Revisiting the Higher-order Statistical Moments in Turbulent Pipe Flow using Direct Numerical Simulations

Abstract

Direct numerical simulations (DNS) of turbulent pipe flow within a flow domain of L = 42R involving a friction Reynolds number of Rer = 180 and two different wall normal grid refinements have been carried out and investigated in terms of turbulent high-order statistics. The phenomenology of !arge local wall-normal velocity fluctuations (velocity spikes), is discussed through time series and instantaneous flow field realizations. Due to their rare appearance both in space and time, statistical high-order moments take long time to converge. A convergence study is performed and for fully converged statistics the sensitivity of the wall-normal kurtosis value on the wall is investigated. The fourth order moment of wall-normal velocity needs to be integrated at least t:,. r + = 2.4 · 10"11 units of an averaging coordinate in time and space to obtain a fully converged flatness value in the very vicinity of the wall. Furthermore, a wall-near grid spacing of t:,. r+ = 0.11 was found to be insufficient to fully satisfy the no-slip boundary condition in terms of wall-normal flatness.