Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous f...Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous flows. In the area far away from the body, the traditional cloud of isotropic points is used, while in the adjacent area, the cloud of anisotropic points is distributed. In this way, the point spacing normal to the wall can be small enough for simulating the boundary layer, and meanwhile, the total number of points in the computational do- main can be controlled due to large spacing in other tangential direction through the anisotropic way. A fast mov- ing technique of clouds of points at each time-step is presented based on the attenuation law of disturbed motion for unsteady flows involving moving boundaries. In the mentioned cloud of points, a uniform weighted least- square curve fit method is utilized to discretize the spatial derivatives of the Navier-Stokes equations. The pro- posed gridless method, coupled with a dual time-stepping method and the Spalart-Allmaras turbulence model, is implemented for the Navier-Stokes equations. The computational results of unsteady viscous flows around a NLR7301 airfoil with an oscillating flap and a pitching NACA0012 airfoil are presented in a good agreement with the available experimental data.展开更多
The unsteady flow of a Casson fluid and heat transfer over a stretching surface in presence of suction/blowing are investigated. The transformed equations are solved numerically by using the shooting method. The exact...The unsteady flow of a Casson fluid and heat transfer over a stretching surface in presence of suction/blowing are investigated. The transformed equations are solved numerically by using the shooting method. The exact solution corre- sponding to the momentum equation for the steady case is obtained. Fluid velocity initially decreases with the increase of unsteadiness parameter. Due to an increasing Casson parameter the velocity field is suppressed. Thermal radiation enhances the effective thermal diffusivity and the temperature rises.展开更多
The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constru...The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell （UCM） model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration （suction） and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration （suction） and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.展开更多
Left ventricular assist device( LVAD) in this study is a mechanical tool that is used to support blood flow in the patient with heart disease. It supports left ventricle by building up the pressure to the pump outlet ...Left ventricular assist device( LVAD) in this study is a mechanical tool that is used to support blood flow in the patient with heart disease. It supports left ventricle by building up the pressure to the pump outlet connected to the aorta. This pump was designed based on the magnetic driven centrifugal pump with a unique small washout hole constructed inside the impeller to generate the washout flow passage to prevent the stagnation at the region underneath and around the rotor. Computational fluid dynamics( CFD) was adopted in this study to assess the performance and optimize the design to avoid recirculation and high shear stress which is the main cause of stagnation and blood damage. Transient simulation was used for this study due to the asymmetric design of the washout hole and the complication of the bottom support of the impeller that has a risk of thrombosis,also,it was used to predict the variation of hydraulic performance caused by the rotation of the impeller and pulsed flow at the pump inlet. The simulation results show no excessive stress and no recirculation observed within the computational domain; in addition,the research result also provides information for further optimization and development to the pump.展开更多
The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems.So,here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of...The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems.So,here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H_(2)O nanofluid on a flat surface in a porous medium is examined.Moreover,the thermal radiation and viscous dissipation effects are considered.The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method.The computed results can reveal many vital findings of practical importance.Firstly,dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows,the solution is unique.The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium.But different shapes of nanoparticles are not disturbing the dual solution existence range,though it has a considerable impact on thermal conductivity of the mixture.Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid,i.e.,the water here.On the other hand,the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium.Regarding the cooling rate of the heated surface,it rises with the permeability parameter,shape factor(related to various shapes of Cu-nanoparticles),and radiation parameter.The surface drag force becomes stronger with the permeability parameter.Also,with growing values of nanoparticle volume fraction,the boundary layer thickness(BLT)increases and the thermal BLT becomes thicker with larger values of shape factor.For decelerating unsteady flow,the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed.The thermal BLT is thicker with radiation parameter.Due to the existence of dual solutions,a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.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
A coupling model is proposed in this paper by using the Green Function and Newman＇s product principle, and the solution method is provided here as well. This model can be used to describe the reservoir inflow and wel...A coupling model is proposed in this paper by using the Green Function and Newman＇s product principle, and the solution method is provided here as well. This model can be used to describe the reservoir inflow and wellbore flow for fishbone wells in an unsteady flow or pseudo-steady flow state. A case study indicates that the bottom hole pressure declines quickly in the unsteady flow period which is very short. The pressure drop per unit time remains unchanged under the pseudo-steady flow conditions. The distribution of flow rate along the main wellbore shows a wave shape under the unsteady flow condition, and the flow rate distribution in each branch is similar. The flow rate distribution along the main wellbore is irregular ＂U＂ shaped under the pseudo-steady flow condition, and the space-symmetrical branches have the same flow distribution pattern. In the initial production period, the flow rate increases significantly as the length of branches and the angle between branches and the main wellbore increase. As the production continues, the length and angle of branches have only a slight effect on the flow in fishbone wells.展开更多
The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnet...The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.展开更多
A numerical simulation method is employed to investigate the effects of the unsteady plasma body force over the stalled NACA 0015 airfoil at low Reynolds number flow conditions. The plasma body force created by a diel...A numerical simulation method is employed to investigate the effects of the unsteady plasma body force over the stalled NACA 0015 airfoil at low Reynolds number flow conditions. The plasma body force created by a dielectric barrier discharge actuator is modeled with a phenomenological method for plasma simulation coupled with the compressible Navier-Stokes equations. The governing equations are solved using an efficient implicit finitevolume method. The responses of the separated flow field to the effects of an unsteady body force in various inter- pulses and duty cycles as well as different locations and magnitudes are studied. It is shown that the duty cycle and inter-pulse are key parameters for flow separation control. Additionally, it is concluded that the body force is able to attach the flow and can affect boundary layer grow that Mach number 0.1 and Reynolds number of 45000.展开更多
To date,there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity,due to the difficulties in theoretical analysis and numerical simulations.In this paper,we study the ch...To date,there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity,due to the difficulties in theoretical analysis and numerical simulations.In this paper,we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us.We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of(13944.7021,13946.5333)by the method of bisection.Through Fourier analysis,it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval.Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram,Kolmogorov entropy and maximal Lyapunov exponent.The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.展开更多
An implicit numerical scheme is developed based on the simplified marker and cell （SMAC） method to solve Reynolds-averaged equations in general curvilinear coordinates for three-dimensional （3-D） unsteady incompre...An implicit numerical scheme is developed based on the simplified marker and cell （SMAC） method to solve Reynolds-averaged equations in general curvilinear coordinates for three-dimensional （3-D） unsteady incompressible turbulent flow. The governing equations include the Reynolds-averaged momentum equations, in which contravariant velocities are unknown variables, pressure-correction Poisson equation and k- s turbulent equations. The governing equations are discretized in a 3-D MAC staggered grid system. To improve the numerical stability of the implicit SMAC scheme, the higherorder high-resolution Chakravarthy-Osher total variation diminishing （TVD） scheme is used to discretize the convective terms in momentum equations and k- e equations. The discretized algebraic momentum equations and k- s equations are solved by the time-diversion multiple access （CTDMA） method. The algebraic Poisson equations are solved by the Tschebyscheff SLOR （successive linear over relaxation） method with alternating computational directions. At the end of the paper, the unsteady flow at high Reynolds numbers through a simplified cascade made up of NACA65-410 blade are simulated with the program written according to the implicit numerical scheme. The reliability and accuracy of the implicit numerical scheme are verified through the satisfactory agreement between the numerical results of the surface pressure coefficient and experimental data. The numerical results indicate that Reynolds number and angle of attack are two primary factors affecting the characteristics of unsteady flow.展开更多
Continuous vorticity panels were used to model general unsteady inviscid, incompressible, two-dimensional flows. The geometry of the airfoil was approximated by series of short straight segments having endpoints that ...Continuous vorticity panels were used to model general unsteady inviscid, incompressible, two-dimensional flows. The geometry of the airfoil was approximated by series of short straight segments having endpoints that lie on the actual surface. A piecewise linear, continuous distribution of vorticity over the airfoil surface was used to generate disturbance flow. The no-penetration condition was imposed at the midpoint of each segment and at discrete times. The wake was simulated by a system of point vortices, which moved at local fluid velocity. At each time step, a new wake panel with uniform vorticity distribution was attached to the trailing edge, and the condition of constant circulation around the airfoil and wake was imposed. A new expression for Kutta condition was developed to study the interference effect between two impulsively started NACA0012 airfoils. The tandem arrangement was found to be the most effective to enhance the lift of the rear airfoil. The interference effect between tidal turbine blades was shown clearly.展开更多
A hybrid Cartesian structured grid method is proposed for solving moving boundary unsteady problems. The near body region is discretized by using the body-fitted structured grids, while the remaining computational dom...A hybrid Cartesian structured grid method is proposed for solving moving boundary unsteady problems. The near body region is discretized by using the body-fitted structured grids, while the remaining computational domain is tessellated with the generated Cartesian grids. As the body moves, the structured grids move with the body and the outer boundaries of inside grids are used to generate new holes in the outside adaptive Cartesian grid to facilitate data communication. By using the alternating digital tree （ADT） algorithm, the computational time of hole-cutting and identification of donor cells can be reduced significantly. A compressible solver for unsteady flow problems is developed. A cell-centered, second-order accurate finite volume method is employed in spatial discreti- zation and an implicit dual-time stepping low-upper symmetric Gauss-Seidei （LU-SGS） approach is employed in temporal discretization. Geometry-based adaptation is used during unsteady simulation time steps when boundary moves and the flow solution is interpolated from the old Cartesian grids to the new one with inverse distance weigh- ting interpolation formula. Both laminar and turbulent unsteady cases are tested to demonstrate the accuracy and efficiency of the proposed method. Then, a 2-D store separation problem is simulated. The result shows that the hybrid Cartesian grid method can handle the unsteady flow problems involving large-scale moving boundaries.展开更多
This paper presents a one-dimensional unsteady flow model and a numerical procedure based on the model. Comparisons between the theory and full scale experiments in a railway tunnel show that the model is capable of p...This paper presents a one-dimensional unsteady flow model and a numerical procedure based on the model. Comparisons between the theory and full scale experiments in a railway tunnel show that the model is capable of produce precise predictions for piston wind and pollutant concentration in railway tunnels.展开更多
基金Supported by the National Natural Science Foundation of China(10372043,11172134)the Fundingof Jiangsu Innovation Program for Graduate Education(CXZZ11-0192)~~
文摘Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous flows. In the area far away from the body, the traditional cloud of isotropic points is used, while in the adjacent area, the cloud of anisotropic points is distributed. In this way, the point spacing normal to the wall can be small enough for simulating the boundary layer, and meanwhile, the total number of points in the computational do- main can be controlled due to large spacing in other tangential direction through the anisotropic way. A fast mov- ing technique of clouds of points at each time-step is presented based on the attenuation law of disturbed motion for unsteady flows involving moving boundaries. In the mentioned cloud of points, a uniform weighted least- square curve fit method is utilized to discretize the spatial derivatives of the Navier-Stokes equations. The pro- posed gridless method, coupled with a dual time-stepping method and the Spalart-Allmaras turbulence model, is implemented for the Navier-Stokes equations. The computational results of unsteady viscous flows around a NLR7301 airfoil with an oscillating flap and a pitching NACA0012 airfoil are presented in a good agreement with the available experimental data.
基金Project supported by the Special Assistance Program,DSA Phase-1,UGC,New Delhi,India
文摘The unsteady flow of a Casson fluid and heat transfer over a stretching surface in presence of suction/blowing are investigated. The transformed equations are solved numerically by using the shooting method. The exact solution corre- sponding to the momentum equation for the steady case is obtained. Fluid velocity initially decreases with the increase of unsteadiness parameter. Due to an increasing Casson parameter the velocity field is suppressed. Thermal radiation enhances the effective thermal diffusivity and the temperature rises.
基金One of the authors(S.M.) was financially supported by UGC New Delhi,India through the Special Assistance Programme DSA Phase-1
文摘The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell （UCM） model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration （suction） and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration （suction） and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.
文摘Left ventricular assist device( LVAD) in this study is a mechanical tool that is used to support blood flow in the patient with heart disease. It supports left ventricle by building up the pressure to the pump outlet connected to the aorta. This pump was designed based on the magnetic driven centrifugal pump with a unique small washout hole constructed inside the impeller to generate the washout flow passage to prevent the stagnation at the region underneath and around the rotor. Computational fluid dynamics( CFD) was adopted in this study to assess the performance and optimize the design to avoid recirculation and high shear stress which is the main cause of stagnation and blood damage. Transient simulation was used for this study due to the asymmetric design of the washout hole and the complication of the bottom support of the impeller that has a risk of thrombosis,also,it was used to predict the variation of hydraulic performance caused by the rotation of the impeller and pulsed flow at the pump inlet. The simulation results show no excessive stress and no recirculation observed within the computational domain; in addition,the research result also provides information for further optimization and development to the pump.
文摘The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems.So,here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H_(2)O nanofluid on a flat surface in a porous medium is examined.Moreover,the thermal radiation and viscous dissipation effects are considered.The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method.The computed results can reveal many vital findings of practical importance.Firstly,dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows,the solution is unique.The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium.But different shapes of nanoparticles are not disturbing the dual solution existence range,though it has a considerable impact on thermal conductivity of the mixture.Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid,i.e.,the water here.On the other hand,the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium.Regarding the cooling rate of the heated surface,it rises with the permeability parameter,shape factor(related to various shapes of Cu-nanoparticles),and radiation parameter.The surface drag force becomes stronger with the permeability parameter.Also,with growing values of nanoparticle volume fraction,the boundary layer thickness(BLT)increases and the thermal BLT becomes thicker with larger values of shape factor.For decelerating unsteady flow,the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed.The thermal BLT is thicker with radiation parameter.Due to the existence of dual solutions,a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.
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support from the National Science and Technology Major Projects of China(Grant No. 2011ZX05031-003)
文摘A coupling model is proposed in this paper by using the Green Function and Newman＇s product principle, and the solution method is provided here as well. This model can be used to describe the reservoir inflow and wellbore flow for fishbone wells in an unsteady flow or pseudo-steady flow state. A case study indicates that the bottom hole pressure declines quickly in the unsteady flow period which is very short. The pressure drop per unit time remains unchanged under the pseudo-steady flow conditions. The distribution of flow rate along the main wellbore shows a wave shape under the unsteady flow condition, and the flow rate distribution in each branch is similar. The flow rate distribution along the main wellbore is irregular ＂U＂ shaped under the pseudo-steady flow condition, and the space-symmetrical branches have the same flow distribution pattern. In the initial production period, the flow rate increases significantly as the length of branches and the angle between branches and the main wellbore increase. As the production continues, the length and angle of branches have only a slight effect on the flow in fishbone wells.
文摘The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.
文摘A numerical simulation method is employed to investigate the effects of the unsteady plasma body force over the stalled NACA 0015 airfoil at low Reynolds number flow conditions. The plasma body force created by a dielectric barrier discharge actuator is modeled with a phenomenological method for plasma simulation coupled with the compressible Navier-Stokes equations. The governing equations are solved using an efficient implicit finitevolume method. The responses of the separated flow field to the effects of an unsteady body force in various inter- pulses and duty cycles as well as different locations and magnitudes are studied. It is shown that the duty cycle and inter-pulse are key parameters for flow separation control. Additionally, it is concluded that the body force is able to attach the flow and can affect boundary layer grow that Mach number 0.1 and Reynolds number of 45000.
基金Project supported by the National Natural Science Foundation of China(Grant No.12162001)the Natural Science Foundation of Ningxia(Grant No.2019AAC03129)the Construction Project of First-Class Disciplines in Ningxia Higher Education(Grant No.NXYLXK2017B09)。
文摘To date,there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity,due to the difficulties in theoretical analysis and numerical simulations.In this paper,we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us.We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of(13944.7021,13946.5333)by the method of bisection.Through Fourier analysis,it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval.Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram,Kolmogorov entropy and maximal Lyapunov exponent.The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.
文摘An implicit numerical scheme is developed based on the simplified marker and cell （SMAC） method to solve Reynolds-averaged equations in general curvilinear coordinates for three-dimensional （3-D） unsteady incompressible turbulent flow. The governing equations include the Reynolds-averaged momentum equations, in which contravariant velocities are unknown variables, pressure-correction Poisson equation and k- s turbulent equations. The governing equations are discretized in a 3-D MAC staggered grid system. To improve the numerical stability of the implicit SMAC scheme, the higherorder high-resolution Chakravarthy-Osher total variation diminishing （TVD） scheme is used to discretize the convective terms in momentum equations and k- e equations. The discretized algebraic momentum equations and k- s equations are solved by the time-diversion multiple access （CTDMA） method. The algebraic Poisson equations are solved by the Tschebyscheff SLOR （successive linear over relaxation） method with alternating computational directions. At the end of the paper, the unsteady flow at high Reynolds numbers through a simplified cascade made up of NACA65-410 blade are simulated with the program written according to the implicit numerical scheme. The reliability and accuracy of the implicit numerical scheme are verified through the satisfactory agreement between the numerical results of the surface pressure coefficient and experimental data. The numerical results indicate that Reynolds number and angle of attack are two primary factors affecting the characteristics of unsteady flow.
基金Sponsored by National Natural Science Foundation (No. 50279004)the National Hi-Tech. R&D Program of China (No. 2002aa516010)
文摘Continuous vorticity panels were used to model general unsteady inviscid, incompressible, two-dimensional flows. The geometry of the airfoil was approximated by series of short straight segments having endpoints that lie on the actual surface. A piecewise linear, continuous distribution of vorticity over the airfoil surface was used to generate disturbance flow. The no-penetration condition was imposed at the midpoint of each segment and at discrete times. The wake was simulated by a system of point vortices, which moved at local fluid velocity. At each time step, a new wake panel with uniform vorticity distribution was attached to the trailing edge, and the condition of constant circulation around the airfoil and wake was imposed. A new expression for Kutta condition was developed to study the interference effect between two impulsively started NACA0012 airfoils. The tandem arrangement was found to be the most effective to enhance the lift of the rear airfoil. The interference effect between tidal turbine blades was shown clearly.
基金supported partly by the National Basic Research Program of China(″973″Program)(No.2014CB046200)
文摘A hybrid Cartesian structured grid method is proposed for solving moving boundary unsteady problems. The near body region is discretized by using the body-fitted structured grids, while the remaining computational domain is tessellated with the generated Cartesian grids. As the body moves, the structured grids move with the body and the outer boundaries of inside grids are used to generate new holes in the outside adaptive Cartesian grid to facilitate data communication. By using the alternating digital tree （ADT） algorithm, the computational time of hole-cutting and identification of donor cells can be reduced significantly. A compressible solver for unsteady flow problems is developed. A cell-centered, second-order accurate finite volume method is employed in spatial discreti- zation and an implicit dual-time stepping low-upper symmetric Gauss-Seidei （LU-SGS） approach is employed in temporal discretization. Geometry-based adaptation is used during unsteady simulation time steps when boundary moves and the flow solution is interpolated from the old Cartesian grids to the new one with inverse distance weigh- ting interpolation formula. Both laminar and turbulent unsteady cases are tested to demonstrate the accuracy and efficiency of the proposed method. Then, a 2-D store separation problem is simulated. The result shows that the hybrid Cartesian grid method can handle the unsteady flow problems involving large-scale moving boundaries.
文摘This paper presents a one-dimensional unsteady flow model and a numerical procedure based on the model. Comparisons between the theory and full scale experiments in a railway tunnel show that the model is capable of produce precise predictions for piston wind and pollutant concentration in railway tunnels.
