Potential and Viscous Interactions for a Multi-Blade-Row Compressor

A computationally efficient time-accurate vortex method for unsteady incompressible flows through multiple blade row systems is presented. The method represents the boundary surfaces using vortex systems. A local coordinate system is assigned to each independently moving blade row. Blade shed vorticity is determined from two generating mechanisms and convected using the Euler equation. The first mechanism of vorticity generation is a potential mechanism from a nonlinear unsteady pressure-type Kutta condition applied at the blade trailing edges. The second mechanism is a viscous mechanism from a viscous wake vorticity (VWV) model implemented to simulate the viscous shear layers on the blade pressure and suction sides. Two different two-blade-row compressor systems, a rotor/stator (R/S) system and a stator/rotor (S/R) system, were used to investigate the interaction forces on each blade row. Computational results of the potential and viscous interaction forces are presented and compared to measurements. The comparison suggests that the viscous wake interaction accounts for 25–30% of the peak loading for an axial spacing of 10% chord length between the blade rows. The efficient computational method is particularly attractive for blade indexing study. Therefore a three-blade-row rotor/stator/rotor (R1/S/R2) compressor system is used to demonstrate the indexing calculations between the two rotor positions. Resultant forces on each blade row are presented for ten rotor indexing positions and three axial gap sizes for the gaps between R1 and S and between S and R2. The unsteady peak-to-peak force can reach 10–15% of inflow dynamic head for the gap spacing investigated. The minimum-to-maximum variation of the unsteady force can account for 40–50% of averaged unsteady force.