Session E11: General Fluid Dynamics I

Mechanics of Flow over Wrinkled Surfaces

The surfaces of many plants and animals are covered with a variety of microtextures such as ribs or 3D tubules which can control surface-mediated properties such as skin friction. Inspired by the drag reducing ability of these natural structures, passive drag reduction methods such as microfabricated riblet surfaces have been developed. Microgroove textures on the surface of objects such as hulls and wings which are aligned in the free-stream direction have been shown to reduce drag by 4-8{\%} in flows with zero or mild pressure gradients [1]. We introduce sinusoidal wrinkles as model ribbed surfaces with drag reducing capabilities. Surface wrinkling arises spontaneously as the result of mismatched deformation of a thin stiff coating bound to a thick soft substrate and can be designed over a wide range of length scales. Using numerical modeling we show that wrinkled surfaces can substantially reduce the skin friction coefficient in high Reynolds number laminar flow. We show that this reduction is a result of purely viscous mechanisms through a geometry-mediated increase in the thickness of the boundary layer and retardation of the flow in the interstitial grooves of the textured surfaces. \\[4pt] [1] D. Bechert \textit{et al.}, Experiments in Fluids \textbf{28} (2000)   

Effective Slip and Drag Reduction in Transitional Flow over Superhydrophobic Surfaces

Superhydrophobic surfaces (SHS) have recently attracted attention as a passive technique for reducing drag in both laminar and turbulent flows [1,2]. These surfaces result in a reduced contact area between a liquid and a solid by trapping air between roughness elements [1,3]. The liquid then glides over the pockets of air between the roughness elements, exhibiting hydrodynamic slip [1]. Most studies considering systems involving SHS focus on laminar or low Reynolds number (\textit{Re}) turbulent flow. Turbulence closure models may be useful when considering large \textit{Re} flows and complicated surface topologies of the SHS. This study explores the behavior of the effective slip length and the drag reduction for Newtonian fluids flowing over SHS in the transitional flow regime using computations and both laminar and traditional turbulence models. For \textit{Re} in the range between 1,000 and 5,000, slip length is observed to differ from that for purely laminar or fully developed turbulent flow. The values obtained using popular models for turbulence, such as the standard k-e and the standard k-w models, are compared, and a possible explanation for the observed variance is explored using predictive models, such as that proposed by Fukagata et al. [4]. \\[4pt] [1] Rothstein, JP, \textit{Annu. Rev. Fluid Mech.}, \textbf{42}, 89, 2010; [2] Voronov, R., Papavassiliou, D.V., and L.L. Lee, \textit{Ind. Eng. Chem. Res}., \textbf{47}(8), 2455, 2008; [3] Heck, M.L., and D.V. Papavassiliou, \textit{Chem. Eng. Com.,} \textbf{200}, 919-934 (2013); [4] Fukagata, K., N. Kasagi, P. Koumoutsakos,\textit{. Phys. Fluids}, \textbf{18}, 051703 (2006).   

Direct numerical simulation of flow past superhydrophobic surfaces

Superhydrophobic surfaces trap a discontinuous air layer through their texture which, in addition to changing the apparent contact angle of water drops, also changes the friction coefficient of a continuous water flow. Locally this effect can be represented through a slip coefficient (\textit{e.g.} Lauga \& Stone, \textit{J. Fluid Mech.} 489, 55--77, 2003), or equivalently through an effective displacement of the wall by a distance (different for each different velocity component) comparable to the spacing of the texture. For this reason they are being considered for drag reduction in turbulent flow, more sensitive to this displacement than laminar flow for its intrisic small features. Since the upper limit on texture size imposed by the destruction of the surface-tension-bound air layer eventually constrains the reduction available, to quantify the effect accurately is essential. In its simplest representation, the superhydrophobic surface may be assumed to be flat and composed of alternating patches of no-slip and free-slip wall. Here direct numerical simulations will be presented of turbulent flow past such a surface, and their results compared with those produced by the corresponding effective wall displacement.   

Properties of the Mean Momentum Balance in Polymer Drag Reduced Channel Flow

The redistribution of mean momentum and the underlying mechanisms of the redistribution process in polymer drag reduced channel flow are investigated by employing a mean momentum equation based analysis. The work is motivated by recent studies that showed (contrary to long-held views) that polymers modify the von Karman coefficient, $\kappa$, at low drag reduction, and at some relatively high drag reduction eradicate the inertially dominated logarithmic region. Since $\kappa$ is a manifestation of the underlying dynamical behaviors of wall-bounded flow, understanding how polymers modify $\kappa$ is inherently important to understanding the dynamics of polymer drag reduced flow, and, consequently, the phenomenon of polymer drag reduction. The goal of the present study is to explore and quantify these effects within the framework of a mean momentum based analysis.   

Why bigger may in fact be better... in the context of table tennis

We submit that table tennis is too fast. Because of the high ball velocities relative to the small table size, players are required to act extremely quickly, often exceeding the limits of human reaction time. Additionally, the Magnus effect resulting from large rotation rates introduces dramatically curved paths and causes rapid direction changes after striking the table or paddle, which effectively reduces reaction time further. Moreover, watching a professional game is often uninteresting and even tiring because the ball is moving too quickly to follow with the naked eye and the action of the players is too subtle to resolve from a distance. These facts isolate table tennis from our quantitatively defined ``fun game club,'' and make it less widely appealing than sports like baseball and soccer. Over the past 100 years, the rules of table tennis have changed several times in an effort to make the game more attractive to players and spectators alike, but the game continues to lose popularity. Here, we experimentally quantify the historic landmark equipment changes of table tennis from a fluid dynamics perspective. Based on theory and observation, we suggest a larger diameter ball for table tennis to make the game more appealing to both spectators and amateur players.