Hydrodynamic instabilities of near-critical CO₂ flow in microchannels: Lattice Boltzmann simulation

Motivated by systematic CO₂ evaporation experiments which recently became available (J. Pettersen, "Flow vaporization of CO₂ in microchannel tubes," Doctor technicae thesis, Norwegian University of Science and Technology, 2002), the present work constitutes an exploratory investigation of isothermal flow of CO₂ near its liquid-vapor critical point through a long 5 μm diameter microchannel. A modified van der Waals constitutive model-with properties closely approximating those of "real" near-critical CO₂-is incorporated in a two-dimensional lattice Boltzmann hydrodynamics model by embedding a dimensionless parameter X, with X → 1 denoting the "real" fluid. The hydrodynamic phenomena resulting by imposing a constant pressure gradient along a periodic channel are investigated by considering two regimes in tandem: (1) transition from bubbly to annular flow with a liquid film formed at the channel walls and (2) destabilization of the liquid film by the Kelvin-Helmholtz instability. Due to numerical constraints, intrinsic modeling errors are introduced and are shown to be associated with discrepancies in the relative vapor-liquid interfacial thickness, which is expressed by X. The effects of these errors are investigated both theoretically and numerically in the physical limit X → 1. Numerically determined flow patterns compare qualitatively well with direct visualization results obtained by Pettersen. Overall, the characteristics of isothermal near-critical two-phase flow in microchannels can be reproduced by the appropriate modification of the thermophysical properties of CO₂.