Pair Of Circular Cylinders Research Articles

Investigation of the steady and unsteady forces acting on a pair of circular cylinders in crossflow up to ultra-high Reynolds numbers

Measurements of the steady and unsteady forces acting on a pair of circular cylinders in crossflow are performed from subcritical up to ultra-high Reynolds numbers. The two cylinders with equal diameters d are arranged inline at two centre-to-centre distances: S/d = 2.8 and 4. The trend of the drag curve for the upstream cylinder Cd_{1}(Re) at both distances is similar to that for a single circular cylinder. The development of the drag curves Cd_{2}(Re, S/d = 2.8, 4) of the downstream cylinder is inverse to that of the upstream cylinder. For both cylinder spacing values, the drag on the downstream cylinder is negative for subcritical Reynolds numbers, increases abruptly to positive values at the beginning of the supercritical regime, and shows a significant dip at transcritical Reynolds numbers. This drag inversion indicates that the critical distance Sc decreases sharply in the supercritical Reynolds number range. For S/d = 2.8 at Rerightarrow 10^{7}, the downstream cylinder experiences once more a thrust force. The curve of the Strouhal number St(Re) of the downstream cylinder for S/d = 4 is very close to that of a single cylinder. For Reynolds numbers of Reapprox 1times10^{6} - 7times10^{6}, the Strouhal numbers have nearly equal values of Stapprox 0.22 - 0.24 for both distances. This is followed by a branching. For Rerightarrow 10^{7} and the case S/d = 2.8, the Strouhal numbers dip at St = 0.17. However, for S/d = 4, they increase up to St = 0.27. In the supercritical range, two peaks occur in the power spectra for the large distance S/d = 4. Based on a wavelet analysis, we can conclude that the low-frequency mode, which does not occur for a single cylinder, is an interference effect.Graphic abstract

Features of flow and heat transfer near a pair of circular cylinders

Synchronous flow and heat transfer study of in a single-phase medium is one of the important engineering and thermophysical problems. To solve this problem, the simultaneous use of PIV and gradient heatmetry is proposed. The investigated model is a pair of heated circular cylinders. Constant cylinders’ surface temperature is ensured by heating with saturated steam. The studies were carried out at various Reynolds numbers and inert-tube distance S, ranging from 0.5d to 4d. The use of gradient heatmetry made it possible to estimate the heat flux pulsations at the second cylinder and then, to compare them with the instantaneous velocity fields obtained using the PIV. The distributions of the heat flux and heat transfer coefficient over the cylinder surface were obtained for the range of Reynolds numbers from 4,8 to 48 × 103. The results are consistent with the data of other authors and show the prospects for the proposed methodology. Moreover, the results on the heat transfer augmentation the same models and in the same modes are presented.

Mathematical interpretation of seismic wave scattering and refraction on tunnel structures of circular cross-section

Mathematical interpretation of the elastic wave diffraction in circular cylinder coordinates is in the focus of this paper. Firstly, some of the most important properties of Bessel functions, pertinent to the elastic wave scattering problem, have been introduced. Afterwards, basic equations, upon which the method of wave function expansions is established, are given for cylindrical coordinates and for plane-wave representation. In addition, steady-state solutions for the cases of a single cavity and a single tunnel are presented, with respect to the wave scattering and refraction phenomena, considering both incident plane harmonic compressional and shear waves. The last part of the work is dealing with the translational addition theorems having an important role in the problems of diffraction of waves on a pair of circular cylinders.

Heat transfer and air flow near a pair of circular cylinders

Convective heat transfer is associated with the nature of the flow near the streamlined solid. Since flow properties vary quickly, it is important to fix their momentary values. We propose a technique for studying heat transfer and air flow based on combined use of gradient heat flux measurement and PIV. The paper presents velocity fields near a pair of circular cylinders and distribution of heat flux per unit area on the surface of the second cylinder. Both cylinders were heated with saturated water steam at atmospheric pressure, thereby keeping temperature of the cylinders constant. The experiments were carried out in the range of Reynolds numbers from 480 to 29800. Differences in vortex structure, dead-air region’s length etc., and heat transfer are revealed depending on the velocity of free stream and the distance between the cylinders. Use of gradient heat flux sensors allows us to estimate pulsations of heat flux at various points of the second cylinder and compare them with the pictures of instantaneous velocity fields. The results are consistent with data from other authors and show the prospects of the proposed methodology.

Steady streaming around a cylinder pair

The steady streaming motion that appears around a pair of circular cylinders placed in a small-amplitude oscillatory flow is considered. Attention is focused on the case where the Stokes layer thickness at the surface of the cylinders is much smaller than the cylinder radius, and the streaming Reynolds number is of order unity or larger. In that case, the steady streaming velocity that persists at the edge of the Stokes layer can be imposed as a boundary condition to numerically solve the outer streaming motion that it drives in the bulk of the fluid. It is investigated how the gap width between the cylinders and the streaming Reynolds number affect the flow topology. The results are compared against experimental observations.

A Numerical Study of the Forces on Two Tandem Cylinders Exerted by Internal Solitary Waves

A three-dimensional numerical wave flume is employed to investigate the forces exerted by internal solitary waves (ISWs) on a pair of circular cylinders in tandem arrangement, using large-eddy simulation (LES) model. The effect of the centre-to-centre distance (L) ranging from 1.5 to 5 diameters (D) is studied for various ISWs amplitudes (ηa) in the two-layer fluid system. Vertical-averaged vorticity distribution and vertical-averaged pressure gradient distribution in each layer are presented to investigate the different hydrodynamic interference between cylinders and the ISWs forces on each cylinder at variousL. Furthermore, the force behaviors of the two cylinders are also compared with that of an isolated cylinder in the same environment. The interaction between the two piles occurs in both layers, and it is found that, for1.5≤L/D<3.5, strong mutual interference appears between two cylinders; for3.5≤L/D<5, the two cylinders continue to influence each other in a weak-interference state; forL/D≥5, the interaction gradually decreases into a noninteracting state. This paper tries to provide some references to structural arrangement of double-cylinder structure and grouped-cylinder structure in stratified flow environment.

Wake Formation From a Pair of Circular Cylinders Traversing Between Small- and Large-Incidence Flow Regimes

Cross flow past a pair of equal-diameter staggered circular cylinders, with either one of the pair subject to forced harmonic transverse oscillation, is investigated experimentally within Reynolds numbers Re = 525–750. The center-to-center pitch ratio and stagger angle of the cylinders at their mean position are 2.5° and 21°, respectively. Results with cylinder excitation frequencies in the range 0.07 ≤ feD/U ≤ 1.18 (D = cylinder diameter, U = mean flow velocity) at a constant oscillation amplitude (peak-to-peak) of 0.44D are reported. Flow visualization of the wake formation region and hot-film measurements of the wake velocity are reported. Emphasis is placed on the mechanisms leading to vortex shedding. Results show that the wake undergoes considerable modification with the oscillation of either of the two cylinders; this modification depends strongly on the value of feD/U. The flow patterns remain essentially the same as those of the corresponding static cases for feD/U < 0.10. However, the flow at higher oscillation frequencies than that can no longer maintain those patterns. In particular, there are distinct regions of fundamental and superharmonic synchronizations between the dominant wake periodicities and the cylinder oscillation over the whole range of feD/U. Moreover, the manner in which the wake responds to the cylinder oscillation depends strongly on whether it is the upstream or downstream cylinder which is being oscillated.

Consolidated Numerical Simulation of Multiple Flows with Heat Transfer using Virtual Flux Method

In this paper, the Cartesian grid approach with virtual flux method based on the usual incompressible Navier-Stokes equations is proposed for simulating the incompressible multiple flows with heat transfer. In this approach, the fluxes on the closest grid points to virtual boundary are estimated to satisfy the velocity, pressure and temperature conditions on the virtual boundary. First, the present method is validated in flows around a circular cylinder and a pair of circular cylinders in transverse arrangement. As a result, this approach gives the good flow fields quantitatively in comparison with the reference results. Then, the method is applied to the consolidated simulations of multiple flows with heat transfer between heated and cooling flows. Therefore, it is concluded that the present approach is very fruitful for the consolidated simulation of incompressible complicated multiple flows with heat transfer.

Oscillatory flow about a cylinder pair

Oscillatory flow about a pair of circular cylinders is considered. The distance between the cylinders can be varied as can the angle that the undisturbed oscillatory flow makes with the line joining the cylinder centres. In common with other fluid flows dominated by oscillatory flow, a time-independent, or steady streaming, motion develops. Attention is focused on the case of high streaming Reynolds numbers and the resulting jets that erupt from the surfaces of the cylinders.

Growth of unsteady Hopf bifurcation modes and their swapping in a transitional coupled wake

The present work is devoted to unfolding the flow physics and the growth of different higher order Hopf bifurcation modes in the supercritical transitional coupled wake of two square cylinders in side-by-side arrangement. Depending on gap to diameter ratio g∗ between the cylinders, the coupled growths of the wakes (and therefore the corresponding Benard von Karman streets) through of each of the antiphase, in-phase, and biased patterns were found to be essentially governed by several dominant unsteady modes of Hopf bifurcations, occurring along the spanwise extended corelines of the shedded vortices. During the transient process of synchronized/biased wake evolution there noted significant spanwise pressure, velocity, and vorticity oscillations along the vortex corelines, which considerably amplified, as the flows reached transitional state. Such an unsteady spanwise oscillation of the wake facilitated the growth of higher order Hopf bifurcation modes and their frequent/random swapping. Instantaneous wakes (synchronized/biased) thereby evolved either through a particular mode of Hopf bifurcation or there remained simultaneous presence of multiple bifurcation modes. The growth of a number of instantaneous local pressure maxima over the spanwise extended corelines of the shedded vortices and the gradual decrease in pressure along two sides of the maximum pressure regions, together with the developed azimuthal pressure fluctuation around the vortex corelines, are found to be responsible for initiating the bifurcations. Notably, the present findings, while remaining closely consistent with recent experimental measurements (performed with a pair of circular cylinders) and the existing theoretical predictions (made on the basis of Landau/Ginzburg–Landau equations), clearly demonstrate the existence of five different transient modes of Hopf bifurcating solutions of the Navier–Stokes equations in the wake of two side-by-side square cylinders. Flow transition in the wake is noted to occur essentially through random swapping of these unsteady Hopf bifurcation modes with arbitrarily varying length scales.

455 渦法による並列二円柱まわりの流れの数値シミュレーション(流体力学II)

455 渦法による並列二円柱まわりの流れの数値シミュレーション(流体力学II)

Validation of Virtual Flux Method for Forced Convection Flows

This paper describes the validation of Virtual Flux Method (VFM) to forced convection flows. The method, one of Cartesian grid methods, can sharply capture boundaries. The method is also designed to calculate flows inside and outside boundaries seamlessly, while many Cartesian grid methods are not. This method is applied to forced convection flows around a circular cylinder and a pair of circular cylinders. The results are well compared with other available numerical results and experiments. Also, heat/fluid flow fields inside and outside a circular cylinder where a heater is placed at the center of the cylinder are seamlessly calculated. These results indicate the reliability of VFM for forced convection flows.

An immersed-boundary finite-volume method for simulation of heat transfer in complex geometries

An immersed boundary method for solving the Navier-Stokes and thermal energy equations is developed to compute the heat transfer over or inside the complex geometries in the Cartesian or cylindrical coordinates by introducing the momentum forcing, mass source/sink, and heat source/sink. The present method is based on the finite volume approach on a staggered mesh together with a fractional step method. The method of applying the momentum forcing and mass source/sink to satisfy the no-slip condition on the body surface is explained in detail in Kim, Kim and Choi (2001, Journal of Computational Physics). In this paper, the heat source/sink is introduced on the body surface or inside the body to satisfy the iso-thermal or iso-heat-flux condition on the immersed boundary. The present method is applied to three different problems : forced convection around a circular cylinder, mixed convection around a pair of circular cylin-ders, and forced convection around a main cylinder with a secondary small cylinder. The results show good agreements with those obtained by previous experiments and numerical simulations, verifying the accuracy of the present method.

나란히 배열된 한 쌍의 원형실린더를 지나는 유동 특성

Two-dimensional flow over a pair of circular cylinders in a side-by-side arrangement at low Reynolds numbers has been numerically investigated in this study Numerical simulations are performed, using the immersed boundary method, for the ranges of 40Re160 and ＜5, where Re and are, respectively, the Reynolds number and the spacing between the two cylinder surfaces divided by the cylinder diameter. Results show that a total of six kinds of wake patterns are observed over the ranges: antiphase-synchronized, inphase-synchronized, flip-flopping, single bluff-body, deflected, and steady wake patterns. It is found that the characteristics of the flow significantly depends both on the Reynolds number and gap spacing, with the latter much stronger than the former. Instantaneous flow fields, time traces, flow statistics and so on are presented to identify the wake patterns and then to understand the underlying mechanism. Moreover, the bifurcation phenomenon where either of two wake patterns can occur is found at certain flow conditions.ons.

201 臨界レイノルズ数付近にある並列二円柱に働く流体力

201 臨界レイノルズ数付近にある並列二円柱に働く流体力

G1104 一様流中の非平行2円柱の後流渦(G.S.11 乱流と渦の構造2)

G1104 一様流中の非平行2円柱の後流渦(G.S.11 乱流と渦の構造2)

513 直列二円柱に働く流体力と流れの可視化

513 直列二円柱に働く流体力と流れの可視化

Navier-Stokes' solutions for a pair of circular cylinders

Navier-Stokes' solutions for a pair of circular cylinders

Heat transfer and interactive buoyant vortex shedding by a pair of circular cylinders in transverse arrangement

The heat transfer and fluid flow patterns in the mixed convection regimes for the double circular cylinders arranged transverse to the vertical air stream are presented. The difficulty of the non-singular grid generation for the present triply-connected region has been effectively resolved by the FEM-FDM grid blending technique which requires embedding of finite elements in the small area of major geometrical difficulty. The unsteady streamfunction values are assigned rigorously on the cylinder surfaces and on the far-field boundary. It has been found that the Karman vortex street breaks down behind the double heated cylinders in a transient manner for a certain Richardson number range due to the buoyancy effect and vortex interaction, in contrast to the sudden breakdown applicable to a single heated cylinder.

Interactive vortex shedding from a pair of circular cylinders in a transverse arrangement

AbstractInteractive vortex shedding in the multiply connected domain formed by a pair of circular cylinders is analysed by the FEM–FDM blending technique. The vorticity–streamfunction formulation is used to solve the incompressible Navier–Stokes equations at Re = 100, with the time‐dependent wall streamfunctions determined from the pressure constraint condition and the far‐field streamfunctions from the integral series formula developed earlier by the authors. The standard Galerkin finite element method is used in the relatively small FEM subdomain and the finite difference method based on the general co‐ordinate system in the rest of the flow domain. Symmetric, antisymmetric and asymmetric wake patterns are obtained confirming the earlier experimental findings. The bistable nature of the asymmetric vortex shedding as well as the intermittent drifting from one status to the other between symmetric and antisymmetric wake patterns are reported.