Stall Flutter of a Cascade of Blades at Low Reynolds Number

Abstract

Due to the requirements for high blade loading, modern turbo‐machine blades operate very close to the stall regime. This can lead to flow separation with periodic shedding of vortices, which could lead to self induced oscillations or stall flutter of the blades. Previous studies on stall flutter have focused on flows at high Reynolds number (Re ~ 106). The Reynolds numbers for fans/propellers of Micro Aerial Vehicles (MAVs), high altitude turbofans and small wind turbines are substantially lower (Re < 105). Aerodynamic characteristics of flows at such low Re is significantly different from those at high Re, due in part to the early separation of the flow and possible formation of laminar separation bubbles (LSB). The present study is targeted towards study of stall flutter in a cascade of blades at low Re. We experimentally study stall flutter of a cascade of symmetric NACA 0012 blades at low Reynolds number (Re ~ 30, 000) through forced sinusoidal pitching of the blades about mean angles of incidences close to stall. The experimental arrangement permits variations of the inter‐blade phase (σ) in addition to the oscillation frequency (f) and amplitude; the inter‐blade phase angle (σ) being the phase difference between the motions of adjacent blades in the cascade. The unsteady moments on the central blade in the cascade are directly measured, and used to calculate the energy transfer from the flow to the blade. This energy transfer is used to predict the propensity of the blades to undergo self‐induced oscillations or stall flutter. Experiments are also conducted on an isolated blade in addition to the cascade. A variety of parameters can influence stall flutter in a cascade, namely the oscillation frequency (f), the mean angle of incidence, and the inter‐blade phase angle (σ). The measurements show that there exists a range of reduced frequencies, k (=πfc/U, c being the chord length of the blade and U being the free stream velocity), where the energy transfer from the flow to the blade is positive, which indicates that the flow can excite the blade. Above and below this range, the energy transfer is negative indicating that blade excitations, if any, will get damped. This range of excitation is found to depend upon the mean angle of incidence, with shifts towards higher values of k as the mean angle of incidence increases. An important parameter for cascades, which is absent in the isolated blade case is the inter‐blade phase angle (σ). An excitation regime is observed only for σ values between ‐450 and 900, with the value of excitation being maximum for σ of 900. Time traces of the measured moment were found to be non‐sinusoidal in the excitation regime, whereas they appear to be sinusoidal in the damping regime. Stall flutter in a cascade has differences when compared with an isolated blade. For the cascade, the maximum value of excitation (positive energy transfer) is found to be an order of magnitude lower compared to the isolated blade case. Further, for similar values of mean incidence angle, the range of excitation is at lower reduced frequencies for a cascade when compared with an isolated blade. A comparison with un‐stalled or classical flutter in a cascade at high Re, shows that the inter‐blade phase angle is a major factor governing flutter in both cases. Some differences are observed as well, which appear to be due to stalled flow and low Re.