An experimental study on the velocity fluctuations generated by the flow past fixed spheres

We perform a series of experiments to study the velocity fluctuations generated by the flow past fixed spheres. Planar particle image velocimetry (PIV) is carried out to characterize the properties of the liquid fluctuation. The fluctuation induced by the spheres can be decomposed into the temporal fluctuation and the spatial fluctuation, which represent the contribution of flow instability and spatial inhomogeneity, respectively. In particularly, we focus on the contributions of temporal fluctuations and spatial fluctuations between low and high Reynolds number. At low Reynolds number (20 < Re <= 200), the total fluctuation mostly comes from the spatial fluctuation and increases as the area of velocity deficit in the wake of the sphere increases. The temporal fluctuation cannot be neglected at larger Reynolds number (200 < Re <= 700), and the total velocity fluctuation is induced by both flow instability and spatial inhomogeneity. Furthermore, the energy distribution in the flow direction and the span direction also changes drastically as the Reynolds number increases. The wavenumber spectra of fluctuations show a -3 slope at large scale, -5/3 slope at small scale. The starting scale of the -3 slope decreases with the increase of the Reynolds number. Specifically, it is consistent with the integral length scale ? for Re > 200, but not for Re < 200. The ending scale is around lambda = 0.5d and decreases slightly as Re increases.

Automated summary

In this study, we conducted a series of experiments to investigate the velocity fluctuations caused by the flow past fixed spheres. The results show that the fluctuations can be classified into temporal fluctuations and spatial fluctuations, representing the contributions of flow instability and spatial inhomogeneity, respectively. At low Reynolds numbers, the total fluctuation is mainly caused by the spatial fluctuation, while at higher Reynolds numbers, both flow instability and spatial inhomogeneity contribute to the total velocity fluctuation. Moreover, the energy distribution and wavenumber spectra of the fluctuations also change significantly with the increase of Reynolds number.