A Stokesian analysis of a submerged viscous jet impinging on a planar wall

A. M J Davis, J. H. Kim, C. Ceritoglu, J. T. Ratnanather

Research output: Contribution to journalArticle

Abstract

The wall pressure and wall shear stress of a submerged viscous jet impinging on an infinite planar wall are derived. The whole creeping flow of semi-infinite extent is generated via distributions on a cylindrical pipe of tangentially and normally directed Stokeslets which are modified to achieve no-slip at the wall in two stages. First the pressure and vorticity jumps associated with the Poiseuille flow upstream in the pipe are readily forced, and then further distributions, of zero density far upstream but with square-root density singularity at the orifice z= h, are added to achieve no-slip on the pipe wall. Thus the adjustment of the interior pipe flow from its upstream parabolic profile to its exit profile is fully included in-and a major feature of-this creeping flow analysis. The maximum plane wall pressure is always located on the axis r= 0, and decreases as h increases to alleviate the obstruction effect of the wall. The interaction of the inflow with the ambient fluid in the neighbourhood of z = 0 causes the wall stress to rise rapidly to a maximum and then decay with the radial position of this maximum increasing as h increases. This behaviour is discussed in the context of physiological experiments on auditory sensory hair cells that motivated this study.

Original languageEnglish (US)
Pages (from-to)531-551
Number of pages21
JournalJournal of Fluid Mechanics
Volume712
DOIs
StatePublished - Dec 10 2012

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Keywords

  • low-Reynolds-number flows
  • Stokesian dynamics

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

Davis, A. M. J., Kim, J. H., Ceritoglu, C., & Ratnanather, J. T. (2012). A Stokesian analysis of a submerged viscous jet impinging on a planar wall. Journal of Fluid Mechanics, 712, 531-551. https://doi.org/10.1017/jfm.2012.435