Numerical Investigation of the Effect of Operating Point on the Aerodynamic Excitation in a Radial Turbine Stage

High cycle fatigue (HCF) is a major source of machine failure in turbomachinery bladings. One of the mechanisms that can lead to HCF is forced response vibrations of the structure under the excitation of unsteady aerodynamic forces from the surrounding flow field. The reliable prediction of these aerodynamic forces is of paramount importance for the accurate vibratory response and durability prediction in the design process. This is usually obtained by large CFD models only at a small number of operating points due to the high computational costs required. For some applications, however, the turbomachine designer is interested in the aerodynamic excitation in a certain operating range of the machine, e.g. when a natural frequency and thus a corresponding resonance crossing can be shifted to a more favorable operating point with lower excitation. Simple scaling approaches are commonly used to reduce computation cost, whose application can be limited to a small range though.

The goal of this study is to propose a workflow for the prediction of the aerodynamic excitation within the whole operating map. Therefore, a radial turbine stage is numerically investigated, in which the rotational speed and expansion ratio are varied at a constant inlet temperature for two temperatures. Surrogate models based on Kriging interpolation are obtained for resonance crossings of the first ten blade modes, available from a FE modal analysis, with a single excitation order based on initial simulation sample set. These models are then successively improved by an adaptive sampling technique, until a satisfactory convergence of the models is achieved. The CFD simulations are performed on a simplified sector model of the stage by means of the nonlinear harmonic method in the frequency domain. The aerodynamic excitation is evaluated by the generalized force criterion.

By tracking the model development and error criteria during the adaptive sampling, it is observed that the trends for the excitation can be reliably interpreted with relatively low iterations number. Looking at the surrogate model prediction, the aerodynamic excitation appears highly mode dependent with some common features. On the one hand, it is found that an increase of the rotational speed does not necessarily yield a higher aerodynamic excitation. On the other hand, a clear monotonic trend is observed for the turbine expansion ratio in the results. Furthermore, the paper deals with the physical mechanisms that cause the changes in the aerodynamic excitation as a function of the varied parameters. Guidelines for better understanding the underlying phenomena and improve machine design are proposed as a consequence. Due to the generality of the implemented workflow, it can be easily applied to other machines and geometries.