By Rodney O. Fox
This survey of the present state-of-the-art in computational versions for turbulent reacting flows rigorously analyzes the strengths and weaknesses of a few of the ideas defined. Rodney Fox specializes in the formula of functional types in place of numerical concerns coming up from their resolution. He develops a theoretical framework according to the one-point, one-time joint chance density functionality (PDF). The examine finds that each one usually hired versions for turbulent reacting flows could be formulated by way of the joint PDF of the chemical species and enthalpy.
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Extra info for Computational Models for Turbulent Reacting Flows
Isotropic turbulence is described by a single-time auto-correlation function ρu (τ ). Thus, an integral time scale can be deﬁned in terms of the auto-correlation function by ∞ τ¯ ≡ ρ(τ ) dτ. 37) 0 This time scale is proportional to the turbulence integral time scale deﬁned by τu ≡ k . 39) by 1/2 τu = Re L τη . 1. 3. 2. 1. Expressed in terms of the turbulence Reynolds number Re L = k 2 /εν. 3/4 For example, L u = Re L η. 3. 1. Expressed in terms of the turbulence Reynolds number Re L = k 2 /εν. 1/2 For example, τu = Re L τη .
In this case, all ﬂuid elements with age α are assumed to interact by exchanging matter with a ﬁctitious ﬂuid element whose concentration is φ(α) . 18)) causes the micromixing term to drop out:22 dφ = S with φ(0) = φin . 16), the micromixing time must be related to the underlying ﬂow ﬁeld. 16) appears in closed form. 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).
A more thorough discussion of the foundations of turbulence modeling can be found in Pope (2000). 28) for the case where the chemical source term is null have been widely studied. 28) in the absence 28 The experienced reader will recognize these CFD models as the so-called RANS turbulence models. 18 Turbulent reacting ﬂows of chemical reactions is linear in the scalar variable, CFD models for the mean scalar ﬁeld closely resemble the corresponding turbulence models for k and ε. 28) using Reynolds averaging.