An investigation of the Sutherland molecular model for DSMC simulations

Lilley, Charles R. and Macrossan, Michael N. (2002) An investigation of the Sutherland molecular model for DSMC simulations. 9/2002, Department of Mechanical Engineering, The University of Queensland.

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Author Lilley, Charles R.
Macrossan, Michael N.
Title An investigation of the Sutherland molecular model for DSMC simulations
School, Department or Centre Department of Mechanical Engineering
Institution The University of Queensland
Open Access Status Other
Report Number 9/2002
Publication date 2002-07-01
Start page 1
End page 18
Total pages 18
Subject 240502 Fluid Physics
290299 Aerospace Engineering not elsewhere classified
Formatted Abstract/Summary
This report presents some details of a molecular model for use in DSMC simulations that reproduces the Sutherland viscosity relation. This Sutherland model gives poor computational efficiency, due to the existence of extremely large collision cross-sections at low collision speeds. A modified version of the Sutherland model is therefore introduced that significantly improves the computational efficiency. It is demonstrated that the modification does not have a significant effect on the accuracy of the model when the temperature is greater than the Sutherland temperature TS. At lower temperatures, there is considerable deviation from the Sutherland viscosity formula. Therefore, if a Sutherland viscosity formula is required at low temperatures, the original rather than the modified version of the model should be used, with its attendant computational expense. At higher temperatures, the modified version should be adopted, as it offers superior computational efficiency with minimal deviation from the Sutherland viscosity formula.

Shock structure simulations were performed using the Sutherland model and the modified version, and compared to the results obtained for hard spheres and variable hard sphere molecules that give a Maxwell viscosity relationship. At an upstream temperature of ∼ 2TS, it is demonstrated that the Sutherland and modified Sutherland models give similar values of the reciprocal shock thickness δ and asymmetry factor Q, over a range of Mach numbers between 2 and 10. Further, it is seen that both models approach a constant value of δ at high Mach numbers. This behaviour is characteristic of hard sphere molecules. At low upstream temperatures, it is seen that both models represent soft molecules, and that the modified model gives higher δ values than the original version, due to the modification introduced.
Keyword DSMC
Sutherland viscosity
CPU efficient
shock structure
modified Sutherland model
Modified Kuscer model
Additional Notes See also Macrossan, Michael N. and Lilley, Charles R. (2005) Modified GHS Collision Model Compared with VHS Model.

Document type: Department Technical Report
Collection: School of Mechanical & Mining Engineering Publications
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Created: Mon, 29 Aug 2005, 10:00:00 EST by Michael N Macrossan on behalf of Faculty Of Engineering, Architecture & Info Tech