Quantitative measurements of three-dim ensional structures in the wake of a circular cylinder

Abstract

The fine scale three-dimensional structures usually associated with streamwise vortices in the near wake of a circular cylinder have been studied at Reynolds numbers ranging from 170 to 2200. Spatially continuous velocity measurements along lines parallel to the cylinder axis were obtained with a scanning laser anemometer. To detect the streamwise vortices in the amplitude modulated velocity field, it was necessary to develop a spatial decomposition technique to split the total flow into a primary flow component and a secondary flow component. The primary flow is comprised of the mean flow and Strouhal vortices, while the secondary flow is the result of the three-dimensional streamwise vortices that are the essence of transition to turbulence. The three-dimensional flow amplitude increases in the primary vortex formation region, then saturates shortly after the maximum amplitude in the primary flow is reached. In the near-wake region the wavelength decreases approximately like Re−0.5, but increases with downstream distance. A discontinuous increase in wavelength occurs below Re = 300 suggesting a fundamental change in the character of the three-dimensional flow. At downstream distances (x/D = 10-20), the spanwise wavelength decreases from 1.42D to 1.03D as the Reynolds number increases from 300 to 1200.

Three-dimensional flow past a fixed or freely vibrating cylinder in the early turbulent regime

“…This trend is supported by the results of Mansy et al [5]. The predicted decrease of the shear layer wavelength as a function of Re is consistent with the existence of distinct spanwise wavelengths in the shear layer and wake regions at high Reynolds numbers [5,9].…”

“…Then a three-dimensional undulation of the primary vortices develops in the wake region; as Re is increased, different regimes, characterized by distinct spanwise wavelengths, are encountered [4]. A wavelength of the order of one body diameter (i.e., the typical wavelength of a regime called mode B) persists over a wide range of Re, as reported by Mansy et al [5] (Re ∈ [300,2200]), Wu et al [6,7] (Re ∈ [200,1800]), Lin et al [8] (Re = 10 000), Chyu and Rockwell [9] (Re = 10 000), and Hayakawa and Hussain [10] (Re = 13 000). A transition occurs in the shear layer region at Re ≈ 1000; it consists in the emergence of small-scale spanwise vortices comparable to those observed in plane mixing layers.…”

“…The predicted decrease of the shear layer wavelength as a function of Re is consistent with the existence of distinct spanwise wavelengths in the shear layer and wake regions at high Reynolds numbers [5,9]. However, it is not clear whether λ z remains constant along the detached shear layers downstream of the cylinder.…”

“…The shear layer region also undergoes a three-dimensional transition, which includes a three-dimensional distortion of the shear layer vortices, as pointed out by Wei and Smith [13] and Rai [21], who visualized this phenomenon for Re ∈ [2400,4500] and Re = 3900, respectively. The streamwise evolution of the flow spanwise wavelength was measured experimentally by Mansy et al [5] and Chyu and Rockwell [9]. Both studies reported a rapid increase of the wavelength as a function of the streamwise distance in the region of formation of the primary wake vortices.…”

Orthogonal wavelet multi-resolution analysis of a turbulent cylinder wake

“…at tU c /d ≈ −3.5, 5.3 and 9.5 in figure 5d and −8. (Mansy, Yang & Williams 1994;Zhang et al 1995;Williamson 1996b;Henderson 1997) at small Reynolds numbers has suggested that there are two modes of streamwise structures. Mode A is of relatively large scale with a spanwise wavelength of about 4d.…”