Sub grid scale model

WangJ, Ge W, LiJ Eulerian simulation of heterogeneous gas-sobd flows in CFB risers EMMS-based sub-grid scale model with a revised cluster description, Chem Eng Sci 63 1553-1571, 2008a. 

Large Eddy Simulation (LES) model in which large-scale eddies caused by turbulence is simulated using Navier-Stokes equation, and the small eddies are simulated by a sub-grid scale model. This model can be regarded as the combination of DNS and Reynolds-averaged method. 

Dhotre MT, Niceno B, Smith BL Large eddy simulation of a bnbble column using dynamic sub-grid scale model, Chem EngJ 136 337—348, 2008. http / dx.doi.org/10.1016/J.ceJ. 2007.04.016. 

Similar remarks apply for CFD models that ignore sub-grid-scale mixing. The problem of closing the chemical source term is discussed in detail in Chapter 5. 

As discussed in Chapter 2, a fully developed turbulent flow field contains flow structures with length scales much smaller than the grid cells used in most CFD codes (Daly and Harlow 1970).29 Thus, CFD models based on moment methods do not contain the information needed to predict x, t). Indeed, only the direct numerical simulation (DNS) of (1.27)-(1.29) uses a fine enough grid to resolve completely all flow structures, and thereby avoids the need to predict x, t). In the CFD literature, the small-scale structures that control the chemical source term are called sub-grid-scale (SGS) fields, as illustrated in Fig. 1.7. 

Another Lagrangian-based description of micromixing is provided by multienvironment models. In these models, the well macromixed reactor is broken up into sub-grid-scale environments with uniform concentrations. A four-environment model is shown in Fig. 5.16. In this model, environment 1 contains unmixed fluid from feed stream 1 environments 2 and 3 contain partially mixed fluid and environment 4 contains unmixed fluid from feed stream 2. The user must specify the relative volume of each environment (possibly as a function of age), and the exchange rates between environments. While some qualitative arguments have been put forward to fit these parameters based on fluid dynamics and/or flow visualization, one has little confidence in the general applicability of these rules when applied to scale up or scale down, or to complex reactor geometries. 

Ghan, S. J., and R. C. Easter, Comments on A Limited-Area-Model Case Study of the Effects of Sub-Grid Scale Variations in Relative Humidity and Cloud upon the Direct Radiative Forcing of Sulfate Aerosol, Geophys. Res. Lett., 25, 1039-1040 (1998). 

Gillani N. V. and Pleim J. E. (1996) Sub-grid-scale features of anthropogenic emissions of NO. and VOC in the context of regional Eulerian models. Atmos. Environ. 30, 2043 —2059. 

As discussed in Chapter 3, with LES, the smallest scale to be resolved is chosen to lie in the inertial sub-range of the energy spectrum, which means the so-called sub-grid scale (SGS) wave numbers are not resolved. As LES can capture transient large-scale flow structures, it has the potential to accurately predict time-dependent macromixing phenomena in the reactors. However, unlike DNS, a SGS model representing interaction of turbulence and chemical reactions will be required in order to predict the effect of operating parameters on say product yields in chemical reactor simulations. These SGS models attempt to represent an inherent loss of SGS information, such as the rate of molecular diffusion, in an LES framework. Use of such SGS models makes the LES approach much less computationally intensive than the DNS approach. DNS... 

This means that larger scale motions can be explicitly resolved and deterministically forecasted. The smaller scale motions, namely turbulence, are not explicitly resolved. Rather, the effects of those sub-grid scales on the larger scales are approximated by turbulence models. These smaller size motions are said to be parameterized by sub-grid scale stochastic (statistical) approximations or modes. The referred experimental data analyzes of the flow in the atmospheric boundary layer determine the basis for the large eddy simulation (LES) approach developed by meteorologists like Deardorff [27] [29] [30]. Large-Eddy Simulation (LES) is thus a relatively new approach to the calculation of turbulent flows. 

Leonard [97] defined the complementary tensor, Ckk + Rkk), and suggested that this term can be added to the filtered pressure, p+ Ckk + Rkk)-In this way the complementary tensor requires no modeling. Analogous to the average turbulent kinetic energy quantity, one can also define a sub-grid scale kinetic energy variable, ksos = Cu + Ru). Hence, the anisotropic SGS... 

Transport occurs at a variety of spatial and temporal scales. In atmospheric models, it is customary to distinguish between motions that can be resolved on the numerical grid of the model (often called large-scale ) and sub-grid scale processes (such as... 

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