Predictive modelling of the dominant axisymmetric pressure mode of a high-speed turbulent jet flow using spectral proper orthogonal decomposition and machine learning

Abstract

Analysis of dominant features associated with coherent structures in turbulent flows is essential for the development of Reduced-Order Models (ROMs) in many fluid dynamics problems. As the first step in this direction, the axisymmetric pressure mode is extracted from the Large Eddy Simulation (LES) of a high-speed round jet flow, analyzed, and reconstructed using flow decomposition and Machine Learning (ML) techniques. The motivation of these data-driven analyses is to ultimately develop robust methods for modeling turbulent flows using only a fraction of the LES time series for training purposes, thus minimizing computing costs. The considered LES solution is based on the high-resolution Compact Accurately Boundary Adjusting high-REsolution Technique accelerated on Graphics Processing Unit cards for conditions of the National Aeronautics and Space Administration Small Hot Jet Acoustic Rig experiment with a round jet at acoustic Mach number 0.9. A frequency-domain Spectral Proper Orthogonal Decomposition (SPOD) of the LES data is performed to extract the time-varying coefficients. The SPOD coefficients condense important unsteady features of the turbulent jet flow, while preserving its spatiotemporal coherence. The coefficients are reconstructed using four machine-learning approaches. The predictive ROMs developed here based on ML are specifically focused on reconstructing the leading SPOD time coefficient of the axisymmetric (m=0) pressure mode at St=0.1 that corresponds to the dominant hydrodynamic mode that is known to strongly contribute to the peak-noise radiation of high-speed round jets at small angles to the jet axis. The first ROM approach employs Feedforward Neural Networks, a technique previously recommended for modeling turbulent flows over a plunging airfoil [Lui and Wolf, “Construction of reduced-order models for fluid flows using deep feedforward neural networks,” J. Fluid Mech. 872, 963–994 (2019)]. The second ROM uses Genetic Programing, a symbolic regression method widely recognized in the optimization literature, though it has not yet been applied to unsteady fluid dynamics problems. The third approach adopts Echo State Networks, a time-series prediction and reconstruction technique originating from the field of Reservoir Computing. Finally, the fourth approach leverages Transformer, one of the most advanced architectures within the family of Artificial Neural Networks. Although transformers have demonstrated efficiency in long-term reconstruction of turbulent wake flows, their application to high-speed jet modeling remains unexplored. The stability and accuracy of the considered ML methods for turbulent signal reconstruction are evaluated in terms of capturing its essential properties, such as the amplitude distribution and convection phase.