Analysis of drag reduction effects in turbulent Taylor–Couette flow controlled via axial oscillation of inner cylinder

Abstract

Analysis of drag reduction effects due to axial oscillation of an inner cylinder in a turbulent Taylor–Couette (TC) flow is performed in the present study. The frictional Reynolds number on the inner cylinder is 218, and the non-dimensional oscillating period is varied from 8 to 32. By examining turbulence statistics, we uncover different impacts of the long- and short-period oscillations on the circumferential (θ) and radial (r) velocity fluctuations in large (uθl, url) and small (uθs, urs) scales. One of the most surprising findings is that the short-period oscillation increases the large-scale Reynolds shear stress ⟨uθlurl⟩ by the strong intensification of uθl exceeding the suppression of url. To understand the phenomena, the spectra of each term in the transport equations of the Reynolds normal stresses ⟨uθ′uθ′⟩ and ⟨ur′ur′⟩ are analyzed. First, it is shown that the short-period oscillation weakens the productions of uθs, urs, and url while it enhances that of uθl. In contrast, the long-period oscillation reduces the productions of uθl and url while it mainly intensifies that of urs. Second, the investigations of the pressure–strain terms indicate that the short-period oscillation mainly impedes the inter-component energy transfer originating from the small-scale background turbulence. However, the long-period oscillation benefits the small-scale inter-component energy communication while it hinders the large-scale one. In addition, the inverse energy transfer in the turbulent TC flow is confirmed by inspecting the inter-scale energy transfer terms. The hindrance of the inter-scale energy transfer by the inner-cylinder oscillation plays a non-negligible role in the reduction of the wall friction drag.