Flow Around Three Square Prisms At A Low Reynolds Number

Slender engineering structures are frequently arranged in groups,for example,high-rise buildings,chimney stacks,tube bundles in heat exchangers,bridge piers,electronic component on board and offshore platforms,etc.An investigation on the flow around three square prisms in side-by-side and tandem arrangements can provide a better understanding of complicated flow physics associated with multiple closely spaced structures.It,therefore,bears significance in both fundamental research and practical applications.For the flow around multiple cylinders/prisms,the two-dimensional simulation at a low Reynolds number has been adopted in many articles.The results at a low Re can provide a clear picture of the wake,including vortex formation and interaction,phase lag between vortex sheddings,evolution process of vortex streets,etc.The results at a lower Re are thus useful to understand the flow physics at a high Re but cannot be directly extrapolated to a high Re flow.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 center-to-center 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 behaviors,shedding frequencies,and fluid forces,are discussed in detail.A 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 CL-peak or amplitude,where CL is the lift force coefficient.Here we reveal the generic and intrinsic origin of the beat 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 inphase,no viscous force acts at the interface(i.e.,at the centerline of the gap)of the two sheddings,resulting in largest fluctuations in streamwise momentum,streamwise velocity,and pressure;the maximum CL amplitude thus features the inphase 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,begetting a minimum CL amplitude.When the phase relationship between the two sheddings changes from inphase to antiphase,the extra viscous force acting at the interface gets larger and causes the CL amplitude altering from a maximum to a minimum.A numerical investigation on the flow around three tandem square prisms at Re = 150 is conducted for L/W = 1.2 ~ 10.0.Extensive analyses are done of flow structures,Strouhal numbers St,fluid forces and vorticity,velocity,and pressure fields.Four distinct flow regimes and their ranges are identified,viz.,single bluff-body flow(regime I,L/W < 3.0),alternating reattachment flow(regime II,3.0 < L/W < 4.3),synchronized coshedding flow(regime III,4.3 < L/W < 7.3)and desynchronized coshedding flow(regime IV,7.3 < L/W ? 10.0).Regime III is further subdivided into two regimes: single St flow(regime IIIA,4.3 < L/W < 5.1)and dual St flow(regime IIIB,5.1 < L/W < 7.3).The dependence on L/W of fluctuating and time-averaged fluid forces,and St of the three prisms in each regime is studied in detail and connected to the flow structures.A secondary vortex street following the primary vortex street is observed for regimes IIIB and IV.The detailed physics of the evolution of the primary vortex street to the secondary is imparted.The inherent frequency associated with the secondary vortex street is smaller than that with the primary.The evolution process of the primary vortex street to the secondary leads to a tertiary frequency.The DMD(dynamic mode decomposition)analysis is proposed for the first time as a useful and quantitative tool to identify and quantify the secondary vortex street and its onset position.The DMD method is a data processing algorithm to extract the coherent structures at a unique frequency and an individual growth/decay rate from an experimental or numerical data sequence.The onset position of the secondary vortex street corresponds to the local maximum vorticity amplitude for DMD mode associated with the secondary frequency.