Low Reynolds number stall flutter of a linear cascade with large amplitudes at low reduced frequencies: Unsteady loads and flow features

Abstract

In this paper, we report on an experimental investigation of stall flutter of a linear cascade undergoing large amplitude heave oscillations (≈ 10% of chord) at low reduced frequencies (k<0.1) and at low Reynolds number (Re≈50,000). Three blade incidence cases are studied representing light, moderate, and deep stall conditions of the cascade. Simultaneous measurements of energy transfer to the blade using a load cell, and flow field measurements using Particle Image Velocimetry (PIV) are carried out while the blades in the cascade are allowed to perform large amplitude heaving oscillations at the prescribed reduced frequency (k) and Inter Blade Phase angle (σ). The resulting normalized energy transfer values (CE¯) indicate that the cascade becomes unstable at low k values for a range of σ values with the range of σ and k within the unstable region increasing as the cascade is pushed deeper into stall. The energy transfer variation with k and σ, for a given blade incidence, are observed to fit the empirical model CE¯=a(k)+b(k)sin(σ+c(k)) with the terms a and c corresponding to quadratic and linear functions of k for all the incidence cases. At very low k values (k∼0.03), the quadratic term is small, and the energy transfer curves are observed to be broadly consistent with the trends reported by Corral and Vega (2016a), with the terms a(k) and c(k) being linear and b(k) being a constant. As the cascade is pushed gradually deeper into stall, the term b(k), which represents the influence of adjacent blades, is observed to go from being nearly a constant value with k for light stall, to a quadratic function of k at deep stall. More importantly, the deviation of b from being a constant is observed to occur at lower k values as the cascade goes deeper into stall. These results indicate that the additional quadratic terms need to be considered in the classical flutter based linear models for the case with deep stall and large oscillation amplitudes. The flow field measurements using PIV indicate the presence of a completely separated shear layer that is alternating between a state of being attached and detached to the blade surface during the oscillation cycle. The results show the shear layer phase (ϕs) with respect to the blade displacement to be close to the phase of the unsteady force (ϕ), thus helping to link the flutter behavior with the unsteady shear layer dynamics for stall flutter of a cascade at low Re.