When a small thin two-dimensional body enters a viscous wall layer

Abstract

If a body enters a viscous-inviscid fluid layer near a wall, then significant effects can be felt from the presence of incident vorticity, viscous forces and nonlinear forces. The focus here is on the response in the outer edge of such a wall layer. Nonlinear two-dimensional unsteady behaviour is examined through modelling, computation and analysis applied for a thin body travelling streamwise upstream or downstream or staying still relative to the wall. The wall layer with its balance between inviscid and viscous effects interacts freely with the body movement, causing relatively high magnitudes of pressure on top of the body and nonlinear responses in the gap between the body and the wall. The study finds explicit solutions for the motion of the body, separation of the flow arising near the wall and possible instabilities occurring over the length scale of any short body.

A body in nonlinear near-wall shear flow: impacts, analysis and comparisons

“…This is a nonlinear near-wall coupling which involves effects from viscous and inviscid dynamics. Our concern is with being of order unity as opposed to the range of large values considered by Palmer & Smith (2019). The argument has been presented for a boundary-layer setting.…”

“…So the representative particle Reynolds number is to and the global Reynolds number may be to , while the Froude number is of the order . Further details on icing conditions and the range of physical parameters are described in Norde (2017) and Palmer & Smith (2019).…”

“…(2006), Wang & Levy (2006), Yu, Phan-Thien & Tanner (2007), Loth & Dorgan (2009), Schmidt & Young (2009), Kishore & Gu (2010), Smith & Ellis (2010), Loisel et al. (2013), Dehghan & Basirat Tabrizi (2014), Smith & Johnson (2016) and Palmer & Smith (2019, 2020). The computational results in this last paper (Palmer & Smith 2020) also highlight wake and upstream influence effects and the importance of scales as the local Reynolds number increases.…”

A body in nonlinear near-wall shear flow: numerical results for a flat plate

“…Further issues surround the possible impacts and clashes between a moving body and a wall and the understanding of separations and eddy formations in the nearby flows either on the body or on the wall, cf. Smith & Ellis (2010), Smith & Wilson (2013), Smith & Johnson (2016), Smith (2017), Smith & Palmer (2019) and Palmer & Smith (2019). Notably, these issues require inclusion of nonlinear effects.…”

“…No other such study has been conducted as far as we know. The works closest to our study are based on high-Reynolds-number theory, namely Palmer & Smith (2019) on a linearised interaction taking place at the edge of a wall layer and the recent paper by Palmer & Smith (2020) on nonlinear interaction inside a wall layer, the latter being the only nonlinear analysis of its kind to date. We aim to provide a qualitative and quantitative comparison at moderate Reynolds numbers with the nonlinear asymptotic theory for a fluid–body interaction.…”