Identification of dimensionless parameters in Rayleigh–Bénard convection through regression neural network

Abstract

We combine advances in computational fluid dynamics and neural networks to develop a tool to study the dynamics of industrial and geophysical flows. Rayleigh–Bénard convection (RBC) is characterized by two key dimensionless numbers: the Rayleigh (Ra) number, which quantifies the vigor of convection, and the Prandtl (Pr) number, the ratio of momentum to thermal diffusivity, as well as the boundary conditions (BCs). We simulate RBC from the laminar to the turbulent regime to create training and testing images for a general purpose deep neural network (DNN) using regression to simultaneously estimate Ra and Pr independently from each single snapshot of temperature and velocities. The data span several orders of magnitude for Pr (1–128) and Ra (105-109). We test the network’s ability to predict Ra and Pr for (i) values not used for training but within the training range and (ii) values beyond the training range (Pr∈[0.35,362] and Ra∈[104.25,109.75]). We find that while individual predictions of Ra and Pr vary significantly, their distribution across simulations is centered on the correct value within the training range. Interestingly, the Grashof number (Gr=Ra/Pr), which measures the ratio of buoyancy forces to viscous dissipation, is predicted more accurately than Ra and Pr. This demonstrates that the network captures essential features to classify flow patterns ranging from laminar to turbulent RBC.