A note on the numerical simulations of flow past a wavy square-section cylinder

Abstract

The flow past a square-section cylinder with a geometric disturbance is investigated by numerical simulations. The extra terms, due to the introduction of mapping transformation simulating the effect of disturbance into the transformed Navier-Stokes equations, are correctly derived, and the incorrect ones in the previous literature are pointed out and analyzed. Furthermore, the relationship between the vorticity, especially on the cylinder surface, and the disturbance is derived and explained theoretically. The computations are performed at two Reynolds numbers of 100 and 180 and three amplitudes of waviness of 0.006, 0.025 and 0.167 with another aim to explore the effects of different Reynolds numbers and disturbance on the vortex dynamics in the wake and forces on the body. Numerical results have shown that, at the mild waviness of 0.025, the Kármán vortex shedding is suppressed completely for Re = 100, while the forced vortex dislocation is appeared in the near wake at the Reynolds number of 180. The drag reduction is up to 21.6% at Re = 100 and 25.7% at Re = 180 for the high waviness of 0.167 compared with the non-wavy cylinder. The lift and the Strouhal number varied with different Reynolds numbers and the wave steepness are also obtained.

Vortex dislocations in wake-type flow induced by spanwise disturbances

“…It may cause the flow to be unsteady irregular vortex flow with some turbulent behavior or suppress the Kármán vortex shedding, making wake flow steady state. Similar behavior and results can be found in the experiments of cylinder wake transition by Williamson 1 and DNS results on wake vortex dynamics behind a wavy square-section cylinder by Darekar and Sherwin, 8 and Ling and Lin, 24 respectively. ͑6͒ There are many close similarities and common features in the mechanism responsible for the generation of vortex dislocation and related flow phenomena between the present wake-type flow evolution and the cylinder wake transition given by previous studies.…”

“…Fluids 21, 073604 ͑2009͒ mechanism for suppression of the Kármán vortex shedding between the present results and those DNS results of flow around a wavy square cylinder given by Darekar and Sherwin, 8 Ling and Lin, 24 and Lin. 25 Those recent studies of square cylinder wake have demonstrated that once the spanwise wavy disturbance is imposed on the geometry of a straight cylinder, both vertical and streamwise vortices are generated on the cylinder surface.…”

“…25 Those recent studies of square cylinder wake have demonstrated that once the spanwise wavy disturbance is imposed on the geometry of a straight cylinder, both vertical and streamwise vortices are generated on the cylinder surface. Ling and Lin 24 and Lin 25 found that the spanwise wavy disturbance with a moderate waviness causes vertical vorticity to grow rapidly in the near wake and induces a local recirculating flow behind the cylinder. The recirculating flow prevents the spanwise vorticity development and suppresses vortex shedding.…”

Wake of wavy elliptic cylinder at a low Reynolds number: wavelength effect

“…Based on experimental tests, Bearman & Owen (1998) at a Reynolds number Re = 4 × 10 4 found that the front-face-wavy square cylinder with a wavelength λ / D m = 5.6 and a waviness a / D m = 0.25 can completely suppress vortex shedding and substantially reduce time-mean drag force by up to 30 %. For the front- and rear-face-wavy square cylinder ( λ / D m = 1–10, a / D m ≤ 0.75), Darekar & Sherwin (2001 a , b ) and Ling & Lin (2008) in numerical simulations ( Re = 10–180) observed pairs of opposite-sign streamwise vortices along the spanwise direction, associated with wide and narrow wakes at the saddle and node planes, respectively. It was further found that the wavy cylinder with λ / D m = 5.6 can attain a time-mean drag reduction of up to 16 % at a / D m = 0.129–0.168 ( Re = 100), 21.6 % at a / D m = 0.167 ( Re = 100) and 25.7 % at a / D m = 0.167 ( Re = 180).…”

“…Flow around the wavy cylinder with a square cross-section has been studied experimentally and numerically in the literature. The wavy surface was implemented on the front face (Bearman & Owen 1998), on both front and rear faces (Darekar & Sherwin 2001 a , b ; Ling & Lin 2008; Lin, Bai & Alam 2015) or on both lateral side faces (Lam et al. 2012; Lin et al.…”