Elastic analyses of heterogeneous hollow cylinders

Two different kinds of heterogeneous elastic hollow cylinders are studied in the present paper. One is a multi-layered cylinder with different values in different layers for both elastic modulus and Poisson’s ratio. Another is an elastic hollow cylinder with continuously graded material properties. By introducing two recursive algorithms, the extrusion stresses between two neighbor layers in the multi-layered cylinder submitted to uniform pressures on the inner and outer surfaces can be simply determined. Then the exact solutions of the multi-layered structure can be found based on Lamé’s solution. For the hollow cylinder with continuously graded properties, the displacement method is used. Both Whittaker equation and hyper-geometric equation are derived and successfully solved, and then the exact solutions are found. The results obtained in the present paper are compared with the numerical solutions and good agreements are found. At the end of the present paper, some inherent properties of these two different kinds of heterogeneous elastic hollow cylinders are presented and discussed. The results obtained in the present paper are useful in the design and analysis for composites reinforced by unidirectional fiber layers.     

Propagation of torsional waves in a radially layered cylindrical waveguide

It was shown in [1–3] that the spectrum of homogeneous solutions for layered bodies with alternating rigid and soft layers splits into the “lower” and “higher” parts. Moreover, the “lower” part is always associated with some applied theory. In [4], the method developed in [1–3] is generalized to problems of steady torsional vibrations of a radially inhomogeneous cylinder and to the dynamic case of the applied theory constructed in [2]. In the present paper, we use analytic and numerical methods to study the propagation of torsional waves in a radially layered cylindrical waveguide.     

Heat conduction and heat wave propagation in functionally graded thick hollow cylinder base on coupled thermoelasticity without energy dissipation

In this paper, heat wave propagation and coupled thermoelasticity without energy dissipation in functionally graded thick hollow cylinder is presented based on Green–Naghdi theory. The material properties are supposed to vary as a power function of radius across the thickness of cylinder. The cylinder is considered in axisymmetry and plane strain conditions and it is divided to many sub-cylinders (layers) across the thickness. Each sub-cylinder is considered to be made of isotropic material and functionally graded property can be created by suitable arrangement of layers. The Galerkin finite element method and Newmark finite difference method are employed to solve the problem. The time history of second sounds and displacement wave propagation are obtained for various values of power function. Computed results agree well with the published data.     

The torsion problem of a multilayered finite cylinder with the multiple interface cylindrical cracks

The torsion axisymmetric problem for a finite cylinder consisting of an arbitrary quantity of cylindrical coaxial layers is solved. Multiple cylindrical cracks with free of loading branches are situated on adjoining surfaces of the layers. The boundary problem is reduced to the system of integro-differential equations, its solution is found with the help of the orthogonal polynomials method. The novelty of the paper is in the construction of a solution for an arbitrary number of cylinder layers which allows the approximation of the initial problem for functionally graded materials by the problem for coaxial cylinders with jumplike changing elastic constants of the materials. Since the solution is built regardless of the number of layers (the elastic parameters of all layers are included in the constructed solution), one can refine an initial problem’s statement by increasing the number of layers. The stress intensity factors are found for an arbitrary number of cylindrical interface cracks in the multilayered cylinder of a finite length.     

应用增量理论考虑应变硬化效应包辛格效应和温度对机械性质影响的自增强厚壁圆筒分析

本文提出的采用增量理论的分析模型和方法可以定量分析应变硬化、包辛格效应和材料机械性质随温度变化等因素对自增强厚壁圆筒中残余应力和操作应力分布的影响.厚壁圆筒看成由N个同轴薄壁圆筒套在一起组成的构件;采用包括弹性、塑性和温度应变的增量型本构关系和相容条件导出了自增强圆筒的基本方程;设计了计算机程序并给出了分析实例。分析结果表明,应变硬化会减小塑性区并降低残余应力;包辛格效应使反向屈服容易出现;温度升高将使残余应力和热应力松驰.     

Suppression of lift fluctuations on a circular cylinder by inducing the symmetric vortex shedding mode

The flow around a stationary circular cylinder modified by two synthetic jets positioned at the mean separation points is numerically studied. The Reynolds number based on the free-stream velocity and the circular cylinder diameter is Re=500. The focus is to present a novel way to suppress the lift fluctuations by changing the vortex shedding mode, and thus particular attention is paid to the interactions between the synthetic jets and wake shear layers and the resulting vortex dynamics. The overall influences of both momentum coefficient and excitation frequency are discussed. In some simulated cases, the vortex lock-on phenomenon is discovered, which causes the typical Kàrmàn type vortex shedding to be converted into the symmetric shedding modes, leading to the complete suppression of lift fluctuations. In other cases, the asymmetric shedding mode still dominates the wake evolution. Detailed vortical evolution for each typical wake pattern is analyzed to reveal the control mechanism. Additionally, the control effectiveness is evaluated, indicating that the present control strategy contributes an effective way to suppress the lift fluctuations and reduce the mean drag.     

Thermal stresses analysis of ceramic/metal functionally gradient material cylinder

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DIRECT NUMERICAL SIMULATIONS ON THE TURBULENT FLOW PAST A CONFINED CIRCULAR CYLINDER WITH THE INFLUENCE OF THE STREAMWISE MAGNETIC FIELDS1)

绕流是托卡马克装置中液态包层内常见的流动形态,对流场与热量分布有着重要的影响.本文通过直接数值模拟(DNS),研究了不同磁场强度下$Re=3900$的圆柱绕流,分析了磁场强度对于湍流尾迹的影响.无磁场情况下,直接数值模拟的结果与前人的实验及模拟结果吻合很好.圆柱下游的尾迹中,随着流向距离的增大, 流向速度剖面逐渐从U型进化呈V型, 并慢慢趋于平缓,这表明尾迹中的流动结构受圆柱影响逐渐减小.圆柱后方两侧的剪切层中,由于Kelvin-Helmholtz不稳定性的影响,可以清晰地看到小尺度剪切层涡的脱落.通过对无磁场的计算结果施加流向磁场,本文计算了哈特曼数($Ha$)分别为20, 40和80的工况,以研究磁场效应对于湍流的影响.结果表明磁场较弱时,流动依然呈三维湍流状态.随着磁场增强, 近圆柱尾流区受磁场抑制明显,回流区被拉长,剪切层失稳位置向下游转移.圆柱后方的涡结构由于受到竖直方向洛伦兹力的挤压作用,随着哈特曼数的增加尾迹区域逐渐变窄.相比于无磁场情况的涡结构,由于磁场的耗散作用,相应的涡结构尺度变小.该研究不仅扩展了现有磁场下湍流运动的参数范围,对于液态包层的设计及安全运行同样具有重要的理论指导意义和工程应用价值.     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

流向磁场作用下圆柱绕流的直接数值模拟

绕流是托卡马克装置中液态包层内常见的流动形态,对流场与热量分布有着重要的影响.本文通过直接数值模拟(DNS),研究了不同磁场强度下$Re=3900$的圆柱绕流,分析了磁场强度对于湍流尾迹的影响.无磁场情况下,直接数值模拟的结果与前人的实验及模拟结果吻合很好.圆柱下游的尾迹中,随着流向距离的增大, 流向速度剖面逐渐从U型进化呈V型, 并慢慢趋于平缓,这表明尾迹中的流动结构受圆柱影响逐渐减小.圆柱后方两侧的剪切层中,由于Kelvin-Helmholtz不稳定性的影响,可以清晰地看到小尺度剪切层涡的脱落.通过对无磁场的计算结果施加流向磁场,本文计算了哈特曼数($Ha$)分别为20, 40和80的工况,以研究磁场效应对于湍流的影响.结果表明磁场较弱时,流动依然呈三维湍流状态.随着磁场增强, 近圆柱尾流区受磁场抑制明显,回流区被拉长,剪切层失稳位置向下游转移.圆柱后方的涡结构由于受到竖直方向洛伦兹力的挤压作用,随着哈特曼数的增加尾迹区域逐渐变窄.相比于无磁场情况的涡结构,由于磁场的耗散作用,相应的涡结构尺度变小.该研究不仅扩展了现有磁场下湍流运动的参数范围,对于液态包层的设计及安全运行同样具有重要的理论指导意义和工程应用价值.      

A NUMERICAL STUDY OF FLOW PAST A ROTATIONALLY OSCILLATING CIRCULAR CYLINDER

Vortex shedding from a rotationally oscillating circular cylinder in a uniform flow is studied by numerical solutions of the two-dimensional incompressible Navier-Stokes equations using primitive variables. To demonstrate the viability and accuracy of the method, we calculate the approach flow past a rotating cylinder with constant angular velocity. For approach flow past a rotationally oscillating cylinder, the object of the study is to examine the effect of oscillating rotation on the flow structure. In the present study, some basic patterns of vortex shedding can be identified according to our calculated results and are in good agreement with available experiments. In addition, the influence of the oscillating frequency and amplitude on the forces acting on the cylinder is also investigated.     

Numerical Study of the Effect of Periodic Velocity Excitation on Aerodynamic Characteristics of an Oscillating Circular Cylinder

A finite element method based on ALE formulation has been adopted in order to examine the effect of periodic velocity excitation on the aerodynamic characteristics of an oscillating circular cylinder. Periodic excitation, which was placed on the cylinder surface, stimulated the separated shear layers around the cylinder, and numerical results showed that some excitation can reduce negative damping, which is caused by unsteady lift force, and thereby stabilize the aerodynamics of the cylinder. Furthermore, the change of lift phase caused by periodic excitation seems to be important in stabilizing the aerodynamics of the cylinder. The simulation also confirmed that periodic excitation can suppress the vortex-induced vibration of the cylinder.     

复合材料圆筒自由边效应的有限元分析

本文分析复合材料圆筒在内压作用下的自由边效应，讨论圆筒的叠层顺序对自由边应力的影响，预报最易发生边界脱层的界面．有限元分析结果表明：层间剪切破坏是该结构发生边界失效的主要原因，不同的叠层顺序可较大地影响自由边层间剪切应力，而大变形情况下线性有限元分析结果与非线性有限元数据相差较大，几何非线性的影响不容忽视．     

Identification of flow regimes around two staggered square cylinders by a numerical study

The flow over two square cylinders in staggered arrangement is simulated numerically at a fixed Reynolds number (\(Re =150\)) for different gap spacing between cylinders from 0.1 to 6 times a cylinder side to understand the flow structures. The non-inclined square cylinders are located on a line with a staggered angle of \(45^{\circ }\) to the oncoming velocity vector. All numerical simulations are carried out with a finite-volume code based on a collocated grid arrangement. The effects of vortex shedding on the various features of the flow field are numerically visualized using different flow contours such as \(\lambda _{2}\) criterion, vorticity, pressure and magnitudes of velocity to distinguish the distinctive flow patterns. By changing the gap spacing between cylinders, five different flow regimes are identified and classified as single body, periodic gap flow, aperiodic, modulated periodic and synchronized vortex shedding regimes. This study revealed that the observed multiple frequencies in global forces of the downstream cylinder in the modulated periodic regime are more properly associated with differences in vortex shedding frequencies of individual cylinders than individual shear layers reported in some previous works; particularly, both shear layers from the downstream cylinder often shed vortices at the same multiple frequencies. The maximum Strouhal number for the upstream cylinder is also identified at \({G}^{*}=1\) for aperiodic flow pattern. Furthermore, for most cases studied, the downstream cylinder experiences larger drag force than the upstream cylinder.     

3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid

The free vibration of an arbitrarily thick orthotropic piezoelectric hollow cylinder with a functionally graded property along the thickness direction and filled with a non-viscous compressible fluid medium is investigated. The analysis is directly based on the three-dimensional exact equations of piezoelasticity using the so-called state space formulations. The original functionally graded shell is approximated by a laminate model, of which the solution will gradually approach the exact one when the number of layers increases. The effect of internal fluid can be taken into consideration by imposing a relation between the fluid pressure and the radial displacement at the interface. Analytical frequency equations are derived for different electrical boundary conditions at two cylindrical surfaces. As particular cases, free vibration of multi-layered piezoelectric hollow cylinder and wave propagation in infinite homogeneous cylinder are studied. Numerical comparison with available results is made and dispersion curves predicted from the present three-dimensional analysis are given. Numerical examples are further performed to investigate the effects of various parameters on the natural frequencies.     

Flow-induced vibration of a flexibly mounted circular cylinder in the proximity of a larger cylinder downstream

A flexibly mounted circular cylinder is placed upstream of a stationary cylinder twice as large. Flow-induced vibration response of the small cylinder is measured with the interfering cylinder placed at 57 relative locations. In most situations, reduced-amplitude vibration or even no vibration is observed. Lock-in resonance remains the dominant vibration behavior, but the reduced velocity of peak lock-in is found to shift to a value higher or lower than the isolated cylinder value, depending on the lateral separation between the two cylinders. When the flexible cylinder is located just in front of the large cylinder, galloping-type vibration of very large amplitude occurs at reduced velocities above 12. Mechanisms of flow-induced vibration are discussed with the aid of flow visualizations. The present study supplements a previous paper reporting amplified vibration of the flexible cylinder with the interfering cylinder placed in various upstream locations.     

Optical visualization of accelerated and decelerated flow over a circular cylinder

Prandtl and Tietjens [1] obtained the spectra of flow over a circular cylinder. Later, other authors returned to this question (see, in particular, [2, 3]). The investigations showed that the time-dependent picture of the separation flow over the cylinder can be divided into two main phases: an initial phase of symmetric flow and a phase of steady, periodic, and asymmetric flow. In the symmetric flow over the cylinder [1] one observes in the neighborhood of the separation points delta-shaped regions, whose structure it would be interesting to elucidate. In the present paper, we present the results of an investigation by a method of optical visualization of some features of the flow over a circular cylinder in regimes when the flow is accelerated and decelerated.Translated from Izvestiya Akademii Nauk SSSE, Mekhanika Zhidkosti i Gaza, No. 2, pp. 136–142, March—April, 1981.     

An investigation on the temperature distribution in thinwalled cylinders during welding up of wear-proof layers

This paper describes an attempt to find the space and timewise temperature-distribution in a thinwalled cylinder during building up by welding several layers on top of each other. From the exact one-dimensional solution (thin ring) we found an approximate solution for the cylinder. The approximation used is made possible by the fact that in practice the angular velocity (which is related to the welding speed) is great with respect to the relaxationtime of heat in the material. A number of experiments are given to verify the theoretical results.     

Vortex shedding flow behind a slowly rotating circular cylinder

This paper investigates flow past a rotating circular cylinder at 3600?Re?5000 and α?2.5. The flow parameter α is the circumferential speed at the cylinder surface normalized by the free-stream velocity of the uniform cross-flow. With particle image velocimetry (PIV), vortex shedding from the cylinder is clearly observed at α<1.9. The vortex pattern is very similar to the vortex street behind a stationary circular cylinder; but with increasing cylinder rotation speed, the wake is observed to become increasing narrower and deflected sideways. Properties of large-scale vortices developed from the shear layers and shed into the wake are investigated with the vorticity field derived from the PIV data. The vortex formation length is found to decrease with increasing α. This leads to a slow increase in vortex shedding frequency with α. At α=0.65, vortex shedding is found to synchronize with cylinder rotation, with one vortex being shed every rotation cycle of the cylinder. Vortex dynamics are studied at this value of α with the phase-locked eduction technique. It is found that although the shear layers at two different sides of the cylinder possess unequal vorticity levels, alternating vortices subsequently shed from the cylinder to join the two trains of vortices in the vortex street pattern exhibit very little difference in vortex strength.     

Interaction of circular cylinder wake with a short asymmetrically located downstream plate

This study reveals the interaction patterns of separated shear layers from a circular cylinder with a short downstream plate and their reflection on the frequency and the formation length of the vortices from the cylinder as a function of plate location relative to the cylinder. The effect of horizontal (G/D) and vertical (Z/D) distances between the cylinder and the plate on the near wake is studied via Digital Particle Image Velocimetry (DPIV) in a water channel for Reynolds numbers of 200, 400 and 750, based on the cylinder diameter D. It is shown that the interaction of wake with the plate of length D can be categorized depending on the horizontal and the vertical distances between the cylinder and the plate. For the vertical distance range of Z/D ≤ 0.7, there is a critical horizontal spacing before which the shear layers from the cylinder are inhibited to form vortices in front of the plate. Resulting elongated recirculation region between the plate and the cylinder suggests modification of the absolutely unstable near wake of free circular cylinder in favor of convective instability. Z/D = 0.9 provides a passage from Z/D ≤ 0.7 to ≥1.1 and is associated with a dominant effect on the near-wake characteristics of interaction of shear layers from the cylinder with those from the downstream plate. For Z/D ≥ 1.1, there is again, yet a smaller critical horizontal spacing after which vortices interact with decreased downstream plate interference. In this vertical separation distance range, a gap flow between the plate and the cylinder plays a determining role on the formation length and St number of vortices for small horizontal spacing values.