二阶非牛顿流体环管流动解析解

本文采用积分变换的方法,找到了一类非牛顿流体在环形管道中不定常流动的解析解,并进行了数值计算,详尽分析了非牛顿性系数和其他各参数对二阶流体不定常流动的影响.指出当二阶流体非牛顿系数相同时,环管流与一般管流相比达到稳定的特征时间较短,并且相应的速度分布、平均速度分布的数值均较小,在外半径相同时,环管流内壁的剪应力较之一般管流,其大小随内半径的大小而变,环管流的外壁剪应力总相应地小于内壁剪应力.     

圆管入口段不可压缩层流流动的解析分析

从不可压缩粘性流体的Navier-Stokes方程出发,给出了在均匀来流条件下的圆管入口段层流流动中央区的速度分布及压力分布的解析解．     

经过修正的层流流动的流动稳定性问题(Ⅰ)——基本概念和理论

本文提出了经过修正的层流流动的流动稳定性理论,并在文中给出平行剪切流中平均速度的一类修正剖面,使这种理论可用于研究平行剪切流的流动稳定性,指出了流动失稳的一条新的可能途径.     

血液流动模拟方法对比分析

对现有主要血液流动模拟方法进行了对比研究.以单个直血管为研究对象,分别用牛顿单相流模型、非牛顿单相流模型、液固两相流剪切稀化模型、液固两相流颗粒动力学模型和血液两相流修正模型计算了血液流场,然后对比了五种模型模拟得到的血液动力学参数:血液流速、红细胞体积分数、流体粘度和壁面剪切应力.结果表明:血液组成和粘度方程的选择对血液速度场计算结果有明显影响;流体本构方程和升力公式对壁面剪切应力计算结果均有明显影响;液固两相流颗粒动力学模型计算得到的血液粘度远偏离正常的血液粘度,模型不适用于模拟稳态血液流动;血液两相流修正模型可以较准确模拟红细胞在血管内的径向分布及其影响.研究结果可为今后相关研究中血液模拟方法的选择提供指导.     

空间分数阶非Newton流体本构及圆管流动规律研究

对非Newton流体的本构及流动规律进行研究是分析、预测和控制非Newton流体在管道中流动的关键.实验表明非Newton流体在流动过程中具有历史记忆性,基于空间分数阶微积分方法,建立了分数阶非Newton流体本构模型;并推导了该模型在圆管中的流速分布、流量、平均流速、压降、平均Reynolds数等管道流动参数;提出了分数阶非Newton流体圆管流态判别准则.研究表明非Newton流体的圆管流层间的切应力可以通过流速的轴向分布大小来描述.对于不含屈服切应力的分数阶非Newton流体,分数阶的阶数越大,断面流速分布越均匀,记忆能力越强.分数阶的阶数大小反映了流体对全域空间的记忆性强弱;而对于含有屈服切应力的分数阶非Newton流体,分数阶的阶数越大,速梯区流速分布越均匀,流核区速度越小.分数阶的阶数大小反映了局部空间记忆性强弱.该研究为非Newton流体的记忆特征提供了一种新的建模方法.     

均匀自由流动的非牛顿流体中连续表面上的磁流体动力学流动和热传递

分析在平行自由流动的非牛顿黏弹性导电流体中,连续平展表面移动时的稳态流和热传递特性,该流动处于横向均匀磁场作用下.以二阶流体构建它的本构方程,得到了速度分布和温度断面图的数值结果.讨论了诸如黏弹性参数、磁场参数和Prandtl数等不同物理参数对诸种动量和热传递特性的影响,并给出相关图示.     

高弹粘流在三维变厚度狭缝流道中流动的数值模拟

用有限块法对高弹粘流在三维变厚度狭缝流道中的流动进行数值模拟.求出流体流量在流道中的分布规律;通过对实际板材挤出模鱼尾型流道中设置阻流块对流动影响的计算,证实有限块法是简易可行的,从而为挤出模的计算机辅助设计提供了一个重要手段.     

解任意形状扁轴对称体Stokes流动的连续奇点分布法

本文以Sampson球形无穷级数作为基本奇点,采用分段等强度和分段二次抛物分布两种体内连续分布法解任意形状扁轴对称体的Stokes流动.通过扁球的无界绕流问题,对这两种方法的收敛性,精度和适用范围做了检验和比较.结果表明,在一定的范围内,无论是阻力系数或压力分布,它们的计算结果都和精确解符合得很好,而且,随着分布函数逼近程度的提高,其收敛性得到改善,适用范围也随之扩大.作为一般算例,分别用这两种方法解决了卡西尼扁卵形体的绕流问题,得到了一致的结果.最后,用分段二次连续分布法计算了具有一定生理意义的红细胞体的Stokes流动,首次得到了它的阻力系数和表面压力分布.     

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．     

经过修正的层流流动的流动稳定性问题(Ⅲ)——经过修正的平行剪切流的非线性稳定性研究

本文根据文[1]给出的经过修正的层流流动的流动稳定性理论及平行剪切流中平均速度的一类修正剖面,研究了平行剪切流的非线性稳定性性质,并在本文的假设下,把背景湍流噪声的干扰引入了流动稳定性计算,对于平面Poiseuille流动和圆管Poiseuille流动,得到了与实验趋势相一致的结果.     

Occurrence of Taylor vortices in the flow between two rotating conical cylinders

The behavior of the flow between two coaxial conical cylinders with the inner one rotating and the outer one stationary is studied numerically. Special attention is paid to the occurrence of Taylor vortices in basic flow and unsteady helical vortices. It is found that, in basic flow, the vortices occur in the direction toward smaller radius, while toward bigger radius in unsteady helical vortices; moreover, the unsteady helical vortices can coexist with unstable steady Taylor vortices. The results suggest that the behavior of conical flow is dominated by a competition between the meridional flow and radial flow. The effect of meridional flow is most significant at small apex angle or in basic flow and helical vortices, while the radial flow dominates the structure at larger apex angle or in steady vortical flow. In order to get better understanding the competition and the transition of Taylor–Couette flow to conical flow, a velocity angle related to velocity components is defined, and the pattern evolution of velocity, streamlines and the velocity angle are examined with respect to apex angle, as well as Reynolds number. Finally, the statistical properties of turbulent conical flow are investigated.     

A gradient flow for the prescribed Gaussian curvature problem on a closed Riemann surface with conical singularity

In this note, we prove that the abstract gradient flow introduced by Baird-Fardoun-Regbaoui [2] is well-posed on a closed Riemann surface with conical singularity. Long time existence and convergence of the flow are proved under certain assumptions. As an application, the prescribed Gaussian curvature problem is solved when the singular Euler characteristic of the conical surface is non-positive.     

平头一锥体无粘超音速绕流的数值计算

复杂外形飞行体的超音速绕流气动力计算,显然是重要的.仅无粘超音速绕流,国内外的工作就很多,如[1]—[5].本文介绍的方法是[1,2]方法的修改与发展.近来我们计算了好几种头部与身部形状的物体在不同来流马赫数与攻角下的超音速绕流的流     

A free boundary problem of elliptic equation arising in supersonic flow past a conical body

We study free boundary value problems of elliptic equation caused by a supersonic flow past a non-symmetric conical body. The flow is described by the potential flow equation. In the self-similar coordinate system the problem can be reduced to a boundary value problem of second order nonlinear elliptic equation with a free boundary. Applying the partial hodograph transformation and the method of nonlinear alternative iteration we proved the existence of solution to this boundary value problem. Consequently, we also proved the conclusion that for the problem of supersonic flow past a conical body, if the conical body is slightly different from a circular cone with its vertex angle less than a given value determined by the parameters of the coming flow, then there exists a weak entropy solution with an attached conical shock.     

Restricted variational principle method for problems of low-density aerodynamics

Rosen's restricted variational principle representation of the Boltzmann equation is applied to the problem of determining the transitional-regime, low-density, hypersonic flow over slender, conical vehicles with diffusely reflecting surfaces. If the trial distribution function is suitably chosen, the Euler-Lagrange equations associated with Rosen's functional result in a semilinear hyperbolic system amenable to solution by classical characteristics methods. Sample calculations are given and compared with the low-density cone flow experiments of Hickman to assess the accuracy of the method presented. It is believed that the present method constitutes the first solution method for boundary value problems in the low-density transitional flow regime.This work was supported by the United States Air Force, Contract No. AF04(695)-1001.     

The flow of a combustible mixture with a Chapman–Jouguet detonation wave around a cone

The flow around a circular cone under conditions of Chapman–Jouguet (CJ) self-sustaining detonation is investigated in the classical formulation of an infinitely thin detonation wave (DW) in an inviscid and non-heat conducting combustible mixture. Such conditions for flow around a cone are remarkable in several respects. In 1959, Chernyi and Kvashnina had already shown that, for supersonic flows of a combustible mixture around a cone, CJ detonation, as in the case of a wedge, is not only possible for a strictly fixed cone angle (the “CJ” angle) but also for angles smaller than this (including a zero angle, that is, when there is no cone). In the case of flow around a wedge with an angle that is less than the corresponding CJ angle, a centred rarefaction wave that turns the supersonic flow in the required direction borders on the CJ DW. In the case of a cone, a conical rarefaction flow also borders on the CJ DW. However, if, in the plane case, a uniform supersonic flow adjoins the centred rarefaction wave along its boundary C⁺-characteristic then the conical rarefaction flow is bounded by a conical shock wave (SW), bordered up to the surface of the cone by a conical compression flow. Only for a zero cone angle does the SW degenerate into the C⁺-characteristic and the conical compression flow degenerates into a uniform supersonic flow. The configuration obtained in the general case became the first example of a self-similar solution with two SW of “one family” (the first of them is the DW) diverging from a single point. The results of calculations carried out in this paper with the construction of streamlines and the characteristics of the two families give a fairly complete representation of the above mentioned features of the flows considered.     

Ricci Flow on Surfaces with Conical Singularities

This paper studies the normalized Ricci flow on surfaces with conical singularities. It’s proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes good geometric sense. For some simple surfaces of this kind, for example, the tear drop and the football, it’s shown that they admit a Ricci soliton metric.     

锥形微通道内液滴自输运特性及力学驱动机制研究

针对液体在微通道内的自输运特性,采用数值仿真与能量解析相结合的方法研究了液滴在锥形微通道内的自输运特性及力学驱动机制,得到微通道的锥形角、液滴与微通道内壁的接触角及微通道的润湿性对液滴自输运特性的影响关系.分析表明,微通道的锥形角、液滴与微通道内壁的接触角均能影响液滴的自输运方向及驱动力大小.对于亲水性微通道,微通道的锥形角、液滴与微通道内壁的接触角其作用效果呈现整体形态;对于疏水性微通道,微通道的锥形角、液滴与微通道内壁的接触角其作用效果呈现局域形态.这可为研究液体在微通道内的自输运机理及界面内液体细观流动机制奠定理论基础.     

关于锥型流计算稳定法的讨论

在空气动力学超音速绕流问题的数值计算中,稳定法是一个相当有效的方法,它的基本想法是:在原来求解的微分方程组中引入一个新的时间变量,并添加一些附加项,得到一个新的方程组,这个方程组为双曲组,若在空向曲面上任给一组初值,求其数值解,则     

A Scalar Curvature Bound Along the Conical Kähler–Ricci Flow

Starting with a model conical Kähler metric, we prove a uniform scalar curvature bound for solutions to the conical Kähler–Ricci flow assuming a semi-ampleness type condition on the twisted canonical bundle. In the proof, we also establish uniform estimates for the potentials and their time derivatives.