The effect of aspect ratio on the inception of primary instabilities in the laminar regime wake of a D-shaped cylinder

Abstract

A numerical investigation was performed to study the wake dynamics of a D-shaped cylinder, and the effect of the aspect ratio of the cylinder on the onset of primary instabilities was explored. The aspect ratio (L/D) is varied by increasing the cylinder’s length (L) while keeping the cylinder’s diameter (D) constant. Five aspect ratios ranging from 1 to 3 in increments of 0.5 were considered for the present study. The essential variables are the Reynolds number (Re) and the aspect ratio (AR). The primary instability analysis was performed using the Stuart-Landau equation to determine the critical Reynolds number value where the instability sets in. At low Reynolds number, the flow is steady and symmetric; at critical Reynolds number, the flow experiences Hopf bifurcation resulting in a time-periodic flow. As the aspect ratio was increased, the critical Reynolds number over which the primary instability sets in was found to increase linearly in the present study. Increasing the aspect ratio leads to significant modification of the flow topology and force coefficients. For aspect ratio two, the wake is more streamlined and narrower leading to a drag reduction of 14.49%. The drag reduction magnitude diminishes with a further increase in aspect ratio due to increased surface area resulting in more friction drag. The phase diagram and Fast Fourier transform (FFT) analysis revealed a reduction in vortex shedding activity, and velocity fluctuations in the wake.

Keywords

Stuart-Landau equation Hopf bifurcation aspect ratio instability Fast Fourier Transform

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