Simulations of flows within turbomachines are challenging because of the complicated rotating geometries and unsteady flow structures. Designers are often required to place airfoils close together to minimize engine weight and size. This leads to aerodynamic interactions between rotor and stator airfoils. Part of the interaction is due to the inviscid potential effect between closely spaced rotor and stator airfoils. Viscous effects also contribute to the unsteady interactions. The angle of attack of an airfoil can vary widely as it passes through the wake of an upstream airfoil, because of the velocity deficit in the wake. Unsteady variations in angle of attack coupled with local adverse pressure gradients can cause unsteady separation. In addition, trailing-edge vortex shedding can increase the unsteadiness of the system. Simulation of the unsteady flow in a turbomachine can lead to an understanding of the aerodynamic interactions that occur.
Most methods used today to simulate flows in turbomachines are for either cascade flows or time-averaged flows through several airfoil rows. Simulations by Davis et al. (1988), Choi and Knight (1988), Subramanian et al. (1986) and Weinberg et al. (1986) are representative of these methods, but by no means make an exhaustive list of the methods available. Perturbation techniques can be applied to these simulations for an estimate of the unsteadiness for weak interactions. Distorting-grid techniques, described by Gibeling et al. (1986), can be used to investigate flows in which relative motion exists between rotors and stators. In these techniques, a single grid is wrapped about both airfoils and sheared as the airfoils move relative to one another. When the distortion in the grid exceeds a certain level, the solution is interpolated onto a new, undistorted grid. However, this method may produce inaccurate solutions because of the grid distortion if the airfoils are too closely spaced.
For this reason, Rai (1987) and Rai and Madavan (1988) used a system of patched and overlaid grids to compute the rotor-stator interaction problem in a single-stage turbine. Body-fitted "O" grids with fine-grid spacing at the airfoil surfaces were used to capture viscous effects near the airfoil surface. These "O" grids were overlaid on sheared Cartesian "H" grids, which were allowed to slip past each other to simulate the interaction problem. The ROTOR-2 code resulted from these efforts to simulate rotor-stator interaction for single-stage turbine configurations. The STAGE-2 code, used in the present study, is an extension of ROTOR-2 for multistage turbomachines. Results from STAGE-2 were compared with experimental data for both a multistage compressor and a single-stage turbine in Gundy-Burlet et al. (1989).
STAGE-2 is currently being used to further investigate the flow in the multistage compressor. The þcompressor geometry was chosen for the present analysis because a large body of experimental data is available for the multistage compressor. Much of the experimental data is summarized and tabulated in Dring and Joslyn (1985). This compressor is also part of the AGARD (1989) collection of test cases for computation of internal flows in aero-engine components. In addition, both steady and unsteady laser doppler velocimetry (LDV) data have been taken in the second stage of the compressor. These data are presented by Stauter, Dring, and Carta (1990) in Part 1 of this paper. Comparisons, in the present report, of STAGE-2 calculations with experimental data include time-averaged pressures and wake velocity profiles. The effect of grid refinement on the solution is studied, and instantaneous entropy contours for the þstage compressor are presented. The computed results are in good agreement with experimental data.