Effect of blade thickness on high frequency gust response

Turbomachinery rotor blades experience gust loading due to both inflow turbulence and circumferential variation in the mean velocity. The unsteady lift forces that result from these velocity disturbances can be a source of unwanted vibration and radiated noise. For incompressible flows, the blade gust response is often modeled using the well-known Sears function, which acts as a transfer function between a sinusoidal component of the gust and the fluctuating lift. However, the Sears function has a relatively slow high frequency roll-off and overpredicts the unsteady lift when the gust wavelength becomes much smaller than the blade chord. A more accurate model can be obtained by including the effect of blade thickness, which causes the gust to become distorted as it approaches the leading edge. This distortion results in attenuation of the higher-frequency components of the gust near the leading edge, which subsequently leads to reduced unsteady lift. In this paper, a model for the thickness effect is developed based on rapid distortion theory. Numerical calculations are made for a step-function gust encountering an elliptical leading edge with several thickness-to-chord ratios. The unsteady lift is calculated in the time domain, and a Fourier transform is used to obtain the frequency response. The results indicate that the gust response of a thick blade can be closely approximated by modifying the Sears function to include an exponential decay factor based on the thickness.