Direct numerical simulation study of turbulent pipe flow with imposed radial rotation

We carry out direct numerical simulations (DNS) of fully developed turbulent pipe flow subjected to radial system rotation, examining a broad range of rotational speed and Reynolds number. In response to the imposed system rotation, strong secondary motions arise in the form of streamwise-aligned counter-rotating eddies, which engage significantly with the boundary layer, exerting a notable influence on the turbulent flow. At high rotation numbers, a Taylor-Proudman region appears, marked by a constant mean axial velocity along the rotation axis. As rotation increases, local flow relaminarisation takes place starting at the suction side of the pipe, ultimately resulting in full relaminarisation when the rotation number is higher than unity. In this regime the near-wall region of the flow exhibits the typical hallmark of laminar Ekman layers, whose strength varies with the azimuthal position along the pipe perimeter. A predictive analytical formula for frictional drag is derived for this ultimate high rotation which accurately reproduces the DNS data. The behaviour of friction is more complex to predict at low-to-intermediate rotation numbers owing to concurrent effects of viscosity, turbulence, secondary motions and rotation, which we quantify in an extended version of the Fukagata-Iwamoto-Kasagi identity.