Direct numerical simulations are used to investigate the `long time' distribution of mass fraction fluctuations in stationary compressible isotropic turbulent binary nitrogen-hydrocarbon mixtures under supercritical pressure conditions. The governing equations are the compressible Navier-Stokes equations together with the cubic Peng-Robinson real gas state equation, and generalized heat and mass diffusion derived from non-equilibrium thermodynamics. A highly efficient procedure is presented which allows for the solution of all thermodynamic quantities without iterations or interpolation tables. The simulations consider equal mass binary mixtures of combinations of nitrogen, heptane, dodecane, and 3-methylhexane, having molecular weight ratios in the range 1 -> 6.08.

It is shown that temperature and pressure gradient induced Soret mass diffusion results in statistically stationary mass fraction distributions at long times. The results reveal that the mass diffusion term due to the pressure gradient acts as a production mechanism in the Favre averaged scalar variance transport equation, and is balanced by Fickian dissipation to produce the stationary states. The resulting scalar probability density function is characterized by a larger than Gaussian flatness factor, and is asymmetric due to the mass fraction dependence of the partial molar volume. The stationary scalar variance amplitude increases both with increasing turbulence Mach number and molecular weight ratio of the species, but is inversely related to the turbulence Reynolds number. The scalar energy spectra exhibit peak values at wavenumbers corresponding to the peak in the velocity dissipation spectra.

The figures at the right depict long time contours from a typical stationary box turbulence simulation conducted on 128 x 128 x 128 grid points. The simulation was intitialized with equal masses of perfectly premixed nitrogen and heptane at a temperature of 700K and at 45atm pressure. The figures present contours of the local Mach number, pressure, temperature, and the heptane mass fraction. It is observed that the inherent temperature and pressure gradients present in the turbulent `anti-diffuse' the mixture due to the Soret diffusion terms. The process is eventually balanced by Fickian diffusion leading to a statistically stationary mass fraction state.

GOVERNING EQUATIONS