Modeling low-Reynolds-number flow over rough airfoils

Micro air vehicles (MAVs) are a class of unmanned aeronautical vehicles (UAVs) that are characterized by airfoils with small chord lengths that operate at relatively low Reynolds numbers (Re). A particular difficulty encountered in the design of these airfoils is the appearance of laminar separation bubbles in the boundary layer upstream of the turbulence transition point at large angles of attack. This flow regime results in a severe increase in drag and potentially catastrophic drop in lift. For these low-Re flows (100, 000 < Re < 1, 000, 000 based on the chord length), preventing boundary layer separation is a critical factor in airfoil design. One approach is to eliminate the possibility of separation bubble formation by designing the shape of the airfoil such that the boundary layer remains laminar and attached over the entire surface. A significant body of research exists discussing the design of such laminar airfoils (see, for example,). A second approach is to eliminate the possibility of laminar boundary layer separation by moving the turbulence transition point far upstream of the region where separation is expected to occur. Turbulent boundary layers are more robust than their laminar counterparts and tend to better resist boundary layer separation. The tradeoff in forcing early transition, however, is a significant increase in skin friction drag compared to that for a laminar boundary layer. Nevertheless, premature boundary layer transition, or boundary layer “tripping” as it is commonly called, is the preferred solution to the problem of laminar boundary layer separation. In practice, fixed transition strips, “trip-strips,” are commonly employed to do this task, but they limit the flexibility of MAV design around a narrow range of vehicle mission speeds. Transition strips that can be turned on and off, vortex generation devices, and various other separation control technologies have been studied extensively. While such devices can be dynamically controlled to provide some protection against boundary-layer separation, they cannot effectively change the chord-wise location of the turbulence transition point over a broad range of Re and angles of attack. Current transition technologies, either via passive means (i.e. laminar airfoil design) or by prematurely forced transition severely limit the overall design space for the airfoil and subsequent aerodynamic performance. Thomas et. al. have developed a class of porovascular composite (PVC) materials that show promise for eliminating these restrictions by providing a means to dynamically alter the aerodynamic properties of a surface by selectively activating or deactivating roughness elements. The PVC material is a polymer laminate with an internal vascular network that connects to sub-millimeter scale pore arrays at the surface. An ionic liquid is pumped into the vascular network that fills surface pore arrays. Through the use of displacement pumping, capillary forces, and electrode-wetting-on-dielectric (EWOD) phenomena, roughness elements can be raised above the surface (e.g., domes) or held just below the surface (e.g., dimples) and actively controlled. Such roughness elements can be changed during operation to tailor the induced drag and vorticity generation to the specific flow conditions. The effect of surface roughness on boundary layer flow is a subject that is still not completely understood, particularly for the transitional Reynolds number regime in which we are interested. Prior modeling and experiments looking at surface roughness effects on flat plate/airfoil aerodynamics (and heat transfer) have focused on roughness scales below and above PVC sub-millimeter roughness scales. For example, Kithcart