What are we learning from simulating wall turbulence?

2007 ◽  
Vol 365 (1852) ◽  
pp. 715-732 ◽  
Author(s):  
Javier Jiménez ◽  
Robert D Moser
Keyword(s):  
Energy Production ◽  
Wall Layer ◽  
Wall Turbulence ◽  
Buffer Layers ◽  
Upper And Lower Bounds ◽  
Nonlinear Structures ◽  
Outer Flow ◽  
Global Properties ◽  
Dynamic Experiments ◽  
Lower Limits

The study of turbulence near walls has experienced a renaissance in the last decade, largely owing to the availability of high-quality numerical simulations. The viscous and buffer layers over smooth walls are essentially independent of the outer flow, and there is a family of numerically exact nonlinear structures that account for about half of the energy production and dissipation. The rest can be modelled by their unsteady bursting. Many characteristics of the wall layer, such as the dimensions of the dominant structures, are well predicted by those models, which were essentially completed in the 1990s after the increase in computer power made the kinematic simulations of the late 1980s cheap enough to undertake dynamic experiments. Today, we are at the early stages of simulating the logarithmic (or overlap) layer, and a number of details regarding its global properties are becoming clear. For instance, a finite Reynolds number correction to the logarithmic law has been validated in turbulent channels. This has allowed upper and lower limits of the overlap region to be clarified, with both upper and lower bounds occurring at much larger distances from the wall than commonly assumed. A kinematic picture of the various cascades present in this part of the flow is also beginning to emerge. Dynamical understanding can be expected in the next decade.

Equilibrium layers and wall turbulence

1961 ◽  
Vol 11 (1) ◽  
pp. 97-120 ◽  
Author(s):  
A. A. Townsend
Keyword(s):  
Energy Production ◽  
Constant Stress ◽  
Wall Turbulence ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Outer Flow ◽  
Law Of The Wall ◽  
Wall Flow ◽  
Flow Similarity ◽  
Stress Layer

In turbulent flow past rigid boundaries, there can be distinguished regions close to the wall in which the local rates of energy production and dissipation are so large that aspects of the turbulent motion concerned with these processes are determined almost solely by the distribution of shear stress within the region and are independent of conditions outside it. These regions are here called equilibrium layers because of the equilibrium existing between local rates of energy production and dissipation. Three kinds of equilibrium layer have been studied experimentally, the constant-stress layer, the transpiration layer and the zero-stress layer, but there are other possible forms. One that is of importance in the theory of self-preserving flow in boundary layers and in diffusers is the ‘linear-stress’ layer in which the stress increases linearly with distance from the wall. The properties of these various equilibrium layers are considered and the distributions of mean velocity are derived from the equation for the turbulent kinetic energy and certain assumptions of flow similarity.The theory of self-preserving wall flow, usually expressed as a combination of the law of the wall and the defect law, assumes compatibility between the outer flow and the equilibrium layer, and the course of development depends on the kind of equilibrium layer. Earlier work by the author, which assumed the defect law, is only valid if the whole of the equilibrium layer is a constant-stress layer and this is not true in strong adverse pressure gradients. A consistent theory is developed for these flows by assuming a ‘linear-stress’ layer, and the solutions show the relation between flows of finite stress and of zero stress and provide a plausible explanation of the phenomenon of downstream instability observed by Clauser. Self-preserving flow in wedges is treated on similar lines.

scholarly journals Velocity and spatial distribution of inertial particles in a turbulent channel flow

2019 ◽  
Vol 872 ◽  
pp. 367-406 ◽  
Author(s):  
Kee Onn Fong ◽  
Omid Amili ◽  
Filippo Coletti
Keyword(s):  
Spatial Distribution ◽  
Particle Velocity ◽  
Turbulent Channel Flow ◽  
Wall Turbulence ◽  
Buffer Layers ◽  
Working Fluid ◽  
Wall Region ◽  
Inertial Particles ◽  
Velocity Fluctuations ◽  
Near Wall

We present experimental observations of the velocity and spatial distribution of inertial particles dispersed in turbulent downward flow through a vertical channel at friction Reynolds numbers $\mathit{Re}_{\unicode[STIX]{x1D70F}}=235$ and 335. The working fluid is air laden with size-selected glass microspheres, having Stokes numbers $St=\mathit{O}(10)$ and $\mathit{O}(100)$ when based on the Kolmogorov and viscous time scales, respectively. Cases at solid volume fractions $\unicode[STIX]{x1D719}_{v}=3\times 10^{-6}$ and $5\times 10^{-5}$ are considered. In the more dilute regime, the particle concentration profile shows near-wall and centreline maxima compatible with a turbophoretic drift down the gradient of turbulence intensity; the particles travel at speed similar to that of the unladen flow except in the near-wall region; and their velocity fluctuations generally follow the unladen flow level over the channel core, exceeding it in the near-wall region. The denser regime presents substantial differences in all measured statistics: the near-wall concentration peak is much more pronounced, while the centreline maximum is absent; the mean particle velocity decreases over the logarithmic and buffer layers; and particle velocity fluctuations and deposition velocities are enhanced. An analysis of the spatial distributions of particle positions and velocities reveals different behaviours in the core and near-wall regions. In the channel core, dense clusters form which are somewhat elongated, tend to be preferentially aligned with the vertical/streamwise direction and travel faster than the less concentrated particles. In the near-wall region, the particles arrange in highly elongated streaks associated with negative streamwise velocity fluctuations, several channel heights in length and spaced by $\mathit{O}(100)$ wall units, supporting the view that these are coupled to fluid low-speed streaks typical of wall turbulence. The particle velocity fields contain a significant component of random uncorrelated motion, more prominent for higher $St$ and in the near-wall region.

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.

scholarly journals Bolometric Light Curves of Symbiotic Novae

1992 ◽  
Vol 151 ◽  
pp. 435-438
Author(s):  
U. Mürset ◽  
H. Nussbaumer
Keyword(s):  
Total Energy ◽  
Energy Production ◽  
Light Curves ◽  
Classical Nova ◽  
Total Energies ◽  
Stellar Masses ◽  
Lower Limits ◽  
Nova Outburst

We determine bolometric light curves and total energies radiated away during the outburst of symbiotic novae. Time integrated lower limits to the total energy of 0.9×1046 <E[erg] < 7×1046 are found. Thus, the output is comparable to, or larger than the total energy production of a classical nova outburst. From the mass-luminosity relation we find the underlying stellar masses to be 0.5 < M/M⊙ < 1.1.

An idealised assessment of Townsend’s outer-layer similarity hypothesis for wall turbulence

2014 ◽  
Vol 742 ◽  
Author(s):  
D. Chung ◽  
J. P. Monty ◽  
A. Ooi
Keyword(s):  
Boundary Conditions ◽  
Order Statistics ◽  
Outer Layer ◽  
Solid Wall ◽  
Turbulent Channel Flow ◽  
Viscous Sublayer ◽  
Wall Turbulence ◽  
Outer Flow ◽  
Similarity Hypothesis ◽  
Stress Boundary Conditions

AbstractDirect numerical simulations of turbulent channel flow at the matched friction Reynolds number of 590, comparing the effect of no-slip versus shear-stress boundary conditions, reveal that the outer flow of wall turbulence, in accord with Townsend’s outer-layer similarity hypothesis, remains largely independent of the viscous sublayer. First- and second-order statistics, including spectra, agree closely from the buffer region out to the centre of the channel. Higher-order statistics also appear to obey the hypothesised similarity, although the influence of boundary conditions is more pronounced than in the lower-order statistics. The statistical agreement in the outer layer, in spite of the structural differences in the viscous sublayer, support Townsend’s idea that the primary effect of the wall is not the no-slip condition, but the impermeability condition imposed by a solid wall.

The minimal flow unit in near-wall turbulence

1991 ◽  
Vol 225 ◽  
pp. 213-240 ◽  
Author(s):  
Javier Jiménez ◽  
Parviz Moin
Keyword(s):  
Wall Stress ◽  
Wall Layer ◽  
Flow Unit ◽  
Wall Turbulence ◽  
Longitudinal Vortex ◽  
Spanwise Direction ◽  
Wall Region ◽  
Low Velocity ◽  
Good Agreement ◽  
Near Wall

Direct numerical simulations of unsteady channel flow were performed at low to moderate Reynolds numbers on computational boxes chosen small enough so that the flow consists of a doubly periodic (in x and z) array of identical structures. The goal is to isolate the basic flow unit, to study its morphology and dynamics, and to evaluate its contribution to turbulence in fully developed channels. For boxes wider than approximately 100 wall units in the spanwise direction, the flow is turbulent and the low-order turbulence statistics are in good agreement with experiments in the near-wall region. For a narrow range of widths below that threshold, the flow near only one wall remains turbulent, but its statistics are still in fairly good agreement with experimental data when scaled with the local wall stress. For narrower boxes only laminar solutions are found. In all cases, the elementary box contains a single low-velocity streak, consisting of a longitudinal strip on which a thin layer of spanwise vorticity is lifted away from the wall. A fundamental period of intermittency for the regeneration of turbulence is identified, and that process is observed to consist of the wrapping of the wall-layer vorticity around a single inclined longitudinal vortex.

The autonomous cycle of near-wall turbulence

1999 ◽  
Vol 389 ◽  
pp. 335-359 ◽  
Author(s):  
JAVIER JIMÉNEZ ◽  
ALFREDO PINELLI
Keyword(s):  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Wall Region ◽  
Streamwise Vortices ◽  
Outer Flow ◽  
Turbulent Fluctuations ◽  
The Mean ◽  
Turbulence Generation ◽  
Near Wall Turbulence ◽  
Near Wall

Numerical experiments on modified turbulent channels at moderate Reynolds numbers are used to differentiate between several possible regeneration cycles for the turbulent fluctuations in wall-bounded flows. It is shown that a cycle exists which is local to the near-wall region and does not depend on the outer flow. It involves the formation of velocity streaks from the advection of the mean profile by streamwise vortices, and the generation of the vortices from the instability of the streaks. Interrupting any of those processes leads to laminarization. The presence of the wall seems to be only necessary to maintain the mean shear. The generation of secondary vorticity at the wall is shown to be of little importance in turbulence generation under natural circumstances. Inhibiting its production increases turbulence intensity and drag.

Structure of Turbulence in an Incipient-Separating Axisymmetric Flow

1995 ◽  
Vol 117 (3) ◽  
pp. 433-438 ◽  
Author(s):  
Rakesh K. Singh ◽  
Ram S. Azad
Keyword(s):  
Pipe Flow ◽  
Energy Production ◽  
Reynolds Shear Stress ◽  
Axisymmetric Flow ◽  
Adverse Pressure Gradient ◽  
Turbulent Energy ◽  
Streamwise Velocity ◽  
Wall Layer ◽  
Diffuser Flow ◽  
Conical Diffuser

The relative intensity, skewness, and flatness of fluctuating streamwise velocity along the centerline of an 8 deg included angle conical diffuser show dramatic rapid growth in the final stages of the flow under the increasing influence of growing instantaneous reversals in the wall-layer. Pulsed-wire anemometry was effectively used for the measurement of quantitative instantaneous reversals and the turbulent flow field. In the severe adverse pressure gradient of the diffuser flow, the maxima of the streamwise and transverse fluctuating velocities, Reynolds shear stress, and turbulent energy production coincide and move away from their near-wall position in the pipe, also the velocity triple products show completely opposite nature as compared to the pipe flow. These measurements reveal the strong influence of instantaneous backflow on the structure of turbulence. The present results further corroborate the ability of the “structural” turbulence model of Nagano and Tagawa (1990) to predict velocity triple products in an axisymmetric diffuser flow.

scholarly journals Turbulence in a conical diffuser with fully developed flow at entry

1973 ◽  
Vol 57 (3) ◽  
pp. 603-622 ◽  
Author(s):  
P. A. C. Okwuobi ◽  
R. S. Azad
Keyword(s):  
Energy Production ◽  
Correlation Coefficients ◽  
Reynolds Numbers ◽  
Turbulent Energy ◽  
Wall Layer ◽  
Pressure Effects ◽  
Mean Velocity ◽  
Fully Developed Flow ◽  
Conical Diffuser ◽  
Mean Pressure

An experimental study of the structure of turbulence in a conical diffuser having a total divergence angle of 8° and an area ratio of 4: 1 with fully developed flow at entry is described. Theresearch has been done for pipe entry Reynolds numbers of 152 000 and 293000 of profiles of the mean pressure, mean velocity, turbulence intensities, correlation coefficients and the one-dimensional energy spectra, but owing to similar behaviour for these two Reynolds numbers, data are presented for a Reynolds number of 293 000.The results show that the rate of turbulent energy production approximately reaches a maximum value at the edge of the wall layer extending to the point of maximum u1-fluctuation. It is found that, within the layer,$\overline{u^2_1}$varies linearly with the distance from the wall and the linear range grows with distance in the downstream direction.The turbulent kinetic energy balance indicates that the magnitude of the energy convective diffusion due to kinetic and pressure effects is comparable with that of the energy production.

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