RANS-CNN: A Physics-Informed Convolutional Neural Network for Solving Reynolds-Averaged Navier-Stokes Equations in Duct Flows

Abstract

Classical Computational Fluid Dynamics (CFD) simulations of turbulent flows in aerospace applications are computationally demanding and limit rapid design exploration. Convolutional Neural Networks (CNN) are being employed as surrogate models to overcome this challenge. Physics-informed approaches have also been applied to CNNs albeit only for simple flow fields such as laminar flow and heat conduction. This study advances Physics-Informed Convolutional Neural Networks (PICNN) to solve the steady incompressible Reynolds-Averaged Navier-Stokes (RANS) equations in wall-bounded geometries. The proposed method employs a higher-order finite difference scheme for computing spatial gradients, thus enhancing numerical accuracy. Additionally, the Dirichlet boundary conditions are strongly enforced in the network architecture using custom output layers and boundary masks. Numerical stabilisation is incorporated to enable the CNN to simulate high Reynolds number flows without losing stability. To assess the capabilities of this approach on aerospace use cases, it is tested on three data-free cases: S-shaped duct, a ducted body force heat exchanger, and flow over a forward facing step along with a backward facing step geometry with sparse labelled data. Moreover, a comparison between zero-equation and one-equation turbulence models is presented when employed in this framework. The RANS-CNN models performed with over 95 % accuracy on geometries with attached flow and 80 % on separated flow cases. The results obtained from the case studies confirm the capability of the RANS-CNN method in developing a robust and computationally efficient surrogate model with sparse data for smooth ducts.