Transonic aeroelasticity analysis for rotor blades

Abstract

A numerical method is presented for calculating the unsteady transonic rotor flow with aeroelasticity effects. The blade structural dynamic equations based on beam theory were formulated by the finite element method and were solved in the time domain instead of the frequency domain. A global-local coordinate-transformation matrix was used to reduce the inaccuracy caused by large blade deformations. A new structure code was developed and was validated by comparing the computed natural frequencies with experimental data of a model rotor blade. For different combinations of precone, droop, and pitch, the correlations are very good in the first three flapping modes and the first twisting mode. However, the predicted frequencies are too high for the first lagging mode at high rotational speeds. This new structure code has been coupled into a transonic rotor flow code, TFAR2, to demonstrate the capability of treating elastic blades in transonic rotor flow calculations. The flowfields for a model-scale rotor in both hover and forward flight are calculated. Results show that the blade elasticity significantly affects the flow characteristics in forward flight. Nomenclature A = blade cross-section area a = local speed of sound a^ -far-field speed of sound a o-<*5 = coefficients in Newmark method fl 0 ,«i = constants for Rayleigh damping [C] = element damping matrix [C] = damping matrix for the blade c = blade chord length E = Young's modulus G = shear modulus [G]= rotational matrix for entire blade I y j z = blade cross-section moments of inertia about y and z axes, respectively / = torsional rigidity K = stiffness matrix for the blade K E = nonrotating element stiffness matrix K G = element geometric stiffness matrix K GT = element geometric-stiffness-like matrix / = blade element length [M] = element mass matrix [M] = mass matrix for the blade n = unit vector normal to the blade surface P(t) = aerodynamic load vector q = flow velocity g, = generalized coordinates