Eddy viscosity models

Eddy Viscosity Models. A large number of closure models are based on the Boussinesq concept of eddy viscosity ... 

In ventilation problems, it is often sufficient to use simpler turbulence models, such as eddy-viscosity models. and Ujt are then re... 

Germano, M., U. Piomelli, P. Moin, and W. H. Cabot (1991). A dynamic subgrid-scale eddy viscosity model. Physics of Fluids 7, 1760-1765. 

The two-equation models (especially, the k-s model) discussed above have been used to simulate a wide range of complex turbulent flows with adequate accuracy, for many engineering applications. However, the k-s model employs an isotropic description of turbulence and therefore may not be well suited to flows in which the anisotropy of turbulence significantly affects the mean flow. It is possible to encounter a boundary layer flow in which shear stress may vanish where the mean velocity gradient is nonzero and vice versa. This phenomenon cannot be predicted by the turbulent viscosity concept employed by the k-s model. In order to rectify this and some other limitations of eddy viscosity models, several models have been proposed to predict the turbulent or Reynolds stresses directly from their governing equations, without using the eddy viscosity concept. 

For LES performed in physical space, the basic sub-grid stress model is the eddy-viscosity model proposed by Smagorinsky . The Smagorinsky model is based on the gradient transport hypothesis and the sub-grid viscosity concept, just as the Reynolds stress models based on the Boussinesq eddy viscosity hypothesis, and expressed as ... 

While the model apparently leads to improved predictions, its complexity has discouraged many researchers. Therefore, in a later study Deardorff [31] reverted to an isotropic eddy-viscosity model in order to decrease the computational costs. In the latter model version an additional equation was used to determine the residual kinetic energy, as the eddy viscosity vsgs was expressed by ... 

Shih T-H, Liou WW, Shabbir A, Zhu J (1995) A New k-e Eddy Viscosity Model for High Reynolds Number Turbulent Elows. Comp Eluids 24(3) 227-238 Smith LM, Reynolds WC (1992) On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models. Phys Fluids A 4(2) 364-390... 

Comparison of time-averaged centerline velocity from nonreactive LES in [3] with present simulations using MILES and a One-Equation Eddy-Viscosity Model (OEEVM) [7] indicates that the near-inlet flow is captured fairly well with LES but can be somewhat sensitive to the actual choice of the specific inlet floating condition (Fig. 11.26). 

The classical turbulence models express the eddy viscosity algebraically in terms of a turbulence scale and intensity that are related, respectively, to the characteristic length dimensions of the flow field and the local mean velocity gradients. This implies an equilibrium between the local turbulence and the mean motion. This requirement of equilibrium has been relaxed in some eddy viscosity models where the intensity and scale of turbulence used to evaluate the eddy viscosity are expressed by partial differential equations for the turbulence kinetic energy and its dissipation rate. This latter class of models is presented in detail, for example, in Refs. 76 and 77. 

FIGURE 6.35 Near-wall eddy viscosity models. 

Shih, T.H. Uou, W.W. Shabbir, A Yang, Z G et al. 1995. A new k-e eddy viscosity model for high Reynolds number turbulent flows. Comput Fluid, 24 3) 227-238. 

A reasonable compromise for model accuracy and computational expense are eddy viscosity models relating the individual Reynolds stresses to mean flow gradients ... 

The family of two-equation A -f models is the most widely used of the eddy viscosity models. Ak-e model consists of two transport equations, one for the turbulent kinetic energy k and one for the energy dissipation rate e. The turbulent eddy viscosity is calculated from ... 

The standard k-s model, as presented by Launder and Spalding [2], is by far the most widely-used two-equation eddy viscosity model, also for modeling turbulence in stirred tank reactors. The popularity of the model and its wide use and testing has thrown light on both its capabilities and its shortcomings, which are well documented in the literature [2-8]. For high turbulent Reynolds numbers, the model may be summarized as follows ... 

Shih, T.-H., W. W. Liou, A. Shabbir, and J. Zhu (1995). A new k-s eddy-viscosity model for high Reynolds number turbulent flows model development and validation, Comput. Eluids, 24, 227-238. 

At present, the eddy viscosity model and Reynolds stress model are commonly used in engineering field. These two kinds of model are described briefly in the subsequent sections. The LES model requires large computing capacity as well as heavy computation work so as the application of this model is limited and still under further development thus only basic idea of this method is given in subsequent section. 

Closure is obtained by modeling the residual-stress tensor, most simply by an eddy-viscosity model. 

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