Modeling cylinder flow vortex shedding with enforced motion using a harmonic balance approach
In recent years, new aeromechanical problems have been encountered in turbomachinery. In particular, non-synchronous vibrations (NSV) in blades have been observed by engine companies and occur as a result of flow instabilities. As a first step towards better understanding the NSV in turbine engine configurations, the two-dimensional shedding flow about a circular cylinder is investigated in this study. The governing nonlinear, unsteady Navier-Stokes equations are solved using a novel harmonic balance method. This method requires one to two orders of magnitude less computational time than conventional time-marching computational fluid dynamic (CFD) techniques. In this paper, results are presented for a stationary cylinder in cross flow and a cylinder with enforced motion in the low Reynolds number regime (47 < Re < 180). A unique phase error method is used to determine the shedding frequency and oscillatory lift for the stationary cylinder case. A relationship between Reynolds number and Strouhal number is determined and compared with existing computational and experimental data. The lock-in effect for the prescribed motion case is observed, and results show that cylinder motion does not significantly affect the unsteady lift for cylinder oscillation amplitudes of 10% or less of the cylinder's diameter and the lift actually decreases for higher oscillatory amplitudes. This is significant because it implies that it may not be necessary to couple the NSV aerodynamic solution with blade motion for some applications, which would require much less computation time than a fully coupled aerodynamic/structural solution. In all cases, the results agreed well with existing experimental and computational data.