Three-Dimensional Laminar-Separation Bubble on a Cambered Thin Wing at Low Reynolds Numbers

Abstract

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

Force Variations Related to Flow Pattern Changes Around a High-Camber Thin Wing

“…However, the present PIV measurements do not allow for accurately determining the occurrence of separation at the leading edge, and this would need further investigation and refined measurements around the leading edge. Moreover, this jump in C L resembles the one observed by Chen et al [26] on a slightly cambered plate with rounded nose at low Re. Their simulations, consistent with experimental results from Pelletier and Muller [27] show a sudden jump in C L (increased slope) at 5°a ngle of attack associated to the growth of a laminar separation bubble.…”

Negative lift characteristics of NACA 0012 aerofoil at low Reynolds numbers

“…C l agrees well with the experimental results till about a ¼ 8 , indicating a validation of the present computational procedure. The difficulties in achieving good agreement between experiments and computations at low to moderate Re are discussed in [3], while in particular, the disagreement observed at high angles of attack is discussed in [9]. Several interesting observations can be made from the lift characteristic curve: non-linear lift curve, negative C l at low angles of attack (a 1 ), recovery from negative C l and sudden change of slope in C l -a curve at a ¼ 3 and 9 .…”

Experimental and numerical studies of low aspect ratio wing at critical Reynolds number

“…Wicox [9] accurately described several transitional boundary layers and nonlinear growth of flow instability using the k-ω two-equation turbulence model. Chen et al [10] predicted the formation and suppression of LSBs caused by 3-D effects on a cambered thin wing with the AR of 6 at low Reynolds numbers using the k-ω shear-stress transport model. Experimentally, Bastedo and Muellert [11] determined the location of LSB through measuring the pressure distribution of Wortmann FX 63-137 wings with AR of 2.…”