Unsteady Newton-Busemamn Flow Theory Part III. Frequency Dependence and Indicial Response

Summary

A complete unsteady Newton-Busemann flow theory, including centrifugal force corrections, was recently given by Hui and Tobak and successfully applied to study the dynamical stability of oscillating aerofoils (Part I) and bodies of revolution (Part II). The present paper extends these results, which are restricted to the first order in frequency, to general frequencies that may be applicable to flutter analysis as well. Furthermore, the new results are used to investigate the behaviour of the indicial response functions in unsteady flow at very high Mach numbers. In particular, it is found that for a family of body shapes in the Newtonian flow, including the cone, the wedge, the delta wing and slender aerofoils, the aerodynamic response to a step change in angle of attack or pitching velocity contains an impulse at the initial instant. This is followed by a rapid adjustment to the new steady-flow conditions, the adjustment time being equal to that required for a fluid particle to travel a distance of the body length. The impulse component appearing at the infinite Mach number limit (Newtonian flow) is in effect an apparent mass term, analogous to that which occurs initially in the aerodynamic indicial response at the zero Mach number limit (incompressible flow). In the latter case the initial impulse is followed by an asymptotic adjustment to the new steady-flow conditions, theoretically taking infinite time, in direct contrast to the rapid adjustment in Newtonian flow.