From steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation
•The critical Reynolds number, Redc, at the first Hopf bifurcation in model porous media is determined.•Ordered and weakly disordered arrays of parallel cylinders of square cross section are considered.•On ordered structure, Redc, must be determined on a domain larger than the geometrical unit cell....
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| Published in: | Computers & fluids 2016-09, Vol.136, p.67-82 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | eng |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | •The critical Reynolds number, Redc, at the first Hopf bifurcation in model porous media is determined.•Ordered and weakly disordered arrays of parallel cylinders of square cross section are considered.•On ordered structure, Redc, must be determined on a domain larger than the geometrical unit cell.•Correlations of Redc, to the porosity are obtained for both ordered and disordered structures.•Orientation of the applied pressure gradient and disorder are shown to strongly impact Redc.
This work focuses on the occurrence of the first Hopf bifurcation, corresponding to the transition from steady to unsteady flow conditions, on 2D periodic ordered and disordered non-deformable porous structures. The structures under concern, representative of real systems for many applications, are composed of cylinders of square cross section for values of the porosity ranging from 15% to 96%. The critical Reynolds number at the bifurcation is determined for incompressible isothermal Newtonian fluid flow by Direct Numerical Simulations (DNS) based on a finite volume discretization method that is second order accurate in space and time. It is shown that for ordered square periodic structures, the critical Reynolds number increases when the porosity decreases and strongly depends on the choice of the Representative Elementary Volume on which periodic boundary conditions are employed. The flow orientation with respect to the principal axes of the structure is also shown to have a very important impact on the value of the Reynolds number of the bifurcation. When structural disorder is introduced, the critical Reynolds number decreases very significantly in comparison to the ordered structure having the same porosity. Correlations between the critical Reynolds number and the porosity are obtained on both ordered and disordered structures over wide ranges of porosities. A frequency analysis is performed on one of the velocity components to investigate pre- and post-bifurcation flow characteristics. |
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| ISSN: | 0045-7930 1879-0747 |