Large-eddy Simulation of Realistic Gas Turbine Combustors

y the presumed beta subgrid P DF and the conditional P DF , ˜P (C|Z) is modeled as a delta
function according to Pierce & Moin [5]. In the present two-phase flow application, the mixture
fraction equation (Eq. 2) consists of a source term due to the evaporation of liquid fuel. By
assuming a beta P DF for ˜P (Z) we implicitly assume that the time-scale of evaporation is small
compared to the scalar mixing time-scale. More advanced micro-mixing models accounting for
spray-chemistry interactions are necessary [12] to better represent the filtered source terms in the
continuity and mixture-fraction equations. Following these assumptions, the flamelet library is
computed and subgrid P DF integrals are evaluated to generate lookup tables to provide filtered
variables as:
ỹ i = ỹ i ( ˜Z, ˜Z ′′ 2
, ˜C), ˜T = ˜T ( ˜Z, ˜Z ′′ 2
, ˜C), ρ g = ρ g ( ˜Z, ˜Z ′′ 2
, ˜C), etc. (7)
where ˜Z ′′ 2
is the mixture fraction variance, ỹ i the species mass fractions, and ˜T the temperature.
Similar expressions are obtained for dynamic viscosity, molecular diffusivities, and other
properties required in the computation.
2.3 Subgrid Scale Models
The dynamic Smagorinsky model by Moin et al. [13] is used to close the subgrid terms as
demonstrated by Pierce & Moin [14]. The unclosed terms in Eqs. (2-4) are modeled using the
eddy-viscosity assumption. The eddy viscosity, eddy diffusivities, and subfilter variance of the
mixture fraction are evaluated as:
µ t = C µ ρ g ∆ 2 |˜S|, ρ g α t = C α ρ g ∆ 2 |˜S|, ρ g
˜Z ′′ 2
= C ˜Zρ g ∆ 2 | ▽ ˜Z| 2 (8)
where |˜S| =
√
˜Sij ˜Sij . The coefficients C µ , C α , and C ˜Z
are evaluated dynamically [14].
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