Towards a general data-driven explicit algebraic Reynolds stress prediction framework

•A data-driven nonlinear extension for eddy viscosity models is proposed.•Neural networks are trained to reproduce the correct model scalar functions behaviour.•The model is valid in any inertial frame of reference.•Our method allows a full coupling with the Navier–Stokes equations.•The validation in complex 2D flows shows very good agreement with the reference data. We propose a method to extend linear eddy-viscosity models up to a second order formulation using machine learning algorithms. The method is applicable to any turbulence model equipped with a transport equation for the wall-normal component of the Reynolds stress tensor v2 and is based on our ITALO framework (Sotgiu et al., 2018). We implement and test our extension using as base the elliptic-blending k−ϵ−ϕ−α linear eddy-viscosity model of Billiard and Laurence (2011). Neural networks are used to derive scalar functional forms for the nonlinear part of the Reynolds stress constitutive equation. The networks have been trained with data from a planar channel at Reτ=1020 and a two-dimensional periodic channel perturbed with corrugations at Reb=32,156. The test cases comprise channel flows at Reynolds numbers ranging from Reτ=180 to Reτ=1020, a periodic square duct at Reb=10,320, and a periodic ribbed channel at Reb=37,200. A comparison with other nonlinear eddy-viscosity models is reported. The new proposed model shows very good agreement with the reference data.