Multistage coupling for unsteady flows in turbomachinery

We present a three-dimensional time-linearized unsteady Enter solver for computing unsteady flows in multistage turbomachines. Using this approach, each blade row is modeled on a computational grid spanning a single blade passage. Within each blade passage, several time-linearized unsteady solutions, each of which have different frequencies and interblade phase angles, are computed. These various solutions are coupled together at the interrow boundaries between the blade rows. The coupling allows one to pass the pressure, entropy, and vorticity waves traveling between neighboring blade rows resulting in an efficient multistage analysis of unsteady flows in turbomachinery. Results that demonstrate the accuracy and efficiency of the method, as well as the importance of multistage effects, are presented for several geometries. In particular, we show that multistage effects can be significant for the aerodynamic loads acting on a given blade row. Furthermore, the method presented is highly efficient. For example, a flutter calculation requires only about three times the CPU time of one steady flow computation for each interblade phase angle and frequency considered.