Development of nonlinear Reynolds average turbulent [formula omitted] models

Abstract

Reynolds Average Navier Stokes (RANS) models are among the most employed models to solve turbulent flows, due to their low computational cost. The majority of RANS models use the Boussinesq approximation, based on a linear relation between the deviatoric part of Reynolds stress tensor and the rate of strain tensor, with the turbulent viscosity as the positive proportionality parameter. However, these models fail in several situations, and a great deal of effort has been made by the scientific community aiming to improve models prediction through the development of nonlinear models. Analysis of higher-order models employing objective orthogonal tensors has shown to be very promising to improve the prediction of the normal components of the Reynolds stress. In this work, nonlinear models based on combinations of the square of the rate-strain tensor and non-persistence tensor are examined for a range of friction Reynolds number from 395 to 5200. Two sets of models employing different tensor basis are proposed, both employing the turbulent kinetic energy as the turbulent characteristic velocity. With respect to the turbulent characteristic length, the first set of models employs the dissipation rate of the turbulent kinetic energy, while the second set employs the intensity of the rate of strain tensor. The models prediction for a channel flow are compared with DNS data. As expected, the nonlinear models present a better adherence to the DNS data. In addition, the new approach with the norm of the deformation replacing the dissipation of turbulent kinetic energy lead to more accurate predictions with respect to the DNS.