Response of a Thin Airfoil Encountering a Strong Density Discontinuity

Abstract

Airfoil theory for unsteady motion has been developed extensively, assuming the undisturbed medium to be of uniform density, a restriction accurate for motion in the atmosphere [1,2,3,4,5,6]. In some instances, notably for airfoils comprising fan, compressor and turbine blade rows, the undisturbed medium may carry density variations or "spots," resulting from non-uniformities in temperature or composition, of a size comparable to the blade chord. This condition exists for turbine blades [7,8] immediately downstream of the main burner of a gas turbine engine where the density fluctuations of the order of 50% may occur. Disturbances of a somewhat smaller magnitude arise from the ingestion of hot boundary layers into fans [9] and exhaust into hovercraft. Because these regions of non-uniform density convect with the moving medium, the airfoil experiences a time varying load and moment which we propose to calculate.