| A computational method for accurately and efficiently predicting unsteady flow through two-dimensional cascades is presented. The goal of the present research is to provide aeroelasticians with tools that predict the unsteady loads associated with inlet distortion, multi-stage interaction and self-excited blade motion. The reason being that unsteady aerodynamic loads directly impact the life and operability of turbomachinery blading. Of particular interest is the ability to predict the onset of stall flutter. In stall flutter, viscous effects significantly impact the aeroelastic stability, hence, previously developed inviscid analyses inadequately model the unsteady aerodynamic interactions. In the present study, the unsteady flow is modeled using a linearized navier-Stokes analysis in which the unsteady flowfield is decomposed into a nonlinear mean flow and a small perturbation, harmonically varying unsteady flow. The equations that govern the perturbation flow, the so-called linearized Reynolds-averaged Navier-Stokes equations, are linear, variable coefficient equations. These equations are discretized on a deforming, multi-block, computational mesh and solved using a finite-volume Lax-Wendroff integration scheme. Numerical modeling issues germane to the development of a viable unsteady aerodynamic analysis tool used for turbo-machinery applications are presented. Particular emphasis is placed on turbulence modeling, numerical stability and conservation, non-reflecting boundary conditions and grid generation. The impact of these modeling issues on an aeroelastic design system is discussed. Results from the present method are compared with analytical solutions, independent numerical simulations and experimental data. Results presented demonstrate the ability of the present linearized analysis to model accurately the unsteady aerodynamics associated with the operation of turbomachinery. The computational efficiency of the present linearized analysis enables the user to not only predict the unsteady loads but design for aeroelastic performance and high cycle fatigue (HCF) avoidance. |
