Low-frequency characteristics in the wake of a circular disk

Abstract

Numerical simulations of flow over a circular disk have been performed in this study at Re = 250, 300, 3000, and 104. The Fourier spectra analysis of the velocity at different positions suggests that together with the natural vortex-shedding frequency and the shear-layer Kelvin-Helmholtz instability frequency, several much lower frequencies are also detected when the Reynolds number (Re) increases to 300: one is fp ≈ 0.03, another one is fr ≈ 0.02, and its second harmonic is at about 0.04 and a low frequency of about 0.05. Considering the limited time length of the data, time-frequency analysis based on wavelet transform is then performed. It is found that the local frequencies of the amplitude peaks for the large-scale vortex shedding and shear-layer Kelvin-Helmholtz instability vary irregularly with time, indicating that the traditional Fourier analysis of the numerical signals would not be representative. Nevertheless, the low frequencies fp ≈ 0.03 and fr ≈ 0.02 are clearly confirmed. The frequencies of about 0.04 and 0.05 are observed to occur in some time periods but with much weaker magnitude. It is found that the low-frequency signals keep nearly invariant as Reynolds number increases. The physical origins of the low frequencies fp ≈ 0.03 and fr ≈ 0.02 are then investigated. The physical origin of fp ≈ 0.03 is due to a low-frequency pumping motion of the recirculation bubble, and the fr ≈ 0.02 signal is due to a low-frequency modulation in the rotation of the azimuthal location of large-scale vortex shedding (i.e., the changing of the rotation direction). To characterize the low-frequency unsteadiness of the recirculation bubble, the temporal evolution of the low-pass filtered flow field is investigated. It is observed that the pumping motion of the recirculation bubble is associated with the growing and shedding of the large toroidal vortices formed in the bubble, which is closely related to the behavior of the separated shear layer. The separated shear layer rolls up later in the state with longer recirculation bubble, whereas it rolls up earlier in the state with shorter bubble.

Coherent structures in the wake of a SAE squareback vehicle model

“…The structures of vortex shedding of opposing shear layers in the horizontal plane are shifted by half a wavelength (Grandemange et al, 2013b). These observations agree with the results of axiymmetric bluff bodies and elliptic flat plates in cross flow (Rigas et al, 2014;Grandemange et al, 2012b,a;Kiya and Abe, 1999a;Yang et al, 2015). In the orthogonal plane to the width of the vehicle the distance of structures grows linear with the distance to the vehicle base.…”

Flow around an inclined circular disk

“…Then the upper one grows at rapidly increasing speed until a local largest length at figure 9(f ) (see movie 1 in the supplementary animations). This process is similar to the wake behind a circular disk of χ = 5 normal to the flow at Re = 300 (Yang et al 2015). Instead of developing arbitrarily at α = 0 • , the flow behind inclined disk is regulated and the periodic vortex shedding is promoted so that at the same Reynolds number the wake is more likely to become periodic.…”

“…Previous studies attributed this to the irregular rotation of the azimuthal location of large-scale vortex shedding (Tomboulides & Orszag 2000;Shenoy & Kleinstreuer 2008) and the low frequency pumping motion of the recirculation region (Berger et al 1990). It is further reported that these two physical origins resulted in different low frequencies at St = 0.02 and St = 0.03 (χ = 5, Re = 300) (Yang et al 2015). Here, the low frequency at St l ≈ 0.026 is obtained in the PSL state (figure 11e); the primary vortex shedding frequency and its higher harmonics are also clear, appearing as a wide frequency band rather than a single well-defined peak.…”

“…Marshall & Stanton 1931;Willmarth et al 1964;Kuo & Baldwin 1967;Roos & Willmarth 1971;Roberts 1973;Berger et al 1990;Fernandes et al 2007;Zhong & Lee 2012) and numerical studies (see, e.g. Michael 1966;Rimon 1969;Rivet et al 1988;Shenoy & Kleinstreuer 2008;Fabre et al 2008;Auguste et al 2010;Chrust et al 2010;Shenoy & Kleinstreuer 2010;Yang et al 2014aYang et al , 2015 have investigated the case of a circular disk. The transition of the wake behind a fixed circular disk normal to the uniform flow is determined by two key parameters, the Reynolds number (Re) and the aspect ratio (χ) of the disk.…”

Flow around an oscillating circular disk at low to moderate Reynolds numbers

“…Interest in the flow around a circular disk goes back many years. Many experimental studies (see, e.g., Marshall & Stanton 1931;Willmarth et al 1964;Kuo & Baldwin 1967;Roos & Willmarth 1971;Roberts 1973;Berger et al 1990;Fernandes et al 2007;Zhong & Lee 2012) and numerical calculations (see, e.g., Michael 1966;Rimon 1969;Rivet et al 1988;Shenoy & Kleinstreuer 2008;Fabre et al 2008;Auguste et al 2010;Chrust et al 2010;Shenoy & Kleinstreuer 2010;Yang et al 2014aYang et al , 2015 addressing this issue have been reported. As a typical case of an axisymmetric body, studies on circular disks are often conducted and discussed together with another typical axisymmetric body, a sphere, which shares some similarities in the transition scenario (Fabre et al 2008;Chrust et al 2010).…”