Shear-free turbulence near a wall

1997 ◽  
Vol 338 ◽  
pp. 363-385 ◽  
Author(s):  
DAG ARONSON ◽  
ARNE V. JOHANSSON ◽  
LENNART LÖFDAHL
Keyword(s):  
Reynolds Stress ◽  
Initial Response ◽  
Wall Turbulence ◽  
Major Influence ◽  
Grid Turbulence ◽  
Normal Velocity ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Wall Interaction ◽  
Near Wall

The mean shear has a major influence on near-wall turbulence but there are also other important physical processes at work in the turbulence/wall interaction. In order to isolate these, a shear-free boundary layer was studied experimentally. The desired flow conditions were realized by generating decaying grid turbulence with a uniform mean velocity and passing it over a wall moving with the stream speed. It is shown that the initial response of the turbulence field can be well described by the theory of Hunt & Graham (1978). Later, where this theory ceases to give an accurate description, terms of the Reynolds stress transport (RST) equations were measured or estimated by balancing the equations. An important finding is that two different length scales are associated with the near-wall damping of the Reynolds stresses. The wall-normal velocity component is damped over a region extending roughly one macroscale out from the wall. The pressure–strain redistribution that normally would result from the Reynolds stress anisotropy in this region was found to be completely inhibited by the near-wall influence. In a thin region close to the wall the pressure–reflection effects were found to give a pressure–strain that has an effect opposite to the normally expected isotropization. This behaviour is not captured by current models.

scholarly journals Near-wall turbulent fluctuations in the absence of wide outer motions

2013 ◽  
Vol 723 ◽  
pp. 264-288 ◽  
Author(s):  
Yongyun Hwang
Keyword(s):  
Reynolds Number ◽  
Skin Friction ◽  
Reynolds Stress ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wall Region ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Full Simulation ◽  
Near Wall

AbstractNumerical experiments that remove turbulent motions wider than ${ \lambda }_{z}^{+ } \simeq 100$ are carried out up to ${\mathit{Re}}_{\tau } = 660$ in a turbulent channel. The artificial removal of the wide outer turbulence is conducted with spanwise minimal computational domains and an explicit filter that effectively removes spanwise uniform eddies. The mean velocity profile of the remaining motions shows very good agreement with that of the full simulation below ${y}^{+ } \simeq 40$, and the near-wall peaks of the streamwise velocity fluctuation scale very well in the inner units and remain almost constant at all the Reynolds numbers considered. The self-sustaining motions narrower than ${ \lambda }_{z}^{+ } \simeq 100$ generate smaller turbulent skin friction than full turbulent motions, and their contribution to turbulent skin friction gradually decays with the Reynolds number. This finding suggests that the role of the removed outer structures becomes increasingly important with the Reynolds number; thus one should aim to control the large scales for turbulent drag reduction at high Reynolds numbers. In the near-wall region, the streamwise and spanwise velocity fluctuations of the motions of ${ \lambda }_{z}^{+ } \leq 100$ reveal significant lack of energy at long streamwise lengths compared to those of the full simulation. In contrast, the losses of the wall-normal velocity and the Reynolds stress are not as large as those of these two variables. This implies that the streamwise and spanwise velocities of the removed motions penetrate deep into the near-wall region, while the wall-normal velocity and the Reynolds stress do not.

Non-universal scaling transition of momentum cascade in wall turbulence

2019 ◽  
Vol 871 ◽  
Author(s):  
Xi Chen ◽  
Fazle Hussain ◽  
Zhen-Su She
Keyword(s):  
Wall Turbulence ◽  
Normal Velocity ◽  
Large Set ◽  
Flow State ◽  
Energy Cascades ◽  
Full Coupling ◽  
Turbulent Momentum ◽  
Analytic Prediction ◽  
Prevailing View ◽  
Near Wall

As a counterpart of energy cascade, turbulent momentum cascade (TMC) in the wall-normal direction is important for understanding wall turbulence. Here, we report an analytic prediction of non-universal Reynolds number ($Re_{\unicode[STIX]{x1D70F}}$) scaling transition of the maximum TMC located at $y_{p}$. We show that in viscous units,$y_{p}^{+}$(and$1+\overline{u^{\prime }v^{\prime }}_{p}^{+}$) displays a scaling transition from$Re_{\unicode[STIX]{x1D70F}}^{3/7}$($Re_{\unicode[STIX]{x1D70F}}^{-6/7}$) to$Re_{\unicode[STIX]{x1D70F}}^{3/5}$($Re_{\unicode[STIX]{x1D70F}}^{-3/5}$) in turbulent boundary layer, in sharp contrast to that from$Re_{\unicode[STIX]{x1D70F}}^{1/3}$($Re_{\unicode[STIX]{x1D70F}}^{-2/3}$) to$Re_{\unicode[STIX]{x1D70F}}^{1/2}$($Re_{\unicode[STIX]{x1D70F}}^{-1/2}$) in a channel/pipe, countering the prevailing view of a single universal near-wall scaling. This scaling transition reflects different near-wall motions in the buffer layer for small$Re_{\unicode[STIX]{x1D70F}}$and log layer for large $Re_{\unicode[STIX]{x1D70F}}$, with the non-universality being ascribed to the presence/absence of mean wall-normal velocity $V$. Our predictions are validated by a large set of data, and a probable flow state with a full coupling between momentum and energy cascades beyond a critical$Re_{\unicode[STIX]{x1D70F}}$is envisaged.

Improved Prediction of Turbomachinery Flows Using Near-Wall Reynolds-Stress Model

2001 ◽  
Vol 124 (1) ◽  
pp. 86-99 ◽  
Author(s):  
G. A. Gerolymos ◽  
J. Neubauer ◽  
V. C. Sharma ◽  
I. Vallet
Keyword(s):  
Experimental Data ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flow Equations ◽  
Near Wall

In this paper an assessment of the improvement in the prediction of complex turbomachinery flows using a new near-wall Reynolds-stress model is attempted. The turbulence closure used is a near-wall low-turbulence-Reynolds-number Reynolds-stress model, that is independent of the distance-from-the-wall and of the normal-to-the-wall direction. The model takes into account the Coriolis redistribution effect on the Reynolds-stresses. The five mean flow equations and the seven turbulence model equations are solved using an implicit coupled OΔx3 upwind-biased solver. Results are compared with experimental data for three turbomachinery configurations: the NTUA high subsonic annular cascade, the NASA_37 rotor, and the RWTH 1 1/2 stage turbine. A detailed analysis of the flowfield is given. It is seen that the new model that takes into account the Reynolds-stress anisotropy substantially improves the agreement with experimental data, particularily for flows with large separation, while being only 30 percent more expensive than the k−ε model (thanks to an efficient implicit implementation). It is believed that further work on advanced turbulence models will substantially enhance the predictive capability of complex turbulent flows in turbomachinery.

On the size of the energy-containing eddies in the outer turbulent wall layer

2012 ◽  
Vol 702 ◽  
pp. 521-532 ◽  
Author(s):  
Sergio Pirozzoli
Keyword(s):  
Outer Part ◽  
Eddy Diffusivity ◽  
Wall Layer ◽  
Wall Turbulence ◽  
Normal Velocity ◽  
Mixing Length ◽  
Mean Velocity ◽  
Local Mean ◽  
Turbulent Wall ◽  
Good Agreement

AbstractWe investigate the scaling of the energy-containing eddies in the outer part of turbulent wall layers. Their spanwise integral length scales are extracted from a direct numerical simulation (DNS) database, which includes compressible turbulent boundary layers and incompressible turbulent Couette–Poiseuille flows. The results indicate similar behaviour for all classes of flows, with a general increasing trend in the eddy size with the wall distance. A family of scaling relationships are proposed based on simple dimensional arguments, of which the classical mixing length approximation constitutes one example. As in previous studies, we find that the mixing length is in good agreement with the size distribution of the eddies carrying wall-normal velocity, which are active in establishing the mean velocity distribution. However, we find that the eddies associated with wall-parallel motions obey a different scaling, which is controlled by the local mean shear and by an effective eddy diffusivity ${\nu }_{t} = { u}_{\tau }^{\ensuremath{\ast} } \delta $, where ${ u}_{\tau }^{\ensuremath{\ast} } $ is the compressible counterpart of the friction velocity, and $\delta $ is the thickness of the wall layer. The validity of the proposed scalings is checked against DNS data, and the potential implications for the understanding of wall turbulence are discussed.

A revisit of the equilibrium assumption for predicting near-wall turbulence

2014 ◽  
Vol 760 ◽  
pp. 304-312 ◽  
Author(s):  
Farid Karimpour ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulent Viscosity ◽  
Wall Turbulence ◽  
Wall Region ◽  
Turbulence Decay ◽  
Prime 2 ◽  
Near Wall Turbulence ◽  
Near Wall

AbstractIn this study, we revisit the consequence of assuming equilibrium between the rates of production ($P$) and dissipation $({\it\epsilon})$ of the turbulent kinetic energy $(k)$ in the highly anisotropic and inhomogeneous near-wall region. Analytical and dimensional arguments are made to determine the relevant scales inherent in the turbulent viscosity (${\it\nu}_{t}$) formulation of the standard $k{-}{\it\epsilon}$ model, which is one of the most widely used turbulence closure schemes. This turbulent viscosity formulation is developed by assuming equilibrium and use of the turbulent kinetic energy $(k)$ to infer the relevant velocity scale. We show that such turbulent viscosity formulations are not suitable for modelling near-wall turbulence. Furthermore, we use the turbulent viscosity $({\it\nu}_{t})$ formulation suggested by Durbin (Theor. Comput. Fluid Dyn., vol. 3, 1991, pp. 1–13) to highlight the appropriate scales that correctly capture the characteristic scales and behaviour of $P/{\it\epsilon}$ in the near-wall region. We also show that the anisotropic Reynolds stress ($\overline{u^{\prime }v^{\prime }}$) is correlated with the wall-normal, isotropic Reynolds stress ($\overline{v^{\prime 2}}$) as $-\overline{u^{\prime }v^{\prime }}=c_{{\it\mu}}^{\prime }(ST_{L})(\overline{v^{\prime 2}})$, where $S$ is the mean shear rate, $T_{L}=k/{\it\epsilon}$ is the turbulence (decay) time scale and $c_{{\it\mu}}^{\prime }$ is a universal constant. ‘A priori’ tests are performed to assess the validity of the propositions using the direct numerical simulation (DNS) data of unstratified channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702). The comparisons with the data are excellent and confirm our findings.

scholarly journals Turbulent boundary layers over permeable walls: scaling and near-wall structure

2011 ◽  
Vol 687 ◽  
pp. 141-170 ◽  
Author(s):  
C. Manes ◽  
D. Poggi ◽  
L. Ridolfi
Keyword(s):  
Turbulent Flows ◽  
Laser Doppler Anemometry ◽  
Wall Turbulence ◽  
Shear Instability ◽  
Wall Structure ◽  
Wall Region ◽  
Mean Velocity ◽  
Wide Range ◽  
Permeable Walls ◽  
Near Wall

AbstractThis paper presents an experimental study devoted to investigating the effects of permeability on wall turbulence. Velocity measurements were performed by means of laser Doppler anemometry in open channel flows over walls characterized by a wide range of permeability. Previous studies proposed that the von Kármán coefficient associated with mean velocity profiles over permeable walls is significantly lower than the standard values reported for flows over smooth and rough walls. Furthermore, it was observed that turbulent flows over permeable walls do not fully respect the widely accepted paradigm of outer-layer similarity. Our data suggest that both anomalies can be explained as an effect of poor inner–outer scale separation if the depth of shear penetration within the permeable wall is considered as the representative length scale of the inner layer. We observed that with increasing permeability, the near-wall structure progressively evolves towards a more organized state until it reaches the condition of a perturbed mixing layer where the shear instability of the inflectional mean velocity profile dictates the scale of the dominant eddies. In our experiments such shear instability eddies were detected only over the wall with the highest permeability. In contrast attached eddies were present over all the other wall conditions. On the basis of these findings, we argue that the near-wall structure of turbulent flows over permeable walls is regulated by a competing mechanism between attached and shear instability eddies. We also argue that the ratio between the shear penetration depth and the boundary layer thickness quantifies the ratio between such eddy scales and, therefore, can be used as a diagnostic parameter to assess which eddy structure dominates the near-wall region for different wall permeability and flow conditions.

An investigation of turbulent plane Couette flow at low Reynolds numbers

1995 ◽  
Vol 286 ◽  
pp. 291-325 ◽  
Author(s):  
Knut H. Bech ◽  
Nils Tillmark ◽  
P. Henrik Alfredsson ◽  
Helge I. Andersson
Keyword(s):  
Couette Flow ◽  
Reynolds Stress ◽  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Turbulence Structure ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Near Wall

The turbulent structure in plane Couette flow at low Reynolds numbers is studied using data obtained both from numerical simulation and physical experiments. It is shown that the near-wall turbulence structure is quite similar to what has earlier been found in plane Poiseuille flow; however, there are also some large differences especially regarding Reynolds stress production. The commonly held view that the maximum in Reynolds stress close to the wall in Poiseuille and boundary layer flows is due to the turbulence-generating events must be modified as plane Couette flow does not exhibit such a maximum, although the near-wall coherent structures are quite similar. For two-dimensional mean flow, turbulence production occurs only for the streamwise fluctuations, and the present study shows the importance of the pressure—strain redistribution in connection with the near-wall coherent events.

Rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence

2012 ◽  
Vol 24 (3) ◽  
pp. 035110 ◽  
Author(s):  
Peter Lenaers ◽  
Qiang Li ◽  
Geert Brethouwer ◽  
Philipp Schlatter ◽  
Ramis Örlü
Keyword(s):  
Wall Turbulence ◽  
Normal Velocity ◽  
Velocity Fluctuations ◽  
Near Wall Turbulence ◽  
Near Wall
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