Large-eddy simulation of turbulent pipe flow at large Reynolds number

We describe large-eddy simulations (LES), using a spectral-element method, of turbulent smooth- and rough-wall pipe flows. The spectral-element code SEMTEX was used (Blackburn and Sherwin {\it J. Comput. Phys.} 2004) in a mode where the axial direction is treated using Fourier modes, with a spectral-element representation within the cross-flow plane with Dirichlet boundary conditions on the circular pipe boundary. The stretched-vortex subgrid-stress model is utilized together with the wall-model of Chung and Pullin ({\it JFM, 2009}). For rough-wall flows, local subgrid roughness is incorporated by the addition of an empirical roughness function $u_\tau\,\Delta^+(k_s^+)$, where $k_s^+ = k_s\,u_\tau/\nu$ and $k_s$ is the equivalent sand roughness. This is used in both the inner-scaling ansatz for the unsteady term of the wall-normal integration of the stream-wise momentum equation, and also in the log-like profile used to give a boundary condition for the outer-flow LES. Results will be discussed that include variation of the skin-friction coefficient as a function of both Reynolds number and the ratio of $k_s$ to the pipe radius, and also mean velocity profiles and some turbulence statistics.