Vortex Shedding from Airfoils in Reverse Flow

Abstract

The vortex shedding characteristics of three airfoils held at static angles of attack through 360 deg are presented with a focus on reverse flow (150 ≤ α ≤ 180 deg). Wind tunnel testing was performed on one airfoil with a sharp trailing edge (NACA 0012) and two airfoils featuring a blunt trailing edge (ellipse and DBLN-526). Time-resolved particle image velocimetry and smoke flow visualization were used to identify three reverse flow wake regimes: slender body vortex shedding, turbulent, and deep stall vortex shedding. The slender body regime is present for low angles of attack and low Reynolds numbers. In the turbulent regime, separation occurs in reverse flow at the sharp aerodynamic leading edge of a NACA 0012, whereas flow separation occurs further down the chord of airfoils with a blunt geometric trailing edge. The deep stall vortex shedding frequency was measured using unsteady force balance measurements. The Strouhal number St d (based on the projected diameter d of the airfoils) was found to be 0.145-0.161 for 45 ≤ α ≤ 135 deg, which is well below the value of St d 0.19 for a corresponding cylinder. The results of the work presented here provide fundamental insight for rotor applications where flow separation and vortex shedding due to reverse flow can lead to unsteady loading, vibrations, and fatigue. Nomenclature = aspect ratio c = airfoil chord, m D u = component of drag force (measured from upper force balance), N d = diameter or projected diameter, m f St = Strouhal frequency, Hz f s = sampling frequency, Hz f vs = vortex shedding frequency (unforced), Hz f = deviation from calculated vortex shedding frequency, % k = scalar used in fast Fourier transform analysis N = signal length n = number of points used in n-point fast Fourier transform analysis Q = peak ratio t∕c = airfoil thickness-to-chord ratio t max = duration of a sample size, s U ∞ = freestream velocity, m∕s α = angle of attack, deg α rev = reverse flow angle of attack α ds rev = minimum angle for which the deep stall vortex shedding regime is present, deg α sb rev = maximum angle for which the slender body vortex shedding regime is present, deg Γ 1;2 = scalar vortex identification algorithm Δf = frequency resolution, Hz ω = vorticity, 1∕ŝ ω x o ∕c = sum of vorticity at station x o ∕c, 1∕s

Unsteady airloads on static airfoils through high angles of attack and in reverse flow

“…The flow over stalled airfoils at high angles of attack and in reverse flow is unsteady and can be either aperiodic or periodic [18]. In light of this unsteady behavior, it is important to verify that values calculated from time-resolved pressure measurements (e.g., time-averaged and unsteady pressures and airloads) have reached a reasonable convergence.…”

“…The unsteady wake of an airfoil in reverse flow can be categorized into one of three flow regimes [18]. The first regime, slender body vortex shedding, occurs at low angles of attack and is characterized by bluff body vortex shedding from a blunt aerodynamic trailing edge.…”

Study on the Mechanism of the Variable-Speed Rotor Affecting Rotor Aerodynamic Performance

“…In Figure 5, the value of the DPL during hover is not sensitive to variation in the rotor speed, which means an increasing η i occurs as rotor speed decreases. From Equation (33), it is known that the induced power is affected by both the value and distribution of the induced inflow and the thrust. If it is assumed that the induced inflow and thrust are uniform, the result given by Equation (33) matches the actuator disc theory.…”

“…From Equation (33), it is known that the induced power is affected by both the value and distribution of the induced inflow and the thrust. If it is assumed that the induced inflow and thrust are uniform, the result given by Equation (33) matches the actuator disc theory. Figure 12 shows the time history of the airfoil coefficient during hover.…”

“…Bowen-Davies and Chopra [31], Lind [32] and Lind and Jones [33][34][35][36] found through a series of simulation and experimental studies on the large advance ratio flight, that Leishman-Beddoes dynamic stall modeling can give a reasonable prediction of the reversal flow within the regular advance ratio (µ < 0.4). However, the modeling is not capable of giving a reasonable prediction when µ > 0.7.…”