Wake interaction between two side-by-side square cylinders in channel flow

Burattini, Paolo; Agrawal, Amit

doi:10.1016/j.compfluid.2013.02.014

Cited by 65 publications

(25 citation statements)

References 40 publications

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“…This model consists of two coupled Landau equations with coupling terms which are proportional the difference between the two amplitudes to model the interaction of the two wakes, and the coefficients were estimated from experimental data. Burattini & Agrawal (2013) adopted this model to interpret their numerical simulation data and showed that the drag and lift coefficients on the square cylinders arranged side-by-side are well reproduced by this model.…”

Section: Introductionmentioning

confidence: 88%

Nonlinear interactions between the two wakes behind a pair of square cylinders

Mizushima¹,

Hatsuda²

2014

J. Fluid Mech.

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Nonlinear interactions between the two wakes behind a pair of square cylinders, which are placed side by side in a uniform flow, are investigated by the linear and weakly nonlinear stability analyses and numerical simulations. It is known from the linear stability analysis that the flow past a pair of cylinders becomes unstable to a symmetric or an antisymmetric mode of disturbance, depending on the gap ratio, the ratio of the gap distance between the two cylinders to the cylinder diameter. The antisymmetric mode gives the critical condition for smaller gap ratios than a threshold value, and for larger gap ratios the symmetric mode becomes the most unstable. We focus on the flow pattern arising through the nonlinear interactions of the two modes of disturbance for gap ratios around the threshold value when both modes are growing. We derive a couple of amplitude equations for the two modes to properly describe the nonlinear interaction between them by applying the weakly nonlinear stability theory. The amplitude equations are shown to have three equilibrium solutions except the null solution such as a mixed-mode solution, symmetric and antisymmetric single-mode solutions. Examination of the stability of each equilibrium solution leads to a conclusion that the mixed-mode solution exchange its stability with both the symmetric and the antisymmetric single-mode solutions simultaneously. In the case where the mixed-mode solution is stable, both the symmetric and antisymmetric modes have finite amplitudes, and the resultant flow has an asymmetric flow pattern comprising of finite amplitudes of the two modes of disturbance superposed on the steady symmetric flow. While in the case where both the single-mode solutions are stable, either of the symmetric-and antisymmetric-mode solutions survives, overwhelming the other. Then, if the symmetric mode attains at an equilibrium finite amplitude and the antisymmetric mode vanishes, the resultant flow is symmetric, and if the antisymmetric mode survives and the symmetric mode decays out, the flow becomes asymmetric with the antisymmetric mode of disturbance superposed on the steady symmetric flow. Thus, the flow appearing due to instability differs depending on the initial condition, not uniquely determined, when both single-mode solutions are stable. We numerically delineated the region in the parameter space of the gap ratio and the Reynolds number where the mixed-mode solution is stable. The theoretical results obtained from the weakly nonlinear stability analyses are confirmed by numerical simulations. The conclusion derived from the stability analysis of the equilibrium solutions of the amplitude equations is widely applicable also to other double Hopf bifurcation problems.

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Section: Introductionmentioning

confidence: 88%

Nonlinear interactions between the two wakes behind a pair of square cylinders

Mizushima¹,

Hatsuda²

2014

J. Fluid Mech.

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“…Alam and Zhou (2013), through flow visualization, found similar 4 regimes at a far lower Reynolds number of 300 with similar g* ranges: single bluff body regime for g*<0.2; narrow and wide streets regime for 0.2<g*<1.1; transition regime for 1.1<g*<1.4; and coupled regime for g*>1.4. Burattini and Agrawal (2013) simulated wake interactions of 2 side-by-side cylinders at Re=73 and 0.5≤g*≤6. Four wake flow regimes:…”

Section: Introductionmentioning

confidence: 99%

Wake of two side-by-side square cylinders at low Reynolds numbers

Kang

Lim

et al. 2017

Physics of Fluids

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Wake of two side-by-side square cylinders was investigated through direct numerical simulation at low Reynolds numbers (16~200). The gap between the two cylinders varied from 0-10D, where D is the dimension of the square cylinder (edge length). 9 different wake patterns and their dependency on both Reynolds number and gap spacing were identified and analysed. A system classification map, demarcated by Reynolds number and gap ratio g* (g/D, where g is the gap spacing between 2 cylinders), was derived for these 9 wake modes. Steady-state wake (mode I) was observed when Reynolds number is lower than the critical Reynolds number, which depends on g*. For gap ratio less than 0.7, only single vortex street was observed. The single vortex street wake can be either symmetric and periodic (mode II), or asymmetric and periodic (mode III), or irregular (mode IV). In this gap ratio range (less than 0.7), shedding frequency decreases with gap ratio due to the damping role of the gap flow. For gap ratio larger than 0.7, two vortex streets were also observed. For gap ratio larger than 1, only two vortex streets were observed. Vortex shedding can be either synchronized and in-phase (mode V), synchronized and anti-phase (mode VI), in-phase dominated with low frequency modulation (mode VII), anti-phase dominated with low frequency modulation (mode VIII), asymmetric synchronized anti-phase (mode IX), or irregular (mode IV). For gap ratio larger than 4, only synchronized anti-phase mode was observed under the conditions of this study. In the two vortex streets regime, shedding frequency is higher than that of a single cylinder, due to stronger gap flow than that in the freestream side. The impact of gap ratio and Reynolds number on the drag and lift forces was also studied.2

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“…As to square cylinders, Burattini and Agrawal computed the two-dimensional flow field around two side-by-side square cylinders while the lateral separations between the cylinders T/D ranges from 0.5 to 6. Three regimes are measured during the varying of intervals, in-phase, inantiphase and quasi-periodic, which has been confirmed by experiment [13]. Supradeepan classified the flow pattern more minutely.…”

Section: Introductionmentioning

confidence: 64%

Flow Features of Three Side-by-side Circular Cylinders at Low Reynolds Number

et al. 2016

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Abstract. In order to study the fluctuation of kinetic parameter of cylinder matrix in incompressible stationary flow, the flow fluid around three side-by-side circular cylinders are simulated using Immersed BoundaryLattice Boltzmann method (IB-LBM). Drag and lift force of the three cylinders are investigated as the interval between each cylinder varied from zero to five times of the cylinder diameter. Five flow patterns are defined according to the vortices structure in the downstream of the cylinders. Power spectrum analysis of lift force is developed to explain the vortex patterns. Through the research, we find the strength and phase of the gap flow play an important role in the vortex formatting process. The vortices shedding from different cylinders neutralize and combine in the near wake, contributing a lot to the variation of forces.

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Wake interaction between two side-by-side square cylinders in channel flow

Cited by 65 publications

References 40 publications

Nonlinear interactions between the two wakes behind a pair of square cylinders

Nonlinear interactions between the two wakes behind a pair of square cylinders

Wake of two side-by-side square cylinders at low Reynolds numbers

Flow Features of Three Side-by-side Circular Cylinders at Low Reynolds Number

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