A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter

The Unsteady Adaptive Stochastic Finite Elements(UASFE)approach is a robust and efficient uncertainty quantification method for resolving the effect of random parameters in unsteady simulations.In this paper,it is shown that the underlying Adaptive Stochastic Finite Elements(ASFE)method for steady problems based on Newton-Cotes quadrature in simplex elements is extrema diminishing(ED).It is also shown that the method is total variation diminishing(TVD)for one random parameter and for multiple random parameters for first degree Newton-Cotes quadrature.It is proven that the interpolation of oscillatory samples at constant phase in the UASFE method for unsteady problems results in a bounded error as function of the phase for periodic responses and under certain conditions also in a bounded error in time.The two methods are applied to a steady transonic airfoil flow and a transonic airfoil flutter problem.

Oscillation quenching and physical explanation on freeplay-based aeroelastic airfoil in transonic viscous flow

Limit Cycle Oscillation(LCO)quenching of a supercritical airfoil(NLR 7301)considering freeplay is investigated in transonic viscous flow.Computational Fluid Dynamics(CFD)based on Navier-Stokes equations is implemented to calculate transonic aerodynamic forces.A loosely coupled scheme with steady CFD and an efficient graphic method are developed to obtain the aerodynamic preload.LCO quenching phenomenon is observed from the nonlinear dynamic aeroelastic response obtained by using time marching approach.As the airspeed increases,LCO appears then quenches,forming the first LCO branch.Following the quenching region,LCO occurs again and sustains until the divergence of the response,forming the second LCO branch.The quenching of LCOs was addressed physically based on the aerodynamic preload and the linear flutter characteristic.An“island”of stable region is observed in the flutter boundary,i.e.the flutter speed versus the mean Angle of Attack(AoA).The LCO quenches when the aerodynamic preload crosses this stable region with the increasing of airspeed.The LCO quenching of this model in transonic flow is essentially induced by destabilizing effect from aerodynamic preload,since the flutter speed is sensitive to AoA due to aerodynamic nonlinearity.