Vorticity forces on an impulsively started finite plate

• Published in: Journal of fluid mechanics Vol. 694; pp. 464 - 492
• Main Authors: Lee, Jian-Jhih, Hsieh, Cheng-Ta, Chang, Chien C., Chu, Chin-Chou
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.03.2012
• Subjects: Aerodynamics; Applied fluid mechanics; Applied sciences; Aspect ratio; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Flow control; Fluid dynamics; Fluid flow; Fluid mechanics; Fundamental areas of phenomenology (including applications); Mathematical analysis; PFA; Physics; Reynolds number; Robotics; Vortices; Vorticity; Wing tip vortices; aerodynamics; swimming/flying; Wing; Biomimetics; Three dimensional flow; Unmanned aerial vehicle; Wing beat; Vorticity; Theoretical study; Aerodynamics; Mobile robots; Miniaturized design; Robotics; Theft
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2011.563

In this study, we consider various contributions to the forces on an impulsively started finite plate from the perspective of a diagnostic vorticity force theory. The wing plate has an aspect ratio (AR) between 1 and 3, and is placed at low and high angles of attack ($\ensuremath{\alpha} \leq $ and ${\gt }2{0}^{\ensuremath{\circ} } $), while the Reynolds number is either 100 or 300. The theory enables us to quantify the contributions to the forces exerted on the plate in terms of all of the fluid elements with non-zero vorticity, such as in the tip vortices (TiVs), leading- and trailing-edge vortices (LEV and TEV) as well on the plate surface. This line of force analysis has been pursued for two-dimensional flow in our previous studies. In contrast to the pressure force analysis (PFA), the vorticity force analysis (VFA) reveals new salient features in its applications to three-dimensional flow by examining sectional force contributions along the spanwise direction. In particular, at a large aspect ratio ($\mathit{AR}= 3$), the force distributions of PFA and VFA show close agreements with each other in the middle sections, while at a lower aspect ratio ($\mathit{AR}= 1$), the force distribution of PFA is substantially larger than that of VFA in most of the sections. The difference is compensated for by the contributions partly by the edge sections and mainly by the vortices in the outer regions. Further investigation is made fruitful by decomposing the vorticity into the spanwise (longitudinal) component (the only one in two-dimensional flow) and the other two orthogonal (transverse) components. The relative importance of the force contributions credited to the transverse components in the entire flow regions as well as in the two outer regions signifies the three-dimensional nature of the flow over a finite plate. The interplay between the LEV and the TiVs at various time stages is shown to play a key role in distinguishing the force contributions for the plate with a smaller aspect ratio and that with a larger aspect ratio. The present VFA provides a better perspective for flow control by relating the forces directly to the various sources of vorticity (or vortex structures) on or near the wing plate.