Reduced Order Modeling of the Unsteady Pressure on Turbine Rotor Blades Using Deep Learning

Abstract In transonic turbine stages, complex interactions between the trailing edge shocks from nozzle guide vanes and the rotor blades generate unsteady wall pressure fields, affecting the rotor aerodynamic performance and structural integrity. While shock-related phenomena are prominent, unsteady pressure fluctuations can also arise in subsonic regimes, where wake interactions alone are sufficient to induce instationarities. Traditional methods like unsteady Reynolds-averaged Navier–Stokes (URANS) simulations, while sufficiently accurate, are computationally expensive. To address this, a novel deep learning-based reduced order model (ROM), built upon a database of URANS simulations, is proposed to predict unsteady pressure fields on a turbine rotor blade at a fraction of the simulation cost. Specifically, the model consists of a variational auto-encoder integrated with a gated recurrent unit to capture time-series data, addressing the limitations of traditional linear ROMs in capturing efficiently nonlinear phenomena, such as moving shocks. The objective of this work is to develop a ROM capable of accurately reproducing the unsteady pressure fields obtained from URANS simulations while significantly reducing computational costs. The proposed ROM is applied to the turbine aero-thermal external flows project configuration, a well-established test case in turbomachinery research that is representative of modern high-pressure turbine stages, particularly in terms of shock-wave interactions and wake dynamics. The model performance is evaluated using a combination of machine learning quality metrics and design-oriented criteria, such as the accuracy of the first harmonic in the Fourier transform of the unsteady pressure field. Additionally, the influence of the simulation database size on the model accuracy is analyzed, recognizing that the number of training simulations required to achieve task-specific accuracy is a key constraint on the industrial applicability of such approaches.