Cascade unsteady flow field prediction method under unknown moment

Abstract

The invention belongs to the technical field of gas turbine turbomachinery cascade modeling and simulation, and particularly relates to a cascade unsteady flow field prediction method at an unknown moment. According to the method, accurate prediction of the cascade unsteady flow field at an unknown moment can be achieved, and the specific process of the method comprises the steps that based on the cascade flow field at a known moment, a flow field reduced-order model is established to select a front-order mode representing a main flow structure of the flow field, and meanwhile, a time coefficient model of the cascade flow field is established; constructing a flow field prediction model based on the time coefficient model of the cascade flow field; training the machine learning model by using the time coefficient of the known cascade flow field, and predicting an unknown time coefficient by using the trained machine learning model; and obtaining a cascade unsteady flow field prediction value at an unknown moment based on the flow field prediction model through a selected mode and a predicted time coefficient.

Description

Technical Field

[0001] The present invention belongs to the technical field of gas turbine turbine blade cascade modeling and simulation, and in particular relates to a method for predicting an unsteady flow field of a blade cascade at an unknown time. Background Art

[0002] Gas turbines are the foundation and key supporting facilities of my country's modern steam turbine industry and are widely used in industries such as power and propulsion. Blades are key components in gas turbine turbomachinery that convert internal energy into mechanical energy. Studying the interaction mechanism between flow structures within the cascade is of great significance for reducing energy loss, improving operating efficiency, and designing gas turbine turbomachinery. When studying flow fields, it is often necessary to obtain data within the flow field. Computational Fluid Dynamics (CFD) methods can capture subtle unsteady flow features in the flow field and are currently the primary means of obtaining high-precision aerodynamic data in the cascade flow field. However, high-precision numerical calculations significantly increase the computational cost and time, and in some cases, the use of high-precision numerical simulations is limited, making it difficult to be widely used in the industrial field. Rapid prediction of flow fields through a prediction method that combines reduced-order models with surrogate models can effectively solve this problem.

[0003] However, when it comes to predicting the unsteady flow field of a cascade at unknown times, the cascade flow field has a large number of grid cells and nodes, requiring a large amount of data to be processed, and is characterized by feature redundancy. Reducing the complexity of the research data, retaining key information while eliminating non-critical information and noise interference, is a major challenge in cascade flow field prediction. Furthermore, existing prediction models only predict parameters at individual spatial points and are not applicable to the entire flow field, presenting certain limitations. Therefore, a method for predicting the unsteady flow field of a cascade at unknown times is urgently needed to predict the flow field parameters and quickly obtain the cascade flow field data at the unknown time. Summary of the Invention

[0004] In view of this, the present invention provides a method for predicting the blade cascade flow field at an unknown time, which can achieve accurate prediction of the blade cascade unsteady flow field at an unknown time.

[0005] The technical solutions for implementing the present invention are as follows: A method for predicting the cascade flow field at unknown time. The specific process is as follows: First, based on the cascade flow field at a known time, a flow field reduction model is established to select the front flow structure that represents the main flow structure of the flow field. order mode, and at the same time establish the time coefficient model of the cascade flow field; Secondly, a flow field prediction model is constructed based on the time coefficient model of the cascade flow field. It is assumed that for the same flow field, the dominant modes of the flow field snapshot subsets at different times remain unchanged or approximately unchanged, and that the time coefficients of the flow fields at different times have a functional relationship. Thirdly, the time coefficient of the known cascade flow field is used to train the machine learning model, and the trained machine learning model is used to predict the unknown time coefficient; Finally, by selecting the mode and the predicted time coefficient, the predicted value of the unsteady flow field of the cascade at the unknown time is obtained based on the flow field prediction model.

[0006] Optionally, the reduced-order model of the present invention is:

[0007] in, Represents the eigenvalues ​​corresponding to each mode. When it is greater than the set threshold, the The first-order mode can represent the main flow structure of the flow field.

[0008] Optionally, the present invention establishes a time coefficient model based on the POD algorithm as follows:

[0009]

[0010] in, is the time coefficient, Indicates the The time coefficient of the first mode, represents an orthogonal basis, and Represents the snapshot matrix of the flow field at a known moment The average matrix and ripple matrix of .

[0011] Optionally, the orthogonal basis of the present invention The method to obtain is: Finding snapshot matrix based on POD method A set of orthogonal bases , so that the snapshot projection on this set of orthogonal bases is maximized:

[0012]

[0013] in, represents the dimension of the orthogonal basis.

[0014] Optionally, the flow field prediction model of the present invention is:

[0015] in, is the number of modes, For the order mode, For the The first mode is The time coefficient corresponding to the moment.

[0016] Optionally, the present invention uses the time coefficient of the known cascade flow field to train the machine learning model, and uses the trained machine learning model to predict the unknown time coefficient; the specific process is: The data set of the time coefficient of the known cascade flow field As a training data set, the machine learning model is trained, where Represents the moments under different samples And the corresponding time coefficients of each mode ; When the output of the machine learning model meets the requirements, the model training is completed, and the trained model is used to predict the coefficients at unknown times.

[0017] Optionally, during training, starting from the second round of training, the input of each round of training is the residual between the predicted value and the true value in the previous round of training, and the predicted values ​​of all rounds of training are added together to obtain the prediction result. .

[0018] Optionally, the machine learning model described in the present invention is an XGBoost model, a long short-term memory network or a Gaussian regression process.

[0019] Optionally, the machine learning model described in the present invention is an XGBoost model, and the objective function of the XGBoost model is composed of a loss function and a complexity function, and the complexity function is composed of the number of leaves and an L2 regularization term.

[0020] Optionally, the flow field at the unknown time described in the present invention is:

[0021] in, represents the time coefficient of the unknown moment, Before The modal matrix of order, Represents the snapshot matrix The average matrix of .

[0022] Beneficial effects: First, the present invention establishes a flow field reduction model to obtain the time coefficients of each modal order; then proposes a flow field prediction hypothesis and constructs a flow field prediction model; then predicts the time coefficient based on a machine learning method; finally, based on the predicted time coefficients of each modal order and the mode used for flow field prediction, a predicted flow field is constructed, which can realize the prediction of the blade flow field at unknown time without relying on the control equation.

[0023] Second, the results of the dual-channel flow field calculation example under the action of periodic wakes using the present invention show that for the prediction results within 60 steps, the average prediction errors of the velocity field and pressure field are 3.43% and 3.2% respectively. The prediction results of the velocity field and pressure field are in good agreement with the numerical calculation results, which provides more intelligent solutions for the design of impeller machinery and lays the foundation for the promotion of CFD methods in the field of gas turbine impeller machinery blade modeling and simulation technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0025] Figure 1 It is the flow chart of the algorithm of the present invention; Figure 2 The geometric structure of the blade used in the embodiment Figure 3 The average pressure coefficient of the numerical calculation results and experimental results of the present invention in the examples given is contrast; Figure 4 The friction coefficients of the present invention are calculated using the numerical results and experimental results in the examples given. contrast; Figure 5 The eigenvalues ​​of each mode of the present invention are used for the embodiment shown. and before The generalized energy contained in the POD mode distribution of Figure 6 The training set and prediction results of the first 10 modal time coefficients of the present invention are used for the embodiments shown in the following figure; among them, (a) is 1-3 orders, (b) is 4-6 orders, (c) is 7-8 orders, and (d) is 9-10 orders; Figure 7 The example uses the present invention to show the temporal trend of the mean residual error (MRE) of the velocity field and pressure field prediction and calculation results. DETAILED DESCRIPTION

[0026] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0027] It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments may be combined with each other; and, based on the embodiments in this disclosure, all other embodiments obtained by persons of ordinary skill in the art without creative work are within the scope of protection of this disclosure.

[0028] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0029] The present application embodiment provides a method for predicting the cascade flow field at an unknown time, and the specific process is as follows: First, based on the cascade flow field at a known time, a flow field reduction model is established to select the front flow structure that represents the main flow structure of the flow field. order mode; secondly, a time coefficient model of the blade flow field is established and a flow field prediction model is constructed, and it is assumed that for the same flow field, the dominant mode of the flow field snapshot subset at different times remains unchanged or approximately unchanged, and there is a functional relationship between the time coefficients of the flow field at different times; thirdly, the time coefficients of the known blade flow field are used to train the machine learning model, and the trained machine learning model is used to predict the unknown time coefficients; finally, by selecting the mode and the predicted time coefficient, the predicted value of the blade unsteady flow field at the unknown time is obtained based on the flow field prediction model.

[0030] This embodiment establishes a flow field reduction model to obtain the time coefficients of each modal order; then proposes a flow field prediction hypothesis and constructs a flow field prediction model; then, the time coefficient is predicted based on a machine learning method; finally, a predicted flow field is constructed based on the predicted time coefficients of each modal order and the modes used for flow field prediction. This enables the prediction of the blade flow field at unknown time without relying on the control equation.

[0031] The algorithm flow chart of the present invention is as follows Figure 1 As shown, the specific steps are: Step 1: Establish a flow field reduction model based on the POD method to obtain the time coefficient model of each modal order; specifically: Common modal decomposition methods include POD method, DMD method, etc. This embodiment uses POD method for illustration. According to POD theory, modal decomposition is performed on the flow field to identify the large-scale flow structure of periodic motion in the flow field, and a set of flow field snapshots at discrete moments are written into a matrix. : (1) (2) in, represents a snapshot of the flow field, Indicates the number of grid nodes, represents the number of discrete moments selected, and Represents matrices The average matrix and ripple matrix of .

[0032] Then, based on the POD method, a set of orthogonal bases for the snapshot matrix is ​​found. , so that the snapshot projection on this set of orthogonal bases is maximized: (3) in, Represents an optional set of basis vectors.

[0033] Calculate the matrix The covariance matrix of , then the covariance matrix The eigenvalues ​​of can be expressed as ,in, Representative The eigenvalue of order, Represents the covariance matrix Basis functions of . Solve for the covariance matrix After the eigenvalues ​​of It can be expressed as a linear combination of the product of the basis function and the original flow field: (4) In addition, each flow field snapshot can be expressed as the various modes of POD The corresponding time coefficient The linear combination of products can be expressed as follows through the time coefficient model: (5) in, is the time coefficient model, Representative The time coefficient of the first mode.

[0034] Eigenvalues ​​corresponding to each mode The size of represents the contribution of the corresponding mode to the flow field, and the results of the first few modes are the main flow characteristics of the flow field. For the calculated flow field, the first few modes can represent the main flow structure of the flow field, and the flow field obtained by reconstructing the first few modes is an approximate result of the original flow field. When analyzing the flow field using the POD method, we can switch from analyzing the instantaneous flow field data to studying the flow field data of the first few modes of POD. The amount of flow field characteristics contained in the order POD mode can be expressed by the generalized energy contained therein: (6) Step 2: Propose a flow field prediction hypothesis and build a flow field prediction model; specifically: The prediction of the flow field can be understood as using the predicted time coefficients and modes to reconstruct the flow field, which is equivalent to using the predicted time coefficients to perform the inverse process of the flow field decomposition process. The flow field prediction model formula can be expressed as: (7) in, is the number of modes, For the order mode, For the The time coefficient corresponding to the first mode.

[0035] In order to obtain all the above parameters, this step makes two assumptions: Assumption 1: For the same flow field, the dominant modes of the flow field snapshot subsets at different times remain unchanged or approximately unchanged; Assumption 2: There is a certain functional relationship between the time coefficients of the flow field at different times.

[0036] Based on assumption 1, if the mode of the control flow field If the modal subset of the flow field snapshot training set remains unchanged or approximately unchanged, the modal subset of the flow field snapshot training set can be selected as the basis function for flow field prediction, that is: (8) Based on assumption 2, the time coefficients of the flow field modes at different times have a certain functional relationship: (9) in, represent Moment, The time coefficient of each modal order is the size of the time coefficient. In step 3, the XGBoost algorithm will be used to train the parameter curve of the time coefficient of each modal order. The prediction of the time coefficient at an unknown time can be solved from the trained curve.

[0037] Step 3: Predict the time coefficient based on machine learning methods; specifically: Common machine learning methods include the XGBoost algorithm, long short-term memory (LSTM) network, Gaussian process regression (GPR), etc. This embodiment uses the XGBoost algorithm as an example for description.

[0038] For the dataset , Represents the moments under different samples And the corresponding time coefficients of each mode , represents the sample number, Represents the amount of data, Represents dimension. According to the XGBoost algorithm, the prediction result can be expressed as: (10) in, Represents the tree number, that is, the number of iterations; Indicates the Iteration error of times; Represents the space of regression trees (also called CART); Representative samples The mapping relationship of each leaf node of the decision tree model; Represents the number of leaves in the tree; is the predicted value of the sample at each leaf node in the regression tree model. Starting from the second round of training, the input of each training round is the residual between the predicted value and the true value in the previous round. The final prediction result is the sum of the predicted values ​​of all training rounds.

[0039] In the XGBoost model, to improve model generalization and prevent overfitting, the XGBoost objective function consists of a loss function and a complexity function. The complexity function is composed of the number of leaves and the L2 regularization term.

[0040] (11) (12) in, Represents the loss function, which represents the difference between the predicted value and the true value and is a convex function; represents the complexity function, which is a regularization term used to penalize the complexity of the model. The loss function combined with the regularization term can balance the fitting accuracy and complexity to avoid overfitting. After the objective function is determined, the model needs to be trained. The result of the objective function after training is: (13) The input is Predicted value, true value and iteration error after training After Taylor expansion and regularization term expansion of the objective function, the minimum value of the objective function can be obtained by calculation: (15) in, and are the first-order derivative and second-order derivative of the loss function, respectively. Since the decision tree result that satisfies the given sample conditions is not unique, it is necessary to find the decision tree result that can make the objective function optimal. Here we choose to use a greedy algorithm to approximate the solution: (16) The model parameters that minimize the objective function can be determined , that is, the time coefficient relationship of the flow field mode at different times, and then based on this, the predicted value of the time coefficient of each order mode at the unknown time is obtained .

[0041] Step 4: Construct the predicted flow field based on the predicted modal time coefficients of each order and the modes used for flow field prediction; specifically: Finally, through the selected mode and the predicted time coefficient, the flow field at the unknown time can be predicted according to the following formula.

[0042] (17) The present invention provides a method for predicting the flow field of a cascade at unknown times. This method primarily addresses the problem of predicting the unsteady flow field of a cascade at unknown times. Based on the proper orthogonal method, a flow field reduction model is established to obtain the time coefficients of each modal order. A flow field prediction hypothesis is then proposed, transforming the flow field prediction problem into the problem of predicting the time coefficients of each modal order. Simultaneously, based on the extreme gradient boosting algorithm, the time coefficients at known times are used as a training set for the model. The trained proxy model is then generalized to a new sample space to complete the prediction of the time coefficients at unknown times. Finally, the predicted time coefficients of each modal order are reconstructed with the modes used for flow field prediction to obtain a predicted flow field.

[0043] Table 1 Geometric parameters of the blades used

[0044] The following is an explanation of the double-channel cascade flow field results under the action of periodic wakes. The blade geometry and parameters used in this embodiment are as follows: Figure 2and as shown in Table 1. Furthermore, to simulate the unsteady effects of the upstream wake in numerical calculations, an inlet section was set up in front of the blade segment. A circular rod wake was used to replace the upstream blade wake. A cylindrical rod with a diameter of 2.05 mm was placed 41% of the axial chord length upstream of the blade leading edge to simulate the periodic upstream wake. This chapter uses the AUTOGRID5 module in NUMECA software to mesh the blade passage; the ICEM module in ANSYS software is used to mesh the inlet section, and an O-shaped mesh is used to refine the mesh near the circular rod wall.

[0045] In order to verify the accuracy of the numerical results, an inlet Reynolds number of 1.6×10 5 The numerical calculation results are compared with the experimental results for verification. Figure 3 and Figure 4 The average pressure coefficients are shown respectively and surface friction coefficient The results show that the numerical calculation results of the embodiment are very close to the experimental results, and the numerical calculation accuracy is within an acceptable range.

[0046] The flow field is reduced by the proposed method. Figure 5 is the eigenvalue of each mode and before The generalized energy contained in the POD mode The energy of the 10th-order mode is 4% of the energy of the 1st-order mode, and the first 10 modes account for 95.32% of the total energy of the pulsating field. Therefore, the first 10 modes are selected as the basis functions for flow field reconstruction and prediction, which ensures the accuracy requirements and reduces the amount of calculation. Then, the time coefficients of each mode at a known time are used as the training set, and the extreme gradient boosting algorithm is used to construct the proxy model. Figure 6 (a)-(d) show the training set and prediction results of the first 10 modal time coefficients. The results show that the prediction results of the first 10 modes are consistent with the changing trend of the training set, and the XGBoost model can accurately capture the fluctuation characteristics of the first 10 modal time coefficients. In addition, the mean residual error (Mean Residual Error, MRE ) to quantify the prediction error, Figure 7 The temporal trends of the prediction errors of the velocity and pressure fields are given, where , represents the dimensionless time of the test set. The results show that for The prediction results within the velocity field and the prediction error of the pressure field MRE Both are lower than 6%, and their average values ​​are 3.43% and 3.2% respectively. Therefore, it can be concluded that the prediction results of the POD-XGBoost method are in good agreement with the numerical calculation results.

[0047] The above specific embodiments merely illustrate the design principles of the present invention. The shapes and names of the components described herein may vary and are not limiting. Therefore, those skilled in the art may modify or substitute equivalents for the technical solutions described in the above embodiments. Such modifications and substitutions, without departing from the inventive spirit and technical solutions of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A method for predicting cascade flow field at unknown time, characterized in that: The specific process is: First, based on the cascade flow field at a known time, a flow field reduction model is established to select the front flow structure that represents the main flow structure of the flow field. order mode, and at the same time establish the time coefficient model of the cascade flow field; Secondly, a flow field prediction model is constructed based on the time coefficient model of the cascade flow field. It is assumed that for the same flow field, the dominant modes of the flow field snapshot subsets at different times remain unchanged or approximately unchanged, and that the time coefficients of the flow fields at different times have a functional relationship. Thirdly, the time coefficient of the known cascade flow field is used to train the machine learning model, and the trained machine learning model is used to predict the unknown time coefficient; Finally, by selecting the mode and the predicted time coefficient, the predicted value of the unsteady flow field of the cascade at the unknown time is obtained based on the flow field prediction model.

2. The method for predicting cascade flow field at unknown time according to claim 1, characterized in that: The reduced-order model is: in, Represents the eigenvalues ​​corresponding to each mode. When it is greater than the set threshold, the The first-order mode can represent the main flow structure of the flow field.

3. The method for predicting cascade flow field at unknown time according to claim 1, characterized in that: The time coefficient model is established based on the POD method: in, is the time coefficient, Indicates the The time coefficient of the first mode, represents an orthogonal basis, and Represents the snapshot matrix of the flow field at a known moment The average matrix and ripple matrix of .

4. The method for predicting cascade flow field at unknown time according to claim 3, characterized in that: The orthogonal basis The method to obtain is: Finding snapshot matrix based on POD method A set of orthogonal bases , so that the projection of the snapshot matrix on this set of orthogonal bases is maximized: in, represents a set of optional basis vectors, represents the dimension of the orthogonal basis.

5. The method for predicting cascade flow field at unknown time according to claim 3, characterized in that: The flow field prediction model is: in, is the number of modes, For the order mode, For the The first mode is The time coefficient corresponding to the moment.

6. The method for predicting cascade flow field at unknown time according to claim 1, characterized in that: The time coefficient of the known cascade flow field is used to train the machine learning model, and the trained machine learning model is used to predict the unknown time coefficient; The specific process is: The data set of the time coefficient of the known cascade flow field As a training data set, the machine learning model is trained, where Represents the moments under different samples And the corresponding time coefficients of each mode ; When the output of the machine learning model meets the requirements, the model training is completed, and the trained model is used to predict the coefficients at unknown times.

7. The method for predicting cascade flow field at unknown time according to claim 6, characterized in that: During training, starting from the second round of training, the input of each round of training is the residual between the predicted value and the true value in the previous round. Finally, the predicted values ​​of all rounds of training are added together to get the predicted result. .

8. The method for predicting cascade flow field at unknown time according to claim 6, characterized in that: The machine learning model is an XGBoost model, a long short-term memory network or a Gaussian regression process.

9. The method for predicting cascade flow field at unknown time according to claim 8, characterized in that: The machine learning model is an XGBoost model, and the objective function of the XGBoost model consists of a loss function and a complexity function, and the complexity function consists of the number of leaves and an L2 regularization term.

10. The method for predicting cascade flow field at unknown time according to claim 5, characterized in that: The flow field at the unknown time is: in, represents the time coefficient of the unknown moment, Before The modal matrix of order, Represents the snapshot matrix The average matrix of .

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