Scalar flux model

This type of model is usually referred to as an algebraic scalar-flux model. Similarmodels for the Reynolds-stress tensor are referred to as algebraic second-moment (ASM) closures. They can be derived from the scalar-flux transport equation by ignoring time-dependent and spatial-transport terms. 

A more sophisticated scalar-flux model could be employed in place of the gradient-diffusion model. However, given the degree of approximation inherent in the multi-environment model, it is probably unwarranted. 

There is no direct information on scalar transport due to velocity fluctuations. A PDF scalar-flux model is required to describe turbulent scalar transport.2... 

In transported PDF methods (Pope 2000), the closure model for A, V, ip) will be a known function26 ofV. Thus, (U,Aj) will be closed and will depend on the moments of U and their spatial derivatives.27 Moreover, Reynolds-stress models derived from the PDF transport equation are guaranteed to be realizable (Pope 1994b), and the corresponding consistent scalar flux model can easily be found. We shall return to this subject after looking at typical conditional acceleration and conditional diffusion models. 

The implications on the scalar-flux model, however, are profound. Indeed, one finds36... 

In many reported applications, a k-e CFD code has been employed, which gives an inconsistent description of the Reynolds stresses. Wouters (1998) has shown that this leads to other subtle problems, most notably in the scalar-flux model. 

One can argue, however, that the improved description of the triple-correlation term in the Reynolds-stress model and the improved scalar-flux model justify this redundancy. 

Adumitroaie, V., D. B. Taulbee, and P. Givi (1997). Explicit algebraic scalar-flux models for turbulent reacting flows. AIChE Journal 43, 1935-1946. 

The turbulent diffusivity, Dt, is assumed to be proportional to the turbulent viscosity. 5q is the turbulent Schmidt number with a typical value of 0.7. Equation (12.5.2-1) assumes that the scalar flux and the mean species concentration gradient are aligned, in contrast with the scalar flux model (Annex 12.5.2.A). This is strictly valid only for isotropic turbulence. Nevertheless, (12.5.2-1) is frequently applied in CFD codes. 

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