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Register a new userA Volume-of-Fluid method for variable-density, two-phase flows at supercritical pressure
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Added by
Jordi Poblador Ibanez
Publication date
2021
fields
Physics
and research's language is
English
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A two-phase, low-Mach-number flow solver is proposed for variable-density liquid and gas with phase change. The interface is captured using a split Volume-of-Fluid method, which solves the advection of the reference phase, generalized for the case where the liquid velocity is not divergence-free and both phases exchange mass. A sharp interface is identified by using PLIC. Mass conservation is achieved in the limit of incompressible liquid, but not with the liquid compressibility and mass exchange. This is a relevant modeling choice for two-phase mixtures at near-critical and supercritical pressure conditions for the liquid but away from the mixture critical temperature. Under this thermodynamic environment, the dissolution of lighter gas species into the liquid phase is enhanced and vaporization or condensation can occur simultaneously at different interface locations. The numerical challenge of solving two-phase, supercritical-pressure flows is greater than simpler two-phase solvers because: a) local phase equilibrium is imposed at each interface cell to determine temperature, composition, or surface tension coefficient; b) a real-fluid thermodynamic model is used to obtain fluid properties; and c) necessary phase-wise values for certain variables are obtained via extrapolation techniques. To alleviate the increased numerical cost, the pressure Poisson equation (PPE) used to solve the low-Mach-number flow is split into a constant-coefficient implicit part and a variable-coefficient explicit part. Thus, a Fast Fourier Transform method can be used for the PPE. Various verification tests are performed to show the accuracy and viability of the present approach. 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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Numerical analysis of a shear layer between a cool liquid n-decane hydrocarbon and a hot oxygen gas at supercritical pressures shows that a well-defined phase equilibrium can be established. Variable properties are considered with the product of density and viscosity in the gas phase showing a nearly constant result within the laminar flow region with no instabilities. Sufficiently thick diffusion layers form around the liquid-gas interface to support the case of continuum theory and phase equilibrium. 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 downstream asymptotes. For all cases, profiles of diffusing-advecting quantities collapse to a similar solution (i.e., function of one independent variable). Validity of the boundary layer approximation and similarity are shown in both phases for Reynolds numbers greater than 239 at 150 bar. Results for other pressures are also taken at high Reynolds numbers. Thereby, the validity of the boundary layer approximation and similarity are expected. However, at very high pressures, the similar one-dimensional profiles vary for different problem constraints.
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