We study the rotational relaxation process in nitrogen using all-atom molecular dynamics (MD) simulations and direct simulation Monte Carlo (DSMC). The intermolecular model used in the MD simulations is shown to (i) reproduce very well the shear viscosity of nitrogen over a wide range of temperatures, (ii) predict the near-equilibrium rotational collision number in good agreement with published trajectory calculations done on ab initio potential energy surfaces, and (iii) produce shock wave profiles in excellent accordance with the experimental measurements. We find that the rotational relaxation process is dependent not only on the near-equilibrium temperature (i.e., when systems relax to equilibrium after a small perturbation), but more importantly on both the magnitude and direction of the initial deviation from the equilibrium state. The comparison between MD and DSMC, based on the Borgnakke-Larsen model, for shock waves (both at low and high temperatures) and one-dimensional expansions shows that a judicious choice of a constant Zrot can produce DSMC results which are in relatively good agreement with MD. However, the selection of the rotational collision number is case-specific, depending not only on the temperature range, but more importantly on the type of flow (compression or expansion), with significant limitations for more complex simulations characterized both by expansion and compression zones. Parker's model, parametrized for nitrogen, overpredicts Zrot for temperatures above about 300 K. It is also unable to describe the dependence of the relaxation process on the direction to equilibrium. Finally, we present a demonstrative cell-based formulation of a rotational relaxation model to illustrate how, by including the key physics obtained from the MD data (dependence of the relaxation process on both the rotational and the translational state of the gas), the agreement between MD and DSMC solutions is drastically improved.
Bibliographical noteFunding Information:
The research is supported by Air Force Office of Scientific Research (AFOSR) under Grant No. FA9550-10-1-0075. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the AFOSR or the U.S. Government. This research is also supported by NASA under Grant No. NNX11AC19G. We would like to thank Paul Norman for providing us with the CTC DSMC results.