Numerical heat and mass transfer analysis of a configuration where a cool liquid hydrocarbon is suddenly introduced to a hotter gas at supercritical pressure shows that a well-defined phase equilibrium can be established before substantial growth of typical hydrodynamic instabilities. The equilibrium values at the interface quickly reach near-steady values. Sufficiently thick diffusion layers form quickly around the liquid-gas interface (e.g., 3-10 µm for the liquid phase and 10-30 µm for the gas phase in 10-100 µs), where density variations become increasingly important with pressure as mixing of species is enhanced. While the hydrocarbon vaporizes and the gas condenses for all analyzed pressures, the net mass flux across the interface reverses as pressure is increased, showing that a clear vaporization-driven problem at low pressures may present condensation at higher pressures. This is achieved while heat still conducts from gas to liquid. Analysis of fundamental thermodynamic laws on a fixed-mass element containing the diffusion layers proves the thermodynamic viability of the obtained results.
Numerical analysis of a shear layer between a cool liquid hydrocarbon and a hotter oxygen gas at supercritical pressures shows that a well-defined phase equilibrium can be established. Variable properties are considered with the product ρµ in the gas phase showing a nearly constant result. Sufficiently thick diffusion layers form around the liquid-gas interface for the selected free-stream velocities at a streamwise distance of x = 1 cm for different pressures (i.e., 10 -18 µm in the liquid phase and 30 -160 µm in the gas phase). While molecules are exchanged for both species at all pressures, net mass flux across the interface shifts as pressure is increased. Net vaporization occurs for low pressures while net condensation occurs at higher pressures. For a mixture of n-decane and oxygen, the transition occurs around 50 bar. The equilibrium values at the interface quickly reach their asymptotes. For all cases, profiles of diffusing-advecting quantities collapse to a similar solution (i.e., function of one independent variable). However, similarity for the normalized results from cases with different boundary conditions is lost when comparing different pressure or temperature cases to each other as the thermodynamics and interface conditions change.
A two-phase, low-Mach-number flow solver is created and verified for variable-density liquid and gas with phase change. The interface is sharply captured using a split volume-of-fluid method generalized for a non-divergence-free liquid velocity and with mass exchange across the interface. Mass conservation to machine-error precision is achieved in the limit of incompressible liquid. This model is implemented for two-phase mixtures at supercritical pressure but subcritical temperature conditions for the liquid, as it is common in the early times of liquid hydrocarbon injection under real-engine conditions. The dissolution of the gas species into the liquid phase is enhanced, and vaporization or condensation can occur simultaneously at different interface locations. Greater numerical challenges appear compared to incompressible two-phase solvers that are successfully addressed for the first time: (a) local thermodynamic phase equilibrium and jump conditions determine the interface solution (e.g., temperature, composition, surface-tension coefficient); (b) a real-fluid thermodynamic model is considered; and (c) phase-wise values for certain variables (e.g., velocity) are obtained via extrapolation techniques. The increased numerical cost is alleviated with a split pressure-gradient technique to solve the pressure Poisson equation for the low-Mach-number flow. Thus, a fast Fourier transform method is implemented, directly solving the continuity constraint without an iterative process. Various verification tests show the accuracy and viability of the current approach. Then, the growth of surface instabilities in a binary system composed of liquid n-decane and gaseous oxygen at supercritical pressures for n-decane is analyzed. Other features of supercritical liquid injection are also shown.
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