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The impact of the unsteadiness in the considered turbulence quantities on the numerical prediction of the aeroelastic behavior of a low-pressure turbine (LPT) rotor blade is evaluated by means of a numerical study. In this context, one of the main objectives of this work is to compare different nonlinear harmonic balance (HB) approaches—one neglecting and one considering the unsteadiness in the employed turbulence models—with a conventional nonlinear solver of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations in the time domain. In order to avoid unphysical oscillations in the turbulence quantities caused by the Gibbs phenomenon in the chosen HB approach, a filter method based on the Lanczos filter is developed. The developed filter method is applied in the course of the HB simulations considering the unsteadiness in the underlying turbulence model. Furthermore, the impact of its application on the solution of the flow field and on the unsteady surface pressure of the rotor blade, in particular, is discussed in the context of this work.

The transient transition behavior of a two-stage low pressure turbine rig facility is investigated in terms of numerical studies. The surface of a second stage stator vane is equipped with a thin film sensor array along its suction side providing time-resolved measurement data of the underlying boundary layer. The measurement data indicate a laminar behavior over the accelerated region of the stator vane. At the decelerated region close to the vane’s trailing edge, alternating transition mechanisms of both bypass and separation induced transition combined with subsequent reattachment can be observed. The measurement data in combination with numerical results from a time-marching full-wheel simulation are used to assess the results from an unsteady flow simulation based on the harmonic balance approach in the frequency domain. For both time and frequency domain simulations, the turbulence behavior is considered by application of Wilcox’ k–ω two equation model in combination with Menter and Langtrys γ-Reθ transition model. The numerical results regarding transient distributions of intermittency and associated shape factor of the boundary layer are compared with proper measurement quantities in order to evaluate the capability of the applied harmonic balance solver to predict the unsteady transition behavior over the investigated vane’s suction side.

The main objective of this study is the validation of numerical forced response predictions through experimental blade vibration measurements for higher order modes of a blade-integrated disk (blisk). To this end, a linearized and a nonlinear frequency domain CFD methods are used, as well as a tip timing measurement system. The focus is on the blade excitation by downstream vanes, in particular, because this study shows that the correct prediction of acoustic modes is of key importance in this case. The analysis of these modes is presented, both experimentally and numerically, in Part I of this publication. The grid independence study for the aerodynamic work on the blade surface conducted in this part shows a possible prediction uncertainty of more than 100% when a coarse grid is chosen. For the validation of the numerical setup, a study was performed using different turbulence and transition models. The results are compared to the measured performance map, to a 2D field traverse conducted with a pneumatic probe, and to data gained by unsteady pressure sensors mounted in the casing of the compressor. Flow features relevant for the prediction of blade stresses are best represented using the SST turbulence model in combination with the γ–ReΘ transition model. Nonlinear simulations with this setup are able to predict the blade stresses due to downstream excitation with an average difference of 23% compared to tip timing measurements. Single row linearized CFD methods have shown to be incapable of making a correct stress prediction when acoustic modes form a major part of the exciting mechanisms. In summary, this two-part publication proves the importance of acoustic rotor–stator interactions for blade vibrational stresses excited by downstream vanes in a state-of-the-art high-pressure compressor.

A partitioned approach for the solution of the adjoint associated to the coupled system of time-dependent fluid-structure interaction is presented. Allowing for an efficient computation of both sensitivity and gradient distributions relying on the adjoint method, an optimization strategy based on the steepest descent algorithm is applied. The performance of the developed shape optimization process improving flow conditions and related cost functionals is demonstrated by application to ducted flow situations and common fluid dynamic design tasks considering the interaction between fluid loads and structural deformations. Both physical capability and feasibility are discussed in terms of theoretical and numerical aspects in order to evaluate the efficiency of the realized optimal control process.