Comparative numerical testing of one- and two-equation turbulence models for flows with separation and reattachment

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

“…The performance and the predictive capabilities of many models including the Baldwin-Lomax, Baldwin-Barth, Spalart-Allmaras, standard k-ε, k-ω, and the SST [27] models are documented in many publications [3,13,42,43,46,51,59,62] and corroborate the quality of the one-equation models, especially the SpalartAllmaras model. There are, however, some limitations in the generality of almost all one-equation models, since they lack a correct prediction of both wall-bounded and free shear flows simultaneously.…”

“…A complete model for ν t was also proposed by Secundov [50] as an extension of the former Nee and Kovasznay model with considerable success. Its current formulation, which was unknown in the English speaking community until its publication in 1995 is called the ν t 92 version [51]. In 1991 Baldwin and Barth [2] derived an elaborate transport model from the classical k-ε model, which had limited success due to its inconsistent numerical behavior at turbulent/nonturbulent interfaces [28,62].…”

A differential equation for approximate wall distance

“…This issue will be addressed below. The initial distribution in the interior domain is given by Equation (5), which represents a trivial solution of Equation (4). The term |grad(G)| 2 is rearranged using the identity…”

“…The t92 model of Secundov [4] for example reduces the distance to the nearest wall d by the quantity k s (d e = d w +0:01k s ) to account for wall roughness. A modiÿed Spalart-Allmaras model for rough wall boundary layers is proposed in Reference [11] which also shifts the distance d by the value R = 0:…”

“…Considering on the other hand the fact that these operations prevent the use of vector acceleration and require massive communication between the domains on parallel architectures to exchange all grid co-ordinates, such a trivial computation turns out to be complicated and computationally expensive, in particular for large problems. Considering the formulations of current turbulence models like the Baldwin and Lomax [1], Baldwin-Barth [2], Spalart-Allmaras [3], Secundov's t92 [4] and Menter's SST [5] model it is apparent, that the near-wall turbulence is often considered in the formulations by explicitly enforcing a dependence of the production or destruction terms, e.g. wall damping terms, on the normal distance d to the nearest wall or on the normalized distance y + = u d= .…”