Explicit Runge-Kutta method for unsteady rotor/stator interaction

Abstract

AbetractA quastthree-dimensional rotor/statcr analysis has been developed for blade-teblade flows in turbomachinery. The analysis solves the unsteady M e r OT thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radiw change, and stream-surface thickness. The Baldwirr Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using a four-stage RungeKutta scheme with a constant time step. Results are shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. M e r and Navier-Stokes results are compared on the scaled singleand multi-passage machine. The method is relatively fast and the quastthree-dimensional fmmulation is a p plicable to a wide range of turbomachinery geometries.

IGV-Rotor Interaction Analysis in a Transonic Compressor Using the Navier-Stokes Equations

“…Moreover, they can be used as target solutions for fine-tuning steady multi-row pitch-averaging techniques. The works of Erdos et al (1977), Rai (1987), Lewis et al (1987), Jorgenson and Chime (1988), Giles (1988a), and Rao et al (1992) are some examples of basic historical contributions to this topic.…”

Unsteady Interaction Between a Transonic Turbine Stage and Downstream Components

“…Significant experimental and numerical research has been performed over the last several years on highlighting and understanding the unsteady aerodynamics of multi-stage turbomachinery (e.g., Reinmoller et al, 2001;Arnone et al, 2001;Gombert and Hohn, 2001;Dorney et al, 2001;Clark et al, 2000;Busby et al, 1998;Rao et al, 1994;Chen et al, 1994;Sharma et al, 1992;Takahashi and Ni, 1991;Giles, 1990;Jorgenson and Chima, 1990;Rai, 1987;Dring et al, 1992). Much of this work has focused on quantifying the unsteady flow field resulting from the interaction between rotors and stators in terms of aerodynamic performance and airfoil surface unsteady pressure.…”

Simulation of time-dependent compressible viscous flows using central and upwind-biased finite-difference techniques

“…This approach, at first glance, appears not to be well suited for the prediction of unsteady flows due to the ad hoc nature of the implicit portion of the algorithm. Recently, however, Jorgensen and Chima [4] demonstrated that such algorithms may be tailored for the unsteady flow problem to yield acceptable results.…”

“…(Re=9500, t=1.0)xvii GCGTVD predicted streamline pattern for impulsively started cylinder flow. (Re=9500, t=1 4). 232 GCGTVD predicted streamline pattern for impulsively staxted cylinder flow.…”

“…4 displays results from a second-order accurate centrally-differenced Runge-Kutta[64] explicit time marching procedure. Again, the blended second and prod uct fourth order dissipation terms were used.Figure 3.5 displays results &om a centrally-differenced Runge-Kutta[64] explicit time marching procedure which was fourth order accurate in both time and space, with added fourth order dissipation terms.…”