On the influence of domain size on POD modes in turbulent plane Couette flow

Numerical Methods in Fluids

Pettersen

2009

SUMMARYA new turbulent flow with distinct three-dimensional characteristics has been designed in order to study the impact of mean-flow skewing on the turbulent coherent vortices and Reynolds-averaged statistics. The skewing of a unidirectional plane Couette flow was achieved by means of a spanwise pressure gradient. Direct numerical simulations of the statistically steady Couette-Poiseuille flow enabled in-depth explorations of the turbulence field in the skewed flow. The imposition of a modest spanwise gradient turned the mean flow about 8 • away from the original Couette flow direction and this turning angle remained nearly the same over the entire cross section. Nevertheless, a substantial non-alignment between the turbulent shear stress angle and the mean velocity gradient angle was observed. The structure parameter turned out to slightly exceed that in the pure Couette flow, contrary to the observations made in some other three-dimensional shear flows.Coherent flow structures, which are known to be associated with the Reynolds shear stress in near-wall regions, were identified by the 2 -criterion. Instantaneous and ensemble-averaged vortices resembled those found in the unidirectional Couette flow. In the skewed flow, however, the vortex structures were turned to align with the local mean-flow direction. The conventional symmetry between Case 1 and Case 2 vortices was broken due to the mean-flow three-dimensionality. The turning of the coherent vortices and the accompanying symmetry-breaking gave rise to secondary and tertiary turbulent shear stress components. By averaging the already ensemble-averaged shear stresses associated with Case 1 and Case 2 vortices in the homogeneous directions, a direct link between the educed near-wall structures and the Reynolds-averaged turbulent stresses was established. These observations provide evidence in support of the hypothesis that the structural model proposed for two-dimensional turbulent boundary layers remains valid also in flows with moderate mean three-dimensionality.

Section: Approach For Solving the Navier-stokes Equationsmentioning

confidence: 99%

Turbulence in a three‐dimensional wall‐bounded shear flow

Holstad

Numerical Methods in Fluids

Pettersen

2009

“…This is due to the extraordinary long structures in plane Couette flow, typically five times longer than in the plane Poiseuille flow. The choice of the size of the computational domain used in the present investigation was based on observations made from the earlier simulation studies by Bech and Andersson , Bech et al , Komminaho et al , Hu et al , Tsukahara et al and Holstad et al in which the domain length and domain width were systematically varied and the results compared, notably the two‐point correlations. The unanimous conclusion of all these investigations is that a domain length of at least about five times the typical Poiseuille flow domain is required for realistic Couette flow simulations.…”

Section: Numerical Proceduresmentioning

confidence: 99%

Turbulence in a skewed three‐dimensional wall‐bounded shear flow: effect of mean vorticity on structure modification

Holstad

Numerical Methods in Fluids

Pettersen

2011

SUMMARY Mean‐flow three‐dimensionalities affect both the turbulence level and the coherent flow structures in wall‐bounded shear flows. A tailor‐made flow configuration was designed to enable a thorough investigation of moderately and severely skewed channel flows. A unidirectional shear‐driven plane Couette flow was skewed by means of an imposed spanwise pressure gradient. Three different cases with 8°, 34°and 52°skewing were simulated numerically and the results compared with data from a purely two‐dimensional plane Couette flow. The resulting three‐dimensional flow field became statistically stationary and homogeneous in the streamwise and spanwise directions while the mean velocity vector V and the mean vorticity vector Ω remained parallel with the walls. Mean flow profiles were presented together with all components of the Reynolds stress tensor. The mean shear rate in the core region gradually increased with increasing skewing whereas the velocity fluctuations were enhanced in the spanwise direction and reduced in the streamwise direction. The Reynolds shear stress is known to be closely related to the coherent flow structures in the near‐wall region. The instantaneous and ensemble‐averaged flow structures were turned by the skewed mean flow. We demonstrated for the medium‐skewed case that the coherent structures should be examined in a coordinate system aligned with V to enable a sound interpretation of 3D effects. The conventional symmetry between Case 1 and Case 2 vortices was broken and Case 1 vortices turned out to be stronger than Case 2. This observation is in conflict with the common understanding on the basis of the spanwise (secondary) mean shear rate. A refined model was proposed to interpret the structure modifications in three‐dimensional wall‐flows. What matters is the orientation of the mean vorticity vector Ω relative to the vortex vorticity vector ωv, that is, the sign of Ω ·ωv. In the present situation, Ω ·ωv > 0 for the Case 1 vortices causing a strengthening relative to the Case 2 vortices. Copyright © 2011 John Wiley & Sons, Ltd.

“…Here they are referred to as Very-Large-Scale Structures (VLSS). There have been some arguments on whether these VLSS are a result of the periodic boundary condition applied in the DNS (Bech et al, 1995), resulting in several studies examining varying sizes of the computational domain (Bech and Andersson, 1994;Komminaho et al, 1996, Holstad et al, 2006, Tsukahara et al, 2006and Gai et al 2015. As a general rule, numerical simulations of plane Couette flows always require a much larger domain size than needed for plane Poiseuille flows to avoid unphysical effects of the periodic boundary condition in the homogeneous directions.…”

Section: Introductionmentioning

confidence: 99%

Turbulent Couette–Poiseuille flow with zero wall shear

Yang

Zhao

International Journal of Heat and Fluid Flow

2017

Self Cite

A particular pressure-driven flow in a plane channel is considered, in which one of the walls moves with a constant speed that makes the mean shear rate and the friction at the moving wall vanish. The Reynolds number considered based on the friction velocity at the stationary wall (uτ,S) and half the channel height (h) is Reτ,S = 180. The resulting mean velocity increases monotonically from the stationary to the moving wall and exhibits a substantial logarithmic region. Conventional near-wall streaks are observed only near the stationary wall, whereas the turbulence in the vicinity of the shear-free moving wall is qualitatively different from typical near-wall turbulence. Large-scale-structures (LSS) dominate in the center region and their spanwise spacing increases almost linearly from about 2.3 to 4.2 channel half-heights at this Reτ,S. The presence of LSS adds to the transport of turbulent kinetic energy from the core region towards the moving wall where the energy production is negligible. Energy is supplied to this particular flow only by the driving pressure gradient and the wall motion enhances this energy input from to the mean flow. About half of the supplied mechanical energy is directly lost by viscous dissipation whereas the other half is first converted from mean-flow energy to turbulent kinetic energy and thereafter dissipated.