Application of the lattice Boltzmann method to transition in oscillatory channel flow

J. A. Cosgrove, James Buick, S. J. Tonge, C. G. Munro, C. A. Greated , D. M. Campbell

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    Abstract

    In this study the applicability of the lattice Boltzmann method to oscillatory channel flow with a zero mean velocity has been evaluated. The model has been compared to exact analytical solutions in the laminar case (Reδ < 100, where Reδ is the Reynolds number based on the Stokes layer) for the Womersley parameter 1 < α < 31. In this regime, there was good agreement between numerical and exact analytical solutions. The model was then applied to study the primary instability of oscillatory channel flow with a zero mean velocity. For these transitionary flows the parameters were varied in the range 400 < Reδ < 1000 and 4 < α < 16. Disturbances superimposed on the numerical solution triggered the two-dimensional primary instability. This phenomenon has not been numerically evaluated over the range of α or Reδ currently investigated. The results are consistent with quasi-steady linear stability theories and previous numerical investigations.
    Original languageEnglish
    Pages (from-to)2609-2620
    JournalJournal of Physics A: Mathematical and General
    Volume36
    Issue number10
    Early online date26 Feb 2003
    DOIs
    Publication statusPublished - 14 Mar 2003

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