Assessment of explicit algebraic stress models in transonic flows

A class of recently developed explicit algebraic stress models (EASM) [2] is subjected to a critical assessment in transonic engineering flows. It is found that the performance and robustness of these models is hampered with inaccuracies due to an inappropriate regularization practice inherent to the stress-strain relation. The origin of the régularisation is attributed to an inadequate closure assumption for the production-to-dissipation ratio in non-equilibrium conditions. To remedy the defect, a simple approximation for an explicit representation of P/ε within the stress-strain relation is proposed. The emerging unregularized EASM satisfies the positivity requirement for the eddy-viscosity and obeys to the realizability principle. Several exemplary 2D and 3D testcases, employing different numerical algorithms, are investigated to assess the predictive capabilities of the present proposal including a linear truncation. Supplementary, the mathematical rigour of the approach is used to combine the non-linear stress-strain relation with a multiscale methodology and pressure-dilatation models. The paper aims to argue the potential advantages of an unregularized EASM methodology in transonic engineering flows.

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Assessment of explicit algebraic stress models in transonic flows