Well resolved DNS of turbulent pipe flow at Reτ = 3000 in a 21D long computational domain

Abstract

As discussed by Chin et al. [1] there has been an inclination towards running [direct numerical] simulations (DNS) at higher Reynolds numbers (Re� ) at the expense of shortening the computational domain length. Following the general argument that the streamwise extent of the characteristic near-wall streaks is constant when scaled in wall units, we performed DNS of turbulent pipe flow at Re� = Du� =� = 1440 in a computational domain of length L = 1:25D measured in diameters (D) [2]. In wall units (+) this corresponds to L+ = 1800: a domain length which was used earlier by e.g. Eggles & Unger [3] for pipe flow DNS at Re� = 360. In [2] we have shown that using such short domains leads to adequate representation of the turbulent flow field and to good overall agreement of mean and rms velocity statistics between DNS results and experimental data. However, it is well known that a substantially larger domain is required to obtain thoroughly converged one- and two-point auto-correlation functions and energy spectra. E.g. Chin et al. [1] performed numerous DNS for moderate Re� � 1000 and found minimum domain lengths between 1:6D and 12:6D depending on Re� and the quantity of interest. For considerably higher Re� , experimental studies (e.g. Monty et al. [4]) show the existence of large and very large scale motions (VLSM) with typical length of more than 10D. To improve the understanding of the characteristica and the origin of the VLSM, we perform DNS of turbulent pipe flow at Reynolds numbers for which a formation of VLSM is to be expected using a computational domain long enough to ensure full representation of even these very large features. The numerical method used to integrate the incompressible Navier-Stokes equations is based on a fourth-order-accurate finite-volume formulation, an explicit leapfrog-Euler scheme and a direct Poisson solver. Further details and the origin of our DNS code are given in [2] and the references therein. Figure 1 exemplarily shows snapshots of the turbulent flow field obtained in a DNS at Re� = 3000 in a domain of length L = 21D. Additionally, the second order statistical moment of the streamwise velocity component is presented in figure 2 for different Re� . The plotted DNS results clearly reveal the tendency to develop a second peak in the outer region (r+ > 50) with growing Re� , an effect which is well know from experiments, e.g. Zhao & Smits [5]. At the conference we will present and discuss the results of a comprehensive statistical analysis. This includes energy spectra, which are known to develop a second far-wall peak with growing Re� . Further, we will discuss the influence of the used domain lengths (1:25D � L � 21D) in the considered Reynolds number range of 360 � Re� � 3000 on this quantities. Currently, we develop a method to analyse the inter-scale turbulent kinetic energy transfer in a pipe flow system in order to study which scales feed the larger structures with energy. The results of this analysis will be presented as well.