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This paper presents the results of numerical simulations of flow in a periodic channel with the walls covered in the central part by spherical elements that have the same overall surface areas but different radii. Two distributions of the sphere are considered, with the subsequent rows placed one after another or shifted. The computations are performed using the high-order code, whereas the solid elements are modelled with the help of the immersed boundary method. For selected cases, the results are validated by comparison with the solutions obtained using the ANSYS Fluent code on a very dense body-fitted mesh. It was found that the increase in the sphere diameter slows down the flow, which is attributed to the larger blockage of the channel cross-section caused by larger spheres and the occurrence of intense mixing (recirculation) between the spheres. The velocity profiles in the vicinity of the sphere are largely dependent on sphere diameter and rise when it increases. It was found that the distribution of the spheres plays an important role only when the spheres are large. In the part of the channel far from the sphere, the velocity profiles are significantly influenced by the sphere diameter but seem to be independent of the sphere distributions.

Numerical Analysis of a Flow over Spheres Embedded on a Flat Wall