Equal-sized Cylinders Research Articles

Investigation of the Natural Convection within a Cold Circular Enclosure Containing Three Equal-Sized Cylinders of Hot Surface

The present work is conducted for studying the natural convection in a circular enclosure that contains three equal-sized cylinders in tandem arrangement. The outer cylinder has a cold surface and the enclosure internals have hot surfaces. The relation between the density of the fluid and the temperature is treated by the Boussinesq approximation. The fluid used for the investigation is Newtonian and incompressible. The results present the roles of some non-dimensional parameters (Rayleigh (Ra) and Prandtl (Pr) numbers) on the buoyancy-driven flow and the convective heat transfer. The obtained results revealed an intensification of the v-velocity component in the annular space and an enhancement in the heat transfer rates with the rise of Rayleigh number.

Wake-induced vibrations of an elastically mounted cylinder located downstream of a stationary larger cylinder at low Reynolds numbers

Two-dimensional numerical simulations of flow past two unequal-sized circular cylinders in tandem arrangement are performed at low Reynolds numbers (Re). The upstream larger cylinder is stationary, while the downstream cylinder has both one (transverse-only) and two (transverse and in-line) degrees of freedom (1-dof and 2-dof, respectively). The Re, based on the free stream velocity U∞ and the downstream cylinder diameter d, varies between 50 and 200 with a wide range of reduced velocities Ur. The diameter of the upstream cylinder is twice that of the downstream cylinder, and the center-to-center spacing is 5.5d. In general, for the 1-dof case, the calculations show that the wake-induced vibrations (WIV) of the downstream cylinder are greatly amplified when compared to the case of a single cylinder or two equal-sized cylinders. The transverse amplitudes build up to a significantly higher level within and beyond the lock-in region, and the Ur associated with the peak amplitude shifts toward a higher value. The dominant wake pattern is 2S mode for Re=50 and 100, while with the increase of Re to 150 and 200, the P+S mode can be clearly observed at some lower Ur. For the 2-dof vibrations, the transverse response characteristics are similar to those presented in the corresponding 1-dof case. The in-line responses are generally much smaller, except for several significant vibrations resulting from in-line resonance. The obvious in-line vibration may induce a C (chaotic) vortex shedding mode for higher Re (Re=200). With regard to the 2-dof motion trajectories, besides the typical figure-eight pattern, several odd patterns such as figure-double eight and single-looped trajectories are also obtained due to the wake interference effect.

Vortex Induced Vibrations of a Pair of Cylinders at Reynolds Number 1000

Vortex induced vibrations of two equal-sized cylinders in tandem and staggered arrangement placed in uniform incompressible flow is studied. A stabilized finite element formulation is utilized to solve the governing equations. The Reynolds number for these 2D simulations is 1000. The cylinders are separated by 5.5 times the cylinder diameter in the streamwise direction. For the staggered arrangement, the cross-flow spacing between the two cylinders is 0.7 times the cylinder diameter. In this arrangement, the downstream cylinder lies in the wake of the upstream one and therefore experiences an unsteady inflow. The wake looses its temporal periodicity, beyond a few diameters downstream of the front cylinder. The upstream cylinder responds as an isolated single cylinder while the downstream one undergoes disorganized motion. Soft-lock-in is observed in almost all the cases.

FLOW-INDUCED OSCILLATIONS OF TWO CYLINDERS IN TANDEM AND STAGGERED ARRANGEMENTS

A stabilized finite element formulation is employed to study flow-induced oscillations of a pair of equal-sized cylinders in tandem and staggered arrangement placed in uniform incompressible flow. Computations, restricted to 2-D, are carried out for Reynolds numbers 100 for various values of the structural frequency of the oscillator. The cylinders are separated by 5·5 times the cylinder diameter in the streamwise direction. For the staggered arrangement, the cross-flow spacing between the two cylinders is 0·7 times the cylinder diameter. In this arrangement, the downstream cylinder lies in the wake of the upstream one and therefore experiences an unsteady in-flow. Since the spacing between the two cylinders is beyond the critical value for proximity interference, it is expected that the upstream cylinder behaves like an isolated single cylinder, while the downstream one experiences wake-induced flutter. The Re=100 flow leads to a very organized wake and large amplitude motion is observed for the downstream cylinder. The trajectory of the upstream cylinder resembles a figure-of-eight. The downstream cylinder shows a similar behaviour for the tandem arrangement. However, for the staggered arrangement, the trajectory of the rear cylinder resembles a tilted oval. Soft lock-in is observed in almost all the cases.

The motion of two cylinders in contact in channel flow

The motion of a doublet consisting of two rigidly connected circular cylinders freely suspended in an incompressible Newtonian fluid in a narrow channel bounded by two parallel planes is studied numerically at zero Reynolds number. The Stokes equations are solved by a finite element method for various positions and orientations of the particle, and the trajectories of the particle are determined for a number of initial configurations. A doublet of equal-sized cylinders is found either to tumble or oscillate in rotation, while a doublet of unequal-sized cylinders possesses a stable, steady equilibrium configuration, at which the particle is located close to the channel centerline with a constant angle of inclination. Thus, doublets of unequal diameters tumble, oscillate in rotation or approach the equilibrium configuration asymptotically, depending on the radius ratio of cylinders, particle size-channel width ratio and initial conditions.

The resistivity and mobility functions for a model system of two equal-sized proteins in a lipid bilayer

We have calculated the mobility and resistivity functions for two equal-sized cylinders moving in a thin viscous sheet surrounded by a lower-viscosity fluid. These functions describe the hydrodynamic interactions between proteins embedded in a lipid bilayer surrounded by an aqueous solution. For a protein of radius a embedded in a biological membrane of thickness h and viscosity μ, a key parameter λ = μh/aμ′, which characterizes the viscosity ratio between the bilayer and surounding solution, is O(100). The method of solution for the hydrodynamic interactions differs depending on the separation distance, r, between the cylinders. When r = O(a), the particles are in the near-field regime, and the solution of the Stokes equations is divided between an inner and outer domain based on the asymptotically large value of λ. The inner solution neglects the flow in the lower-viscosity fluid and is solved numerically using a bipolar expansion. The outer solution is based on the fluid flows in all phases, but the cylinders are approximated by net forces. When r [Gt ] O(a), the particles are in the far-field regime, and we use the method of reflections to solve for the hydrodynamic interactions. The uniformly valid approximations, constructed from a combination of the near-field and far-field solutions, agree with the analytic solutions obtained within the lubrication and far-field regimes. Our results show that the hydrodynamic interactions between the cylinders are long range, perarting on a lengthscale of O(λ). The range of the hydrodynamic interactions is much longer than that of non-hydrodynamic interparticle forces, suggesting that hydrodynamic interactions will be significant determinants of the structure and dynamics of biological membranes.

FLOW OF WATER INTO CERAMIC TUBES SIMULATING ROOT SYSTEMS

In model root systems constructed of porous ceramic tubing, accumulated outflow volumes of water from four inner tubes, simulating plant roots, surrounded by 12 outer tubes was reduced when spacings narrowed below 2.0 mm in both sandy loam and silt soils. Soil water contents and, simultaneously, capillary conductivity decreased faster at close tube spacings than at wider ones in the order of the decrease at 1.0 mm > at 1.5 mm > at 2.0 mm = that at 3.0 mm = that at 6.0 mm. The ratio of outflow from 12 tubes to that from four, surrounded by the 12, is 3 and constant if all tubes receive water from discrete equal-sized cylinders of soil. At less than 2.0 mm between tubes, the ratio increased with time to maximum of about 9 and 5 for sandy loam and silt loam, respectively, indicating soil cylinder overlap for the particular suction of −0.9 bar imposed on the tubes. At 2.0 mm spacing or greater, the ratio was relatively constant and reasonably close to 3. Radial flow of water may be quickly restricted at root spacings below some limiting distance that is probably dependent upon the demand potential at the soil–root interface.

Account of a peculiarity in the distribution of the arteries sent to the limbs of slow-moving animals; together with some other similar facts. In a letter from Mr. Anthony Carlisle, Surgeon, to John Symmons, Esq. F. R. S

This peculiarity was first observed in the axillary arteries and in the iliacs of the Lemur tardigradus, which at their entrance into the upper and lower limbs were found to be suddenly divided into a considerable number of equal-sized cylinders, which occasionally anastomosed with each other, and were regularly distributed on the muscles; whilst the arteries proceeding to the other parts of the body divided in the usual arborescent form. Upon prosecuting this inquiry, it was found that the Bradypus tridactylus, and in some measure also the didactylus, has a similar distribution of these arteries.

VI. Account of a peculiarity in the distribution of the arteries sent to the limbs of slow-moving animals; together with some other similar facts. In a letter from Mr. Anthony Carlisle, surgeon, to John Symmons, Esq. F. R. S

Dear Sir, The Maucauco you have been so obliging as to give me for the purpose of dissection, has proved a subject of considerable interest. This animal, the Lemur tardigradus of Linnæus, was injected, with a view to exhibit the course of the arteries; and they present a very unusual deviation from the ordinary arrange­ment of this class of blood-vessels in animals generally. Before I had leisure to inquire further into this peculiarity, I presented a drawing of the appearances to my friend Dr. Shaw, of the British Museum, for the purpose of being made public in his work of natural history, now in the press. Since that time, I have, through Dr. Shaw’s assistance, been enabled to investi­gate this subject somewhat farther; and, if you consider the following account in any degree worthy the attention of the Royal Society, I shall receive an additional honour by its pro­ceeding through your hands. The Lemur tardigradus , in its injected state, accompanies this paper; and, for the kind of preparation, the vessels are filled with more than ordinary success. The arteries alone are injected; and the peculiarity of their arrangement is to be observed in the axillary arteries, and in the iliacs. These vessels, at their entrance into the upper and lower limbs, are suddenly divided into a number of equal-sized cylinders, which occasionally anastomose with each other. They are exclusively distributed on the muscles; whilst the arteries sent to all the parts of the body, excepting the limbs, divide in the usual arborescent form; and, even those arteries of the limbs which are employed upon substances not muscular, branch off like the common blood-­vessels. I counted twenty-three of these cylinders, parallel to each other, about the middle of the upper arm; and seventeen in the inguinal fasciculus.