ENGINEERING AND CFD

Introduction

A large amount of the energy needed to push fluids through pipes worldwide is dissipated by viscous turbulence in the vicinity of solid walls. Therefore the study of wall-bounded turbulent flows is not only of theoretical interest but also of practical importance for many engineering applications. In wall-bounded turbulence the energy of the turbulent fluctuations is distributed among different scales. The largest energetic scales are denoted as superstructures or very-large-scale motions (VLSMs). In our project we carry out direct numerical simulations (DNSs) of turbulent pipe flow aiming at the understanding of the energy exchange between VLSMs and the small-scale coherent structures [1].

While the near-wall small-scale structures scale in viscous units, the outer flow VLSMs scale in bulk units. Hence the range of scales increases as the Reynolds number of the flow increases. In order to study the interaction between these structures, we carried out DNSs of friction Reynolds numbers up to Re_Τ=2880, where Re_Τ=u_ΤR/ν is based on the friction velocity, the pipe radius and the kinematic viscosity. Besides a large Reynolds number, required for large scale separation, a sufficiently long computational domain is needed for VLSMs to settle. In a preliminary study the required computational domain length was estimated to L=42R [2].

Resulting instantaneous streamwise velocity fluctuations for Re_Τ=1500 are depicted as iso-volumes in Fig. 1.  As their small-scale counterparts, the VLSMs visible in the instantaneous picture occur alternately as high- and low-speed streaky structures. In azimuthal direction three low- and high-speed structures are clearly visible. The average extension of VLSMs can be extracted from velocity correlations, as shown in Fig. 2. With a threshold of 0.1, the average streamwise length of VLSMs is measured as approximately 7R. In addition, the velocity correlation shows an inclination towards the wall, a feature that is characteristic for both small-scale motions and VLSMs. We reported on the scaling and convergence of high-order statistical moments and contributions from VLSMs on these moments [2]. Particularly very large local wall-normal velocity fluctuations in the vicinity of the wall --- so called velocity spikes --- are modulated by outer flow VLSMs, which reflects in the wall-normal velocity flatness. Regarding the origin of the kinetic energy of VLSMs, we analysed the turbulent kinetic energy transport equation of the low-pass filtered velocity field, the latter basically consisting of VLSMs. By comparing our results with what is known from the small-scale near-wall cycle, we found that VLSMs are fed with energy by the mean velocity field via a turbulent production mechanism similar to their small-scale counterparts [4]. Regarding the transfer of energy between different scales, however, VLSMs behave strictly opposite to the small-scale motions. While for the last mentioned, the forward energy cascade --- energy transfer from larger to smaller scales --- correlates with low-speed structures and the backward transfer correlates with high-speed structures, for VLSMs the opposite is the case.