Highly dilute gas flows over an ellipse

TL;DR

This paper investigates free molecular flows over an ellipse using gaskinetic theory, deriving analytical flowfield expressions and validating them with DSMC simulations, providing baseline references for high Knudsen number flows.

Contribution

It introduces analytical expressions for flowfields and surface properties over an ellipse, validated by DSMC, advancing understanding of high Knudsen number gas flows.

Findings

Analytical flowfield expressions for ellipse flows.

Validation of expressions with DSMC simulations.

Baseline load coefficients for high Knudsen number flows.

Abstract

This paper presents recent investigation results on free molecular flows over a diffusely or specularly reflective ellipse, by using the gaskinetic theory. A virtual density distribution along the a diffusely reflective surface is introduced to aid the investigations. Many local surface properties are obtained, including surface slip velocity, coefficients for pressure, friction, and heat flux. Global coefficients for aerodynamic forces and moments, mass center-force center distances, are also obtained by integrating the local surface distributions. In the end, analytical expressions for the flowfields around a diffusely or a specularly reflective ellipse are also obtained. Special non-parameters, such as temperature and speed ratios, are explicitly embedded in these expressions. Particle simulations with the direct simulation Monte Carlo (DSMC) method are performed to validate the above results. Those expressions need computers for evaluations, however, the cost is very minor when compared with DSMC simulations. The approaches are heuristic to investigate other external collisionless flows, and the load coefficients can be considered as baseline references at the high Knudsen number limit. It is feasible to further study less rarefied gas flows over an ellipse. Swift parameter studies based on these solutions are feasible to study their influences.