Modelling Sub-Grid Passive Scalar Statistics in Moderately Dense Evaporating Sprays

Spray evaporation in spatially decaying turbulence is simulated using carrier-phase direct numerical simulations (CP-DNS). The CP-DNS cover a much wider parameter range than earlier fully resolved DNS of regular droplet arrays that were used to calibrate scaling laws for sub-grid closures of the distribution of mixture fraction and its conditionally averaged scalar dissipation. The scaling laws include the effects of sub-grid interactions between droplet evaporation and turbulence, and here they are assessed by direct comparison with the statistics from the CP-DNS. Two issues can be observed: Firstly, care must be taken when interpreting the CP-DNS statistics as the lack of resolution of the point particle surface could impact on the values in DNS cells that are located within the (unresolved) quasi-laminar wake. Secondly, the scaling laws present similar agreement with CP-DNS data as had been observed before for the fully resolved DNS. The scaling law for the scalar dissipation approximates the DNS statistics well, independent of the droplet number density, Stokes number and turbulence intensity. The estimated mixture fraction distribution (the PDF) is good for the mixture fraction values larger than a suitable average value but deteriorates for smaller mixture fractions due to inherent model limitations. The data corroborate that the scaling laws for turbulent micro-mixing can potentially serve as sub-grid closures for mixture fraction based combustion models such as flamelet and conditional moment closure approaches in large eddy simulations and may provide better approximations than existing expressions derived from single-phase non-premixed combustion.