Data-Driven Reduced-Order Modeling of Turbulent Flows: A Case Study in Aerospace Engineering

Abstract

Turbulent flows have high dimensions of turbulence, nonlinearity and multiscale nature are some of the most challenging to model accurately in aerospace engineering. Conventional computational fluid dynamics (CFD) solutions, which are highly accurate, require many computational resources and, therefore, cannot be used in real time prediction, optimization, and control. Reduced-order modeling (ROM) is an attractive option because it attempts to evaluate the required flow physics in a smaller-dimensional subspace, and hence can provide significant economies of scale in computing without significant loss in predictive performance. In the current case study, different data-based ROM approaches are to be used to investigate the turbulent flow around a NACA 0012 airfoil at Reynolds number of 1 x 106 and subsonic Mach number. Three have been explored: (i) Proper Orthogonal Decomposition (POD) which is a leading energy bearing mode; (ii) Dynamic Mode Decomposition (DMD) which captures time-spatial flow dynamics and coherent structures; (iii) an autoencer-based neural ROM which utilizes deep learning to identify nonlinear latent representations of the flow field. Moreover, a hybrid architecture was constructed between POD mode extraction and autoencoder-based regression to trade-off between physics interpretability and machine learning adaptability. The results indicate that the hybrid model provided an optimal computation of 90 percent less than the conventional CFD with an error margin of less than 5 percent variation of the lift and drag coefficient. Compared analysis showed that POD and DMD are useful at coherent structure captivity of large scale but less effective at replication of broader turbulence, whilst the autoencoder-based model was more efficient in reconstruction of finer-scale details. The findings indicate the possible practical utility of data-driven ROMs in aerospace industry that may involve the optimization of aerodynamic design, digital twins, real-time flow regulation, and quantification of uncertainty. The present work proves that physics-based and machine learning methods are a promising route to effective and accurate modeling of the complex turbulent flows associated with aerospace systems.