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The flow structure in the narrow gaps of compound channels: a linear stability analysis

ABSTRACT A linear stability analysis is performed to explain the formation of coherent structures in the narrow regions of a rectangular channel containing a cylindrical rod and a channel formed by two rectangular ducts connected through a narrow slot. This stability analysis introduces small perturbations of the velocity and the pressure in the governing equations. The linearised equations are transformed into a generalised eigenvalue problem solved using the spectral Tau-Chebyshev collocation method. The obtained critical Reynolds number variations with gap size are in qualitative agreement with published experimental data. The iso-contours of the streamwise and transverse velocities, obtained from the preferred modes solution, confirm the presence, in the narrow regions, of counter-rotating vortices, generated by the flow instability and resulting from the velocity profile in the middle of the gap. The vortices’ spatial arrangement, convective speed, spacing and Strouhal number for both configurations have qualitatively similar variations with relative gap sizes.