Shock Induced Vortices in Transonic Compressors: Aerodynamic Effects and Design Correlations
Authors: Knobbe Henry , Nicke Eberhard 
Published: July 2013

Gas turbine total pressure ratio, efficiency and accurate stage matching prediction are of increasing importance in multi-stage compressor design. These highly challenging objectives can only be met if all components are highly loaded and optimally designed. Stage matching and efficiency improvements still depend on the designer’s experience and on empirical correlations. The upper blade part in highly loaded transonic compressors is especially difficult to design because of complex flow phenomena like compression shocks. On the one hand this region is of major interest, because of the high pressure ratios. On the other hand it is the most difficult area for the designer because of blade row interaction effects, tip leakage flows and high gradients in general. Recent publications investigated shock induced vortices (SIV), caused by the rotor bow shock. The shock interacts with the trailing edge of the upstream stator/IGV blade row. These vortices convect downstream through the rotor passage.
But the unsteady flow phenomena inside transonic compressors are still worthwhile endeavor because of insufficient understanding regarding the unsteady effects onto the overall compressor performance. The vortex trajectory is predictable inside the rotor-passage. However, correlations for vorticity magnitude, vortex-frequency (number of vortices) and vortex-trajectory on the overall compressor performance were never described by equations. Furthermore it has not yet been clarified whether a small or a wide axial spacing is beneficial in highly loaded axial compressors.
Therefore a transonic front stage (DLR Test Rig 250, 4 front stages of a state of the art gas turbine compressor) was chosen. The Q3D (quasi 3D) planes were extracted from 3D-Simulations for IGV/Rotor1 and Stator1/Rotor2. The approach is to separate the blade to blade effects from 3D effects, like tip leakage flow. This was achieved by different Q3D streamtubes in the upper blade part. These streamtubes allow a variation of the axial spacing without changing the steady flow solution. A wide range of the axial spacings have been simulated to get an overview about the resulting performance change. Furthermore a change of blade count ratio, inlet condition, outlet conditions and computational domain should lead to a better understanding. Physical relations between the shedded vortices and compressor overall performance should be derived.
The results show a wide spreading of the compressor performance speedlines. This spreading indicates the unsteady effects caused by interaction effects. The spreading becomes wider towards the surge margin. The reduced number of IGVs result into a smaller spreading. The higher inlet temperature result into a neglectable change in data spreading. The changed computational domain (stator/rotor) result into a very small data spreading, compared to the front stage data distribution.
The change of performance data is periodic to the established B3-factor [1]. This factor predicts the vortex trajectory inside the rotor passage. The analysis of rotor pre shock Mach number and blade count ratio leads to a systematic correlation factor (HK). This correlation takes the pre shock Mach number, the blade count ratio, the B3-factor and some algebraic elements into account to make a prediction of the unsteady effects regarding the total pressure ratio: HK = pt, unsteady−pt, steady.
The developed correlations may be useful in 3D to calculate optimal axial spacings at a specific blade to blade plane or to make compressor performance prediction during the design process based on RANS-Simulations (reduced gap between simulation and measurement). Furthermore it was identified that neither a wide nor a short axial spacing is beneficial for a transonic compressor inside a blade to blade plane.