Finite inflation of a hyperelastic toroidal membrane over a cylindrical rim

The present paper is devoted to the study of finite inflation of a hyperelastic toroidal membrane on a cylindrical rim under uniform internal pressure. Both compliant and rigid frictionless rims have been considered. The compliant cylindrical rim is modeled as a linear distributed stiffness. The initial cross-section of the torus is assumed to be circular, and the membrane material is assumed to be a homogeneous and isotropic Mooney–Rivlin solid. The problem is formulated as a two point boundary value problem and solved using a shooting method by employing the Nelder–Meads search technique. The optimization function is constructed on a two (three) dimensional search space for the compliant cylinder (rigid cylinder). The effect of the inflation pressure, material properties and elastic properties of the rim on the state of stretch and stress, and on the geometry of the inflated torus have been studied, and some interesting results have been obtained. The stability of the inflated configurations in terms of occurrence of the impending wrinkling state in the membrane has also been studied.     

Investigation of two‐dimensional channel flow with a partially compliant wall using finite volume–finite difference approach

This paper presents a numerical simulation of steady two‐dimensional channel flow with a partially compliant wall. Navier–Stokes equation is solved using an unstructured finite volume method (FVM). The deformation of the compliant wall is determined by solving a membrane equation using finite difference method (FDM). The membrane equation and Navier–Stokes equation are coupled iteratively to determine the shape of the membrane and the flow field. A spring analogy smoothing technique is applied to the deformed mesh to ensure good mesh quality throughout the computing procedure. Numerical results obtained in the present simulation match well with that in the literature. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical Simulation of the Unsteady Laminar Flow Past a Circular Cylinder with a Perforated Sheath

The unsteady two-dimensional laminar flow past a circular cylinder encased in a perforated sheath is numerically simulated. On the basis of the calculated results a technique for controlling the wake flow by diverting a portion of the flow from the forward stagnation point through internal ducts to orifices in the sheath located in the separation zone, is analyzed.     

Numerical Study of the Flow Behind a Rotary Oscillating Circular Cylinder

A numerical study is performed of flow behind a rotationally oscillating circular cylinder in a uniform flow by solving the two-dimensional incompressible Navier-Stokes equations. The flow behavior in lock-on regime and the timing of vortex formation from the oscillating cylinder are studied. When the frequency of excitation of the cylinder is in the vicinity of the natural vortex formation frequency, a lock-on vortex formation regime appears. As the excitation frequency being increased relative to the natural frequency the initially formed vorticity concentration switches to the opposite side of the cylinder. The effects of oscillating frequency and amplitude on the vortex structures formed in the near wake of the cylinder are also investigated. Based on the present calculated results, some complicated vortex patterns are identified and are consistent with the previous experimental visualizations.     

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Reslts show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds numberRe and rotation parameter α, is built by a kinematic analysis of the steady flow fields. The project supported by the National Natural Science Foundation of China     

CHARACTERISTICS OF LOW-FREQUENCY VARIATIONS EMBEDDED IN VORTEX-SHEDDING PROCESS

Experiments were made to study the flow characteristics in the near-wake region of a two-dimensional bluff body, namely a trapezoidal cylinder (prism) or a circular cylinder. The instantaneous velocity signals obtained at the inner edge of the separated shear layer and in the neighbourhood of the rear end of the vortex formation region show the presence of low-frequency variations at Reynolds numbers of 10⁴. The low-frequency variations noted in the velocity signals and the base pressure measured at the bluff body appear to be well correlated. These experimental observations suggest a physical picture that the variations of vortex formation length and base pressure are closely related in a real-time manner.     

The critical separation reynolds number for streaming flow past a circular cylinder

Employing a complex variable approach to the equations of motion for an incompressible viscous fluid and a more general approximation to the convecting stream function it is possible to calculate an approximation to the vorticity on the boundary for streaming flow past a circular cylinder without solving first for the complete flow field. In particular it is found that separation at the rear stagnation point first occurs when $\text{R1 = 2.78}$, where $\text{R1}$ is the critical Reynolds number. This result is in good agreement with the value of $\text{R1}$ obtained by experiment and the value obtained numerically. The convecting stream function satisfies the conditions of no slip and vorticity is not convected through the cylinder as it is in small Reynolds number Oseen theory.     

Numerical study on the suppression of the vortex-induced vibration of an elastically mounted cylinder by a traveling wave wall

In the present paper, the commercial CFD code “Fluent” was employed to perform 2-D simulations of an entire process that included the flow around a fixed circular cylinder, the oscillating cylinder (vortex-induced vibration, VIV) and the oscillating cylinder subjected to shape control by a traveling wave wall (TWW) method. The study mainly focused on using the TWW control method to suppress the VIV of an elastically supported circular cylinder with two degrees of freedom at a low Reynolds number of 200. The cross flow (CF) and the inline flow (IL) displacements, the centroid motion trajectories and the lift and drag forces of the cylinder that changed with the frequency ratios were analyzed in detail. The results indicate that a series of small-scale vortices will be formed in the troughs of the traveling wave located on the rear part of the circular cylinder; these vortices can effectively control the flow separation from the cylinder surface, eliminate the oscillating wake and suppress the VIV of the cylinder. A TWW starting at the initial time or at some time halfway through the time interval can significantly suppress the CF and IL vibrations of the cylinder and can remarkably decrease the fluctuations of the lift coefficients and the average values of the drag coefficients; however, it will simultaneously dramatically increase the fluctuations of the drag coefficients.     

Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number

Two- and three-dimensional numerical simulations of the flow around two circular cylinders in tandem arrangements are performed. The upstream cylinder is fixed and the downstream cylinder is free to oscillate in the transverse direction, in response to the fluid loads. The Reynolds number is kept constant at 150 for the two-dimensional simulations and at 300 for the three-dimensional simulations, and the reduced velocity is varied by changing the structural stiffness. The in-line centre-to-centre distance is varied from 1.5 to 8.0 diameters, and the results are compared to that of a single isolated flexible cylinder with the same structural characteristics, m^?=2.0 and ζ=0.007. The calculations show that significant changes occur in the dynamic behaviour of the cylinders, when comparing the flow around the tandem arrangements to that around an isolated cylinder: for the tandem arrangements, the lock-in boundaries are wider, the maximum displacement amplitudes are greater and the amplitudes of vibration for high reduced velocities, outside the lock-in, are very significant. The main responsible for these changes appears to be the oscillatory flow in the gap between the cylinders.     

An experimental study of the dynamic characteristics in boundary layer in the flow past a two-dimensional circular cylinder at subcritical reynolds numbers

An experimental study of the dynamic characteristics of flow past a two-dimensional circular cylinder is described. The fluctuationsoof wall shear stress, surface-pressure and velocity of the flow are measured with hot-film, hot-wire and pressure transducer. The frequency feature of fluctuations of wall shear stress is given. The cross-correlation functions of these fluctuations at any two points are calculated. The experimental results reveal that there is an overall syncronous fluctuation, at the shedding frequency, in boundary layer in the flow past a two-dimensional circular cylinder at subcritical Reynolds number.     

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.     

APPLICATION OF THE LES METHOD TO THE OSCILLATING FLOW PAST A CIRCULAR CYLINDER

The oscillating flow of an incompressible fluid over a circular cylinder is investigated by solving the vorticity/stream-function version of the two-dimensional Navier Stokes equations using a finite-difference Large Eddy Simulation (LES) method. Two different subgrid scale (SGS) models are tested. They are the classical Smagorinsky model and Yoshizawa's Two-Scale Direct-Interaction Approximation (TSDIA) model, both of which require the input of constants in the specification of the subgrid scale viscosity. In addition, a solution was obtained with no subgrid scale model for comparison purposes. Yoshizawa's model is based on the combination of Kraichman's Direct Interaction Analysis (1964) with the separation of scales of mean (grid scale) and fluctuating (subgrid scale) fields. This TSDIA model has the length scale as a function of space and time so that it incorporates the effects of local time rate of change and advection of the resolvable field. Both models are applied to the classical problem of an oscillating two-dimensional flow over a circular cylinder at various KC values atβ =1035.Calculated lift and in-line force coefficients compare favorably with available experimental data for KC≤2 with the best solutions developed from the Yoshizawa model. The solution for KC>2 demonstrates that the two-dimensional model is inadequate to describe the flow accurately.     

Flow-induced deformation of an elastic membrane adhering to a wall

The flow-induced deformation of a two-dimensional membrane with a circular unstressed shape clamped at the two ends on a plane wall at an arbitrary contact angle is considered. Working under the auspices of generalized shell theory, the membrane is allowed to develop in-plane tensions, transverse tensions, and bending moments determined by the curvature of the resting and deformed shapes. A system of ordinary differential equations governing the membrane shape is formulated, and the associated boundary-value problem is solved by numerical methods. Numerical results are presented to illustrate the deformation of a clamped membrane due to gravity or a negative transmural pressure. The shell formulation is coupled with a boundary-integral formulation for Stokes flow, and an efficient iterative scheme is developed to describe deformed equilibrium shapes of a membrane attached to a plane wall in the presence of an overpassing shear flow. Computations for different contact angles and shear rates reveal a wide variety of profiles and illustrate the distribution of the membrane tension developing due to the flow-induced deformation.     

Diffusion toward a cylinder in the case of an arbitrary viscous flow. Diffusive boundary layer approximation

Steady convective diffusion of a dissolved substance toward the surface of a cylinder (optionally circular) in a viscous flow is examined. An analytical solution is obtained in [1, 2] for the case of laminar flow around a curved cylinder when the freestream flow is straight and uniform. More complex hydrodynamical problems are examined in [3, 4]. In the present work an approximate analytical expression is obtained for diffusive flow of a substance toward the surface of a solid cylinder in the case of an arbitrary two-dimensional flow. Formulas are given for calculating the mass transfer at a circular cylinder in some shear flows of a viscous, incompressible fluid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 163–166, September–October, 1976.The authors thank Yu. P. Gupalo and Yu. S. Ryazantseva for formulating the problem and their attention to the work.     

Vortex shedding from a circular cylinder with a slit and concave rear surface

Vortex shedding from short circular cylinders with a slit was studied using a flow visualization and amplitude spectrum analysis of a thermoanemometry probe signal. It was found that a circular cylinder with a slit and concave rear surface produces stronger vortices than other bluff cylinders but that these vortices are very vulnerable to the end wall conditions. It was established that two small splitter plates (tails) fixed directly behind the cylinder at the end walls effectively isolate the vortices shed from the cylinder from the end wall boundary layer effects. For this arrangement a perfect regularity of vortex shedding and almost constant Strouhal number were achieved in the Reynolds number test range of about 250 to 43,000.On a leave from Technical University, 60965 Poznan, Piotrowo 3, Poland.     

NUMERICAL SIMULATION OF FLOW INDUCED BY A CYLINDER ORBITING IN A LARGE VESSEL

The flow field induced by a circular cylinder orbiting in a large vessel filled with fluid is investigated numerically. A finite-volume method is applied to the two-dimensional incompressible Navier–Stokes equations to compute the unsteady laminar flow fields. Moving reference systems are employed to allow an easy imposition of boundary conditions and to avoid grid deformation. Aspects of numerical accuracy related to the number of grid points and time steps employed are discussed. The flow is governed by two dimensionless parameters: a Reynolds number and a Keulegan–Carpenter number. These are varied systematically in order to find their influence on the flow pattern. In particular, the temporal development of the vorticity field and the lift on the cylinder are examined.     

Vortex shedding and three-dimensional behaviour of flow past a cylinder confined in a channel

A numerical investigation of the flow past a circular cylinder centred in a two-dimensional channel of varying width is presented. For low Reynolds numbers, the flow is steady. For higher Reynolds numbers, vortices begin to shed periodically from the cylinder. In general, the Strouhal frequency of the shedding vortices increases with blockage ratio. In addition, a two-dimensional instability of the periodic vortex shedding is found, both empirically and by means of a Floquet stability analysis. The instability leads to a beating behaviour in the lift and drag coefficients of the cylinder, which occurs at a Reynolds number higher than the critical Reynolds number for the three-dimensional mode A-type instability, but lower than a Reynolds number for any mode B-type instability.     

Flapping dynamics of a piezoelectric membrane behind a circular cylinder

The flapping dynamics of a piezoelectric membrane placed behind a circular cylinder, which are closely related to its energy harvesting performance, were extensively studied near the critical regime by varying the distance between the cylinder and the membrane. A total of four configurations were used for the comparative study: the baseline configuration in the absence of the upstream circular cylinder, and three configurations with different distances (S) between the cylinder and the membrane (S/D=0, 1, and 2). A polyvinylidene fluoride (PVDF) membrane was configured to flutter at its second mode in these experiments. The Reynolds number based on the membrane’s length was 6.35×10⁴ to 1.28×10⁵, resulting in a full view of membrane dynamics in the subcritical, critical, and postcritical regimes. The membrane shape and the terminal voltage were simultaneously measured with a high-speed camera and an oscilloscope, respectively. The influence of the upstream cylinder on the membrane dynamics was discussed in terms of time-mean electricity, instantaneous variations and power spectra of terminal voltage and membrane shape, fluctuating voltage amplitude, and flapping frequency. The experimental results overwhelmingly demonstrated that the terminal voltage faithfully reflected various unsteady events embedded in the membrane’s flapping motion. For all configurations, dependency of the captured electricity on a flow speed beyond the critical status was found to follow the parabolic relationship. In the two configurations in which S/D=0 and 1, the extraneously induced excitation by the Kármán vortex street behind the circular cylinder substantially reduced the critical flow speed, giving rise to effective energy capture at a lower flow speed and a relatively high gain in power output. However, in the configuration in which S/D=2, the intensified excitation by the Kármán vortex street on the membrane considerably reduced the captured energy. Finally, a transient analysis of the membrane’s flapping dynamics in the configuration in which S/D=0 was performed in terms of phase-dependent variations of the membrane segment’s moving speed, membrane curvature, and terminal voltage; the analysis resulted in a full understanding of the energy harvesting process with consecutive inter transfer of elastic, kinetic, and electric energies.     

Numerical analysis of vortex cell efficiency in laminar and turbulent flows past a circular cylinder with embedded rotating bodies

The effect of flow intensification in small-sized vortex cells on the flow pattern in the near wake downstream of a cylinder and the cylinder drag in laminar and turbulent flows is analyzed on the basis of a numerical simulation of the two-dimensional steady-state flow past a circular cylinder with rotating cylindrical bodies built into the cylinder contour. St. Petersburg, Saratov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–96, July–August, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 99-01-01115 and 99-01-00772).     

NUMERICAL STUDY ON THE FLOW AROUND A CIRCULAR CYLINDER WITH SURFACE SUCTION OR BLOWING USING VORTICITY-VELOCITY METHOD

A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme (MILU-CG). The effects of surface suction or blowing ' s position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re = 100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen , can reduce the drag force significantly , too.