A Novel Algebraic Stress Model with Machine-Learning-Assisted Parameterization

Abstract

Reynolds-stress closure modeling is critical to Reynolds-averaged Navier-Stokes (RANS) analysis, and it remains a challenging issue in reducing both structural and parametric inaccuracies. This study first proposes a novel algebraic stress model named as tensorial quadratic eddy-viscosity model (TQEVM), in which nonlinear terms improve previous model-form failure due to neglection of nonlocal effects. Then a data-driven regression model based on a fully-connected deep neural network is designed to determine the TQEVM coefficients. The well-trained data-driven model using high-fidelity direct numerical simulation (DNS) data successfully learned the underlying input-output relationships, further obtaining spatial-dependent optimal values of these coefficients. Finally, detailed validations are made in wall-bounded flows where nonlocal effects are expected to be significant. Comparative results indicate that TQEVM provides improvements both for the stress-strain misalignment and stress anisotropy, which are clear advantages over linear and quadratic eddy-viscosity models. TQEVM extends to the scope of resolution to the wall distance y + ≈ 9 as well as provides a realizable solution. RANS simulations with TQEVM are also carried out and the obtained mean-flow quantities of interest agree well with DNS. This work, therefore, results in a high-fidelity representation of Reynolds stresses and contributes to further understanding of machine-learning-assisted turbulence modeling and regression analysis.Energies 2020, 13, 258 2 of 21 improving sensitivity to curvature and/or rotation effects, such as introducing corrections into the eddy viscosity equation [10], the dissipation rate equation [11], the specific dissipation rate equation [12], and introducing corrections into eddy-viscosity coefficient [12,13]. However, none of the essential changes occur in the baseline framework of closure modeling. Obviously, the variant closure coefficients cannot improve the inherent limitations due to the underlying model-form inaccuracy rooted in Boussinesq hypothesis.Linear stress-strain relationship origins from the Boussinesq hypothesis that turbulence react locally to the changes of mean-flow behavior in equilibrium flows. However, that is not really the case. In most turbulent flows, there exists a large misalignment in stress-strain response which has been repeatedly confirmed with high-fidelity DNS investigation [14][15][16]. In view of pressure-strain correlations in the exact Reynolds-stress transport equations, the stress-strain misalignment is theoretically generated from the nonlocal response of the pressure to the entire flow field through Green's functions [17]. As a result, the in-phase type EVMs certainly experience failure, especially in flows with strong spatial inhomogeneity (e.g., rotation/curvature [10,18], three-dimensionality [19], secondary-flow [20], etc.). These flow effects make changes in the mean shear (i.e., spatial inhomogeneity) and turbulence structures [21][22][23], further enhancing nonlocality on the...

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