Magnetothermodynamic stress and perturbation of magnetic field vector in a non-homogeneous thermoelastic cylinder

This paper presents a theoretical method for analyzing magnetothermoelastic responses and perturbation of the magnetic field vector in a conducting non-homogeneous thermoelastic cylinder subjected to thermal shock. By making use of finite Hankle integral transforms the analytical expressions for magnetothermodynamic stress and perturbation response of an axial magnetic field vector in the non-homogeneous cylinder are obtained. From sample numerical calculations both magnetothermostress and perturbation of the axial magnetic field vector in a non-homogeneous cylinder is revealed and discussed.     

Elastodynamic solution of a non-homogeneous orthotropic hollow cylinder

A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure. The project supported by the National Natural Science Foundation of China (10172075 and 10002016)     

Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer

An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric (FGP) layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton’s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different parameters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.     

Large eddy simulation of bluff body wake in planar shear flow

Large eddy simulation of planar shear flow past a square cylinder has been investigated. Dynamic Smagorinsky model has been used to model subgrid scale stress. The shear parameter, K, namely the nondimensional streamwise velocity gradient in the lateral direction, is 0.0, 0.1 and 0.2. Reynolds number based on the centerline velocity is fixed at Re=21400. The time and span‐averaged velocity components, pressure coefficient, Reynolds stresses for uniform are in good agreement with the literature. In shear flow the calculated flow structure and mean velocity components are shown to be markedly different from those of the uniform flow. With increasing shear parameter, the cylinder wake is dominated by clockwise vortices. Both the velocity components in shear flow are compared with respective components in uniform flow. Comparison of normal and shear stresses between shear and no shear case have also been presented. Copyright © 2009 John Wiley & Sons, Ltd.     

A numerical investigation of the effects of the spanwise length on the 3-D wake of a circular cylinder

The numerical prediction of vortex-induced vibrations has been the focus of numerous investigations to date using tools such as computational fluid dynamics. In particular, the flow around a circular cylinder has raised much attention as it is present in critical engineering problems such as marine cables or risers. Limitations due to the computational cost imposed by the solution of a large number of equations have resulted in the study of mostly 2-D flows with only a few exceptions. The discrepancies found between experimental data and 2-D numerical simulations suggested that 3-D instabilities occurred in the wake of the cylinder that affect substantially the characteristics of the flow. The few 3-D numerical solutions available in the literature confirmed such a hypothesis. In the present investigation the effect of the spanwise extension of the solution domain on the 3-D wake of a circular cylinder is investigated for various Reynolds numbers between 40 and 1000. By assessing the minimum spanwise extension required to predict accurately the flow around a circular cylinder, the infinitely long cylinder is reduced to a finite length cylinder, thus making numerical solution an effective way of investigating flows around circular cylinders. Results are presented for three different spanwise extensions, namely πD/2, πD and 2πD. The analysis of the force coefficients obtained for the various Reynolds numbers together with a visualization of the three-dimensionalities in the wake of the cylinder allowed for a comparison between the effects of the three spanwise extensions. Furthermore, by showing the different modes of vortex shedding present in the wake and by analysing the streamwise components of the vorticity, it was possible to estimate the spanwise wavelengths at the various Reynolds numbers and to demonstrate that a finite spanwise extension is sufficient to accurately predict the flow past an infinitely long circular cylinder.     

Mixed Boundary Value Problem in a Non-homogeneous Medium Under Steady Distribution of Temperature

This paper is concerned with a mixed boundary value problem of a non-homogeneous medium under steady distribution of temperature whose elastic constants are exponential functions of y. By using Fourier cosine transforms the mixed boundary value problem of heat conduction is reduced to a Fredholm integral equation of the second kind. Then the elastic problem of the non-homogeneous semi-infinite half-plane under distribution of load over a plane face is solved. The influence of the non-homogeneity of the material on the thermal stress distribution is illustrated graphically.     

An h4 accurate vorticity-velocity formulation for calculating flow past a cylinder

A method of solution for the two-dimensional Navier-Stokes equations for incompressible flow past a cylinder is given in which the euquation of continuity is solved by a step-by-step integration procedure at each stage of an interative process. Thus the formulation involves the solution of one first-order and one second-order equation for the velocity components, together with the vorticity transport equation. the equations are solved numerically by h⁴-accurate methods in the case of steady flow past a circular cylinder in the Reynolds number range 10–100. Results are in satisfactory agreement with recent h⁴-accurate calculations. An improved approximation to the boundary conditions at large distance is also considered.     

Tomographic and time resolved PIV measurements on a finite cylinder mounted on a flat plate

Tomographic and time resolved PIV measurements were performed to examine the 3D flow topology and the flow dynamic above the upper surface of a low-aspect ratio cylinder at Re ≈ 1 ×  10⁵. This generic experiment is of fundamental interest because it represents flow features which are relevant to many applications such as laminar separation bubbles and turbulent reattachment. At Re  ≈ 1 × 10⁵, laminar separation bubbles arise on the side of the cylinder. Furthermore, on the top of the cylinder a separation with reattachment is of major interest. The tomographic PIV measurement, which allows to determine all three velocity components in a volume instantaneously, was applied to examine the flow topology and interaction between the boundary layer and wake structures on the top of the finite cylinder. In the instantaneous flow fields the tip vortices and the recirculation region becomes visible. However, it is also observed that the flow is quite unsteady due to the large separation occurring on the top of the cylinder. In order to study the temporal behaviour of the separation, time resolved PIV was applied. This technique allows capturing the dynamic processes in detail. The development of vortices in the separated shear layer is observed and in addition regions with different dominant frequencies are identified.     

On problem of transient coupled thermoelasticity of an annular fin

In this paper, the radial deformation and the corresponding stresses in a homogeneous annular fin for an isotropic material has been investigated. A numerical technique is proposed to obtain the solution of the transient coupled thermoelasticity in an annular fin cylinder with it’s base suddenly subject to a heat flux of a decayed exponential function of time. The system of fundamental equations is solved by using an implicit finite-difference method. The present method is a second-order accurate in time and space and unconditionally stable. A numerical method is used to calculate the temperature, displacement and the components of stresses with time t and through the radial of the annular fin cylinder. The results indicate that the effect of coupled thermoelasticity on temperature, stresses and displacement is very pronounced. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of coupled thermoelasticity.     

Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders

This paper presents an analysis of the thermomechanical behavior of hollow circular cylinders of functionally graded material (FGM). The solutions are obtained by a novel limiting process that employs the solutions of homogeneous hollow circular cylinders, with no recourse to the basic theory or the equations of non-homogeneous thermoelasticity. Several numerical cases are studied, and conclusions are drawn regarding the general properties of thermal stresses in the FGM cylinder. We conclude that thermal stresses necessarily occur in the FGM cylinder, except in the trivial case of zero temperature. While heat resistance may be improved by sagaciously designing the material composition, careful attention must be paid to the fact that thermal stresses in the FGM cylinder are governed by more factors than are its homogeneous counterparts. The results that are presented here will serve as benchmarks for future related work.     

The Method of R-Functions in the Solution of Elastic Problems on the Basis of Reissner's Mixed Variational Principle

A method is presented for solving boundary-value elastic problems on the basis of the variational–structural method of R-functions and Reissner's mixed variational principle. A mathematical formulation is given to problems on the deformation of elastic bodies under mixed boundary conditions and bodies interacting with smooth rigid dies. Solutions satisfying all the boundary conditions are proposed. For undetermined components of these solutions, the resolving equations are derived and their properties are studied. A posteriori estimation of numerical solutions is made. As examples, solutions are found to a problem on the stress–strain state of a short cylinder and to a contact problem on a cylinder interacting with a smooth die. A numerical method of solving such problems is analyzed for convergence, and the accuracy of the solutions is estimated.     

Potential Flow Past a Slightly Deformed Porous Circular Cylinder

A uniform potential flow past a porous circular cylinder with a core of different permeability is discussed. The porous circular cylinder is slightly deformed whose radius is r=r₁(1+ecosm q){r=r_1(1+\epsilon \cos m \theta)} , where | e | << 1{\mid\epsilon\mid\ll 1} and m is a positive integer. Here r, θ are the polar coordinates and r ₁ is the characteristic radius of the cylinder. The drag force exerted by the exterior flow on the surface of the cylinder is calculated and it depends on the thickness of the porous material and on the permeabilities of the two porous regions. As special cases, porous cylinder with hollow core, rigid core, and deformed cylinder is discussed.     

Measurements of the dynamic lift force acting on a circular cylinder in cross-flow and exposed to acoustic resonance

A piezoelectric transducer is developed to perform direct measurements of the dynamic lift force acting on a circular cylinder in cross-flow, in the presence and absence of acoustic resonance. Details of the force transducer design are presented in the paper. The dynamic lift force is measured for a single cylinder with two different diameters, D=12.7 and 15.8 mm. During the tests, the first transverse acoustic mode of the duct housing the cylinder is self-excited. The fluctuating pressure on the top wall of the duct is measured simultaneously with the dynamic lift force. In the absence of acoustic resonance, the measured dynamic lift coefficients agree favorably with those reported in the literature. However, when the acoustic resonance is initiated, the dynamic lift experiences a drastic increase in amplitude associated with abrupt changes in the phase between the lift force and the acoustic pressure. A methodology to extract the hydrodynamic lift component from the total lift measured during acoustic resonance is also proposed. The hydrodynamic lift force is then decomposed into in-phase and out-of-phase components, with respect to the resonant sound pressure. This decomposition procedure provides new insights into the nature of the aeroacoustic sources in the cylinder wake. The proposed methodology, together with the test results provide a general design approach to assess the increase in the dynamic fluid loading on bluff bodies in cross-flow due to the excitation of acoustic resonance.     

Slot/slots air jet impinging cooling of a cylinder for different jets–cylinder configurations

Heat transfer characteristics of a slot/slots jet air impinging on a cylinder have been experimentally investigated for two different orientations of slot/slots jet plan with respect to cylinder axis. The experiments were carried out to study the effects of orientation of slot/slots jet plan with respect to cylinder axis on the rate of heat transfer from the cylinder. Two different jet–cylinder configurations were studied: (1) single slot jet aligned with cylinder axis (slot length = cylinder length), and (2) multiple slot jets equally spaces distributed orthogonal to cylinder axis (each slot length = cylinder diameter and sum of slots lengths = cylinder length). For each configuration, parametric effects of Reynolds numbers (Re) ranging from 1,000 to 10,000, dimensionless slot widths (W/d) ranging from 0.125 to 0.5, and dimensionless slot orifice-to-cylinder spacing (Z/W) ranging from 1 to 12 on local and average Nusselt numbers around cylinder surface have been investigated. The results showed that: (1) cooling the cylinder by multiple slots jets situated orthogonal to cylinder axis gave more uniform surface temperature distributions and higher heat transfer rate than the case of cooling the cylinder by single slot jet aligned with cylinder axis, (2) for both configurations the Nusselt number around the cylinder increased with increasing Re and W/d, and (3) for both configurations there was a certain Z/W in the range 4<Z/W<6 at which the stagnation and mean Nusselt number were maximum. Correlations for the mean Nusselt numbers around cylinder surface have been presented for both configurations. Comparisons between the correlations predictions and the present and other previous experimental data have been conducted.     

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.     

An experimental investigation of flow past a dual step cylinder

Flow development in the wake of a dual step cylinder has been investigated experimentally using Laser Doppler Velocimetry and flow visualization. The dual step cylinder model is comprised of a large diameter cylinder (D) mounted at the mid-span of a small diameter cylinder (d). The experiments have been performed for a Reynolds number (Re _D ) of 1,050, a diameter ratio (D/d) of 2, and a range of large cylinder aspect ratios (L/D). The results show that the flow development is highly dependent on L/D. The following four distinct flow regimes can be identified based on vortex dynamics in the wake of the large cylinder: (1) for L/D ≥ 15, three vortex shedding cells form in the wake of the large cylinder, one central cell bounded by two cells of lower frequency, (2) for 8 < L/D ≤ 14, a single vortex shedding cell forms in the wake of the large cylinder, (3) for 2 < L/D ≤ 6, vortex shedding from the large cylinder is highly three-dimensional. When spanwise vortices are shed, they deform substantially and attain a hairpin shape in the near wake, (4) for 0.2 ≤ L/D ≤ 1, the large cylinder induces vortex dislocations between small cylinder vortices. The results show that for Regimes I to III, on the average, the frequency of vortex shedding in the large cylinder wake decreases with L/D, which is accompanied by a decrease in coherence of the shed vortices. In Regime IV, small cylinder vortices connect across the large cylinder wake, but these connections are interrupted by vortex dislocations. With decreasing L/D, the frequency of dislocations decreases and the dominant frequency in the large cylinder wake increases toward the small cylinder shedding frequency.     

Vortex-shedding from single and tandem cylinders in the presence of applied sound

A single cylinder and two tandem cylinder configurations with longitudinal pitch ratios L/D=1.75 and 2.5 were rigidly mounted in an open circuit wind tunnel and a standing acoustic pressure wave was imposed so that the acoustic particle velocity was normal to both the cylinder axis and the mean flow velocity. The effect of sound on the vortex-shedding was investigated for various amplitudes by means of pressure taps on the cylinders and wake hot-wire probes. These tests show that applied sound can entrain and shift the natural vortex-shedding frequency to the frequency of excitation and produce nonlinearities in the wake. The lock-in envelope for the tandem cylinders is considerably larger than for the single cylinder. The lock-in range for the smaller tandem cylinder spacing was broader still than either the single cylinder, or the L/D=2.5 tandem cylinder case. The pressure and hot-wire measurements show for the single cylinder, and tandem cylinder configuration with pitch ratio L/D=2.5, that there was a phase jump near the coincidence of the vortex-shedding frequency and the excitation frequency, while there was no jump for the pitch ratio of 1.75. As well, the applied sound field was also noted to induce vortex-shedding in the gap for the L/D=2.5 case, while no vortex-shedding was noted for the smaller pitch ratio.     

Thermal stresses in infinite circular cylinder subjected to rotation

The present investigation is concerned with the effect of rotation on an infinite circular cylinder subjected to certain boundary conditions.An analytical procedure for evaluation of thermal stresses,displacements,and temperature in rotating cylinder subjected to thermal load along the radius is presented.The dynamic thermal stresses in an infinite elastic cylinder of radius a due to a constant temperature applied to a variable portion of the curved surface while the rest of surface is maintained at zero temperature are discussed.Such situation can arise due to melting of insulating material deposited on the surface cylinder.A solution and numerical results are obtained for the stress components,displacement components,and temperature.The results obtained from the present semi-analytical method are in good agreement with those obtained by using the previously developed methods.     

Aerodynamic characteristics of a square cylinder with a rod in a staggered arrangement

The aerodynamic characteristics of a square cylinder with an upstream rod in a staggered arrangement were examined. The pressure measurement was conducted in a wind tunnel at a Reynolds number of Re_D=82,000 (based on the width of the square cylinder) and the flow visualization was carried out in a water tunnel with the hydrogen bubble technique at Re_D=5,200. When the rod and the square cylinder were in tandem, the reduction of drag was mainly caused by the increase of the rear suction pressure. When the staggered angle was introduced, the shield and disturbance effect of the rod on the square cylinder diminished, which results in the increase of the cylinder drag. The side force induced by the staggered angle is small (the maximum value is 20% of the drag of the isolate square cylinder). There were six different flow modes with various staggered angles and spacing ratios, and the corresponding flow patterns are presented in present paper.     

Numerical study of the effects occurring near a circular cylinder in stratified fluid flows with short buoyancy periods

Flow around a two-dimensional circular cylinder of a stratified fluid with periods buoyancy T_b = 25.2 and 6.28 sec is studied numerically over a wide range of Reynolds and Froude numbers. It is found that in the presence of a perturbation ahead of a cylinder which moves downstream with increasing Reynolds number, the salinity isolines have the shape of a semi-circular comb with sharp teeth. The shape change of the attached waves and the occurrence of fluid layers of different densities in the cylinder wake are studied. In flows with a buoyancy period T_b = 6.28 sec at Reynolds numbers Re < 60, stagnant zones are found in the cylinder wake, and at Re > 60, these zones are absent.