The pseudoplastic circular Couette flow （CCF） in annuli is investigated. The viscosity is dependent on the shear rate that directly affects the conservation equations solved by the spectral method in the present stu...The pseudoplastic circular Couette flow （CCF） in annuli is investigated. The viscosity is dependent on the shear rate that directly affects the conservation equations solved by the spectral method in the present study. The pseudoplastic model adopted here is shown to be the suitable representative of nonlinear fluids. Unlike the previous studies, where only the square of the shear ered to ease the numerical manipulations, quadratic power is also taken into account. rate term in the viscosity expression is consid- in the present study, the term containing the The curved streamlines of the CCF can cause the centrifugal instability leading to toroidal vortices, known as the Taylor vortices. It is further found that the critical Taylor number becomes lower as the pseudoplastic effect increases. The comparison with the existing measurements on the pseudoplastic CCF results in good agreement.展开更多
The pinch instability for a cylindrical jet of liquid metal passed through by an axial electrical current is investigated. Besides the pinch effect originating from surface tension, the Lorentz force, created by the a...The pinch instability for a cylindrical jet of liquid metal passed through by an axial electrical current is investigated. Besides the pinch effect originating from surface tension, the Lorentz force, created by the axial current density and the corresponding azimuthal magnetic field, causes an electromagnetic pinch effect. This effect has drawn attention in electrical engineering, because it can be used in the construction of liquid metal current limit- ers with self-healing properties. In this paper a simple model is derived using the shallow water approximation： the equations describing the full system are reduced to two one-dimensional evolution equations for the axial velocity and the radius of the jet. A stability analysis for this reduced system is carried out yielding critical current density and the growth rate for the instability. To investigate the nonlinear behaviour of the pinch instability for finite perturbations simulations, the shallow water model are performed.展开更多
We investigate numerical approximations based on polynomials that are orthogonal with respect to a weighted discrete inner product and develop an algorithm for solving time dependent differential equations.We focus on...We investigate numerical approximations based on polynomials that are orthogonal with respect to a weighted discrete inner product and develop an algorithm for solving time dependent differential equations.We focus on the family of super Gaussian weight functions and derive a criterion for the choice of parameters that provides good accuracy and stability for the time evolution of partial differential equations.Our results show that this approach circumvents the problems related to the Runge phenomenon on equally spaced nodes and provides high accuracy in space.For time stability,small corrections near the ends of the interval are computed using local polynomial interpolation.Several numerical experiments illustrate the performance of the method.展开更多
文摘The pseudoplastic circular Couette flow （CCF） in annuli is investigated. The viscosity is dependent on the shear rate that directly affects the conservation equations solved by the spectral method in the present study. The pseudoplastic model adopted here is shown to be the suitable representative of nonlinear fluids. Unlike the previous studies, where only the square of the shear ered to ease the numerical manipulations, quadratic power is also taken into account. rate term in the viscosity expression is consid- in the present study, the term containing the The curved streamlines of the CCF can cause the centrifugal instability leading to toroidal vortices, known as the Taylor vortices. It is further found that the critical Taylor number becomes lower as the pseudoplastic effect increases. The comparison with the existing measurements on the pseudoplastic CCF results in good agreement.
基金the Deutsche Forschungsgemeinschaft in the French-German DFG-CNRS research program 'Numerische Strmungssimulation-Simulation Numérique d'Ecoulements'National Nataral Science Foundation of China under granted number 10772044
文摘The pinch instability for a cylindrical jet of liquid metal passed through by an axial electrical current is investigated. Besides the pinch effect originating from surface tension, the Lorentz force, created by the axial current density and the corresponding azimuthal magnetic field, causes an electromagnetic pinch effect. This effect has drawn attention in electrical engineering, because it can be used in the construction of liquid metal current limit- ers with self-healing properties. In this paper a simple model is derived using the shallow water approximation： the equations describing the full system are reduced to two one-dimensional evolution equations for the axial velocity and the radius of the jet. A stability analysis for this reduced system is carried out yielding critical current density and the growth rate for the instability. To investigate the nonlinear behaviour of the pinch instability for finite perturbations simulations, the shallow water model are performed.
文摘We investigate numerical approximations based on polynomials that are orthogonal with respect to a weighted discrete inner product and develop an algorithm for solving time dependent differential equations.We focus on the family of super Gaussian weight functions and derive a criterion for the choice of parameters that provides good accuracy and stability for the time evolution of partial differential equations.Our results show that this approach circumvents the problems related to the Runge phenomenon on equally spaced nodes and provides high accuracy in space.For time stability,small corrections near the ends of the interval are computed using local polynomial interpolation.Several numerical experiments illustrate the performance of the method.
