Vollständige Darstellung der turbulenten Geschwindigkeitsverteilung in glatten Leitungen

Reichardt, H.

doi:10.1002/zamm.19510310704

Cited by 625 publications

(188 citation statements)

References 1 publication

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“…Equations (8) to (10) have been confirmed to agree well with equations proposed by Reichardt [22]. In present simulations, these equations were used to calculate axial velocity, U(r) of each point.…”

Section: Average Velocity Profilesupporting

confidence: 79%

Discrete Tracer Point Method to Evaluate Turbulent Diffusion in Circular Pipe Flow

Widiatmojo¹,

Sasaki²,

Widodo³

et al. 2013

JFCMV

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Diffusion of a solute in turbulent flows through a circular pipe or tunnel is an important aspect of environmental safety. In this study, the diffusion coefficient of turbulent flow in circular pipe has been simulated by the Discrete Tracer Point Method (DTPM). The DTPM is a Lagrangian numerical method by a number of imaginary point displacement which satisfy turbulent mixing by velocity fluctuations, Reynolds stress, average velocity profile and a turbulent stochastic model. Numerical simulation results of points' distribution by DTPM have been compared with the analytical solution for turbulent plug-flow. For the case of turbulent circular pipe flow, the appropriate DTPM calculation time step has been investigated using a constant β, which represents the ratio between average mixing lengths over diameter of circular pipe. The evaluated values of diffusion coefficient by DTPM have been found to be in good agreement with Taylor's analytical equation for turbulent circular pipe flow by giving β = 0.04 to 0.045. Further, history matching of experimental tracer gas measurement through turbulent smooth-straight pipe flow has been presented and the results showed good agreement.

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Section: Average Velocity Profilesupporting

confidence: 79%

Discrete Tracer Point Method to Evaluate Turbulent Diffusion in Circular Pipe Flow

Widiatmojo¹,

Sasaki²,

Widodo³

et al. 2013

JFCMV

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“…The comparison of ␦ CP and the traditional estimate of DSLT by ␦ CB indicated that, on average, ␦ CB was 30% larger than the ␦ CP (Table 2). An inspection of D/v ϭ 1/Sc and E t /v (proposed in this study) or E t /v (proposed by Reichardt 1951) at the top of Table 2). The depth at which the two relative diffusivities were comparable, E t /v ഠ D/v, was, on average, 30% smaller than the traditional DSLT ␦ CB .…”

Section: Resultsmentioning

confidence: 92%

“…The eddy diffusivity for momentum and the eddy diffusivity for mass are related through the turbulent Schmidt number Sc t ϭ E t /D t , where E t is the turbulent diffusion coefficient for momentum transfer. Several different algebraic turbulence models for E t have been proposed (Reichardt 1951;Van Driest 1956;Shaw and Hanratty 1977). All models are empirical, depict similar vertical distance dependence of E t , and display a common rapid decrease in E t as the solid surface is approached (Fig.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Universal scaling of dissolved oxygen distribution at the sediment-water interface: A power law

et al. 2005

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Dissolved oxygen (DO) distribution at the sediment-water interface of a flow over a smooth bed is investigated for Reynolds numbers Ͼ360 and Ͻ4,090. These conditions are commonly encountered in streams, wetlands, and lakes. A power-law scaling of DO distribution is derived and compared with experimental data. The scaling analysis is based on DO flux at the sediment-water interface in a turbulent flow. The power-law model with diffusive sublayer thickness (DSLT) as a fitting parameter agrees well with the data over the investigated range of Reynolds numbers. Using the proposed power-law model with a limited number of DO and flow properties away from the sediment-water interface provides the distribution of DO concentrations and corresponding DSLT at a submillimeter resolution. The estimate of DSLT is, on average, 30% lower than the traditional estimate, defined as a thin fluid layer bounded at the lower boundary by a sediment bed and extended upward in the main water column to where a bulk DO concentration intersects with a linear DO gradient at the bed.The transport processes across the sediment-water interface are of fundamental importance to biological and chemical processes in streams, rivers, and lakes (Boudreau and Jørgensen 2001). In most cases, researchers are concerned about quantifying the distribution and corresponding flux of a particular substance at the sediment-water interface. The dissolved oxygen (DO) concentration in water has been considered one of the most important ecological parameters determining the water quality and associated biological composition of aquatic environments. The sediments, being a repository for decaying biological material with a large organic content, are a major contributor to the DO reduction in the water column.Significant laboratory and field measurements have been devoted to addressing the DO transport process at the sediment-water interface (e.g., Jørgensen and Des Marais 1990; Mackenthun and Stefan 1998;Røy et al. 2002). Microstructure DO measurements with microsensors (e.g., Jørgensen and Revsbech 1985;Lorke et al. 2003;Røy et al. 2004) have been very instrumental in the advancement of theories and models fundamental to the DO transport at the sedimentwater interface. Knowledge of the characteristics of the diffusive sublayer thickness (DSLT) for the DO transport and corresponding DO distribution at the sediment-water interface is crucial in benthic ecology. The difficulty in the characterization of the diffusive sublayer lies in its thinness, usually Ͻ5 mm, and the proximity of a solid boundary.

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“…The absence of a term of order y4 in za/p is worth noticing. Eg., Reichardt [72] advocated n = 3, but in a footnote remarked that n = 4 might apply if certain correlations (viz. ffOg/~z) were absent.…”

Section: X2( U2 )mentioning

confidence: 99%

Nonlocal stochastic mixing-length theory and the velocity profile in the turbulent boundary layer

Dekker

Leeuw²,

Brink

1995

Physica A: Statistical Mechanics and its Applications

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Nonlocal stochastic mixing-length theory and the velocity profile in the turbulent boundary layer Dekker, H.; de Leeuw, G.; Maassen van den Brin, A. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. AbstractTurbulence mixing by finite size eddies will be treated by means of a novel formulation of nonlocal K-theory, involving sample paths and a stochastic closure hypothesis, which implies a well defined recipe for the calculation of sampling and transition rates. The connection with the general theory of stochastic processes will be established. The relation with other nonlocal turbulence models (e.g. transilience and spectral diffusivity theory) is also discussed. Using an analytical sampling rate model (satisfying exchange) the theory is applied to the boundary layer (using a scaling hypothesis), which maps boundary layer turbulence mixing of scalar densities onto a nondiffusive (Kubo-Anderson or kangaroo) type stochastic process. The resulting transport equation for longitudinal momentum Px = ptJ is solved for a unified description of both the inertial and the viscous sublayer including the crossover. With a scaling exponent ~ 0.58 (while local turbulence would amount to s ~ oo) the velocity profile U+ =f(y+) is found to be in excellent agreement with the experimental data. Inter alia (i) the significance of e as a turbulence Cantor set dimension, (ii) the value of the integration constant in the logarithmic region (i.e. if y+ --* oo), (iii) linear timescaling, and (iv) finite Reynolds number effects will be investigated. The (analytical) predictions of the theory for near-wall behaviour (i.e. if y+ ~ 0) of fluctuating quantities also perfectly agree with recent direct numerical simulations. Introduction The velocity profileDimensional analysis of simple shear flow along an infinitely extended smooth surface immediately yields that the nondimensional mean velocity U+ = t J/u, (in the x-direction) must be a function of y+ = u,y/v, where u, is a reference (friction) velocity, y is the distance from the surface, and v is the kinematic viscosity. The friction * Corresponding author. Dekker et al./ Physica A 218 (1995) velocity is defined by means of the total stress z = pu2, in the boundary layer (p being the fluid mass density). In fully developed turbulent fl...

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Vollständige Darstellung der turbulenten Geschwindigkeitsverteilung in glatten Leitungen

Cited by 625 publications

References 1 publication

Discrete Tracer Point Method to Evaluate Turbulent Diffusion in Circular Pipe Flow

Discrete Tracer Point Method to Evaluate Turbulent Diffusion in Circular Pipe Flow

Universal scaling of dissolved oxygen distribution at the sediment-water interface: A power law

Nonlocal stochastic mixing-length theory and the velocity profile in the turbulent boundary layer

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