离心泵叶轮内宾汉流体湍流流场的数值计算

考虑宾汉流体本构关系特点,建立了任意曲线坐标系（ζ,η）下宾汉流体湍流流动的基本方程,应用压力加权校正算法,实现了速度场和压力场的关联,采用交错网格技术,解决了非物理压力振荡问题,在此基础上,对离心泵叶轮内回转面上宾汉流体湍流流动进行了数值模拟,并分析探讨了离心泵叶轮内宾汉流体湍流流动机理。     

宾汉流体物性参数对湍流强度影响的研究

考虑宾汉流体本构关系的特点，建立了适用于宾汉流体的修正动量方程和Ｋτ－ετ模型方程。采用压力耦合半隐式ＳＩＭＰＬＥ算法，通过流场的数值计算研究，指出了宾汉流体本身的物性参数（如屈服应力、塑性粘度）对其湍流强度有着重要影响。     

匀低速曲柄滑块机构近似解与精确解比较

叙述和比较了曲柄滑块机构滑块运动方程的近似解和精确解. 导出了理想状态下滑块的运动方程的精确表达式;使用Taylor公式将精确表达式展开获得近似表达式,并保留一阶和二阶;通过数值算例分别比较了滑块的位移、速度和加速度表达式的近似解和精确解;观察数值结果:只有当曲柄和连杆长度比值较小时,近似解才接近精确解;它们的比值较大时,近似解和精确解的差别较大.     

Bingham流体在旋转圆盘上流动的数值解

导出了描述Ｂｉｎｇｈａｍ流体在旋转圆盘上流动的基本方程,用差分方法数值解薄膜厚度分布方程,得到二种类型的厚度分布。数值解分别和计算机磁盘的厚度分布,Ｊｅｎｅｋｈｅ等的实验结果定性一致。     

求一类非线性振动微分方程的近似解的新方法

本文利用非线性振动微分方程中的非线性项是小量的特点,并利用变量置换,把原微分方程近似地变换成为常系数线性微分方程,求得了一级近似解.算例表明,一级近似解具有颇高的精度,且计算过程十分简单.     

双筒黏度计中牛顿流体振荡的近似解析解

双筒黏度计中牛顿流体的流动问题,已经得到了数值解￣［１］．本文利用变量变换及加权残值法,得到了该问题的近似解析解。算例表明,当隙宽很小时,近似解与已有准确解（数值数）十分符合。     

关于“非线性Duffing方程的高精度近似解”一文的商榷

本文认为文[1]中的参数迭代法实际上就是一种加权残量法,而不是一种新的方法．通过选取不同的配置点,可得到精度更高的近似解．     

重力梯度力矩近似公式适用条件的探讨

教材中重力梯度力矩经典近似公式是基于常规尺寸空间结构推导的,如果直接应用于超大尺寸结构可能会导致精度不够、甚至错误的结果.以超大空间哑铃结构为研究对象,对比了基于重力梯度力矩非近似公式与经典近似公式得到的姿态动力学响应,指出了经典近似公式的局限性.通过提高重力梯度力矩中近似项的保留精度,提出了修正公式,并验证了该公式的适用性.所得结论是对重力梯度力矩教学内容的有益扩展,对工程应用也有帮助.     

经典悬链线理论精确解与近似解的非线性数值计算

针对经典悬链线数学解中存在两个未知参数,即水平张力h和广义倾角α迄今尚未妥善解决的问题,进行了深入细致的分析。利用悬链线两点边值约束条件和不可拉伸假设,推导出求解隐含独立未知量水平张力的超越方程。引进互逆的无量纲参数求解超越方程中的水平张力,使得水平张力形式上具有最简单的参数依赖关系。探讨了广义倾角β,α和θ与几何参数的相互关系,得出广义倾角α不是独立未知参数的结论。提出了水平距离趋于0和趋于极限距离的各种近似解、在真小数全局计算范围内的近似解以及这些近似解关于精确解的误差程度,其结果在工程上具有应用价值。     

粘性液体混合的自型问题的近似分析解

不可压缩粘性液体混合的自型问题,只是少数几种情况得到了分析解,其它情形只能用数值法求解。本文用最小二乘法求出了这个问题的近似分析解。对于壁面具有式(3.2)的形状的渠道中的流动,本文得到了λ_1很小时流速的计算公式。     

On the flow of a Bingham fluid passing through an electric field

We study the action of an electric field on a Bingham fluid from the point of view of existence and uniqueness of solutions. We also give an upper bound for the stopping time.     

Nonlinear stability of Poiseuille flow of a Bingham fluid: theoretical results and comparison with phenomenological criteria

We present new results on the nonlinear stability of Bingham fluid Poiseuille flows in pipes and plane channels. These results show that the critical Reynolds number for transition, Re_c, increases with Bingham number, B, at least as fast as Re_cB^1/2 as B→∞. Estimates for the rate of increase are also provided. We compare these bounds and existing linear stability bounds with predictions from a series of phenomenological criteria for transition, as B→∞, concluding that only Hanks [AIChE J. 9 (1963) 306; 15 (1) (1963) 25] criteria can possibly be compatible with the theoretical criteria as B→∞. In the more practical range of application, 0≤B≤50, we show that there exists a large disparity between the different phenomenological criteria that have been proposed.     

Dispersion in a Bingham plastic fluid: Effects of peripheral layer

The dispersion of a soluble matter in a plastic fluid flowing through a tube and a channel has been analysed by taking into account the variations of viscosity, diffusivity and yield stress. It has been shown that in the special case of a Bingham fluid, surrounded by a peripheral layer of a Newtonian fluid, the effective dispersion coefficient with which the solute disperses across a plane moving with the mean speed of the flow decreases with the viscosity of the peripheral layer fluid but increases as the molecular diffusion coefficient of this layer decreases. Further, the effective dispersion coefficient also decreases as the yield stress of the Bingham fluid increases.     

Squeeze flow of Bingham fluids under slip with friction boundary condition

This paper develops a theoretical analysis of a Bingham fluid in slipping squeeze flow. The flow field decomposition consists in combining a central extensional flow zone in the plane of symmetry and shear flow zones near the plates. It is also considered that the slipping zone is located around a central sticking zone as previously shown from experiments. It is assumed that the shear stress at the plates is constant in the slipping zone and equals a fixed friction yield value. The squeeze force required to compress a Bingham fluid under the slipping behaviour as well as the radial evolution of the transition point between both sticking and slipping zones are finally determined.     

Start-up Flow of a Bingham Fluid in a Pipe

We present an analytical solution of axisymmetric motion for a Bingham fluid initially at rest subjected to a constant pressure gradient applied suddenly. Using the Laplace transform, we obtain expressions which allow the calculation of the instantaneous velocity, plug radius and rate of flow as a function of time. We also give a relation for the shear stress in the plug and in the region where the behaviour of the fluid is Newtonian.     

Very slow flow of Bingham viscoplastic fluid around a circular cylinder

Numerical simulations have been used to study the flow of a Bingham viscoplastic fluid around a circular cylinder in an infinite medium with negligible inertia effects. Papanastasiou's regularisation technique has been adopted to approximate the model. The case corresponding to preponderant plasticity effects has been particularly studied and convergence of the solutions examined in detail. The flow kinematics and stresses have been determined. The rigid zones have been identified and characterised. At large Oldroyd numbers, when plasticity effects become preponderant, a viscoplastic boundary layer appears around the cylinder. The characteristics of this viscoplastic boundary layer are quantified. The results are compared with existing theoretical results, concerning particularly the predictions of the viscoplastic boundary layer theory and the plasticity theory.     

Layered model of electrorheological fluid under flow

We present a theoretical model of the behavior of a concentrated electrorheological fluid (ERF) which explicitly takes into account the effects of conductivity. The increase in shear viscosity under an electric field is due to a layered structure between the electrodes, made up of the remnants of particle chains adhering to the electrodes by electrostatic image forces, and a freely flowing liquid layer where all the shear flow is concentrated. This layered model can explain the variation of electric current with shear rate, as well as the rheological response of a dynamic yield stress proportional to the square of the applied electric field.     

Instability of Bingham fluids in Taylor-Dean flow between two concentric cylinders at arbitrary gap spacings

Stability of Bingham fluids is investigated numerically in azimuthal pressure-driven flow between two infinitely long concentric cylinders. An infinitesimal perturbation is introduced to the basic flow and its time evolution is monitored using normal mode linear stability analysis. An eigenvalue problem is obtained which is solved numerically using pseudo-spectral collocation method. Numerical results are obtained for two different cases: (i) the inner cylinder is rotating at constant velocity while the outer cylinder is fixed (i.e., the Taylor-Dean flow) and (ii) both cylinders are fixed (i.e., the Dean flow). The results show that the yield stress always has a stabilizing effect on the Taylor-Dean flow. But, for the Dean flow the effect of the yield stress is predicted to be stabilizing or destabilizing depending on the magnitude of the Bingham number and also the gap size.     

Interaction between two circular cylinders in slow flow of Bingham viscoplastic fluid

The interaction between two circular cylinders was studied in the slow flow of a Bingham viscoplastic fluid in an infinite medium without any inertia effects. The configuration studied is that in which the flow direction is parallel to the centre line of the cylinders. Finite-element numerical simulations were used with an approximation by Papanastasiou's regularisation method. The case of high yield stress effect was particularly examined. The convergence of the solutions was examined in detail. Changes in the rigid zones, kinematics and stresses were determined in relation to the degree of interaction, which is a function of the distance between the cylinders and the effect of yield stress. The results compared with the case of a single cylinder show that yield stress reduces interaction effects. The transition between configurations with interacting cylinders and configuration with isolated cylinders was examined as a function of the effect of yield stress. Correlations were proposed for the drag coefficient and the stability criterion when the cylinders are interacting.