Direct numerical simulations (DNS) are conducted of a model hydrocarbon–nitrogen
mixing layer under supercritical conditions. The temporally developing mixing layer
configuration is studied using heptane and nitrogen supercritical fluid streams at a
pressure of 60 atm as a model system related to practical hydrocarbon-fuel/air systems.
An entirely self-consistent cubic Peng–Robinson equation of state is used to describe
all thermodynamic mixture variables, including the pressure, internal energy, enthalpy,
heat capacity, and speed of sound along with additional terms associated with the
generalized heat and mass transport vectors. The Peng–Robinson formulation is based
on pure-species reference states accurate to better than 1% relative error through
comparisons with highly accurate state equations over the range of variables used in
this study (600 [les ] T [les ] 1100 K, 40 [les ] p [les ] 80 atm) and is augmented by an accurate
curve fit to the internal energy so as not to require iterative solutions. The DNS results
of two-dimensional and three-dimensional layers elucidate the unique thermodynamic
and mixing features associated with supercritical conditions. Departures from the
perfect gas and ideal mixture conditions are quantified by the compression factor and
by the mass diffusion factor, both of which show reductions from the unity value. It
is found that the qualitative aspects of the mixing layer may be different according to
the specification of the thermal diffusion factors whose value is generally unknown,
and the reason for this difference is identified by examining the second-order statistics:
the constant Bearman–Kirkwood (BK) thermal diffusion factor excites fluctuations
that the constant Irwing–Kirkwood (IK) one does not, and thus enhances overall
mixing. Combined with the effect of the mass diffusion factor, constant positive large
BK thermal diffusion factors retard diffusional mixing, whereas constant moderate IK
factors tend to promote diffusional mixing. Constant positive BK thermal diffusion
factors also tend to maintain density gradients, with resulting greater shear and
vorticity. These conclusions about IK and BK thermal diffusion factors are species-pair dependent, and therefore are not necessarily universal. Increasing the temperature
of the lower stream to approach that of the higher stream results in increased layer
growth as measured by the momentum thickness. The three-dimensional mixing layer
exhibits slow formation of turbulent small scales, and transition to turbulence does not
occur even for a relatively long non-dimensional time when compared to a previous,
atmospheric conditions study. The primary reason for this delay is the initial density
stratification of the flow, while the formation of strong density gradient regions both
in the braid and between-the-braid planes may constitute a secondary reason for the
hindering of transition through damping of emerging turbulent eddies.
Coherent Structures of a Supersonic Mixing Layer by Direct Numerical Simulations.
