A series of direct numerical simulations of the fully developed plane Couette flow at a Reynolds number of 6000（based on the relative wall speed and half the channel height h） with different streamwise and spanwise ...A series of direct numerical simulations of the fully developed plane Couette flow at a Reynolds number of 6000（based on the relative wall speed and half the channel height h） with different streamwise and spanwise lengths are conducted to investigate the effects of the computational box sizes on the secondary flow（SF）. Our focuses are the number of counter-rotating vortex pairs and its relationship to the statistics of the mean flow and the SF in the small and moderate computational box sizes. Our results show that the number of vortex pairs is sensitive to the computational box size, and so are the slope parameter, the rate of the turbulent kinetic energy contributed by the SF, and the ratio of the kinetic energy of the SF to the total kinetic energy. However, the averaged spanwise width of each counter-rotating vortex pair in the plane Couette flow is found, for the first time, within 4（1 ± 0.25）h despite the domain sizes.展开更多
By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growt...By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.展开更多
The dissipation function in turbulent plane Poiseuille flows(PPFs) and plane Couette flows(PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is cons...The dissipation function in turbulent plane Poiseuille flows(PPFs) and plane Couette flows(PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs.However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations,when the rotation number increases, the dissipation function first decreases and then increases.展开更多
Despite recent progress, laminar-turbulent coexistence in transitional planar wall-bounded shear flows is still not well understood. Contrasting with the processes by which chaotic flow inside turbulent patches is sus...Despite recent progress, laminar-turbulent coexistence in transitional planar wall-bounded shear flows is still not well understood. Contrasting with the processes by which chaotic flow inside turbulent patches is sustained at the local(minimal flow unit) scale, the mechanisms controlling the obliqueness of laminar-turbulent interfaces typically observed all along the coexistence range are still mysterious. An extension of Waleffe's approach [Waleffe, 1997] is used to show that,already at the local scale, drift flows breaking the problem's spanwise symmetry are generated just by slightly detuning the modes involved in the self-sustainment process. This opens perspectives for theorizing the formation of laminar-turbulent patterns.展开更多
Direct numerical simulation of rotating plane Couette flow(RPCF) at Re_w= 1300 and Ro = 0.02 was performed with different mesh resolutions and different sizes of computation domain. Our results showed that a grid reso...Direct numerical simulation of rotating plane Couette flow(RPCF) at Re_w= 1300 and Ro = 0.02 was performed with different mesh resolutions and different sizes of computation domain. Our results showed that a grid resolution in wall units with ?x^+=8.51, ?z^+= 4.26, ?y^+|_(min)= 0.0873 and ?y^+|_(max)= 3.89 is fine enough to simulate the problem at the present parameters. The streamwise length Lxand spanwise length Lzof the computational box have different impacts on the flow statistics, where the statistics were converged if Lxis longer than 8πh, while no converged results were obtained for different Lz. More importantly,our results with very long simulation time showed that a state transition would happen if L_x≥ 8πh, from a state with four pairs of roll cells to a state with three pairs of roll cells with L_z= 6πh. Each state could survive for more than 1500 h/U_w, and the flow statistics were different.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 turbulence in plane Couette flow subjected to system rotation is investigated. The anti-cyclonic rotation rate is well above the range in which roll-cells occurand close to the upper bound, beyond which no station...The turbulence in plane Couette flow subjected to system rotation is investigated. The anti-cyclonic rotation rate is well above the range in which roll-cells occurand close to the upper bound, beyond which no stationary turbulent states of motionexist. The mean velocity profile exhibits a linear region over 80% of the cross-section, inwhich the mean absolute vorticity is driven to zero. Viscous effects still prevail in narrow regions next to the walls, whereas the quasi-homogeneous central core exhibitsabnormal anisotropies of the Reynolds stress tensor, the vorticity tensor and the energy dissipation rate tensor. In spite of the distinctly higher turbulence level observed,a 13% drag reduction is found. This paradoxical finding is ascribed to configurationalchanges in the turbulence field brought about by the system rotation.展开更多
We simulated rapid flow in transient plane Couette flows of granular particles using the smoothed particle hydrodynamics （SPH） solutions of a set of continuum equations, This simulation was performed to test the via...We simulated rapid flow in transient plane Couette flows of granular particles using the smoothed particle hydrodynamics （SPH） solutions of a set of continuum equations, This simulation was performed to test the viability of SPH in solving the equations for the solid phase of the two-fluid model associated with fluidization. We found that SPH requires the handling of fewer particles in simulating the collective behavior of rapid granular flow, thereby bolstering expectations of solving the equations for the solid phase in the two-fluid modeling of fluidization. Further work is needed to investigate the effect of terms describing pressure and viscous stress of solids on stability in simulations.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11221061,11272013,and 11302006)
文摘A series of direct numerical simulations of the fully developed plane Couette flow at a Reynolds number of 6000（based on the relative wall speed and half the channel height h） with different streamwise and spanwise lengths are conducted to investigate the effects of the computational box sizes on the secondary flow（SF）. Our focuses are the number of counter-rotating vortex pairs and its relationship to the statistics of the mean flow and the SF in the small and moderate computational box sizes. Our results show that the number of vortex pairs is sensitive to the computational box size, and so are the slope parameter, the rate of the turbulent kinetic energy contributed by the SF, and the ratio of the kinetic energy of the SF to the total kinetic energy. However, the averaged spanwise width of each counter-rotating vortex pair in the plane Couette flow is found, for the first time, within 4（1 ± 0.25）h despite the domain sizes.
基金Project supported by the National Natural Science Foundation of China(Nos.91752203,11490553,and 11602148)
文摘By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.
基金Project supported by the National Natural Science Foundation of China(Nos.11772297 and11822208)
文摘The dissipation function in turbulent plane Poiseuille flows(PPFs) and plane Couette flows(PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs.However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations,when the rotation number increases, the dissipation function first decreases and then increases.
文摘Despite recent progress, laminar-turbulent coexistence in transitional planar wall-bounded shear flows is still not well understood. Contrasting with the processes by which chaotic flow inside turbulent patches is sustained at the local(minimal flow unit) scale, the mechanisms controlling the obliqueness of laminar-turbulent interfaces typically observed all along the coexistence range are still mysterious. An extension of Waleffe's approach [Waleffe, 1997] is used to show that,already at the local scale, drift flows breaking the problem's spanwise symmetry are generated just by slightly detuning the modes involved in the self-sustainment process. This opens perspectives for theorizing the formation of laminar-turbulent patterns.
基金supported by the National Natural Science Foundation of China(Grant Nos.11822208,11772297,11672123,and 91752201)
文摘Direct numerical simulation of rotating plane Couette flow(RPCF) at Re_w= 1300 and Ro = 0.02 was performed with different mesh resolutions and different sizes of computation domain. Our results showed that a grid resolution in wall units with ?x^+=8.51, ?z^+= 4.26, ?y^+|_(min)= 0.0873 and ?y^+|_(max)= 3.89 is fine enough to simulate the problem at the present parameters. The streamwise length Lxand spanwise length Lzof the computational box have different impacts on the flow statistics, where the statistics were converged if Lxis longer than 8πh, while no converged results were obtained for different Lz. More importantly,our results with very long simulation time showed that a state transition would happen if L_x≥ 8πh, from a state with four pairs of roll cells to a state with three pairs of roll cells with L_z= 6πh. Each state could survive for more than 1500 h/U_w, and the flow statistics were different.
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).
文摘The turbulence in plane Couette flow subjected to system rotation is investigated. The anti-cyclonic rotation rate is well above the range in which roll-cells occurand close to the upper bound, beyond which no stationary turbulent states of motionexist. The mean velocity profile exhibits a linear region over 80% of the cross-section, inwhich the mean absolute vorticity is driven to zero. Viscous effects still prevail in narrow regions next to the walls, whereas the quasi-homogeneous central core exhibitsabnormal anisotropies of the Reynolds stress tensor, the vorticity tensor and the energy dissipation rate tensor. In spite of the distinctly higher turbulence level observed,a 13% drag reduction is found. This paradoxical finding is ascribed to configurationalchanges in the turbulence field brought about by the system rotation.
基金financially supported by the Ministry of Science and Technology of the People's Republic of China under Grant No.2012CB215003the National Natural Science Foundation of China under Grant Nos.21176240 and 21406081the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDA07080100
文摘We simulated rapid flow in transient plane Couette flows of granular particles using the smoothed particle hydrodynamics （SPH） solutions of a set of continuum equations, This simulation was performed to test the viability of SPH in solving the equations for the solid phase of the two-fluid model associated with fluidization. We found that SPH requires the handling of fewer particles in simulating the collective behavior of rapid granular flow, thereby bolstering expectations of solving the equations for the solid phase in the two-fluid modeling of fluidization. Further work is needed to investigate the effect of terms describing pressure and viscous stress of solids on stability in simulations.
