斜螺旋曲线的构造

斜螺旋曲线是指三维欧氏空间中主法向量场与一固定方向成固定角的曲线.研究斜螺旋曲线的构造.首先求解一个关于活动标架的线性常微分方程组,然后通过积分来确定斜螺旋曲线的位置向量.最后给出了一个例子.     

Jeffrey流体流过有限长圆柱管时磁流体动力学的蠕动流

研究Jeffrey流体流过有限长管道时的蠕动流.在外加磁场作用时,流体呈导电性.分析是在长波长和低Reynolds数近似假设下完成.得到了压力梯度、体积流量、平均体积流量和局部壁面剪应力的表达式.研究了松弛时间、延迟时间和Hartman数,对压力、局部壁面剪应力以及蠕动泵机械效率的影响.还研究了回流现象,调查了沿管道壁波数非整倍数时的传播情况,研究有限长管道传播的内在特性.     

通过有漏孔管道时的层流解析解

研究了通过有漏孔管道时的层流,并解析地求解了动量方程和能量守恒方程．由Hagen-Poiseuille的速度分布,同时定义轴向和径向速度分量的未知函数,得到了压力和质量输运方程,并根据不同的参数,画出其分布图．结果表明,管道中的轴向速度、径向速度、质量输运参数和压力,随着流体沿管道的流动而减小．     

非牛顿流体偏心环空螺旋流的解析解

石油和化工中许多问题需要求解非牛顿流体偏心环空螺旋流。本文全面地研究了幂律流体和宾汉流体在偏心环空中层流螺旋流的流动规律与流动状态的判别。在理论上,根据流体力学原理,运用数学方法,在作者同心环空螺旋流的理论基础上,通过对偏心环空螺旋流流场的无限细分法,给出了该流场的视粘度分布、速度分布、流量和压降方程,进而建立了判别流态的稳定性参数。     

变截面圆形管道粘性流动的伽辽金-摄动杂交解

采用伽辽金-摄动杂交法来研究壁面是正弦形状的变截面圆形管道的粘性流动,从而避免了摄动小参数的局限性和单纯伽辽金法基函数选取的任意性的困难．讨论了边界和雷诺数对流动的影响,获得流动分离点和附着点的位置,还分析了壁面剪应力和摩擦系数沿轴向的变化情况．在小参数的情况下,计算所获得的结果与摄动解吻合良好．     

激波在变截面管道中的传播及新激波的产生与发展

由于爆炸或各种不同的原因在介质中引起的压缩作用,如以超声速传播就形成激波。当一个强激波进入变截面管道后,由于管道截面积的变化,激波强度也发生变化,其后面形成不定常气流。为了探讨激波及其后面的不定常气流的变化规律,我们用三种方法进行数值计算,即:一维特征线法,一维两步二阶差分法及轴对称二维两步二阶差分法。计算结果,三种方法相辅相成,并弄清了管内的流场。计算表明,第一个激波过后在连续流中很快出现了新的激波,并逐渐增强。二维不定常方法还算出了三叉波的形成。     

研究鼻道的分流作用对嗅觉反应的影响

考虑了中、下鼻道的分流作用,把总鼻道内气流的截面平均速度描述为轴向位置的函数,建立了不定常的二维嗅觉模型,并得到了该模型的精确解,精确解揭示了各生理参数之间的内在联系。计算结果表明理论结果与实验结果是一致的,这对进一步研究嗅觉机理具有一定的参考价值。     

斜螺面犁翼优越性之浅见——犁体螺旋面设计的特征参数与自锁理论

问题的提出 我国南方水田通用型犁体的犁翼曲面,近似于斜螺旋而.经过用倾斜动线法扫描,显露了粗略的规律性.为了将它提升到理性认识,验算国内外螺旋犁面在实践中得到的经验参数,和论证犁面设计采用的斜螺面犁翼优于国外用正螺面构成的犁壁,进行了螺旋犁面自锁问题的研究.     

伴有挥发的液相连续反应过程的数学模型

化工生产中,在泡罩塔、筛板塔或填充塔等轴向具有浓度梯度的鼓泡式反应装置中进行的液相连续反应过程,如果反应中伴有某组分向气流挥发,则将影响到轴向的浓度分布。为适应此类反应过程的设计计算,本文提出了各级伴有等量挥发的多级理想混和模型。文中讨论了用不挥发物质进行脉冲示踪以测定虚拟级数的方法,并在测定的虚拟级数的基础上,讨论了简单反应和复杂反应的图解计算法。在烃类液相氧化的模型装置上,进行了乙苯液相连续氧化试验。按照本文所述流动模型进行计算的结果与实测数据获得较好的吻合。     

一类变截面管内轴对称螺旋流的衰减规律分析

针对一类变截面管内的轴对称弱螺旋流情况,讨论了其沿下游的演变规律,对于层流情况得到了指数衰减性的结论,对于湍流情况,则在Boussinesq涡粘性假设下得到了局部环量放大的必要条件。     

Analytical solutions of laminar swirl decay in a straight pipe

In this work, the laminar swirl flow in a straight pipe is revisited and solved analytically by using prescribed axial flow velocity profiles. Based on two axial velocity profiles, namely a slug flow and a developed parabolic velocity profiles, the swirl velocity equation is solved by the separation of variable technique for a rather general inlet swirl velocity distribution, which includes a forced vortex in the core and a free vortex near the wall. The solutions are expressed by the Bessel function for the slug flow and by the generalized Laguerre function for the developed parabolic velocity. Numerical examples are calculated and plotted for different combinations of influential parameters. The effects of the Reynolds number, the pipe axial distance, and the inlet swirl profiles on the swirl velocity distribution and the swirl decay are analyzed. The current results offer analytical equations to estimate the decay rate and the outlet swirl intensity and velocity distribution for the design of swirl flow devices.     

圆截面螺旋管道内非定常流动研究

以血液流动为背景,利用双参数摄动法研究了圆截面螺旋管内低频振荡流动,得到问题的二阶摄动解,分析了轴向速度、二次流、壁面剪应力在不同时刻的特点及随时间和Womersley数的变化情况。研究表明:挠率对圆截面曲线管道内低频振荡流动的影响不可忽略,尤其是轴向压力梯度绝对值很小时,挠率将对二次流动结构起主要影响作用。流函数的剧烈变化只发生在正、负数值发生转变的很小的时间段内,大部分时间段内变化平缓。壁面剪应力随θ的变化也很大。     

精确计算Bingham流体圆管层流压降及速度分布规律的新方法

Bingham(宾汉)模型情况下,多采用通用公式进行圆管层流压降的解析计算,即将Bingham模型本构方程代入粘性流体圆管层流流动通用公式进行计算,仅能得到压降的解析解.新方法结合Bingham流体本构方程与运动方程,建立有关力学平衡方程,并运用代数方程的根式解理论对圆管层流流动时的非线性方程进行求解,可直接求得Bingham流体圆管层流压降及速度流核区半径的解析解,进一步可求得圆管层流速度解析解;Bingham流体圆管层流速度的直接影响因素为流量、塑性粘度和屈服值,研究发现速度流核宽度与屈服值成正比,与流量及塑性粘度成反比,且流核的宽度越大,流核区的速度越小.     

Eulerian and Lagrangian predictions of particulate two-phase flows: a numerical study

To predict particulate two-phase flows, two approaches are possible. One treats the fluid phase as a continuum and the particulate second phase as single particles. This approach, which predicts the particle trajectories in the fluid phase as a result of forces acting on particles, is called the Lagrangian approach. Treating the solid as some kind of continuum, and solving the appropriate continuum equations for the fluid and particle phases, is referred to as the Eulerian approach.Both approaches are discussed and their basic equations for the particle and fluid phases as well as their numerical treatment are presented. Particular attention is given to the interactions between both phases and their mathematical formulations. The resulting computer codes are discussed.The following cases are presented in detail: vertical pipe flow with various particle concentrations; and sudden expansion in a vertical pipe flow. The results show good agreement between both types of approach.The Lagrangian approach has some advantages for predicting those particulate flows in which large particle accelerations occur. It can also handle particulate two-phase flows consisting of polydispersed particle size distributions. The Eulerian approach seems to have advantages in all flow cases where high particle concentrations occur and where the high void fraction of the flow becomes a dominating flow controlling parameter.     

Uniaxial exchange flows of two Bingham fluids in a cylindrical duct

Buoyancy driven flows of two Bingham fluids in an inclined ductare considered, providing a simplified model for many oilfieldcementing processes. The flows studied are near-uniaxial andstratified, with the heavy fluid moving down the incline, displacingthe lighter fluid upwards. Existence and uniqueness resultsare obtained for quite general flows and for those which satisfyan axial flow rate constraint. Parametric dependence of thesolutions on the axial pressure gradient is studied. Flows whichsatisfy a zero net axial flow constraint result from an axialpressure gradient which minimizes the viscous dissipation, butnot the plastic dissipation. A regularization method is usedto compute solutions to these problems for (more or less) arbitraryfluid-fluid interfaces and duct-cross sections. Examples relatedto a number of practical applications are presented.     

On Fully Developed Flows of Fluids with a Pressure Dependent Viscosity in a Pipe

Stokes recognized that the viscosity of a fluid can depend on the normal stress and that in certain flows such as flows in a pipe or in channels under normal conditions, this dependence can be neglected. However, there are many other flows, which have technological significance, where the dependence of the viscosity on the pressure cannot be neglected. Numerous experimental studies have unequivocally shown that the viscosity depends on the pressure, and that this dependence can be quite strong, depending on the flow conditions. However, there have been few analytical studies that address the flows of such fluids despite their relevance to technological applications such as elastohydrodynamics. Here, we study the flow of such fluids in a pipe under sufficiently high pressures wherein the viscosity depends on the pressure, and establish an explicit exact solution for the problem. Unlike the classical Navier-Stokes solution, we find the solutions can exhibit a structure that varies all the way from a plug-like flow to a sharp profile that is essentially two intersecting lines (like a rotated V). We also show that unlike in the case of a Navier-Stokes fluid, the pressure depends both on the radial and the axial coordinates of the pipe, logarithmically in the radial coordinate and exponentially in the axial coordinate. Exact solutions such as those established in this paper serve a dual purpose, not only do they offer solutions that are transparent and provide the solution to a specific but simple boundary value problems, but they can be used also to test complex numerical schemes used to study technologically significant problems.     

A study of pressure distribution for a slider bearing lubricated with a second‐grade fluid

An infinitely wide lubricated bearing consisting of connected surfaces of second‐grade fluid is analyzed in the present study. The velocity and pressure fields are obtained by a homotopy analysis method (HAM). Two cases, namely, inclined and parabolic slider bearings are considered. The viscoelastic effects play an important role even under the assumption of the order of the magnitude of the variable. However, inertial term does not contribute. Graphical results are interpreted. Comparison between the numerical values for the inclined and parabolic slider bearing is also presented. In addition to that for a meaningful solution, the graphs of convergence parameter, residual error, and numerical comparison are also presented. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1231–1241, 2011     

Implicit fully mesh-less method for compressible viscous flow calculations

A dual-time implicit mesh-less scheme is developed for solution of governing viscous flow equations. The computational efficiency of the method is enhanced by adopting accelerating techniques such as local time stepping and residual smoothing. The Taylor series least square method is used for approximation of derivatives at each node which leads to a central difference spatial discretization. The capabilities of the method are demonstrated by flow computations about standard cases at subsonic and transonic laminar flow conditions. Results are presented which indicate good agreements with the alternative numerical and experimental data. The computational time is considerably reduced when using the proposed mesh-less method compared with the explicit mesh-less and finite-volume counterparts using the same distribution of points.     

Statistical characteristics and time autocorrelation coefficients of the turbulent swirl flow in pipe

In this paper is presented experimental investigation of the turbulent swirl flow in pipe generated by three axial fans of various geometries. One of these fans (model ZP) generates Rankine swirl, while other two, industrial fans, produce mainly solid body circumferential velocity profile. One-component laser Doppler anemometry (LDA) is employed in this research. Downstream transformations of the non-dimensional time-averaged velocity profiles are analyzed. Distributions of turbulence levels are discussed for all three fans in both measuring sections, as well as statistical moments of higher orders for fluctuations in the axial, radial and circumferential directions. Applied correlation theory revealed turbulence structure and its statistical nature. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)