Computational domain length and Reynolds number effects on large-scale coherent motions in turbulent pipe flow

Abstract

We present results from direct numerical simulations (DNS) of turbulent pipe flow at shear Reynolds numbers up to Reτ = 1500 using different computational domains with lengths up to L / R = 42. The objectives are to analyse the effect of the finite size of the periodic pipe domain on large flow structures in dependency of Reτ and to assess a minimum L / R required for relevant turbulent scales to be captured and a minimum Reτ for very large-scale motions (VLSM) to be analysed. Analysing one-point statistics revealed that the mean velocity profile is invariant for L / R > 7. The wall-normal location at which deviations occur in shorter domains changes strongly with increasing Reτ from the near-wall region to the outer layer, where VLSM are believed to live. The root mean square velocity profiles exhibit domain length dependencies for pipes shorter than 14R and 7R depending on Reτ . For all Reτ , the higher-order statistical moments show only weak dependencies and only for the shortest domain considered here. However, the analysis of one- and two-dimensional pre-multiplied energy spectra revealed that even for larger L / R, not all physically relevant scales are fully captured, even though the aforementioned statistics are in good agreement with the literature. We found L / R > 42 to be sufficiently large to capture VLSM-relevant turbulent scales in the considered range of Reτ based on our definition of an integral energy threshold of 10%. The requirement to capture at least 1/10 of the global maximum energy level is justified by a 14% increase of the streamwise turbulence intensity in the outer region between Reτ = 720 and 1500, which can be related to VLSM-relevant length scales. Based on this scaling anomaly, we found Reτ = 1500 to be a necessary minimum requirement to investigate VLSM-related effects in pipe flow, even though the streamwise energy spectra does not yet indicate sufficient scale separation between the most energetic and the very long motions.