Kolmogorov's 1941 theory(K41)of similarity hypotheses and the-5/3 law for energy spectrum are considered as the most important theoretical achievement in turbulence research and the success of the modem turbulence...Kolmogorov's 1941 theory(K41)of similarity hypotheses and the-5/3 law for energy spectrum are considered as the most important theoretical achievement in turbulence research and the success of the modem turbulence theory.The assumptions of sufficient high Reynolds number and isotropy of turbulence that K41 based upon,however,cannot generally be met in practice,and thus discrepancy is often observed between the f law and direct numerical simulation(DNS)results of boundary layers in wall bounded turbulence,especially for moderate to low Reynolds number flows.Liutex vector is a recently defined new physical quantity which is extracted from turbulent flow to represent the rigid rotation part of fluid motion.Actually,Liutex is free from viscous dissipation and thus independent of Reynolds number,relaxing the very high Reynold number assumption of K41.Liutex similarity has been solidly demonstrated by DNS for a moderate Reynolds number turbulent boundary layer(Reθ≈1000),both the frequency and wavenumber spectrum of Liutex accurately matches the-5/3 law,which is obviously much better than the turbulence energy spectrum,while vorticity and other popular vortex identification methods,Q criterion for example,do not possess such a distinguished feature due to stretching and shearing contamination.展开更多
The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow.In this method,it is demonstrated that the transition to turbulenc...The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow.In this method,it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance,for given imposed disturbance.For a given flow geometry and fluid properties,when the maximum of the function K(a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction)in the flow field is larger than a certain critical value,it is expected that instability would occur for some initial disturbances.In this paper,using the energy gradient analysis,the equation for calculating the energy gradient function K for plane Couette flow is derived.The result indicates that K reaches the maximum at the moving walls.Thus,the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain.The critical value of K at turbulent transition,which is observed from experiments,is about 370 for plane Couette flow when two walls move in opposite directions(anti-symmetry).This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow(385-389).Therefore,it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure(symmetrical case)and shear driven flows(anti-symmetrical case).展开更多
The stability of the flow under the magnetic force is one of the classical problems in fluid mechanics.In this paper,the flow in a rectangular duct with different Hartmann(Ha)number is simulated.The finite volume meth...The stability of the flow under the magnetic force is one of the classical problems in fluid mechanics.In this paper,the flow in a rectangular duct with different Hartmann(Ha)number is simulated.The finite volume method and the SIMPLE algorithm are used to solve a system of equations and the energy gradient theory is then used to study the(associated)stability of magnetohydrodynamics(MHD).According to the energy gradient theory,K represents the ratio of energy gradient in transverse direction and the energy loss due to viscosity in streamline direction.Position with large K will lose its stability earlier than that with small K.The flow stability of MHD flow for different Hartmann(Ha)number,from Ha=1 to 40,at the fixed Reynolds number,Re=190 are investigated.The simulation is validated firstly against the simulation in literature.The results show that,with the increasing Ha number,the centerline velocity of the rectangular duct with MHD flow decreases and the absolute value of the gradient of total mechanical energy along the streamwise direction increases.The maximum of K appears near the wall in both coordinate axis of the duct.According to the energy gradient theory,this position of the maximum of K would initiate flow instability(if any)than the other positions.The higher the Hartmann number is,the smaller the K value becomes,which means that the fluid becomes more stable in the presence of higher magnetic force.As the Hartmann number increases,the K value in the parallel layer decreases more significantly than in the Hartmann layer.The most dangerous position of instability tends to migrate towards wall of the duct as the Hartmann number increases.Thus,with the energy gradient theory,the stability or instability in the rectangular duct can be controlled by modulating the magnetic force.展开更多
Numerical simulation based on the Euler equation and one-step reaction model is carried out to investigate the process of deflagration to detonation transition(DDT)occurring in a straight duct.The numerical method use...Numerical simulation based on the Euler equation and one-step reaction model is carried out to investigate the process of deflagration to detonation transition(DDT)occurring in a straight duct.The numerical method used includes a high resolution fifth-order weighted essentially non-oscillatory(WENO)scheme for spatial discretization,coupled with a third order total variation diminishing Runge-Kutta time stepping method.In particular,effect of energy release on the DDT process is studied.The model parameters used are the heat release at q=50,30,25,20,15,10 and 5,the specific heat ratio at 1.2,and the activation temperature at Ti=15,respectively.For all the cases,the initial energy in the spark is about the same compared to the detonation energy at the Chapman-Jouguet(CJ)state.It is found from the simulation that the DDT occurrence strongly depends on the magnitude of the energy release.The run-up distance of DDT occurrence decreases with the increase of the energy release for q=5020,and increases with the increase of the energy release for q=205.This phenomenon is found to be in agreement with the analysis of mathematical stability theory.It is suggested that the factors to strengthen the DDT would make the detonation more stable,and vice versa.Finally,it is concluded from the simulations that the interaction of the shock wave and the flame front is the main reason for leading to DDT.展开更多
In the present work,both computational and experimentalmethods are employed to study the two-phase flow occurring in a model pump sump.The twofluid model of the two-phase flow has been applied to the simulation of the...In the present work,both computational and experimentalmethods are employed to study the two-phase flow occurring in a model pump sump.The twofluid model of the two-phase flow has been applied to the simulation of the threedimensional cavitating flow.The governing equations of the two-phase cavitating flow are derived from the kinetic theory based on the Boltzmann equation.The isotropic RNG k−ε−kca turbulence model of two-phase flows in the form of cavity number instead of the formof cavity phase volume fraction is developed.The RNG k−ε−kca turbulence model,that is the RNG k−εturbulence model for the liquid phase combined with the kca model for the cavity phase,is employed to close the governing turbulent equations of the two-phase flow.The computation of the cavitating flow through a model pump sump has been carried out with this model in three-dimensional spaces.The calculated results have been compared with the data of the PIV experiment.Good qualitative agreement has been achievedwhich exhibits the reliability of the numerical simulation model.展开更多
文摘Kolmogorov's 1941 theory(K41)of similarity hypotheses and the-5/3 law for energy spectrum are considered as the most important theoretical achievement in turbulence research and the success of the modem turbulence theory.The assumptions of sufficient high Reynolds number and isotropy of turbulence that K41 based upon,however,cannot generally be met in practice,and thus discrepancy is often observed between the f law and direct numerical simulation(DNS)results of boundary layers in wall bounded turbulence,especially for moderate to low Reynolds number flows.Liutex vector is a recently defined new physical quantity which is extracted from turbulent flow to represent the rigid rotation part of fluid motion.Actually,Liutex is free from viscous dissipation and thus independent of Reynolds number,relaxing the very high Reynold number assumption of K41.Liutex similarity has been solidly demonstrated by DNS for a moderate Reynolds number turbulent boundary layer(Reθ≈1000),both the frequency and wavenumber spectrum of Liutex accurately matches the-5/3 law,which is obviously much better than the turbulence energy spectrum,while vorticity and other popular vortex identification methods,Q criterion for example,do not possess such a distinguished feature due to stretching and shearing contamination.
文摘The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow.In this method,it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance,for given imposed disturbance.For a given flow geometry and fluid properties,when the maximum of the function K(a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction)in the flow field is larger than a certain critical value,it is expected that instability would occur for some initial disturbances.In this paper,using the energy gradient analysis,the equation for calculating the energy gradient function K for plane Couette flow is derived.The result indicates that K reaches the maximum at the moving walls.Thus,the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain.The critical value of K at turbulent transition,which is observed from experiments,is about 370 for plane Couette flow when two walls move in opposite directions(anti-symmetry).This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow(385-389).Therefore,it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure(symmetrical case)and shear driven flows(anti-symmetrical case).
基金This work is supported by National Natural Science Foundation of China(Nos.51536008,51579224)Zhejiang Province Science and Technology Plan Project(No.2017C34007)Zhejiang Province Key Research and Development Plan Project(No.2018C03046).
文摘The stability of the flow under the magnetic force is one of the classical problems in fluid mechanics.In this paper,the flow in a rectangular duct with different Hartmann(Ha)number is simulated.The finite volume method and the SIMPLE algorithm are used to solve a system of equations and the energy gradient theory is then used to study the(associated)stability of magnetohydrodynamics(MHD).According to the energy gradient theory,K represents the ratio of energy gradient in transverse direction and the energy loss due to viscosity in streamline direction.Position with large K will lose its stability earlier than that with small K.The flow stability of MHD flow for different Hartmann(Ha)number,from Ha=1 to 40,at the fixed Reynolds number,Re=190 are investigated.The simulation is validated firstly against the simulation in literature.The results show that,with the increasing Ha number,the centerline velocity of the rectangular duct with MHD flow decreases and the absolute value of the gradient of total mechanical energy along the streamwise direction increases.The maximum of K appears near the wall in both coordinate axis of the duct.According to the energy gradient theory,this position of the maximum of K would initiate flow instability(if any)than the other positions.The higher the Hartmann number is,the smaller the K value becomes,which means that the fluid becomes more stable in the presence of higher magnetic force.As the Hartmann number increases,the K value in the parallel layer decreases more significantly than in the Hartmann layer.The most dangerous position of instability tends to migrate towards wall of the duct as the Hartmann number increases.Thus,with the energy gradient theory,the stability or instability in the rectangular duct can be controlled by modulating the magnetic force.
基金supported by Science Foundation of Zhejiang Sci-Tech University(ZSTU)underGrant No.11130032241201 and the opening research foundation of State Key Laboratory ofHigh Temperature Gas Dynamics in Institute of Mechanics of Chinese Academy of Sciences.
文摘Numerical simulation based on the Euler equation and one-step reaction model is carried out to investigate the process of deflagration to detonation transition(DDT)occurring in a straight duct.The numerical method used includes a high resolution fifth-order weighted essentially non-oscillatory(WENO)scheme for spatial discretization,coupled with a third order total variation diminishing Runge-Kutta time stepping method.In particular,effect of energy release on the DDT process is studied.The model parameters used are the heat release at q=50,30,25,20,15,10 and 5,the specific heat ratio at 1.2,and the activation temperature at Ti=15,respectively.For all the cases,the initial energy in the spark is about the same compared to the detonation energy at the Chapman-Jouguet(CJ)state.It is found from the simulation that the DDT occurrence strongly depends on the magnitude of the energy release.The run-up distance of DDT occurrence decreases with the increase of the energy release for q=5020,and increases with the increase of the energy release for q=205.This phenomenon is found to be in agreement with the analysis of mathematical stability theory.It is suggested that the factors to strengthen the DDT would make the detonation more stable,and vice versa.Finally,it is concluded from the simulations that the interaction of the shock wave and the flame front is the main reason for leading to DDT.
基金This research work was funded by the Chinese National Foundation of Natural Science(Nos.51076077,51176168,51249003 and 51076144)This work is also supported by Science Foundation of Zhejiang Sci-Tech University(ZSTU) under Grant No.11130032241201.
文摘In the present work,both computational and experimentalmethods are employed to study the two-phase flow occurring in a model pump sump.The twofluid model of the two-phase flow has been applied to the simulation of the threedimensional cavitating flow.The governing equations of the two-phase cavitating flow are derived from the kinetic theory based on the Boltzmann equation.The isotropic RNG k−ε−kca turbulence model of two-phase flows in the form of cavity number instead of the formof cavity phase volume fraction is developed.The RNG k−ε−kca turbulence model,that is the RNG k−εturbulence model for the liquid phase combined with the kca model for the cavity phase,is employed to close the governing turbulent equations of the two-phase flow.The computation of the cavitating flow through a model pump sump has been carried out with this model in three-dimensional spaces.The calculated results have been compared with the data of the PIV experiment.Good qualitative agreement has been achievedwhich exhibits the reliability of the numerical simulation model.