Mixing Losses in Steady and Unsteady Simulations of Turbomachinery Flows

The aim of the present work is to facilitate insight into the modeling errors in the context of blade row coupling approaches which capture unsteady flow phenomena at different levels of detail. The focus is on RANS-based steady mixing plane computations as well as time domain and frequency domain unsteady computations. The concept of mixing loss is revisited to quantify the amount of unsteadiness in a flow field. Following an idea by Fritsch and Giles, we compute a second order approximation of the mixing losses which are generated at blade row interfaces. The resulting formula decomposes the entropy jump into contributions of circumferential and temporal fluctuations. The mathematical derivation, however, is based upon simpler arguments. It is shown that Fritsch and Giles’ main result can be extended to non-ideal gases. Moreover, the second order mixing loss formula is applied to time and frequency domain unsteady simulations. It is shown that an additional term has to be computed which accounts for the interaction of evanescent acoustic modes if the method is applied to unsteady flows. The methodology decomposes the overall mixing entropy into contributions of single perturbation types and harmonics. This may be used to assess whether unsteady flow phenomena of interest are adequately resolved and, in particular, to quantify the unsteadiness contained in the unresolved harmonics. A detailed investigation of the transonic IGV-rotor configuration of DLR’s Rig 250 compressor demonstrates the approach.