Mechanics Research Communications 37 (2010) 432–435 Contents lists available at ScienceDirect Mechanics Research Communications journal homepage: www.elsevier.com/locate/mechrescom Drag reduction over embedded cavities in Couette flow A.W. Lang ∗ , T.J. Johnson Aerospace Engineering & Mechanics, University of Alabama, Tuscaloosa, AL 35487, United States article info Article history: Received 24 February 2010 Received in revised form 23 April 2010 Available online 4 May 2010 Keywords: Couette flow Drag reduction Cavity flow Low Reynolds number abstract Using a newly developed Couette flow facility with high viscosity oil as the working fluid, drag mea- surements over a patterned surface consisting of two-dimensional square embedded cavities orientated transversely to the main flow were experimentally obtained. Drag data was then compared to that obtained over a flat plate. Results show that for Re < 15 (where Re is based on the gap height) an appre- ciable drag reduction of >5% is obtained. This reduction, known as the “roller bearing effect”, is due to the formation of embedded vortices within the cavities. Also, as the Re decreases the theoretical Stokes limit of 18% drag reduction is approached. © 2010 Elsevier Ltd. All rights reserved. 1. Introduction Drag reduction via altering the no-slip condition, often achieved through micro-geometries or micro-patterning which can trap fluid, is a topic that has received attention over the years and is first attributed to Girard (Goldstein, 1938; Priezjev and Troian, 2006). Most recently, Ou and Rothstein (2005) and Daniello et al. (2009) have experimentally demonstrated that using a hydrophobic sur- face, and trapping air inside micro-grooves aligned parallel to the flow, appreciable drag reduction can be achieved under both lami- nar and turbulent channel flow conditions where the main fluid is liquid. They argue that this drag reduction benefit is greater than if the channel height was only increased, and realize the poten- tial benefit as well to external flows. However, this application is limited to liquid flows and the application of a similar concept, con- sisting of a slip boundary condition, for gas flows would be useful for air applications. This would have potential applications to micro-air vehicles as well as micro-fluidic applications in gases. This work has focused on achieving sub-laminar drag via pat- terning a surface with transverse, square grooves with walls of minimum thickness. As the flow passes over a single groove, an embedded cavity vortex is formed allowing the outer flow to pass over the cavities (see Fig. 1). The no-slip condition is only imposed on the flow at the tops of the minimally thick walls, and as the flow passes over the embedded vortex a partial slip condition is imposed on the outer flow. Additionally, the flow reversed in the cavity imposes a shear stress at the bottom of the cavity which acts as a small thrust adding to the net reduction in drag for the surface. ∗ Corresponding author. E-mail address: alang@eng.ua.edu (A.W. Lang). This is a concept first proposed by Bushnell (1983) and was termed the “roller bearing effect”. However, the concept was proven not to result in drag reduction for higher Reynolds number turbulent flows due to the injection/ejection of fluid into/out of the cavities (Savill, 1988). The results herein presented are the first to exper- imentally demonstrate that drag reduction via the “roller bearing effect” is possible provided laminar flow is maintained. In the case where Re = Uh/, an appreciable (>5%) sub-laminar drag is achiev- able for Re < 15 for two-dimensional square embedded cavities. The current results provided by the authors are the first to pro- vide data that bridges the Re gap between the analytical results associated with the Stokes limit (Re → 0) and higher Re numeri- cal results. First, Gatski and Grosch (1985) studied drag reduction numerically over a single, square cavity immersed in a laminar boundary layer. They computationally examined how changing the ratio of the size of a square cavity, l, to the boundary layer thick- ness, ı, affected the drag and compared it to a flat plate for a Re ı ∼ 1200. This study found that at higher cavity Re (here Re = Ul/ and varied from 300 to 1200), the cavity vortex moved towards the downstream side of the cavity. This asymmetry increased the net pressure drag on the cavity with a corresponding decrease in drag reduction. However, over the four cases studied they calculated a net drag reduction of 1–2% as compared to a flat plate. They did not investigate a series of cavities with minimum wall thickness, but postulated that higher drag reduction was indeed possible under such a scenario. Next, Wang (1994, 2003) analytically studied the drag and par- tial slip across a finned plate in a creeping or Stokes flow, Re → 0, under shear flow conditions above the plate. Wang (1994) claimed an increase in drag across the finned plate under Couette condi- tions when compared to a flat plate, where the reference drag was that due to flow in a gap over a flat plate with no fins. This is true 0093-6413/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechrescom.2010.04.011