Direct numerical simulation of a transitional supercritical binary mixing layer: heptane and nitrogen
Authors: OKONG'O NORA A. , BELLAN JOSETTE 
Published: September 2002

Direct numerical simulations (DNS) of a supercritical temporal mixing layer are
conducted for the purpose of exploring the characteristics of high-pressure transitional
mixing behaviour. The conservation equations are formulated according to
fluctuation-dissipation (FD) theory, which is consistent with non-equilibrium thermodynamics
and converges to kinetic theory in the low-pressure limit. According to FD
theory, complementing the low-pressure typical transport properties (viscosity, diffusivity
and thermal conductivity), the thermal diffusion factor is an additional transport
property which may play an increasingly important role with increasing pressure. The
Peng–Robinson equation of state with appropriate mixing rules is coupled to the
dynamic conservation equations to obtain a closed system. The boundary conditions
are periodic in the streamwise and spanwise directions, and of non-reflecting outflow
type in the cross-stream direction. Due to the strong density stratification, the layer is
considerably more difficult to entrain than equivalent gaseous or droplet-laden layers,
and exhibits regions of high density gradient magnitude that become very convoluted
at the transitional state. Conditional averages demonstrate that these regions contain
predominantly the higher-density, entrained fluid, with small amounts of the lighter,
entraining fluid, and that in these regions the mixing is hindered by the thermodynamic
properties of the fluids. During the entire evolution of the layer, the dissipation is
overwhelmingly due to species mass flux followed by heat flux effects with minimal viscous
contribution, and there is a considerable amount of backscatter in the flow. Most of
the species mass flux dissipation is due to the molecular diffusion term with significant
contributions from the cross-term proportional to molecular and thermal diffusion.
These results indicate that turbulence models for supercritical fluids should primarily
focus on duplicating the species mass flux rather than the typical momentum flux,
which constitutes the governing dissipation in atmospheric mixing layers. Examination
of the passive-scalar probability density functions (PDFs) indicates that neither the
Gaussian, nor the beta PDFs are able to approximate the evolution of the DNS-extracted
PDF from its inception through transition. Furthermore, the temperature–species
PDFs are well correlated, meaning that their joint PDF is not properly approximated
by the product of their marginal PDFs; this indicates that the traditional
reactive flow modelling based on replacing the joint PDF representing the reaction
rate by the product of the marginal PDFs is not appropriate. Finally, the subgrid-scale
temperature–species PDFs are also well correlated, and the species PDF exhibits important
departures from the Gaussian. These results suggest that classic PDFs used in
atmospheric pressure flows would not capture the physics of this supercritical mixing
layer, either in an assumed PDF model at the larger scale, or at the subgrid scale.