Numerical Simulation of Two-Dimensional Flow over Three Cylinders by Lattice Boltzmann Method

The numerical simulation using the multiple relaxation time lattice Boltzmann method （MRT-LBM） is carried out for the purpose of investigating the two-dimensional flow around three circular cylinders. Among these three circular cylinders, one of the three cylinders on which a forced in-line vibrating is used to do this research and attempt to find out the effects of the moving cylinder and the other two rigid cylinders on the wake characteristics and vortex formation. As a benchmark problem to discuss the problem of lift coefficient r.m.s for these cylinders with spacing ratios T/ D between other rigid side-by-side cylinders, and the calculation is carried out with two compared cases at Reynolds number of 100, two of the cylinders are rigid and the other one is an in-line vibrated cylinder lying downstream, in addition, forced vibrating amplitude and frequency are A/D = 0.5 and fv= 0.4 （where A is the forced amplitude, D is the cylinder diameter, and fv stands for the vibrating frequency, respectively）. The calculated results not only indicate that the spacing ratios T/D （T is the center-to-center spacing between the two upstream cylinders） have influence on the wake patterns and the formation of vortex shedding, but also analyze the lift coefficient r.m.s for the three cylinders with the spacing ratios S/D （where S is the center-to-center spacing between the center of upstream two side-by-side cylinders and downstream cylinder）.

WAKE SHIELDING EFFECTS OF THREE CYLINDERS IN CURRENTS

A large amount of experimental work has been carried out in the past tounderstand mean and fluctuating forces on a single circular cylinder in cross flows. In comparisonsubstantially less work can be found on the interference between multiple cylinders and the numberof publications a-vailable becomes drastically smaller as the number of cylinders involvedincreases. The current experimental work systematically examines the wake shielding effects of threecylinders in a towing tank. Though staggered, the three cylinders are arranged mainly along theflow direction with the downstream cylinders situating in the wakes of the upstream cylinders. Thetests are mainly carried out in the sub-critical Reynolds number regime with the upper end close tothe critical Reynolds number regime. Significant drag reduction on downstream cylinders isidentified.

VORTEX SHEDDING FREQUENCY DETERMINED BY SURFACE PRESSURE FLUCTUATIONS OF THREE EQUISPACED CYLINDERS

In his paper, the frequency of vortex shedding from three cylinders of the same diameter in equilateral triangular arrangement is determined experimentally by the spectrum analysis of surface pressure fluctuations at a Reynolds number of 3.0×10 4. For α=0°, there exists ‘bistable’ flow at the spacing 2.0. For α=30°, the vortex shedding of the front cylinder is found at small spacing less than 2.0. It is quite different from the case of two cylinders in tandem arrangement only. The side cylinder has great effects on the flow between the other two cylinders in close arrangement. For α=60°, there exists a critical spacing of about 2.5 that the frequency of each cylinders is nearly half of f s below this spacing and equal to f s above it respectively. The interference among three cylinders was negligible in the spacing range above 3.0 at α=0 and 60 deg., and each cylinder behaves as a single cylinder with the same vortex shedding frequency f s. In these small spacing (spacing<3.0), interference occurs seriously and has great effects in a complex fashion on the flow state around three cylinders.