Reynolds stress scaling in the near-wall region of wall-bounded flows
TL;DR: In this article, a new scaling is derived that yields a Reynolds number independent profile for all components of the Reynolds stress in the near-wall region of wall bounded flows, including channel, pipe and boundary layer flows.
Abstract: A new scaling is derived that yields a Reynolds number independent profile for all components of the Reynolds stress in the near-wall region of wall bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence behavior.
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TL;DR: In this article, a 3D geometry of the statistically significant eddies from multi-point wall-turbulence datasets is extracted for direct implementation into coherent structure-based models to improve their predictions.
7 citations
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TL;DR: In this article, a 3D geometry of the statistically significant eddies from multi-point wall-turbulence datasets is extracted for direct implementation into coherent structure-based models to improve their predictions.
Abstract: Predictions of the spatial representation of instantaneous wall-bounded flows, via coherent structure-based models, are highly sensitive to the geometry of the representative structures employed by them. In this study, we propose a methodology to extract the three-dimensional (3-D) geometry of the statistically significant eddies from multi-point wall-turbulence datasets, for direct implementation into these models to improve their predictions. The methodology is employed here for reconstructing a 3-D statistical picture of the inertial wall coherent turbulence for all canonical wall-bounded flows, across a decade of friction Reynolds number ($Re_{\tau}$). These structures are responsible for the $Re_{\tau}$-dependence of the skin-friction drag and also facilitate the inner-outer interactions, making them key targets of structure-based models. The empirical analysis brings out the geometric self-similarity of the large-scale wall-coherent motions and also suggests the hairpin packet as the representative flow structure for all wall-bounded flows, thereby aligning with the framework on which the attached eddy model (AEM) is based. The same framework is extended here to also model the very-large-scaled motions, with a consideration of their differences in internal versus external flows. Implementation of the empirically-obtained geometric scalings for these large structures into the AEM is shown to enhance the instantaneous flow predictions for all three velocity components. Finally, an active flow control system driven by the same geometric scalings is conceptualized, towards favourably altering the influence of the wall coherent motions on the skin-friction drag.
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19 Dec 1975
TL;DR: In this paper, the authors present a method to find the optimal set of words for a given sentence in a sentence using the Bibliogr. Index Reference Record created on 2004-09-07, modified on 2016-08-08
Abstract: Note: Bibliogr. : p. 413-424. Index Reference Record created on 2004-09-07, modified on 2016-08-08
3,758 citations
TL;DR: In this paper, a direct numerical simulation of incompressible channel flow at a friction Reynolds number of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows.
Abstract: A direct numerical simulation of incompressible channel flow at a friction Reynolds number ( ) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Karman constant . There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits dependence over a short range in wavenumber . Further, consistent with previous experimental observations, when these spectra are multiplied by (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the range.
910 citations
TL;DR: In this article, a new friction factor relation is proposed which is within ± 1.2% of the data for Reynolds numbers between 10×103 and 35×106, and includes a term to account for the near-wall velocity profile.
Abstract: Measurements of the mean velocity profile and pressure drop were performed in a fully developed, smooth pipe flow for Reynolds numbers from 31×103 to 35×106. Analysis of the mean velocity profiles indicates two overlap regions: a power law for 60 9×103). Von Karman's constant was shown to be 0.436 which is consistent with the friction factor data and the mean velocity profiles for 600 5%) than those predicted by Prandtl's relation. A new friction factor relation is proposed which is within ±1.2% of the data for Reynolds numbers between 10×103 and 35×106, and includes a term to account for the near-wall velocity profile.
794 citations
TL;DR: In this article, the authors used a low-speed, high-Reynolds-number facility and a high-resolution laser-Doppler anemometer to measure Reynolds stresses for a flat-plate turbulent boundary layer from Reθ = 1430 to 31 000.
Abstract: Despite extensive study, there remain significant questions about the Reynolds-number scaling of the zero-pressure-gradient flat-plate turbulent boundary layer. While the mean flow is generally accepted to follow the law of the wall, there is little consensus about the scaling of the Reynolds normal stresses, except that there are Reynolds-number effects even very close to the wall. Using a low-speed, high-Reynolds-number facility and a high-resolution laser-Doppler anemometer, we have measured Reynolds stresses for a flat-plate turbulent boundary layer from Reθ = 1430 to 31 000. Profiles of u′2, v′2, and u′v′ show reasonably good collapse with Reynolds number: u′2 in a new scaling, and v′2 and u′v′ in classic inner scaling. The log law provides a reasonably accurate universal profile for the mean velocity in the inner region.
776 citations