Vortex Stretching of Non-premixed, Diluted Hydrogen/Oxygen Flamelets

A three-dimensional flamelet model considering vortex stretching with unitary Lewis number is used to simulate diluted hydrogen-oxygen diffusion flames. Non-reacting nitrogen is used as the diluent gas in the fuel stream. Unitary Lewis number provides a common thermal and mass diffusivity from which to create scalar dissipation rate. Both stable and unstable branches of flammability curves (S-curves) are calculated with three vorticity levels and plotted against multiple input and output parameters. The description of the three-dimensional flamelet structure, allowing vorticity and variable density to produce a centrifugal effect, is seen to be necessary for an accurate determination of the $\mathrm{H_2O}$ production rate when ambient inflow strain rate $(S^*)$ and vorticity $(\omega)$ are chosen as the key parameters. Maximum temperature and integrated $\mathrm{H_2O}$ production rate each nearly collapse to a single curve when plotted versus maximum scalar dissipation rate $(\chi_{max})$ but do not collapse when plotted versus the local maximum strain rate $(S^*_{local})$ or $S^*$. Additionally, $S^*_{local}$ and scalar dissipation rate $(\chi)$ depend strongly on vorticity and ambient inflow strain rate. It is argued that the controlling inputs for a flamelet embedded in a turbulent eddy are the ambient vorticity and strain rate which are thus the natural choice of parameterizing variables. These ambient quantities can be readily linked to the averaged or filtered turbulent flow by leveraging cascade theory, as opposed to local strain rate or scalar dissipation rate within the flame zone, which do not have a widely accepted, first-principles scaling connection to the turbulence cascade.