Consistency,stability and convergence of the finite-difference equations for flow about a rotating sphere in an axial stream

The finite-difference equations which have previously been developed to solve the problem of laminar boundary layer flow about a rotating sphere in an axial stream are analysed according to the available numerical stability theories. This analysis is necessary to determine the restrictions on velocities and mesh sizes required to obtain a convergent numerical solution. Convergence can be achieved if both consistency and stability of the finite-difference equations are fulfilled. The analysis reported in the present paper shows that the developed finite-difference equations are consistent with their original partial differential equations. Also, the analysis proves that the developed finite-difference procedure is numerically stable for all mesh sizes as long as the downstream meridional velocity is non-negative, i.e.as long as no flow reversals occur within the domain of solution.     

Stability analysis of a substructured model of the rotating beam

One of the most well-known situations in which nonlinear effects must be taken into account to obtain realistic results is the rotating beam problem. This problem has been extensively studied in the literature and has even become a benchmark problem for the validation of nonlinear formulations. Among other approaches, the substructuring technique was proven to be a valid strategy to account for this problem. Later, the similarities between the absolute nodal coordinate formulation and the substructuring technique were demonstrated. At the same time, it was found the existence of a critical angular velocity, beyond which the system becomes unstable that was dependent on the number of substructures. Since the dependence of the critical velocity was not so far clear, this paper tries to shed some light on it. Moreover, previous studies were focused on a constant angular velocity analysis where the effects of Coriolis forces were neglected. In this paper, the influence of the Coriolis force term is not neglected. The influence of the reference conditions of the element frame are also investigated in this paper.     

混合边界条件下的三维定常 旋转Navier-Stokes方程的原始变量有限元计算

本文利用原始变量有限元法求解混合边界条件下的三维定常旋转Navier-Stokes方程,证明了离散问题解的存在唯一性,得到了有限元解的最优误差估计.给出了求解原始变量有限元逼近解的简单迭代算法,并证明了算法的收敛性.针对三维情况下计算资源的限制,采用压缩的行存储格式存储刚度矩阵的非零元素,并利用不完全的LU分解作预处理的GMRES方法求解线性方程组.最后分析了简单迭代和牛顿迭代的优劣对比,数值算例表明在同样精度下简单迭代更节约计算时间.     

研测动态问题的旋转孔径散斑照相法Ⅰ:双孔、四扇孔

本文提出一种研测动态问题的实验新方法——旋转孔径散斑照相法。该法设备简单,利用一个旋转孔径装置,能在一张散斑图上记录下物体动态变形的全过程,然后在全场波滤分析时把各瞬时的信息分离出来,可得任意时刻的瞬态位移场。转孔法能应用于振动和非周期性动态问题,并以三个实验证实其可行性。实验结果表明,散斑条纹清晰可靠,定量分析与其它方法所得结果一致。     

The influence of Hall current on the rotating oscillating flows of an Oldroyd-B fluid in a porous medium

In this article, analysis is presented to study the effect of Hall current on the rotating flow of a non-Newtonian fluid in a porous medium taking into consideration the modified Darcy's law. The Oldroyd-B fluid model is used to characterize the non-Newtonian fluid behavior. The governing equations for unsteady rotating flow have been modeled in a porous medium. The analysis includes the flows induced by general periodic oscillations and elliptic harmonic oscillations of a plate. The effect of the various emerging parameters is discussed on the velocity distribution. The analytical results are confirmed mathematically by giving comparison with previous studies in the literature. It is observed that the velocity distribution increases with an increase of Hall parameter. The behavior of permeability is similar to that of the Hall parameter.     

Zonal flow induced by longitudinal librations of a rotating cylindrical cavity

Longitudinal librations represent oscillations about the axis of a rotating axisymmetric fluid filled cavity. An analytical theory is developed for the case of a cylindrical cavity in the limit when the libration frequency is small in comparison with the rotation rate, but large in comparison with the inverse of the spin-up time. It is shown that through the nonlinear advection in the Ekman layers the librations cause the fluid to rotate more slowly.     

反射转镜式干涉光谱仪光程差的一般表达式

对反射转镜式干涉光谱仪的原理进行了介绍,从马吕斯定律和角反射体的反射特性入手,选择转镜反射面的旋转中心作为入射光束和出射光束等波面的参考点,对反射转镜式干涉光谱仪的光程差进行了分析计算,给出反射转镜式干涉光谱仪任意时刻光程差及最大光程差的一般表达式,分析影响最大光程差和光程差变化周期的因素,为反射转镜式干涉光谱仪的设计与研制提供理论指导。     

Forced precession in a spinning wheel supported on a rotating pivot

This paper deals with the mechanics involved in a spinning wheel of which the pivot is not fixed as usual but is forced to rotate along the circumference of a circle on the horizontal plane. The usual Euler equations are extended so that, in addition to the three well-known rotations (Euler angles), they also include a fourth one related to the rotation of the motor that induces the forced precession. This study aims at offering a first insight in one of the renowned Laithwaite's experiments. The derived theoretical expressions are accompanied by computer simulation.     

Room Temperature Ionic Liquid Carbon Nanotube Paste Electrodes: Overcoming Large Capacitive Currents Using Rotating Disk Electrodes

The voltammetric response of graphite or carbon nanotube paste electrodes, which incorporate the room temperature ionic liquid, N‐butyl‐N‐methyl pyrrolidinium bis(trifluoromethylsulfonyl) imide or [C₄mpyrr][NTf₂], (RTIL‐CNTPE and RTIL‐CPE respectively) as the binder, towards anionic, cationic and neutral redox probes is examined and compared to conventional paste electrodes which use mineral oil as the binder. The RTIL paste electrodes are found to suffer from very large background currents due to capacitive charging. This is exacerbated further when CNTs are combined with RTILs in the paste. The large charging currents obscure any Faradaic processes of interest, especially at low analyte concentrations. By employing steady state voltammetry at a rotating disk electrode made of the RTIL pastes this problem can be overcome. This allows the electroanalytical properties of these interesting electrode substrates, which combine the attractive properties of CNTs with RTILs to be further explored and developed.     

A study of direct- and pulse-current chromium electroplating on rotating cylinder electrode (RCE)

Direct- and pulse-current (DC and PC) chromium electroplating on Cr-Mo steel were performed in a sulfate-catalyzed chromic acid solution at 50 °C using a rotating cylinder electrode (RCE). The electroplating cathodic current densities were at 30, 40, 50 and 60 A dm⁻², respectively. The relationship between electroplating current efficiency and the rotating speed of the RCE was studied. The cross-sectional microstructure of Cr-deposit was examined by transmission electron microscope (TEM). Results showed that DC-plating exhibited higher current efficiency than the PC-plating under the same conditions of electroplating current density and the rotating speed. We found the critical rotating speed of RCE used in the chromium electroplating, above this rotating speed the chromium deposition is prohibited. At the same plating current density, the critical rotating speed for DC-plating was higher than that for PC-plating. The higher plating current density is, the larger difference in critical rotating speeds appears between DC- and PC-electroplating. Equiaxed grains, in a nanoscale size with lower dislocation density, nucleate on the cathodic surface in both DC- and PC-electroplating. Adjacent to the equiaxed grains, textured grains were found in other portion of chromium deposit. Fine columnar grains were observed in the DC-electroplated deposit. On the other hand, very long slender grains with high degree of preferred orientation were detected in PC-electroplated deposit.