Research · Turbulent combustion modeling
Multiple Mapping Conditioning (MMC) is a probability density function approach to turbulent combustion. Coupled with large eddy simulation, it lets us predict flames that ignite, extinguish and re-ignite, in gaseous jets and spray flames. Our solvers are built in OpenFOAM.
Background: instantaneous temperature in a piloted jet flame with three mixing models
LES resolves the large turbulent eddies and models the rest. Combustion, however, happens at the smallest scales, where fuel and oxidizer mix molecularly. MMC represents that unresolved mixing with stochastic particles that carry the full thermochemical composition.
The key idea is to localize mixing in composition space. Each particle is conditioned on a reference variable, here the LES-filtered mixture fraction, and mixes only with particles that are close to it in that reference space. This keeps the particles from mixing across the flame, which is what lets MMC capture local extinction.
Because the particles are only weakly tied to the LES grid, the sparse-Lagrangian implementation uses far fewer particles than grid cells, which makes detailed chemistry affordable.
Particles in MMC relax towards each other over a minor mixing time scale. This time scale sets the level of compositional fluctuation, and with it whether a model predicts local extinction. It is modeled from the particle separation in reference space, dx, and the molecular and sub-filter diffusion:
The coefficient Cf is usually a fixed constant. In our dyn-aISO model it is computed locally instead. At the grid filter Δ, the sub-filter variance of mixture fraction is modeled as
and the same model is written at a test filter . Because the difference between the two filter levels is resolved, it gives an identity from which Cf follows directly, with no tuning:
The coefficients for the sub-filter scalar variance and its dissipation therefore adapt to the local flow, which is what lets the model follow flames from strong burning to near extinction.
Sandia piloted CH4/air jet flames, a standard test of a model's ability to capture extinction and re-ignition.
The fixed-coefficient models either over-predict burning or extinguish too much. With the dynamic model, the predicted level of local extinction, and the re-ignition further downstream, follow the measurements across the flame series.
Sharma, De & Cleary, Combust. Flame 238 (2022) 111872
Sydney piloted ethanol spray flames (AcF series), with evaporating droplets tracked as Lagrangian parcels and two-phase MMC for the gas-phase chemistry.
The dynamic time-scale model carries over to sprays, where evaporation adds a second source of mixture-fraction fluctuations. Scatter plots of temperature against mixture fraction show how each model spreads the particles between burning and extinguished states, and the radial temperature profiles are compared across four flames of the series.
Sharma & De, Combust. Flame 251 (2023) 112708
Sharma, De & Cleary, Proc. Combust. Inst. 38 (2020) 3399
Before moving to LES, the group developed RANS-based stochastic MMC for lifted jet flames in vitiated coflows, auto-igniting CH4/air and dimethyl ether flames, and turbulent premixed combustion. These studies laid the groundwork for the sparse-Lagrangian MMC-LES solvers.