二锥形分离杯之间血液流动稳定性的窄间隙理论

本文在获得血液分离器锥形分离杯内(其中一杯静止,另一杯以ω等角速旋转)血液流动的边界摄动解的基础上[1],采用窄间隙稳定性理论,证明了带轴向流的二锥形分离杯(其中一杯静止,另一杯以ω等角速旋转)之间旋转密度分层血液流动的稳定性.     

血液分离杯溢口的流体动力设计及影响血液分离的物理参数

本文在“血液锥形分离杯内血液流动稳定性的边界摄动解”[1]的分析基础上,对血液分离杯研制过程中出现的“已分层血液成份重新相混”的现象进行了分析,提出了合理的溢口几何形状,并分析了影响血液分离的各项物理参数. 理论分析得到上海医疗器械研究所实验的证实.     

一种避开大转动奇异点的角速度数值积分方法

采用三参数描述有限转动会不可避免地遇到奇异性问题,这给由角速度积分求解转动参数带来了数值困难.系统地研究了采用转动矢量描述空间大转动的奇异性问题,在此基础上提出了一种避开转动矢量奇异点的数值积分方法.利用方向相同、模相差2π的两个转动矢量对应同一有限转动这一性质,在数值积分过程中将靠近奇异点的转动矢量切换到与之对应但远离奇异点的数值稳定区,从而避开了转动矢量奇异性给角速度数值积分带来的困难.数值算例表明所提方法简单、稳定、有效.     

齿轮啮合理论的数学基础(二)

二、齿轮啮合的一般理论引言 齿轮传动是依靠两轮间齿面的啮合,将一个运动,通常是转动,带动另一个运动.一般两组运动可以认为是先给定的.例如依两平行轴的两转动,由一个带动另一个,就是所谓的圆柱齿轮传动;它们转动的角速度的比值,称为传动比;传动比可以是常量,也可以是时间参数 t 的函数(后者通常称为非圆齿轮传动).又例如蜗轮蜗杆的传动就是带动两个相错轴(既不平行也不相交的两轴)的转动的装置;一般传动比是常值.带动两     

同轴旋转圆台间流场稳定性的数值研究

给出了两同轴旋转圆台间流动的稳定性分区.数值模拟的结果显示,在内外圆台的平均半径分别和内外圆柱的半径相同的情况下,圆台间的流动比圆柱间的流动更容易失稳.除此之外,通过对不同倾斜角进行数值模拟发现,倾斜角越小,圆台间的流动越容易失稳.     

不同角度Y型狭窄血管血液流动的数值模拟

根据粘性不可压Navier-Stokes方程,建立Y型分又血管中血液流动的数学模型,进而采用有限元方法研究不同分又角Y型血管动脉狭窄位置对血液流动的影响,得到了不同角度不同狭窄位置和无狭窄病变时的数值模拟结果,主要给出了各种情况下血液流动的流线图和压力图.一方面,观察流线图可知,血液流经狭窄区域时,出现流动分离,并在一定区域产生涡流,且随着狭窄位置不同,涡流位置和涡流区域面积也随之不同;另一方面,从计算的压力图中可以看到当血液流过狭窄区域时,压力发生迅速变化,且相同分叉角度下狭窄位置不同,狭窄区域压力不同;狭窄位置相同时,不同分叉角度的血管分又区域压力也有差别.     

血液流动与血管壁运动

本文讨论了哺乳动物循环系统的血液流动与血管壁运动之间的相互作用问题.在假定流动处于稳定的振荡流动情况下,导得了一组血液流动速度分布公式,压力分布公式以及约束应力公式,管壁位移公式.把Kuchar的公式从定常流动情况推广到非定常的振荡流动情况.文中还讨论了动脉血管壁的弹性效应问题.     

两个旋转球之间粘性不可压缩流动的Lorenz系统

两个不同角速度旋转球之间粘性流动问题是地球外部大气流动的简化模型.通过引入球Bessel函数的有理表达式,得到Stokes算子特征值与特征函数的有理表达形式.利用Stokes算子特征函数作为基函数系,对两个旋转球间流动问题进行谱Galerkin逼近.由三模态的Glerkin逼近方程得到—个类Lorenz系统,我们对此系统进行分歧问题和吸引子的讨论,从而得到原问题的稳定性判定.     

锥面间流体流动考虑流动惯性的近似解

本文采用锥坐标下的Navier-Stokes方程式,利用迭代近似解法,求出了考虑流动惯性时锥面间流体流动的速度分布、压力分布以及流量的解析式;并对轴对称过流流动的外向流和内向流进行了比较.     

双非对称双自旋航天器的姿态运动

本文将渐近法、平均法与文献[1—3]的方法相结合,讨论了双非对称双自旋航天器的姿态运动稳定性,并研究消旋过程中转子自转角速度接近相对转动角速度时航天器所产生的非线性姿态运动响应——陷阱状态,指出该状态是由于双非对称耦合所引起的.     

Influence of Thermal Stratification on the Stability of Ekman-Couette-Flow

The Ekman-Couette-System consists of two infinitely extended plates which are sheared in opposite directions over a fluid and are additionally rotated about their normal axis. In the case of angular velocities which tend to zero, the system becomes the classical Couette-System, whereas for high angular velocities the boundary layers of the upper and lower plate are separated and represent Ekman boundary layers. For both limit cases the influence of thermal stratification on the stability of the base flow has been a subject of research for some time, but not so for moderate angular velocities. This was the motivation for doing a linear stability analysis for that case, including both stable and unstable stratification for a Prandtl number equal to unity. The results show, that as expected, stable stratification is suppressing the emergence of stationary as well as Type I- and Type II-shear-instabilities, while unstable stratification is supporting them. For unstable stratification, the system can also become unstable to a convection instability with all its properties known from other systems, except for that their orientation angle is not coincidental but determined due to the influence of the shear and Coriolis forces. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Couette flow of dipolar fluids

An exact solution for the problem of steady flow of an incompressible, isothermal and homogeneous dipolar fluid in the annular space between two concentric circular cylinders rotating with uniform angular velocities is obtained. The effect of the material constants on the torque acting on the cylinders is studied particular cases.     

Stability and bifurcation of couette flow in the case of a narrow gap between rotating cylinders : PMM vol. 38, n 6, 1974, pp. 1025–1030

Stability and bifurcation of Couette flow between concentric rotating cylinders are investigated for the case when the ratios of their radii R and angular velocities Ω are nearly equal to unity. The limiting problem in the linear theory when R → 1 and Ω → 1 is the problem of convection stability in the layer [1]. We find that this is also correct in the case of a nonlinear problem. Below we show that solution of the problem of free convection yields the principal term of the expansion of the secondary flow (Taylor vortex) in the powers of a small parameter δ = R − 1. Therefore the results of [2, 3] can be used to provide, in the present case, a strict justification for the use of the Liapunov-Schmidt method to compute the Taylor vortices. The numerical results obtained for the critical Reynolds' number and the amplitude of the secondary flow provide a good illustration of the asymptotic passage as δ → 0.     

Numerical study of multiple periodic flow states in spherical Couette flow

The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference method. For comparison with experiments of Nakabayashi et al. and Wimmer, a narrow gap and a medium gap with clearance ratio β=0.06 and 0.18 respectively are considered for the Reynolds number range covering the     

Numerical study of multiple periodic flow states in spherical Couette flow

The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference method. For comparison with experiments of Nakabayashi et al. and Wimmer, a narrow gap and a medium gap with clearance ratio β=0.06 and 0.18 respectively are considered for the Reynolds number range covering the first Hopf bifurcation point. With adequate initial conditions and temporary imposition of small wave-type perturbation, multiple periodic flow states with three different pair numbers of spiral Taylor-Görtler (TG) vortices have been simulated successfully for β=0.06, of which the 1-pair and 2-pair of spiral TG vortices are newly obtained. Three different periodic flow states with shear waves, Stuart vortices or wavy outflow boundary, have been obtained for β=0.18. Analysis of the numerical results reveals these higher flow modes in terms of fundamental frequency, wave number and spatial structure.     

Betrachtungen zu den Hauptproblemen der mathematischen Aussenballistik

Summary The paper provides a short survey of the actual state of the theoretical exterior ballistics. In particular the fundammental equations defining the motion of a rotating projectile are given in a form suitable for numerical calculation. Then, using the argument that a projectile possesses full rotational and also mirror summetry, the explicit development of the force and moment components is given in terms of the linear and angular velocities. Finally this development is compared with the experimentally known aerodynamic coefficients and stability derivatives.     

Stability of a Generalized Sobolev System

The linear stability problem of the rotational motion of a rigid body around a fixed point containing an inner cavity filled up with an ideal fluid is considered. In this paper, we also assume that the fluid is rotating. The effect of the angular velocities of the rigid body and the fluid in the stability problem is studied. The case of a cavity ellipsoidal is presented in detail.     

Slow flow between concentric cones

This paper considers the low-Reynolds-number flow of an incompressiblefluid contained in the gap between two coaxial cones with coincidentapices and bounded by a spherical lid. The two cones and thelid are allowed to rotate independently about their common axis,generating a swirling motion. The swirl induces a secondary,meridional circulation through inertial effects. For specificconfigurations complex eigenmodes representing an infinite sequenceof eddies, analogous to those found in two-dimensional cornerflows and some three-dimensional geometries, form a componentof this secondary circulation. When the cones rotate these eigenmodes,arising from the geometry, compete with the forced modes todetermine the flow near the apex. This paper studies the relative dominance of these two effectsand maps out regions of parameter space, with attention to howshear and overall rotation can destroy the infinite sequenceof eddies that may be present when only the lid is rotated.A qualitative picture of the number of eddies visible in themeridional circulation is obtained as a function of the rotationrates of cones and lid, for various choices of angles. The resultsare discussed in the context of previous work, including theirsignificance for applications to the mixing of viscous fluidsin this geometry.