Correction to "Accounting for Uncertainty in the Analysis of Overlap Layer Mean Velocity Models" (original) (raw)
Physics of Fluids, 2000
The possibility of a power-law scaling in the overlapping part of the inner and outer regions of wall-bounded turbulent flows was first considered by Millikan 1 and later analyzed by George et al., 2 George and Castilio, 3 and Barenblatt and coworkers ͑Refs. 4-8͒. However, there are some differences between the different approaches taken in these studies and this type of power-law should not be confused with the power-law used to represent the profile of the entire wallbounded layer in engineering approximations. In Refs. 4-5 pipe flow was considered. In recent work 6-8 the authors have extended their approach to zero-pressure gradient turbulent boundary layers. Using results from measurements made on the test-section floor of the NDF facility at IIT by Hites, 9 they claim good agreement. 7 Recent analysis of their results by Ron Panton ͑private communication͒, reveals inconsistencies in the length scale extracted from the two relations defining their power law that are of the order of 25%-30%. In the recent manuscript by Barenblatt et al., 6 the authors use the data obtained from measurements in a zero pressure-gradient turbulent boundary layer by Ö sterlund 10 and made available on the internet. 11 The authors claim that the conclusions obtained by Ö sterlund et al. 12 are incorrect and that ''Properly processed these data lead to the opposite conclusion.
The Origin of the Log Law Region for Wall-bounded Turbulent Boundary Layer Flows
2011
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Wall-layer model for the velocity profile in turbulent flows
AIAA Journal, 1989
There is no satisfactory model to explain the mean velocity profile of the whole turbulent layer in canonical wall-bounded flows. In this paper, a mean velocity profile expression is proposed for wall-bounded turbulent flows based on a recently proposed stochastic representation of fluid flows dynamics. This original approach, called modeling under location uncertainty introduces in a rigorous way a subgrid term generalizing the eddy-viscosity assumption and an eddy-induced advection term resulting from turbulence inhomogeneity. This latter term gives rise to a theoretically well-grounded model for the transitional zone between the viscous sublayer and the turbulent sublayer. An expression of the small-scale velocity component is also provided in the viscous zone. Numerical assessments of the results are provided for turbulent boundary layer flows, pipe flows and channel flows at various Reynolds numbers.
Acta Mechanica, 2001
The open equations of a turbulent boundary layer subjected to a pressure gradient analysed for classical two layers (inner wall and outer wake), while matched in the overlap region of MAX through the Millikan-Kolmogorov hypothesis leads to an open functional equation, and its classical solution for the velocity distribution is the log. region. It is shown here that the same open functional equation also predicts a power law velocity distribution and a power law skin friction in the overlap region. The uniformly valid solution for the composite wall power law and wake velocity profile is obtained. The connection between the power law and the classical log. law solutions of the open functional equation is analyzed. At large Reynolds number, the power law solutions reduce to the classical log. law solutions, and the equivalence predicts a certain relationship between the constants in power and log. laws. The results are compared with the experimental data.
Bursts and the law of the wall in turbulent boundary layers
Journal of Fluid Mechanics, 1992
The bursting mechanism in two different high-Reynolds-number boundary layers has been analysed by means of conditional sampling. One boundary layer develops on a smooth, flat plate in zero pressure gradient; the other, also in zero pressure gradient, is perturbed by a rough-to-smooth change in surface roughness and the new internal layer has not yet recovered to the local equilibrium condition a t the measurement station. Sampling on the instantaneous uv signal in the logarithmic region confirms the presence of two related structures, 'ejections' and 'sweeps' which, in the smooth-wall layer, appear to be responsible for most of the turbulent energy production, and to effect virtually all that part of the spectral energy transfer that is universal. Ejections show features similar to those of Falco's 'typical eddies ' while sweeps appear to be inverted ejections moving down towards the wall. The inertial structures associated with ejections show attributes of the true universal motion (Townsend's 'attached' eddies) of the inner layer and these are therefore identified as 'bursts '. In the outer layer, these become 'detached ' from the wall. The large-scale structures associated with sweeps also appear to be 'detached ' eddies ('splats '), but these induce low-wave-number inactive motion near the wall and this is not universal even though the sweep itself is. Neither ejections nor sweeps detected in the rough-to-smooth layer are near a condition of energy equilibrium. The relation of ejections and sweeps to the law of the wall and other accepted laws is discussed.
A Lie-group derivation of a multi-layer mixing length formula for turbulent channel and pipe flow
First principle based prediction of mean flow quantities of wall-bounded turbulent flows (channel, pipe, and turbulent boundary layer-TBL) is of great importance from both physics and engineering standpoints. Physically, a non-equilibrium physical principle governing spatial distribution of mean quantities is yet unknown, so that quantitative theories of technological flows are essentially empirical. Here (Part I), we present a symmetry-based approach which derives analytic expressions governing the mean velocity profile (MVP) from an innovative Lie-group analysis. The new approach begins by identifying a set of order functions (e.g. stress length, shear-induced eddy length), in analogy with the order parameter in Landau's mean-field theory, which aims at capturing symmetry aspects of the fluctuations (e.g. Reynolds stress, dissipation). The order functions are assumed to satisfy a dilation group invariance-representing the effects of the wall on fluctuationswhich allows us to postulate three new kinds of invariant solutions of the mean momentum equation (MME), focusing on group invariants of the order functions (rather than those of the mean velocity as done in previous studies). The first-a power law solution-gives functional forms for the viscous sublayer, the buffer layer, the log-layer, and a newly identified central 'core' (for channel and pipe, but non-existent for TBL). The second-a defect power law of form 1 − r m (r being the distance from the centerline)-describes the 'bulk zone' (the region of balance between production and dissipation). The third-a relation between the group invariants of the stress length function and its first derivative-describes scaling transition between adjacent layers. A combination of these three expressions yields a multi-layer formula covering the entire flow domain, identifying three important parameters: scaling exponent, layer thickness, and transition sharpness. All three kinds of invariant solutions are validated, individually and in combination, by data from direct numerical simulations (DNS). In subsequent parts, we will show the existence of a universal bulk flow constant 0.45, which asymptotes to the true Karman constant at large Reynolds numbers (Re's) (Part II), and an accurate description of more than 40 sets of recent experimental and numerical MVPs for channel and pipe and for Re covering over three decades (Part III). The theory equally applies to the quantification of TBL (Part IV), and of the effects of roughness, pressure gradient, compressibility, and buoyancy, and to the study of Reynolds-averaged Navier-Stokes (RANS) models, such as K − ω, with a significant improvement of prediction accuracy (Part III & IV). These results affirm that a simple and unified theory of wall-bounded turbulence is viable with appropriate symmetry considerations.
A note on the overlap region in turbulent boundary layers
Physics of Fluids, 2000
Two independent experimental investigations of the behavior of turbulent boundary layers with increasing Reynolds number were recently completed. The experiments were performed in two facilities, the MTL wind tunnel at KTH and the NDF wind tunnel at IIT. Both experiments utilized oil-film interferometry to obtain an independent measure of the wall-shear stress. A collaborative study by the principals of the two experiments, aimed at understanding the characteristics of the overlap region between the inner and outer parts of the boundary layer, has just been completed. The results are summarized here, utilizing the profiles of the mean velocity, for Reynolds numbers based on the momentum thickness ranging from 2,500 to 27,000. Contrary to the conclusions of some earlier publications, careful analysis of the data reveals no significant Reynolds number dependence for the parameters describing the overlap region using the classical logarithmic relation. However, the data analysis demonstrates that the viscous influence extends within the buffer region to y + ≈ 200, compared to the previously assumed limit of y + ≈ 50. Therefore, the lowest Re θ value where a significant logarithmic overlap region exists is about 6,000. This probably explains why a Reynolds number dependence had been found from the data analysis of many previous experiments. The parameters of the logarithmic overlap region are found to be constant and are estimated to be: κ = 0.38, B = 4.1 and B 1 = 3.6 (δ = δ 95).