Effect of viscosity on slip boundary conditions in rarefied gas flows

Nam T. P. Le


The viscosity of gases plays an important role in the kinetic theory of gases and in the continuum-fluid modeling of the rarefied gas flows. In this paper we investigate the effect of the gas viscosity on the surface properties as surface gas temperature and slip velocity in rarefied gas simulations. Three various viscosity models in the literature such as the Maxwell, Power Law and Sutherland models are evaluated. They are implemented into OpenFOAM to work with the solver “rhoCentralFoam” that solves the Navier-Stokes-Fourier equations. Four test cases such as the pressure driven backward facing step nanochannel, lid-driven micro-cavity, hypersonic gas flows past the sharp 25-55-deg. biconic and the circular cylinder in cross-flow cases are considered for evaluating three viscosity models. The simulation results show that, whichever the first-order or second-order slip and jump conditions are adopted, the simulation results of the surface temperature and slip velocity using the Maxwell viscosity model give good agreement with DSMC data for all cases studied.


Sutherland; Power Law; Maxwell viscosity models; rarefied gas flows; slip velocity; surface gas temperature

Full Text:



N. T. P. Le, C. J. Greenshields, and J. M. Reese. Evaluation of nonequilibrium boundary conditions for hypersonic rarefied gas flows. Progress in Flight Physics, 3, (2012), pp. 217–230. https://doi.org/10.1051/eucass/201203217.

G. N. Patterson. Molecular flow of gases. JohnWiley and Sons, (1956).

C. R. Lilley and M. N. Macrossan. DSMC calculations of shock structure with various viscosity laws. In The twenty-third Proceeding International Symposium Rarefied Gas Dynamics, (2003), pp. 663–670.

K. B. Jordan. Direct numeric simulation of shock wave structures without the use of artificial viscosity. PhD thesis, Marquette University, (2011).

H. Alsmeyer. Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam. Journal of Fluid Mechanics, 74, (3), (1976), pp. 497–513. https://doi.org/10.1017/s0022112076001912.

M. N. Macrossan. m -DSMC: a general viscosity method for rarefied flow. Journal of Computational Physics, 185, (2), (2003), pp. 612–627. https://doi.org/10.1016/s0021-9991(03)00009-3.

A. M. Mahdavi, N. T. P. Le, E. Roohi, and C. White. Thermal rarefied gas flow investigations through micro-/nano-backward-facing step: Comparison of DSMC and CFD subject to hybrid slip and jump boundary conditions. Numerical Heat Transfer, Part A: Applications, 66, (7), (2014), pp. 733–755. https://doi.org/10.1080/10407782.2014.892349.

A. Mohammadzadeh, E. Roohi, H. Niazmand, and S. K. Stefanov. Detailed investigation of thermal and hydrodynamic flow behaviour in micro/nano cavity using DSMC and NSF equations. In The nineth Proceeding International ASME Conference Nanochannels, Microchannels and Minichannels. American Society of Mechanical Engineers, (2011), pp. 341–350.

J. N. Moss and G. A. Bird. Direct simulation Monte Carlo simulations of hypersonic flows with shock interactions. AIAA Journal, 43, (12), (2005), pp. 2565–2573. https://doi.org/10.2514/1.12532.

A. J. Lofthouse, L. C. Scalabrin, and I. D. Boyd. Velocity slip and temperature jump in hypersonic aerothermodynamics. Journal of Thermophysics and Heat Transfer, 22, (1), (2008), pp. 38–49. https://doi.org/10.2514/1.31280.

J. C. Maxwell. On stresses in rarefied gases arising from inequalities of temperature. Philosophical Transactions of the Royal Society, 170, (1878), pp. 231–256.

M. Smoluchowski von Smolan. Üeber Wärmeleitung in verdünnten gasen. Annalender Physik und Chemie, 64, (1898), pp. 101–130.

N. T. P. Le and E. Roohi. A new form of the second-order temperature jump boundary condition for the low-speed nanoscale and hypersonic rarefied gas flow simulations. International Journal of Thermal Sciences, 98, (2015), pp. 51–59. https://doi.org/10.1016/j.ijthermalsci.2015.06.017.

OpenFOAM. http://www.openfoam.org. Accessed 12/2018.

E. H. Kennard. Kinetic theory of gases. McGraw-Hill, (1938).

S. Chapman and T. G. Cowling. The mathematical theory of non-uniform gases. Cambridge University Press, (1970).

N. T. P. Le, C. White, J. M. Reese, and R. S. Myong. Langmuir–Maxwell and Langmuir–Smoluchowski boundary conditions for thermal gas flow simulations in hypersonic aerodynamics. International Journal of Heat and Mass Transfer, 55, (19-20), (2012), pp. 5032–5043. https://doi.org/10.1016/j.ijheatmasstransfer.2012.04.050.

DOI: https://doi.org/10.15625/0866-7136/13564 Display counter: Abstract : 265 views. PDF : 29 views.


  • There are currently no refbacks.

Copyright (c) 2019 Vietnam Academy of Science and Technology


Editorial Office of Vietnam Journal of Mechanics

3rd Floor, A16 Building, 18B Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam
Tel: (+84) 24 3791 7103
Email: vjmech@vjs.ac.vn