Effects of Planform Geometry and Pivot Axis Location on the Aerodynamics of Pitching Low Aspect Ratio Wings

Abstract

We consider aerodynamic forces and flow development for several wing planforms with the same aspect ratio (AR = 4) and mean chord, undergoing a constant-rate pitch change between 0 and 45º. The wing planforms studied are rectangular, trapezoidal and triangular, which correspond to taper ratios 1, 0.5 and 0, respectively. Three pivot axes are considered: leading edge, mid chord and trailing edge. The reduced pitch rate based on chord and free stream speed is K = 0.39 and the Reynolds number is Re = 8.9k. We consider also the case K = ∞ with the same rotation rate as the other cases and zero free stream velocity. Noncirculatory effects are found for leading edge and trailing edge pivot axes, and absent for mid-chord pivot for all wing planforms. The lift and drag coefficients during the constant pitch rate part of the motion increase as the taper ratio decreases due to rotation rate effects, which is contrary to steady flow behavior in which lift and drag coefficients are only functions of aspect ratio, independent of wing planform geometry. Lifting-line theory including rotation rate effects gives reasonable estimation of lift. Flow visualization show primarily 2D flow during the pitch-up motion. The three-dimensional swirl flow in the wake due to tip vortices is observed after the end of the pitch motion. It develops faster for lower tapper ratio wings. OH 45433-7542, Michael.Ol@wpafb.af.mil, AIAA Associate Fellow Downloaded by KUNGLIGA TEKNISKA HOGSKOLEN KTH on July 27, 2015 | http://arc.aiaa.org | Nomenclature AR = physical aspect ratio (=2), 2 / bS , m AR eff = effective aspect ratio, 2*AR , m b = wing wetted span, 2*c, m C D = drag coefficient, 2*D/U  S, 1 C L = lift coefficient, 2*L/U ∞ S, 1 c = wing mean chord (=5.08cm), m c t = wing tip chord, m c r = wing root chord, m D = drag force, N e = relaxation coefficient, 1 F A = axial force, N F N = normal force, N Fx = X component of force in sensor frame of reference, N Fy = Y component of force in sensor frame of reference, N h = hold parameter, 1 K = reduced pitch rate, /2 m K c U     , 1 L = lift force, N  = kinematic viscosity, m 2 /s Re = Reynolds number, / cU   , 1 S = wing wetted area, * bc , m 2 St = Stoke's number, 2 / m c   , 1 s = start parameter, 1 t 1 = point in time when a wing starts to pitch-up in an unsmooth motion trace, s t 2 = point in time when a wing starts to hold in an unsmooth motion trace, s t 4 = point in time when a wing starts to return in an unsmooth motion trace, s t 3 = point in time when a wing returns back to initial position in an unsmooth motion trace, s t c = convective time, c/U ∞ , s t p = pitch time, / mm   , s U ∞ = free-stream velocity, m/s () t  = angle of attack in time, deg m  = maximum angle of attack, deg () t  = pitch rate in time, deg/s m   = maximum pitch rate, deg/s m   = maximum pitch acceleration, deg/s 2

Direct Force Measurements During Transient Flow about Pitching Flat Plates

“…However, both trapezoidal and triangular wings give close steady forces. Similar behaviors are also reported by [8] for pitching wings at a constant rate. Figure 16 shows the ratio of lift coefficient to drag coefficient as a function of angle of attack.…”

“…The wing was mounted on the water channel by fastening it to a force sensor through a sensor adapter plate and a rod clamped to the rotary table (see [8] for a description of the installation). The force sensor and rotary table were mounted on a motorized traverse above water channel free surface.…”