Flow around in-line sphere array at moderate Reynolds number

Abstract

In the present study, we perform a series of water-tunnel experiments to investigate the flow around an in-line sphere array at the Reynolds number of 1000, based on the free-stream velocity and sphere diameter, focusing on how the sphere wake changes by the additional spheres located behind while the spacing between them being varied. We try to capture the qualitative picture of the wake behind each sphere and to measure quantitative distribution of flow statistics using dye visualization and particle image velocimetry techniques. When the spacing is less than one sphere diameter, the gap flow is steady and axisymmetric, while the last wake is planar symmetric with a weaker turbulence level. When the spacing is twice larger than the sphere diameter, on the other hand, the flows in the gap and final wake tend to recover the axisymmetric feature, which is similar to that of a single sphere wake at the same Reynolds number. Between these two regimes, there is a transitional flow regime (the spacing is comparable to the sphere diameter) where the flow is still planar symmetric, but the turbulence level is enhanced. Depending on the flow topology, it is found that the characteristic frequencies (i.e., Strouhal number) in the shear layers and the gap are also affected. Finally, based on our analysis, we propose a flow regime map for each wake in the considered sphere arrays and also estimate the pressure distribution from the velocity measurements, by which the forces acting on each sphere can be assessed.