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

doi:10.1088/0305-4470/36/10/320

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 (Re_δ < 100, where Re_δ 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 < Re_δ < 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 Re_δ currently investigated. The results are consistent with quasi-steady linear stability theories and previous numerical investigations.

Original language	English
Pages (from-to)	2609-2620
Journal	Journal of Physics A: Mathematical and General
Volume	36
Issue number	10
Early online date	26 Feb 2003
DOIs	https://doi.org/10.1088/0305-4470/36/10/320
Publication status	Published - 14 Mar 2003

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Journal of Physics A: Mathematical and General © Copyright (2003) IOP Publishing Ltd. “This is an author-created, un-copyedited version of an article accepted for publication in [insert name of journal]. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0305-4470/36/10/320."
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title = "Application of the lattice Boltzmann method to transition in oscillatory channel flow",

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.",

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T1 - Application of the lattice Boltzmann method to transition in oscillatory channel flow

AU - Cosgrove, J. A.

AU - Buick, James

AU - Tonge, S. J.

AU - Munro, C. G.

AU - Greated , C. A.

AU - Campbell, D. M.

N1 - “This is an author-created, un-copyedited version of an article accepted for publication in [insert name of journal]. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0305-4470/36/10/320."

PY - 2003/3/14

Y1 - 2003/3/14

N2 - 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.

AB - 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.

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 10

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

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