'Effective boundary conditions at a regularly microstructured wall' by Alessandro Bottaro (Università di Genova)

Duration: 54 mins 58 secs

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'Effective boundary conditions at a regularly microstructured wall' by Alessandro Bottaro (Università di Genova)'s image

Description:	Talk given by Prof Alessandro Bottaro (Università di Genova) at Department of Engineering, University of Cambridge, 6 December 2019, as part of the CUED Fluids seminar series.


Created:	2019-12-16 09:14
Collection:	Cambridge Engineering Dept Fluids Seminars
Publisher:	University of Cambridge
Copyright:	Prof Alessandro Bottaro
Language:	eng (English)


Abstract:	The talk will discuss effective boundary conditions, correct to second order in a small parameter epsilon, for a rough wall with periodic micro-indentations. The length scale of the indentations is l, and epsilon = l/L << 1, with L a characteristic length of the macroscopic problem. At leading order the Navier slip condition is recovered; at next order the slip velocity includes a term arising from the streamwise pressure gradient. At second order also a transpiration velocity appears at the fictitious wall where the effective boundary conditions are enforced. For ease of derivation, the microscopic theory, based on a power series expansion of the dependent variables, will be limited to the case of two- dimensional roughness, the three-dimensional extension being trivial. The application to a macroscopic problem is carried out considering the case of the Hiemenz stagnation point flow over a rough wall.

Abstract:

The talk will discuss effective boundary conditions, correct to second order in a small parameter epsilon, for a rough wall with periodic micro-indentations. The length scale of the indentations is l, and epsilon = l/L << 1, with L a characteristic length of the macroscopic problem. At leading order the Navier slip condition is recovered; at next order the slip velocity includes a term arising from the streamwise pressure gradient. At second order also a transpiration velocity appears at the fictitious wall where the effective boundary conditions are enforced. For ease of derivation, the microscopic theory, based on a power series expansion of the dependent variables, will be limited to the case of two- dimensional roughness, the three-dimensional extension being trivial. The application to a macroscopic problem is carried out considering the case of the Hiemenz stagnation point flow over a rough wall.

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