Characterization of flow pattern past two spheres in proximity

Abstract

As a follow-up study of flow-induced forces on two nearby spheres [D. Yoon and K. Yang, Phys. Fluids 19, 098103 (2007)], this paper establishes a systematic characterization of flow pattern past two identical spheres in proximity at Re=300. We consider all possible arrangements of two spheres in terms of the distance between the spheres and the angle inclined with respect to the main flow direction. It turns out that significant changes in shedding characteristics are noticed depending on how the two spheres are positioned. Ten distinct flow patterns are identified in total, and a detailed description is given to each pattern. Collecting all the numerical results obtained, we propose two comprehensive tables, one for flow pattern for each arrangement of the spheres and the other for Strouhal number of the corresponding vortex shedding. The perfect geometrical symmetry implied in the flow configuration allows one to use those tables for any two identical spheres arbitrarily positioned in physical space with respect to the main flow direction.

Stratified flow past a sphere at moderate Reynolds numbers

“…The Strouhal number derived from the frequency spectra of instantaneous C d is St = 0.138. It compares well with St = 0.136 and St = 0.137 reported in [18,4] and [53,57], respectively.…”

“…The smallest distance of 0.005D between points corresponds to the thickness of the first prismatic layer from the sphere surfaces, while the largest elements of the primary mesh reach the approximate dimensions of 1D near the outer boundaries. This configuration and setup have been chosen to facilitate a quantitative comparison with the neutrally stratified flow solution at Re = 300 in [57].…”

Simulations of stably stratified flow past two spheres at Re = 300

“…For the closest arrangements of spheres (l/D < 1) they are about half a period out of phase, while when the spheres are further apart (l/D ≥ 1.5) the histories of the oscillations for both spheres become identical. Figure 5 compares each sphere's normalised frequency of vortex-shedding, obtained using the NFT-FV model, with those reported in both experimental 20 and numerical 17,20 studies. The vortex-shedding frequencies, f , are derived from the frequency spectra 3 of the drag coefficient and are normalised by the frequency obtained for a single sphere f s = 0.138.…”

“…The validity of the NFT-FV scheme operating on unstructured meshes has been successfully demonstrated for a range of stratified flows past orography 5,6,24 and a single sphere 3,15 , in addition to global simulations of the Earth's atmosphere employing meshes with a combination of a quasi-uniform octahedral distribution in the horizontal and prismatic spacing in the vertical 25 . The present work provides additional comparisons with numerical and experimental results available in the literature 17,20 for two spheres immersed in a neutrally-stratified flow, where we illustrate the scheme's efficacy together with its ability to reproduce flow intricacies generated by the presence of multiple objects. Direct Numerical Simulations (DNS) of stably-stratified flows for Froude numbers Fr ∈ [0.25, ∞] past two spheres are also contrasted with the previously documented computations for a single sphere 3 .…”

“…The size of the domain is dependent on the arrangement of spheres. It is chosen to maintain a minimum distance (15D) between any sphere and the external boundaries 17 , to be large enough to adequately simulate the far-wake field (cf. Ref.…”