditions, this application first establishes a flow field reduced-order model based on the sparse enhanced dynamic mode decomposition method to obtain the flow field reduced-order parameters. Then, a flow field prediction hypothesis is proposed to transform the flow field prediction problem into a problem of predicting the flow field reduced-order parameters. At the same time, based on the Gaussian process regression model, the reduced-order parameters under known working conditions are used as the model training set, and the characteristic parameters under unknown working conditions are predicted according to the surrogate model. Finally, the predicted characteristic parameters are reconstructed with the modes used for flow field prediction to obtain the unsteady flow field prediction result under unknown working conditions.

[0040] Table 1 Geometric parameters of the used blade

[0041] The results of the three-dimensional cascade flow field example under the action of periodic wakes are described below. The three-dimensional cascade flow field is an internal flow field, which contains large-scale flow structures such as periodic upstream wakes, passage vortices, and leakage vortices, and is suitable as a verification example for prediction methods. The blade geometric structures and parameters used in this embodiment are as Figure 2 shown in Table 1. At the same time, in order to simulate the unsteady effect of the upstream wake in the numerical calculation, an inlet section needs to be set upstream of the blade section. The influence of the wake generated by the upstream blade on the downstream of the passage is equivalent to the influence of the wake generated by a circular rod on the downstream of the passage. Because the boundary layer separation of the circular rod periodically generates vortex clusters near the circular rod and then propagates downstream, its effect is similar to the wake generated by the blade. Therefore, in this paper, the role of the upstream blade wake is replaced by the circular rod wake. At 41% of the position upstream of the blade leading edge, a circular rod with a diameter of 2.05 mm is set to simulate the periodic upstream wake. Select k- the SST model as the numerical calculation model for this embodiment, and use the AUTOGRID5 module in the NUMECA software and the ICEM module in the ANSYS software for grid division.

[0042] To verify the accuracy of the numerical results, the numerical calculation results with an inlet Reynolds number of 1.6×10 5 are compared with the experimental results for verification. Figure 3 and Figure 4 respectively show the comparison results of the average pressure coefficient and the surface friction coefficient . The results show that the numerical calculation results of the exemplified embodiment are very close to the experimental results, and the numerical calculation accuracy is within an acceptable range.

[0043] Use the flow field mode subset under the condition of an inlet Reynolds number of 2.4×10 5 as the basis function for flow field prediction. Figure 5 The first 11 modes for flow field prediction and the real and imaginary parts of the eigenvalues and the corresponding energy distributions of all the calculated modes are given. Then, the Gaussian regression method is used to model the characteristic parameters under the known working conditions, and then the characteristic parameters under the unknown working conditions are predicted according to the model, and further the cascade flow field under the exemplified embodiment is predicted. Figure 6 The fitting curves of the amplitude modulus lengths of each order mode are given. Through the above flow field prediction model, the transient flow characteristics of the exemplified embodiment at a specific Reynolds number can be predicted with relatively low data requirements. In addition, the total pressure loss and vorticity distributions of the predicted flow field and the calculated flow field under the condition of a Reynolds number of are also compared, as Figure 7As shown, the results indicate that for the prediction results within one cycle, the prediction errors MRE of the velocity field and the pressure field are both within the range of 5% - 17% and fluctuate with time, verifying the accuracy of the algorithm proposed in the present invention.

[0044] The above specific embodiments only describe the design principle of the present invention. The shapes and names of the components in this description can be different and are not limited. Therefore, those skilled in the art of the present invention can modify or equivalently replace the technical solutions recorded in the foregoing embodiments; and these modifications and replacements do not depart from the spirit and technical solutions of the present invention, and should all fall within the protection scope of the present invention.

Claims

1. A method for predicting the unsteady flow field of a turbine under unknown operating conditions, characterized in that, The specific process is as follows: First, establish the snapshot matrix of the turbine unsteady flow field under known working conditions and perform modal decomposition, decomposing the process snapshot matrix into modal, eigenvalue, and amplitude matrices; Second, establish an objective function based on the flow field snapshot matrix and the reconstruction matrix, and obtain the optimal modal subset for predicting unknown working conditions based on the objective function. The number of modes in the subset is the optimal number of modes for prediction; Third, based on the optimal number of modes and the modal decomposition form of the flow field snapshot matrix, establish a flow field reconstruction model; Fourth, use the eigenvalues and amplitudes of the turbine unsteady flow field under known working conditions for model training, and predict the eigenvalues and amplitudes under unknown working conditions based on the trained model; Finally, substitute the predicted eigenvalues and amplitudes under unknown working conditions into the flow field reconstruction model to calculate the predicted values of the turbine unsteady flow field under unknown working conditions.

2. The method for predicting the unsteady flow field of a turbine under unknown working conditions according to claim 1, characterized in that The flow field reconstruction model is: Among them, is the snapshot matrix of the flow field at a certain moment, is the optimal number of modes, is the th-order mode, is the amplitude of the th-order mode, is the eigenvalue corresponding to the th-order mode at a certain moment.

3. The method for predicting the unsteady flow field of a turbine under unknown working conditions according to claim 1, wherein Given the following assumptions for flow field prediction: Assumption 1: For the flow fields under different working conditions, their dominant modes remain unchanged or approximately unchanged; Assumption 2: Under different inlet conditions, there is a functional relationship between the characteristic parameters corresponding to the dominant mode.

4. The method for predicting the unsteady flow field of a turbine under unknown working conditions according to claim 3, wherein Based on the flow field prediction assumptions, the specific process of using the parametric regression model to predict eigenvalues and amplitudes under unknown working conditions is: Select the flow field modal subset under known working conditions as the basis function for flow field prediction, and train the parametric regression model so that the parametric regression model represents the functional relationship; Use the trained parametric regression model to predict the eigenvalues and amplitudes under unknown working conditions.

5. The turbine unsteady flow field prediction method under unknown working conditions according to claim 4, characterized in that The parametric regression model is: the Gaussian process regression GPR model.

6. The method for predicting the unsteady flow field of a turbine under unknown working conditions according to claim 1, characterized in that Establish the Frobenius norm of the difference between the objective functions and the penalty function based on the flow field snapshot matrix and the reconstruction matrix, and construct the objective function.

7. The method for predicting the unsteady flow field of a turbine under unknown working conditions according to claim 1, wherein, The objective function is: Among them, represents the flow field snapshot matrix, represents the reconstruction matrix; is the penalty function, represents the hyperparameter; represents the set of the selected modal amplitude values of each order; is the introduced parameter; The reconstruction matrix is: the flow field snapshot Through the spatial structure information of the original flow field Approximately projected onto a low-dimensional vector Obtained.

8. The method for predicting the unsteady flow field of a turbine under unknown working conditions according to claim 7, characterized in that, The penalty function is: Among them, represents the number of selected modes, represents the -th order modal amplitude value.

9. The method for predicting the unsteady flow field of a turbine under unknown working conditions according to claim 1, characterized in that, Use the sparse-perturbed dynamic mode decomposition (SPDMD) method for modal decomposition, decomposing the process snapshot matrix into modal, eigenvalue, and amplitude matrices.

10. The method for predicting the unsteady flow field of a turbine under unknown working conditions according to claim 1, characterized in that, Use the dynamic mode decomposition (DMD) method to establish the snapshot matrix of the turbine unsteady flow field under known working conditions.

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