APPLICABILITY OF THE PINN METHOD FOR HEAT TRANSFER IN A SQUARE CHANNEL AT VARIOUS PRANDTL NUMBERS
Al.A. Luk'yanov1, G.A. Kukhta1, An.A. Luk'yanov1, D.I. Zaripov2, M.P. Tokarev1
1Kutateladze Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
2Institute of Energy and Advanced Technologies, Kazan Scientific Center of the Russian Academy of Sciences, Kazan, Russia
Keywords: physics-informed neural networks, PINN, deep learning, heat conduction, Reynolds-averaged Navier - Stokes equation, RANS, small Prandtl number, turbulent flow
Abstract
The feasibility of using physics-informed neural networks (PINNs) to modify the Reynolds-averaged Navier-Stokes (RANS) equations for solving a heat transfer problem in a square channel is explored. A method for approximating solutions to differential equations based on the PINN approach is studied for estimating the mean flow temperature field with various heat transfer fluids. We consider a fully developed turbulent flow at a high Reynolds number (Re = 6100) and small to moderate Prandtl numbers (Pr = 0.025-1.000), typical of fuel elements using liquid metals and gas mixtures as coolants. Two models employing different approaches to approximating the turbulent heat flux are implemented: the gradient diffusion hypothesis (GDH) and an improved GDH hypothesis with two trainable coefficients that accounts for the shortest distance to the channel wall. The use of the PINN approach is shown to allow a significant reduction in computational cost. Model training takes approximately 2 h on a single GPU, whereas direct numerical simulation (DNS) of a similar problem on a supercomputer cluster requires several weeks of computation. The proposed approach is shown to be effective for parametric optimization, especially at small Prandtl numbers. When PINNs are used with DNS data, the accuracy of solving the RANS equations is higher than with conventional RANS modeling. The highest accuracy is achieved by the model using the modified GDH approximation.
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