On alignments and small scale structure in turbulent pipe flow

Abstract

The data base of an extensive DNS of turbulent flow in a pipe (Eggels et al. J. Fluid Mech. 268 (1994) 175) at Re = 7000, based on the pipe diameter and the centerline velocity or Ref = 360 based on the friction velocity u~, has been used to study some of the alignments discovered recently in quasi-isotropic and shear turbulent flows and attracted considerable attention. These are the alignments between the velocity u and vorticity vectors to, between the vorticity to and the eigenvectors of the rate of strain tensor sij, and between to and the vortex stretching vector Wi = toj sij. Comparison of these alignments strongly indicates that the quasi-two-dimensional (QTD) state of turbulent pipe flow in regions of strong alignment between to and the intermediate eigenvector ,~int of the rate of strain tensor sij is qualitatevly different from purely two-dimensional one. This is manifested in stronger alignments between to and W in these regions as well as in larger enstrophy generation ((.OiWjSij) =-(o)iWi) and large (W2), which are identically zero for a purely two-dimensional flow.The same is true of regions with concentrated vorticity, most of which are embedded into the regions with strong alignment between to and ~[int.

A numerical investigation of turbulent flows in a spanwise rotating channel

“…The probability density functions (PDF) of turbulence fluctuations are relevant to the motion of small scales in the wall-shear turbulence [12,13]. Orlandi [11] asserted that the PDF of helicity and Lamb vector fluctuations are closely related to the wall drag reduction and turbulence statistics of rotating pipe flow.…”

Geometrical Properties of the Resolved-Scale Velocity and Temperature Fields Predicted using Large-Eddy Simulation

“…(11)], the DTDM-HF of Peng and Davidson [46] [cf. (14)] does not require the SGS heat flux to be aligned with the negative resolved temperature gradient vector, instead, it modifies the heat flux vector h j in response to both the resolved strain rate tensor and temperature gradient in all three coordinate directions through the contraction betweenS jk and ∂T/∂ x k .…”

“…Previous approaches for studying the geometrical property of the fluid vectors and tensors have primarily utilized direct numerical simulation (DNS) [2][3][4][9][10][11][12] and experimental [5,8] approaches based on unfiltered turbulent flows. Recently, study of the statistical geometry of turbulence at the filtered-(or, resolved-) scale based on LES has become a relevant research topic.…”

“…This is due to the evidence that many important physical phenomena (both local and global) of thermal fluid flows can be observed and reproduced at a given filtered level using the approach of LES, temporally and spatially. Tao et al [13] analyzed the holographic particle image velocimetry (HPIV) measurements of a quasi-isotropic flow at the center of a square duct using the a priori LES approach, and observed that many geometrical alignment trends of the filtered turbulence agree with those of unfiltered turbulence [3,4,[9][10][11][12]. For example, Tao et al [13] were able to reproduce the canonical preferential alignment pattern between the resolved vorticity vector (ω) and the eigenvector (e Sβ ) corresponding to the intermediate eigenvalue of the resolved strain rate tensor in the context of LES.…”

“…According to DNS studies of iso-thermal wall-bounded flows [7,10,11] and recent LES studies of turbulent iso-thermal Couette flows [20,21], the presence of the wall in a flow field has a significant anisotropic impact on the geometrical properties of quantities such as enstrophy generation, the alignment pattern of the vorticity vector with respect to the eigenframe of the resolved strain rate tensor, and the ratio of the eigenvalues (or, principal values) of the resolved strain rate tensor. In contrast to previous investigations based on LES of iso-thermal flows, in the present research, we aim at addressing the influence of wall-imposed anisotropy in conjunction with buoyancy on the geometrical properties of the temperature and velocity fields of a non-isothermal vertical channel flow.…”