Revisiting the Higher-Order Statistical Moments in Turbulent Pipe Flow Using Direct Numerical Simulations

Abstract

Direct numerical simulations of turbulent pipe flow in a flow domain of length $L=42R$ and a friction Reynolds number of $Re_{\tau } =180$ and two different wall normal grid refinements were carried out and investigated in terms of turbulent high-order statistics. The phenomenology of large 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 component value on the wall is investigated. The fourth order statistical moment of the wall-normal velocity needs to be integrated at least $\varDelta \tau ^+ = 2.4\cdot 10^{11}$ 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 near-wall grid spacing of at least $\varDelta r^+=0.11$ is needed to fully satisfy the no-slip boundary condition in terms of wall-normal flatness.