  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 water burning rate. Both maximum temperature and
integrated water burning rate nearly collapse to a single curve when plotted
versus maximum scalar dissipation rate but do not collapse when plotted versus
the local maximum strain rate or the ambient strain rate; however, local strain
rate and scalar dissipation rate depend strongly on vorticity and ambient
strain rate. It is argued that the controlling inputs and natural parameters
for a flamelet embedded in a turbulent eddy are the ambient vorticity and
strain rate which are thus the natural parameterizing variables as opposed to
local strain rate or scalar dissipation rate within the flame zone.
Furthermore, established practices of the scaling of velocity derivatives exist
in the literature while scaling laws for scalar gradients are sparse and
unsubstantiated, further supporting the use of ambient parameterizing
quantities.
