Abstract
Two-dimensional incompressible Navier-Stokes equations are numerically solved using the high resolution spectral element method at Reynolds number 200. The flow between three cylinders in an equilateral-triangular arrangement is investigated. The center-to-center spacing distance ratio between two circular cylinders is varied from 1.5 to 12. Present numerical results show that the flow patterns and force characteristics are the result of the combined effects of Reynolds number, spacing distance, configuration arrangement, and incident angle. For the small spacing distance ratio of 1.5, the well-known biased flow phenomenon in the gap of downstream cylinders is found. And the biased flow is bistable in our study but not monostable. A small spacing distance means lower Strouhal number, drag, and root-mean-square lift coefficients. In the medium spacing distance ratio of 4.0, the suppressed effect of vortex shedding for the presence of the side-by-side downstream cylinders disappeared. Mean drag coefficients of downstream cylinders are basically identical to the value of flow past around a single circular cylinder. For the large spacing distance ratio of 8.0, the effects between three cylinders basically disappeared. The mean drag and lift coefficients, root-mean-square lift coefficients, and Strouhal number of three cylinders are essentially equivalent to those values of a single circular cylinder.
Highlights
Flows around circular cylinders are widespread among the modern industrial production and engineering practice, such as landing gear systems, heat exchanger tubes, offshore platforms pillar groups, and nuclear reactors
In order to validate the exponential convergence rate of the numerical scheme, we consider the two-dimensional Kovasznay flow in a rectangular area Ω = [−0.5, 1] × [−0.5, 1.5]. This flow problem is a good test for the algorithm because an analytical closed form solution exists for the incompressible flow field
It is of interest that we find the biased flow is bistable in our study, but not monostable in literatures [7, 16]
Summary
Flows around circular cylinders are widespread among the modern industrial production and engineering practice, such as landing gear systems, heat exchanger tubes, offshore platforms pillar groups, and nuclear reactors. Barros et al [8] presented the convective laminar flow and heat transfer of three cylinders in a triangular arrangement at Re = 100, Prandtl number Pr = 0.71 using finite volume method. Wu [10] using the secondorder immersed boundary method carried out the numerical simulation of three equilateral-triangular array cylinders with different incident angle. All the above researches showed that the flow patterns and force characteristics are the results of the combined effect of Re, spacing distance, configuration arrangement, and incident angle. Numerous numerical algorithms have been used to solve the flow around cylinders, such as finite volume method, finite element method, immersed boundary method, spectral method, and meshless method. More details can be obtained from the literatures [20, 24, 25]
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