A method for analyzing unstable flow characteristics of a pump-turbine based on modal decomposition

Abstract

This invention proposes a method for analyzing the unsteady flow characteristics of a pump-turbine based on modal decomposition, belonging to the field of pump-turbine flow field simulation analysis technology. First, the three-dimensional or two-dimensional flow field data obtained from large eddy simulation (LES) calculations of the pump and turbine operating conditions are sorted according to the time dimension of the runner operation to form a data matrix. Then, the order reduction method is used to restore and replace the data with lower-dimensional data. The data matrix is ​​constructed based on the energy of each mode, and the POD modes and time coefficients are calculated. The approximate matrix is ​​found using the DMD method, and its eigenvalues ​​and eigenvectors are calculated to determine the DMD modes. Modal energy analysis is performed to identify the main modes. The flow field structure is reconstructed using the main modes, and transient error analysis of the reconstructed flow field is conducted to determine the characteristics of the unsteady modes, providing guidance for optimization design and flow field control while reducing the computational burden.

Description

Technical Field

[0001] This invention belongs to the field of flow field simulation and analysis technology for water pumps and turbines, specifically, it relates to a method for analyzing the unsteady flow characteristics of water pumps and turbines based on modal decomposition. Background Technology

[0002] The energy inherent in fluid motion is one of the most promising energy sources, especially in areas with poor sunlight coverage. To reduce reliance on fossil fuels, the development of clean energy has become a top priority. Pumped storage, with its flexible operation, ability to meet the high-efficiency operation of the power grid, and excellent performance indicators, has attracted increasing attention and is gradually becoming a mainstream means of energy storage and grid regulation. The reversible pump-turbine is the core device of a pumped storage power station, responsible for peak shaving, frequency regulation, and phase regulation during power grid supply, thus improving the reliability of the entire power grid. During periods of low electricity demand, the turbine reverses to act as a pump, utilizing excess electrical energy in the grid to increase and store the potential energy of the water. When electricity demand reaches its peak, the turbine acts as a turbine, using the potential energy of the water to generate electricity. However, due to the technical complexity of the unit and frequent changes in operating conditions, many instability issues still exist in the actual operation of the power station during transition processes. Considering the high cost of experimental operation of the original unit and the difficulty of adjustment experiments, numerical simulation methods are needed to conduct in-depth analysis of the flow characteristics under two different operating conditions: pump and turbine. In terms of computational methods, traditional Reynolds-averaged methods smooth out the spatiotemporal details of turbulent fluctuations, removing information about these fluctuations and failing to fully capture the unsteady motion characteristics of the flow field. In contrast, large eddy simulation (LES) methods are more applicable than Reynolds-averaged models, especially for analyzing velocity distribution, vorticity variations, and vortex motion in unsteady flow domains. LES uses filtering functions to delineate vortex scales, allowing for direct numerical simulation of large-scale vortices, while small-scale vortices are closed using theoretical models. Although the computational load is higher, it remains within the limits of current computing resources.

[0003] Currently, simulation has become the mainstream method for studying complex flow phenomena. However, accurately extracting the flow structure from complex flow fields and deeply studying its underlying mechanisms remains challenging. The vast majority of information contained in complex fluid motion resides in high-dimensional data. While this data provides rich and detailed information, the increasing dimensionality presents greater challenges for subsequent data processing. Therefore, while extracting important features from the data, it is necessary to perform mode reduction processing to remove useless information and improve data processing efficiency. Modal decomposition (MDD) models are a convenient and efficient computational mechanism that decomposes and reconstructs complex flow field data obtained from unsteady calculations, allowing for analysis and research in a low-dimensional representation. Simultaneously, based on the decomposed modes, the main motion patterns in complex flows can be studied, thereby elucidating the mechanism of unstable operation of pumps and turbines. This helps analyze the coupling relationships between multiple physical quantities in fluid motion and improves the understanding of complex flow processes. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes an analysis method for complex flow fields in water pump turbines. Based on flow field modal decomposition, it analyzes and studies unstable flow phenomena during the operation of water pump turbines, analyzes numerical results, decomposes and reconstructs the transient complex flow field of water pump turbines, studies the spatiotemporal evolution characteristics of the flow field structure in a low-dimensional form, explores the formation mechanism of unstable flow characteristics in water pump turbines, and explores methods to improve unstable flow.

[0005] This invention is achieved through the following technical solution:

[0006] An analysis method for complex flow fields in water pump turbines: The method specifically includes the following steps:

[0007] Step 1: Data preparation and preprocessing; The three-dimensional or two-dimensional flow field data obtained from the large eddy simulation calculation of the pump and turbine operating conditions during pump-turbine operation are sorted according to the time dimension of the runner operation to form a data matrix.

[0008] Step 2: Use the POD method to reduce the order of the flow field data from Step 1, removing high-dimensional and complex data; replace it with low-dimensional data; construct a data matrix, perform singular value decomposition, calculate POD modes and time coefficients, and sort them according to the energy magnitude of each mode;

[0009] Step 3: By applying the linear hypothesis v i+1 Represented as Av i The relationship is used to find an approximate matrix to replace the high-dimensional matrix A using the DMD method, thereby achieving order reduction. Then, its eigenvalues ​​and eigenvectors are calculated, sorted by the size of the eigenvalues, and the DMD modes are further calculated.

[0010] Step 4: Perform modal energy analysis, analyze the eigenvalues ​​of POD and DMD to evaluate the energy contribution of each mode, and determine the dominant mode;

[0011] Step 5: Simplify the flow field by reorganizing the flow field structure by retaining the first few major modes with higher energy; perform transient error analysis of the flow field reconstruction.

[0012] Step 6: Analyze the formation mechanism of the unsteady flow characteristics of the pump turbine based on the modal decomposition results;

[0013] Step 7: Based on the analysis results, determine the characteristics of the unstable modes to provide guidance for unit optimization design and flow field control, and reduce the computational burden.

[0014] Further, in step 1, the data matrix is ​​specifically:

[0015]

[0016] In this matrix, each row corresponds to m data nodes in the selected region's internal flow field, while the columns represent the time-series N. Here, x1 represents the first point captured in the spatial dimension. m This represents the last point captured in the spatial dimension, while t1 is the initial time of the time series. N This represents the end of the time series. u(x1,t1) represents the velocity value at the first node of the initial time, while u(x... m ,t N ) represents the velocity value at node m at time N; thus forming the velocity field structure of the entire plane.

[0017] Data from the result files generated at different times are extracted and arranged into the matrix form described above, which is then used for subsequent mode decomposition processing.

[0018] Furthermore, in step 2, N transient velocity fields are selected, and the instantaneous velocity is decomposed into average value and pulsation quantity:

[0019]

[0020] Calculate the time-averaged flow field using velocity field data The calculated time-averaged flow field is also known as the 0th-order mode of the POD, representing the flow structure that does not evolve with time. Then, the instantaneous velocity matrix u, composed of the potential velocities at different points on the cross section, is used. i (x,t) minus the time-averaged flow field matrix Obtain the pulsating velocity matrix u′ at different times i (x,t);

[0021] Reconstruct the pulsating velocity matrix u′i (x,t), reduce the order of the velocity fluctuation by using the first few orders of the few POD modes u j (x) Time-dependent modal coefficients a j (t i The product of ) is represented as:

[0022]

[0023] Based on the selected N transient velocity fields, a set of fluctuating velocity fields at N time points is formed, resulting in the time-varying velocity field matrix U′(x,t):

[0024]

[0025] The velocity fluctuation matrix described above is decomposed into three distinct matrices based on the SVD method, namely U′(x,t)=BSV T Matrix, where B∈R m×n , S∈R n×n V∈R n×n B is the spatial mode matrix, S is a rectangular diagonal matrix composed of singular values ​​arranged in descending order, and V is the construction mode matrix.

[0026] Solve for the time coefficient: a = S·V T ;

[0027] Calculate the modal energy, i.e., the eigenvalue λ, of each order. j :λ j =S j 2

[0028] By retaining the first few high-energy modes to reorganize the flow field structure, the flow field is simplified, and then the main structural features of the flow field are analyzed; the final spatial mode B of the POD is obtained. j (x) and time coefficient a j The reconstructed velocity field jointly represented by (t):

[0029]

[0030] Furthermore, in step 3, the number of time sampling points is N, and the number of spatial sampling points is m; let there be two snapshots v i With v i+1 The time interval is Δt, and by assuming linearity v i+1 It can be represented as Av i , A∈R m×m ;

[0031] Similar to the POD processing, the calculated velocity matrix is ​​substituted into the DMD processing; that is, the DMD algorithm finds an approximate matrix to replace the high-dimensional matrix A, achieving order reduction. This order reduction process can be achieved through v i Obtained by performing singular value decomposition;

[0032]

[0033] v i =U∑W T

[0034]

[0035] The above singular value decomposition, U T U = I, Σ is a diagonal matrix whose diagonal elements are arranged in descending order; a low-dimensional approximation matrix is ​​used. Approximating A to the limit; simultaneously approximating the low-dimensional matrix Perform eigenvalue decomposition. The eigenvalues ​​of are equal to the eigenvalues ​​of A, while the eigenvectors of A are given by the modes:

[0036]

[0037] The modes of dynamic modes are:

[0038] q = v i+1 WΣ -1 m

[0039] The decay rate and frequency of the modal exponent are represented by the real and imaginary parts of the logarithm of the eigenvalues:

[0040] w=Re(ln(λ i ) / Δt)

[0041] f=Im(ln(λ i ) / Δt) / (2π)

[0042] The initial value matrix b corresponding to the DMD mode is calculated as follows:

[0043] q·b=v x1

[0044] Thus, the original flow field is reconstructed, in which To store the Vandermonde matrix with varying eigenvalues:

[0045]

[0046] Furthermore, in step 4, based on the POD mode obtained in step 2 and the DMD mode obtained in step 3, the energy proportion of each mode is calculated to determine the main mode that makes a significant contribution to the flow field characteristics.

[0047] Furthermore, in step 5, the main modes identified in step 4 are used to reconstruct the flow field, and the errors of the reconstructed smoothness and the original smoothness are compared. The distribution of the errors in the flow field is analyzed, and problem areas in the reconstruction are identified.

[0048] Furthermore, in step 6, the spatial performance characteristics of each mode are analyzed, the modal characteristics are combined with physical quantities, the complex flow field and disturbance factors are analyzed, and the key factors leading to instability are identified by combining frequency domain dominant frequency analysis.

[0049] An analysis system for complex flow fields in water pump turbines:

[0050] The analysis system includes a preprocessing module, a POD module, a DMD module, an analysis module, and an optimization module;

[0051] The preprocessing module prepares and preprocesses the data; it sorts the three-dimensional or two-dimensional flow field data obtained from the pump operating conditions and the unsteady calculation of the turbine operating conditions during pump-turbine operation into a data matrix according to the time dimension of the turbine runner operation.

[0052] The POD module uses the POD method to reduce the order of the flow field data in the preprocessing module, removing high-dimensional and complex data; it restores and replaces the data with low-dimensional data; it sorts the data according to the energy magnitude of each mode, constructs a data matrix, calculates and removes the mean field; it performs singular value decomposition, and calculates the POD modes and time coefficients.

[0053] The DMD module uses the DMD method to find an approximate matrix to replace the high-dimensional matrix, thereby achieving order reduction. It also calculates the eigenvalues ​​and eigenvectors, sorts them according to the size of the eigenvalues, and further calculates the DMD modes.

[0054] The analysis module performs modal energy analysis, analyzes the eigenvalues ​​of POD and DMD to evaluate the energy contribution of each mode, and determines the main modes; it reorganizes the flow field structure by retaining the first few main modes with higher energy to simplify the flow field; it performs transient error analysis of flow field reconstruction; and it analyzes the formation mechanism of unstable flow characteristics of pump turbine based on the modal decomposition results.

[0055] The optimization module provides guidance for unit optimization design and flow field control based on the analysis results, reducing the computational burden.

[0056] An electronic device includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the above method.

[0057] A computer-readable storage medium for storing computer instructions that, when executed by a processor, implement the steps of the above-described method.

[0058] Beneficial effects of the invention

[0059] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0060] (1) In terms of calculation method: The large eddy simulation is used for calculation. Compared with the Reynolds time-averaged model currently used, it can capture and collect the unsteady motion characteristics of the flow field. It can especially depict complex flows such as turbulence in more detail and more vividly represent the information of pulsating motion.

[0061] (2) In terms of flow field analysis: Two processing methods, intrinsic orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are used to reconstruct the complex flow field by reducing its order. This allows for the study of the spatiotemporal evolution of the main structure of the pump turbine flow field in a low-dimensional form, which is more intuitive and effective. Based on the energy of each mode arranged from largest to smallest, the first few modes are identified as having the main flow characteristics of the flow field. Combined with the dominant frequency analysis, the main modes that cause unstable flow can be identified, the dominant features and behaviors in the flow field can be extracted, the instability of the flow field can be analyzed, and then the flow field can be reconstructed based on the first few modes to better understand the essence of fluid flow.

[0062] (3) In principle: Currently, rich flow field information can be obtained through numerical calculations and PIV technology. However, due to the complex and variable operating conditions of water pumps and turbines, and the coupling of various nonlinear factors, there are still certain limitations in accurately extracting complex flow field structures and studying the intrinsic flow mechanism. Therefore, constructing a reduced-order model based on mathematical principles to perform modal decomposition of the flow field is an important research method. The establishment of a reduced-order model can simplify the complex flow, obtain the main characteristics of the complex flow, improve the understanding of the instability of the flow field during the operation of fluid machinery, and help to more accurately predict and control the behavior of the flow field. Attached Figure Description

[0063] Figure 1 This is a flowchart of the method for analyzing the unsteady flow characteristics of a water pump turbine based on modal decomposition, as described in this invention.

[0064] Figure 2 This is a schematic diagram of the modal processing method in this invention;

[0065] Figure 3 (a) is the energy percentage EW of each of the first 20 POD modes after POD decomposition of the internal flow field under pump conditions in this invention. Figure 3 (b) is the sum of the energy proportions of the first 20 modes after POD decomposition of the internal flow field under pump conditions in this invention;

[0066] Figure 4These are the POD reconstructed flow field and modal characteristic diagrams of this invention; where (a) is the original flow field, (b) is the reconstructed flow field, (c) is the average flow field, (d) is the first-order mode, (e) is the second-order mode, and (f) is the third-order mode.

[0067] Figure 5 This is the Fourier spectrum analysis diagram of the POD time coefficient in this invention;

[0068] Figure 6 (a) is the energy percentage EW of each of the first 20 DMD modes after DMD decomposition of the internal flow field under pump conditions in this invention. Figure 6 (b) The sum of the energy proportions of the first 20 modes after DMD decomposition of the internal flow field under pump conditions in this invention: TEW;

[0069] Figure 7 This is a modal stability judgment diagram of DMD in this invention, where (a) is the distribution of characteristic roots and (b) is the relationship between attenuation rate and frequency.

[0070] Figure 8 These are the characteristic diagrams of the reconstructed flow field and various modes in the DMD of this invention; where (a) is the original flow field, (b) is the reconstructed flow field, (c) is the first-order mode, (d) is the second-order mode, (e) is the third-order mode, and (f) is the third-order conjugate mode.

[0071] Figure 9 (a) shows the relationship between DMD mode frequency and energy in this invention. Figure 9 (b) shows the relationship between the DMD modal frequency and amplitude in this invention;

[0072] Figure 10 This is a graph showing the evolution of the DMD modal time coefficients over time in this invention;

[0073] Figure 11 These are comparison diagrams of the original flow field and the reconstructed flow field under pump conditions in this invention; where (a) is the reconstructed flow field under POD conditions, (b) is the original flow field, and (c) is the reconstructed flow field under DMD conditions.

[0074] Figure 12 This is the flow field reconstruction error cloud map based on modal decomposition under the pump operating condition in this invention; wherein

[0075] (a) Flow field reconstruction error using POD, (b) Flow field reconstruction error using DMD;

[0076] Figure 13 This is the transient error diagram of flow field reconstruction based on modal decomposition under the pump operating condition in this invention. Detailed Implementation

[0077] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0078] Unless otherwise specified, the experimental methods used in the following examples are conventional methods. Unless otherwise specified, the materials, reagents, methods, and instruments used are all conventional materials, reagents, methods, and instruments in the art, and can be obtained commercially by those skilled in the art.

[0079] This invention performs modal decomposition based on flow field data, including but not limited to velocity, pressure, and density, obtained from large eddy simulation calculations. It employs two processing methods, intrinsic orthogonal decomposition (POD) and dynamic mode decomposition (DMD), to perform order reduction and reconstruction, thereby analyzing the generation mechanism of unstable flow during unit operation.

[0080] An analysis method for complex flow fields in water pump turbines, the method specifically includes the following steps:

[0081] Step 1: Data preparation and preprocessing;

[0082] The time-series flow field data saved during the unsteady calculations of pump and turbine operating conditions are imported into the POD and DMD processing and analysis process. The processing methods of these two methods are used to reduce the order of the flow field data, remove high-dimensional complex data, and restore and replace it with low-dimensional data. At the same time, the main structure of the flow field is analyzed according to the specific manifestation of each mode. The main structure of the flow field is analyzed based on the mainstream structure of the flow motion. In addition, the dominant frequency of different modes can be analyzed to obtain the inducing factors of flow instability, thus providing data support for improvement and optimization.

[0083] As attached Figure 1 As shown in the processing flow, the three-dimensional or two-dimensional flow field data obtained from the unsteady calculation of the pump turbine under pump and turbine operating conditions are sorted according to the time dimension of the runner operation to form a data matrix.

[0084]

[0085] The rows of the matrix correspond to the number of internal flow field data nodes in the selected region, which is m. The columns of the matrix represent the time dimension sequence N (consistent with the spatiotemporal sampling N), where x1 is the first point intercepted in the spatial dimension, for example, selecting the first grid node of a plane. Similarly, x... m This refers to the last point selected in the spatial dimension, such as the last grid node on a plane. t1 is the initial time of the time series, and t...N This represents the end of the time series. u(x1,t1) represents the velocity value at the first node of the initial time, while u(x... m ,t N This represents the velocity value at node m at time N. This constitutes the velocity field structure of the entire plane.

[0086] Data from the result files generated at different times are extracted and arranged into the matrix form described above, which is then used for subsequent mode decomposition processing.

[0087] Step 2: Eigenorthogonal decomposition (POD),

[0088] The POD method is used to reduce the order of flow field data and remove high-dimensional and complex data; low-dimensional data is used for restoration and replacement; and the main flow structure is determined by sorting the energy of each mode.

[0089] Construct the data matrix; calculate and remove the mean field; perform singular value decomposition; calculate the POD modes and time coefficients;

[0090] POD (Positive Decomposition of Flow Parameters) can decompose data into spatially orthogonal modes, sorting them according to their energy magnitude to determine the main flow structure. Its core idea is to start with a set of spatial data (physical quantities at grid points) arranged in a time series, and use orthogonal decomposition to represent the fluctuating data using a finite product of orthogonal bases and mode coefficients. Higher-order data are represented using a finite number of basis quantities. Taking transient velocity fields as an example: selecting N transient velocity fields, the instantaneous velocity is decomposed into average values ​​and fluctuating quantities.

[0091]

[0092] Calculate the time-averaged flow field using velocity field data This represents a flow structure that does not evolve over time. The calculated time-averaged flow field is also known as the 0th-order mode of the POD, representing a flow structure that does not evolve over time. Then, the instantaneous velocity matrix u, composed of the potential velocities at different points on the cross section, is used. i (x,t) minus the time-averaged flow field matrix Obtain the pulsating velocity matrix u′ at different times i (x,t).

[0093] Reconstruct the pulsating velocity matrix u′ i (x,t), reduce the order of the velocity fluctuation by using the first few orders of the few POD modes u j (x) Time-dependent modal coefficients a j (t i The product of ) is represented as:

[0094]

[0095] Based on the selected N transient velocity fields, a set of fluctuating velocity fields at N time points is formed, resulting in the time-varying velocity field matrix U′(x,t):

[0096]

[0097] The velocity fluctuation matrix described above is decomposed into three distinct matrices based on the SVD method, namely U′(x,t)=BSV T Matrix, where B∈R m×n , S∈R n×n V∈R n×n B is the spatial mode matrix, S is a rectangular diagonal matrix composed of singular values ​​arranged in descending order, and V is the construction mode matrix.

[0098] Solve for the time coefficient: a = S·V T ;

[0099] Calculate the modal energy, i.e., the eigenvalue λ, of each order. j :λ j =S j 2

[0100] At the same time, according to the appendix Figure 2 As shown, the original flow field velocity matrix is ​​decomposed into a spatial mode matrix and a time coefficient matrix. Therefore, the flow field structure can be reorganized by retaining the first few modes with higher energy, thereby simplifying the flow field and allowing for the analysis of its main structural features. The final obtained spatial mode B of the POD... j (x) and time coefficient a j The reconstructed velocity field jointly represented by (t):

[0101]

[0102] Taking the water pump operating condition as an example, see attached Figure 3 The energy percentage (EW) of each of the first 20 POD modes after modal decomposition of the velocity field in the axial rotor region calculated using the large eddy model is shown, as well as the sum of the energy percentages of the first 20 modes (TEW).

[0103] Step 3: Dynamic Mode Decomposition (DMD)

[0104] By linear hypothesis v i+1 Represented as Av i The relational DMD method is used to describe the changes of various physical quantities over time and extract the characteristic frequencies of the data; it finds an approximate matrix to replace the high-dimensional matrix A to achieve order reduction.

[0105] Perform singular value decomposition on the data matrix; calculate its eigenvalues ​​and eigenvectors; calculate the DMD modes;

[0106] DMD describes the changes of various physical quantities over time, extracts the characteristic frequencies of the data, and thus observes the influence of flow characteristics at different frequencies on the flow field. Its core idea lies in defining a spatiotemporal signal U. tx Here, x represents the data at the signal acquisition point, and t represents the change in the entire signal over time. Again, taking the velocity field as an example, the number of time sampling points (time dimension sequence) is N, and the number of spatial sampling points is m.

[0107] Suppose there are two snapshots v i With v i+1 The time interval is Δt, and by assuming linearity v i+1 It can be represented as Av i , A∈R m×m The DMD algorithm finds an approximate matrix to replace the high-dimensional matrix A, achieving order reduction. This order reduction process can be achieved through v i The result is obtained by performing singular value decomposition. Based on the linear assumption, the flow field structure at the next moment can be effectively predicted based on the existing flow field, thus realizing the visualization of flow field prediction.

[0108] Similar to the POD processing, the calculated velocity matrix is ​​substituted into the DMD processing. That is, the DMD algorithm finds an approximate matrix to replace the high-dimensional matrix A, achieving order reduction. This order reduction process can be achieved through v i It is obtained by performing singular value decomposition.

[0109]

[0110] v i =U∑W T

[0111]

[0112] The above singular value decomposition, U T U = I, where Σ is a diagonal matrix with its diagonal elements arranged in descending order. A low-dimensional approximation matrix is ​​used. The limit approximation of A is achieved. Simultaneously, the low-dimensional approximation matrix is ​​appro Perform eigenvalue decomposition. The eigenvalues ​​of are equal to the eigenvalues ​​of A, while the eigenvectors of A are given by the modes:

[0113]

[0114] The modes of dynamic modes are:

[0115] q = v i+1 WΣ -1 m

[0116] The decay rate and frequency of the modal exponent are represented by the real and imaginary parts of the logarithm of the eigenvalues:

[0117] w=Re(ln(λ i ) / Δt)

[0118] f=Im(ln(λ i ) / Δt) / (2π)

[0119] The initial value matrix b corresponding to the DMD mode is calculated as follows:

[0120] q·b=v x1

[0121] Thus, the original flow field is reconstructed, in which To store the Vandermonde matrix with varying eigenvalues:

[0122]

[0123] The transient file obtained from the above pump operating condition calculations is used for dynamic mode decomposition using DMD to obtain the attached... Figure 6 The velocity field of the axial rotor region shown is obtained by modal decomposition, which yields the energy percentage (EW) of each of the first 20 DMD modes and the sum of the energy percentages of the first 20 modes (TEW).

[0124] Step 4: Perform modal energy analysis; analyze the eigenvalues ​​of POD and DMD to assess the energy contribution of each mode and determine the dominant modes;

[0125] Based on the POD mode obtained in step 2 and the DMD mode obtained in step 3, the energy proportion of each mode is calculated to determine the main mode that makes a significant contribution to the flow field characteristics.

[0126] Analyzing the energy proportions of each mode obtained from the pod decomposition method reveals the dominant flow structure. The energy distribution in the figure clearly shows that the first-order mode has the highest energy proportion, with the proportions of each subsequent order gradually decreasing. Notably, the energy decrease is relatively large for the first few orders, while the energy proportions of higher-order modes become very small and tend to stabilize with increasing order. Overall, the first 10 modes have a large energy proportion, indicating that within a certain order range, the flow information can be largely reconstructed using lower-order modes. Furthermore, the highest energy proportion of the first-order mode suggests the existence of a dominant flow structure, which may be related to the main vortices or flow characteristics in the system. The decreasing energy proportions of higher-order modes with increasing order indicate that these higher-order modes contribute relatively little to the overall flow.

[0127] Therefore, when reducing the order of data and simplifying the flow field, the flow information can be effectively reconstructed by retaining the first few modes, thereby reducing the computational burden. That is, by selecting an appropriate modal order, the main flow characteristics can be preserved while reducing computational complexity.

[0128] Based on the energy proportions of each mode mentioned above, and combined with the specific manifestations, pod mode analysis was performed: the first 20 modes were used for mode reduction and reconstruction, as shown in the appendix. Figure 4 The description shows the original flow field, the average flow field obtained after POD decomposition, the reconstructed flow field of the first 20 modes, and the flow field distribution of each mode. It can be considered that the reconstructed flow field is formed by superimposing each mode onto the average flow field, thus reproducing the distribution characteristics of the original flow field. Based on the above modal information distribution, it is clear that the water flow is drawn into the impeller from the tailpipe and moves with the impeller's rotation. There is a certain degree of fluctuation within the impeller region. When entering the guide vane region, the presence of the guide vanes has a significant impact on the liquid flow, resulting in obvious flow separation and vortex pulsation distribution. In the first few modes, it is clear that the flow structure in the guide vane region has a considerable influence on the flow field, playing a dominant role. In the first three modes, the velocity field exhibits a significant pulsation distribution. In the guide vane region, the modal data shows alternating positive and negative values, revealing the influence caused by dynamic and static interference. The presence of the guide vanes changes the flow direction and velocity distribution, making the pulsation phenomenon more pronounced. This dynamic change may be related to the complexity of the interaction between the guide vanes and the water flow. In addition, there are local pulsations on the suction side of the blade. The generation of these pulsations is closely related to the flow separation of the fluid entering the impeller and acting on the suction side. At the same time, local pulsation effects also appear on the pressure side at the impeller inlet, which is consistent with the cyclic backflow at that location.

[0129] Combined with appendix Figure 5 Fourier spectrum analysis of the POD time coefficient can identify fluctuations in influencing factors. Analyzing the POD time coefficients of the decomposed modal data reveals the contribution of each mode to the overall flow field, thus deepening the understanding of complex flow conditions. The dominant frequencies of the first five modes are concentrated in the low-frequency range, with certain differences in their specific amplitude values, indicating varying degrees of dominance in the flow field. As the mode order increases, the complexity of the flow involved also increases. Simultaneously, spectrum analysis can be compared with fluctuations in experimentally acquired data to further confirm the emergence of instability factors, thereby enabling optimization of the problem.

[0130] The POD method can efficiently extract the main flow structure in a flow field, but it cannot determine the stability of the modes. In contrast, the DMD method can extract the main structure of the flow field, directly obtain the modes and their corresponding frequencies, and also determine their stability.

[0131] Consistent with POD decomposition, DMD energy analysis was performed first. In DMD modal decomposition, the first-order energy still accounts for the highest proportion. As the order increases, the proportion of each order's energy gradually decreases, with a relatively large decrease. The difference is that the proportion of the first-order mode in DMD decomposition is extremely high compared to POD, indicating that the first-order mode in DMD has a much greater impact on the flow field structure than other modes, possessing the main characteristics of the flow field's motion structure.

[0132] The velocity field will be obtained after DMD decomposition. Figure 7 The distribution of eigenvalues ​​and the relationship between attenuation rate and frequency are shown. Combined with... Figure 7 Determining the stability of the DMD. The left figure depicts the distribution of eigenvalues ​​corresponding to each mode on a coordinate system with the real part as the horizontal axis and the imaginary part as the vertical axis. The number of discrete points in the figure corresponds one-to-one with the flow field snapshots. Using the unit circle as a reference, it is found that the discrete points are basically located on or inside the unit circle, indicating that each mode is stable. The discrete points in the right figure correspond to the distribution of the center point in the left figure. The attenuation rate is less than zero, indicating that the mode coefficients are convergent. The consistency with points on or inside the unit circle also indicates that the mode is stable. The frequency of the first-order mode is zero, and it is located on the unit circle, indicating that the first-order mode represents the time-averaged mode of the flow field and does not change with time, thus confirming the characteristic phenomenon of the highest energy corresponding to the first-order mode.

[0133] The reconstructed flow fields of the first 20 modes and the flow field distributions of each mode are obtained from the instantaneous velocity field decomposition by DMD, as shown in the attached figure. Figure 8 As shown, observations comparing the characteristics of the reconstructed flow field with the original flow field indicate that the flow field reconstructed based on the DMD modal decomposition method is more detailed and fully reproduces the complex flow in the guide vane and impeller regions. It is particularly clear in describing turbulent vortices and is more suitable for capturing the fine structure of the flow field. Since the DMD method describes the evolution of various physical quantities over time at the dynamic level, in-depth research on the manifestation of each mode helps to gain a deeper understanding of the generation of vortices and the mechanism and characteristics of their influence on the flow field.

[0134] According to the appendix Figure 8Modal analysis reveals that the first-order mode exhibits negative values, representing the time-averaged flow outcome, and has the highest influence on the flow field among all modes. The second-order mode focuses on describing the pulsating flow in the guide vane region, especially between the moving and fixed guide vanes, where its energy contribution is significantly higher than that of later modes, indicating that pulsation in the guide vane region is the primary characteristic of flow instability. Starting with the third-order mode, adjacent modes exhibit the phenomenon of having the same energy proportion. These adjacent modes share the same structure, indicating that they are conjugate modes, meaning their eigenvalues ​​are conjugate. Since each mode is extracted based on the real part of the eigenvalues, conjugate modes can be considered as the same mode. In the third-order mode, the characteristic scale is relatively smaller. Further observation of the modal evolution reveals pulsating clusters on the suction side of the impeller blades. As the number of modes increases, the flow field characteristics gradually become more complete. By comparing the evolution of the modal structure, we can gain a deeper understanding of the differences between POD and DMD in extracting flow field characteristics. This comparative analysis of modal structure evolution helps to guide the selection of appropriate modal decomposition methods and improves the overall understanding of the flow field reconstruction process.

[0135] Appendix Figure 9 These are the modes arranged according to their energy and amplitude. The energy of a mode is defined as the sum of the squares of the amplitude at each moment and point. The frequency-energy relationship diagram clearly shows that the first-order mode has extremely high energy, the second-order mode has slightly lower energy but is of the same order of magnitude, while the remaining modes have lower energy, gradually decreasing and stabilizing. The third-order mode has a frequency of 9fn, which is the frequency at which the blades pass through, indicating that the rotor's operation dominates the flow field. In the amplitude arrangement, the first and second-order modes do not have the largest amplitudes; the largest amplitude is concentrated in the third-order mode, followed closely by the second-order mode. The first-order mode has the fifth largest amplitude. The different forms of energy and amplitude representation indicate that the characteristics of each mode differ depending on the arrangement method. This shows that different standards for mode arrangement result in different representations. Choosing an appropriate classification standard requires consideration of specific calculation conditions to ensure the accuracy of the DMD method.

[0136] Appendix Figure 10The time coefficients for the first five modes of the DMD are shown to change over time. Since the first mode has a frequency of zero, representing the average state of the flow field and having the highest energy proportion, its time coefficient remains the largest and stable, showing almost no change. The second mode has a significant impact, with a particularly large initial value, which decays and approaches a steady state after a period of time. The third mode has the strongest initial impact, then gradually oscillates and decays, its value approaching zero, and its impact almost disappears. The fourth mode is similar to the fifth, with a relatively strong initial impact, but its subsequent impact gradually weakens. Based on the time coefficient behavior of the first five modes, it can be determined that the degree of influence of a mode at different time periods is related to the modal composition proportion of the flow field at a certain moment. Therefore, research on different modes helps in analyzing the factors and solutions for flow instability.

[0137] Step 5: Flow field reconstruction and error analysis: The flow field structure is reconstructed by retaining the first few modes with higher energy to simplify the flow field; transient error analysis of the flow field reconstruction is performed to show the changes in the flow field reproduction of POD and DMD over time;

[0138] In summary, this analysis focuses on the unsteady flow characteristics of a pump-turbine based on the flow field modal decomposition method. By analyzing the characteristics of each mode, the instability factors of the flow can be further identified, thereby quickly identifying the composition of the flow field, analyzing the coupling relationships between multiple physical quantities in fluid motion, and improving the understanding of complex flow processes. Finally, to further observe the reconstruction effects of the POD and DMD modal decomposition methods on the flow field, the original flow field of the pump operating condition was compared with the reconstructed flow fields of the two methods. The applicability of modal decomposition was confirmed by comparing the reconstruction effects, and the superiority of the two methods was also compared.

[0139] As attached Figure 11 As shown in the figure, a comparison reveals that both POD and DMD methods can effectively reproduce the main characteristics of the flow field, especially in the blade region, where significant flow pulsation is observed. Furthermore, according to the attached... Figure 12 As can be seen from the error contour plots compared to the original flow field, the main error in the reconstruction lies in the characterization of the flow field in the guide vane region. POD has some shortcomings in reconstructing certain details, possibly due to the large number of complex variables involved in the vortex area, resulting in the loss of some minor data during order reduction. In contrast, DMD, which also uses the first 20 modes for flow field reconstruction, shows a more inadequate characterization, mainly at the runner outlet and guide vane. This is because the flow in these regions is extremely complex, exhibiting multi-frequency structures. For DMD decomposition on a time scale, using only the first few modes cannot accurately reproduce the original flow field. However, the overall error is not significant, and more modes are needed for reconstruction.

[0140] To better confirm the error situation of flow field processing using mode decomposition, an additional... Figure 13 The transient error in the flow field reconstruction shown represents the change over time in the flow field reconstruction performed by POD and DMD. The error is expressed as the absolute average of the velocity errors. In the POD representation, there are significant error fluctuations at the beginning and end, indicating numerical fluctuations in the flow field at these points. Furthermore, since the first 20 modes are selected for reconstruction, some early and later high-proportion modes may be ignored, confirming the instability of the flow in this region. In contrast, the DMD shows a larger calculation error in the initial stage, mainly due to the complex flow field and numerous pulsating structures, leading to some deviation in the initial reconstruction. The limited number of modes is not representative. However, as time increases, the flow fluctuation range becomes smaller, and the reconstructed flow field error decreases until it stabilizes.

[0141] The flow field is reconstructed using the main modes identified in step 4. The error between the reconstructed flow field and the original flow field is compared, the distribution of the error in the flow field is analyzed, and the problem areas in the reconstruction are identified.

[0142] Step 6: Analyze the formation mechanism of unstable flow characteristics of water pump turbine through modal decomposition results; analyze the spatial performance characteristics of each mode, combine modal characteristics with physical quantities, analyze complex flow fields and disturbance factors, and identify key factors leading to instability by combining frequency domain dominant frequency analysis.

[0143] Based on the POD mode, as can be seen from the energy distribution above, the low-order mode dominates the main information of the flow field, while the high-order mode reflects local subtle changes. The characteristic phenomena in the guide vane region, the suction side of the blade, and the runner inlet indicate that factors such as dynamic-static interference, flow separation, and swirling backflow lead to instability.

[0144] Based on DMD modes, the first-order mode has an extremely high energy proportion and zero frequency, the second-order mode focuses on pulsation in the guide vane region, and the third-order and conjugate modes have pulsating clusters on the suction side of the runner blades. As the order increases, the characteristic scale decreases, and different standards are used to represent different modes. The time coefficient further reflects the influence of each mode on the instability characteristics of the flow field at different times. Based on the above two modal decomposition methods, it is confirmed that the complex vortex flow caused by flow separation in the guide vane region and the pulsating backflow at the runner inlet are the key factors of instability during unit operation.

[0145] Step 7: Based on the analysis results, determine the characteristics of the unstable modes to provide guidance for unit optimization design and flow field control, and reduce the computational burden;

[0146] By analyzing modal characteristics, the turbine unit can be optimized by improving blade shape, angle, and number, and by refining its layout. Furthermore, the stability of the flow field can be controlled by adjusting pump speed and flow rate, and optimizing turbine load. To confirm flow instability, a novel auxiliary analysis method is proposed, along with improvement schemes.

[0147] An analysis system for complex flow fields in water pump turbines:

[0148] The analysis system includes a preprocessing module, a POD module, a DMD module, an analysis module, and an optimization module;

[0149] The preprocessing module prepares and preprocesses the data; it sorts the three-dimensional or two-dimensional flow field data obtained from the pump operating conditions and the unsteady calculation of the turbine operating conditions during pump-turbine operation into a data matrix according to the time dimension of the turbine runner operation.

[0150] The POD module uses the POD method to reduce the order of the flow field data in the preprocessing module, removing high-dimensional and complex data; it restores and replaces the data with low-dimensional data; it sorts the data according to the energy magnitude of each mode, constructs a data matrix, calculates and removes the mean field; it performs singular value decomposition, and calculates the POD modes and time coefficients.

[0151] The DMD module uses the DMD method to find an approximate matrix to replace the high-dimensional matrix, thereby achieving order reduction. It also calculates the eigenvalues ​​and eigenvectors, sorts them according to the size of the eigenvalues, and further calculates the DMD modes.

[0152] The analysis module performs modal energy analysis, analyzes the eigenvalues ​​of POD and DMD to evaluate the energy contribution of each mode, and determines the main modes; it reorganizes the flow field structure by retaining the first few main modes with higher energy to simplify the flow field; it performs transient error analysis of the flow field reconstruction; and it analyzes the formation mechanism of the unstable flow characteristics of the pump turbine based on the modal decomposition results.

[0153] The optimization module provides guidance for unit optimization design and flow field control based on the analysis results, reducing the computational burden.

[0154] An electronic device includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the above method.

[0155] A computer-readable storage medium for storing computer instructions that, when executed by a processor, implement the steps of the above-described method.

[0156] The memory in the embodiments of this application can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDR SDRAM), enhanced synchronous DRAM (ESDRAM), synchronous linked DRAM (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory of the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0157] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired means such as coaxial cable, optical fiber, digital subscriber line, DSL, or wireless means such as infrared, wireless, microwave, etc. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium such as a floppy disk, hard disk, magnetic tape; an optical medium such as a high-density digital video disc, DVD; or a semiconductor medium such as a solid-state disk, SSD, etc.

[0158] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0159] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as execution by a hardware decoding processor, or as execution by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0160] The above provides a detailed description of the method for analyzing the unsteady flow characteristics of a pump-turbine based on modal decomposition proposed in this invention. The principles and implementation methods of this invention have been explained. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for analyzing the unsteady flow characteristics of a pump-turbine based on mode decomposition, characterized in that: The method specifically includes the following steps: Step 1: Data preparation and preprocessing; The three-dimensional or two-dimensional flow field data obtained from the large eddy simulation calculation of the pump and turbine operating conditions during pump-turbine operation are sorted according to the time dimension of the runner operation to form a data matrix. Step 2: Use the POD method to reduce the order of the flow field data from Step 1, removing high-dimensional and complex data; replace it with low-dimensional data; construct a data matrix, perform singular value decomposition, calculate POD modes and time coefficients, and sort them according to the energy magnitude of each mode; Step 3: By applying the linear hypothesis v i+1 Represented as Av i The relationship is used to find an approximate matrix to replace the high-dimensional matrix A using the DMD method, thereby achieving order reduction. Then, its eigenvalues ​​and eigenvectors are calculated, sorted by the size of the eigenvalues, and the DMD modes are further calculated. Step 4: Perform modal energy analysis, analyze the eigenvalues ​​of POD and DMD to evaluate the energy contribution of each mode, and determine the dominant mode; Step 5: Simplify the flow field by reorganizing the flow field structure by retaining the first few major modes with higher energy; perform transient error analysis of the flow field reconstruction. Step 6: Analyze the formation mechanism of the unsteady flow characteristics of the pump turbine based on the modal decomposition results; Step 7: Based on the analysis results, determine the characteristics of the unstable modes to provide guidance for unit optimization design and flow field control, and reduce the computational burden.

2. The analytical method according to claim 1, characterized in that: In step 1, the data matrix is ​​specifically: In this matrix, each row corresponds to m data nodes in the selected region's internal flow field, while the columns represent the time-series N. Here, x1 represents the first point captured in the spatial dimension. m This represents the last point captured in the spatial dimension, while t1 is the initial time of the time series. N This represents the end of the time series. u(x1,t1) represents the velocity value at the first node of the initial time, while u(x... m ,t N ) represents the velocity value at node m at time N; thus forming the velocity field structure of the entire plane. Data from the result files generated at different times are extracted and arranged into the matrix form described above, which is then used for subsequent mode decomposition processing.

3. The analytical method according to claim 2, characterized in that: In step 2, N transient velocity fields are selected, and the instantaneous velocity is decomposed into average value and fluctuating quantity: Calculate the time-averaged flow field using velocity field data The calculated time-averaged flow field is also known as the 0th-order mode of the POD, representing the flow structure that does not evolve with time. Then, the instantaneous velocity matrix u, composed of the potential velocities at different points on the cross section, is used. i (x,t) minus the time-averaged flow field matrix Obtain the pulsating velocity matrix u at different times i ′(x,t); Reconstruct the pulsating velocity matrix u i ′(x,t), reducing the order of the velocity fluctuations by using the first few orders of a few POD modes u j (x) Time-dependent modal coefficients a j (t i The product of ) is represented as: Based on the selected N transient velocity fields, a set of fluctuating velocity fields at N time points is formed, resulting in the time-varying velocity field matrix U′(x,t): The velocity fluctuation matrix described above is decomposed into three distinct matrices based on the SVD method, namely U′(x,t)=BSV T Matrix, where B∈R m×n , S∈R n×n , V∈R n×n ; B is the spatial mode matrix, S is a rectangular diagonal matrix composed of singular values ​​arranged in descending order, and V is the construction mode matrix; Solve for the time coefficient: a = S·V T ; Calculate the modal energy, i.e., the eigenvalue λ, of each order. j :λ j =S j 2 ; By retaining the first few high-energy modes to reorganize the flow field structure, the flow field is simplified, and then the main structural features of the flow field are analyzed; ultimately The obtained spatial mode B of POD j (x) and time coefficient a j The reconstructed velocity field jointly represented by (t):

4. The analytical method according to claim 3, characterized in that: In step 3, the number of time sampling points is N, and the number of spatial sampling points is m; let there be two snapshots v. i With v i+1 The time interval is Δt, and by assuming linearity v i+1 It can be represented as Av i , A∈R m×m ; Similar to the POD processing, the calculated velocity matrix is ​​substituted into the DMD processing; that is, the DMD algorithm finds an approximate matrix to replace the high-dimensional matrix A, achieving order reduction. This order reduction process can be achieved through v i Obtained by performing singular value decomposition; in i =U∑W T The above singular value decomposition, U T U = I, Σ is a diagonal matrix whose diagonal elements are arranged in descending order; a low-dimensional approximation matrix is ​​used. Approximating A to the limit; simultaneously approximating the low-dimensional matrix Perform eigenvalue decomposition. The eigenvalues ​​of are equal to the eigenvalues ​​of A, while the eigenvectors of A are given by the modes: The modes of dynamic modes are: q=v i+1 WΣ -1 m The decay rate and frequency of the modal exponent are represented by the real and imaginary parts of the logarithm of the eigenvalues: w=Re(ln(λ i ) / Δt) f=Im(ln(λ i ) / Δt) / (2π) The initial value matrix b corresponding to the DMD mode is calculated as follows: q·b=v x1 Thus, the original flow field is reconstructed, in which To store the Vandermonde matrix with varying eigenvalues:

5. The analytical method according to claim 4, characterized in that: In step 4, based on the POD mode obtained in step 2 and the DMD mode obtained in step 3, the energy proportion of each mode is calculated to determine the main mode that makes a significant contribution to the flow field characteristics.

6. The analytical method according to claim 5, characterized in that: In step 5, the main modes identified in step 4 are used to reconstruct the flow field. The error between the reconstructed flow field and the original flow field is compared, the distribution of the error in the flow field is analyzed, and the problem areas in the reconstruction are identified.

7. The analytical method according to claim 6, characterized in that: In step 6, the spatial performance characteristics of each mode are analyzed, the modal characteristics are combined with physical quantities, the complex flow field and disturbance factors are analyzed, and the key factors leading to instability are identified by combining frequency domain dominant frequency analysis.

8. An analysis system for performing the modal decomposition-based method for analyzing the unsteady flow characteristics of a pump-turbine as described in any one of claims 1 to 7, characterized in that: The analysis system includes a preprocessing module (computation module, which uses large eddy simulation to accurately identify instability features), a POD module, a DMD module, an analysis module, and an optimization module; The preprocessing module prepares and preprocesses the data; it sorts the three-dimensional or two-dimensional flow field data obtained from the pump operating conditions and the unsteady calculation of the turbine operating conditions during pump-turbine operation into a data matrix according to the time dimension of the turbine runner operation. The POD module uses the POD method to reduce the order of the flow field data in the preprocessing module, removing high-dimensional and complex data; it restores and replaces the data with low-dimensional data; it sorts the data according to the energy magnitude of each mode, constructs a data matrix, calculates and removes the mean field; it performs singular value decomposition, and calculates the POD modes and time coefficients. The DMD module uses the DMD method to find an approximate matrix to replace the high-dimensional matrix, thereby achieving order reduction. It also calculates the eigenvalues ​​and eigenvectors, sorts them according to the size of the eigenvalues, and further calculates the DMD modes. The analysis module performs modal energy analysis, analyzes the eigenvalues ​​of POD and DMD to evaluate the energy contribution of each mode, and determines the main modes; it reorganizes the flow field structure by retaining the first few main modes with higher energy to simplify the flow field; it performs transient error analysis of the flow field reconstruction; and it analyzes the formation mechanism of the unstable flow characteristics of the pump turbine based on the modal decomposition results. Based on the analysis results, the optimization module determines the characteristics of unstable modes, providing guidance for unit optimization design and flow field control, and reducing the computational burden.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 7.

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