Effect of internal degrees of freedom in rarefied gas problems: Plane Couette flow

Abstract

Present paper studies the influence of internal degrees of freedom (IDOF) on rarefied gas flow in a classic plane Couette problem. The numerical study is performed using Direct Simulation Monte Carlo method in a wide range of gas rarefaction, plates relative velocities and for different values of accommodation coefficients (ACs) on the walls. It is shown that: (1) in presence of IDOF a noticeable thermal non-equilibrium between translational and internal energy modes is observed, which increases with gas rarefaction and with plates relative velocity; (2) presence of IDOF can noticeably decrease shear stress and heat flux to the walls, which is mainly explained by the drain of energy from over-excited translational mode into internal ones, leading to lower values of translational temperature and, hence, viscosity; (3) the magnitude of IDOF influence is a non-monotonic function of gas rarefaction, taking maximal values in transitional regimes Kn≈1; (4) values of ACs can significantly change the influence of IDOF, both qualitatively and quantitatively; (5) the rate of energy exchange between translational and internal modes has a noticeable influence on the results, but the energy exchange model itself is not principal as long as this rate is reproduced correctly; (6) increasing number of IDOF leads to more noticeable influence on shear stress and heat flux. Therefore the influence of IDOF will be more significant for polyatomic gases.