Since the classical investigation of the Taylor vortex by G. I. Taylor in 1923, many researchers have studied the Taylor vortex as one of the most important vortex types in flow. In this study, the inner cylinder is r...Since the classical investigation of the Taylor vortex by G. I. Taylor in 1923, many researchers have studied the Taylor vortex as one of the most important vortex types in flow. In this study, the inner cylinder is rotating, while the outer cylinder, which is concentric with the inner cylinder, is stationary. In addition, the measurement of the velocity distribution is carried out by the PIV (Particle Image Velocimetry) method. The radius of the inner cylinder is 20 mm, and that of the outer cylinder is 30 mm. In this study, Re = 650-1,200 is assumed. In the upper part of the apparatus, movable ends are fixed to the upper and lower sides of the cylinder to change the aspect ratio. The aspect ratio is defined as the ratio of cylinder height to gap distance. A servo motor to rotate the inner cylinder, a servo-motor control device, a servo amplifier for rotation speed control, and a YAG laser light source are installed in the apparatus. For the visualization of Taylor vortex flow, aluminum powder composed of scale like fine particles is used. As tracer particles used in the PIV method, fluorescent particles with a size of 48 Ixm were used. The governing equations are Navier-Stokes equations with cylindrical coordinates (r, θ, z) and the equations of continuity. Each physical value is nondimensionalized using the angular velocity of the inner cylinder as the representative velocity, and the radius difference between the inner and outer cylinders as the representative length. Discretization of the governing equations is based on the MAC method. The results of EFD and CFD (computational fluid dynamics) are compared. The mode bifurcation is observed, and the flow structure is investigated.展开更多
In the present paper, based on the incomepressible finite Larmor radius (FLR) magnetohydrodynamic ( MHD ) equations, we consider the stabilizing effect of the finite Larmor radius on the Rayleigh-Taylor ( RT ) i...In the present paper, based on the incomepressible finite Larmor radius (FLR) magnetohydrodynamic ( MHD ) equations, we consider the stabilizing effect of the finite Larmor radius on the Rayleigh-Taylor ( RT ) instability in implosions of annular Z-pinch plasma. Here, the FLR is considered as a type of viscositytll, independent of any collisions (i.e., collisionless viscosity, or gyrouiscosity ). Since we are introducing a sheared velocity,展开更多
The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian c...The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian coordinates. To deal with the free surface, instead of using the transformation to Lagrangian coordinates, the perturbed equations in Eulerian coordinates are transformed to an integral form and the two-fluid flow is formulated as a single-fluid flow in a fixed domain, thus offering an alternative approach to deal with the jump conditions at the free interface. First, the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, both fluids being in(unstable) equilibrium is analyzed. By a general method of studying a family of modes, the smooth(when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces are constructed, thus leading to a global instability result for the linearized problem.Then, by using these pathological solutions, the global instability for the corresponding nonlinear problem in an appropriate sense is demonstrated.展开更多
The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, by using the dynamic transition theory and geometric theory of incompressible flows developed recently...The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, by using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In particular, it is shown that as the Taylor number crosses the critical number, the system undergoes either a continuous or a jump dynamic transition, dictated by the sign of a computable, nondimensional parameter R. In addition, it is also shown that the new transition states have the Taylor vortex type of flow structure, which is structurally stable.展开更多
文摘Since the classical investigation of the Taylor vortex by G. I. Taylor in 1923, many researchers have studied the Taylor vortex as one of the most important vortex types in flow. In this study, the inner cylinder is rotating, while the outer cylinder, which is concentric with the inner cylinder, is stationary. In addition, the measurement of the velocity distribution is carried out by the PIV (Particle Image Velocimetry) method. The radius of the inner cylinder is 20 mm, and that of the outer cylinder is 30 mm. In this study, Re = 650-1,200 is assumed. In the upper part of the apparatus, movable ends are fixed to the upper and lower sides of the cylinder to change the aspect ratio. The aspect ratio is defined as the ratio of cylinder height to gap distance. A servo motor to rotate the inner cylinder, a servo-motor control device, a servo amplifier for rotation speed control, and a YAG laser light source are installed in the apparatus. For the visualization of Taylor vortex flow, aluminum powder composed of scale like fine particles is used. As tracer particles used in the PIV method, fluorescent particles with a size of 48 Ixm were used. The governing equations are Navier-Stokes equations with cylindrical coordinates (r, θ, z) and the equations of continuity. Each physical value is nondimensionalized using the angular velocity of the inner cylinder as the representative velocity, and the radius difference between the inner and outer cylinders as the representative length. Discretization of the governing equations is based on the MAC method. The results of EFD and CFD (computational fluid dynamics) are compared. The mode bifurcation is observed, and the flow structure is investigated.
文摘In the present paper, based on the incomepressible finite Larmor radius (FLR) magnetohydrodynamic ( MHD ) equations, we consider the stabilizing effect of the finite Larmor radius on the Rayleigh-Taylor ( RT ) instability in implosions of annular Z-pinch plasma. Here, the FLR is considered as a type of viscositytll, independent of any collisions (i.e., collisionless viscosity, or gyrouiscosity ). Since we are introducing a sheared velocity,
基金supported by the National Natural Science Foundation of China(Nos.11101044,11271051,11229101,11301083,11371065,11471134)the Fujian Provincial Natural Science Foundation of China(No.2014J01011)+1 种基金the National Basic Research Program(No.2011CB309705)the Beijing Center for Mathematics and Information Interdisciplinary Sciences
文摘The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian coordinates. To deal with the free surface, instead of using the transformation to Lagrangian coordinates, the perturbed equations in Eulerian coordinates are transformed to an integral form and the two-fluid flow is formulated as a single-fluid flow in a fixed domain, thus offering an alternative approach to deal with the jump conditions at the free interface. First, the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, both fluids being in(unstable) equilibrium is analyzed. By a general method of studying a family of modes, the smooth(when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces are constructed, thus leading to a global instability result for the linearized problem.Then, by using these pathological solutions, the global instability for the corresponding nonlinear problem in an appropriate sense is demonstrated.
基金supported by the National Science Foundation, the Office of Naval Research and the National Natural Science Foundation of China
文摘The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, by using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In particular, it is shown that as the Taylor number crosses the critical number, the system undergoes either a continuous or a jump dynamic transition, dictated by the sign of a computable, nondimensional parameter R. In addition, it is also shown that the new transition states have the Taylor vortex type of flow structure, which is structurally stable.