两个同心旋转圆柱之间的两种流体的交界面几何形状问题

研究两个同心旋转圆柱之间的两种流体的交界面几何形状问题．利用张量分析工具,给出了忽略耗散能量影响下交界面几何形状是一种能量泛函的临界点,其对应的Euler-Lagrange方程是1个非线性椭圆边值问题．对于粘性引起的耗散能量不能忽略的情况下,同样给出了1个带有耗散能量的能量泛函,其临界点是交界面几何形状,相应的Euler-Lagrange方程也是1个二阶的非线性椭圆边值问题．这样,交界面几何形状问题转化为求解非线性椭圆边值问题．     

同心球间旋转流动类Lorenz方程组的分歧问题

本文对同心球间旋转流动的Navier-Stokes方程谱展开后进行三模态截断,研究了所得到的类Lorenz型方程组的分歧问题.推导了同心球间旋转流动的Navier-Stokes方程的流函数-涡度形式,给出了静态奇异点的条件,并计算出解分支.     

两同心球间旋转流动类Lorenz方程组的静态分歧

对同心球间旋转流动的N av ier-S tokes方程谱展开后进行三模态截断,讨论了所得到的类Lorenz型方程组的分歧问题.给出了静态奇异点的条件,并计算出解分支.首先,简要介绍了Lorenz方程组以及用Lorenz截断法讨论非线性问题的意义,其次,推导同心球间旋转流动N av ier-S tokes方程的流函数-涡度形式,最后,讨论同心球间旋转流动的类Lorenz型方程组的分歧问题.     

透平机械内部三维可压缩Navier-Stokes方程的流面方法和维数分裂算法

在这篇文章中,运用经典的张量分析方法,把流动区域用-个二维流形序列分割成一系列流层之并,推得在流层内半测地坐标之下的Navier-Stokes方程,在流形的法线方向应用向后Euler差分,推导了两维流形上的可压缩Navier-Stokes方程,和流函数满足的方程.在这个基础上,提出了一种维数分裂法的新算法.这种方法不同于区域分解法.对于三维问题,在区域分解法中我们必须在每个子区域上仍解三维问题,但是在这种新方法中,只需要在每个子区域上求解二维问题,不过是几个二维流形上的NS方程.文中还给出了-个透平机械内部流动的数值计算实例.     

两同心旋转球间流动的弱解的存在唯一性

研究了两个同心旋转球间的轴对称不可压缩的粘性流动。该流动广泛应用于大气物理和地球物理等学科中,为了得到流动的流函数－速度形式的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的弱解的存在性和唯一性,首先发现了该方程中非线性项之间关系,并引入一个有限维的辅助问题,通过紧性而得到了结论。     

圆柱振荡绕流的三维不稳定性研究

通过数值求解三维不可压缩Navier-Stokes方程,研究了振荡圆柱绕流的旋涡不稳定性.研究表明,在一定的参数范围内,由于旋涡不稳定性,振荡流动由二维演化成三维流动,并沿圆柱轴向形成交错排列的三维涡结构.数值计算合理地预测了三维涡结构的空间失稳波长,并与实验测试值相符很好.文中还进一步研究了圆柱的受力特性,通过求解Morison方程,计算了圆柱的阻力和惯性力特性,其计算结果与已有的实验数据相吻合.     

二维流面上的流动问题的速度图方法

对于一些特殊的流动,尤其是平面上的位势流动,速度图方法有其显著的优点．对于理想流体来说,流面总是存在的,在流面上,流动的速度向量总是在其切空间里．通过引入流函数和势函数,采用张量分析作为工具,给出了二维曲流面上位势流动的速度图方法,得到了流函数满足的速度图方程,为一些特殊的流动问题提供了一类分析方法．并且,对于得到的二维速度图方程,得到了相应的特征方程和特征根,从而可以对方程的类型进行分类．最后,给出了一些特殊流动的实例．     

流面上的流动速度图方法

平面位势流动的速度图方法,对于一些特殊流动,有特别明显的优点。本文利用张量分析工具,对任意流面上的位势流,建立速度图方程,为解决一些特殊流动问题,提供一个分析方法。     

求解不定常圆柱绕流的区域分裂法

本文把区域分裂法与涡点格法相结合,以此构造一类并行算法,数值模拟不定常圆柱绕流在高Reynolds数情况下的初期流动. §1.基本问题 假设有一个半径为a的圆柱体,在静止的不可压粘性流体中,以速度U突然起动,此流动满足二维不定常Navier-Stokes无量纲化方程:     

慢扩张旋转流的稳定性分析（Ⅰ）—理论研究

本文研究了无粘不可压慢扩张旋转流的稳定性问题，采用多重尺度展开法对有慢扩张的旋转流的非对称扰动进行浅化稳定性研究，导出了零阶及一阶扰动模所应满足的微分方程及由于慢扩张引起振幅变化的控制方程，将Ｐｌａｓｃｈｋｏ关于慢扩张喷流的结果推广到具有慢扩张的旋转流情况。     

Numerical stability analysis of the Taylor-Couette flow in the two-dimensional case

The stability of the laminar flow between two rotating cylinders (Taylor-Couette flow) is numerically studied. The simulation is based on the equations of motion of an inviscid fluid (Euler equations). The influence exerted on the flow stability by physical parameters of the problem (such as the gap width between the cylinders, the initial perturbation, and the velocity difference between the cylinders) is analyzed. It is shown that the onset of turbulence is accompanied by the formation of large vortices. The results are analyzed and compared with those of similar studies.     

On the Bifurcation of Flows of a Heat-Conducting Fluid between Two Rotating Permeable Cylinders

Sufficient conditions are found for the bifurcation of flow of a viscous heat-conducting fluid between two rotating permeable cylinders.     

On the flow of a viscous incompressible fluid between two coaxial rotating porous cylinders

Exact solution of the Navier-Stokes equations for the laminar flow of a viscous incompressible fluid between two coaxial rotating porous cylinders, kept at constant temperatures, has been studied. The rate of injection at one cylinder is taken to be the same as the rate of suction at the other. Expressions for the velocity and temperature distributions and for the torque required to turn the outer cylinder are obtained. The effects of λ (injection parameter), σ (the ratio of the radii of the cylinders) and Pé (Péclet number = λPr) on them are shown graphically.     

Helical symmetric solution of 3d Navier-Stokes equations arising from geometric shape of the boundary

In this article, we investigate three-dimensional solution with helical symmetry in a gap between two concentric rotating cylinders, inside is a helicoidal surface (screw propeller) while outside is a cylindrical surface. Establish the partial differential equations and its variational formulation satisfied by a helical solution in a helical coordinate system using tensor analysis method, we provide a computational method for the power and propulsion of the screw. The existence and uniqueness of weak helical solutions are proved.     

Couette-Taylor流的谱Galerkin逼近

利用谱方法对轴对称的旋转圆柱间的Couette-Taulor流进行数值模拟．首先给出Navier-Stokes方程流函数形式,利用Couette流把边界条件齐次化．其次给出Stokes算子的特征函数的解析表达式,证明其正交性,并对特征值进行估计．最后利用Stokes算子的特征函数作为逼近子空间的基函数,给出谱Galerkin逼近方程的表达式．证明了Navier-Stokes方程非奇异解的谱Galerkin逼近的存在性、唯一性和收敛性,给出了解谱Galerkin逼近的误差估计,并展示了数值计算结果．     

Flow between torsionally oscillating noncoaxial cylinders

The flow of an incompressible viscous fluid between two torsionally oscillating noncoaxial cylinders has been investigated. Closed form solutions for symmetric and first order asymmetric flow are obtained for the cases when the gap between the cylinders is finite. Solutions of the governing equations under the geometrical restriction of narrow gap are also presented. These solutions coincide with the solutions of the finite gap by incorporating in them the condition of narrow gap. The components of the force acting on the inner cylinder are calculated.     

Pulsating magnetohydrodynamic flow in an annular channel

Pulsating laminar flow of a viscous incompressible electrically conducting fluid in an annular channel between two infinitely long circular cylinders under a radial impressed magnetic field is considered. The solutions of magnetohydrodynamic equations have been obtained on the assumption that the space between two cylinders is small compared to their mean radius. The solutions were also obtained on the assumption of small magnetic Reynolds number with special consideration of those for low and high frequencies.     

Analytical and numerical solutions of a generalized hyperbolic non-Newtonian fluid flow

Generalized hyperbolic non-Newtonian fluid model first proposed by Al-Zahrani [1] is considered. The model was successfully applied to some drilling fluids with better performance in relating shear stress and velocity gradient compared to power-law and Hershel-Bulkley model. Special flow geometries namely pipe flow, parallel plate flow and flow between two rotating cylinders are treated. For the first two cases, analytical solutions of velocity profiles in the form of integrals are presented. For the flow between two rotating cylinders, the differential equation is solved by Runge-Kutta method combined with shooting. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The onset of resonance processes in the Couette–Taylor problem close to the point of codimension-2 bifurcation

The bifurcations on passing around the point of intersection of two neutral curves (points of codimension-2 bifurcation) are considered in the Couette–Taylor problem of the fluid motion between rotating cylinders. The secondary modes in a small neighbourhood of a point of codimension-2 bifurcation are studied using a system of non-linear amplitude equations in a central manifold. The steady-state solutions of the amplitude systems, to which secondary periodic modes of the travelling-wave type, non-linear mixtures of travelling waves and unsteady two-, three- and four-frequency quasiperiodic solutions of the system of Navier–Stokes equations correspond, are analysed. A numerical analysis of the conditions for the existence and stability of irrotationally symmetric steady-state fluid flows between unidirectionally rotating cylinders is carried out.     

Rapid gravity flow of cohesionless granular materials down inclined chutes

This paper is concerned with the analysis of the flow of cohesionless granular materials down inclined chutes. The stress tensor is assumed to be composed of two contributions, a rate-independent Coulomb part and a non-linear dynamic or viscous part. Plausible forms are chosen for these two stress contributions; the rate-dependent viscous part is based upon previous viscometric experiments of the present authors. The equations of motion are solved for the velocity and solids concentration for the case of two-dimensional stress and velocity fields. The two-dimensional analysis is then extended in a simple but approximate way to handle the effects of friction on the vertical side walls of a rectangular cross-sectioned channel. The predicted velocities and flow rates are compared with experiments of Savage for flowing polystyrene beads and reasonable agreement is found.