Sub-grid-scale, SGS

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. 

Chapter 3 will be employed. Thus, in lieu of (x, t), only the mixture-fraction means ( ) and covariances ( , F) (/, j e 1,..., Nm() will be available. Given this information, we would then like to compute the reacting-scalar means and covariances (require additional information about the mixture-fraction PDF. A similar problem arises when a large-eddy simulation (LES) of the mixture-fraction vector is employed. In this case, the resolved-scale mixture-fraction vector (x, t) is known, but the sub-grid-scale (SGS) fluctuations are not resolved. Instead, a transport equation for the SGS mixture-fraction covariance can be solved, but information about the SGS mixture-fraction PDF is still required to compute the resolved-scale reacting-scalar fields. 

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... 

Niceno B, Dhotre MT, Deen NG One-equation sub-grid scale (SGS) modelhng forEuler-Euler large eddy simulation (EELES) of dispersed bubbly flow, Chem Eng Sci 63 3923-3931, 2008. http //dx.doi.Org/10.1016/j.ces.2008.04.050. 

The sub-grid-scale turbulent Schmidt number has a value of Scsgs 0.4 (Pitsch and Steiner 2000), and controls the magnitude of the SGS turbulent diffusion. Note that due to the filtering process, the filtered scalar field will be considerably smoother than the original field. For high-Schmidt-number scalars, the molecular diffusion coefficient (T) will be much smaller than the SGS diffusivity, and can thus usually be neglected. 

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... 

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