On the drag of two-dimensional flow about a normal flat plate

Abstract

An experimental investigation of the twodimensional(2-D) flow normal to a flat plate at low to medium Reynolds numbers (ranging from 25 to 393 based on the breadth of the plate) is described. Both horizontal and vertical soap film tunnels are used to set up a truly experiment. The flow in the soap film is very thin and is a close approximation to flow. Momentum defect measurements are used to obtain the time averaged mean drag coefficient, cl, experienced by a normal flat plate via laser Doppler velocimetry. It is found that cl = 2.1 for the current Re range. The present data agree well with available nominally experimental results from previously published papers which were obtained in traditional towing tank, wind tunnel and water tunnel experiments with high plate aspect ratios. This measurement implies that the intrinsic 3-D motions in the previously nominally experiments are not significant on cl and the computational fluid dynamics results from previously published papers which are reviewed have overestimated cl. Introduction Bluff body flows are by nature very complex. Inevitably they involve boundary layer, free shear layer and wake flows, all accompanied by associated instabilities and non-linear interactions with each other and with the bluff body itself. Bluff body wake flows have direct engineering significance. The alternate shedding of vorticies in the near wake, in the classical vortex street configuration, leads to large fluctuating pressure forces in a direction some cases can trigger failure. A normal flat plate is in many ways the simp* Associate Professor, Department of Mechanical Engineering , Member AIAA ** Graduate Research Assistant, Department of Mechanical Engineering Copyright O 1998 by the American Institute of Aeronautics and Astronautics Inc . All right reserved. lest possible bluff body, since it has geometrically fixed separation points, and since the interaction between the body and the near wake formation region is minimized. However, in comparison to the bulk of contemporary literature dealing with circular cylinder flows, very few results have been published for normal flat plates. Of the normal flat plate results which are available, typically Strouhal shedding frequency, force and/or pressure coefficients are presented only as time averaged mean quantities. Lisoski' has reviewed published experimental and computational results for time averaged mean drag coefficient, cT, and Strouhal number, St, of nomianlly noraml flat plates extensively. The main thing to note about the reviewed results is the large difference in cT between the experimental results( typically c7 = 2.0 ) and the numerical models( typically c7 = 3.2 ),which in some cases have a drag of almost twice the experimental values. There has been a tendency to think of these truly computer models as being wrong, and to modify them by various means so that their results conform with 2-D experiments which are indeed threedimensional. As has been noted by Lisoski, is the wrong approach. He then went on investigating the intrinsic( small scale ) and extrinsic( large scale ) 3-D motions in the towing tank and water channel experiments. A vortex element numerical model developed by Chua was also used for comparison with his experimental results. It is shown that agreement between normally experimental and numerical-model results is good at early times, indicating the experiments are until the breakdown of the closed wake bubble following the initial accerlation. The approach of this paper is different. A truly experiment is conducted to have a direct comparison with the previously numerical results on cl. Freely suspended flowing soap films are used to set up the truly flows. These films, which have a thickness of the order of a micron, offer an excellent opportunity for studying hydrodynamics American Institute of Aeronautics and Astronautics Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.