22nd Australasian Fluid Mechanics Conference AFMC2020 Brisbane, Australia, 7–10 December 2020 https://doi.org/10.14264/dadeda8 Flow-induced vibrations in cylinder arrays are moderated by convective instabilities N. Hosseini 1 , M.D. Griffith 1 and J.S. Leontini 1 1 Swinburne University of Technology, Hawthorn VIC 3122, Australia Abstract This study investigates the flow in rows of large numbers of cylinders. When the cylinders are fixed in place, we show that the dynamics are dictated by a cascade of regimes - fluctua- tion, vortex shedding, convectively unstable region - that repeat as the flow traverses the row, the convectively unstable regions acting as “event horizons” allowing no information to pass up- stream. For moderate cylinder spacings, we show that these same regimes govern the flow-induced vibration response when the cylinders are elastically-mounted. Keywords Flow-induced vibration; flow stability; wakes. Introduction While the flow past a single cylinder, and that cylinder’s subse- quent flow-induced vibration, has been extensively studied, the flow past groups of cylinders in close proximity is less well un- derstood. This is despite such configurations occurring through- out engineering and nature. The coupling effects between bod- ies, even when only a single extra cylinder is added, give rise to flow-induced vibration phenomena that are not present for the single cylinder, such as wake-induced vibration and wake interference [2, 1, 10]. Here, we present results of flows past moderate numbers of rows of cylinders, both fixed and elastically mounted and free to move in the transverse direction. In the fixed case, we first establish that there is a “cascade” of regimes that occurs, with the flow progressing from periodic fluctuation, to fully-fledged vortex formation and shedding, to a convective two-row struc- ture with progression downstream. This progression is then re- peated, but on a longer wavelength and lower frequency when the two-row structure breaks down into a new periodic fluctu- ation. In the elastically mounted case, we show that similar wake structures can occur which lead to a number of unique flow-induced vibration characteristics. Methodology Computational method Two-dimensional simulations have been conducted using a sharp-interface immersed-boundary method solving the incom- pressible Navier-Stokes equations. The spatial discretisation employs a second-order finite difference scheme. The tem- poral discretisation is done using two-way time-splitting, with second-order schemes used for the advection and diffusion terms. The details of the implementation can be found in Grif- fith and Leontini [4]. For the elastically mounted cases, each cylinder is treated as mounted on a linear spring and free to move in the direction transverse to the freestream flow. Each cylinder has identical diameter, spring stiffness and mass, and is independent. The spacing between subsequent cylinders is also kept constant. The fully-coupled fluid-structure system is solved using a Newmark- β method. Validation for flow-induced vibration problems, in- cluding those involving multiple cylinders, can be found in Grif- fith, Lo Jacono, Sheridan, and Leontini [5]. Boundary conditions for velocity are a constant Dirichlet con- dition imposing a freestream velocity at the upstream and trans- verse boundaries, and a zero-normal-gradient outflow. For pres- sure, a zero-normal-gradient condition is applied at the up- stream and transverse boundaries, with a constant Dirichlet con- dition at the outflow. At the cylinder surfaces, a Dirichlet con- dition for velocity is imposed matching the boundary velocity to the velocity of the cylinder, and a zero-normal-gradient con- dition is imposed for the pressure. Problem setup The cylinders of diameter D are mounted in a straight line that is parallel to the direction of the freestream of velocity U , with the distance between cylinders given by the nondimensional pitch p = x s /D, where x s is the streamwise centre-to-centre spacing between cylinders. The pitch is kept constant at p = 5 through- out this study. The Reynolds number is also kept constant as Re = UD/ν = 200, where ν is the kinematic viscosity. This is high enough to allow complex dynamics, but not so high to completely invalidate the two-dimensional assumption [3]. Our previous studies have also shown the dynamics to be reasonably insensitive to Re [6]. The structural parameters are the nondimensional mass ratio which is kept constant as m ∗ = m/m f = 2.546, where m is the cylinder mass and m f is the mass of the displaced fluid, and the reduced velocity U ∗ = U /( f n D) where f n =  k/m/(2π) is the natural structural frequency in vacuo. The reduced velocity is varied in the range 3  U ∗  12. Results Fixed cylinders showing a cascade of regimes Figure 1 shows the flow structure generated for this setup when only two cylinders are present in the array. The gap between the cylinders is large enough to allow vortex shedding that is essen- tially the same as that from a single cylinder. These vortices impinge on the second cylinder, which then pass over it and form a two-row structure in the wake. This two-row structure is clearly evident in the mean flow, presenting as two elongated, thick, shear layers that are separated by a region of zero vortic- ity. The mean separating streamlines shown in figure 1 show two recirculation regions in the wake of the second cylinder, in- dicating that the region of zero vorticity is also a region of very low velocity. We have analysed the stability characteristics of this mean flow using a quasi-parallel analysis, with the same technique and code as outlined in Leontini, Thompson, and Hourigan [9]. The primary outcome of this analysis is the calculation of a complex frequency at each downstream distance. The imaginary com- ponent of this frequency indicates whether perturbations will grow in place - indicative of absolute instability - or grow as perturbations are washed downstream - indicative of convective