Direct numerical simulations are used to investigate the mixing of initially segregated nitrogen and heptane in stationary compressible isotropic turbulence 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 initially segregated nitrogen and heptane. The heptane is initialized in the form of a single spherical `droplet' located in the center of the domain. Based on the periodic boundary conditions, the simulations provide an idealized model of the interior of a high pressure turbulent fuel spray.

Two simulations are conducted, both at a resoltuion of 192 x 192 x 192 grid points on a parallel supercomputer. Both simulations are initialized with a fully developed turbulent velocity field and spherical heptane droplets. In the first simulation (Run 1) the complete form of the generalized diffusion terms, including Soret and Dufour diffusion, are included in the formulation. The second simulation is identical in every way except that only the `standard' Fickian and Fourier mass and thermal diffusion are included. The time averaged conditions for the quasi-stationary flows are P=45atm, T=700K, Re=80, and Mc=0.55. In both cases, a cubic real gas state equation is employed.

Figure 1 at the right depicts the early time evolution of the heptane mass fraction contours for simualtion Run 1 showing the breakup and mixing of the droplet. The contours are presented as cross sections through the center of the cubic domain. The results were used to investigate the behavior of several aspects of probability density function based combustion and mixing models in supercritical conditions. It is observed that the evolution of the conditional expected diffusion, and the conditional expected dissipation can be dramatically altered by the Soret and Dufour diffusion; particularly at long times. These results will appear shortly.

GOVERNING EQUATIONS