By Rodney O. Fox
This survey of the present state-of-the-art in computational types for turbulent reacting flows rigorously analyzes the strengths and weaknesses of a number of the thoughts defined. Rodney Fox makes a speciality of the formula of sensible types in preference to numerical concerns bobbing up from their answer. He develops a theoretical framework in keeping with the one-point, one-time joint chance density functionality (PDF). The examine unearths that each one quite often hired types for turbulent reacting flows should be formulated when it comes to the joint PDF of the chemical species and enthalpy.
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Additional info for Computational Models for Turbulent Reacting Flows (Cambridge Series in Chemical Engineering)
M K K )h(m 1 1, . . 34) m K =1 N S(ψ n ). 34) follows by approximating S evaluated at the bin center by its value at a sample point contained in the bin. In the limit where the ﬁne grid becomes inﬁnitely ﬁne, the last term is just the spatial-average chemical source term: S L L = 0 S(φ(x)) dx = lim N →∞ 1 N N S(ψ n ). 32 In summary, the FM approach to turbulent reacting ﬂows is closely connected (either directly or indirectly) with the determination of the joint composition PDF. , in terms of S instead of S L ).
17). 16) are found by averaging with respect to the internal-age transfer function23 H (α, β) and the environments:24 ∞ 2 φ(α) = pn n=1 φ(n) (β)H (α, β) dβ. 18) 0 For the PFR and the CSTR, H (α, β) has particularly simple forms: Hpfr (α, β) = δ(β − α) 21 22 23 24 and Hcstr (α, β) = E cstr (β). , non-equal-volume mixing), the IEM model yields poor predictions. , the E-model of Baldyga and Bourne (1989)) that account for the evolution of p1 should be employed to model non-equal-volume mixing. In Chapter 6, this is shown to be a general physical requirement for all micromixing models, resulting from the fact that molecular diffusion in a closed system conserves mass.
9). , local ﬂuid-element interactions due to molecular diffusion). 14) to predict the outlet concentrations in the framework of RTD theory. For non-ideal reactors, extensions of RTD theory to model micromixing have been proposed in the CRE literature. ) However, due to the non-uniqueness between a ﬂuid element’s concentrations and its age, micromixing models based on RTD theory are generally ad hoc and difﬁcult to validate experimentally. 3 Zone models An alternative method to RTD theory for treating non-ideal reactors is the use of zone models.