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 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
This study experimentally investigates the hydrodynamic characteristics,geometric configurations,fluttering motions of the codend,and the instantaneous flow fields inside and around the codend,with and without a liner...This study experimentally investigates the hydrodynamic characteristics,geometric configurations,fluttering motions of the codend,and the instantaneous flow fields inside and around the codend,with and without a liner,under varying catch sizes and inflow velocities.A proper orthogonal decomposition method is employed to extract phase-averaged mean properties of unsteady turbulent flows from flow measurement data obtained using an electromagnetic current velocity meter inside and around the codend.The results reveal that as catch size increases,the drag force,codend motion,Reynolds number,and codend volume increase while the drag coefficient decreases.Owing to the codend shape and pronounced motion,a complex fluid–structure interaction occurs,demonstrating a strong correlation between drag force and codend volume.The oscillation amplitudes of the hydrodynamic forces and codend motions increase with increasing catch size,and their oscillations mainly involve low-frequency activity.A significant reduction in the flow field occurs inside and around the unlined codend without a catch.The flow field is 5.81%,14.39%,and 27.01%lower than the unlined codend with a catch,the codend with a liner but without a catch,and the codend with both a liner and a catch,respectively.Fourier analysis reveals that the codend motions and hydrodynamic forces are mainly characterized by low-frequency activity and are synchronized with the unsteady turbulent flow street.Furthermore,the proper orthogonal decomposition results reveal the development of unsteady turbulent flow inside and around the codend,driven by flow passage blockage caused by the presence of the liner,intense codend motions,and the catch.Understanding the hydrodynamic characteristics and flow instabilities inside and around the codend,particularly those associated with its fluttering motions,is crucial for optimizing trawl design and improving trawl selectivity.展开更多
Accurate real-time simulations of nuclear reactor circuit systems are particularly important for system safety analysis and design.To effectively improve computational efficiency without reducing accuracy,this study e...Accurate real-time simulations of nuclear reactor circuit systems are particularly important for system safety analysis and design.To effectively improve computational efficiency without reducing accuracy,this study establishes a thermal-hydraulics reduced-order model(ROM)for nuclear reactor circuit systems.The full-order circuit system calculation model is first established and verified and then used to calculate the thermal-hydraulic properties of the circuit system under different states as snapshots.The proper orthogonal decomposition method is used to extract the basis functions from snapshots,and the ROM is constructed using the least-squares method,effectively reducing the difficulty in constructing the ROM.A comparison between the full-order simulation and ROM prediction results of the AP1000 circuit system shows that the proposed ROM can improve computational efficiency by 1500 times while achieving a maximum relative error of 0.223%.This research develops a new direction and perspective for the digital twin modeling of nuclear reactor system circuits.展开更多
Segregated incompressible large eddy simulation and acoustic perturbation equations were used to obtain the flow field and sound field of 1:25 scale trains with three,six and eight coaches in a long tunnel,and the aer...Segregated incompressible large eddy simulation and acoustic perturbation equations were used to obtain the flow field and sound field of 1:25 scale trains with three,six and eight coaches in a long tunnel,and the aerodynamic results were verified by wind tunnel test with the same scale two-coach train model.Time-averaged drag coefficients of the head coach of three trains are similar,but at the tail coach of the multi-group trains it is much larger than that of the three-coach train.The eight-coach train presents the largest increment from the head coach to the tail coach in the standard deviation(STD)of aerodynamic force coefficients:0.0110 for drag coefficient(Cd),0.0198 for lift coefficient(Cl)and 0.0371 for side coef-ficient(Cs).Total sound pressure level at the bottom of multi-group trains presents a significant streamwise increase,which is different from the three-coach train.Tunnel walls affect the acoustic distribution at the bottom,only after the coach number reaches a certain value,and the streamwise increase in the sound pressure fluctuation of multi-group trains is strengthened by coach number.Fourier transform of the turbulent and sound pressures presents that coach number has little influence on the peak frequencies,but increases the sound pressure level values at the tail bogie cavities.Furthermore,different from the turbulent pressure,the first two sound pressure proper orthogonal decomposition(POD)modes in the bogie cavities contain 90%of the total energy,and the spatial distributions indicate that the acoustic distributions in the head and tail bogies are not related to coach number.展开更多
In this article, a reduced mixed finite element （MFE） formulation based on proper orthogonal decomposition （POD） for the non-stationary conduction-convection problems is presented. Also the error estimates between...In this article, a reduced mixed finite element （MFE） formulation based on proper orthogonal decomposition （POD） for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.展开更多
A proper orthogonal decomposition（POD） method was successfully used in the reduced-order modeling of complex systems.In this paper,we extend the applications of POD method,namely,apply POD method to a classical fini...A proper orthogonal decomposition（POD） method was successfully used in the reduced-order modeling of complex systems.In this paper,we extend the applications of POD method,namely,apply POD method to a classical finite element（FE） formulation for second-order hyperbolic equations with real practical applied background,establish a reduced FE formulation with lower dimensions and high enough accuracy,and provide the error estimates between the reduced FE solutions and the classical FE solutions and the implementation of algorithm for solving reduced FE formulation so as to provide scientific theoretic basis for service applications.Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions.Moreover,it is shown that the reduced FE formulation based on POD method is feasible and efficient for solving FE formulation for second-order hyperbolic equations.展开更多
In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equatio...In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.展开更多
In this article, a proper orthogonal decomposition （POD） method is used to study a classical splitting positive definite mixed finite element （SPDMFE） formulation for second- order hyperbolic equations. A POD redu...In this article, a proper orthogonal decomposition （POD） method is used to study a classical splitting positive definite mixed finite element （SPDMFE） formulation for second- order hyperbolic equations. A POD reduced-order SPDMFE extrapolating algorithm with lower dimensions and sufficiently high accuracy is established for second-order hyperbolic equations. The error estimates between the classical SPDMFE solutions and the reduced-order SPDMFE solutions obtained from the POD reduced-order SPDMFE extrapolating algorithm are provided. The implementation for solving the POD reduced-order SPDMFE extrapolating algorithm is given. Some numerical experiments are presented illustrating that the results of numerical computation are consistent with theoretical conclusions, thus validating that the POD reduced-order SPDMFE extrapolating algorithm is feasible and efficient for solving second-order hyperbolic equations.展开更多
A proper orthogonal decomposition （POD） technique is used to reduce the finite volume element （FVE） method for two-dimensional （2D） viscoelastic equations. A reduced-order fully discrete FVE algorithm with fewer...A proper orthogonal decomposition （POD） technique is used to reduce the finite volume element （FVE） method for two-dimensional （2D） viscoelastic equations. A reduced-order fully discrete FVE algorithm with fewer degrees of freedom and sufficiently high accuracy based on POD method is established. The error estimates of the reduced- order fully discrete FVE solutions and the implementation for solving the reduced-order fully discrete FVE algorithm are provided. Some numerical examples are used to illus- trate that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order fully discrete FVE algorithm is one of the most effective numerical methods by comparing with corresponding numerical results of finite element formulation and finite difference scheme and that the reduced-order fully discrete FVE algorithm based on POD method is feasible and efficient for solving 2D viscoelastic equations.展开更多
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.
基金sponsored by the National Natural Science Foundation of China(Grant No.32373187)the Research Fund for International Scientists of the National Natural Science Foundation of China(Grant No.32350410404)the Natural Science Foundation of Shanghai(Grant No.23ZR1427000).
文摘This study experimentally investigates the hydrodynamic characteristics,geometric configurations,fluttering motions of the codend,and the instantaneous flow fields inside and around the codend,with and without a liner,under varying catch sizes and inflow velocities.A proper orthogonal decomposition method is employed to extract phase-averaged mean properties of unsteady turbulent flows from flow measurement data obtained using an electromagnetic current velocity meter inside and around the codend.The results reveal that as catch size increases,the drag force,codend motion,Reynolds number,and codend volume increase while the drag coefficient decreases.Owing to the codend shape and pronounced motion,a complex fluid–structure interaction occurs,demonstrating a strong correlation between drag force and codend volume.The oscillation amplitudes of the hydrodynamic forces and codend motions increase with increasing catch size,and their oscillations mainly involve low-frequency activity.A significant reduction in the flow field occurs inside and around the unlined codend without a catch.The flow field is 5.81%,14.39%,and 27.01%lower than the unlined codend with a catch,the codend with a liner but without a catch,and the codend with both a liner and a catch,respectively.Fourier analysis reveals that the codend motions and hydrodynamic forces are mainly characterized by low-frequency activity and are synchronized with the unsteady turbulent flow street.Furthermore,the proper orthogonal decomposition results reveal the development of unsteady turbulent flow inside and around the codend,driven by flow passage blockage caused by the presence of the liner,intense codend motions,and the catch.Understanding the hydrodynamic characteristics and flow instabilities inside and around the codend,particularly those associated with its fluttering motions,is crucial for optimizing trawl design and improving trawl selectivity.
基金supported by the National Natural Science Foundation of China(No.12205389)Guangdong Basic and Applied Basic Research Foundation(No.2022A1515011735)Science and Technology on Reactor System Design Technology Laboratory(No.KFKT-05-FWHT-WU-2023014).
文摘Accurate real-time simulations of nuclear reactor circuit systems are particularly important for system safety analysis and design.To effectively improve computational efficiency without reducing accuracy,this study establishes a thermal-hydraulics reduced-order model(ROM)for nuclear reactor circuit systems.The full-order circuit system calculation model is first established and verified and then used to calculate the thermal-hydraulic properties of the circuit system under different states as snapshots.The proper orthogonal decomposition method is used to extract the basis functions from snapshots,and the ROM is constructed using the least-squares method,effectively reducing the difficulty in constructing the ROM.A comparison between the full-order simulation and ROM prediction results of the AP1000 circuit system shows that the proposed ROM can improve computational efficiency by 1500 times while achieving a maximum relative error of 0.223%.This research develops a new direction and perspective for the digital twin modeling of nuclear reactor system circuits.
基金supported by the National Natural Science Foundation of China (Grant No. 52072267)Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems (Grant No. 23DZ2229029)
文摘Segregated incompressible large eddy simulation and acoustic perturbation equations were used to obtain the flow field and sound field of 1:25 scale trains with three,six and eight coaches in a long tunnel,and the aerodynamic results were verified by wind tunnel test with the same scale two-coach train model.Time-averaged drag coefficients of the head coach of three trains are similar,but at the tail coach of the multi-group trains it is much larger than that of the three-coach train.The eight-coach train presents the largest increment from the head coach to the tail coach in the standard deviation(STD)of aerodynamic force coefficients:0.0110 for drag coefficient(Cd),0.0198 for lift coefficient(Cl)and 0.0371 for side coef-ficient(Cs).Total sound pressure level at the bottom of multi-group trains presents a significant streamwise increase,which is different from the three-coach train.Tunnel walls affect the acoustic distribution at the bottom,only after the coach number reaches a certain value,and the streamwise increase in the sound pressure fluctuation of multi-group trains is strengthened by coach number.Fourier transform of the turbulent and sound pressures presents that coach number has little influence on the peak frequencies,but increases the sound pressure level values at the tail bogie cavities.Furthermore,different from the turbulent pressure,the first two sound pressure proper orthogonal decomposition(POD)modes in the bogie cavities contain 90%of the total energy,and the spatial distributions indicate that the acoustic distributions in the head and tail bogies are not related to coach number.
基金supported by the National Science Foundation of China (10871022 11061009+5 种基金 40821092)the National Basic Research Program (2010CB428403 2009CB421407 2010CB951001)Natural Science Foundation of Hebei Province (A2010001663)Chinese Universities Scientific Fund (2009-2-05)
文摘In this article, a reduced mixed finite element （MFE） formulation based on proper orthogonal decomposition （POD） for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.
基金supported by the National Science Foundation of China (11061009,40821092)the National Basic Research Program (2010CB428403,2009CB421407,2010CB951001)Natural Science Foundation of Hebei Province (A2010001663)
文摘A proper orthogonal decomposition（POD） method was successfully used in the reduced-order modeling of complex systems.In this paper,we extend the applications of POD method,namely,apply POD method to a classical finite element（FE） formulation for second-order hyperbolic equations with real practical applied background,establish a reduced FE formulation with lower dimensions and high enough accuracy,and provide the error estimates between the reduced FE solutions and the classical FE solutions and the implementation of algorithm for solving reduced FE formulation so as to provide scientific theoretic basis for service applications.Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions.Moreover,it is shown that the reduced FE formulation based on POD method is feasible and efficient for solving FE formulation for second-order hyperbolic equations.
基金supported by the National Science Foundation of China(11271127 and 11061009)Science Research Program of Guizhou(GJ[2011]2367)the Co-Construction Project of Beijing Municipal Commission of Education
文摘In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.
基金supported by the National Science Foundation of China(11271127,11361035)Science Research of Guizhou Education Department(QJHKYZ[2013]207)Natural Science Foundation of Inner Mongolia(2012MS0106)
文摘In this article, a proper orthogonal decomposition （POD） method is used to study a classical splitting positive definite mixed finite element （SPDMFE） formulation for second- order hyperbolic equations. A POD reduced-order SPDMFE extrapolating algorithm with lower dimensions and sufficiently high accuracy is established for second-order hyperbolic equations. The error estimates between the classical SPDMFE solutions and the reduced-order SPDMFE solutions obtained from the POD reduced-order SPDMFE extrapolating algorithm are provided. The implementation for solving the POD reduced-order SPDMFE extrapolating algorithm is given. Some numerical experiments are presented illustrating that the results of numerical computation are consistent with theoretical conclusions, thus validating that the POD reduced-order SPDMFE extrapolating algorithm is feasible and efficient for solving second-order hyperbolic equations.
基金supported by the National Science Foundation of China(12271227,11061009 and 11061021)Natural Science Foundation of Inner Mongolia(2012MS0106)+3 种基金Science Research Program of Guizhou(GJ[2011]2367)Science Research Program of Inner Mongolia Advanced Education(NJ10006)Special Funds for Co-construction Project of BeijingNorth China Electric Power University
文摘A proper orthogonal decomposition （POD） technique is used to reduce the finite volume element （FVE） method for two-dimensional （2D） viscoelastic equations. A reduced-order fully discrete FVE algorithm with fewer degrees of freedom and sufficiently high accuracy based on POD method is established. The error estimates of the reduced- order fully discrete FVE solutions and the implementation for solving the reduced-order fully discrete FVE algorithm are provided. Some numerical examples are used to illus- trate that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order fully discrete FVE algorithm is one of the most effective numerical methods by comparing with corresponding numerical results of finite element formulation and finite difference scheme and that the reduced-order fully discrete FVE algorithm based on POD method is feasible and efficient for solving 2D viscoelastic equations.
