Numerical simulation of the electro-convective onset and complex flows of dielectric liquid in an annulus

We conducted a numerical study on the onset of electro-convection as well as the complex flow phenomena of dielectric liquid subjected to unipolar autonomous charge injection in the annular gap between two concentric circular cylindrical electrodes. The Nernst-Planck equations governing the charge density transport, the Poisson equation for the electric potential and the Navier-Stokes equations for the fluid flow are solved numerically using the finite volume method. The developed code is validated by comparing the critical stability parameter values for the onset of electro-convection with those obtained from the linear stability analysis. We identify in a parameter space the stable hydrostatic state and the electro-convection state. The electro-convection is again divided into three regimes: stationary, oscillatory and chaotic. For inner cylinder radius r _i ≥ 1.0, we observed an increase in the number of charged plumes and vortex pairs with stability parameter T before the electro-convection becomes chaotic. For outer injection, although the onset of electroconvection starts at T higher than the inner injection, the onset of chaotic motion occurs at lower T.     

起重机箱形伸缩臂整体稳定性分析

起重机伸缩臂由多节可轴向相对滑动的变截面箱形臂套接组成.箱形伸缩臂承受全部弯矩,而轴向力是通过搭接处的摩擦力与内置油缸共同承受,其力学模型不等同于变截面阶梯柱模型和完全由油缸承受轴力的变截面箱形臂模型.如何准确计入油缸支撑作用及搭接摩擦力的影响,对起重机箱形伸缩臂稳定性分析计算具有十分重要的意义.从挠度微分平衡方程出发,给出起重机箱形伸缩臂三种计算模型的欧拉临界力的分析推导,并着重讨论考虑油缸支撑和伸缩吊臂间搭接摩擦力协同作用的变截面箱形伸缩臂计算模型.分析结果表明,考虑油缸支撑和箱形吊臂间搭接摩擦力协同作用时吊臂的失稳临界力介于完全由油缸承受轴力的变截面箱形臂模型与变截面阶梯柱模型的失稳临界力之间.     

Experimental study on the vortex flow in a concentric annulus with a rotating inner cylinder

This experimental study concerns the characteristics of vortex flow in a concentric annulus with a diameter ratio of 0.52, whose outer cylinder is stationary and inner one is rotating. Pressure losses and skin friction coefficients have been measured for fully developed flows of water and of 0.4% aqueous solution of sodium carboxymethyl cellulose (CMC), respectively, when the inner cylinder rotates at the speed of 0-600 rpm. Also, the visualization of vortex flows has been performed to observe the unstable waves. The results of present study reveal the relation of the bulk flow Reynolds number Re and Rossby number Ro with respect to the skin friction coefficients. In somehow, they show the existence of flow instability mechanism. The effect of rotation on the skin friction coefficient is significantly dependent on the flow regime. The change of skin friction coefficient corresponding to the variation of rotating speed is large for the laminar flow regime, whereas it becomes smaller as Re increases for the transitional flow regime and, then, it gradually approach to zero for the turbulent flow regime. Consequently, the critical (bulk flow) Reynolds number Re_c decreases as the rotational speed increases. Thus, the rotation of the inner cylinder promotes the onset of transition due to the excitation of Taylor vortices.     

Refined analysis of axi-symmetric circular cylinder in the axial magnetic field without ad hoc assumption

The refined theory for axi-symmetric magnetoelastic circular cylinder is deduced systematically and directly from linear magnetoelasticity theory. Based on the general solution of magnetoelastic equation and the Lur’e method, the refined theory yields the solutions for magnetoelastic circular cylinder without ad hoc assumptions. On the basis of the refined theory developed in the present study, solutions are obtained for magnetoelastic circular cylinder with homogeneous and non-homogenous boundary conditions, respectively. For the circular cylinder with homogeneous boundary conditions, the refined theory provides exact solutions that satisfy all of the governing equations. The exact solutions can be divided into three parts: the 2-orders equation, the transcendental equation, and the magnetic equation. In the case of non-homogenous boundary conditions, the approximate governing equations are accurate up to the high-order terms with respect to cylinder radius.     

动载荷作用下区分厚壁圆筒和薄壁圆筒的一个准则

从厚壁圆筒弹性动应力解出发,给出了厚壁圆筒内外径处的环向应力的简化计算公式,并提出了在动载荷作用下区分厚壁圆筒和薄壁圆筒的一个准则,认为当K≤1.14时,可以将圆筒视作薄壁圆筒。     

The elastic-plastic analysis of a thick spherical shell under thermal loading—A comparison of three numerical procedures

The elastic-plastic response of a thick spherical shell subjected to thermal loading is predicted by three independent numerical analyses. Heat radiation from the inner face of a sufficiently large hollow cylinder is applied to an initially unloaded hollow sphere having a thickness equal to the inner radius of the sphere. Solutions obtained by a finite difference program and two independent finite element programs compare well with an exact elastic solution before yielding occurs. The post yield analyses of the three programs follow a consistent pattern.     

Numerical simulation of natural convection in annuli with internal fins

The solution for the natural convection in internally finned horizontal annuli is obtained by using a numerical simulation of time-dependent and two-dimensional governing equations. The fins existing in annuli influence the flow pattern, temperature distribution and heat transfer rate. The variations of the fin configuration suppress or accelerate the free convective effects compared to those of the smooth tubes. The effects of fin configuration, number of fins and ratio of annulus gap width to the inner cylinder radius on the fluid flow and heat transfer in annuli are demonstrated by the distribution of the velocity vector, isotherms and streamlines. The governing equations are solved efficiently by using a parallel implementation. The technique is adopted for reduction of the computation cost. The parallelization is performed with the domain decomposition technique and message passing between sub-domains on the basis of the MPI library. The results from parallel computation reveal in consistency with those of the sequential program. Moreover, the speed-up ratio shows linearity with the number of processor.     

厚壁筒受正弦分布压力之解及圆筒无限长时的极限

对厚壁圆筒在柱面上受正弦分布压力的情况,给出了解析解。应用一个新的应力函数,解决轴对称问题。同时,给出了压力沿轴向不变时的极限,导出了厚壁圆筒著名的Lame解答。     

厚壁筒柱面受双曲余弦分布压力、端面受常力之解及圆筒无限长时的极限

在三维空间中构建了一个既满足双调和方程又满足边界条件的新应力函数，对厚壁圆筒在柱面上受双曲余弦分布压力、端面受正压力总和为常力的情况，给出了解析解。避免了长期以来利用均布压力近似代替变力来求解轴对称问题所造成的误差。同时，给出了压力沿轴向不变时的极限，导出了厚壁圆筒著名的Lame解答。     

Effect of optimum plastic depth on stresses and load-bearing capacity of autofrettaged cylinder

Autofrettage is an effective measure to even distribution of stresses and raise load-bearing capacity for (ultra-)high pressure apparatus. Currently, the research on autofrettage has focused mostly on specific engineering problems, while general theoretical study is rarely done. To discover the general law contained in autofrettage theory, by the aid of the authors’ previous work and according to the third strength theory, theoretical problems about autofrettage are studied including residual stresses and their equivalent stress, total stresses and their equivalent stress, etc. Because of the equation of optimum depth of plastic zone which is presented in the authors’ previous work, the equations for the residual stresses and their equivalent stress as well as the total stress and their equivalent stress are simplified greatly. Thus the law of distribution of the residual stresses and their equivalent stress as well as the total stress and their equivalent stress and the varying tendency of these stresses are discovered. The relation among various parameters are revealed. The safe and optimum load-bearing conditions for cylinders are obtained. According to the results obtained by theoretical analysis, it is shown that if the two parameters, namely ratio of outside to inside radius, k, and depth of plastic zone, kj, meet the equation of optimum depth of plastic zone, when the pressure contained in an autofrettaged cylinder is lower than two times the initial yield pressure of the unautofrettaged cylinder, the equivalent residual stress and the equivalent total stress at the inside surface as well as the elastic-plastic juncture of a cylinder are lower than yield strength. When an autofrettaged cylinder is subjected to just two times the initial yield pressure of the unautofrettaged cylinder, the equivalent total stress within the whole plastic zone is just identically equal to the yield strength, or it is a constant. The proposed research theoretically depicts the stress state of ultra-)high pressure autofrettaged cylinder more accurately and more reasonably and provides the reference for design of (ultra-)high pressure apparatus.     

厚壁半球形液压缸的强度计算及其与圆筒形液压缸对比分析

半球形液压缸是缸梁一体式压力机的主要承力构件,它与传统的三梁四柱式液压机的圆筒形液压缸相比,结构上和受力状态都发生很大的改变,从而使承压能力有近一倍的提高。导出半球形液压缸强度计算公式,对于厚壁球壳,最薄弱区域是球的内壁,在该处有最大的经(纬)向拉应力与代数值最小(绝对值最大)的径向压应力。按照Tresca 强度准则或Mises强度准则均可算出数值相同的最大当量应力,强度计算公式表明该应力应小于或等于材料的许用应力。并将该式与圆筒形液压缸强度计算公式进行对比,在相同条件下(相同许用应力、相同内压及相同内半径),计算结果表明,半球形液压缸的壁厚要远小于圆筒形液压缸,减重效果明显。     

The Twente turbulent Taylor-Couette (T3C) facility: strongly turbulent (multiphase) flow between two independently rotating cylinders

A new turbulent Taylor-Couette system consisting of two independently rotating cylinders has been constructed. The gap between the cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 × 10(6) with water as working fluid. With this Taylor-Couette system, the parameter space (Re(i), Re(o), η) extends to (2.0 × 10(6), ±1.4 × 10(6), 0.716-0.909). The system is equipped with bubble injectors, temperature control, skin-friction drag sensors, and several local sensors for studying turbulent single-phase and two-phase flows. Inner cylinder load cells detect skin-friction drag via torque measurements. The clear acrylic outer cylinder allows the dynamics of the liquid flow and the dispersed phase (bubbles, particles, fibers, etc.) inside the gap to be investigated with specialized local sensors and nonintrusive optical imaging techniques. The system allows study of both Taylor-Couette flow in a high-Reynolds-number regime, and the mechanisms behind skin-friction drag alterations due to bubble injection, polymer injection, and surface hydrophobicity and roughness.     

活塞偏心倾斜对双筒液压减振器动态阻尼特性影响分析*

考虑活塞偏心和倾斜后活塞与缸筒之间的摩擦与润滑因素,研究充气式双筒液压减振器动态阻尼特性;建立活塞偏心和倾斜的双筒式液压减振器的动态阻尼特性数学模型和动压润滑方程,求解减振器动态阻尼特性数学方程;采用雷诺空化边界条件,对Reynolds方程采用五点差分法进行离散,利用超松弛迭代法(SOR)迭代求解,得到摩擦阻尼力;分析活塞偏心距比、活塞倾斜角度,活塞倾斜时活塞运动速度、活塞半径、活塞宽度等因素对摩擦阻尼的影响,以及各摩擦因素对减振器动态阻尼特性的影响。结果表明:活塞偏心和倾斜时,随活塞速度、偏心距比、活塞倾斜角度、活塞宽度等的增加,减振器活塞与缸筒之间的油膜摩擦力均增加,而随活塞半径的增加,油膜摩擦力减小。减振器活塞发生倾斜时,会造成阻尼力的大幅增加,严重影响车辆行驶的舒适性能,且活塞速度越快,对舒适性影响越严重。     

部分充有粘性流体的转子系统稳定性的理论分析

在直接对二维 Navier- Stokes方程进行线性化的基础上 ,详细分析了二维粘性旋转流体模型 ,得到了旋转流体对转子作用力的表达式 ,然后研究了部分充液转子系统的稳定性问题 ,分析了转子系统的各参数对稳定性的影响     

Analysis on autofrettage of cylinders

Autofrettage is an effective technique to improve load-bearing capacity and safety for pressure vessels.For autofrettaged cylinder,the depth of plastic zone,or overstrain is a key factor which affects load-bearing capacity and safety.The previous research on overstrain was not done in terms of the point of view of raising load-bearing capacity as far as possible and simultaneously avoiding compressive yield for cylinders experiencing autofrettage handling,and there were no analytic solutions of autofrettage in the above view point presented,the 3rd and 4th strength theories were not applied synthetically in the research to compare the results from these two theories.In this paper,with the aid of the analytic method,based on summing up the authors’ previous research,results from autofrettage of a cylinder based on the 3rd and 4th strength theories are studied and compared,and the laws contained in the results are looked into.Then,the essential cause and reason for the obtained laws are analyzed and the inherent and meaning relations between various parameters in autofrettage theory are revealed.It is shown that the maximum radius ratio for equivalent residual stress at inside surface never exceeds the yield strength even for a cylinder experiencing wholly yielded autofrettage,or the critical radius ratio is kc=2.218 457 489 916 7…,irrespective of the 3rd or 4th strength theories.The equation relating the depth of plastic zone with the thickness of a cylinder is identical for the 3rd and 4th strength theories.In form,the optimum load-bearing capacity of an autofrettaged cylinder is two times the initial yield pressure of the unautofrettaged cylinder irrespective of the 3rd or 4th strength theory.The revealed inherent relations between various parameters and varying laws of the parameters as well as the forms of the relations under the 3rd and 4th strength theories not only have theoretical meanings but also have prospects in engineering application.     

A study on the solid-liquid 2 phase helical flow in an inclined annulus

An investigation is conducted to understand hydraulic transport characteristics of a solid-liquid mixture flowing vertically upward. Namely, this is the instance that solid particles are carried by non-Newtonian fluids in a slim hole concentric annulus with rotating inner cylinder. In this study a clear acrylic pipe was used in order to observe the movement of solid particles. The bulk axial velocities varied from 0.4 m/s to 1.2 m/s. The mud systems which were utilized included aqueous solution of sodium carboxymethyl cellulose (0.2∼0.4%CMC) and 5% bentonite solutions. Solid volumetric concentration and pressure drops were measured for the various parameters such as inclined annulus, flow rate, and rotational speed of inner cylinder. For both CMC and bentonite solutions, the higher the concentration of the solid particles are, the larger the pressure drops become. This paper was presented at the 9^th Asian International Conference on Fluid Machinery (AICFM9), Jeju, Korea, October 16–19, 2007.     

Buckling of a thin annular plate subjected to two opposite locally acting pressures and supported at two opposite points

The paper treats the elastic stability of a thin annular plate with constant thickness. Based on the stress expressions obtained by using the complex Fourier series, the study deals with the asymmetrical buckling of an annular plate which is supported at two opposite points in the outer boundary and is subjected to two opposite locally acting pressures in the vicinity of these two supporting points. By the energy method and direct integration of the strain energy of bending and the work done by the stresses, the analytical expression of the coefficients used to calculate the critical value of the loads had been derived, and then the critical load was found numerically for any ratio of its radii. Since the study deals with a thin plate, some simplifications have been made. The experiments were made for the case of an annular plate with a thickness of 3 mm, outer radius 300 mm and inner radius 100 mm. The difference between the critical load obtained theoretically and calculated numerically and the critical load obtained with experiments is less than 6%.     

Prediction of Hot Spots by Correlating Finite Element Analysis and Measurement for an Automotive Disk Brake

Generally, the thermoelastic instability (TEI) theory, which considers disk critical speed as one of the most significant factors, is used for investigating judder vibration. However, since the solution of judder problems by the TEI theory requires numerous assumptions, the experimental and the TEI results do not agree well. In addition, during experiments the critical speed varies with the pressure between the disk and the pads. In this study, for a TEI analysis, critical speeds of the disk brakes are obtained by using Hotspotter ^TM , and the experimental critical speeds and the number of hot spots are obtained with a chassis dynamometer and IR camera. Pressure distributions of the brake pad are calculated by a finite element analysis (FEA). Regression analysis and linear interpolation are performed to find the correlation between the experimental results for pressure of the master cylinder, the pad arc length, and the two disk specimens. The results show that the pressure interpolation results of the experimental equation have significant effects on the TEI analysis results.     

缩套超高压缸的最佳化设计

首先推导了双层筒体基于最佳化设计原则的缩套界面压力的计算公式及径比条件。然后对某超高压缸的径比及应力进行了分析计算,发现其径比不符合最佳化设计原则,且应力分布很不均匀。最后针对该超高压缸所存在的问题,采用双层缩套圆筒的最佳化设计原则进行了最佳化设计,求得了最佳径比及尺寸,并作了应力分析。最佳化设计后的超高压缸在重量、外形体积及应力分布等方面均比原超高压缸有较大的改善,表明最佳化设计方案具有较好的技术经济效果。     

Steady-flow characteristics and its influence on spray for direct injection diesel engine

Flow and spray characteristics are critical factors that affect the performance and exhaust emissions of a direct injection diesel engine. It is well known that the swirl control system is one of the useful ways to improve the fuel consumption and emission reduction rate in a diesel engine. However, until now there have only been a few studies on the effect of flow on spray. Because of this, the relationship between the flow pattern in the cylinder and its influence on the behavior of the spray is in need of investigation. First, in-cylinder flow distributions for 4-valve cylinder head of Dl (Direct Injection) Diesel engine were investigated under steady-state conditions for different SCV (Swirl Control Valve) opening angles using a steady flow rig and 2-D LDV (Laser Doppler Velocimetry). It was found that swirl flow was more dominant than that of tumble in the experimented engine. In addition, the in-cylinder flow was quantified in terms of swirl/tumble ratio and mean flow coefficient. As the SCV opening angle was increased, high swirl ratios more than 3.0 were obtained in the case of SCV -70ΰ and 90ΰ. Second, spray characteristics of the intermittent injection were investigated by a PDA (Phase Doppler Anemometer) system. A Time Dividing Method (TDM) was used to analyze the microscopic spray characteristics. It was found that the atomization characteristics such as velocity and SMD (Sauter Mean Diameter) of the spray were affected by the in-cylinder swirl ratio. As a result, it was concluded that the swirl ratio improves atomization characteristics uniformly.