The effects of rarefaction on gas viscosity are investigated through the simulation of isothermal, low speed flow in a long straight channel using the Direct Simulation Monte Carlo (DSMC) method. Following convergence to the flow field inside the channel, the effective viscosity is calculated directly from its definition using shear stress calculations in each individual cell assuming that the gas flow is close to a local equilibrium state. Averaging over the cross-sectional area at different positions down the pressure gradient allows the determination of the gas viscosity as a function of the local Knudsen number (Kn) along the channel. Following an extensive investigation of this dependence over a wide range of Kn values, it was conveniently found that a Bosanquet-type of approximation describes very satisfactorily the Knudsen number dependence of the viscosity over the entire transition regime, i.e., from the slip-flow to the freemolecular flow limit. Such a simple functional dependence is expected to facilitate significantly phenomenological descriptions and numerical computations of rarefied flows that rely on the notion of an effective viscosity in the transition regime.
A two-dimensional two-phase lattice-Boltzmann model is presented and used for the study of interfacial phenomena under static and flow conditions. The model is based on the nonideal lattice-Boltzmann model proposed originally by Swift, Osborn, and Yeomans [Phys. Rev. Lett. 75, 830 (1995)] and makes it possible to couple a prescribed equation of state with the pressure tensor at the interface and the excess free-energy density formalism. The characteristic feature of the present model is that Galilean invariance is restored in the presence of interfaces without sacrificing any of the merits of the original model and, hence, the Navier-Stokes equation is adequately (to second order) recovered. The fluid properties can be prescribed in a thermodynamically consistent manner, which remains accurate at states close to the critical point. The model is first validated through static equilibrium tests and then applied to flow systems. It is shown that the simulator can reproduce some known two-phase flow configurations, like the motion of deformable droplets under the action of an external flow field. The simulator can also capture some interesting events during jet breakup and can be useful for the parametric study of the process in the two-dimensional case.
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