Experimental and numerical studies have shown similarities between localized turbulence in channel and pipe flows.By scaling analysis of a disturbed-flow model,this paper proposes a local Reynolds number Re M to chara...Experimental and numerical studies have shown similarities between localized turbulence in channel and pipe flows.By scaling analysis of a disturbed-flow model,this paper proposes a local Reynolds number Re M to characterize the threshold of transition triggered by finite-amplitude disturbances.The Re M represents the maximum contribution of the basic flow to the momentum ratio between the nonlinear convection and the viscous diffusion.The lower critical Re M observed in experiments of plane Poiseuille flow,pipe Poiseuille flow and plane Couette flow are all close to 323,indicating the uniformity of mechanism governing the transition to localized turbulence.展开更多
The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. "Optimal" perturbations are distinguished as extrema of certain functionals, and differe...The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. "Optimal" perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2D simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria: energy of the initial condition, energy dissipation of the initial condition, and amplitude of noise in a stochastic transition. We find that the states triggering the transition are different in the three cases, but show the same scaling with Reynolds number.展开更多
Recent experimental and numerical investigations reveal that the onset of turbulence in plane-Poiseuille flow and planeCouette flow has some similar stages separated with different threshold Reynolds numbers.Based on ...Recent experimental and numerical investigations reveal that the onset of turbulence in plane-Poiseuille flow and planeCouette flow has some similar stages separated with different threshold Reynolds numbers.Based on these observations and the energy equation of a disturbed fluid element,a local Reynolds number Re L is derived to represent the maximum ratio of the energy supplement to the energy dissipation in a cross section.It is shown that along the sequence of transition stages,which include transient localized turbulence,"equilibrium" localized turbulence,spatially intermittent but temporally persistent turbulence and uniform turbulence,the corresponding thresholds of Re L for plane-Couette flow,Hagen-Poiseuille flow and plane-Poiseuille flow are consistent,indicating that the critical(threshold) states during the laminar-turbulent transition are determined by the local properties of the base flow and are independent of global features,such as flow geometries(pipe or channel) and types of driving forces(shear driving or pressure driving).展开更多
Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the ...Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence c (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where c = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y+= 1, where y+ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of c against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, c - 25, and for plate flow, c - 151.5. These findings suggest that a certain combination of c and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence.展开更多
This paper reviews the current state of understanding of the L-H transition phenomenon in tokamak plasmas with a focus on two central issues: (a) the mechanism for turbulence quick suppression at the L-H transitio...This paper reviews the current state of understanding of the L-H transition phenomenon in tokamak plasmas with a focus on two central issues: (a) the mechanism for turbulence quick suppression at the L-H transition; (b) the mechanism for subsequent generation of sheared flow. We briefly review recent advances in the understanding of the fast suppression of edge turbulence across the L-H transition. We uncover a comprehensive physical picture of the L-H transition by piecing together a number of recent experimental observations and insights obtained from 1D and 2D simulation models. Different roles played by diamagnetic mean flow, neoclassical-driven mean flow, turbulence-driven mean flow, and turbulence-driven zonal flows are discussed and clarified. It is found that the L-H transition occurs spontaneously mediated by a shift in the radial wavenumber spectrum of edge turbulence, which provides a critical evidence for the theory of turbulence quench by the flow shear. Remaining questions and some key directions for future investigations are proposed.展开更多
In order to understand the mechanism of the confinement bifurcation and H-mode power threshold in magnetically confined plasma,a new dynamical model of the L-H transition based on edge instability phase transition(E...In order to understand the mechanism of the confinement bifurcation and H-mode power threshold in magnetically confined plasma,a new dynamical model of the L-H transition based on edge instability phase transition(EIPT) has been developed.With the typical plasma parameters of the EAST tokamak,the self-consistent turbulence growth rate is analyzed using the simplest case of pressure-driven ballooning-type instability,which indicates that the L-H transition can be caused by the stabilization of the edge instability through EIPT.The weak E?×?B flow shear in L-mode is able to increase the ion inertia of the electrostatic motion by increasing the radial wave number of the tilted turbulence structures,which play an important role for accelerating the trigger process of EIPT rather than directly to suppress the turbulent transport.With the acceleration mechanism of E?×?B flow shear,fast L-H and H-L transitions are demonstrated under the control of the input heating power.Due to the simplified scrape-offlayer boundary condition applied,the ratio between the heating powers at the H-L and L-H transition respectively differs from the ratio by Nusselt number.The results of the modeling reveal a scaling of the power threshold of the L-H transition,P_(L-H)?∝?n^(0.76) B^(0.8) for deuterium plasma.It is found finite Larmor radius induces an isotope effect of the H-mode power threshold.展开更多
This paper discusses edge oscillatory plasma flows, geodesic acoustic mode (GAM) and limit cycle oscillations (LCOs), which have been measured by Doppler reflectometry prior to the high confinement mode (H-mode)...This paper discusses edge oscillatory plasma flows, geodesic acoustic mode (GAM) and limit cycle oscillations (LCOs), which have been measured by Doppler reflectometry prior to the high confinement mode (H-mode) in the HL-2A tokamak. The complex relations between the flows and background turbulence have been analyzed. It was observed that the GAM and LCO coexist, and these two flows and turbulence have strong nonlinear interactions during the intermediate confinement phase (I-phase). Dynamics of the shear flows and turbulence prior to the H-mode shows that the oscillatory flows quench the turbulence along with the increase of the mean E x B flow at the early stage of the I-phase, then the oscillatory flows are damped and the further increased mean flow takes over the role in turbulence suppression. The reduced turbulent transport results in the formation of a steep edge transport barrier. It suggests that the oscillatory flows can initiate the L-H transition through providing a positive feedback for the increase of the mean E × B flow strength.展开更多
基金supported by the NSFC (10972007,10921202 and 2009CB724100)
文摘Experimental and numerical studies have shown similarities between localized turbulence in channel and pipe flows.By scaling analysis of a disturbed-flow model,this paper proposes a local Reynolds number Re M to characterize the threshold of transition triggered by finite-amplitude disturbances.The Re M represents the maximum contribution of the basic flow to the momentum ratio between the nonlinear convection and the viscous diffusion.The lower critical Re M observed in experiments of plane Poiseuille flow,pipe Poiseuille flow and plane Couette flow are all close to 323,indicating the uniformity of mechanism governing the transition to localized turbulence.
基金supported in part by the German Research Foundation within FOR 1182
文摘The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. "Optimal" perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2D simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria: energy of the initial condition, energy dissipation of the initial condition, and amplitude of noise in a stochastic transition. We find that the states triggering the transition are different in the three cases, but show the same scaling with Reynolds number.
基金supported by the National Natural Science Foundation of China(Grant Nos. 10972007 and 10921202) and (Grant No.2009CB724100)
文摘Recent experimental and numerical investigations reveal that the onset of turbulence in plane-Poiseuille flow and planeCouette flow has some similar stages separated with different threshold Reynolds numbers.Based on these observations and the energy equation of a disturbed fluid element,a local Reynolds number Re L is derived to represent the maximum ratio of the energy supplement to the energy dissipation in a cross section.It is shown that along the sequence of transition stages,which include transient localized turbulence,"equilibrium" localized turbulence,spatially intermittent but temporally persistent turbulence and uniform turbulence,the corresponding thresholds of Re L for plane-Couette flow,Hagen-Poiseuille flow and plane-Poiseuille flow are consistent,indicating that the critical(threshold) states during the laminar-turbulent transition are determined by the local properties of the base flow and are independent of global features,such as flow geometries(pipe or channel) and types of driving forces(shear driving or pressure driving).
文摘Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence c (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where c = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y+= 1, where y+ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of c against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, c - 25, and for plate flow, c - 151.5. These findings suggest that a certain combination of c and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence.
文摘This paper reviews the current state of understanding of the L-H transition phenomenon in tokamak plasmas with a focus on two central issues: (a) the mechanism for turbulence quick suppression at the L-H transition; (b) the mechanism for subsequent generation of sheared flow. We briefly review recent advances in the understanding of the fast suppression of edge turbulence across the L-H transition. We uncover a comprehensive physical picture of the L-H transition by piecing together a number of recent experimental observations and insights obtained from 1D and 2D simulation models. Different roles played by diamagnetic mean flow, neoclassical-driven mean flow, turbulence-driven mean flow, and turbulence-driven zonal flows are discussed and clarified. It is found that the L-H transition occurs spontaneously mediated by a shift in the radial wavenumber spectrum of edge turbulence, which provides a critical evidence for the theory of turbulence quench by the flow shear. Remaining questions and some key directions for future investigations are proposed.
基金supported by National Natural Science Foundation of China under Contract Nos.11575235 and 11422546China Postdoctoral Science Foundation under Contract No.2016M602043+2 种基金the National Magnetic Confinement Fusion Science Program of China under Contract No.2015GB101002Key Research Program of Frontier Sciences,CAS,Grant No.QYZDB-SSW-SLH001K C Wong Education Foundation
文摘In order to understand the mechanism of the confinement bifurcation and H-mode power threshold in magnetically confined plasma,a new dynamical model of the L-H transition based on edge instability phase transition(EIPT) has been developed.With the typical plasma parameters of the EAST tokamak,the self-consistent turbulence growth rate is analyzed using the simplest case of pressure-driven ballooning-type instability,which indicates that the L-H transition can be caused by the stabilization of the edge instability through EIPT.The weak E?×?B flow shear in L-mode is able to increase the ion inertia of the electrostatic motion by increasing the radial wave number of the tilted turbulence structures,which play an important role for accelerating the trigger process of EIPT rather than directly to suppress the turbulent transport.With the acceleration mechanism of E?×?B flow shear,fast L-H and H-L transitions are demonstrated under the control of the input heating power.Due to the simplified scrape-offlayer boundary condition applied,the ratio between the heating powers at the H-L and L-H transition respectively differs from the ratio by Nusselt number.The results of the modeling reveal a scaling of the power threshold of the L-H transition,P_(L-H)?∝?n^(0.76) B^(0.8) for deuterium plasma.It is found finite Larmor radius induces an isotope effect of the H-mode power threshold.
基金partially supported within the framework of the cooperation between the French Commissariat à l’Energie Atomique et aux Energies Alternatives (CEA) and the China National Nuclear Corporation (CNNC)partially supported by National Natural Science Foundation of China under Grant Nos. 11305053, 10990213, 10975049, 11475057, 11275062, 11375057 and 11575055partially supported by Chinese National Fusion Project for ITER under Grant Nos. 2013GB107000 and 2014GB108000
文摘This paper discusses edge oscillatory plasma flows, geodesic acoustic mode (GAM) and limit cycle oscillations (LCOs), which have been measured by Doppler reflectometry prior to the high confinement mode (H-mode) in the HL-2A tokamak. The complex relations between the flows and background turbulence have been analyzed. It was observed that the GAM and LCO coexist, and these two flows and turbulence have strong nonlinear interactions during the intermediate confinement phase (I-phase). Dynamics of the shear flows and turbulence prior to the H-mode shows that the oscillatory flows quench the turbulence along with the increase of the mean E x B flow at the early stage of the I-phase, then the oscillatory flows are damped and the further increased mean flow takes over the role in turbulence suppression. The reduced turbulent transport results in the formation of a steep edge transport barrier. It suggests that the oscillatory flows can initiate the L-H transition through providing a positive feedback for the increase of the mean E × B flow strength.