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TURBULENCE-INDUCED SECONDARY FLOWS IN A SQUARE DUCT USING A MULTIPLE-RELAXATION-TIME LATTICE-BOLTZMANN APPROACH

Martin J. Pattison
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106

Kannan N. Premnath
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106, USA

Sanjoy Banerjee
Department of Chemical Engineering University of California at Santa Barbara, Santa Barbara, California, 93106

Abstract

Turbulent fluid flow through a square duct is characterised by the existence of net flows is directions perpendicular to the duct axis. These secondary circulations take the form of eight counter-rotating vertices, bounded by the wall, a wall bisector and a corner bisector. The velocities are relatively small, significantly lower than the turbulent fluctuations, and are relatively difficult to capture in numerical simulations. A multiple-relaxation-time lattice Boltzmann method has been applied to this problem, using a Smagorinsky eddy viscosity subgrid scale model with a van Driest wall damping function to model the unresolved stresses. A Reynolds number of 300 (based on mean friction velocity and duct width) was used and the flow was driven by a pressure gradient in the streamwise direction, with periodic boundary conditions applied in this direction. The large eddy simulations using this method correctly predicted the existence of the secondary flows, and turbulent statistics were found to be in good quantitative agreement with prior data from high resolution numerical simulations.