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Numerical study of bifurcating flow through sudden expansions: effect of divergence and geometric asymmetry

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Abstract

A numerical study of laminar flow through symmetric and slightly asymmetric sudden expansion, of expansion ratio 1:3, in channels with increasing cross section, is carried out using two different approaches: Conventional CFD and Lattice Boltzmann Method. The effect of divergence of walls of the channel, after a sudden expansion, on the symmetry of flow and recirculation is studied for various Reynolds numbers. It is seen that the angles of the walls play an active role in disrupting the symmetry of flow. For non-parallel walls, the symmetry breaking bifurcation phenomenon no longer exists and the loss of symmetry is a gradual process. The effect of asymmetry of geometry on flow is also studied by considering two types of asymmetry: First type is at the plane of expansion where the steps on either side are of unequal heights, while the second one deals the walls of the channel are at a different inclination with the direction of inflow. The present study reveals that small asymmetry impedes the sharp transition and thus ‘smoothens’ the pitchfork bifurcation. Increased asymmetry finally leads to the unique solution of the governing Equations, indicating complete loss of bifurcation pattern.

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Acknowledgements

Simulations are carried out on the computers provided by the Indian Institute of Technology Kanpur (IITK) (www.iitk.ac.in/cc) and the manuscript preparation as well as data analysis has been carried out using the resources available at IITK. This support is gratefully acknowledged. Discussion with Dr. A. K. Saha (IIT Kanpur) is also gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, UP, 208016, India

    M. Jithin & Malay K. Das

  2. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, UP, 208016, India

    Alok Mishra & Ashoke De

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  1. M. Jithin
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  2. Alok Mishra
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  3. Ashoke De
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Correspondence to Ashoke De.

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Jithin, M., Mishra, A., De, A. et al. Numerical study of bifurcating flow through sudden expansions: effect of divergence and geometric asymmetry. Int J Adv Eng Sci Appl Math 8, 259–273 (2016). https://doi.org/10.1007/s12572-016-0175-0

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