Experimental investigation of the wake behind a rotating sphere

Abstract

The wake behind a sphere, rotating about an axis aligned with the streamwise direction, has been experimentally investigated in a low-velocity water tunnel using LIF visualizations and PIV measurements. The measurements focused on the evolution of the flow regimes that appear depending on two control parameters, namely the Reynolds number Re and the dimensionless rotation or swirl rate Ω, which is the ratio of the maximum azimuthal velocity of the body to the free stream velocity. In the present investigation, we cover the range of Re smaller than 400 and Ω from 0 and 4. Different wakes regimes such as an axisymmetric flow, a low helical state and a high helical mode are represented in the (Re, Ω) parameter plane.

Description of the transitional wake behind a strongly streamwise rotating sphere

“…However, the harmonic 2f a develops at the near wake, as observed in the spectrum of w , although its magnitude is weak in comparison with the main peak. Interestingly, if the sphere's rotation frequency is denoted as f r , the ratio f a /f r 1 3 , which agrees well with previously reported values by Pier (2013) and Skarysz et al (2018) for low Ω.…”

“…First, it is observed that, for Ω 1.4, m = 1 (m 1 ) and m = 0 (m 0 ) symmetries are the most energetic at the wake. In particular, the enstrophy of mode m 0 grows monotonously with Ω until it reaches a saturated value around 1.4, in line with the experimental results of Skarysz et al (2018). Therefore, the initial growth in ε(m 0 ) during the periodic and quasi-periodic regimes can be attributed to the linear addition of cyclonic vorticity due to the rotation of the sphere.…”

“…Additionally, there is a pair of vortices that detach from the shroud of negative x surrounding the sphere (see also pressure fluctuations close to the separation points in figure 4d) that wrap around the outer spirals while convected downstream, although they are soon dissipated. A similar double-threaded helical structure has been recently observed experimentally by Skarysz et al (2018) for Ω = 1.6. Now, fluctuating time histories of c x and c y becomes irregular (see figure 3a), leading to complex phase diagrams of (c y , c z ) and (c l , c x ) in figure 3(b,c), anticipating the existence of multiple frequency components.…”

“…In particular, the new linear trend displayed by ε(m 2 ) allows a first estimation of the threshold of instability for the mode of f m 2 (figure 7), by means of Landau's model, E K • (Ω − Ω cr ), giving a critical value of Ω cr 1.57 (note that a similar experimental value was recently identified by Skarysz et al (2018) for the transition between m 1 and m 2 ).…”

“…In fact, wake regimes behind a streamwise rotating sphere seem to be comparatively more complex, already at Re = 350, as Pier (2013) showed, denoting such regimes as irregular, since they show little coherence in the shedding process, especially at very low (Ω < 0.2) and high (0.8 < Transitional wake behind a streamwise rotating sphere 896 A18-3 Ω < 1) rotation rates. These regimes have been also characterized experimentally for Re < 400 by Skarysz et al (2018), using flow visualizations and modal decomposition techniques.…”