ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
In this study, the grand (translational) friction tensor for free-molecule (large Knudsen number) flows over two, unequal-size cylinders is obtained analytically considering both "shielding'' effects and multiple collisions off cylinder surfaces, as well as including both diffuse and specular molecule-surface boundary conditions. A perturbation solution is used where the leading-order term accounts for molecular collisions from the free-streaming gas including all shielding effects. The first-order correction term is also obtained here and accounts for collisions by molecules reflected off neighboring surfaces from the free-stream gas. It is shown that the grand friction tensor is symmetric under the conditions of small ratios of the free-stream gas velocity to the thermal gas velocity, the same type of molecular reflection boundary condition on both cylinders, and constant temperature. It is also shown that the two-term expansion formula is accurate under isothermal conditions in the so-called "far-field'' limit where the surface to surface cylinder separation distance is greater than approximately one to two cylinder diameters for equal-size cylinders. The accuracy of the two-term expansion is also shown to diminish as the two cylinders approach one another ("near field'' behavior). It is also demonstrated how the far-field results given here can be extended to more than two cylinders and to cylinders moving relative to the free-stream gas. This study compliments an earlier study [R. Ying and M. H. Peters, J. Fluid Mech. 207, 353 (1989)] for small Knudsen numbers, or the "slightly rarefied gas'' case. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.868888
