Earth’s magnetic field,which is generated in the liquid outer core through the dynamo action,undergoes changes on timescales of a few years to several million years,yet the underlying mechanisms responsible for the f...Earth’s magnetic field,which is generated in the liquid outer core through the dynamo action,undergoes changes on timescales of a few years to several million years,yet the underlying mechanisms responsible for the field variations remain to be elucidated.In this study,we apply a novel data analysis technique developed in fluid dynamics,namely the dynamic mode decomposition,to analyze the geomagnetic variations over the last two decades when continuous satellite observations are available.The dominant dynamic modes are extracted by solving an eigen-value problem,so one can identify modes with periods longer than the time span of data.Our analysis show that similar dynamic modes are extracted from the geomagnetic secular variation and secular acceleration,justifying the validity of applying the dynamic mode decomposition method to geomagnetic field.We reveal that the geomagnetic field variations are characterized by a global mode with period of 58 years,a localized mode with period of 16 years and an equatorially trapped mode with period of 8.5 years.These modes are possibly related to magnetohydrodynamic waves in the Earth’s outer core.展开更多
In recent years,subsynchronous resonance(SSR)has frequently occurred in DFIG-connected series-compensated systems.For the analysis and prevention,it is of great importance to achieve wide area monitoring of the incide...In recent years,subsynchronous resonance(SSR)has frequently occurred in DFIG-connected series-compensated systems.For the analysis and prevention,it is of great importance to achieve wide area monitoring of the incident.This paper presents a Hankel dynamic mode decomposition(DMD)method to identify SSR parameters using synchrophasor data.The basic idea is to employ the DMD technique to explore the subspace of Hankel matrices constructed by synchrophasors.It is analytically demonstrated that the subspace of these Hankel matrices is a combination of fundamental and SSR modes.Therefore,the SSR parameters can be calculated once the modal parameter is extracted.Compared with the existing method,the presented work has better dynamic performances as it requires much less data.Thus,it is more suitable for practical cases in which the SSR characteristics are timevarying.The effectiveness and superiority of the proposed method have been verified by both simulations and field data.展开更多
To identify the parameters of the extended Debye model of XLPE cables,and therefore evaluate the insulation performance of the samples,the sparsity-promoting dynamicmode decomposition(SPDMD)methodwas introduced,aswell...To identify the parameters of the extended Debye model of XLPE cables,and therefore evaluate the insulation performance of the samples,the sparsity-promoting dynamicmode decomposition(SPDMD)methodwas introduced,aswell the basics and processes of its applicationwere explained.The amplitude vector based on polarization current was first calculated.Based on the non-zero elements of the vector,the number of branches and parameters including the coefficients and time constants of each branch of the extended Debye model were derived.Further research on parameter identification of XLPE cables at different aging stages based on the SPDMD method was carried out to verify the practicability of the method.Compared with the traditional differential method,the simulation and experiment indicated that the SPDMD method can effectively avoid problems such as the relaxation peak being unobvious,and possessing more accuracy during the parameter identification.And due to the polarization current being less affected by the measurement noise than the depolarization current,the SPDMD identification results based on the polarization current spectral line proved to be better at reflecting the response characteristics of the dielectric.In addition,the time domain polarization current test results can be converted into the frequency domain,and then used to obtain the dielectric loss factor spectrum of the insulation.The integral of the dielectric loss factor on a frequency domain can effectively evaluate the insulation condition of the XLPE cable.展开更多
A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of t...A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of the flow past a cylinder at supercritical state, Re = 50, is studied by the combination for both the exponential growing and the limit cycle regimes. The Ritz values, energy spectrum, and modes for both regimes are presented and compared with the Koopman eigenvalues. For harmonic-like periodic flow in the limit cycle, global analysis from the combination gives the same results as those from the Koopman analysis. For transient flow as in the exponential growth regime, the combination can provide more reasonable results. It is demonstrated that the combination of the lattice Boltzmann method and the dynamic mode decomposition is powerful and can be used for stability analysis for more complex flows.展开更多
The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in go...The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform.Furthermore,the cavitating flow field is reconstructed by the first four modes,and the dominant flow features are well captured with the reconstructed error below 12%when compared to the simulated flow field.This paper offers a reference for observing and reconstructing the flow fields,and gives a novel insight into the transient cavitating flow features.展开更多
This study presents the assumptions and strategies for the practical implementation of the dynamic mode decomposition approach in the wide-area monitoring system of the Italian transmission system operator,Terna.The p...This study presents the assumptions and strategies for the practical implementation of the dynamic mode decomposition approach in the wide-area monitoring system of the Italian transmission system operator,Terna.The procedure setup aims to detect poorly damped interarea oscillations of power systems.Dynamic mode decomposition is a data-driven technique that has gained increasing attention in different fields;the proposed implementation can both characterize the oscillatory modes and identify the most influenced areas.This study presents the results of its practical implementation and operational experience in power system monitoring.It focuses on the main characteristics and solutions identified to reliably monitor the interarea electromechanical modes of the interconnected European power system.Moreover,conditions to issue an appropriate alarm in case of critical operating conditions are described.The effectiveness of the proposed approach is validated by its application in three case studies:a critical oscillatory event and a short-circuit event that occurred in the Italian power system in the previous years,and a 15-min time interval of normal grid operation recorded in March 2021.展开更多
The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic op-timization.In this letter,the solution of unsteady adjoint equations is accelerated by dynamic mode decomposi-...The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic op-timization.In this letter,the solution of unsteady adjoint equations is accelerated by dynamic mode decomposi-tion(DMD).The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system.Thereafter,DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching.First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step.Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example,the efficiency of solving unsteady adjoint equations is significantly improved.Re-sults show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics,and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors,which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.展开更多
This article presents a novel approach for predicting transition locations over airfoils,which are used to activate turbulence model in a Reynolds-averaged Navier-Stokes flow solver.This approach combines Dynamic Mode...This article presents a novel approach for predicting transition locations over airfoils,which are used to activate turbulence model in a Reynolds-averaged Navier-Stokes flow solver.This approach combines Dynamic Mode Decomposition(DMD)with e^Ncriterion.The core idea is to use a spatial DMD analysis to extract the modes of unstable perturbations from a steady flowfield and substitute the local Linear Stability Theory(LST)analysis to quantify the spatial growth of Tollmien–Schlichting(TS)waves.Transition is assumed to take place at the stream-wise location where the most amplified mode’s N-factor reaches a prescribed threshold and a turbulence model is activated thereafter.To improve robustness,the high-order version of DMD technique(known as HODMD)is employed.A theoretical derivation is conducted to interpret how a spatial highorder DMD analysis can extract the growth rate of the unsteady perturbations.The new method is validated by transition predictions of flows over a low-speed Natural-Laminar-Flow(NLF)airfoil NLF0416 at various angles of attack and a transonic NLF airfoil NPU-LSC-72613.The transition locations predicted by our HODMD/e^Nmethod agree well with experimental data and compare favorably to those obtained by some existing methods■.It is shown that the proposed method is able to predict transition locations for flows over different types of airfoils and offers the potential for application to 3D wings as well as more complex configurations.展开更多
We present dynamic mode decomposition (DMD) for studying the hairpin vortices generated by hemisphere protuberance measured by two-dimensional (2D) time-resolved (TR) particle image velocimetry (PIV) in a water channe...We present dynamic mode decomposition (DMD) for studying the hairpin vortices generated by hemisphere protuberance measured by two-dimensional (2D) time-resolved (TR) particle image velocimetry (PIV) in a water channel. The hairpins dynamic information is extracted by identifying their dominant frequencies and associated spatial structures. For this quasi-periodic data system, the resulting main Dynamic modes illustrate the different spatial structures associated with the wake vortex region and the near-wall region. By comparisons with proper orthogonal decomposition (POD), it can be concluded that the dynamic mode concentrates on a certain frequency component more effectively than the mode determined by POD. During the analysis, DMD has proven itself a robust and reliable algorithm to extract spatial-temporal coherent structures.展开更多
Unsteady flow in the hub endwall region has long been a hot topic in the turbomachinery community.However important it is to the performance of the whole engine,the coherent unsteady flow phenomena are still not well ...Unsteady flow in the hub endwall region has long been a hot topic in the turbomachinery community.However important it is to the performance of the whole engine,the coherent unsteady flow phenomena are still not well understood.In this paper,the complex flow field in the hub endwall of a cantilevered compressor cascade has been investigated through numerical approach.The predicted results were validated by experimental data.To highlight the dominant flow structures among irregular and chaotic motions of various vortices,a Dynamic Mode Decomposition(DMD)method was utilized.The results show that there exist three dominant periodic flow structures:the oscillation of the leakage vortex,a circumferential migration of a Breakdown Induced Vortex(BIV)and the fluctuation of the passage vortex.These three coherent structures all together form a self-sustained closed loop which accounts for the flow unsteadiness of the studied cascade.During this process,the BIV plays a key role in inducing the flow unsteadiness.Only if the BIV is strong enough to affect the passage vortex,the flow unsteadiness occurs.This study expands current knowledge base of flow unsteadiness in a compressor environment,and shows the efficacy of the DMD method for revealing the origin of flow unsteadiness.展开更多
The present work uses dynamic mode decomposition(DMD) to analyze wake flow of NACA0015 airfoil with Gurney flap.The physics of DMD is first introduced.Then the PIV-measured wake flow velocity field is decomposed into ...The present work uses dynamic mode decomposition(DMD) to analyze wake flow of NACA0015 airfoil with Gurney flap.The physics of DMD is first introduced.Then the PIV-measured wake flow velocity field is decomposed into dynamical modes.The vortex shedding pattern behind the trailing edge and its high-order harmonics have been captured with abundant information such as frequency,wavelength and convection speed.It is observed that high-order dynamic modes convect faster than low-order modes;moreover the wavelength of the dynamic modes scales with the corresponding frequency in power law.展开更多
Dynamic Mode Decomposition(DMD)is a data-driven and model-free decomposition technique.It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data.Conceptually,DMD perfor...Dynamic Mode Decomposition(DMD)is a data-driven and model-free decomposition technique.It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data.Conceptually,DMD performs a low-dimensional spectral decomposition of the data into the following components:the modes,called DMD modes,encode the spatial contribution of the decomposition,whereas the DMD amplitudes specify their impact.Each associated eigenvalue,referred to as DMD eigenvalue,characterizes the frequency and growth rate of the DMD mode.In this paper,we demonstrate how the components of DMD can be utilized to obtain temporal and spatial information from time-dependent flow fields.We begin with the theoretical background of DMD and its application to unsteady flow.Next,we examine the conventional process with DMD mathematically and put it in relationship to the discrete Fourier transform.Our analysis shows that the current use of DMD components has several drawbacks.To resolve these problems we adjust the components and provide new and meaningful insights into the decomposition:we show that our improved components capture the spatio-temporal patterns of the flow better.Moreover,we remove redundancies in the decomposition and clarify the interplay between components,allowing users to understand the impact of components.These new representations,which respect the spatio-temporal character of DMD,enable two clustering methods that segment the flow into physically relevant sections and can therefore be used for the selection of DMD components.With a number of typical examples,we demonstrate that the combination of these techniques allows new insights with DMD for unsteady flow.展开更多
Noise is generated in a two-dimensional mixing layer due to the growing of instability waves and vortex pairings. The adjoint-based control methodology has shown to be a robust tool to suppress noise radiation. The mo...Noise is generated in a two-dimensional mixing layer due to the growing of instability waves and vortex pairings. The adjoint-based control methodology has shown to be a robust tool to suppress noise radiation. The mode decomposition algorithms such as the compressible version of proper orthogonal decomposition （POD） and dynamic mode decomposition （DMD） are employed to analyze the spatial/spatial-temporal coherent structures for a consecutive data sets of the controlled mixing layer and its uncontrolled counterpart. The analyses of POD indicate that the y-direction body force control mainly modify the most energetic spatial structures, and increase the uniformity of the flow. The analyses of DMD show us prevalent frequencies and corresponding mode structures, and the stability characteristics of each mode can be obtained from DMD-spectrum. The spectral signatures illustrate that a lot of neutral/slightly damping modes emerging in uncontrolled flow within the frequency range （w 〈 0.4） are suppressed due to control, relevant spatial-temporal structures are also varied, which is coincident with the change of far-field noise spectra. From the view of mode decomposition, the action of control redistribute the energy for frequency components of ~ 〈 0.4 by weakening nonlinearities and regularizing corresponding dynamic structures in streamwise direction, and thus suppress the noise radiation. Moreover, the POD- and DMD-analysis in this study demon- strate that DMD can serve as an important supplement for POD in analyzing a time-resolved physical process.展开更多
The flow field structure within the clearances of turbomachinery is complex and diverse, exhibiting high-dimensional nonlinearity. How to accurately extract the main structures that affect the internal flow within the...The flow field structure within the clearances of turbomachinery is complex and diverse, exhibiting high-dimensional nonlinearity. How to accurately extract the main structures that affect the internal flow within the turbine from the complex clearance flow has always been a key issue. To explore the impact of the dynamic structure of the clearance flow on the mainstream region in a centrifugal pump, this study combines the dynamic mode decomposition (DMD) method to conduct a thorough analysis of the velocity and pressure pulsation frequencies in the multi-physics fields within the clearance. The study has identified the main characteristic structures under different physical conditions in the clearance and has established the relationship between the characteristic structure frequencies in different physical fields and the impeller frequency. The research indicates that the internal flow within the clearance affects the occurrence of vortices in the volute. Under design conditions, the velocity field within the clearance is primarily influenced by high-order harmonic frequencies of the impeller, and the pressure field is mainly affected by low-order harmonic frequencies of the impeller. This reflects the crucial influence of impeller frequency and inlet flow on the coherent structures within the clearance flow. The research results offer new insights and methods for analyzing complex internal flows in large turbomachinery.展开更多
The flow around a circular cylinder for Re=1000 is characterized by flow separation and Karman vortex street.The typical flow features can be captured to study the correlation between fluid fields and sound fields.In ...The flow around a circular cylinder for Re=1000 is characterized by flow separation and Karman vortex street.The typical flow features can be captured to study the correlation between fluid fields and sound fields.In this paper,the three-dimensional circular cylinder is taken as the research object,and the probes of surface fluctuating pressure and far field sound pressure are arranged every 10°.The directional diagram and the coherence of fluctuating pressure and sound pressure are analyzed.The relationship between the flow mode and hydrodynamic noise is studied by using dynamic mode decomposition(DMD).The characteristics of the dipole and quadrupole sound source term of a long span cylinder are studied.The results show that at the angles between 30°–120°and 190°–350°,the fluctuating pressure contributes more to the generation of dipole sounds.The quadrupole sound source shows three-dimensional effects,which is more obvious in a cylinder with large spanwise length.展开更多
Model order reduction(MOR)is considered as a good alternative to reduce the computational scale for electro-magnetic problems.The aim of this work is to introduce the use of dynamic mode decomposition(DMD)as a promisi...Model order reduction(MOR)is considered as a good alternative to reduce the computational scale for electro-magnetic problems.The aim of this work is to introduce the use of dynamic mode decomposition(DMD)as a promising tool for MOR to analyze its effectiveness in creating a fast model-based design platform for the permanent magnet motor design for ur-ban aerial vehicles(UAVs).Using a singular value decomposition(SVD)based DMD,the design process is constructed and verified against different scenarios.展开更多
The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approxima...The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate thenonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation beforeapproximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic modedecomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, anovel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid oferror data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.展开更多
The objective is to study the vortical structural behaviors of a transient pitching hydrofoil and their effects on the hydrodynamic performance. The pitching motion of the hydrofoil is set to pitch up with an almost c...The objective is to study the vortical structural behaviors of a transient pitching hydrofoil and their effects on the hydrodynamic performance. The pitching motion of the hydrofoil is set to pitch up with an almost constant rate from 5° to 15° and then back to 5°, with the Reynolds number 4.4×10^(5) and the frequency 2 Hz. The results show that the main coherent structures around the pitching hydrofoil include small-scale laminar separation bubble (LSB), large-scale second vortex (SV) and trailing edge vortex (TEV) which are all vortical. The relationship between the vortical structure and the lift is investigated with the finite-domain impulse theory. It indicates that the major part of the lift is contributed by the LSB, whereas the shedding and the formation of the SV and TEV cause the fluctuation of the lift. The proper orthogonal decomposition (POD) method is applied to capture the most energetic modes, revealing that the LSB mode occupies a large amount of energy in the flow field. The dynamic mode decomposition (DMD) method accurately extracts the dominant frequency and modal characteristics, with the first mode corresponding to the mean flow, the second mode corresponding to the LSB structure and the third and fourth modes corresponding to the vortex shedding.展开更多
As a high-dimensional complex nonlinear dynamic system,the analysis of the essence of flow has always been a difficult problem,especially in the flow including phase change.In recent years,it has become a feasible met...As a high-dimensional complex nonlinear dynamic system,the analysis of the essence of flow has always been a difficult problem,especially in the flow including phase change.In recent years,it has become a feasible method to reduce the dimension of flow structure by reduced-order modeling(ROM)methods.In this paper,through the cavitation numerical simulation of NACA0015 hydrofoil,two ROM methods are used to reduce and restore three different cavitation respectively-proper orthogonal decomposition(POD)and dynamic mode decomposition(DMD).The applicability of two methods in cavitation is discussed and reasons are analyzed.The results show that for stable cavitation,POD,DMD methods can accurately restore the flow field of a few modes with high energy.For unstable cavitation,only POD method can restore real flow field well.This situation is mainly due to the fact that POD,DMD method are applicable to different energy ratios,and different main mode selection criterion of DMD will lead to different main mode.ROM can greatly simplify the complexity of flow.Selecting a reasonable ROM can improve the accuracy of a small amount of database,and provide a basis for intelligent prediction of flow analysis.展开更多
This paper proposes two concepts: the ecological footprint component index(EFCI) and the biocapacity component index(BCCI), based on the ecological footprint(EF) and Shannon entropy approaches. Per capita EFCI and BCC...This paper proposes two concepts: the ecological footprint component index(EFCI) and the biocapacity component index(BCCI), based on the ecological footprint(EF) and Shannon entropy approaches. Per capita EFCI and BCCI in China 1949-2013 are analyzed using empirical mode decomposition(EMD). Nonlinear models of per capita EFCI and BCCI in China 1949-2013 are presented and their cycles and predictions from 2014 to 2023 are analyzed. The results over the last 65 years show:(1) EFCI in China has increased constantly with fluctuations, while BCCI has slowly decreased. Their annual change rates are 2.81% and-1.26%, respectively. The increasing EFCI indicates a gradual improvement in China's sustainable development potential; the decreasing BCCI indicates severe environmental and population challenges.(2) The cycles of per capita EFCI have periods of 5.4 and 16.3 years, while cycles of per capita BCCI have periods of 3.6, 13,and 21.7 years. The predictive models indicate that EFCI will first decrease, reaching 0.02725 in2014, and will subsequently increase to 0.03261 in 2021. BCCI will increase, reaching 0.01365 in2014 and 0.01541 in 2022. EFCI and BCCI will reach 0.03037 and 0.01537, respectively, in 2023.Policymakers should ensure that the EFCI and BCCI increase in 2023.展开更多
基金supported by Macao Science and Technology Development Fund grant 0001/2019/A1Macao Foundation+1 种基金the preresearch Project on Civil Aerospace Technologies of CNSA(Grants No.D020303 and D020308)the National Natural Science Foundation of China(41904066,42142034)。
文摘Earth’s magnetic field,which is generated in the liquid outer core through the dynamo action,undergoes changes on timescales of a few years to several million years,yet the underlying mechanisms responsible for the field variations remain to be elucidated.In this study,we apply a novel data analysis technique developed in fluid dynamics,namely the dynamic mode decomposition,to analyze the geomagnetic variations over the last two decades when continuous satellite observations are available.The dominant dynamic modes are extracted by solving an eigen-value problem,so one can identify modes with periods longer than the time span of data.Our analysis show that similar dynamic modes are extracted from the geomagnetic secular variation and secular acceleration,justifying the validity of applying the dynamic mode decomposition method to geomagnetic field.We reveal that the geomagnetic field variations are characterized by a global mode with period of 58 years,a localized mode with period of 16 years and an equatorially trapped mode with period of 8.5 years.These modes are possibly related to magnetohydrodynamic waves in the Earth’s outer core.
基金supported by the China Key Technology Research on Risk Perception of Sub-Synchronous Oscillation of Grid with Large-Scale New Energy Access SGTYHT/21-JS-223.
文摘In recent years,subsynchronous resonance(SSR)has frequently occurred in DFIG-connected series-compensated systems.For the analysis and prevention,it is of great importance to achieve wide area monitoring of the incident.This paper presents a Hankel dynamic mode decomposition(DMD)method to identify SSR parameters using synchrophasor data.The basic idea is to employ the DMD technique to explore the subspace of Hankel matrices constructed by synchrophasors.It is analytically demonstrated that the subspace of these Hankel matrices is a combination of fundamental and SSR modes.Therefore,the SSR parameters can be calculated once the modal parameter is extracted.Compared with the existing method,the presented work has better dynamic performances as it requires much less data.Thus,it is more suitable for practical cases in which the SSR characteristics are timevarying.The effectiveness and superiority of the proposed method have been verified by both simulations and field data.
基金supported by the Science and Technology Project of Guizhou Power Grid Co.,Ltd. (No.GZKJXM20210405).
文摘To identify the parameters of the extended Debye model of XLPE cables,and therefore evaluate the insulation performance of the samples,the sparsity-promoting dynamicmode decomposition(SPDMD)methodwas introduced,aswell the basics and processes of its applicationwere explained.The amplitude vector based on polarization current was first calculated.Based on the non-zero elements of the vector,the number of branches and parameters including the coefficients and time constants of each branch of the extended Debye model were derived.Further research on parameter identification of XLPE cables at different aging stages based on the SPDMD method was carried out to verify the practicability of the method.Compared with the traditional differential method,the simulation and experiment indicated that the SPDMD method can effectively avoid problems such as the relaxation peak being unobvious,and possessing more accuracy during the parameter identification.And due to the polarization current being less affected by the measurement noise than the depolarization current,the SPDMD identification results based on the polarization current spectral line proved to be better at reflecting the response characteristics of the dielectric.In addition,the time domain polarization current test results can be converted into the frequency domain,and then used to obtain the dielectric loss factor spectrum of the insulation.The integral of the dielectric loss factor on a frequency domain can effectively evaluate the insulation condition of the XLPE cable.
文摘A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of the flow past a cylinder at supercritical state, Re = 50, is studied by the combination for both the exponential growing and the limit cycle regimes. The Ritz values, energy spectrum, and modes for both regimes are presented and compared with the Koopman eigenvalues. For harmonic-like periodic flow in the limit cycle, global analysis from the combination gives the same results as those from the Koopman analysis. For transient flow as in the exponential growth regime, the combination can provide more reasonable results. It is demonstrated that the combination of the lattice Boltzmann method and the dynamic mode decomposition is powerful and can be used for stability analysis for more complex flows.
基金the National Key R&D Program of China(Grants 2016YFC0300800 and 2016YFC0300802)the National Natural Science Foundation of China(Grants 11772340 and 11672315)the Science and Technology on Water Jet Propulsion Laboratory(Grant 6142223190101).
文摘The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform.Furthermore,the cavitating flow field is reconstructed by the first four modes,and the dominant flow features are well captured with the reconstructed error below 12%when compared to the simulated flow field.This paper offers a reference for observing and reconstructing the flow fields,and gives a novel insight into the transient cavitating flow features.
文摘This study presents the assumptions and strategies for the practical implementation of the dynamic mode decomposition approach in the wide-area monitoring system of the Italian transmission system operator,Terna.The procedure setup aims to detect poorly damped interarea oscillations of power systems.Dynamic mode decomposition is a data-driven technique that has gained increasing attention in different fields;the proposed implementation can both characterize the oscillatory modes and identify the most influenced areas.This study presents the results of its practical implementation and operational experience in power system monitoring.It focuses on the main characteristics and solutions identified to reliably monitor the interarea electromechanical modes of the interconnected European power system.Moreover,conditions to issue an appropriate alarm in case of critical operating conditions are described.The effectiveness of the proposed approach is validated by its application in three case studies:a critical oscillatory event and a short-circuit event that occurred in the Italian power system in the previous years,and a 15-min time interval of normal grid operation recorded in March 2021.
基金the Natural Science Foundation of Jiangsu Province(Grants No.BK20230202)Basic Science(Natural Science)Re-search Project of Colleges and Universities in Jiangsu Province(Grant No.22KJB130005)+3 种基金Changzhou Science and Technology Project(Grant No.CJ20220242)for financial supportJiaqing Kou would like to thank the support of the Alexander von Humboldt Foundation(Ref 3.5-CHN-1227287-HFST-P)Wenkai Yang would like to thank the support of the National Natural Science Foundation of China(Grant No.52205335)supported by Changzhou Sci&Tech Pro-gram(Grant No.CM20223013).
文摘The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic op-timization.In this letter,the solution of unsteady adjoint equations is accelerated by dynamic mode decomposi-tion(DMD).The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system.Thereafter,DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching.First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step.Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example,the efficiency of solving unsteady adjoint equations is significantly improved.Re-sults show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics,and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors,which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.
基金supported by the National Natural Science Foundation of China (No. 11772261)the Aeronautical Science Foundation of China (No. 2016ZA53011)+1 种基金the ATCFD Project (No. 2015-F-016)the 111 Project of China (No. B17037)
文摘This article presents a novel approach for predicting transition locations over airfoils,which are used to activate turbulence model in a Reynolds-averaged Navier-Stokes flow solver.This approach combines Dynamic Mode Decomposition(DMD)with e^Ncriterion.The core idea is to use a spatial DMD analysis to extract the modes of unstable perturbations from a steady flowfield and substitute the local Linear Stability Theory(LST)analysis to quantify the spatial growth of Tollmien–Schlichting(TS)waves.Transition is assumed to take place at the stream-wise location where the most amplified mode’s N-factor reaches a prescribed threshold and a turbulence model is activated thereafter.To improve robustness,the high-order version of DMD technique(known as HODMD)is employed.A theoretical derivation is conducted to interpret how a spatial highorder DMD analysis can extract the growth rate of the unsteady perturbations.The new method is validated by transition predictions of flows over a low-speed Natural-Laminar-Flow(NLF)airfoil NLF0416 at various angles of attack and a transonic NLF airfoil NPU-LSC-72613.The transition locations predicted by our HODMD/e^Nmethod agree well with experimental data and compare favorably to those obtained by some existing methods■.It is shown that the proposed method is able to predict transition locations for flows over different types of airfoils and offers the potential for application to 3D wings as well as more complex configurations.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10832001 and 10872145)the State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences
文摘We present dynamic mode decomposition (DMD) for studying the hairpin vortices generated by hemisphere protuberance measured by two-dimensional (2D) time-resolved (TR) particle image velocimetry (PIV) in a water channel. The hairpins dynamic information is extracted by identifying their dominant frequencies and associated spatial structures. For this quasi-periodic data system, the resulting main Dynamic modes illustrate the different spatial structures associated with the wake vortex region and the near-wall region. By comparisons with proper orthogonal decomposition (POD), it can be concluded that the dynamic mode concentrates on a certain frequency component more effectively than the mode determined by POD. During the analysis, DMD has proven itself a robust and reliable algorithm to extract spatial-temporal coherent structures.
基金supports of National Natural Science Foundation of China(Nos.51790512,52176045)the National Major Science and technology Project of China(No.J2017-Ⅱ-0010-0024)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China(No.CX201911)。
文摘Unsteady flow in the hub endwall region has long been a hot topic in the turbomachinery community.However important it is to the performance of the whole engine,the coherent unsteady flow phenomena are still not well understood.In this paper,the complex flow field in the hub endwall of a cantilevered compressor cascade has been investigated through numerical approach.The predicted results were validated by experimental data.To highlight the dominant flow structures among irregular and chaotic motions of various vortices,a Dynamic Mode Decomposition(DMD)method was utilized.The results show that there exist three dominant periodic flow structures:the oscillation of the leakage vortex,a circumferential migration of a Breakdown Induced Vortex(BIV)and the fluctuation of the passage vortex.These three coherent structures all together form a self-sustained closed loop which accounts for the flow unsteadiness of the studied cascade.During this process,the BIV plays a key role in inducing the flow unsteadiness.Only if the BIV is strong enough to affect the passage vortex,the flow unsteadiness occurs.This study expands current knowledge base of flow unsteadiness in a compressor environment,and shows the efficacy of the DMD method for revealing the origin of flow unsteadiness.
基金supported by National Natural Science Foundation of China(Grant No.10832001)Vision Foundation of Beijing University of Aeronautics and Astronautics (Grant No.YWF-10-20-003)
文摘The present work uses dynamic mode decomposition(DMD) to analyze wake flow of NACA0015 airfoil with Gurney flap.The physics of DMD is first introduced.Then the PIV-measured wake flow velocity field is decomposed into dynamical modes.The vortex shedding pattern behind the trailing edge and its high-order harmonics have been captured with abundant information such as frequency,wavelength and convection speed.It is observed that high-order dynamic modes convect faster than low-order modes;moreover the wavelength of the dynamic modes scales with the corresponding frequency in power law.
文摘Dynamic Mode Decomposition(DMD)is a data-driven and model-free decomposition technique.It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data.Conceptually,DMD performs a low-dimensional spectral decomposition of the data into the following components:the modes,called DMD modes,encode the spatial contribution of the decomposition,whereas the DMD amplitudes specify their impact.Each associated eigenvalue,referred to as DMD eigenvalue,characterizes the frequency and growth rate of the DMD mode.In this paper,we demonstrate how the components of DMD can be utilized to obtain temporal and spatial information from time-dependent flow fields.We begin with the theoretical background of DMD and its application to unsteady flow.Next,we examine the conventional process with DMD mathematically and put it in relationship to the discrete Fourier transform.Our analysis shows that the current use of DMD components has several drawbacks.To resolve these problems we adjust the components and provide new and meaningful insights into the decomposition:we show that our improved components capture the spatio-temporal patterns of the flow better.Moreover,we remove redundancies in the decomposition and clarify the interplay between components,allowing users to understand the impact of components.These new representations,which respect the spatio-temporal character of DMD,enable two clustering methods that segment the flow into physically relevant sections and can therefore be used for the selection of DMD components.With a number of typical examples,we demonstrate that the combination of these techniques allows new insights with DMD for unsteady flow.
基金supported by the National Natural Science Foundation of China (11072238, 11232011)111 project (B07033)
文摘Noise is generated in a two-dimensional mixing layer due to the growing of instability waves and vortex pairings. The adjoint-based control methodology has shown to be a robust tool to suppress noise radiation. The mode decomposition algorithms such as the compressible version of proper orthogonal decomposition （POD） and dynamic mode decomposition （DMD） are employed to analyze the spatial/spatial-temporal coherent structures for a consecutive data sets of the controlled mixing layer and its uncontrolled counterpart. The analyses of POD indicate that the y-direction body force control mainly modify the most energetic spatial structures, and increase the uniformity of the flow. The analyses of DMD show us prevalent frequencies and corresponding mode structures, and the stability characteristics of each mode can be obtained from DMD-spectrum. The spectral signatures illustrate that a lot of neutral/slightly damping modes emerging in uncontrolled flow within the frequency range （w 〈 0.4） are suppressed due to control, relevant spatial-temporal structures are also varied, which is coincident with the change of far-field noise spectra. From the view of mode decomposition, the action of control redistribute the energy for frequency components of ~ 〈 0.4 by weakening nonlinearities and regularizing corresponding dynamic structures in streamwise direction, and thus suppress the noise radiation. Moreover, the POD- and DMD-analysis in this study demon- strate that DMD can serve as an important supplement for POD in analyzing a time-resolved physical process.
基金Project supported by the National Natural Science Foundation of China(Grant No.52079142).
文摘The flow field structure within the clearances of turbomachinery is complex and diverse, exhibiting high-dimensional nonlinearity. How to accurately extract the main structures that affect the internal flow within the turbine from the complex clearance flow has always been a key issue. To explore the impact of the dynamic structure of the clearance flow on the mainstream region in a centrifugal pump, this study combines the dynamic mode decomposition (DMD) method to conduct a thorough analysis of the velocity and pressure pulsation frequencies in the multi-physics fields within the clearance. The study has identified the main characteristic structures under different physical conditions in the clearance and has established the relationship between the characteristic structure frequencies in different physical fields and the impeller frequency. The research indicates that the internal flow within the clearance affects the occurrence of vortices in the volute. Under design conditions, the velocity field within the clearance is primarily influenced by high-order harmonic frequencies of the impeller, and the pressure field is mainly affected by low-order harmonic frequencies of the impeller. This reflects the crucial influence of impeller frequency and inlet flow on the coherent structures within the clearance flow. The research results offer new insights and methods for analyzing complex internal flows in large turbomachinery.
基金supported by the National Natural Science Foundation of China(Grant Nos.52201372,52131102).
文摘The flow around a circular cylinder for Re=1000 is characterized by flow separation and Karman vortex street.The typical flow features can be captured to study the correlation between fluid fields and sound fields.In this paper,the three-dimensional circular cylinder is taken as the research object,and the probes of surface fluctuating pressure and far field sound pressure are arranged every 10°.The directional diagram and the coherence of fluctuating pressure and sound pressure are analyzed.The relationship between the flow mode and hydrodynamic noise is studied by using dynamic mode decomposition(DMD).The characteristics of the dipole and quadrupole sound source term of a long span cylinder are studied.The results show that at the angles between 30°–120°and 190°–350°,the fluctuating pressure contributes more to the generation of dipole sounds.The quadrupole sound source shows three-dimensional effects,which is more obvious in a cylinder with large spanwise length.
基金This work was supported by Dong-A University research fund.(Corresponding author:J.Chang)
文摘Model order reduction(MOR)is considered as a good alternative to reduce the computational scale for electro-magnetic problems.The aim of this work is to introduce the use of dynamic mode decomposition(DMD)as a promising tool for MOR to analyze its effectiveness in creating a fast model-based design platform for the permanent magnet motor design for ur-ban aerial vehicles(UAVs).Using a singular value decomposition(SVD)based DMD,the design process is constructed and verified against different scenarios.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11871400 and 11971386)the Natural Science Foundation of Shaanxi Province,China(Grant No.2017JM1019).
文摘The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate thenonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation beforeapproximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic modedecomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, anovel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid oferror data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.52279081,51839001)supported by the Beijing Natural Science Foundation (Grant No.3232033)the Fundamental Research Funds for the Central Universities (Grant No.2023CX01004).
文摘The objective is to study the vortical structural behaviors of a transient pitching hydrofoil and their effects on the hydrodynamic performance. The pitching motion of the hydrofoil is set to pitch up with an almost constant rate from 5° to 15° and then back to 5°, with the Reynolds number 4.4×10^(5) and the frequency 2 Hz. The results show that the main coherent structures around the pitching hydrofoil include small-scale laminar separation bubble (LSB), large-scale second vortex (SV) and trailing edge vortex (TEV) which are all vortical. The relationship between the vortical structure and the lift is investigated with the finite-domain impulse theory. It indicates that the major part of the lift is contributed by the LSB, whereas the shedding and the formation of the SV and TEV cause the fluctuation of the lift. The proper orthogonal decomposition (POD) method is applied to capture the most energetic modes, revealing that the LSB mode occupies a large amount of energy in the flow field. The dynamic mode decomposition (DMD) method accurately extracts the dominant frequency and modal characteristics, with the first mode corresponding to the mean flow, the second mode corresponding to the LSB structure and the third and fourth modes corresponding to the vortex shedding.
基金Project supported by the National Natural Science Foundation of China(Grant No.52079142,51909131)supported by the Chinese Universities Scientific Fund(Grant No.2021TC107).
文摘As a high-dimensional complex nonlinear dynamic system,the analysis of the essence of flow has always been a difficult problem,especially in the flow including phase change.In recent years,it has become a feasible method to reduce the dimension of flow structure by reduced-order modeling(ROM)methods.In this paper,through the cavitation numerical simulation of NACA0015 hydrofoil,two ROM methods are used to reduce and restore three different cavitation respectively-proper orthogonal decomposition(POD)and dynamic mode decomposition(DMD).The applicability of two methods in cavitation is discussed and reasons are analyzed.The results show that for stable cavitation,POD,DMD methods can accurately restore the flow field of a few modes with high energy.For unstable cavitation,only POD method can restore real flow field well.This situation is mainly due to the fact that POD,DMD method are applicable to different energy ratios,and different main mode selection criterion of DMD will lead to different main mode.ROM can greatly simplify the complexity of flow.Selecting a reasonable ROM can improve the accuracy of a small amount of database,and provide a basis for intelligent prediction of flow analysis.
基金supported by the Opening Foundation of Jiangsu Key Laboratory of Environment Change&Ecological ConstructionNational Natural Science Foundation of China:[Grant Number 41372182]Research Center of Resource-exhausted Cities Transformation and Development:[Grant Number Kf2013y08]
文摘This paper proposes two concepts: the ecological footprint component index(EFCI) and the biocapacity component index(BCCI), based on the ecological footprint(EF) and Shannon entropy approaches. Per capita EFCI and BCCI in China 1949-2013 are analyzed using empirical mode decomposition(EMD). Nonlinear models of per capita EFCI and BCCI in China 1949-2013 are presented and their cycles and predictions from 2014 to 2023 are analyzed. The results over the last 65 years show:(1) EFCI in China has increased constantly with fluctuations, while BCCI has slowly decreased. Their annual change rates are 2.81% and-1.26%, respectively. The increasing EFCI indicates a gradual improvement in China's sustainable development potential; the decreasing BCCI indicates severe environmental and population challenges.(2) The cycles of per capita EFCI have periods of 5.4 and 16.3 years, while cycles of per capita BCCI have periods of 3.6, 13,and 21.7 years. The predictive models indicate that EFCI will first decrease, reaching 0.02725 in2014, and will subsequently increase to 0.03261 in 2021. BCCI will increase, reaching 0.01365 in2014 and 0.01541 in 2022. EFCI and BCCI will reach 0.03037 and 0.01537, respectively, in 2023.Policymakers should ensure that the EFCI and BCCI increase in 2023.
