Boundary layer development in the flow field between a rotating and a stationary disk

K.M.P. Eeten, van, J. Schaaf, van der, J.C. Schouten, G.J.F. Heijst, van

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Abstract

This paper discusses the development of boundary layers in the flow of a Newtonian fluid between two parallel, infinite disks. One of the disks is rotating at a constant angular velocity while the other remains stationary. An analytical series approximation and a numerical solution method are used to describe the velocity profiles of the flow. Both methods rely on the commonly used similarity transformation first proposed by Von Kármán [T. von Kármán, ZAMM 1, 233 (1921)]10.1002/zamm.19210010401. For Reh <18, the power series analytically describe the complete velocity profile. With the numerical model a Batchelor type of flow was observed for Reh > 300, with two boundary layers near the disks and a non-viscous core in the middle. A remarkable conclusion of the current work is the coincidence of the power series’ radius of convergence, a somewhat abstract mathematical notion, with the physically tangible concept of the boundary layer thickness. The coincidence shows a small deviation of only 2% to 4%.
Original languageEnglish
Article number033601
Pages (from-to)033601-1/18
Number of pages18
JournalPhysics of Fluids
Volume24
Issue number3
DOIs
Publication statusPublished - 2012

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