Turbulence statistics in fully developed channel flow at low Reynolds number

Kim, John; Moin, Parviz; Moser, Robert D.

doi:10.1017/s0022112087000892

Cited by 4,256 publications

(3,224 citation statements)

References 34 publications

Supporting

446

Mentioning

2,656

Contrasting

Unclassified

Order By: Relevance

“…They are longer than both p and w, but not wider. The wall-normal velocity is both shorter and narrower than the other two components, as first observed in the buffer layer by Kim et al (1987). Together with the vertical correlation results in figure 5(b), these observations define the general geometry of the three velocity components.…”

Section: Spectrasupporting

confidence: 78%

“…Thus, a Q2 ejection that crosses the centreline masquerades as a Q3 sweep in the other side of the channel. At the centreline itself there is no way to distinguish between Ql and Q4, or between Q2 and Q3 (Kim et al 1987). That some structures cross deeply into the opposite half of the channel is shown in figure 5(b), which displays the y-correlation of the wall-normal velocity,…”

Section: Intermittencymentioning

confidence: 99%

See 1 more Smart Citation

Turbulent boundary layers and channels at moderate Reynolds numbers

et al. 2010

View full text Add to dashboard Cite

The behaviour of the velocity and pressure fluctuations in the outer layers of wall-bounded turbulent flows is analysed by comparing a new simulation of the zero-pressure-gradient boundary layer with older simulations of channels. The 99 % boundary-layer thickness is used as a reasonable analogue of the channel half-width, but the two flows are found to be too different for the analogy to be complete. In agreement with previous results, it is found that the fluctuations of the transverse velocities and of the pressure are stronger in the boundary layer, and this is traced to the pressure fluctuations induced in the outer intermittent layer by the differences between the potential and rotational flow regions. The same effect is also shown to be responsible for the stronger wake component of the mean velocity profile in external flows, whose increased energy production is the ultimate reason for the stronger fluctuations. Contrary to some previous results by our group, and by others, the streamwise velocity fluctuations are also found to be higher in boundary layers, although the effect is weaker. Within the limitations of the non-parallel nature of the boundary layer, the wall-parallel scales of all the fluctuations are similar in both the flows, suggesting that the scale-selection mechanism resides just below the intermittent region, y/S =0.3-0.5. This is also the location of the largest differences in the intensities, although the limited Reynolds number of the boundary-layer simulation (Reg «2000) prevents firm conclusions on the scaling of this location. The statistics of the new boundary layer are available from http://torroja.dmt.upm.es/ftp/blayers/.

show abstract

Section: Spectrasupporting

confidence: 78%

Section: Intermittencymentioning

confidence: 99%

Turbulent boundary layers and channels at moderate Reynolds numbers

et al. 2010

View full text Add to dashboard Cite

show abstract

“…The corresponding resolution is given in wall units in table 1 (y + 10 is the height of the 10th wall-normal grid point and y + c is the centreline resolution). These numbers improve on or match those found adequate by Kim et al (1987) in their channel. (The Runge-Kutta scheme is also a slight improvement on their Adams-Bashforth scheme.)…”

Section: Numerical Considerationssupporting

confidence: 75%

“…The simulation is performed using a version of the Fourier/Chebyshev spectral channel code of Kim, Moin & Moser (1987), from which it differs algorithmically in the time integration: a third-order Runge-Kutta/Crank-Nicolson scheme is used here. Moving-wall boundary conditions have also been added, and the reference frame for time integration is at the average velocity of the two walls.…”

Section: Numerical Considerationsmentioning

confidence: 99%

The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation

2009

View full text Add to dashboard Cite

Wall-bounded turbulence in pressure gradients is studied using direct numerical simulation (DNS) of a Couette–Poiseuille flow. The motivation is to include adverse pressure gradients, to complement the favourable ones present in the well-studied Poiseuille flow, and the central question is how the scaling laws react to a gradient in the total shear stress or equivalently to a pressure gradient. In the case considered here, the ratio of local stress to wall stress, namely τ+, ranges from roughly 2/3 to 3/2 in the ‘wall region’. By this we mean the layer believed not to be influenced by the opposite wall and therefore open to simple, universal behaviour. The normalized pressure gradients p+ ≡ dτ+/dy+ at the two walls are −0.00057 and +0.0037. The outcome is in broad agreement with the findings of Galbraith, Sjolander & Head (Aeronaut. Quart. vol. 27, 1977, pp. 229–242) relating to boundary layers (based on measured profiles): the logarithmic velocity profile is much more resilient than two other, equally plausible assumptions, namely universality of the mixing length ℓ = κy and that of the eddy viscosity νt = uτκy. In pressure gradients, with τ+ ≠ 1, these three come into conflict, and our primary purpose is to compare them. We consider that the Kármán constant κ is unique but allow a range from 0.38 to 0.41, consistent with the current debates. It makes a minor difference in the interpretation. This finding of resilience appears new as a DNS result and is free of the experimental uncertainty over skin friction. It is not as distinct in the (rather strong) adverse gradient as it is in the favourable one; for instance the velocity U+ at y+ = 50 is lower by 3% on the adverse gradient side. A plausible cause is that the wall shear stress is small and somewhat overwhelmed by the stress and kinetic energy in the bulk of the flow. The potential of a correction to the ‘law of the wall’ based purely on p+ is examined, with mixed results. We view the preference for the log law as somewhat counter-intuitive in that the scaling law is non-local but also as becoming established and as highly relevant to turbulence modelling.

show abstract

“…The numerical code integrates the Navier-Stokes equations in the form of evolution problems for the wall-normal vorticity ω y and for the Laplacian of the wall-normal velocity ∇ 2 v, as in Kim, Moin & Moser (1987). The spatial discretization uses dealiased Fourier expansions in the wall-parallel planes, and Chebychev polynomials in y.…”

Section: The Numerical Experimentsmentioning

confidence: 99%

Scaling of the energy spectra of turbulent channels

et al. 2004

View full text Add to dashboard Cite

The spectra and correlations of the velocity fluctuations in turbulent channels, especially above the buffer layer, are analysed using new direct numerical simulations with friction Reynolds numbers up to Re$_{\tau}\,{=}\,1900$. It is found, and explained, that their scaling is anomalous in several respects, including a square-root behaviour of their width with respect to their length, and a velocity scaling of the largest modes with the centreline velocity $U_c$. It is shown that this implies a logarithmic correction to the $k^{-1}$ energy spectrum, and that it leads to a scaling of the total fluctuation intensities away from the wall which agrees well with the mixed scaling of de Graaff & Eaton (2000) at intermediate Reynolds numbers, but which tends to a pure scaling with $U_c$ at very large ones.

show abstract

Turbulence statistics in fully developed channel flow at low Reynolds number

Cited by 4,256 publications

References 34 publications

Turbulent boundary layers and channels at moderate Reynolds numbers

Turbulent boundary layers and channels at moderate Reynolds numbers

The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation

Scaling of the energy spectra of turbulent channels

Contact Info

Product

Resources

About