Cylinders In Tandem Arrangement Research Articles

Flow past tandem cylinders under forced vibration

Flow past two cylinders in tandem arrangement under forced vibration has been studied experimentally employing the hydrogen bubble visualization technique. The Reynolds number, based on the cylinder diameter, is fixed at Re=250. In stationary state of the two cylinders with P/D=2.0, dual vortex shedding frequencies fL (St=0.14) and fH (St=0.18) are identified. fL is associated with the shear layer reattachment behavior and fH is related to the single bluff body behavior. Under a variety of forced vibrations of the two cylinders at a fixed vibration amplitude A/D=0.25, diverse and highly-repetitive vortex patterns are yielded. They are classified into two typical modes—a low-frequency mode and a high-frequency mode. The two modes are represented by two vortex patterns yielded from in-phase vibration of the two cylinders with P/D=2.0 and at vibration frequencies fe≈fL and fe≈fH. The difference between the two modes is on the number of vortices formed per vibration cycle. For the low-frequency mode, the number is four; for the high-frequency model, it is two. In both modes, the vortex formation is phase-locked to the cylinder motion. For a specified mode with a fixed vortex number per cycle, the way the vortices evolve in the wake can be somewhat different by changing the vibration frequency, pitch ratio, as well as the vibration type. These affecting factors have been examined in this work, and the associated vortex patterns have been characterized and compared.

Numerical Simulation of Two-Dimensional Flows Using the Feedback Force Immersed Boundary Method

In this paper, numerical simulation of flow around a cylinder using the feedback force immersed boundary method is carried out. The feasibility of algorithm is verified by the numerical simulation of flow past two cylinders in tandem arrangement. The Cartesian adaptive mesh refinement is used in the whole flow field, and the dynamic distribution characteristics of flow field around a single cylinder and double cylinders are obtained when Re=100. Compared with the results in other literatures, the simulation shows a good agreement.

Numerical Simulation of Two-Dimensional Flows Using the Feedback Force Immersed Boundary Method

In this paper, numerical simulation of flow around a cylinder using the feedback force immersed boundary method is carried out. The feasibility of algorithm is verified by the numerical simulation of flow past two cylinders in tandem arrangement. The Cartesian adaptive mesh refinement is used in the whole flow field, and the dynamic distribution characteristics of flow field around a single cylinder and double cylinders are obtained when Re=100. Compared with the results in other literatures, the simulation shows a good agreement.

Power-Law Fluid Flow Passing Two Square Cylinders in Tandem Arrangement

Two-dimensional laminar flow of a power-law fluid passing two square cylinders in a tandem arrangement is numerically investigated in the ranges of 1< Re< 200 and 1 ≤ G ≤ 9. The fluid viscosity power-law index lies in the range 0.5 ≤ n ≤ 1.8, which covers shear-thinning, Newtonian and shear-thickening fluids. A finite volume code based on the SIMPLEC algorithm with nonstaggered grid is used. In order to discretize the convective and diffusive terms, the third order QUICK and the second-order central difference scheme are used, respectively. The influence of the power-law index, Reynolds number and gap ratio on the drag coefficient, Strouhal number and streamlines are investigated, and the results are compared with other studies in the literature to validate the methodology. The effect of the time integration scheme on accuracy and computational time is also analyzed. In the ranges of Reynolds number and power-law index studied here, vortex shedding is known to occur for square cylinders in tandem. This study represents the first systematic investigation of this phenomenon for non-Newtonian fluids in the open literature. In comparison to Newtonian fluids, it is found that the onset of leading edge separation occurs at lower Reynolds number for shear-thinning fluids and is delayed to larger values for shear-thickening fluids.

Natural convection in power-law fluids from two square cylinders in tandem arrangement at moderate Grashof numbers

In this work, free convective flow and heat transfer in power-law fluids from two heated square cylinders in tandem arrangement is studied. The governing differential equations have been solved numerically over wide ranges of Grashof number, 10 ≤ Gr ≤ 1,000, Prandtl number, 0.71 ≤ Pr ≤ 50 and power-law index, 0.4 ≤ n ≤ 1.8. In order to elucidate the extent of inter-cylinder interaction, the non-dimensional inter-cylinder spacing, L/d is varied in the range, 2 ≤ L/d ≤ 6. The results are interpreted in terms of streamline and isotherm contours in the proximity of two cylinders to gain physical insights into the nature of flow. At the next level, the distribution of the local Nusselt number along the surface of the cylinders is presented. At the minimum inter-cylinder spacing due to the intense interference, the downstream cylinder contributes much less to the overall heat transfer whereas it experiences much higher hydrodynamic drag than the upstream cylinder. Broadly, the local and average Nusselt number for both cylinders show a positive dependence on both Grashof and Prandtl numbers. Also, all else being equal, shear-thinning fluid behaviour promotes the rate of heat transfer and shear-thickening fluid behaviour impedes it. Finally, the present numerical results have been correlated by using simple forms of equations thereby enabling the estimation of Nusselt number in a new application.

Numerical Study of Atmospheric Icing on Non Rotating Circular Cylinders in Tandem Arrangement

Numerical study of atmospheric ice accretion on two non-rotating circular cylinders in tandem arrangement was carried out at different operating and geometric conditions. To validate the numerical model, initially the results of ice accretion on single circular cylinder were compared with the experimental data obtained from CIGELE atmospheric icing research wind tunnel (CAIRWT) [1, 2]. A good agreement was found between experimental and numerical results. Numerical analyses of ice accretion on two circular cylinders in tandem arrangement showed that accreted ice loads decreases with the increase in distance between the cylinders and also affects the rate and shape of ice accretion. Parametric study at different droplet sizes and temperatures showed a significant change in ice accretion. This research work provides a useful base for better understanding and further investigation of atmospheric ice accretion on circular overhead power network cables in tandem arrangement, installed in the cold regions.

Power-law fluids flow and heat transfer over two tandem square cylinders: effects of Reynolds number and power-law index

The low-Reynolds numbers free-stream flow of power-law fluids and forced convection heat transfer around a square cylinder and two square cylinders in a tandem arrangement are numerically investigated. In the single cylinder case, the power-law index and Reynolds numbers range from n = 0.7 − 1.4 and Re = 60 − 160 at Pr = 0.7. In the tandem case, the spacing between the cylinders is four widths of each cylinder side and the power-law index ranges from 0.7 to 1.6 at Re = 40, 100, 160 and Pr = 0.7. All simulations are performed with a finite volume code based on the SIMPLEC algorithm and a non-staggered grid. The effect of spatial resolution on the results is also studied for a single cylinder and tandem cylinders. The mean and instantaneous streamlines, vorticity and temperature contours, the global quantities such as pressure and friction coefficients, the rms lift and drag coefficients, Strouhal and Nusselt numbers are determined and discussed for various power-law indexes at different Reynolds numbers. A comparison between the results of the single cylinder case and the two cylinders in tandem arrangement shows that there are relatively similar results for the single cylinder and the upstream cylinder of the tandem case.

Ghost Cell Immersed Boundary Method for Simulating Flow over Two Circular Cylinders in Tandem Arrangement

In this work, a ghost cell immersed boundary method is applied to the numerical simulation of a uniform flows over a circular cylinder and two circular cylinders in tandem arrangement. The Navier-Stokes equations are solved using an implicit fractional step method employed on collocated arrangement variables. Immersed boundary method permit the use of structured Cartesian meshes to simulate flows involving complex boundaries. The shedding of vortices and flow interference between two circular cylinders in tandem arrangement are investigated numerically. The calculations are validated against the experimental and numerical results obtained by other researchers to prove the accuracy and effectiveness.

Correlating Flow Pattern with Force Coefficients in Air Flow past a Tandem Unit of Three Circular Cylinders

Air Flow past three circular cylinders in tandem arrangement is simulated at 20 different Reynolds numbers ranging from 20 to 300. The spacing ratio L=D is set at 2, where L is center to center distance. The drag of all three cylinders is assessed with varying Reynolds number. Accordingly, pressure and velocity distribution in the near vicinity of cylinders is closely examined. It is found that Reynolds numbers of 42, 63 and 150 are critical Reynolds numbers for pressure, viscous and total drag forces respectively. Moreover, time evolutions of force coefficients are investigated to find the transitional Reynolds number at which the flow becomes unsteady and vortices are shed from the cylinders. It was observed that transition starts at Re = 101 and vortex shedding occurs at Re = 105 for the first time. Flow pattern is illustrated at a specific moment for all steady, transitional and unsteady states at various Reynolds numbers. Also, the time evolution of flow pattern is depicted for unsteady cases. It was observed that frequency of vortex shedding and also Strouhal number increase with Re.

Effect of Prandtl number on heat transfer from tandem square cylinders immersed in power-law fluids in the low Reynolds number regime

In this work, forced convection heat transfer from two square cylinders in tandem arrangement to power-law and Newtonian fluids has been investigated. The governing differential equations (continuity, momentum and energy balance) have been solved numerically. The results reported herein encompass wide ranges of the pertinent dimensionless parameters, namely, Prandtl number, 0.71⩽Pr⩽100, Reynolds number, 0.1⩽Re⩽40, power-law index, 0.2⩽n⩽1 and centre-to-center cylinder spacing, 2⩽L/d⩽6, albeit limited results were also obtained for L/d=24 to retrieve the limiting case of non-interacting cylinders. The range of the center-to-center gap between the two cylinders is such that it corresponds to strong to virtually no interactions between the two cylinders. Furthermore, the range of Reynolds number is such that the flow is expected to be steady. The detailed heat transfer characteristics are interpreted in terms of the isotherm patterns in the close proximity of each cylinder and the variation of the local Nusselt number on the surface of each cylinder. Finally, the surface averaged values of the Nusselt number are expressed in terms of Reynolds number, power-law index and Prandtl number for center-to-center distances L/d=2, 4 and 6. These results are also expressed in terms of the usual Colburn j-factor as a function of the Reynolds number and power-law index over the range of conditions spanned here.

Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method

The numerical investigation of the two-dimensional laminar flow past two rotating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.

Secondary instability in the near-wake past two tandem square cylinders

Floquet stability analysis has been carried out to detect the onset of the secondary instability in the laminar flow past two identical square cylinders in tandem. Presence of a neighbouring cylinder alters flow topology, leading to change of stability characteristics. A parametric study has been performed with the gap between the two square cylinders as the key parameter. Three distinct patterns of base flow are found depending on the gap, and distinctive modes of the secondary instability are identified for each pattern of the base flow. The modes exhibit either odd reflection-translation symmetry or even RT symmetry. The critical Reynolds number and the corresponding dominant spanwise wavelength are presented for a wide range of the gap. Temporal and spatial characteristics of the dominant Floquet modes are described in detail. A hysteresis is also noticed in a certain range of the gap. Neutral stability curves are presented for some selected values of the gap. The averaged in-plane vorticity of the dominant normalized Floquet mode is depicted as a function of the downstream distance from the rear face of the cylinder that sheds vortices. Comparison of stability characteristics is also made between the current flow and the flow past two circular cylinders in tandem arrangements.

Spectral-element discontinuous Galerkin lattice Boltzmann simulation of flow past two cylinders in tandem with an exponential time integrator

In this paper, a spectral-element discontinuous Galerkin (SEDG) lattice Boltzmann discretization and an exponential time-marching scheme are used to study the flow field past two circular cylinders in tandem arrangement. The basic idea is to discretize the streaming step of the lattice Boltzmann equation by using the SEDG method to get a system of ordinary differential equations (ODEs) whose exact solutions are expressed by using a large matrix exponential. The approximate solution of the resulting ODEs are obtained from a projection method based on a Krylov subspace approximation. This approach allows us to approximate the matrix exponential of a very large and sparse matrix by using a matrix of much smaller dimension. The exponential time integration scheme is useful especially when computations are carried out at high Courant–Friedrichs–Lewy (CFL) numbers, where most explicit time-marching schemes are inaccurate. Simulations of flow were carried out for a circular cylinder at Re=20 and for two circular cylinders in tandem at Re=40 and a spacing of 2.5D, where D is the diameter of the cylinders. We compare our results with those from a fourth-order Runge–Kutta scheme that is restricted by the CFL number. In addition, important flow parameters such as the drag coefficients of the two cylinders and the wake length behind the rear cylinder were calculated by using the exponential time integration scheme. These results are compared with results from our simulation using the RK scheme and with existing benchmark results.

低間隔における直列２円柱の流れ方向および流れ直交方向の流力振動に関する３次元数値解析

We present numerical results for hydrodynamic vibrations of two circular cylinders in tandem arrangement, which are mounted in a uniform flow. Two circular cylinders are assumed as each rigid body, and the circular cylinders are supported by damper-spring systems in in-line and cross-flow directions. In our computations, the gap ratio between the centers of two circular cylinders is set as 3 which is smaller than the critical gap ratio of two stationary circular cylinders. In addition, the Scruton number is given by 0.99. Vibration amplitudes in the in-line and cross-flow directions of the circular cylinders are computed by a third-order upwind finite element scheme and the numerical results are discussed in detail.

Numerical simulation of fluid flow and forced convection heat transfer from tandem circular cylinders using overset grid method

Forced convection heat transfer from two and three isothermal circular cylinders in tandem arrangement is studied numerically. In addition, the flow field and the vortex shedding behavior in the wake of the cylinders are investigated. The governing equations consist of continuity, momentum and energy equations are solved for laminar unsteady flow regime. The numerical simulations are performed with a developed finite volume code using the overset grid method. A general orthogonal boundary fitted coordinate system is used for the grid generation. This simulation is performed for the Prandtl numbers of 0.7 and 7 at the Reynolds numbers of 100 and 200. The spacing ratio L/ D is set at 2, 3, 4, 5, 7 and 10. In order to analyze the heat transfer from isothermal cylinders, the mean and local Nusselt numbers and isotherm plots are presented and discussed for different values of the problem parameters. In addition, the mean and instantaneous drag and lift coefficients and Strouhal numbers are computed to elucidate the role of the Reynolds number and spacing ratio. Furthermore, two new correlations for the calculation of the mean Nusselt number, in terms of the spacing ratio and the Reynolds and Prandtl numbers, is proposed. In order to validate the solution, the obtained results are compared with available results in the published literature.

Numerical Study of Particle Dispersion in the Wake of Two Tandem Square Cylinders Using Discrete Vortex Method

This study has been conducted to investigate numerically the particle dispersion in the wake of dilute particle-laden gas flows past two identical square cylinders in tandem arrangement at Reynolds number of 10,000,000. In the numerical method, the discrete vortex method is employed to calculate the gas flow fields, and the Lagrangian approach is applied to track individual solid particles. A dispersion function is defined to represent the lateral dispersion scale of particles. The wake vortex patterns and the distributions of particles with various Stokes numbers ranging from 0.01 to 10 are obtained. The numerical results reveal that: (1) the particles with St = 0.01 can distribute both in the vortex core and around the vortex periphery, whereas the particles with St = 1.0, 10 congregate mainly around the vortex periphery; (2) the particles with St = 0.01, 0.1 are trapped by the vortices into the gap between the two square cylinders, while very few particles with St = 1.0, 10 are distributed within the gap; (3) the particle's dispersion intensity along the lateral direction decreases greatly as St is increased from 0.01 to 10.

Numerical simulation of flows around two unyawed and yawed wavy cylinders in tandem arrangement

The turbulent flows around two fixed unyawed and yawed wavy cylinders in tandem arrangement at a subcritical Reynolds number of 3900 were studied using three-dimensional large eddy simulation. A range of spacing ( L) between the cylinders from 1.5 D m to 5.5 D m with yaw angles of α=0°, 30° were investigated so as to identify the effects of cylinder spacing ratio and yaw angle as well as the coupling effects of the two wavy cylinders in tandem. The instantaneous near wake flow patterns around the cylinders were captured. Flows around circular cylinders with the same configurations were also obtained for comparison. The effects of the vortex shedding from the upstream cylinder on the fluid-dynamic forces acting on the downstream one were examined. Results show that vortex shedding behind the upstream wavy cylinder occurs at a further downstream position compared with that of the circular upstream cylinder. This leads to the weakening of the effect of bodies' vibration of the cylinders as well as an evident reduction of drag. With a yaw angle of 30°, the vortex formation lengths behind both the upstream and downstream cylinders decrease, typically for the wavy cylinders configuration. However, the effects of drag reduction and the control of bodies' vibration still exist except for the spacing ratio of L/ D m =3.5, which is in the critical spacing ratio regime for two wavy cylinders in tandem.

Bi-stable flow around tandem cylinders of different diameters at low Reynolds number

The flow around two circular cylinders in tandem arrangement with different diameters has been investigated numerically. The upstream to downstream cylinder diameter ratio was kept constant at a value of d/D=2/3 and the centre-to-centre distance was varied from 1.2D to 5D. The Reynolds number based on upstream cylinder diameter and free-stream velocity used in this study is equal to 200. Force coefficients and flow frequencies have been obtained from 2D fluid flow finite-element simulations. Single-wake shedding, reattachment and co-shedding regimes have been observed. The results show that, depending on initial perturbations, reattachment and co-shedding can be observed on a wide range of centre-to-centre distances (L/D∊[1.8, 3.8]), which defines the bi-stable flow range. The lower part of the bi-stable range is characterized by a lock-in phenomenon for which vortex-shedding from the upstream and downstream cylinders are synchronized when there are co-shedding flow conditions.

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.

Vortex- and wake-induced vibrations of a tandem arrangement of two flexible circular cylinders with far wake interference

The dynamic response of two flexible cylinders in tandem arrangement partially immersed in a uniform flow is analysed. The centre-to-centre separations, larger than 4 and up to 8 diameters, were chosen to fall in the regime in which two separate wakes exist behind each one of the models. For the cases presented here, it has been confirmed that the main excitation mechanism is wake-induced vibration (WIV). The rear cylinder shows large amplitudes of response, at reduced velocities over the expected ones at lock-in when a cylinder is undergoing VIV being isolated. This type of response has been also observed by other researchers in experiments with flexibly mounted cylinders in the wake of stationary ones, we also provide data here, for cases with the front cylinder being stationary.