On the effect of Reynolds number for flow around a row of square cylinders

Flow across a row of identical square cylinders placed side-by-side has been found to show interesting flow patterns which have complex characteristics depending upon the spacing (s/d) between the cylinders and the Reynolds number (Re). The combined effects of cylinder spacing and Reynolds number on the flow across a row of cylinders are numerically studied for 30 <= Re <= 140 and 1.0 <= s/d <= 4.0, where s is the surface-to-surface distance between two cylinders and d is the size of cylinder. It is found that the critical Reynolds number for the onset of vortex shedding increases with increase in gap ratio. The Reynolds number is found to have a strong effect on the flow especially at s/d=3.0, 4.0. Secondary frequency in the signal for lift and drag coefficients significantly contributes to the forces experienced by the cylinders. It is observed that at s/d =3.0, 4.0 the secondary frequency disappears at larger Reynolds number and the primary frequency dominates the flow. This means that the interaction of the wakes behind the cylinders at these gap ratios weakens with an increase in the Reynolds number. It is proposed that wake interaction is strongly influenced by the jets in the gap region, the nature of which alters with spacing and Reynolds number. This is confirmed by computing the average wake size as a function of Reynolds number. Based on this, two critical gap ratios, 2.0 and 4.0 for the range of Reynolds number under consideration are proposed. These gap ratios separate synchronous, quasiperiodic-I and quasiperiodic-II flow regimes depending on the Reynolds number. The mechanism of wake interaction has been studied to bring out these critical gap ratios. (C) 2009 [DOI: 10.1063/1.3210769

Simulation of flow across a row of transversely oscillating square cylinders

A numerical study of flow across a row of transversely oscillating square cylinders (of diameter d) has been undertaken using the lattice Boltzmann method, for a better understanding of fluid-structure interaction problems. The effects of cylinder oscillation frequency ratio (f(e)/f(o), where f(e) is the cylinder oscillation frequency and f(o) is the corresponding vortex shedding frequency for stationary row of cylinders), amplitude ratio (A/d), non-dimensional spacing between the cylinders (s/d) and Reynolds number (Re) on ensuing flow regimes and flow parameters have been studied to understand the flow physics. Six different flow regimes observed in this study are the quasi-periodic non-lock-on-I, synchronous lock-on, quasi-periodic lock-on, quasi-periodic non-lock-on-II, synchronous non-lock-on and chaotic non-lock-on. It is observed that the range of the lock-on regime depends upon the relative dominance of incoming flow and cylinder motion. Although the lock-on regime in the case of Re = 80, s/d = 4 and A/d = 0.2 is substantially larger as compared to that for a single oscillating cylinder, the range of the lock-on regime shrinks with a reduction in the cylinder spacing, increase in the Reynolds number or decrease in the oscillation amplitude. It is also observed that the wake interaction behind the cylinders weakens with an increase in f(e)/f(o), Re, A/d or s/d, leading to the formation of independent wakes and synchronous nature of the flow. For f(e)/f(o) >= 1.2, independent and intact oscillating wakes are noted and an additional frequency (wake oscillation frequency) is obtained in the time series of the lift coefficient. Although it was expected that the complexity in the wake interaction would increase with cylinder oscillation or amplitude ratio, an opposite effect (that is, formation of independent wakes) is noted from the results

On energy transfer in flow around a row of transversely oscillating square cylinders at low Reynolds number

In this paper, the effects of cylinder spacing, cylinder oscillation frequency, amplitude of cylinder oscillations and Reynolds number on the ensuing flow regimes and energy transition for flow across a row of transversely oscillating cylinders have been studied numerically using the lattice Boltzmann method. The lift and drag coefficient signals are analyzed in detail for finding the extent of lock-on regime and wake interaction mechanism at different spacings. It is noticed that the magnitude of the mean drag coefficient is large at small spacings, which is consistent with a strong wake interaction at small spacings. The effect of wake interaction can also be noticed from the non-monotonic variation of rms lift. The average energy transfer per cylinder oscillation cycle is large when the cylinders oscillate with a frequency near to the natural vortex shedding frequency. The direction of energy transfer changes between positive and negative values with small changes in the cylinder oscillation frequency, suggesting that the direction of energy transfer is very sensitive to this parameter. It is shown that the instantaneous lift coefficient and the cylinder velocity govern the energy transfer from or to the fluid. While the different parameters affect the flow regimes, the cylinder oscillation frequency primarily governs the energy transfer. (c) 2012 Elsevier Ltd. All rights reserved

Flow around six in-line square cylinders

The flow around six in-line square cylinders has been studied numerically and experimentally for 0.5 <= s/d <= 10.0 and 80 <= Re <= 320, where s is the surface-to-surface distance between two cylinders, d is the size of the cylinder and R e is the Reynolds number. The effect of spacing on the flow regimes is initially studied numerically at Re = 100 for which a synchronous flow regime is observed for 0.5 <= s/d <= 1.1, while quasi-periodic-I, quasi-periodic-II and chaotic regimes occur between 1.2 <= s/d <= 1.3, 1.4 <= s/d <= 5.0 and 6.0 <= s/d <= 10.0, respectively. These regimes have been confirmed via particle-image-velocimetry-based experiments. A flow regime map is proposed as a function of spacing and Reynolds number. The flow is predominantly quasi-periodic-II or chaotic at higher Reynolds numbers. The quasi-periodic and chaotic nature of the flow is due to the wake interference effect of the upstream cylinders which becomes more severe at higher Reynolds numbers. The appearance of flow regimes is opposite to that for a row of cylinders. The Strouhal number for vortex shedding is the same for all the cylinders, especially for synchronous and quasi-periodic-I flow regimes. The mean drag (C-Dmean) experienced by the cylinders is less than that for an isolated cylinder, irrespective of the spacing. The first cylinder is relatively insensitive to the presence of downstream cylinders and the C-Dmean is almost constant at 1.2. The C-Dmean for the second and third cylinders may be negative, with the value of C-Dmean increasing monotonically with spacing. The changes in root mean square lift coefficient are consistent with changes in C-Dmean. Interestingly, the instantaneous lift force can be larger than the instantaneous drag force on the cylinders. These results should help improve understanding of flow around multiple bluff bodies

Modeling the pore level fluid flow in porous media using the immersed boundary method

This chapter demonstrates the potential of the immersed boundary method for the direct numerical simulation of the flow through porous media. A 2D compact finite differences method was employed to solve the unsteady incompressible Navier-Stokes equations with fourth-order Runge-Kutta temporal discretization and fourth-order compact schemes for spatial discretization. The solutions were obtained in a Cartesian grid, with all the associated advantages. The porous media is made of equal size square cylinders in a staggered arrangement and is bounded by solid walls. The transverse and longitudinal distances between cylinders are equal to two cylinder diameters and at the inlet a fully developed velocity profile is specified. The Reynolds number based on the cylinder diameter and maximum inlet velocity ranges from 40 to 80. The different flow regimes are identified and characterised, along with the prediction of the Reynolds number at which transition from steady to unsteady flow takes place. Additionally, the average drag and lift coefficients are presented as a function of the Reynolds number