Fluid/structure Coupled Aeroelastic Computations for Transonic Flows in Turbomachinery

The present study demonstrates the capabilities of a fluid/structure coupled computational approach which consists of an unsteady three-dimensional Navier-Stokes flow solver, TFLO, and a finite element structural analysis package, MSC/NASTRAN. The parallelized flow solver relies on a multiblock cell-centered finite volume discretization and the dual time stepping time integration scheme with multigrid for convergence acceleration. High accuracy is pursued with respect to load transfer, deformation tracking and synchronization between the two disciplines. As a result, the program successfully predicts the aeroelastic responses of a high performance fan, NASA Rotor 67, over a range of operational conditions. The results show that the unsteady pressure generated at the shock may act to damp or excite the blade motion mainly depending on the inter-blade phase angle. It is concluded that the level of sophistication in the individually sophisticated disciplines together with an accurate coupling interface will allow for accurate prediction of flutter boundaries of turbomachinery components. INTRODUCTION The unstable, self-excited or forced vibrations of rotor blades must be avoided in the design of high performance turbomachinery components because they may induce structural fail∗Current address: Technical Research and Development Institute, Japan Defense Agency, 1-2-10 Sakae-cho, Tachikawa, Tokyo, 190-8533, Japan †Assistant Professor ures. In order to predict these instabilities, the presence of strong shocks in the flow needs to be accounted for, especially for transonic flows. It is, therefore, necessary to use the Euler equations or the Reynolds-averaged Navier-Stokes (RANS) equations to represent the unsteady flow fields. Unsteady aerodynamics around oscillating cascades has been studied using these nonlinear equations by many researchers. For these approaches, timemarching methods (Gerolymos, 1993; He, 1994; Bakhle, 1997; Ji, 1999) or time-linearized methods (Hall, 1993; Ning, 1998) are used to calculate aerodynamic work per cycle over a period of oscilaation prescribing frequencies and mode shapes. On the other hand, the coupling of a structural model and a fully nonlinear aerodynamic model requires a time-marching method and determines the frequency of the problem rather than specifying it as an input parameter. The most noticeable work on the coupled computations is done by Vahdati, Imregun and their colleagues (Vahdati, 1995; Chew, 1998). In their work, a mode superposition of the structure is incorpolated into a finite element RANS solver. However, since the methodologies of each individual discipline have matured independently, each methodology has usually evolved to use a different type of grid generation, a different discretization method and a different time integration scheme so that high accuracy and efficiency individually can be achieved. In order to take advantage of the maturity of both, a reasonable alternative would be to construct an interface procedure between a flow solver and a structural solver for direct integrations of structural equations, in which the two solvers exchange the interface information given by updating the fluid and 1 Copyright  2002 by ASME structural variables alternatively. The present study explores this possibility by integrating an unsteady RANS flow solver and a finite element structural solver for aeroelastic problems in turbomachinery, using advanced fluid/structure coupling techniques. The flow solver used here is an unsteady three-dimensional RANS solver called TFLO (Yao, 2000; Yao, 2001), originally developed to simulate unsteady flows due to blade row interactions in turbomachinery. The structural solver used here is one of the industrial standards, MSC/NASTRAN. Furthermore, the interface procedure is based on the approach proposed by Brown (Brown, 1997). Using this coupling approach, the aeroelastic responses of a compressor rotor are predicted, and the influence of the flow fields on the stabilities is observed. DESCRIPTION OF THE METHOD In order to predict the dynamic response of a flexible structure in a fluid flow, the equations of motion of the structure and the fluid equations must be interacted. One difficulty in handling the fluid/structure coupling numerically comes from the fact that the structural equations are usually formulated with material (Lagrangian) coordinates while the fluid equations are typically written using spatial (Eulerian) coordinates. In such an approach, the procedure is advanced in time by solving the flow field and the structural deformation alternatively by independent flow and structural solvers which exchange information on the structural body surface as illustrated in Figure 1. The flow solver provides the aerodynamic loads to the structural solver in order for the structural solver to calculate the displacement field of the structure. In return, the structural solver provides the surface deflections to the flow solver which changes the flow fields through the boundary conditions on the structural body surface.