Numerical investigation of blade flutter at or near stall in axial turbomachines

Abstract: During the design of the compressor and turbine stages oftoday's aeroengines aerodynamically induced vibrations becomeincreasingly important since higher blade load and betterefficiency are desired. Aerodynamically induced vibrations inturbomachines can be classified into two general categories,i.e. selfexcited vibrations, usually denoted as flutter, andforced response. In the first case the aerodynamic forcesacting on the structure are dependent on the motion of thestructure. In the latter case the aerodynamic forces can beconsidered to be independent of the structural motion. In thisthesis the development of a method based on the unsteady,compressible Navier-Stokes equations in two dimensions isdescribed in order to study the physics of flutter for unsteadyviscous flow around cascaded vibrating blades at stall.The governing equations are solved by a finite differencetechnique in boundary fitted coordinates. The numerical schemeuses the Advection Upstream Splitting Method to discretize theconvective terms and central differences discretizing thediffusive terms of the fully non-linear Navier-Stokes equationson a moving H-type mesh. The unsteady governing equations areexplicitly and implicitly marched in time in a time-accurateway using a four stage Runge-Kutta scheme on a parallelcomputer or an implicit scheme of the Beam-Warming type on asingle processor. Turbulence is modelled using theBaldwin-Lomax turbulence model. The blade flutter phenomenon issimulated by imposing a harmonic motion on the blade, whichconsists of harmonic body translation in two directions and arotation, allowing an interblade phase angle betweenneighbouring blades. An aerodynamic instability is given whichcan lead to a flutter problem, if the computed unsteadypressure forces amplify the imposed blade motion.Non-reflecting boundary conditions are used for the unsteadyanalysis at inlet and outlet of the computational domain. Thecomputations are performed on multiple blade passages in orderto account for nonlinear effects. Unsteady boundary conditionsare developed considering primary and secondary gust effectstowards the investigation of the forced response problem withthe presented method.Subsonic massively stalled and transonic separated unsteadyflow cases in compressor and turbine cascades are studied. Theresults, compared with experiments and the predictions of otherresearchers, show good agreement for inviscid and viscous flowcases for the investigated flow situations with respect to thesteady and unsteady pressure distribution on the blade in thevicinity of shocks and in separated flow areas.The results show the applicability of the new scheme forstalled flow around cascaded blades. As expected the viscousand inviscid methods show different results in areas whereviscous effects are important, i.e. separated flow and shockwaves. In particular, different predictions for inviscid andviscous flow for the aerodynamic damping for the investigatedflow cases are found.Keywords: turbomachinery, flutter, forced response, gust,unsteady aerodynamics, Navier-Stokes equations, AdvectionUpstream Splitting Method, implicit scheme, non-reflectingboundary conditions, gust boundary conditions, parallelcomputing