Space–Time Gradient Method for Unsteady Bladerow Interaction—Part II: Further Validation, Clocking, and Multidisturbance Effect

Abstract

For efficient and accurate unsteady flow analysis of blade row interactions, a space–time gradient (STG) method has been proposed. The development is aimed at maintaining as many modeling fidelities (the interface treatment in particular) of a direct unsteady timedomain method as possible while still having a significant speedup. The basic modeling considerations, main method ingredients and some preliminary verification have been presented in Part I of the paper. Here in Part II, further case studies are presented to examine the capability and applicability of the method. Having tested a turbine stage in Part I, here we first consider the applicability and robustness of the method for a threedimensional (3D) transonic compressor stage under a highly loaded condition with separating boundary layers. The results of the STG solution compare well with the direct unsteady solution while showing a speed up of 25 times. The method is also used to analyze rotor–rotor/stator–stator interferences in a twostage turbine configuration. Remarkably, for stator–stator and rotor–rotor clocking analyses, the STG method demonstrates a significant further speedup. Also interestingly, the twostage case studies suggest clearly measurable clocking dependence of blade surface timemean temperatures for both stator–stator clocking and rotor–rotor clocking, though only small efficiency variations are shown. Also validated and illustrated is the capacity of the STG method to efficiently evaluate unsteady blade forcing due to the rotor–rotor clocking. Considerable efforts are directed to extending the method to more complex situations with multiple disturbances. Several techniques are adopted to decouple the disturbances in the temporal terms. The developed capabilities have been examined for turbine stage configurations with inlet temperature distortions (hot streaks), and for three bladerow turbine configurations with nonequal blade counts. The results compare well with the corresponding direct unsteady solutions.