Double-flux model for supercritical multicomponent flows at low Mach numbers with preconditioning method

A double-flux model for preconditioned systems was developed for supercritical multi-component flows under low Mach-number conditions. The mechanism of spurious oscillations in a preconditioned system was classified based on the temporal variation of binary and different temperature fluids in a one-dimensional Euler system. Double-flux models with the original and simplified preconditioning matrices were demonstrated in one-dimensional advection problems, where the latter ignored the partial derivatives of density with respect to the mass fraction for simplicity. The assumption of uniform mass fraction and temperature in the double-flux approach improved the pressure and temperature equilibrium at the material interface, if the simplified preconditioning matrix was used, while the original preconditioning matrix satisfied them by the uniform temperature assumption. A conservation-error analysis was conducted for the one-dimensional advection of the n-dodecane interface using the double-flux model coupled with the preconditioning method. The double flux treatment affected the conservation of not only the total energy but also mass and momentum, because of the preconditioning matrix. The present method enabled the simulation of the advection of methane in an n-dodecane atmosphere and the natural convection of n-dodecane without spurious oscillations, even though these are the binary fluid flow condition or the transcritical conditions. Finally, as a practical application for reactive flows under transcritical conditions, a simulation of n-dodecane with the pyrolysis reaction in a heated circular tube was carried out. Pyrolysis occurred near the heating wall, and the density rapidly changed because of the transition to the supercritical state and the decomposed lower hydrocarbon. When applying the double-flux model, converged results without any spurious oscillations were obtained. The outlet conversion rates were compared with the experimental data, and the present method could reproduce the pyrolysis reaction of n-dodecane in a heated circular pipe.