Direct numerical simulations of turbulence subjected to a straining and destraining cycle

Abstract

In many turbulent flows, significant interactions between fluctuations and mean velocity gradients occur in nonequilibrium conditions, i.e., the turbulence does not have sufficient time to adjust to changes in the velocity gradients applied by the large scales. The simplest flow that retains such physics is the time dependent homogeneous strain flow. A detailed experimental study of initially isotropic turbulence subjected to a straining and destraining cycle was reported by Chen et al. ͓"Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle," J. Fluid Mech. 562, 123 ͑2006͔͒. Direct numerical simulation ͑DNS͒ of the experiment of Chen et al. ͓"Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle," J. Fluid Mech. 562, 123 ͑2006͔͒ is undertaken, applying the measured straining and destraining cycle in the DNS. By necessity, the Reynolds number in the DNS is lower. The DNS study provides a complement to the experimental one including time evolution of small-scale gradients and pressure terms that could not be measured in the experiments. The turbulence response is characterized in terms of velocity variances, and similarities and differences between the experimental data and the DNS results are discussed. Most of the differences can be attributed to the response of the largest eddies, which, even if are subjected to the same straining cycle, evolve under different conditions in the simulations and experiment. To explore this issue, the time evolution of different initial conditions parametrized in terms of the integral scale is analyzed in computational domains with different aspect ratios. This systematic analysis is necessary to minimize artifacts due to unphysical confinement effects of the flow. The evolution of turbulent kinetic energy production predicted by DNS, in agreement with experimental data, provides a significant backscatter of kinetic energy during the destraining phase. This behavior is explained in terms of Reynolds stress anisotropy and nonequilibrium conditions. From the DNS, a substantial persistency of anisotropy is observed up to small scales, i.e., at the level of velocity gradients. Due to the time dependent deformation, we find that the major contribution in the Reynolds stresses budget is provided by the production term and by the pressure/strain correlation, resulting in large time variation of velocity intensities. The DNS data are compared with predictions from the classical Launder-Reece-Rodi isoptropic production ͓B. E. Launder et al., "Progress in the development of a Reynolds stress turbulence closure," J. Fluid Mech. 68, 537 ͑1975͔͒ Reynolds stress model, showing good agreement with some differences for the redistribution term.

Inertial particle acceleration in strained turbulence

“…The objective of this work is to investigate the effects of flow straining on the Lagrangian dynamics of small, sub-Kolmogorov scale, passive and inertial particles. Our motivation stems both from the fact that many practical turbulent flows are subject to straining motions, such as the external flows over bluff or streamlined bodies and internal flows in variable cross sections (Batchelor (1953); Hunt (1973); Hunt & Carruthers (1990); Warhaft (1980); Chen et al (2006); Ayyalasomayajula & Warhaft (2006); Gualtieri & Meneveau (2010)). A mean straining flow naturally appears in the proximity of stagnation points.…”

The alignment of vortical structures in turbulent flow through a contraction

“…Homogeneous isotropic conditions were first obtained at a maximum Re λ of 113, before starting the mean-straining simulations. A similar time-dependent strain rate in DNS was adopted previously by Gualtieri & Meneveau (2010). They simulated the strainingdestraining experiments by Chen et al (2006) up to a maximum Re λ of 40.…”

Effect of geometry and Reynolds number on the turbulent separated flow behind a bulge in a channel

“…In addition to the non-homogeneous effects induced by the wall, it is fundamental to address the non-homogeneous effects in the streamwise direction where the dynamics of turbulent fluctuations occurs under rapidly changing conditions, see e.g. Chen et al (2006); Gualtieri & Meneveau (2010) for a similar study in the context of turbulent flows subjected to rapid time variations of the mean flow.…”