A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal ...A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal decomposition(POD),and low-dimensional data are used to train an autoencoder(AE). By integrating the POD operator with the decoder, a nonlinear solution form is established and incorporated into a new maximum-a-posteriori(MAP)-based objective for online reconstruction.The numerical results on the two-dimensional(2D) Bhatnagar-Gross-Krook-Boltzmann(BGK-Boltzmann) equation, wave equation, shallow-water equation, and satellite data show that Gappy POD-AE achieves higher accuracy than gappy proper orthogonal decomposition(Gappy POD), especially for the data with slowly decaying singular values,and is more efficient in training than gappy autoencoder(Gappy AE). The MAP-based formulation and new gappy procedure further enhance the reconstruction accuracy.展开更多
Proper Orthogonal Decomposition （POD） provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition （CPOD） is presented as an innovati...Proper Orthogonal Decomposition （POD） provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition （CPOD） is presented as an innovative form of the POD based on cross power spectral density matrices. By introducing a discretizing scheme, the CPOD-based spectral representation method is obtained for use in stochastic simulation. Moreover, some criteria are proposed that allow the truncation order of CPOD to be conveniently determined. A numerical example to illustrate the application of the proposed method for the simulation of a wind velocity field is provided.展开更多
Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To...Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures（CSs） over a smooth surface and riblets, the proper orthogonal decomposition（POD） and finite-time Lyapunov exponent（FTLE） are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.展开更多
The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are base...The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.展开更多
The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are ...The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.展开更多
A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body ...A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric.The proper orthogonal decomposition(POD)analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1%of the turbulent kinetic energy,and hence their impact on the wake dynamics is studied.The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point.The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction.In addition,the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.展开更多
Proper orthogonal decomposition （POD） is an effective statistical technique for data reduction and feature extraction of the random field including the wind field. This paper introduces the theory of the POD and ill...Proper orthogonal decomposition （POD） is an effective statistical technique for data reduction and feature extraction of the random field including the wind field. This paper introduces the theory of the POD and illustrates engineering of structures. Using the POD technique, it is shown that wind pressure data can be accurately reconstructed with a limited number of modes using the wind pressure data from wind tunnel test. Comparing the reconstructed values by POD with the original measured values from the wind tunnel test both in the time and frequency domains, it is concluded that the proper orthogonal decomposition（POD） is an efficient and practical technique for deriving the random wind pressure field from limited known data as shown in the pitched roof example in this paper.展开更多
The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The b...The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The boundary value method(BVM),based on the finite difference method(FDM),can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield,which can reduce the storage burden of the RTM data.Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces,we develop a source wavefield reconstruction strategy based on the finite element method(FEM),using proper orthogonal decomposition(POD)to enhance computational efficiency.In this method,we divide the whole time period into several segments,and construct the POD basis functions to get a reduced order model(ROM)for the source wavefield reconstruction in each segment.We show the corresponding quantitative analysis of the storage requirement of the POD-FEM.Numerical tests on the homogeneous model show the effectiveness of the proposed method,while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method(FSM)and the BVM,and can be effectively applied in imaging.展开更多
Over the recent years there has been an increased trend in the use of Reduced Order Models （ROM） for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method （POD）...Over the recent years there has been an increased trend in the use of Reduced Order Models （ROM） for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method （POD） has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the case with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.展开更多
The proper orthogonal decomposition(POD)and the singular value decomposition(SVD) are used to study the finite difference scheme(FDS)for the nonstationary Navier-Stokes equations. Ensembles of data are compiled from t...The proper orthogonal decomposition(POD)and the singular value decomposition(SVD) are used to study the finite difference scheme(FDS)for the nonstationary Navier-Stokes equations. Ensembles of data are compiled from the transient solutions computed from the discrete equation system derived from the FDS for the nonstationary Navier-Stokes equations.The optimal orthogonal bases are reconstructed by the elements of the ensemble with POD and SVD.Combining the above procedures with a Galerkin projection approach yields a new optimizing FDS model with lower dimensions and a high accuracy for the nonstationary Navier-Stokes equations.The errors between POD approximate solutions and FDS solutions are analyzed.It is shown by considering the results obtained for numerical simulations of cavity flows that the error between POD approximate solution and FDS solution is consistent with theoretical results.Moreover,it is also shown that this validates the feasibility and efficiency of POD method.展开更多
A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accura...A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.展开更多
Large eddy simulation(LES)is used to calculate the in-cylinder turbulent flow field in a direct injection spark ignition(DISI)engine.The computations are carried out for three different maximum valve lifts(MVL)and thr...Large eddy simulation(LES)is used to calculate the in-cylinder turbulent flow field in a direct injection spark ignition(DISI)engine.The computations are carried out for three different maximum valve lifts(MVL)and throughout 100 consecutive engine cycles.The simulated results as well as corresponding particle image velocimetry(PIV)measurement database are analyzed by the proper orthogonal decomposition(POD)method.Through a new developed POD quadruple decomposition the instantaneous in-cylinder flow fields are decomposed into four parts,named mean field,coherent field,transition field and turbulent field,respectively.Then the in-cylinder turbulent flow characteristics and cycle-to-cycle variations(CCV)are studied separately upon the four part flow fields.Results indicate that each part exhibits its specific characteristics and has close connection with others.The mean part contains more than 50%of the total kinetic energy and the energy cascade phenomenon occurs among the four part fields;the coherent field part possesses the highest CCV level which dominates CCV of the bulk flow.In addition,it is observed that a change in MVL affects significantly the in-cylinder flow behavior including CCV,especially for the coherent part.Furthermore,the POD analysis demonstrates that at least 25 sample cycles for the mean velocity and 50 sample cycles for the RMS velocity are necessary for obtaining converged and correct results in CCV.展开更多
Direct numerical simulation(DNS) of forcing homogeneous isotropic turbulence with polymers was performed.In order to understand the polymers effect on turbulent coherent structures,proper orthogonal decomposition was ...Direct numerical simulation(DNS) of forcing homogeneous isotropic turbulence with polymers was performed.In order to understand the polymers effect on turbulent coherent structures,proper orthogonal decomposition was performed to identify coherent structures based on DNS data,so as to analyze the remarkable difference due to the addition of polymers.The results showed that the numbers for eigenmodes required for capturing coherent structures were 32 and 24 for the Newtonian fluid and polymer solution flows,respectively,which means the decrease of the complexity in polymer solution flow.Through the POD energy spectrum,it was found that the turbulent kinetic energy is distributed onto a large number of eigenmodes whether in the Newtonian fluid flow or polymer solution flow,suggesting that polymer solution flow is still turbulent in one aspect.Besides,the POD eigenmodes were investigated,which found that the small-scale structures are inhibited in polymer solution flow.展开更多
To clarify the complex relation between the pump blade shape and its corresponding hydraulic performance,the knowledge mining method of centrifugal pump impeller based on proper orthogonal decomposition(POD)was propos...To clarify the complex relation between the pump blade shape and its corresponding hydraulic performance,the knowledge mining method of centrifugal pump impeller based on proper orthogonal decomposition(POD)was proposed.The pump blade shape was parameterized by cubic Bezier curve.The Latin hypercube design method was employed to supply the necessary samples for producing the perturbations of blade wrap angle,and blade angle at inlet and outlet.The hydraulic efficiency and head were optimized by NSGA-II and RBF hybrid algorithm.The Pareto-optimal solutions were obtained.In order to further illustrate the relationship between the centrifugal pump blade shape and its hydraulic performance,the POD method was used to discover the effects of optimized blade shape to the flow solutions.For the optimization of centrifugal pump MH48-12.5,blade shape and relative velocity field in impeller from Pareto-optimal solutions were analyzed.The results demonstrate that larger blade angle and smaller wrap angle increase the average kinetic energy in impeller,resulting in higher pump head design.Smaller blade angle and larger wrap angle decrease the velocity gradient from the pressure side to suction side,resulting in smaller hydraulic loss and higher efficiency design.展开更多
The Proper Orthogonal Decomposition method is applied to the instantaneous velocity field within the rotor-stator inter-row region of a high-speed high-pressure centrifugal compressor. The processed data come from exp...The Proper Orthogonal Decomposition method is applied to the instantaneous velocity field within the rotor-stator inter-row region of a high-speed high-pressure centrifugal compressor. The processed data come from experiments and numerical simulations. In comparison with a Fourier transform, the POD gives the best modal approximation for both initial fields, in terms of the energy expressed on any given number of modes to be taken into account： to reach 98% of the total energy of the velocity field, the required number of POD modes is around nine times smaller than the number of Fourier harmonics. The individual POD modes are given and show that the unsteady rotor-stator interaction is already present in the very first modes.展开更多
The unsteady cloud cavitation shedding in fuel nozzles greatly influences the flow characteristics and spray break-up of fuel,thereby causing erosion damage.With the application of high-pressure common rail systems in...The unsteady cloud cavitation shedding in fuel nozzles greatly influences the flow characteristics and spray break-up of fuel,thereby causing erosion damage.With the application of high-pressure common rail systems in diesel engines,this phenomenon frequently occurs in the nozzle;however,cloud cavitation shedding frequency and its mechanism have yet to be studied in detail.In this study,a visualization experiment and proper orthogonal decomposition(POD)method were used to study the variations in the cavitation shedding frequency and analyze the cavitation flow structure in a 3 mm square nozzle.In addition,large eddy simulation(LES)was performed to explore the causes of cavitation shedding,and the relationship between cavitation and vortices.With the increase of the inlet and outlet pressure differences,and fuel temperatures,the degree of cavitation intensified and the frequency of cavitation cloud shedding gradually decreased.LES demonstrated the relationship between the vortices,and the development,shedding,and collapse of the cavitation clouds.Further,the re-entrant jet mechanism was found to be the main reason for the shedding of cavitation clouds.Through comparative experiments,the fluctuation of the vapor volume fraction in the nozzle hole accurately predicted the regions with stable cavitation,re-entrant jet,cavitation cloud shedding,and collapse.The frequency of cavitation shedding can then be calculated.This study employed an instantaneous POD method based on instantaneous cavitation images,which can distinguish the evolution process and characteristics of cavitation in the nozzle hole of diesel engines.展开更多
The objective of this work is to reveal the effect of a passive control method called wedge-type cavitating-bubble generator(WCG)on the cloud cavitation dynamics of National Advisory Committee for Aeronautics(NACA)66 ...The objective of this work is to reveal the effect of a passive control method called wedge-type cavitating-bubble generator(WCG)on the cloud cavitation dynamics of National Advisory Committee for Aeronautics(NACA)66 hydrofoil.The simulations are performed using the Partially-averaged Navier-Stokes(PANS)method coupled with the Zwart cavitation model.The proper orthogonal decomposition(POD)method is applied to extract the dominant flow structures.The results show that the WCG can induce the attached cavity to occur just behind the WCG instead of the hydrofoil leading edge.During the periodical time-evolution process of the unsteady cavity,it is found that the attached cavity with a larger scale around the hydrofoil with WCG has a rougher surface,accompanied with more shedding behaviors of small cavities.This is further illustrated by the POD modes,that is,the mode 1 and modes 2–4 present the large and small cavity vortex structures respectively.Meanwhile,the dominant frequencies of 50 Hz,47.5 Hz are given by the POD method respectively for the hydrofoils without and with WCG,which is in good agreement with that of FFT analysis.In addition,the correlation distribution of POD modal coefficients shows that the WCG can strengthen the vortex energy as well as the turbulence intensity.展开更多
Improved delay detached eddy simulation is performed to explore the flow features and aero-optical effects of turrets with different bottom cylinder height at a freestream Mach number Ma=0.7.Analysis of both the time-...Improved delay detached eddy simulation is performed to explore the flow features and aero-optical effects of turrets with different bottom cylinder height at a freestream Mach number Ma=0.7.Analysis of both the time-averaged and instantaneous flow features demonstrate that the shock motion causes the oscillation of separated shear layer.In flow analysis,two unsteady shock-wake-correlated modes are discerned:the asymmetric shifting mode and the symmetric breathing mode.With the increase of cylinder height,the relative energy of shock gradually increases,which goes from 26%to 59%.The proper orthogonal decomposition analysis yields the single frequency peak for the two dominant modes.The frequency peaks of shifting mode are generally at StD<0.23,while the frequency peaks of breathing mode are generally at StD>0.26.The dynamic mode decomposition analysis gives range of frequency peak.The frequency peaks of shifting mode are in the range of StD=0.11-0.23,and the frequency peaks of breathing mode are in range of StD=0.26-0.41.Optical distortion analysis indicates that the distortion calculated in five cases is linked to the breathing mode.When the beam passes through the turbulent wake,it exhibits the high-frequency and high-amplitude characteristics.展开更多
The intrinsic interaction mechanism of flutter between the flow and structure of a rectangular plate remains a mystery from the viewpoint of unsteady flow.The present study provides a novel insight into this interacti...The intrinsic interaction mechanism of flutter between the flow and structure of a rectangular plate remains a mystery from the viewpoint of unsteady flow.The present study provides a novel insight into this interaction mechanism based on an adequate understanding of the formation and evolution of the flapping leading-edge vortex(LEV).A series of wind tunnel tests was conducted to investigate the nonlinear flutter instability of an 8∶1 rectangular plate.The complete flow fields around the model throughout the flutter process were obtained by a particle image velocimetry(PIV)technique using two synchronous cameras with an interpolation and resampling method.To acquire the flow structures corresponding to the characteristic frequency of flutter,the spectral proper orthogonal decomposition(SPOD)method was extended to a noninertial frame to reconstruct the low-rank flow field during flutter and extract the characteristic flow pattern coupled with oscillations.It was found that when the 8∶1 rectangular plate undergoes flutter,the LEVs exhibit a periodic flapping phenomenon induced by the structure oscillations.A two-dimensional correlation analysis of the flapping LEVs was conducted for different inflow velocities.The results demonstrate that there is a substantial phase lead phenomenon in the LEV evolution downstream for a higher inflow velocity.This phenomenon may be related to a phase offset of aerodynamic forces,and finally,it gives rise to flutter.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 d...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
基金supported by the National Natural Science Foundation of China(No.12472197)。
文摘A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal decomposition(POD),and low-dimensional data are used to train an autoencoder(AE). By integrating the POD operator with the decoder, a nonlinear solution form is established and incorporated into a new maximum-a-posteriori(MAP)-based objective for online reconstruction.The numerical results on the two-dimensional(2D) Bhatnagar-Gross-Krook-Boltzmann(BGK-Boltzmann) equation, wave equation, shallow-water equation, and satellite data show that Gappy POD-AE achieves higher accuracy than gappy proper orthogonal decomposition(Gappy POD), especially for the data with slowly decaying singular values,and is more efficient in training than gappy autoencoder(Gappy AE). The MAP-based formulation and new gappy procedure further enhance the reconstruction accuracy.
基金Research Fund for Communications in Western China Under Grant No. 200431800028
文摘Proper Orthogonal Decomposition （POD） provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition （CPOD） is presented as an innovative form of the POD based on cross power spectral density matrices. By introducing a discretizing scheme, the CPOD-based spectral representation method is obtained for use in stochastic simulation. Moreover, some criteria are proposed that allow the truncation order of CPOD to be conveniently determined. A numerical example to illustrate the application of the proposed method for the simulation of a wind velocity field is provided.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11332006,11732010,11572221,and 11502066)the Natural Science Foundation of Tianjin City(Grant No.18JCQNJC5100)
文摘Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures（CSs） over a smooth surface and riblets, the proper orthogonal decomposition（POD） and finite-time Lyapunov exponent（FTLE） are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.
基金Project supported by the National Natural Science Foundation of China(Nos.11232011,11402262,11572314,and 11621202)
文摘The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.
基金National Natural Science Foundation of China (No.10671153)
文摘The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.
文摘A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric.The proper orthogonal decomposition(POD)analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1%of the turbulent kinetic energy,and hence their impact on the wake dynamics is studied.The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point.The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction.In addition,the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.
基金Acknowledgements The authors are grateful for the support of this research by the Committee of National Science Foundation of China （50908077） and Foundation of Heilongjiang Province Educational Committee （11551368）.
文摘Proper orthogonal decomposition （POD） is an effective statistical technique for data reduction and feature extraction of the random field including the wind field. This paper introduces the theory of the POD and illustrates engineering of structures. Using the POD technique, it is shown that wind pressure data can be accurately reconstructed with a limited number of modes using the wind pressure data from wind tunnel test. Comparing the reconstructed values by POD with the original measured values from the wind tunnel test both in the time and frequency domains, it is concluded that the proper orthogonal decomposition（POD） is an efficient and practical technique for deriving the random wind pressure field from limited known data as shown in the pitched roof example in this paper.
基金This work was supported by Natural Science Basic Research Program of Shaanxi(Program No.2023-JC-YB-269)the National Natural Science Foundation of China(Grant No.41974122).
文摘The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The boundary value method(BVM),based on the finite difference method(FDM),can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield,which can reduce the storage burden of the RTM data.Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces,we develop a source wavefield reconstruction strategy based on the finite element method(FEM),using proper orthogonal decomposition(POD)to enhance computational efficiency.In this method,we divide the whole time period into several segments,and construct the POD basis functions to get a reduced order model(ROM)for the source wavefield reconstruction in each segment.We show the corresponding quantitative analysis of the storage requirement of the POD-FEM.Numerical tests on the homogeneous model show the effectiveness of the proposed method,while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method(FSM)and the BVM,and can be effectively applied in imaging.
文摘Over the recent years there has been an increased trend in the use of Reduced Order Models （ROM） for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method （POD） has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the case with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.
基金the National Natural Science Foundation of China(Grant Nos.10471100,40437017,and 60573158)Beijing Jiaotong University Science and Technology Foundation
文摘The proper orthogonal decomposition(POD)and the singular value decomposition(SVD) are used to study the finite difference scheme(FDS)for the nonstationary Navier-Stokes equations. Ensembles of data are compiled from the transient solutions computed from the discrete equation system derived from the FDS for the nonstationary Navier-Stokes equations.The optimal orthogonal bases are reconstructed by the elements of the ensemble with POD and SVD.Combining the above procedures with a Galerkin projection approach yields a new optimizing FDS model with lower dimensions and a high accuracy for the nonstationary Navier-Stokes equations.The errors between POD approximate solutions and FDS solutions are analyzed.It is shown by considering the results obtained for numerical simulations of cavity flows that the error between POD approximate solution and FDS solution is consistent with theoretical results.Moreover,it is also shown that this validates the feasibility and efficiency of POD method.
基金supported by National Natural Science Foundation of China (Grant Nos. 10871022, 10771065,and 60573158)Natural Science Foundation of Hebei Province (Grant No. A2007001027)
文摘A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.
基金supported by the National Natural Science Foundation of China(Grant Nos.51176020 and 51376029)
文摘Large eddy simulation(LES)is used to calculate the in-cylinder turbulent flow field in a direct injection spark ignition(DISI)engine.The computations are carried out for three different maximum valve lifts(MVL)and throughout 100 consecutive engine cycles.The simulated results as well as corresponding particle image velocimetry(PIV)measurement database are analyzed by the proper orthogonal decomposition(POD)method.Through a new developed POD quadruple decomposition the instantaneous in-cylinder flow fields are decomposed into four parts,named mean field,coherent field,transition field and turbulent field,respectively.Then the in-cylinder turbulent flow characteristics and cycle-to-cycle variations(CCV)are studied separately upon the four part flow fields.Results indicate that each part exhibits its specific characteristics and has close connection with others.The mean part contains more than 50%of the total kinetic energy and the energy cascade phenomenon occurs among the four part fields;the coherent field part possesses the highest CCV level which dominates CCV of the bulk flow.In addition,it is observed that a change in MVL affects significantly the in-cylinder flow behavior including CCV,especially for the coherent part.Furthermore,the POD analysis demonstrates that at least 25 sample cycles for the mean velocity and 50 sample cycles for the RMS velocity are necessary for obtaining converged and correct results in CCV.
基金supported by the National Natural Science Foundation of China (Grant No.10872060)the Fundamental Research Funds for the Central Universities (Grant Nos.HIT.BRET1.2010008, HIT.NSRIF.2012070)+1 种基金the Doctoral Fund of Ministry of Education of China (Grant No.20112302110020)the China Postdoctoral Science Foundation (Grant No.2011M500652)
文摘Direct numerical simulation(DNS) of forcing homogeneous isotropic turbulence with polymers was performed.In order to understand the polymers effect on turbulent coherent structures,proper orthogonal decomposition was performed to identify coherent structures based on DNS data,so as to analyze the remarkable difference due to the addition of polymers.The results showed that the numbers for eigenmodes required for capturing coherent structures were 32 and 24 for the Newtonian fluid and polymer solution flows,respectively,which means the decrease of the complexity in polymer solution flow.Through the POD energy spectrum,it was found that the turbulent kinetic energy is distributed onto a large number of eigenmodes whether in the Newtonian fluid flow or polymer solution flow,suggesting that polymer solution flow is still turbulent in one aspect.Besides,the POD eigenmodes were investigated,which found that the small-scale structures are inhibited in polymer solution flow.
基金supported by the National Key Research and Development Program of China(2016YFB0200901)the National Natural Science Foundation of China(51979135,51976183)the Longyuan Young Innovative Talents Program。
文摘To clarify the complex relation between the pump blade shape and its corresponding hydraulic performance,the knowledge mining method of centrifugal pump impeller based on proper orthogonal decomposition(POD)was proposed.The pump blade shape was parameterized by cubic Bezier curve.The Latin hypercube design method was employed to supply the necessary samples for producing the perturbations of blade wrap angle,and blade angle at inlet and outlet.The hydraulic efficiency and head were optimized by NSGA-II and RBF hybrid algorithm.The Pareto-optimal solutions were obtained.In order to further illustrate the relationship between the centrifugal pump blade shape and its hydraulic performance,the POD method was used to discover the effects of optimized blade shape to the flow solutions.For the optimization of centrifugal pump MH48-12.5,blade shape and relative velocity field in impeller from Pareto-optimal solutions were analyzed.The results demonstrate that larger blade angle and smaller wrap angle increase the average kinetic energy in impeller,resulting in higher pump head design.Smaller blade angle and larger wrap angle decrease the velocity gradient from the pressure side to suction side,resulting in smaller hydraulic loss and higher efficiency design.
文摘The Proper Orthogonal Decomposition method is applied to the instantaneous velocity field within the rotor-stator inter-row region of a high-speed high-pressure centrifugal compressor. The processed data come from experiments and numerical simulations. In comparison with a Fourier transform, the POD gives the best modal approximation for both initial fields, in terms of the energy expressed on any given number of modes to be taken into account： to reach 98% of the total energy of the velocity field, the required number of POD modes is around nine times smaller than the number of Fourier harmonics. The individual POD modes are given and show that the unsteady rotor-stator interaction is already present in the very first modes.
基金This work was supported by of the National Natural Science Foundation of China(No.50906041).
文摘The unsteady cloud cavitation shedding in fuel nozzles greatly influences the flow characteristics and spray break-up of fuel,thereby causing erosion damage.With the application of high-pressure common rail systems in diesel engines,this phenomenon frequently occurs in the nozzle;however,cloud cavitation shedding frequency and its mechanism have yet to be studied in detail.In this study,a visualization experiment and proper orthogonal decomposition(POD)method were used to study the variations in the cavitation shedding frequency and analyze the cavitation flow structure in a 3 mm square nozzle.In addition,large eddy simulation(LES)was performed to explore the causes of cavitation shedding,and the relationship between cavitation and vortices.With the increase of the inlet and outlet pressure differences,and fuel temperatures,the degree of cavitation intensified and the frequency of cavitation cloud shedding gradually decreased.LES demonstrated the relationship between the vortices,and the development,shedding,and collapse of the cavitation clouds.Further,the re-entrant jet mechanism was found to be the main reason for the shedding of cavitation clouds.Through comparative experiments,the fluctuation of the vapor volume fraction in the nozzle hole accurately predicted the regions with stable cavitation,re-entrant jet,cavitation cloud shedding,and collapse.The frequency of cavitation shedding can then be calculated.This study employed an instantaneous POD method based on instantaneous cavitation images,which can distinguish the evolution process and characteristics of cavitation in the nozzle hole of diesel engines.
基金Project supported by the National Natural Science Foundation of China(Grant No.52076108).
文摘The objective of this work is to reveal the effect of a passive control method called wedge-type cavitating-bubble generator(WCG)on the cloud cavitation dynamics of National Advisory Committee for Aeronautics(NACA)66 hydrofoil.The simulations are performed using the Partially-averaged Navier-Stokes(PANS)method coupled with the Zwart cavitation model.The proper orthogonal decomposition(POD)method is applied to extract the dominant flow structures.The results show that the WCG can induce the attached cavity to occur just behind the WCG instead of the hydrofoil leading edge.During the periodical time-evolution process of the unsteady cavity,it is found that the attached cavity with a larger scale around the hydrofoil with WCG has a rougher surface,accompanied with more shedding behaviors of small cavities.This is further illustrated by the POD modes,that is,the mode 1 and modes 2–4 present the large and small cavity vortex structures respectively.Meanwhile,the dominant frequencies of 50 Hz,47.5 Hz are given by the POD method respectively for the hydrofoils without and with WCG,which is in good agreement with that of FFT analysis.In addition,the correlation distribution of POD modal coefficients shows that the WCG can strengthen the vortex energy as well as the turbulence intensity.
基金funded by the National Key Lab Foundation,China(No.2020KLF030101)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China(No.CX2025031)Shaanxi Innovative Research Team of Artificial Intelligence for Fluid Mechanics,China(No.2024RS-CXTD-16)。
文摘Improved delay detached eddy simulation is performed to explore the flow features and aero-optical effects of turrets with different bottom cylinder height at a freestream Mach number Ma=0.7.Analysis of both the time-averaged and instantaneous flow features demonstrate that the shock motion causes the oscillation of separated shear layer.In flow analysis,two unsteady shock-wake-correlated modes are discerned:the asymmetric shifting mode and the symmetric breathing mode.With the increase of cylinder height,the relative energy of shock gradually increases,which goes from 26%to 59%.The proper orthogonal decomposition analysis yields the single frequency peak for the two dominant modes.The frequency peaks of shifting mode are generally at StD<0.23,while the frequency peaks of breathing mode are generally at StD>0.26.The dynamic mode decomposition analysis gives range of frequency peak.The frequency peaks of shifting mode are in the range of StD=0.11-0.23,and the frequency peaks of breathing mode are in range of StD=0.26-0.41.Optical distortion analysis indicates that the distortion calculated in five cases is linked to the breathing mode.When the beam passes through the turbulent wake,it exhibits the high-frequency and high-amplitude characteristics.
基金The National Natural Science Foundation of China(No.52178470)the National Key Research and Development Program of China(No.2022YFC3005303).
文摘The intrinsic interaction mechanism of flutter between the flow and structure of a rectangular plate remains a mystery from the viewpoint of unsteady flow.The present study provides a novel insight into this interaction mechanism based on an adequate understanding of the formation and evolution of the flapping leading-edge vortex(LEV).A series of wind tunnel tests was conducted to investigate the nonlinear flutter instability of an 8∶1 rectangular plate.The complete flow fields around the model throughout the flutter process were obtained by a particle image velocimetry(PIV)technique using two synchronous cameras with an interpolation and resampling method.To acquire the flow structures corresponding to the characteristic frequency of flutter,the spectral proper orthogonal decomposition(SPOD)method was extended to a noninertial frame to reconstruct the low-rank flow field during flutter and extract the characteristic flow pattern coupled with oscillations.It was found that when the 8∶1 rectangular plate undergoes flutter,the LEVs exhibit a periodic flapping phenomenon induced by the structure oscillations.A two-dimensional correlation analysis of the flapping LEVs was conducted for different inflow velocities.The results demonstrate that there is a substantial phase lead phenomenon in the LEV evolution downstream for a higher inflow velocity.This phenomenon may be related to a phase offset of aerodynamic forces,and finally,it gives rise to flutter.
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.
