Scalar flux reacting scalars

The first term on the right-hand side of this expression is the molecular transport term that scales as Sc Re 1. Thus, at high Reynolds numbers,26 it can be neglected. The two new unclosed terms in (3.88) are the scalar flux (u.ja), and the mean chemical source term (Sa(chemical reacting flows, the modeling of (Sa(0)) is of greatest concern, and we discuss this aspect in detail in Chapter 5. 

The transport equation for the scalar flux of a reacting scalar [Pg.103]

Similar techniques have been employed to derive ASM models for turbulent reacting flows (Adumitroaie et al. 1997). It can be noted from (3.102) on p. 84 that the chemical source term will affect the scalar flux. For example, for a scalar involved in a first-order... 

Thus, the ASM scalar flux in a first-order reacting flow will decrease with increasing reaction rate. For higher-order reactions, the chemical source term in (3.102) will be unclosed, and its net effect on the scalar flux will be complex. For this reason, transported PDF methods offer a distinct advantage terms involving the chemical source term are closed so that its effect on the scalar flux is treated exactly. We look at these methods in Chapter 6. 

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

The Eulerian (bottom-up) approach is to start with the convective-diffusion equation and through Reynolds averaging, obtain time-smoothed transport equations that describe micromixing effectively. Several schemes have been proposed to close the two terms in the time-smoothed equations, namely, scalar turbulent flux in reactive mixing, and the mean reaction rate (Bourne and Toor, 1977 Brodkey and Lewalle, 1985 Dutta and Tarbell, 1989 Fox, 1992 Li and Toor, 1986). However, numerical solution of the three-dimensional transport equations for reacting flows using CFD codes are prohibitive in terms of the numerical effort required, especially for the case of multiple reactions with... 

Practical schemes for constructing polarimeters up to 1970 can be found in [11]. All detectors of optical radiation react to a change of intensity of luminous flux, but do not react to a state of its polarization. Therefore all methods for determining polarization are grounded in the transformation of the Stokes vector a scalar value. A polarization modulator installed prior to the detector is used for this purpose. The simplest modulator is used for the analysis of linearly polarized radiation. It may be a Polaroid, prism, grating... 

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