Intrinsic features of flow past three square prisms in side-by-side arrangement

Abstract

An investigation on the flow around three side-by-side square prisms can provide a better understanding of complicated flow physics associated with multiple, closely spaced structures in which more than one gap flow is involved. In this paper, the flow around three side-by-side square prisms at a Reynolds number $Re=150$ is studied systematically at $L/W=1.1{-}9.0$, where $L$ is the prism centre-to-centre spacing and $W$ is the prism width. Five distinct flow structures and their ranges are identified, viz. base-bleed flow ($L/W<1.4$), flip-flopping flow $(1.4<L/W<2.1)$, symmetrically biased beat flow $(2.1<L/W<2.6)$, non-biased beat flow $(2.6<L/W<7.25)$ and weak interaction flow $(7.25<L/W<9.0)$. Physical aspects of each flow regime, such as vortex structures, vortex dynamics, gap-flow behaviours, shedding frequencies and fluid forces, are discussed in detail. A secondary (beat) frequency other than the Strouhal frequency (primary frequency) is observed in the symmetrically biased and non-biased beat flows, associated with the beat-like modulation in $C_{L}$-peak or amplitude, where $C_{L}$ is the lift force coefficient. Here we reveal the generic and intrinsic origin of the secondary frequency, establishing its connections with the phase lag between the two shear-layer sheddings from the two sides of a gap. When the two sheddings are in phase, no viscous force acts at the interface (i.e. at the centreline of the gap) of the two sheddings, resulting in the largest fluctuations in streamwise momentum, streamwise velocity and pressure; the maximum $C_{L}$ amplitude thus features the in-phase shedding. Conversely, when the two sheddings are antiphase, a viscous force exists at the interface of the two sheddings and restricts the momentum fluctuation through the gap, yielding a minimum $C_{L}$ amplitude. When the phase relationship between the two sheddings changes from in phase to antiphase, the extra viscous force acting at the interface becomes larger and causes the $C_{L}$ amplitude to change from a maximum to a minimum.