Experiments in Fluids 33 (2002) 66–74 DOI 10.1007/s00348-002-0458-z
Vortex shedding from tapered plates I.P. Castro, P. Rogers
66 Abstract An experimental study of vortex shedding behind flat plates placed normal to an airstream is presented for Reynolds numbers of O(104). Apart from a parallelsided plate used as the reference case, all the plates were tapered in the spanwise direction so that the cross-stream width of the plate varied linearly with spanwise distance along it. The data allow significant extension of the conclusions of previously published work and demonstrate that ‘‘cellular’’ shedding occurs in many cases. Within each (spanwise) cell, the shedding frequency is constant despite the changing plate width, and it is shown that the location and extent of the cells are functions of the degree of taper, the spanwise aspect ratio and the end conditions. Unlike the corresponding case of tapered cylinders (i.e. cones), the Reynolds number is not normally a dominant parameter.
List of symbols AR spanwise aspect ratio, W/dav Cd drag coefficient d local width of the plate dav average width of the plate between the endplates (or tunnel walls), m do base width of the plate (i.e. at z=0), m dt plate width at the ‘‘far’’ end (i.e. at z/W=1) f shedding frequency, Hz H dimension of the tunnel cross-section normal to the plate symmetry axis, m He splitter plate height (see Fig. 1) L total length of plate (between base, where d=do, and tip, where d=0), m Le, Lf splitter plate dimensions (see Fig. 1)
Received: 25 January 2002 / Accepted: 28 March 2002 Published online: 25 June 2002 Springer-Verlag 2002 I.P. Castro (&), P. Rogers School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK E-mail:
[email protected] Tel.: +44-23-80593394 The experiments would have been impossible without the technical skill of the engineering workshop staff at the Universities of Surrey and Southampton; they are therefore gratefully acknowledged. We are also grateful for help with some of the experiments by a visiting vacation student, Philippe Konieczny, and for useful comments from the referees.
Ls q St Sto TR U Um W b Dq Dz
length of splitter plate (see Fig. 1) upstream dynamic head local Strouhal number, fd/U Strouhal number based on base width, fdo/U taper ratio, 2L/do measured free-stream velocity, m/s corrected free-stream velocity, m/s distance between endplates, m blockage ratio, dav/H blockage constant effective change in upstream dynamic head due to wind tunnel blockage spanwise separation between two points (at the same x,y location)
1 Introduction Vortex shedding from two-dimensional bluff bodies of all kinds is a well-known and much-studied phenomenon and is covered by a vast literature. However, remarkably little attention has been given to bodies which have spanwise taper, thus introducing inherent three-dimensionality into the flow. Intuitively, one expects that if the degree of taper is very small, so that the local body width, d, normal to the flow varies only very slowly with spanwise position (z) then strong vortex shedding will occur as usual. It is less clear how the shedding frequency might vary with z; if it were to vary continuously so that the local Strouhal number, St=fd/U, remained constant, then amongst other changes the (originally spanwise) vortex lines must presumably be inclined, whereas, if it remained constant over a certain span, there would eventually be a significant mismatch between the local diameter and the frequency needed to provide the expected Strouhal number (based on the value for the parallel-sided body), leading to a ‘‘dislocation’’ in the shedding and a jump in shedding frequency. In fact, this latter ‘‘cellular’’ shedding has been clearly demonstrated in the case of low-Reynolds-number flow over very slender cones (Gaster 1969; Papangellou 1992). In those experiments the taper ratio, TR, defined here as the ratio of the total body length (L, from base to tip) to the average width (do/2, where do is the base width) lay in the range 250
