Rarefaction effects on gas viscosity in the Knudsen transition regime
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 free-molecular 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.
KeywordsRarefied flow Effective viscosity DSMC Straight channel
- Bird GA (1994) Molecular gas dynamics and the direct simulation of gas flows. Clarendon Press, OxfordGoogle Scholar
- Chapman S, Cowling TG (1970) The mathematical theory of non-uniform gases, 3rd edn. Cambridge University Press, New YorkGoogle Scholar
- Fan J, Shen C (1999) Statistical simulation of low-speed unidirectional flows in transition regime. In: Brun R, Campargue R, Gatignol R, Lengrand JC (eds) Rarefied gas dynamics, vol 2. Cepadus-Editions, ToulouseGoogle Scholar