Computational Fluid Dynamics Study of Three-Dimensional Dynamic Stall of Various Planform Shapes A. Spentzos, * G. N. Barakos, † K. J. Badcock, ‡ B. E. Richards, § F. N. Coton, ¶ and R. A. McD. Galbraith ¶ University of Glasgow, Glasgow, G12 8QQ Scotland, United Kingdom and E. Berton ** and D. Favier †† Laboratoire d’Aérodynamique et de Bioméchanique du Mouvement, 13288 Marseille Cedex 9, France DOI: 10.2514/1.24331 Numerical simulation of 3-D dynamic stall has been undertaken using computational fluid dynamics. As a first step, validation calculations have been performed for cases in which experimental data were available. Although the amount and quality of the experimental data available for 3-D dynamic stall does not match what is available for 2-D cases, the computational fluid dynamics was found capable of predicting this complex 3-D flow with good accuracy. Once confidence on the computational fluid dynamics method was established, further calculations were conducted for several wing planforms. The calculations revealed the detailed structure of the 3-D dynamic stall vortex and its interaction with the tip vortex. Remarkably, strong similarities in the flow topology were identified for wings of very different planforms. Nomenclature C L = lift coefficient, L=2SU 2 1  C p = pressure coefficient, p  p 1 =2U 2 1  c = chord length of the aerofoil d = distance along the normal to chord direction k = reduced frequency of oscillation, !c=2U 1  L = lift force p = pressure Re = Reynolds number, U 1 c= S = planform area t = nondimensional time U 1 = freestream velocity u = local streamwise velocity x, y, z = coordinate directions  = instantaneous incidence angle  0 = mean incidence angle for oscillatory cases  1 = amplitude of oscillation   = nondimensional pitch rate, _ c=U 1 _  = pitch rate  = dynamic viscosity  = density  1 = density at freestream  = phase angle ! = angular frequency I. Introduction T HE phenomenon of dynamic stall (DS) is central in rotorcraft aerodynamics and has so far been investigated by various authors. A review up to 1996 of all computational fluid dynamics (CFD) efforts related to DS has been provided by Ekaterinaris et al. [1] and Ekaterinaris and Platzer [2]. Since then, several papers on DS have appeared in the literature [3] and the reader could consult the recent paper by Barakos and Drikakis [4] for an update. A literature survey indicated that since 1995 only three CFD investigations attempted to make the step from 2-D to 3-D simulation of DS with little evidence of success. Newsome [5] focused on the laminar flow regime and attempted to simulate the experiments of Schreck and Helin [6]. Newsome’s work predicted the 3-D dynamic stall vortex (DSV) but provided very little information regarding the interaction of this vortex with the tip vortex of the wing. This interaction, as we will show in this work, is important. The work by Morgan and Visbal [7] considered the oscillatory motion of a square wing at laminar flow conditions with end plates at both tips. The objective was to approximate the conditions inside a wind tunnel with the model spanning the test section and was focused on the development of vorticity near the wing surface. The work of Ekaterinaris [8] is the most recent in 3-D DS but to a great extend deals with 2-D configurations, and the 3-D problem is provided as a demonstration of the capabilities of CFD. Regardless of the lack of CFD investigations, experimental works on 3-D DS were more successful. Table 1 provides a summary of all works the authors have identified in the literature, along with the flow conditions, measured quantities, and experimental techniques. One cannot fail to notice that pressure measurements dominate, whereas flow visualization and velocity profile measurements are rare. In addition, no measurements have been conducted for high aspect ratio (AR) wings or twisted wings, and data for DS of rotating blades are inexistent. It is evident from Table 1 that all experimental effort is so far devoted to the study of the fundamental unsteady aerodynamics problem of DS. In the present work two objectives have been set: 1) to validate a CFD method for 3-D DS and 2) to investigate the flow topology during the evolution of 3-D DS over various wing planforms. The Presented as Paper 2005-1107 at the 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13 January 2005; received 29 March 2006; revision received 7 August 2006; accepted for publication 7 August 2006. Copyright © 2007 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0021-8669/07 $10.00 in correspondence with the CCC. * Postgraduate Student, CFD Laboratory, Department of Aerospace Engineering. † Senior Lecturer, CFD Laboratory, Department of Aerospace Engineering; currently Department of Engineering, University of Liverpool, Liverpool, L69 3GH England, U.K.; g.barakos@liverpool.ac.uk (Corresponding Author). ‡ Reader, CFD Laboratory, Department of Aerospace Engineering. § Professor, CFD Laboratory, Department of Aerospace Engineering. ¶ Professor, Low Speed Aerodynamics Group, Department of Aerospace Engineering. ** Professor. †† Research Director. JOURNAL OF AIRCRAFT Vol. 44, No. 4, July–August 2007 1118