Unsteady flow past a rotating circular cylinder at Reynolds numbers 10³ and 10⁴

Abstract

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

Experimental investigation of flow-induced vibration of a rotating circular cylinder

“…This is generally known as the Magnus effect, and it has been extensively studied over the past century (e.g. Tietjens & Prandtl 1957;Coutanceau & Ménard 1985;Badr et al 1990;Kang et al 1999;He et al 2000;Stojković et al 2002;Mittal & Kumar 2003;Rao et al 2013). A net transverse force is generated by the asymmetric pressure distribution.…”

“…Williamson & Roshko (1988), Badr et al (1990), Khalak & Williamson (1999), Carberry et al (2001), Mittal & Kumar (2003), Rao et al (2013) and Zhao et al (2014a) have discovered and categorised the wake patterns of forced rotation on rigidly mounted cylinders and non-rotating cylinders undergoing free and forced vibrations. The wake structure can vary significantly f rom t he K ármán v ortex s treets t ypically o bserved f or a stationary cylinder.…”

“…Asymmetric vortex shedding occurs in the wake for 0 < α 2; and many experimental and numerical works have shown this alternating vortex shedding over a wide range of Reynolds number (e.g. Coutanceau & Ménard 1985;Badr et al 1990;Kang, Choi & Lee 1999;He et al 2000;Stojković, Breuer & Durst 2002;Mittal & Kumar 2003;Rao et al 2013). Over a small range of α 4 there is a secondary region of wake unsteadiness, comprising low-frequency one-sided vortices, as shown by Mittal & Kumar (2003), Stojković et al (2003) and Pralits, Brandt & Giannetti (2010).…”

Streamwise forced oscillations of circular and square cylinders

“…Streamwise forcing is just one method of active open-loop flow control that can be employed on the cylinder wake. Others include, but are not limited to, transverse (cross-stream) oscillation, [1][2][3][4] rotational oscillation of the cylinder, [5][6][7][8] constant rotation of the cylinder, 9,10 and actuation by synthetic jets from the surface of the cylinder and base bleed. [11][12][13] Previous studies of streamwise forced oscillation [14][15][16][17] have investigated the synchronization between the forcing and the vortex shedding.…”

Proper orthogonal decomposition analysis of vortex shedding behind a rotating circular cylinder

“…[1][2][3][4][5][6]), yet much continues to be unknown about the flow structure and dynamics of this geometrically simple, turbulent flow. Vortical structures in the flow and their interactions are believed to play an important role in the generation of turbulent stresses, turbulent kinetic energy, wake entrainment and growth and mean flow development.…”