3-D inviscid self-excited vibrations of a blade row in the last stage turbine

Presented here is a three-dimensional (3-D) nonlinear time-marching method for the aeroelastic behaviour of an oscillating turbine blade row. The approach has been based in the solution of a coupled fluid–structure problem where the aerodynamic and structural dynamic equations are integrated simultaneously in time. This provides the correct formulation of a coupled problem, as the interblade phase angle (IBPA) at which stability (instability) would occur is also a part of solution. The ideal gas flow around multiple interblade passages (with periodicity in the entire annulus) is described by the unsteady Euler equations in conservative form, which are integrated by using the explicit monotonic second-order accurate Godunov–Kolgan finite-volume scheme and a moving hybrid H–O (or H–H) grid. The fluid and the structural equations are solved using the modal superposition method. An aeroelasticity prediction of a turbine blade of 0.765 m is presented. The natural frequencies and modal shapes of the blade were calculated by using 3-D finite element models. The instability regions for five mode shapes and the distribution of the aerodamping coefficient along the blade length were shown for harmonic oscillations with an assumed IBPA. The coupled fluid–structure oscillations in which the IBPA is part of the solution are shown.