ANALYSIS OF THE MOTION OF A GYRO-THEODOLITE

With the method of analytical mechanics,this paper studies the motions of a gyro-theodolite under the action of (1) the torque of gravity only,(2)the torque applied by theband suspension.(3)the torque of the band suspension with air damping considered,theequations of motion are then established and their solutions are found.Furthermore,analysis of the law of motion and the behaviour of gyro-theodolite during the orientation ismade.     

FLOW OF A TRAIN OF DEFORMABLE FLUID PARTICLES IN A TUBE

I.IntroductionWangandSkalakll]studiedforsolidspheresintubes.HymanandSkalak12--31studiedthemovementofacompactfluidspheres(non-deformable)intubes.Theyonlystudiedcompactdropswhoseradiusesarenotbiggerthan0.7.Pozrikidisl4]studiedthenlotiollofdeformabletluidparticlesintubes.Inthispaper,westudiedtwo-phasenowregime,consistingofaperiodictrainofequallyspacedliquidslugsmovingaxisymmetricallyinacontinuousliquidphasewhichisimmisciblewiththeslugphase(Fig.l(a)).Wereportnumericalsolutionsforthehydrodynamic…     

PROPERTIES OF A HALF SPACE INCLUDING A TWISTED SHAFT OF REVOLUTION

The properties of an elastic half space including a partly embedded twisting shaft of revolution are studied. Without knowing the exact solution of the torsion problem of agiven embedded shaft, these properties can indicate some features of thc displacement or stress field of the half space and can sometimes be used for checking a numerical sohttion. An example for checking the correct stress distribution on surfaces of twisted rigid cylindrical shaft embedded in a half space is given.     

MID-FACETS OF A SIMPLEX

The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order to obtain the expression, the exterior differential method was presented. Furthermore, the properties of the mid-facets of a simplex analogous to median lines of a triangle ( such us for all mid-facets of a simplex,there exists another simplex such that its edge-lengths equal to these mid-facets area respectively, and all of the mid-facets of a simplex have a common point) were proved.Finally, by applying the analytic expression, a number of inequalities which combine edge-lengths, circumradius , median line, bisection area and facet area with the mid-facet area for a simplex were established.     

SUGGESTION OF A NEW DEFINITION OF ANGULAR STRAIN

A new definition of angular strain is put forward in this paper. Analogous to the definition of linear strain, angular strain is also defined as a rate of change (of angular displacement). It is verified that the new definition is equivalent to the original besides being more convenient for geometrical interpretations. Using this new definition we have deduced the transformation formulas for rotation of coordinate axes, established the strain tensor and proved the Hooke's law for shearing.     

ON GRAMMATICAL COMPLEXITY OF A CLASS OF ATTRACTORS

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A METHOD OF DETERMINING BUCKLED STATES OF THIN PLATES AT A DOUBLE EIGENVALUE

A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective.     

A STUDY OF J-INTEGRAL OF THE ORTHOTROPIC COMPOSITE MATERIAL

ＡＳＴＵＤＹＯＦＪ－ＩＮＴＥＧＲＡＬＯＦＴＨＥＯＲＴＨＯＴＲＯＰＩＣＣＯＭＰＯＳＩＴＥＭＡＴＥＲＩＡＬＷａｎｇＡｉ－ｑｉｎ（王蔼勤）；ＦｅｎｇＢａｏ－ｌｉａｎ（冯宝莲）；ＹａｎｇＷｅｉ－ｙａｎｇ（杨维阳）（ＴａｉｙｕａｎＨｅａｖｙＭａｃｈｉｎｅｒｙ．...     

THE ASYMPTOTIC SOLUTION OF A KIND OF STEFAN PROBLEM

In this paper,a kind of Stefan problem subject to general initial condition is studied.The slab considered is divided into three regions.There is a different time scale in each one.By means of PLK method or like multi-scales method,the asympto-tic solution of each one is obtained.Finally we discuss the asymptotic solution and draw some conclusions.     

A CLASS OF ALTERNATING GROUP METHOD OF BURGERS' EQUATION

IntroductionWeconsiderthefollowingnonlinearBurgers’equation : u t u u x=ε 2 u x2 ,　　 0 0 ,( 1 )withtheinitialandtheboundaryconditions　　　　　u(x,0 ) =f(x) ,　　 0 相似文献   

An analytic solution of dense two-phase flow in a vertical pipeline

According to a mathematical model for dense two-phase flows presented in theprevious paper,a dense two-phase flow in a vertical pipeline is analytically solved,and theanalytic expressions of velocity of each continuous phase and dispersed phase arerespectively derived The results show that when the drag force between two phases dependslinearly on their relative velocity,the relative velocity profile in the pipeline coincides withDarcy’s law except for the thin layer region near the pipeline wall,and that the theoreticalassumptions in the dense two-phase flow theory mentioned are reasonable.     

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θmodel of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θmodel in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θmodel has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θmodel was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.     

Y型微通道两相流内部流动特性

利用显微粒子图像测速技术、高速度数码显微系统及数值模拟方法研究了Y 型微通道内液滴的形成. 主要考虑了Y 型角度（45°,90°,135°,180°）、两相流量大小等因素的影响. 发现在挤压机制中,Y 型微通道内分散相液滴的形成主要受到来自连续相的剪切作用,Y 型角度越小,分散相所受到的剪切作用越大. 在液滴生成过程中,连续相速度剖面呈非对称抛物线型分布. 当Y 型角度小于180°时,角度的变化对液滴直径大小影响较小,但角度的减小会加快液滴的生成时间. 当Y 型角度为180°时,生成的液滴体积最大且生成时间最长. 毛细数对液滴直径和生成时间的变化同时产生影响,连续相毛细数的增大使得连续相在两相交汇位置处对分散相的作用力更集中,导致分散相更易破裂.      

Volume of fluid approach of boiling flows in concentrated solar plants

The Computational Fluid Dynamics (CFD) model proposed in this paper allows the flow patterns that evolve during progressive boiling inside large scale horizontal tubes to be simulated from the initial vapor generation stage to large vapor slugs. The volume of fluid (VOF) model was employed in combination with relatively simple hypothesis. The aim of the present work is to improve the design of receiver tubes at concentrated solar power plants with direct steam generation by simulating the evolution of flow regimes within these tubes. Despite numerous studies conducted in the past years on convective boiling, only a few made use of the VOF model to simulate large flow regime transitions. This work presents a preliminary and relatively qualitative approach to address this problem. Heat and mass transfer at the tube inner wall and at the liquid-gas interface were solved with the additional transport of two scalars. One accounts for the enthalpy field and the other represents the dispersed vapor phase of the liquid. This new phase was created at the wall surface of the liquid phase and rises up to the liquid-vapor interface. Different phenomena linked to the boiling process were taken into account: vapor creation at the wall, its transport, recondensation and the creation of large structures. This model was validated with boiling flow in a bent tube at different mass flow rates and heat fluxes, which allowed us to observe the evolution of two-phase flow patterns. Finally, numerical simulation of direct steam generation inside a concentrated solar plant receiver clearly showed the apparition and evolution of various two-phase flow patterns.     

Y型微通道两相流内部流动特性刘

利用显微粒子图像测速技术、高速度数码显微系统及数值模拟方法研究了Y 型微通道内液滴的形成. 主要考虑了Y 型角度（45°,90°,135°,180°）、两相流量大小等因素的影响. 发现在挤压机制中,Y 型微通道内分散相液滴的形成主要受到来自连续相的剪切作用,Y 型角度越小,分散相所受到的剪切作用越大. 在液滴生成过程中,连续相速度剖面呈非对称抛物线型分布. 当Y 型角度小于180°时,角度的变化对液滴直径大小影响较小,但角度的减小会加快液滴的生成时间. 当Y 型角度为180°时,生成的液滴体积最大且生成时间最长. 毛细数对液滴直径和生成时间的变化同时产生影响,连续相毛细数的增大使得连续相在两相交汇位置处对分散相的作用力更集中,导致分散相更易破裂.     

Study of two-phase flows in reduced gravity using ground based experiments

Experimental studies have been carried out to support the development of a framework of the two-fluid model along with an interfacial area transport equation applicable to reduced gravity two-phase flows. The experimental study simulates the reduced gravity condition in ground based facilities by using two immiscible liquids of similar density namely, water as the continuous phase and Therminol 59^® as the dispersed phase. We have acquired a total of eleven data sets in the bubbly flow and bubbly to slug flow transition regimes. These flow conditions have area-averaged void (volume) fractions ranging from 3 to 30% and channel Reynolds number for the continuous phase between 2,900 and 8,800. Flow visualization has been performed and a flow regime map developed which is compared with relevant bubbly to slug flow regime transition criteria. The comparison shows that the transition boundary is well predicted by the criterion based on critical void fraction. The value of the critical void fraction at transition was experimentally determined to be approximately 25%. In addition, important two-phase flow local parameters, including the void fraction, interfacial area concentration, droplet number frequency and droplet velocity, have been acquired at two axial locations using state-of-the-art multi-sensor conductivity probe. The radial profiles and axial development of the two-phase flow parameters show that the coalescence mechanism is enhanced by either increasing the continuous or dispersed phase Reynolds number. Evidence of turbulence induced particle interaction mechanism is highlighted. The data presented in this paper clearly show the marked differences in terms of bubble (droplet) size, phase distribution and phase interaction in two-phase flow between normal and reduced gravity conditions.     

On the Two-Phase Navier–Stokes Equations with Boussinesq–Scriven Surface Fluid

Two-phase flows with interface modeled as a Boussinesq–Scriven surface fluid are analysed concerning their fundamental mathematical properties. This extended form of the common sharp-interface model for two-phase flows includes both surface tension and surface viscosity. For this system of partial differential equations with free interface it is shown that the energy serves as a strict Ljapunov functional, where the equilibria of the model without boundary contact consist of zero velocity and spheres for the dispersed phase. The linearizations of the problem are derived formally, showing that equilibria are linearly stable, but nonzero velocities may lead to problems which linearly are not well-posed. This phenomenon does not occur in absence of surface viscosity. The present paper aims at initiating a rigorous mathematical study of two-phase flows with surface viscosity.     

Structure of the nonisothermal swirling gas-droplet flow behind an abrupt tube expansion

Flow structure and heat and mass transfer in a swirling two-phase stream is numerically modeled using the Reynolds stress transport model. The gas phase is described by the 3DRANS system of equations with account for the inverse influence of particles on the transport processes in the gas. The gas phase turbulence is calculated using the Reynolds stress transport model with account for the presence of disperse particles. The two-phase nonswirling flow behind an abrupt tube expansion contains a secondary corner vortex which is absent from the swirling flow. The disperse phase is redistributed over the tube cross-section. Large particles are concentrated in the wall region of the channel under the action of the centrifugal forces, while the smaller particles are in the central zone of the chamber.     

Two-phase non-linear model for blood flow in asymmetric and axisymmetric stenosed arteries

The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetric stenosed narrow arteries is analyzed, treating blood as a two-phase model with the suspension of all the erythrocytes in the core region as the Herschel-Bulkley material and plasma in the peripheral layer as the Newtonian fluid. The perturbation method is applied to solve the resulting non-linear implicit system of partial differential equations. The expressions for various flow quantities are obtained. It is found that the pressure drop, plug core radius, wall shear stress increase as the yield stress or stenosis height increases. It is noted that the velocity increases, longitudinal impedance decreases as the amplitude increases. For asymmetric stenosis, the wall shear stress increases non-linearly with the increase of the axial distance. The estimates of the increase in longitudinal impedance to flow of the two-phase Herschel-Bulkley material are significantly lower than those of the single-phase Herschel-Bulkley material. The results show the advantages of two-phase flow over single-phase flow in small diameter arteries with stenosis.