Reynolds-stress root modeling based on a statistical theory

Abstract

A new methodology of turbulence modeling is proposed by combining a statistical theory [T. Ariki, Phys. Fluids 31, 065104 (2019)] and the Reynolds-stress-root method [T. Ariki, Phys. Rev. E 92, 053010 (2015)], aiming at realizing practical turbulence model of wider applicability with the help of theoretical support. The resultant model integrates, at the same time, the following five features: coordinate covariance, realizability condition, near-wall behavior, history effect, and streamline curvature effect, which are all key ingredients to build up better turbulence model mimicking realistic behaviors. Numerical assessments of the model are conducted for homogeneous shear flow, channel flow, flow in a rotating pipe, and flow between concentric annuli, all of which show reasonable agreement with direct numerical simulations and experiments.