Modal reduction method and system for cavitation flow field of centrifugal pump based on dynamic modal decomposition

Abstract

The present invention belongs to the technical field of centrifugal pump fault detection, and discloses a method and system for modal reduction of cavitation flow field of a centrifugal pump based on dynamic modal decomposition. The method performs three-dimensional modeling on the centrifugal pump, and uses the impeller, volute, and inlet and outlet sections of the centrifugal pump to form a flow calculation domain; performs geometric modeling in Solidworks according to the size and performs geometric processing on the flow calculation domain modeling, and then imports the geometric model constructed in Solidworks into the ICEM software to perform mesh division of the flow calculation domain, and sequentially generates meshes of various components of the centrifugal pump; imports the divided meshes into the commercial software fluent for numerical simulation to obtain simulation data; changes the inlet pressure in fluent to obtain different cavitation states. The present invention has certain significance for quickly identifying cavitation in a centrifugal pump and preventing cavitation hazards caused by vaporization, thereby preventing centrifugal pumps from malfunctioning.

Description

Technical Field

[0001] The invention belongs to the technical field of centrifugal pump fault detection, and in particular relates to a centrifugal pump cavitation flow field modal reduction method and system based on dynamic modal decomposition. Background Art

[0002] Due to the limitations of objective experimental conditions and the advancement of computer technology, computational fluid dynamics (CFD) has been increasingly widely used in the calculation and simulation of fluid machinery. A large number of numerical calculations have been made for the cavitation of centrifugal pumps, saving a lot of time and greatly improving research efficiency. Many cavitations that are difficult to observe can be combined with CFD through various optimization methods of computational simulation to improve the performance and efficiency of centrifugal pumps. Although CFD has been nearly perfected for centrifugal pump simulation, the number of grids in CFD determines the size of the spatial domain. In the research process, in order to obtain more detailed flow field information, it is very necessary to encrypt the grid. The increase in the number of grids will inevitably increase the requirements for computer performance, including processing power and memory capacity, which will lead to a significant increase in calculation time in flow field simulation and prediction. In addition, CFD mainly describes the macroscopic level of the flow field, and the microscopic research on the flow field needs to be improved.

[0003] At present, there are two typical modal decompositions: proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), both of which are data-driven modal decomposition algorithms. DMD was proposed by Professor Schmid. It is based on the decomposition of the Koopman complex system and uses the iterative Krylov technique to process time-resolved data snapshots to extract dynamic flow characteristics and decompose experimental data into dynamic modes. It has been widely studied and applied in orifice jets, open cavity flows, wakes, and wave packets. DMD can not only realize the decomposition and reconstruction of the flow field, but also obtain the dominant frequency modal characteristics of the flow field. DMD is introduced to quickly identify cavitation in centrifugal pumps and better analyze the characteristics of the flow field of centrifugal pumps. There are still few studies on DMD for centrifugal pumps, especially for the study of cavitation flow fields of centrifugal pumps. The cavitation flow field caused by centrifugal pumps shows a high degree of complexity, and the modal decomposition research on its flow field is still insufficient.

[0004] Through the above analysis, the problems and defects of the prior art are as follows: the prior art cannot more accurately analyze the flow field under cavitation state for the gas-liquid flow characteristics of centrifugal pumps. The effect of quickly identifying cavitation in centrifugal pumps and preventing cavitation damage caused by vaporization to prevent centrifugal pumps from malfunctioning is poor. Summary of the invention

[0005] In order to overcome the problems existing in the related art, the disclosed embodiments of the present invention provide a method and system for modal order reduction of centrifugal pump cavitation flow field based on dynamic modal decomposition. In order to shorten the calculation time and reduce the solution dimension of model simulation, the purpose of the present invention is to use a dynamic modal decomposition (DMD) method based on singular value decomposition (SVD Singular value decomposition) to conduct an in-depth study on the characteristics of the centrifugal pump cavitation flow field, thereby providing a new idea for the rapid order reduction of the flow field.

[0006] The technical solution is as follows: A modal reduction method for cavitation flow field of a centrifugal pump based on dynamic modal decomposition, comprising:

[0007] S1, three-dimensional modeling of the centrifugal pump, using the impeller, volute, and inlet and outlet sections of the centrifugal pump to form the flow calculation domain;

[0008] S2, according to the design parameters of the centrifugal pump, geometric modeling is performed in Solidworks according to the dimensions and the flow calculation domain modeling is geometrically processed, the geometric model constructed in Solidworks is imported into the ICEM software to perform mesh division of the flow calculation domain, and the meshes of the various components of the centrifugal pump are generated in sequence;

[0009] S3, import the divided grid into the software fluent for numerical simulation to obtain simulation data;

[0010] S4, the inlet pressure was changed in the software fluent to obtain different cavitation states, and the flow field snapshots at different times were obtained under transient simulation, exported as Tecplot files, and after data processing, DMD modal decomposition was performed in the compiled MATLAB program.

[0011] In step S3, the boundary conditions are set as total pressure inlet and mass flow outlet in the software fluent. The impeller area in the flow calculation domain adopts the rotating coordinate system, and the remaining areas are the refined coordinate system. The residual convergence accuracy is , the wall is a non-slip wall; the working medium of the centrifugal pump is water, the saturated vapor pressure of water is set to 3167Pa, the cavitation volume fraction at the inlet is 0, and the volume fraction of water is 1; the time step is recorded once when the impeller rotates 5°. Under the condition of rated speed of 2900rpm, the time interval is .

[0012] In step S4, in step S4, flow field snapshots at different times are obtained under transient simulation, including:

[0013] Get snapshot sequence for:

[0014]

[0015] In the formula, For the A snapshot of the flow field data at a certain moment. for A collection of matrices. For the DMD modes, for matrix, for The modal amplitudes, for The calculated value, For Find the diagonal matrix, For the eigenvalues, for Line and Column eigenvalues, It is the solution method of Vandermonde matrix;

[0016] The evolution of the flow field is calculated by the Vandermonde matrix Implementation, including indivual Eigenvalues ​​of a matrix.

[0017] Further, we get the snapshot sequence Before you start:

[0018] Using the DMD method, the raw data collected from experiments or simulations are arranged in chronological order into a vector form of continuous snapshots, which is in the following form:

[0019]

[0020] In the formula, No. A snapshot of the flow field data at a certain moment. is the total number of data snapshots of the flow field, for A snapshot of flow field data;

[0021] If the flow field data is a linear relationship, there exists a constant linear mapping A that takes the flow field data snapshot With the next flow data snapshot Connect them, that is:

[0022]

[0023] Using the flow field snapshots from time 1 to N, construct two snapshot matrices and According to the above formula, we can get:

[0024]

[0025] In the formula, For the A snapshot of flow field data at a certain moment;

[0026] Based on the above linear assumption, it can be expressed as:

[0027]

[0028] In the formula, is the linear relationship of the second flow field, For the The linear relationship of the flow field, For the The linear relationship of the flow field;

[0029] The snapshot Compared with the previous snapshots form a linear combination, and we get:

[0030]

[0031] In the formula, are linear coefficients, is the residual vector, is the linear coefficient;

[0032] According to formula (2) and formula (5), we can get:

[0033]

[0034] In the formula, is a matrix, is the residual value, is the N-1th unit vector;

[0035] matrix It is expressed as:

[0036]

[0037] In the formula, is the linear coefficient;

[0038] The DMD method based on singular value decomposition (SVD) is adopted to improve the robustness of DMD. Perform SVD decomposition to obtain:

[0039]

[0040]

[0041] In the formula, is a unitary matrix, is semi-positive A diagonal matrix of order, For the matrix The conjugate transpose of for The matrix after matrix similarity transformation, For the matrix The conjugate transpose of , the diagonal elements contain singular values; in the singular value decomposition process, choose to keep only The main singular values ​​are truncated and the remaining small singular values ​​are reduced to reduce numerical noise. The unitary matrix obtained by singular value decomposition and satisfy and ,in, is the identity matrix, is a diagonal matrix, is the identity matrix;

[0042] matrix The calculation process is the minimization problem of the Frobenius norm, and the expression is:

[0043]

[0044] In the formula, To find the F-norm, To find the minimum value of matrix A, for A snapshot of flow field data;

[0045] According to formula (8) and formula (9), formula (10) can be expressed as:

[0046]

[0047] In the formula, To find the similarity matrix of matrix A The minimum value of is the flow field matrix;

[0048] At this time Approximately:

[0049]

[0050] In the formula, is the inverse matrix of the diagonal matrix;

[0051] Since the matrix yes Similarity transformation, matrix Include The main eigenvalues ​​of No. The characteristic value is , the eigenvector is ; then The DMD modes are:

[0052]

[0053] In the formula, For the DMD modalities;

[0054] Let the eigenvector The column vector of , K To include The diagonal matrix of singular values ​​is The characteristic decomposition of is expressed as:

[0055]

[0056] In the formula, To calculate the symbol, is the first eigenvalue, is the inverse matrix of W, For the eigenvalues; the flow field snapshot at any time is:

[0057]

[0058] definition Each column of is a DMD mode, according to formula (13):

[0059]

[0060]

[0061] In the formula, is the modal amplitude, For the The modal amplitude represents the modal amplitude relative to the initial snapshot. Contribution is a linear relationship, For the The modal amplitudes, is the transformed rank matrix;

[0062] Substituting formula (16) and formula (17) into formula (15), we can obtain the predicted flow field at any time:

[0063]

[0064] In the formula, To predict the flow field data of the flow field, is the residual, For the The DMD mode of the column, is the characteristic value, For the modal amplitudes;

[0065] Finally, we get the snapshot sequence .

[0066] In step S4, after data processing, DMD modal decomposition is performed in the compiled MATLAB program, including:

[0067] definition is the growth rate, and the frequency is , we get the following relationship:

[0068]

[0069]

[0070] In the formula, is the characteristic value, For each smooth snapshot time interval, For Take the logarithm, To obtain The real part of To obtain The imaginary part of

[0071] After DMD reduction and reconstruction of the flow field, the loss function is used to evaluate the relationship between the reduction and reconstruction. The loss relationship of the reduction is as follows:

[0072]

[0073] In the formula, is the loss error after order reduction, is a DMD mode for each column, For F-norm of the matrix;

[0074] After sorting the obtained DMD amplitudes in order of size, the velocity field reconstructed at any time is obtained as follows:

[0075]

[0076] In the formula, is the reconstructed velocity field, For the DMD modes, For the The modal amplitudes, is the number of flow fields, The characteristic value Power;

[0077] According to formula (23) and numerical simulation results, the error of reconstructing the flow field at any time is obtained as:

[0078]

[0079] In the formula, for Simulation results The velocity field at time, is the error between the reconstructed flow field and the CFD numerical simulation flow field.

[0080] Another object of the present invention is to provide a centrifugal pump cavitation flow field modal order reduction system based on dynamic modal decomposition, which is implemented by the centrifugal pump cavitation flow field modal order reduction method based on dynamic modal decomposition, and the method comprises:

[0081] The centrifugal pump 3D modeling module is used to perform 3D modeling of the centrifugal pump, using the impeller, volute, and inlet and outlet sections of the centrifugal pump to form the flow calculation domain;

[0082] The mesh generation module for each component of the centrifugal pump is used to perform geometric modeling according to the dimensions in Solidworks and geometric processing on the flow calculation domain modeling based on the design parameters of the centrifugal pump, import the geometric model constructed by Solidworks into the ICEM software to perform mesh division of the flow calculation domain, and generate the meshes of each component of the centrifugal pump in turn;

[0083] The numerical simulation module is used to import the divided grids into the software Fluent for numerical simulation and obtain simulation data;

[0084] The cavitation state module is used to change the inlet pressure in the software fluent to obtain different cavitation states, obtain flow field snapshots at different times under transient simulation, export them as Tecplot files, and perform DMD modal decomposition in the compiled MATLAB program after data processing.

[0085] Furthermore, the system is applied in the simulation of centrifugal pump cavitation flow fields in the fields of orifice jet, open cavity flow, wake flow and wave packet.

[0086] Furthermore, the system is mounted on a computer device, which includes: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor, and when the processor executes the computer program, the functions of the above-mentioned centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition are implemented.

[0087] Furthermore, the system is mounted on a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it can realize the functions of the above-mentioned centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition.

[0088] Furthermore, the system is mounted on an information data processing terminal, which is used to provide a user input interface to implement the functions of the centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition as described above when executed on an electronic device.

[0089] In combination with all the above technical solutions, the beneficial effects of the present invention are as follows:

[0090] 1. The present invention adopts the DMD method based on SVD to perform characteristic analysis on the cavitation flow field of the centrifugal pump, aiming to deeply understand the gas-liquid flow characteristics of the centrifugal pump, so as to more accurately analyze the flow field under the cavitation state. DMD is of great value for the rapid order reduction, modal decomposition and reconstruction of the cavitation flow field of the centrifugal pump. It is of certain significance for the rapid identification of cavitation in the centrifugal pump and the prevention of cavitation damage caused by vaporization, thereby preventing the centrifugal pump from malfunctioning.

[0091] 2. The present invention accurately extracts the modal information of the flow field: Through the dynamic modal decomposition (DMD) method based on singular value decomposition (SVD), the modal information of the flow field in the cavitation state of the centrifugal pump, including the frequency change in the flow field, is accurately extracted. This method can clearly reflect that the flow field is periodic or stable, in which the first-order mode, as the time-averaged mode, occupies most of the energy of the flow field and effectively shows the characteristics of the time-averaged flow field.

[0092] 3. The present invention significantly shortens the flow field analysis time: The DMD method can significantly shorten the order reduction time of the flow field analysis and quickly capture the main features of the flow field. The DMD method can complete the detailed analysis, prediction and flow field reconstruction of the flow field in just tens of seconds. In addition, DMD can effectively identify the core dynamic modes in the system behavior, which is especially critical for processing complex flow fields such as cavitation. This modal recognition technology can not only simplify the model structure, but also compared to traditional CFD analysis, it can significantly shorten the processing time from tens of hours or even hundreds of hours to a shorter time window while ensuring accuracy, thereby greatly saving computing costs and improving analysis efficiency.

[0093] 4. High precision of flow field reconstruction and prediction of the present invention: The DMD method can be used for rapid order reduction of the cavitation flow field of a centrifugal pump. The reconstruction error decreases with the increase of the mode, and the error between the original flow field and the reduced-order flow field can be reduced to less than 3.2% in the end. The error between the predicted flow field and the original flow field is kept at about 5%, showing a relatively ideal effect. DMD can achieve rapid order reduction, flow field reconstruction and prediction of the flow field in the cavitation state of a centrifugal pump. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] The accompanying drawings herein are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the description, serve to explain the principles of the present disclosure;

[0095] Figure 1 It is a flow chart of a modal reduction method for cavitation flow field of a centrifugal pump based on dynamic modal decomposition provided by an embodiment of the present invention;

[0096] Figure 2 It is a simulation geometric model diagram of four parts of the calculation domain of a centrifugal pump provided by an embodiment of the present invention and an enlarged diagram of the impeller part;

[0097] Figure 3 Schematic diagram of a centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition provided by an embodiment of the present invention;

[0098] Figure 4 is a characteristic value distribution diagram of a flow field provided by an embodiment of the present invention;

[0099] Figure 5 is a loss diagram of the reduced-order flow field and the original flow field of a centrifugal pump provided by an embodiment of the present invention;

[0100] Figure 6 is a graph showing an error between a reconstructed flow field and an original flow field provided by an embodiment of the present invention;

[0101] In the figure: 1. Centrifugal pump three-dimensional modeling module; 2. Centrifugal pump component mesh generation module; 3. Numerical simulation module; 4. Cavitation state module. DETAILED DESCRIPTION

[0102] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0103] The innovation of the present invention lies in that the present invention utilizes the DMD method to quickly reduce and reconstruct the flow field of a centrifugal pump, and more accurately restores the flow field characteristics of the centrifugal pump. Compared with conventional CFD, it can save a lot of time, which is conducive to making rapid judgments on centrifugal pump fault detection in the later stage, and provides certain support for the rapid identification and diagnosis of centrifugal pump faults in the future.

[0104] Embodiment 1: In the modal order reduction method of centrifugal pump cavitation flow field based on dynamic modal decomposition provided by the embodiment of the present invention, the mathematical model involved in the application is as follows:

[0105] DMD decomposes complex flow fields into simple representations based on several structures in time and space. The DMD method arranges the raw data collected from experiments or simulations into vector forms of continuous snapshots in chronological order, in the following form:

[0106]

[0107] In the formula, No. A snapshot of the flow field data at a certain moment. is the total number of data snapshots of the flow field, for A snapshot of flow field data;

[0108] If the flow field data is a linear relationship, there exists a constant linear mapping A that takes the flow field data snapshot With the next flow data snapshot Connect them, that is:

[0109]

[0110] Using the flow field snapshots from time 1 to N, construct two snapshot matrices and , according to the assumption of formula (2), we get:

[0111]

[0112] In the formula, For the A snapshot of flow field data at a certain moment;

[0113] Based on the above linear assumption, it can be expressed as:

[0114]

[0115] In the formula, is the linear relationship of the second flow field, For the The linear relationship of the flow field, For the The linear relationship of the flow field;

[0116] The snapshot Compared with the previous snapshots form a linear combination, and we get:

[0117]

[0118] In the formula, are linear coefficients, is the residual vector, is the linear coefficient;

[0119] According to formula (2) and formula (5), we can get:

[0120]

[0121] In the formula, is a matrix, is the residual value, is the N-1th unit vector;

[0122] matrix It is expressed as:

[0123]

[0124] In the formula, is the linear coefficient;

[0125] The above method is based on the transformation of unitary matrix, but in the flow field snapshot with noise or uncertainty factors, it is particularly important to ensure the accurate extraction of multi-order modes. At the same time, in order to improve the robustness of DMD, a DMD method based on singular value decomposition (SVD) is adopted. It can be understood that the technical role of the above formula (1)-formula (7) is to model the centrifugal pump system based on the theoretical basis, construct the centrifugal pump mathematical model of dynamic mode decomposition, and provide a theoretical basis for Matlab code.

[0126] Through Perform SVD decomposition to obtain:

[0127]

[0128]

[0129] In the formula, is a unitary matrix, is semi-positive A diagonal matrix of order, For the matrix The conjugate transpose of for The matrix after matrix similarity transformation, For the matrix The conjugate transpose of , the diagonal elements contain singular values; in the singular value decomposition process, choose to keep only The main singular values ​​are truncated and the remaining small singular values ​​are reduced to reduce numerical noise. The unitary matrix obtained by singular value decomposition and satisfy and ,in, is the identity matrix, is a diagonal matrix, is the identity matrix;

[0130] matrix The calculation process is the minimization problem of the Frobenius norm, and the expression is:

[0131]

[0132] In the formula, To find the F-norm, To find the minimum value of matrix A, for A snapshot of flow field data;

[0133] According to formula (8) and formula (9), formula (10) can be expressed as:

[0134]

[0135] In the formula, To find the similarity matrix of matrix A The minimum value of is the flow field matrix;

[0136] At this time Approximately:

[0137]

[0138] In the formula, is the inverse matrix of the diagonal matrix;

[0139] Since the matrix yes Similarity transformation, matrix Include The main eigenvalues ​​of No. The characteristic value is , the eigenvector is ; then The DMD modes are:

[0140]

[0141] In the formula, For the DMD modalities;

[0142] Let the eigenvector The column vector of , To include The diagonal matrix of singular values ​​is The characteristic decomposition of is expressed as:

[0143]

[0144] In the formula, To calculate the symbol, is the first eigenvalue, is the inverse matrix of W, For the eigenvalues; the flow field snapshot at any time is:

[0145]

[0146] definition Each column of is a DMD mode, according to formula (13):

[0147]

[0148]

[0149] In the formula, is the modal amplitude, For the The modal amplitude represents the modal amplitude relative to the initial snapshot. Contribution is a linear relationship, For the The modal amplitudes, is the transformed rank matrix;

[0150] Substituting formula (16) and formula (17) into formula (15), we can obtain the predicted flow field at any time:

[0151]

[0152] In the formula, To predict the flow field data of the flow field, is the residual, For the The DMD mode of the column, is the characteristic value, For the modal amplitudes;

[0153] Finally, we get the snapshot sequence for:

[0154]

[0155] In the formula, For the A snapshot of the flow field data at a certain moment. for A collection of matrices. For the DMD modes, for matrix, for The modal amplitudes, for The calculated value, For Find the diagonal matrix, For the eigenvalues, for Line and Column eigenvalues, It is the solution method of Vandermonde matrix;

[0156] In the formula, the evolution of the flow field is obtained through the Vandermonde matrix Implemented, including indivual The technical function of the above formulas (16) to (19) is to extract the eigenvalues ​​and modal amplitude parameters in the flow field, provide corresponding variables and parameters for flow field order reduction and subsequent reconstruction, and play a role in evaluating the effect of modal order reduction.

[0157] like Figure 1 As shown, the modal reduction method of centrifugal pump cavitation flow field based on dynamic modal decomposition provided by the embodiment of the present invention takes IS-65-50-160 centrifugal pump as the object and uses DMD to analyze its cavitation. Specifically, it includes:

[0158] S1, three-dimensional modeling of the centrifugal pump, using the impeller, volute, and inlet and outlet sections of the centrifugal pump to form the flow calculation domain;

[0159] S2, according to the design parameters of the centrifugal pump, geometric modeling is performed in Solidworks according to the dimensions and the flow calculation domain modeling is geometrically processed, the geometric model constructed in Solidworks is imported into the ICEM software to perform mesh division of the flow calculation domain, and the meshes of the various components of the centrifugal pump are generated in sequence;

[0160] Figure 2It is a simulation geometric model of the four parts of the calculation domain of the centrifugal pump. Then the geometric model constructed in Solidworks is imported into the ICEM software to mesh the flow calculation domain, and the meshes of the various components of the centrifugal pump are generated in turn. The shell and impeller parts have irregular curved shapes and complex structures, and the hexahedral structured grid cannot better meet the needs. Unstructured grids can flexibly adapt to complex and irregular geometric shapes, can accurately capture complex boundaries and internal details, and have advantages in dealing with multi-physics field problems such as fluid flow, heat transfer and mass transfer. Therefore, unstructured grids are used for the volute and impeller. Generate mesh files for each component of the centrifugal pump in turn;

[0161] S3, import the divided grid into the software fluent for numerical simulation to obtain simulation data;

[0162] In the software fluent, the boundary conditions are set as total pressure inlet and mass flow outlet. The impeller area in the flow calculation domain adopts the rotating coordinate system, and the remaining areas are the refined coordinate system. The residual convergence accuracy is , the wall is a non-slip wall; the working medium of the centrifugal pump is water, the saturated vapor pressure of water is set to 3167Pa, the cavitation volume fraction at the inlet is 0, and the volume fraction of water is 1; the time step is recorded once when the impeller rotates 5°. Under the condition of rated speed of 2900rpm, the time interval is ;

[0163] S4, the inlet pressure was changed in the software fluent to obtain different cavitation states, and the flow field snapshots at different times were obtained under transient simulation, exported as Tecplot files, and after data processing, DMD modal decomposition was performed in the compiled MATLAB program.

[0164] Changing the inlet pressure of a centrifugal pump will cause a series of parameters to change, including the speed; changing the inlet pressure will not conflict with the following calculations. Changing the inlet pressure can obtain a series of different effects, and this calculation is just one of them. There will be no conflict.

[0165] The flow field snapshots at different times are obtained under transient simulation and exported as Tecplot files. After data processing, DMD modal decomposition is performed in the compiled MATLAB program.

[0166] definition is the growth rate, and the frequency is , we get the following relationship:

[0167]

[0168]

[0169] In the formula, is the characteristic value, For each smooth snapshot time interval, For Take the logarithm, To obtain The real part of To obtain The imaginary part of

[0170] After DMD reduction and reconstruction of the flow field, the loss function is used to evaluate the relationship between the reduction and reconstruction. The loss relationship of the reduction is as follows:

[0171]

[0172] In the formula, is the loss error after order reduction, is a DMD mode for each column, For F-norm of the matrix;

[0173] After sorting the obtained DMD amplitudes in order of size, the velocity field reconstructed at any time is obtained as follows:

[0174]

[0175] In the formula, is the reconstructed velocity field, For the DMD modes, For the modal amplitudes;

[0176] According to formula (23) and numerical simulation results, the error of reconstructing the flow field at any time is obtained as:

[0177]

[0178] In the formula, for Simulation results The velocity field at time, is the error between the reconstructed flow field and the CFD numerical simulation flow field.

[0179] The above formula (20) - formula (24) can be drawn Figure 4 The data source is Figure 4 It shows that the eigenvalues ​​of DMD are all on the unit circle, and the data are all convergent, indicating that the mode of the flow field in the pump is periodic or stable. It shows that the application of DMD method in the reduction and reconstruction of the cavitation flow field of the pump is feasible.

[0180] Embodiment 2, as Figure 3As shown, an embodiment of the present invention provides a centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition, the system comprising:

[0181] Centrifugal pump three-dimensional modeling module 1, used for three-dimensional modeling of the centrifugal pump, using the impeller, volute and inlet and outlet sections of the centrifugal pump to form a flow calculation domain;

[0182] The mesh generation module 2 of each component of the centrifugal pump is used to perform geometric modeling according to the size in Solidworks according to the design parameters of the centrifugal pump and perform geometric processing on the modeling of its flow calculation domain, import the geometric model constructed by Solidworks into the ICEM software to perform mesh division of the flow calculation domain, and generate meshes of each component of the centrifugal pump in turn;

[0183] Numerical simulation module 3, used to import the divided grid into the software fluent for numerical simulation to obtain simulation data;

[0184] The cavitation state module 4 is used to change the inlet pressure in the software fluent to obtain different cavitation states, obtain the flow field snapshots at different times under transient simulation, export them as Tecplot files, and perform DMD modal decomposition in the compiled MATLAB program after data processing.

[0185] To further illustrate the effects of the embodiments of the present invention, the following experiment was conducted. Figure 4 The eigenvalue distribution of the flow field is shown. The horizontal axis in the attached figure represents the real part of the eigenvalue, and the vertical axis is the imaginary part of the eigenvalue. The horizontal and vertical axes are used to mark the real and imaginary parts. It can be seen from the figure that the eigenvalue is symmetrical along the horizontal axis, indicating that the eigenvalue appears as a conjugate pair, and its modulus can be used to represent the stability of the flow field. It can also be seen that most of the eigenvalue points are distributed on the dotted unit circle, indicating that the mode of the flow field in the pump is periodic or stable. The blue dotted part is the generated unit circle. The function of the unit circle is to represent the distribution of the circles of the eigenvalues. If the circles of the eigenvalues ​​are all distributed on the unit circle, it means that the mode is stable and the modal reduction is ideal. The circle represented by the red cross is the distribution of the first four modes. It can be seen from the figure that the modes are symmetrically distributed, which further confirms that the results of the modal reduction are relatively ideal.

[0186] Figure 5 This is the error diagram of the original flow field of the centrifugal pump and the flow field after reduction. The error of the 100th-order mode is selected. It can be seen from the figure that with the increase in the number of modes, the error between the reconstructed centrifugal pump cavitation flow field and the original flow field shows a downward trend as a whole, and the modal loss is gradually reduced. When the mode is at the 100th order, the error between the reduced-order flow field and the original flow field is only 3.2%.

[0187] Figure 6This is the error curve between the reconstructed flow field and the original flow field. Figure 6 It can be seen that within one cycle, the reconstruction error can eventually drop to less than 5%, and the reconstructed flow field is not much different from the original flow field. Therefore, the reconstructed flow field is relatively ideal.

[0188] The DMD method has the following advantages:

[0189] (1) The DMD method based on SVD can accurately obtain the modal information of the flow field of the centrifugal pump under the empty state and extract the frequency changes in the flow field.

[0190] (2) The DMD method can significantly shorten the order reduction time of flow field analysis and quickly capture the main features of the flow field. The DMD method can complete detailed analysis, prediction and reconstruction of the flow field in just tens of seconds. In addition, DMD can effectively identify the core dynamic modes in the system behavior, which is particularly critical for dealing with complex flow fields such as cavitation. This modal identification technology can not only simplify the model structure, but also, compared with traditional CFD analysis, it can significantly shorten the processing time from tens of hours or even hundreds of hours to a shorter time window while ensuring accuracy, thereby greatly saving computing costs and improving analysis efficiency.

[0191] (3) DMD can be used for rapid order reduction of the cavitation flow field of a centrifugal pump. The reconstruction error decreases with the increase of modes, and the error between the original flow field and the reduced-order flow field can be reduced to less than 3.2%. The error between the predicted flow field and the original flow field can be maintained at about 5%, which is an ideal effect. DMD can achieve rapid order reduction, flow field reconstruction and prediction of the centrifugal pump under cavitation state.

[0192] The present invention is mainly used in the flow field reduction and reconstruction of centrifugal pumps. It can quickly process the flow field to achieve flow field reduction and reconstruction. It can be mainly used to post-process the flow field when cavitation occurs in the centrifugal pump. The flow field of the centrifugal pump under normal working conditions can also be subjected to dynamic modal decomposition, which can be extended to the flow field of the centrifugal pump under common faults. The application scenarios are relatively wide.

[0193] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. A modal reduction method for cavitation flow field of a centrifugal pump based on dynamic modal decomposition, characterized in that: The method includes: S1, three-dimensional modeling of the centrifugal pump, using the impeller, volute, and inlet and outlet sections of the centrifugal pump to form the flow calculation domain; S2, according to the design parameters of the centrifugal pump, geometric modeling is performed in Solidworks according to the dimensions and the flow calculation domain modeling is geometrically processed, the geometric model constructed in Solidworks is imported into the ICEM software to perform mesh division of the flow calculation domain, and the meshes of the various components of the centrifugal pump are generated in sequence; S3, import the divided grid into the software fluent for numerical simulation to obtain simulation data; S4, changing the inlet pressure in the software fluent to obtain different cavitation states, obtaining snapshots of the flow field at different times under transient simulation, exporting them as Tecplot files, and performing DMD modal decomposition in the compiled MATLAB program after data processing; In step S4, flow field snapshots at different times are obtained under transient simulation, including: Get snapshot sequence for: ； In the formula, For the A snapshot of the flow field data at a certain moment. for A collection of matrices. For the DMD modes, for matrix, for The modal amplitudes, for The calculated value, For Find the diagonal matrix, For the eigenvalues, for Line and Column eigenvalues, It is the solution method of Vandermonde matrix; The evolution of the flow field is calculated by the Vandermonde matrix Implementation, including indivual Eigenvalues ​​of a matrix; In step S4, after data processing, DMD modal decomposition is performed in the compiled MATLAB program, including: definition is the growth rate and the frequency is , we get the following relationship: ； In the formula, is the characteristic value, For each smooth snapshot time interval, For Take the logarithm, To obtain The real part of To obtain The imaginary part of After DMD reduction and reconstruction of the flow field, the loss function is used to evaluate the relationship between the reduction and reconstruction. The loss relationship of the reduction is as follows: ； In the formula, is the loss error after order reduction, is a DMD mode for each column, For F-norm of the matrix; After sorting the obtained DMD amplitudes in order of size, the velocity field reconstructed at any time is obtained as follows: ； In the formula, is the reconstructed velocity field, For the DMD modes, For the The modal amplitudes, is the number of flow fields, is the power of the eigenvalue; According to formula (23) and numerical simulation results, the error of reconstructing the flow field at any time is obtained as: ； In the formula, For simulation The velocity field at time, is the error between the reconstructed flow field and the CFD numerical simulation flow field.

2. The modal reduction method of centrifugal pump cavitation flow field based on dynamic modal decomposition according to claim 1 is characterized in that: Get snapshot sequence Before you start: Using the DMD method, the raw data collected from experiments or simulations are arranged in chronological order into a vector form of continuous snapshots, which is in the following form: ； In the formula, No. A snapshot of the flow field data at a certain moment. is the total number of data snapshots of the flow field, for A snapshot of flow field data; If the flow field data is a linear relationship, there exists a constant linear mapping A that takes the flow field data snapshot With the next flow data snapshot Connect them, that is: ； Using the flow field snapshots from time 1 to N, construct two snapshot matrices and According to the above formula, we can get: ； In the formula, For the A snapshot of flow field data at a certain moment; Based on the above linear assumption, it can be expressed as: ； In the formula, is the linear relationship of the second flow field, For the The linear relationship of the flow field, For the The linear relationship of the flow field; Snapshot Compared with before The snapshots are combined into a linear combination, and we get: ； In the formula, are linear coefficients, is the residual vector, is the linear coefficient; According to formula (2) and formula (5), we can get: ； In the formula, is a matrix, is the residual value, is the N-1th unit vector; matrix It is expressed as: ； In the formula, is the linear coefficient; The DMD method based on singular value decomposition (SVD) is adopted to improve the robustness of DMD. Perform SVD decomposition to obtain: ； In the formula, is a unitary matrix, is semi-positive A diagonal matrix of order, For the matrix The conjugate transpose of for The matrix after matrix similarity transformation, For the matrix The conjugate transpose of , the diagonal elements contain singular values; in the singular value decomposition process, choose to keep only The main singular values ​​are decomposed and the remaining small singular values ​​are truncated to reduce the numerical noise. The unitary matrix obtained by singular value decomposition and satisfy and ,in, is the identity matrix, is a diagonal matrix, is the identity matrix; matrix The calculation process is the minimization problem of the Frobenius norm, and the expression is: ； In the formula, To find the F-norm, To find the minimum value of matrix A, for A snapshot of flow field data; According to formula (8) and formula (9), formula (10) can be expressed as: ； In the formula, To find the similarity matrix of matrix A The minimum value of is the flow field matrix; At this time Approximately: ； In the formula, is the inverse matrix of the diagonal matrix; Since the matrix yes Similarity transformation, matrix Include The main eigenvalues ​​of No. The characteristic value is , the eigenvector is ; then The DMD modes are: ； In the formula, For the DMD modalities; Let the eigenvector The column vector of is, , To include The diagonal matrix of singular values ​​is The characteristic decomposition of is expressed as: ； In the formula, To calculate the symbol, is the first eigenvalue, is the inverse matrix of W, For the eigenvalues; The flow field snapshot at any time is: ； Each column is defined as a DMD mode, and according to formula (13): ； In the formula, is the modal amplitude, For the The modal amplitude represents the modal amplitude relative to the initial snapshot. Contribution is a linear relationship, For the The modal amplitudes, is the transformed rank matrix; Substituting formula (16) and formula (17) into formula (15), we can obtain the predicted flow field at any time: ； In the formula, To predict the flow field data of the flow field, is the residual, is the DMD mode of the column, is the characteristic value, For the modal amplitudes; Finally, we get the snapshot sequence .

3. The method for modal reduction of centrifugal pump cavitation flow field based on dynamic modal decomposition according to claim 1 is characterized in that: In step S3, the boundary conditions are set as total pressure inlet and mass flow outlet in the software fluent. The impeller area in the flow calculation domain adopts the rotating coordinate system, and the remaining areas are the refined coordinate system. The residual convergence accuracy is , the wall is a non-slip wall; the working medium of the centrifugal pump is water, the saturated vapor pressure of water is set to 3167Pa, the cavitation volume fraction at the inlet is 0, and the volume fraction of water is 1; the time step is recorded once when the impeller rotates 5°. Under the condition of rated speed of 2900rpm, the time interval is .

4. A centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition, characterized in that: The system is implemented by the centrifugal pump cavitation flow field modal reduction method based on dynamic modal decomposition according to any one of claims 1 to 3, and the method comprises: A centrifugal pump three-dimensional modeling module (1) is used to perform three-dimensional modeling on a centrifugal pump, using the impeller, volute, and inlet and outlet sections of the centrifugal pump to form a flow calculation domain; The mesh generation module (2) of each component of the centrifugal pump is used to perform geometric modeling according to the dimensions in Solidworks according to the design parameters of the centrifugal pump and perform geometric processing on the modeling of its flow calculation domain, import the geometric model constructed by Solidworks into the ICEM software to perform mesh division of the flow calculation domain, and generate meshes of each component of the centrifugal pump in turn; Numerical simulation module (3), used to import the divided grid into the software Fluent for numerical simulation to obtain simulation data; The cavitation state module (4) is used to change the inlet pressure in the software fluent to obtain different cavitation states, obtain flow field snapshots at different times under transient simulation, export them as Tecplot files, perform data processing, and perform DMD modal decomposition in the compiled MATLAB program.

5. The centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition according to claim 4 is characterized in that: The system is applied in the simulation of centrifugal pump cavitation flow field in the fields of orifice jet, open cavity flow, wake flow and wave packet.

6. The centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition according to claim 4, characterized in that: The system is mounted on a computer device, which includes: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor. When the processor executes the computer program, the functions of the centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition are implemented.

7. The centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition according to claim 4, characterized in that: The system is mounted on a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the functions of the centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition can be realized.

8. The centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition according to claim 4, characterized in that: The system is mounted on an information data processing terminal, which is used to provide a user input interface to implement the functions of the centrifugal pump cavitation flow field modal reduction system based on dynamic modal decomposition when executed on an electronic device.

Images