In this work we studied the applicability of the Lattice Boltzmann Method (LBM) to the numerical simulations of Stokes’ Boundary Layer (SBL) on a flat and wavy wall. The flow was obtained simulating an oscillating wall in a fluid otherwise at rest, whereas in the available letterature the oscillatory boundary layer is always obtained accelerating the fluid by an ideal pressure gradient. The Reynolds number Red, is the only characteristic parameter and laboratory experiments show laminar regime if Red < 100. In this case, the Navier-Stokes Equations (NSE) can be solved exactly and the analytical solution shows a good agreement with experiments. Comparing our numerical results with this solution we prove that LBM reproduces this time varying flow with high accuracy. Experiments show that at increasing Red, transition to turbulence takes place at different steps. A first transition occurs in the range 100 ·< Red < 500 where the flow remains essentially bidimensional but significant differences from the laminar solution are present. At the state of the art, different mechanisms responsible to trigger transition have been highlighted (Akhavan et al., 1991a,b; Blondeaux and Vittori, 1994). Wall perturbation has been proven to be consistent with experimental results (Vittori and Verzicco, 1998). We present LBM numerical simulation of SBL induced by an oscillating wavy wall at Red = 300. The perturbation is a regular square wave of amplitude 1/10 of the boundary layer thickness. Preliminary results show that disturbances of the laminar velocity profile are due to the formation of vortex-jets.

Lattice Boltzmann numerical simulation of Stokes' boundary layer on a flat and wavy wall / L.Cappietti; B.Chopard. - STAMPA. - (2004), pp. 77-84. (Intervento presentato al convegno 29° Convegno di Idraulica e Costruzioni Idrauliche tenutosi a Trento - Italia nel 2004).

Lattice Boltzmann numerical simulation of Stokes' boundary layer on a flat and wavy wall

CAPPIETTI, LORENZO;
2004

Abstract

In this work we studied the applicability of the Lattice Boltzmann Method (LBM) to the numerical simulations of Stokes’ Boundary Layer (SBL) on a flat and wavy wall. The flow was obtained simulating an oscillating wall in a fluid otherwise at rest, whereas in the available letterature the oscillatory boundary layer is always obtained accelerating the fluid by an ideal pressure gradient. The Reynolds number Red, is the only characteristic parameter and laboratory experiments show laminar regime if Red < 100. In this case, the Navier-Stokes Equations (NSE) can be solved exactly and the analytical solution shows a good agreement with experiments. Comparing our numerical results with this solution we prove that LBM reproduces this time varying flow with high accuracy. Experiments show that at increasing Red, transition to turbulence takes place at different steps. A first transition occurs in the range 100 ·< Red < 500 where the flow remains essentially bidimensional but significant differences from the laminar solution are present. At the state of the art, different mechanisms responsible to trigger transition have been highlighted (Akhavan et al., 1991a,b; Blondeaux and Vittori, 1994). Wall perturbation has been proven to be consistent with experimental results (Vittori and Verzicco, 1998). We present LBM numerical simulation of SBL induced by an oscillating wavy wall at Red = 300. The perturbation is a regular square wave of amplitude 1/10 of the boundary layer thickness. Preliminary results show that disturbances of the laminar velocity profile are due to the formation of vortex-jets.
2004
29° Convegno di Idraulica e Costruzioni Idrauliche
Trento - Italia
2004
L.Cappietti; B.Chopard
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/363045
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