Parametric study of the transition in the wake of oblate spheroids and flat cylinders

Abstract

International audienceAn exhaustive parametric study of the transition scenario in the wake of oblate spheroids and flat cylinders placed with their rotation axis parallel to the flow is presented. The flatness of the investigated objects is classified by the aspect ratio χ defined as χ = d/a for spheroids (with d the diameter and a the length of the polar axis) and as χ = d/ h for cylinders (with h the cylinder height). We find a significant qualitative similarity between both configurations. At large aspect ratios (χ > 2.3 for spheroids and χ > 4 for cylinders), the secondary bifurcation giving rise to a periodic state without planar symmetry is subcritical with a hysteresis interval of about two Reynolds number units. For spheroids, the sphere-like scenario is recovered only at aspect ratios very close to one (χ > 1 are considered), while for cylindrical bodies the same holds for χ 6 1.7. For intermediate aspect ratios, a domain of states with non-zero net helicity separates states typical for the sphere wake from those of an infinitely flat disk

Numerical study on instabilities behind a circular disk in a uniform flow

“…The critical Reynolds number well matches the report by Fernades et al (2007), Chrust et al (2010), and the experimental result by Szaltys et al (2011) with consideration of the effect of the aspect ratio. The present result is measured by spectrum analysis of the fluctuating velocity, as shown in Fig.…”

“…The natural vortex shedding frequency St is generally sensitive to Reynolds number, whereas it increases slightly with Re in this mode. The value of St is in good agreement with the result of Fabre et al (2008), Chrust et al (2010), Shenoy and Kleinstreuer (2008).…”

“…The critical Reynolds number was found at Re % 280. An extensive parametric study dealing with oblate spheroids and flat cylinders in the range v 2 [1,1], Re 2 [100,300] was recently carried out by Chrust et al (2010). It basically confirmed the bifurcation scenarios summarized above and delimited the domain of existence of each state in the (v, Re) plane.…”

“…According to previous nonlinear analysis (Meliga et al, 2009) and numerical simulations (Fabre et al, 2008;Chrust et al, 2010;Shenoy and Kleinstreuer, 2008), the flow in the Re range of 152-265 has three intermediate states, namely reflectional-symmetry-breaking (RSB) mode (Fabre et al, 2008), standing wave (SW) mode (Fabre et al, 2008;Meliga et al, 2009) or called unsteady state with plane of symmetry and zero-mean lift (Shenoy and Kleinstreuer, 2008), and unsteady state with planar symmetry and non-zero mean lift (Chrust et al, 2010). Fig.…”

Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability

“…Most of these observations are concerned with large-amplitude chaotic regimes that take place at larger values of the control parameter than well-defined regimes such as planar zigzag (see, e.g., [59][60][61]). For instance, it has been observed with light rising spheres [59] that increasing the Galilei number (the body-to-fluid density ratio being kept fixed) yields successively rectilinear, steady oblique, oscillating oblique, planar zigzagging, and chaotic paths.…”