Rarefied gas flow through a diverging conical pipe into vacuum

The paper is devoted to the study of a rarefied gas flow through a finite length conical pipe into vacuum. The problem is solved in the complete geometrical setup, which included not only the pipe, but also high- and low-pressure reservoirs. The analysis is based on the direct numerical solution of the Boltzmann kinetic equation with the S-model collision integral in three space dimensions. The method of the solution is based on the recent implicit total variation diminishing (TVD) method on unstructured spatial meshes. It is conservative with respect to the collision integral and work across all flow regimes. The results are provided for various ratios of the outlet and inlet diameters, pipe's lengths and Knudsen numbers. The computed flow rates are compared with the case of the circular pipe of constant radius as well as an approximate method for very long pipes. The influence of the pipe geometry on the flow field is also examined. The presented results can be used as a benchmark for calculations by other methods and codes.