Three-dimensional laminar-separation bubbles on a cambered thin wing with an aspect ratio of 6 at a Reynolds number of 60,000 have been investigated by solving the Reynolds-averaged Navier-Stokes equations. The k-ω shearstress transport γ-Re θ turbulence-transition model is used to account for the effect of transition on the laminar separation-bubble development. The aerodynamic forces are compared with the experimental data available for validation. The laminar-separation bubble is shown to evolve in its shape and dimension in both chord and span directions with increasing incidence due to its interaction with the wing-tip flow and the trailing-edge separation. The strongest three-dimensional effects are found at a moderate incidence of 6 deg and at higher incidences beyond 10 deg. Within the incidence range, the two-dimensional airfoil results are not reproduced at any of the span locations, including the symmetry plane, in the three-dimensional wing case. Generally, the chordwise development of the threedimensional laminar-separation-bubble at the symmetry plane is delayed as compared with the two-dimensional laminar-separation bubble. Another noticeable point is the association of a sudden increase in lift-curve slope due to abrupt expansion of the laminar-separation bubble at a certain incidence. This phenomenon is observed in both the two-and three-dimensional cases, but at different incidences. Nomenclature= three-dimensional and two-dimensional drag, respectively, N L, l = three-dimensional and two-dimensional lift, respectively, N L bc ∕c = laminar-separation-bubble length in chordwise direction L bz ∕z = laminar-separation-bubble length in spanwise direction Re c = Reynolds number based on chord S = wing area, m 2 T i = turbulence-intensity level t = thickness, m u ∞ = incoming flow velocity, m∕s X R ∕c = reattachment point X S ∕c = separation point X Tr ∕c = transition point y = distance in wall coordinates z∕c = spanwise location α = incidence/angle of attack, deg γ = intermittency Δu = velocity changes over the length of the bubble Δx = bubble length θ s = momentum thickness at separation μ = molecular viscosity μ t = eddy viscosity v = kinematic viscosity ρ = density τ = wall shear stress ω = specific turbulence dissipation rate
To understand the planform effects on low-Reynolds-number aerodynamic characteristics for micro air vehicles, various cambered thin plate wings were studied by numerical simulations based on Reynolds-averaged Navier-Stokes solutions with transition modeling. Six wing planforms, with the same wing aspect ratio and area, a positive camber at the quarter chord location, and a reflex camber near the trailing edge for longitudinal stability were selected for the study. They include a rectangular wing, four taped wings with the same taper ratio but different leading-edge sweeps, a Zimmerman wing, and an inverse-Zimmerman wing. For validation with available windtunnel experimental data, an investigation of a circular wing planform with a similarly cambered profile is also presented. The results show that the Zimmerman wing planform gives the best lift-to-drag ratio at the design condition, whereas the tapered wing with higher leading-edge sweep produces higher maximum lift. Flow separation and vortical flow structures on the upper wing surface are presented to gain insight into the different aerodynamic characteristics for the different planforms.
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