The 2008 review of large-eddy simulation (LES) of turbulent reacting flows by Pitsch, Desjardins, Balarac and Ihme (Progress in Aerospace Sciences 44:466-478) assembled three closure developments of the Stanford group - an accurate conservative level set/ghost fluid method (ACLS/GFM) for primary atomization, a dynamic sub-filter mixture-fraction-variance model derived from a filter expansion, and a flamelet/progress-variable model for NO formation with radiative heat loss - and posed one common unfinished objective: converting these closures into quantitative, experimentally validated LES prediction of pollutant emissions in representative aircraft-engine spray combustors, where the paper's Pratt & Whitney combustor LES still overpredicted exit-averaged NO by roughly 38% when radiation was included.

Background

Large-eddy simulation (LES) computes the large, energy-containing turbulent scales of a flow directly and models the effect of the unresolved sub-filter scales; direct numerical simulation (DNS) resolves all scales down to the viscous scale and serves as reference data for sub-filter models. Predictive LES of an aircraft gas-turbine combustor must represent a chain of coupled processes: liquid injection, primary atomization (the breakup of the liquid jet into ligaments and droplets), droplet transport and evaporation, turbulent fuel-air mixing, chemical reaction, pollutant formation, and radiative heat loss.

Several specialist ingredients are involved. The mixture fraction ZZ is a conserved scalar measuring local fuel-air mixedness; flamelet-based combustion models tabulate chemistry as functions of ZZ, a progress variable CC tracking the extent of reaction, and (when heat loss matters) enthalpy - the flamelet/progress-variable (FPV) formulation. Because LES filters the fields, the reaction-rate closure needs the probability density function (PDF) of ZZ within a filter volume, which is usually presumed (e.g. a beta PDF, a flexible two-parameter distribution on the unit interval) once the filtered mean and the sub-filter variance Z′Z′‾\overline{Z'Z'} are known; the variance is therefore a load-bearing quantity that must itself be modeled, dynamically if possible. For the liquid side, the accurate conservative level set/ghost fluid method (ACLS/GFM) of Desjardins, Moureau and Pitsch (2008) combines a conservative level-set field (a smooth marker that is transported and reinitialized to keep a sharp, mass-conserving interface) with a ghost fluid treatment (assigning ghost states across the interface so density jumps and surface-tension forces remain sharp without spurious currents) - enabling sharp-interface DNS/LES of atomization at large liquid-gas density ratios. Nitric oxide (NO) is a regulated pollutant formed mainly through the temperature-sensitive, slow thermal (Zeldovich) mechanism, so its prediction is sensitive to flame temperature, radiative heat loss (turbulence-radiation interaction), and residence time, and it evolves on time scales longer than flame-element transit times; Ihme and Pitsch (2008) therefore solved a separate transported NO equation with flamelet-derived sources and an enthalpy/radiation extension of FPV. Two conventions for model assessment matter: a priori testing evaluates a closure on filtered DNS data, while a posteriori testing runs the closure inside an actual LES and compares statistics with experiment or DNS.

The 2008 review by Pitsch, Desjardins, Balarac and Ihme presented the three closures above but each was validated only in a limited setting: the dynamic variance model of Balarac, Pitsch and Raman (2008) was derived for a Gaussian-type filter expansion and tested a priori with a box filter on DNS of homogeneous isotropic turbulence; the NO/radiation model was demonstrated on Sandia flame D, a piloted nonpremixed jet flame; and the ACLS/GFM atomization method lacked mesh-refinement and grid-convergence studies in realistic injector geometries. Applied to a Pratt & Whitney aircraft combustor (the configuration earlier simulated by Moin and Apte, 2006), the combined LES still overpredicted exit-averaged NO by roughly 38% when radiation was included. The paper's stated next steps were a database of DNS results for engine-relevant atomization configurations (turbulent liquid jets, air-assisted co-annular liquid jets, and liquid jets in cross-flow), mesh-refinement studies and parameter variations completing the preliminary ACLS simulations, and the development of sub-filter atomization models from those DNS data to enable LES of aircraft-engine combustion with accurate NO prediction. On the numerical side, raw grid convergence of atomizing-spray simulation has been argued to require regularization (for example explicit volume diffusion) before convergence is definable (Abbas et al., 2021).

Problem Statement

Achieve the common scientific objective that Pitsch, Desjardins, Balarac and Ihme (2008) posed for LES of turbulent reacting engine flows: quantitative, experimentally validated LES prediction of NO emissions in a representative aircraft-engine spray combustor, bringing to that standard the three closure developments presented there - an accurate conservative level set/ghost fluid method (ACLS/GFM) for primary atomization, a dynamic sub-filter mixture-fraction-variance model derived from a filter expansion, and a flamelet/progress-variable model for NO formation with radiative heat loss. The source-documented starting point is the LES of the Pratt & Whitney combustor at take-off conditions, which overpredicted the exit-plane-averaged NO mole fraction by 38% with radiation included (simulation/experiment ratio 1.3803; about 4.2 without radiation). The work to be carried out is: (i) a primary-atomization DNS database for the engine-relevant regime, that is, the regime of large liquid-gas density ratio, turbulent inflow and high Weber and Reynolds numbers (large ratios of inertial forces to surface-tension and to viscous forces, respectively), covering the source's three named target configurations - turbulent liquid jets, air-assisted co-annular liquid jets, and liquid jets in cross-flow; (ii) a mesh-refinement and parameter-variation study of turbulent atomization in that regime that fixes a grid family, an observable and a tolerance justified by the refinement behaviour, exhibits monotone reduction of that observable under refinement, with regularization of the atomizing-spray simulation admissible where raw convergence is unattainable, and reports the method's performance in complex injector geometries and coupled spray workflows; (iii) sub-filter atomization models derived from the part-(i) DNS that reproduce that DNS's sub-filter quantities on held-out data - a configuration, Reynolds/Weber number or resolution different from the derivation case, with the model not fitted to its evaluation data - and are demonstrated in LES; (iv) the dynamic sub-filter mixture-fraction-variance closure, whose filtered variance and scalar dissipation are to agree a priori with the part-(i) DNS on such held-out data, validated against DNS rather than experiment because no experiment measures these quantities; and (v) the flamelet/progress-variable NO model with radiative heat loss together with the integrated prediction built from items (i)-(iv), in which that integrated LES is to reproduce the measured exit-plane-averaged NO mole fraction of the Pratt & Whitney combustor at take-off conditions - the measurement and its comparison being those reported by Moin and Apte (2006) and Pitsch et al. (2008), with a baseline simulation/experiment ratio of 1.3803 with radiation - to within the experimental uncertainty of that measurement and two-sided, so that under-prediction is as far from the measured value as the overprediction documented at the outset. The ACLS/GFM method is the sharp-interface approach the source developed for this program; other sharp-interface methods may be used.

References

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