A general one-equation turbulence model for free shear and wall-bounded flows

Abstract

The purpose of this work is to introduce a complete and general one-equation model capable of correctly predicting a wide class of fundamental turbulent flows like boundary layer, wake, jet, and vortical flows. The starting point is the mature and validated two-equation k-ω turbulence model of Wilcox. The newly derived one-equation model has several advantages and yields better predictions than the Spalart-Allmaras model for jet and vortical flows while retaining the same efficiency and quality of the results for near-wall turbulent flows without using a wall distance. The derivation and validation of the new model using findings computed by the Spalart-Allmaras and the k-ω models are presented and discussed for several free shear and wall-bounded flows.

Impact of transversal traveling surface waves in a non-zero pressure gradient turbulent boundary layer flow

“…This associated convection velocity depends on the distance from the wall. The final velocity component u RANS, m , which is provided by an upstream RANS solution based on the Fares-Schröder turbulence model [5] and the normalized stochastic fluctuation u m of Eq. 3 that undergoes a Cholesky decomposition.…”

Exploring k and ϵ with R–Equation Model Using Elliptic Relaxation Function

“…Probably, it is the most essential step, since the generality of the reconstructed k and must be guaranteed through a wide range of flows. The most appropriate assumption concerning such a reconstruction is the Bradshaw hypothesis [10] implemented directly into many turbulence models [7]. With the Bradshaw-relation, k may be expressed using the tentative eddy viscosity (C μ f n μ R) through the turbulence structure parameter:…”

“…Recent DNS and experimental data indicate that the Bradshaw-hypothesis is neither exactly valid in the viscous sublayer of the turbulent boundary layer nor in the free shear layers [7,8]. However, it is to be expected that the introduction of Eq.…”

“…A number of innovative ideas have been devoted to improving the accuracy of one-equation models, comprising the equilibrium and non-equilibrium flows [3][4][5][6][7][8][9]. The Baldwin-Barth (BB) model [3] derived using the k-closure is among the first one-equation models to be self-consistent by avoiding the use of algebraic length scales.…”

“…However, they improve the predictive capabilities of the models in wall-bounded nonequilibrium flows compared with the SA model and retain their wall-distance-free feature. Fares and Schröder [7] devise a one-equation model using the findings of the SA and k-ω models that predicts a wide range of flows especially jets and vortical flows more accurately than the SA model while retaining the same quality of results for near-wall flows, and to be more efficient than the k-ω model. Nagano et al [8] propose a low-Reynolds number (LRN) one-equation model derived from an LRN two-equation k-model using the modified Bradshaw-relation that accounts for near-wall turbulence.…”