scholarly journals On the mixing length eddies and logarithmic mean velocity profile in wall turbulence

2020 ◽  
Vol 887 ◽  
Author(s):  
Michael Heisel ◽  
Charitha M. de Silva ◽  
Nicholas Hutchins ◽  
Ivan Marusic ◽  
Michele Guala
Keyword(s):  
Velocity Profile ◽  
Wall Turbulence ◽  
Mixing Length ◽  
Logarithmic Mean ◽  
Mean Velocity ◽  
Image Position

A Model for Velocity Profile in Turbulent Boundary Layer with Drag Reducing Surfactants

2005 ◽  
Vol 15 (3) ◽  
pp. 152-159 ◽  
Author(s):  
A. Krope ◽  
J. Krope ◽  
L.C. Lipus
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
General Problem ◽  
Frictional Resistance ◽  
Mixing Length ◽  
Mean Velocity ◽  
Pipe Section ◽  
Turbulent Water

Abstract A new model for mean velocity profile of turbulent water flow with added drag-reducing surfactants is presented in this paper. The general problem of drag due to frictional resistance is reviewed and drag reduction by the addition of polymers or surfactants is introduced. The model bases on modified Prandtl's mixing length hypothesis and includes three parameters, which depend on additives and can be evaluated by numerical simulation from experimental datasets. The advantage of the model in comparison with previously reported models is that it gives uniform curve for whole pipe section and can be determined for a new surfactant with less necessary measurements. The use of the model is demonstrated for surfactant Habon-G as an example.

On the size of the energy-containing eddies in the outer turbulent wall layer

2012 ◽  
Vol 702 ◽  
pp. 521-532 ◽  
Author(s):  
Sergio Pirozzoli
Keyword(s):  
Outer Part ◽  
Eddy Diffusivity ◽  
Wall Layer ◽  
Wall Turbulence ◽  
Normal Velocity ◽  
Mixing Length ◽  
Mean Velocity ◽  
Local Mean ◽  
Turbulent Wall ◽  
Good Agreement

AbstractWe investigate the scaling of the energy-containing eddies in the outer part of turbulent wall layers. Their spanwise integral length scales are extracted from a direct numerical simulation (DNS) database, which includes compressible turbulent boundary layers and incompressible turbulent Couette–Poiseuille flows. The results indicate similar behaviour for all classes of flows, with a general increasing trend in the eddy size with the wall distance. A family of scaling relationships are proposed based on simple dimensional arguments, of which the classical mixing length approximation constitutes one example. As in previous studies, we find that the mixing length is in good agreement with the size distribution of the eddies carrying wall-normal velocity, which are active in establishing the mean velocity distribution. However, we find that the eddies associated with wall-parallel motions obey a different scaling, which is controlled by the local mean shear and by an effective eddy diffusivity ${\nu }_{t} = { u}_{\tau }^{\ensuremath{\ast} } \delta $, where ${ u}_{\tau }^{\ensuremath{\ast} } $ is the compressible counterpart of the friction velocity, and $\delta $ is the thickness of the wall layer. The validity of the proposed scalings is checked against DNS data, and the potential implications for the understanding of wall turbulence are discussed.

The Ultimate Asymptote and Mean Flow Structure in Toms’ Phenomenon

1970 ◽  
Vol 37 (2) ◽  
pp. 488-493 ◽  
Author(s):  
P. S. Virk ◽  
H. S. Mickley ◽  
K. A. Smith
Keyword(s):  
Velocity Profile ◽  
Drag Reduction ◽  
Flow Structure ◽  
Viscous Sublayer ◽  
Mixing Length ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Length Constant ◽  
The Mean

The maximum drag reduction in turbulent pipe flow of dilute polymer solutions is ultimately limited by a unique asymptote described by the experimental correlation: f−1/2=19.0log10(NRef1/2)−32.4 The semilogarithmic mean velocity profile corresponding to and inferred from this ultimate asymptote has a mixing-length constant of 0.085 and shares a trisection (at y+ ∼ 12) with the Newtonian viscous sublayer and law of the wall. Experimental mean velocity profiles taken during drag reduction lie in the region bounded by the inferred ultimate profile and the Newtonian law of the wall. At low drag reductions the experimental profiles are well correlated by an “effective slip” model but this fails progressively with increasing drag reduction. Based on the foregoing a three-zone scheme is proposed to model the mean flow structure during drag reduction. In this the mean velocity profile segments are (a) a viscous sublayer, akin to Newtonian, (b) an interactive zone, characteristic of drag reduction, in which the ultimate profile is followed, and (c) a turbulent core in which the Newtonian mixing-length constant applies. The proposed model is consistent with experimental observations and reduces satisfactorily to the Taylor-Prandtl scheme and the ultimate profile, respectively, at the limits of zero and maximum drag reductions.

On the logarithmic mean profile

2009 ◽  
Vol 638 ◽  
pp. 73-93 ◽  
Author(s):  
J. KLEWICKI ◽  
P. FIFE ◽  
T. WEI
Keyword(s):  
Numerical Simulation ◽  
Velocity Profile ◽  
Stress Profile ◽  
Logarithmic Mean ◽  
Self Similarity ◽  
Mean Velocity ◽  
Von Karman ◽  
The Mean ◽  
Von Kármán ◽  
Logarithmic Dependence

Elements of the first-principles-based theory of Wei et al. (J. Fluid Mech., vol. 522, 2005, p. 303), Fife et al. (Multiscale Model. Simul., vol. 4, 2005a, p. 936; J. Fluid Mech., vol. 532, 2005b, p. 165) and Fife, Klewicki & Wei (J. Discrete Continuous Dyn. Syst., vol. 24, 2009, p. 781) are clarified and their veracity tested relative to the properties of the logarithmic mean velocity profile. While the approach employed broadly reveals the mathematical structure admitted by the time averaged Navier–Stokes equations, results are primarily provided for fully developed pressure driven flow in a two-dimensional channel. The theory demonstrates that the appropriately simplified mean differential statement of Newton's second law formally admits a hierarchy of scaling layers, each having a distinct characteristic length. The theory also specifies that these characteristic lengths asymptotically scale with distance from the wall over a well-defined range of wall-normal positions, y. Numerical simulation data are shown to support these analytical findings in every measure explored. The mean velocity profile is shown to exhibit logarithmic dependence (exact or approximate) when the solution to the mean equation of motion exhibits (exact or approximate) self-similarity from layer to layer within the hierarchy. The condition of pure self-similarity corresponds to a constant leading coefficient in the logarithmic mean velocity equation. The theory predicts and clarifies why logarithmic behaviour is better approximated as the Reynolds number gets large. An exact equation for the leading coefficient (von Kármán coefficient κ) is tested against direct numerical simulation (DNS) data. Two methods for precisely estimating the leading coefficient over any selected range of y are presented. These methods reveal that the differences between the theory and simulation are essentially within the uncertainty level of the simulation. The von Kármán coefficient physically exists owing to an approximate self-similarity in the flux of turbulent force across an internal layer hierarchy. Mathematically, this self-similarity relates to the slope and curvature of the Reynolds stress profile, or equivalently the slope and curvature of the mean vorticity profile. The theory addresses how, why and under what conditions logarithmic dependence is approximated relative to the specific mechanisms contained within the mean statement of dynamics.

Revisiting the mixing-length hypothesis in the outer part of turbulent wall layers: mean flow and wall friction

2014 ◽  
Vol 745 ◽  
pp. 378-397 ◽  
Author(s):  
Sergio Pirozzoli
Keyword(s):  
Velocity Profile ◽  
Turbulent Flows ◽  
Outer Part ◽  
Wall Layer ◽  
Wall Friction ◽  
Mixing Length ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
Turbulent Wall

AbstractWe reconsider foundations and implications of the mixing length theory as applied to wall-bounded turbulent flows in uniform pressure gradient. Based on recent channel-flow direct numerical simulation (DNS) data at sufficiently high Reynolds number, we find that Prandtl’s hypothesis of linear variation of the mixing length with the wall distance is rather inaccurate, hence overlap arguments are stronger in justifying the formation of a logarithmic layer in the mean velocity profile. Regarding the core region of the wall layer, we find that Clauser’s hypothesis of uniform eddy viscosity is strictly connected with the observed size of the eddy structures, and it delivers surprisingly good agreement with DNS and experiments for channels, pipes, and boundary layers. We show that the analytically derived composite mean velocity profiles can be used to accurately predict skin friction in canonical wall-bounded flows with a minimal number of adjustable parameters directly related to the mean velocity profile, and to obtain some insight into transient growth phenomena.

scholarly journals Revisiting the law of the wake in wall turbulence

2016 ◽  
Vol 811 ◽  
pp. 421-435 ◽  
Author(s):  
Dominik Krug ◽  
Jimmy Philip ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Outer Region ◽  
Wall Turbulence ◽  
State Model ◽  
Flow State ◽  
Mean Velocity ◽  
Measured Velocity ◽  
Log Law ◽  
Two State Model

The streamwise mean velocity profile in a turbulent boundary layer is classically described as the sum of a log law extending all the way to the edge of the boundary layer and a wake function. While there is theoretical support for the log law, the wake function, defined as the deviation of the measured velocity profile from the log law, is essentially an empirical fit and has no real physical underpinning. Here, we present a new physically motivated formulation of the velocity profile in the outer region, and hence for the wake function. In our approach, the entire flow is represented by a two-state model consisting of an inertial self-similar region designated as ‘pure wall flow state’ (featuring a log-law velocity distribution) and a free stream state, which results in a jump in velocity at the interface separating the two. We show that the model provides excellent agreement with the available high Reynolds number mean velocity profiles if this interface is assumed to fluctuate randomly about a mean position with a Gaussian distribution. The new concept can also be extended to internal geometries in the same form, again confirmed by the data. Furthermore, adopting the same interface distribution in a two-state model for the streamwise turbulent intensities, with unchanged parameters, also yields a reliable and consistent prediction for the decline in the outer region of these profiles in all geometries considered. Finally, we discuss differences between our model interface and the turbulent/non-turbulent interface (TNTI) in turbulent boundary layers. We physically interpret the two-state model as lumping the effects of internal shear layers and the TNTI into a single discontinuity at the interface.

Mean velocity scaling for compressible wall turbulence with heat transfer

2016 ◽  
Vol 28 (2) ◽  
pp. 026102 ◽  
Author(s):  
Andrew Trettel ◽  
Johan Larsson
Keyword(s):  
Heat Transfer ◽  
Wall Turbulence ◽  
Mean Velocity

Оdrеđivаnjе brzinе struјаnjа vаzduhа u prаvоugаоnоm zаtvоrеnоm cevovodu korišćenjem metoda polja brzina

2021 ◽  
Vol 23 (2) ◽  
pp. 57-63
Author(s):  
Marija Lazarevikj ◽  
◽  
Valentino Stojkovski ◽  
Viktor Iliev
Keyword(s):  
Velocity Profile ◽  
Flow Rate ◽  
Air Flow ◽  
Displacement Transducer ◽  
Linear Displacement ◽  
Local Velocity ◽  
Air Flow Rate ◽  
Mean Velocity ◽  
Measured Velocity ◽  
Integration Techniques

In the technical practice, it is often necessary to measure or control the fluid flow rate in pipelines and channels. The velocity-area method requires a number of meters located at specified points in a suitable cross-section of closed conduits. Simultaneous measurements of local mean velocity with the meters are integrated over the gauging section to provide the discharge. In this paper, three approaches of this method are applied on a rectangular closed conduit to determine the air flow rate with integration techniques used to compute the discharge assume velocity distributions that closely approximate known laws, especially in the neighborhood of solid boundaries. For this purpose, meters for velocity were 7 Pitot tubes placed vertically in predefined measurement points covering the conduit height, and moved horizontally along the conduit width. The position of the Pitot tubes along the conduit width was monitored and controlled by a linear displacement transducer. Pressure is measured using digital sensors. The first technique for determination of air flow rate is on basis of fixed (stopping) measuring points across the conduit width as averaged values of local velocity, the second one is semi continual measurement of velocity profile by applying interpolation between the average local velocity on fixed (stopping) points and measured velocity in the movement between two positions, and the third is by continuously moving the Pitot tubes without stopping. The results of the three techniques are calculated and presented using different types of software. Considering the last technique, comparison of results is made applying different movement speeds of the Pitot tubes in order to examine their influence on the velocity profile.

scholarly journals Effect of the Flame Dome Depth and Improvement of the Pressure Loss in the Dump Diffuser

1998 ◽  
Author(s):  
Shinji Honami ◽  
Wataru Tsuboi ◽  
Takaaki Shizawa
Keyword(s):  
Velocity Profile ◽  
Reynolds Stress ◽  
Flow Rate ◽  
Pressure Loss ◽  
Total Pressure ◽  
Flow Behavior ◽  
Sudden Expansion ◽  
Mean Velocity ◽  
The Mean ◽  
Stress Profiles

This paper presents the effect of flame dome depth on the total pressure performance and flow behavior in a sudden expansion region of the combustor diffuser without flow entering the dome head. The mean velocity and turbulent Reynolds stress profiles in the sudden expansion region were measured by a Laser Doppler Velocitmetry (LDV) system. The experiments show that total pressure loss is increased, when flame dome depth is increased. Installation of an inclined combuster wall in the sudden expansion region is suggested from the viewpoint of a control of the reattaching flow. The inclined combustor wall is found to be effective in improvement of the diffuser performance. Better characteristics of the flow rate distribution into the branched channels are obtained in the inclined wall configuration, even if the distorted velocity profile is provided at the diffuser inlet.

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