A rarefied gas flow around a rotating sphere: diverging profiles of gradients of macroscopic quantities. (4th January 2019)

• Record Type: Journal Article
• Authors: Taguchi, Satoshi; Saito, Kazuyuki; Takata, Shigeru
• Is Part Of: Journal of fluid mechanics. Volume 862(2019)
• Page Start: 5
• Page End: 33
• Publication Date: 2019-01-04
• Subjects: kinetic theory, -- micro-/nano-fluid dynamics, -- rarefied gas flow; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.946
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : The steady behaviour of a rarefied gas around a rotating sphere is studied numerically on the basis of the linearised ellipsoidal statistical model of the Boltzmann equation, also known as the ES model, and the Maxwell diffuse–specular boundary condition. It is demonstrated numerically that the normal derivative of the circumferential component of the flow velocity and that of the heat flux diverge on the boundary with a rate $s^{-1/2}$, where $s$ is the normal distance from the boundary. Further, it is demonstrated that the diverging term is proportional to the magnitude of the jump discontinuity of the velocity distribution function on the boundary, which originates from the mismatch of the incoming and outgoing data on the boundary. The moment of force exerted on the sphere is also obtained for a wide range of the Knudsen number and for various values of the accommodation coefficient.