2020/05/06 by Muhammad I. Zafar, Heng Xiao, Zafar, Muhammad I. +11 · 1 citation
Engineering · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Aerodynamics and Fluid Dynamics Research #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2005.02599
Transition prediction is an important aspect of aerodynamic design because of\nits impact on skin friction and potential coupling with flow separation\ncharacteristics. Traditionally, the modeling of transition has relied on\ncorrelation-based empirical formulas based on integral quantities such as the\nshape factor of the boundary layer. However, in many applications of\ncomputational fluid dynamics, the shape factor is not straightforwardly\navailable or not well-defined. We propose using the complete velocity profile\nalong with other quantities (e.g., frequency, Reynolds number) to predict the\nperturbation amplification factor. While this can be achieved with regression\nmodels based on a classical fully connected neural network, such a model can be\ncomputationally more demanding. We propose a novel convolutional neural network\ninspired by the underlying physics as described by the stability equations.\nSpecifically, convolutional layers are first used to extract integral\nquantities from the velocity profiles, and then fully connected layers are used\nto map the extracted integral quantities, along with frequency and Reynolds\nnumber, to the output (amplification ratio). Numerical tests on classical\nboundary layers clearly demonstrate the merits of the proposed method. More\nimportantly, we demonstrate that, for Tollmien-Schlichting instabilities in\ntwo-dimensional, low-speed boundary layers, the proposed network encodes\ninformation in the boundary layer profiles into an integral quantity that is\nstrongly correlated to a well-known, physically defined parameter -- the shape\nfactor.\n