How the elastic axis folds the transonic flutter boundary: shock energy transfer and conformally calibrated active learning

원문 초록

Isogai's case A, a pitch-plunge aerofoil whose elastic axis lies half a chord ahead of the leading edge, has a folded transonic flutter boundary in inviscid flow, with several flutter speeds at one Mach number. We map this boundary and its elastic-axis family with coupled Euler simulations, a Gaussian-process surrogate of the damping trained by batch active learning, and distribution-free split conformal prediction, which bounds the marginal error rate of stability calls. Three failure modes of damping labels are invisible in the residuals, and the half-degree mean incidence left by an impulsive start at $1^\circ$ freestream incidence raises the flutter speed at the dip by 2.8%, more than any numerical setting. With 80 simulations the learned case A boundary labels 63 of 64 independent runs correctly, and at most 1.8% of calibrated calls on held-out runs are wrong. Over Mach number, elastic axis and flutter speed index, 193 simulations show that, for the case A structure about the axis, the inviscid fold exists only for axes more than about 0.4 chord ahead of the leading edge, on two meshes. Chordwise energy budgets, closed three ways, explain both branches. On the lower branch the falling reduced frequency, at unchanged shock phase, raises the shock input and lowers the upstream damping similarly. On the upper branch the shock is pinned at the trailing edge; moving the axis aft brings the flutter-mode pivot towards the section, so the upstream damping falls faster than the residual shock input and the fold closes.