Low-Reynolds-number effects on near-wall turbulence (original) (raw)
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Low-Reynolds-number effects in a fully developed turbulent channel flow
Journal of Fluid Mechanics, 1992
Low-Reynolds-number effects are observed in the inner region of a fully developed turbulent channel flow, using data obtained either from experiments or by direct numerical simulations. The Reynolds-number influence is observed on the turbulence intensities and to a lesser degree on the average production and dissipation of the turbulent energy. In the near-wall region, the data confirm Wei & Willmarth's (1989) conclusion that the Reynolds stresses do not scale on wall variables. One of the reasons proposed by these authors to account for this behaviour, namely the 'geometry ' effect or direct interaction between inner regions on opposite walls, was investigated in some detail by introducing temperature at one of the walls, both in experiment and simulation. Although the extent of penetration of thermal excursions into the opposite side of the channel can be significant a t low Reynolds numbers, the contribution these excursions make to the Reynolds shear stress and the spanwise vorticity in the opposite wall region is negligible. In the inner region, spectra and cospectra of the velocity fluctuations u and v change rapidly with the Reynolds number, the variations being mainly confined to low wavenumbers in the u spectrum. These spectra, and the corresponding variances, are discussed in the context of the active/inactive motion concept and the possibility of increased vortex stretching a t the wall. A comparison is made between the channel and the boundary layer a t low Reynolds numbers.
Reynolds Number Effects in Wall-Bounded Turbulent Flows
Applied Mechanics Reviews, 1994
This paper reviews the state of the art of Reynolds number effects in wall-bounded shear-flow turbulence, with particular emphasis on the canonical zero-pressure-gradient boundary layer and two-dimensional channel flow problems. The Reynolds numbers encountered in many practical situations are typically orders of magnitude higher than those studied computationally or even experimentally. High-Reynolds number research facilities are expensive to build and operate and the few existing are heavily scheduled with mostly developmental work. For wind tunnels, additional complications due to compressibility effects are introduced at high speeds. Full computational simulation of high-Reynolds number flows is beyond the reach of current capabilities. Understanding of turbulence and modeling will continue to play vital roles in the computation of high-Reynolds number practical flows using the Reynolds-averaged Navier-Stokes equations. Since the existing knowledge base, accumulated mostly through physical as well as numerical experiments, is skewed towards the low Reynolds numbers, the key question in such high-Reynolds number modeling as well as in devising novel flow control strategies is: what are the Reynolds number effects on the mean and statistical turbulence quantities and on the organized motions? Since the mean flow review of Coles (1962), the coherent structures, in low-Reynolds number wall-bounded flows, have been reviewed several times. However, the Reynolds number effects on the higher-order statistical turbulence quantities and on the coherent structures have not been reviewed thus far, and there are some unresolved aspects of the effects on even the mean flow at very high Reynolds numbers. Furthermore, a considerable volume of experimental and full-simulation data have been accumulated since 1962. The present article aims at further assimilation of those data, pointing to obvious gaps in the present state of knowledge and highlighting the misunderstood as well as the ill-understood aspects of Reynolds number effects. CONTENTS Nomenclature 308 1. Introduction 309 1.1 Field versus laboratory flows 309 1.2 Reynolds number 309 1.3 Outline of present review 310 2. Contemporary relevance 311 2.1 Primary issues 311 2.2 Turbulence modeling 311 2.3 Flow control and post-transition memory 312 3. Flow regimes 313 3.1 Viscous region 313 3.2 Constant-Reynolds stress region ". 314 3.3 Outer Layer 315 Comparison to other shear flows 316 Mean flow 319 5.1 Streamwise velocity 319 5.2 Von Karman constant 320 The illusory asymptotic state 321 Is self-preservation ever achieved? 322 Alternatives to the logarithmic profile 324 Higher-order statistics 325 6.1 Root-mean-square velocity fluctuations 325 Reynolds stress 330 6.
Numerical experiments on wall turbulence at low Reynolds number
Thermal Science, 2006
o , the tur bu lent dis si pa tion rate van ishes at the wall, lead ing to a sig nif i cant re duc tion of the wall shear stress. For the sim u lated flow case the lo cal value of wall shear stress re duc tion was found to ex ceed the wall shear stress re duc tion SR @ 92% which cor re sponds to a fully de vel oped lam i nar chan nel flow with smooth walls at the same Reynolds num ber.
The large-scale dynamics of near-wall turbulence
Journal of Fluid Mechanics, 2004
The dynamics of the sublayer and buffer regions of wall-bounded turbulent flows are analysed using autonomous numerical simulations in which the outer flow, and on some occasions specific wavelengths, are masked. The results are compared with a turbulent channel flow at moderate Reynolds number. Special emphasis is put on the largest flow scales. It is argued that in this region there are two kinds of large structures: long and narrow ones which are endogenous to the wall, in the sense of being only slightly modified by the presence or absence of an outer flow, and long and wide structures which extend to the outer flow and which are very different in the two cases. The latter carry little Reynolds stress near the wall in full simulations, and are largely absent from the autonomous ones. The former carry a large fraction of the stresses in the two cases, but are shown to be quasi-linear passive wakes of smaller structures, and they can be damped without modifying the dynamics of other spectral ranges. They can be modelled fairly accurately as being infinitely long, and it is argued that this is why good statistics are obtained in short or even in minimal simulation boxes. It is shown that this organization implies that the scaling of the near-wall streamwise fluctuations is anomalous.
Effect of wall-boundary disturbances on turbulent channel flows
Journal of Fluid Mechanics, 2006
The interaction between the wall and the core region of turbulent channels is studied using direct numerical simulations at friction Reynolds number Re τ ≈ 630. In these simulations the near-wall energy cycle is effectively removed, replacing the smooth-walled boundary conditions by prescribed velocity disturbances with non-zero Reynolds stress at the walls. The profiles of the first-and second-order moments of the velocity are similar to those over rough surfaces, and the effect of the boundary condition on the mean velocity profile is described using the equivalent sand roughness. Other effects of the disturbances on the flow are essentially limited to a layer near the wall whose height is proportional to a length scale defined in terms of the additional Reynolds stress. The spectra in this roughness sublayer are dominated by the wavenumber of the velocity disturbances and by its harmonics. The wall forcing extracts energy from the flow, while the normal equilibrium between turbulent energy production and dissipation is restored in the overlap region. It is shown that the structure and the dynamics of the turbulence outside the roughness sublayer remain virtually unchanged, regardless of the nature of the wall. The detached eddies of the core region only depend on the mean shear, which is not modified beyond the roughness sublayer by the wall disturbances. On the other hand, the large scales that are correlated across the whole channel scale with U LOG = u τ κ −1 log(Re τ ), both in smooth-and in rough-walled flows. This velocity scale can be interpreted as a measure of the velocity difference across the log layer, and it is used to modify the scaling proposed and validated by delÁlamo et al. (J.
The minimal flow unit in near-wall turbulence
Journal of Fluid Mechanics, 1991
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 ...
Computers and Fluids, 2010
In this paper, we analyze the influence of aiding and opposing buoyancy on the statistics of the wall transfer rates in a mixed convection turbulent flow at low Reynolds numbers in a vertical plane channel. The analysis is carried out using a database obtained from direct numerical simulations performed with a second-order finite volume code. The aiding/opposing buoyancy produces an overall decrease/increase of the intensities of the fluctuations of the wall shear stresses in comparison with the forced convection flow. The near wall structures responsible for the positive extreme values of the fluctuations of the wall shear stress, educed by a conditional sampling technique, consist in two quasi-parallel counterrotating streamwise vortices that convect high momentum fluid towards the wall in the region between them. Buoyancy produces an overall increase of the Reynolds stresses near the cold wall in comparison with the hot wall. This affects the streamwise length, the orientation, the velocity and the intensity of these flow structures near the two walls of the channel. It is found that the flow structures near the cold wall are shorter and produce more intense fluctuations than those near the hot wall.
Turbulence statistics in fully developed channel flow at low Reynolds number
Journal of Fluid Mechanics, 1987
A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on thc mean centreline velocity and channel half-width, with about 4 x los grid points (192 x 129 x 160 in 2, y, 2). All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behaviour of turbulence correlations near the wall. In addition, a number of statistical correlations which are complementary to the existing experimental data are reported for the first time. 10' 10' kz FIQURE 3. One-dimensional energy spectra: -, Euu; ----, Evv; ---, Eww. (a) Streamwise; ( b ) spanwise.
Effect of Roughness on Wall-Bounded Turbulence
Flow Turbulence and Combustion, 2004
Direct numerical simulation of turbulent incompressible plane-channel flow between a smooth wall and one covered with regular three-dimensional roughness elements is performed. While the impact of roughness on the mean-velocity profile of turbulent wall layers is well understood, at least qualitatively, the manner in which other features are affected, especially in the outer layer, has been more controversial. We compare results from the smooth- and rough-wall sides of the channel for three different roughness heights of h += 5.4, 10.8, and 21.6 for Re τ of 400, to isolate the effects of the roughness on turbulent statistics and the instantaneous turbulence structure at large and small scales. We focus on the interaction between the near-wall and outer-layer regions, in particular the extent to which the near-wall behavior influences the flow further away from the surface. Roughness tends to increase the intensity of the velocity and vorticity fluctuations in the inner layer. In the outer layer, although the roughness alters the velocity fluctuations, the vorticity fluctuations are relatively unaffected. The higher-order moments and the energy budgets demonstrate significant differences between the smooth-wall and rough-wall sides in the processes associated with the wall-normal fluxes of the Reynolds shear stresses and turbulence kinetic energy. The length scales and flow dynamics in the roughness sublayer, the spatially inhomogeneous layer within which the flow is directly influenced by the individual roughness elements, are also examined. Alternative mechanisms involved in producing and maintaining near-wall turbulence in rough-wall boundary layers are also considered. We find that the strength of the inner/outer-layer interactions are greatly affected by the size of the roughness elements.
Spectral Characteristics of the Near-Wall Turbulence in an Unsteady Channel Flow
Journal of Applied Mechanics, 2007
The modulation characteristics of the turbulent wall shear stress and longitudinal intensities in the inner layer are experimentally investigated in an unsteady channel flow wherein the centerline velocity varies in time in a sinusoidal manner. The fluctuating wall shear stress and velocity signals are temporally filtered and subsequently phase averaged. It is shown that the outer structures corresponding to the low spectrum range have a constant time lag with respect to the centerline velocity modulation. The inner active structures, in particular those with a frequency band containing the mean ejection frequency of the corresponding steady flow dominate the dynamics of the near-wall unsteady turbulence. The structures respond to the imposed shear oscillations in a complex way, depending both on their characteristic scales and the thickness of the oscillating shear zone in which they are embedded.