The influence of pipe length in direct numerical simulation

A direct numerical simulation (DNS) of fully developed turbulent pipe flow is performed at Reτ ≈ 170 and 500 to examine the effect of the streamwise domain length on the convergence of turbulence statistics. Computational domain lengths vary from the πδ to 20πδ. Lower order statistics such as mean flow, turbulence intensities, Reynolds stress, correlations and higher order statistics including energy spectra, skewness and flatness were computed. The findings show that in the near wall region (below the buffer region, r+ ≤ 30), the required pipe length for all turbulence statistics to converge requires a minimum viscous length of O(6300) wall units. It was also found that for convergence of turbulence statistics at the outer region, a proposed pipe length of 8πδ seems sufficient for the Reynolds numbers considered in this study. Introduction The vast amount of data that can be obtained from DNS has enabled scientists to better understand turbulent flow physics and is becoming an important tool in turbulence research [17]. One of the pioneering study using DNS is that of a three-dimensional isotropic turbulence by Orszag & Patterson [21]. The advancement in computer technology has led to more DNS studies being carried out on turbulent wall-bounded flows, see figure 1. With Reynolds numbers of DNS approaching nominally similar Reynolds numbers as experiments, it is therefore possible to compare turbulence statistics between them. However, early hot-wire experiments have shown that long streamwise structures exist in wall-bounded turbulent flows [9, 24], and recent experiments by Kim & Adrian [16] have shown from premultiplied spectra that these structures were longer than previously appreciated. Balakumar & Adrian [4] termed these structures as “large-scale motions” (LSMs) as motions with wavelength of up to 2-3δ, where δ is the half channel height, pipe radius or boundary later thickness and “very-large-scale motions” (termed VLSMs with wavelength of more than 3δ). A recent study by Hutchins & Marusic [11] reported long meandering features exceeding 20δ in the logarithmic region of turbulent boundary layers, and termed them as “superstructures”. Other reports by Monty et al. [19, 18] showed that these long meandering features in pipe and channel are up to 25δ in length. Therefore, it is important to better understand how statistics are influenced by how the boundary conditions interact with the largest scale motion in DNS, since its impractical to have a computational domain of infinite length. In this paper, we will investigate the length of domain required in order to obtain converged statistics and the effects of computational domain length on turbulence statistics. The Reynolds numbers chosen for this study are Reτ ≈ 170 and 500.