Quadruple decomposition of current-dominated pulsatile rough-wall turbulent pipe flow

Abstract

The physics of pulsatile rough-wall turbulent pipe flow is investigated using data from direct numerical simulation (DNS). Three geometrically-scaled sinusoidal roughness topographies are considered — the amplitude and wavelength of each surface are systematically varied whilst holding their amplitude-towavelength ratio constant. Pulsation is achieved by imposing a time-harmonic axial pressure gradient. The resulting flow-field is triple phase-averaged (in two spatial directions and also in time) which permits a quadruple decomposition of the instantaneous field variables to be invoked. The four components of the quadruple decomposition are: (i) a global-averaged mean component; (ii) a steady roughness-induced fluctuation; (iii) an unsteady pulsation-induced fluctuation and (iv) the remaining turbulent fluctuation. We compare statistics of (i)-(iv) against their non-pulsatile counterpart using past results from related work [1, 2]. Whilst the pulsatile and non-pulsatile data collapse well in the outer region, clear differences are observed in the near-roughness region. In particular, profiles of the mean axial velocity, roughness-induced stress and turbulence-induced stress exhibit consistently lower magnitudes below the roughness crests under pulsatile conditions.