Flow Around A Square Plate At Low Reynolds Numbers

Thin plates,e.g.falling leaves,animal wings,aircraft wings and heave plates in offshore platforms,are widely found and of great significance in nature and industry.The interaction between fluid and thin plates,accompanied with flow separation,vortex shedding and wake transition,has attracted great interests.The inclination of thin plates is found to significantly affect the flow characteristics and wake transition.Here the incidence angle,the angle between the axis of the plate and the incoming flow,is denoted as ?,where ?=0° refers to the condition where the plates is placed normal to the incoming flow.Comparing to the infinite flat plate,the square plate is a more real and common three-dimensional structure.The flow around it is more likely to be complex.However,the study on the flow around square plates is very limited.It is necessary to conduct such a study on the flow around an inclined square plate.The ratio of the side edges length and thickness of square plates is selected as 50,representing a reasonably thin plate.The Reynolds number(Re)and the incidence angle(?)is in the range of[50,350]and[0°,60°],respectively.Extensive numerical simulations of the flow past a square plate using DNS(direct numerical simulation)method are conducted.Firstly,the flow and wake transition behind the square plate placed normal to the flow are simulated.Then,the results of the flow behind the inclined square plate are presented.Here,the conditions where the square plate is inclined about its short symmetry axis and long symmetry axis are simply denoted as IS and IL,respectively.Lastly,the effect of the inclination on the flow is also discussed and comparison of wake transition between a square plate and a circular disk is carried out.When the square plate is fixed normal to the incoming flow,the flow behind it is steady and reflectional symmetric with four symmetry planes at very low Reynolds numbers.After the first regular bifurcation,the number of symmetry planes reduces to one.As the Reynolds number increases,the Hopf bifurcation leads the unsteadiness of the vortex shedding,giving rise to a periodic flow with loss of reflectional symmetry.With further increasing Re,the reflectional symmetry is recovered.Before the flow becomes fully chaotic with loss of symmetry and periodic features,it experiences a quasi-periodic state.Similar wake transition behind a circular disk or a sphere is also observed at low Re in the open literatures.In the considered Re-? parametric space,four flow regimes are observed under condition IS and defined respectively as:(?)steady and planar-symmetric(SP)state,(?)periodic and planar-symmetric(PP)state,(?)quasi-periodic and planar-symmetric(QPP)state and(?)chaotic and asymmetric(CA)state.Under IL condition,also,four flow regimes are observed and defined as:(?)steady and planar-symmetric(SP)state,(?)periodic and planar-symmetric(PP)state,(?)quasi-periodic and asymmetric(QPA)state and(?)chaotic and asymmetric(CA)state.Flow characteristics,including three-dimensional vortical structures,force coefficients,velocity field,etc.are presented.The flow regimes of an inclined square plate,i.e.,SP,PP and CA,have same features under IL and IS condition,but difference exists between QPA and QPP state.Lastly,the effect of the inclination on the wake transition is discussed.The inclination is found to select the exclusive symmetry plane,accelerate the vortex shedding frequency and strengthen the modulation of the low frequency component.The comparison of the flow behind a square plate and a circular disk is discussed.In general,the flow regimes and wake transition behind them is found to be quite similar.