Comment on the Clauser chart method for determining the friction velocity

Journal of Hydraulic Engineering, 2012

Although the experimental work of the authors must be acknowledged, their theoretical reasoning leads to conclusions that are questionable. In particular, (1) we show subsequently that the main result of the work, namely, the use of a modification coefficient, m R , depending on the aspect ratio and affecting the Reynolds number in the Prandtl friction law, is not supported by observation;

Journal of Fluid Mechanics, 2019

Streamwise velocity and wall-shear stress are acquired simultaneously with a hot-wire and an array of azimuthal/spanwise-spaced skin friction sensors in large-scale pipe and boundary layer flow facilities at high Reynolds numbers. These allow for a correlation analysis on a per-scale basis between the velocity and reference skin friction signals to reveal which velocity-based turbulent motions are stochastically coherent with turbulent skin friction. In the logarithmic region, the wall-attached structures in both the pipe and boundary layers show evidence of self-similarity, and the range of scales over which the self-similarity is observed decreases with an increasing azimuthal/spanwise offset between the velocity and the reference skin friction signals. The present empirical observations support the existence of a self-similar range of wall-attached turbulence, which in turn are used to extend the model of Baarset al.(J. Fluid Mech., vol. 823, p. R2) to include the azimuthal/spanw...

Journal of Geophysical Research, 2007

1] The dynamics of estuaries and coastal waters is strongly influenced by friction, which must be modeled with great accuracy in order to construct reliable hydrodynamic and morphodynamic models of these regions. We show that using appropriate global scaling (which does not depend on the detailed distribution of mean velocity and momentum) together with a single numerical coefficient, which is analytically calculated, the entire friction laws in tubes, channels, and oscillatory flow can be made to collapse into one single curve for both smooth and rough (granular type) walls. This suggests that wall friction has a global nature, which allows the derivation of a new unified expression for turbulent friction that is valid for all these flows and is noticeably more accurate than existing formulae (including Prandtl's universal law of friction for smooth pipes and subsequent refinements based on the Princeton superpipe experiment). In the light of previous work by the authors we consider finally the case of high roughness, for which simple turbulent friction laws cease to be valid, showing that observation is consistent with an upper bound for the flux of longitudinal momentum toward the wall that turbulence can generate. This leads to a new expression for the law of friction appropriate to high roughness cases which is shown to be in excellent agreement with observation.

Correlations of friction factors are presented for the general case of purely viscous non-Newtonian fluids without requiring a priori the adoption of a rheological model. They are based on an empirical estimate of the shift in the wall layer edge and the Kolmogorov point. The predictions of friction factors have the same level of accuracy as those of the Dodge-Metzner correlation but the visualisation is more compatible with measured velocity profiles. The general correlations obtained can be used to easily retrieve correlations for specific rheological models.

Physics of Fluids, 2002

An exact relationship for the local skin friction is derived for the compressible turbulent wall-bounded flow ͑channel, pipe, flat plate͒. This expression is an extension of the compressible case of that derived by Fukagata et al. ͓Phys. Fluids 14, L73 ͑2002͔͒ in the case of incompressible wall-bounded flows. This decomposition shows that the skin friction can be interpreted as the contribution of four physical processes, i.e., laminar, turbulent, compressible, and a fourth coming from the interaction between turbulence and compressibility. Compressible numerical simulations show that, even at Mach number M = 2, the main contribution comes from the turbulence, i.e., the Reynolds stress term.

Geophysical Research Letters, 2011

1] The experimental results of Nikuradse and the concept of hydraulically smooth, transitional, and rough flow regimes are commonly used as a benchmark for data interpretation and modeling of hydraulic resistance. However, Nikuradse's experiments were carried out in pipes with impermeable rough-walls whereas many geophysical flows occur over permeable walls and thus the permeability effects need to be quantified and accounted for. On the basis of our own experimental results, it is shown that wall permeability influences flow resistance dramatically and that the conventional 'hydraulically-rough regime', for which the friction factor depends only on the ratio of the roughness size to the flow thickness, does not apply to flows over permeable walls. Indeed, even at high Reynolds number (Re), the friction factor progressively increases with increasing Re. Possible mechanisms that explain this behavior, as well as the implications of these results for modeling of the friction factors and hyporheic exchange in porous-bed rivers are discussed. Citation: Manes, C., D. Pokrajac, V. I. Nikora, L. Ridolfi, and D. Poggi (2011), Turbulent friction in flows over permeable walls, Geophys. Res. Lett., 38, L03402,

Physica D: Nonlinear Phenomena, 2010

In this paper we derive an accurate composite friction factor vs. Reynolds number correlation formula for laminar, transition and turbulent flow in smooth pipes. The correlation is given as a rational fraction of rational fractions of power laws which is systematically generated by smoothly connecting linear splines in log-log coordinates with a logistic dose curve algorithm. This kind of correlation seeks the most accurate representation of the data independent of any input from theories arising from the researchers ideas about the underlying fluid mechanics. As such, these correlations provide an objective metric against which observations and other theoretical correlations may be applied. Our correlation is as accurate, or more accurate, than other correlations in the range of Reynolds numbers in which the correlations overlap. However, our formula is not restricted to certain ranges of Reynolds number but instead applies uniformly to all smooth pipe flow data for which data is available. The properties of the classical logistic dose response curve are reviewed and extended to problems described by multiple branches of power laws. This extended method of fitting which leads to rational fractions of power laws is applied to data Marusic and Perry 1995 for the velocity profile in a boundary layer on a flat plate with an adverse pressure gradient, to data of Nikuradse 1932 and McKeon et al. 2004 on friction factors for flow in smooth pipes and to the data of Nikuradse 1933 for effectively smooth pipes.

Due to the lack of analytic representation of frictional resistance in open channels, the traditional Manning or Chezy equation for steady uniform flow is usually assumed to be suitable as well as a practical representation of frictional resistance expected for unsteady flow. No much attention has been given to any other frictional formula in application related to unsteady non-uniform flow or tidal phenomena in open channels and rivers. The purpose of this research is to demonstrate the application of alternative equations of resistance, such as the rough turbulent formula, the Williamson equation and the Colebrook White equation. Differences between, and limitations of each formula are also presented. An approach to the solution of Colebrook White formula in an explicit form in open channels is given. A comparative study between this formula and other explicit formulae is also highlightedl representation of frictional resistance expected for unsteady flow. No much attention has been given to any other frictional formula in application related to unsteady non-uniform flow or tidal phenomena in open channels and rivers. The purpose of this research is to demonstrate the application of alternative equations of resistance, such as the rough turbulent formula, the Williamson equation and the Colebrook White equation. Differences between, and limitations of each formula are also presented. An approach to the solution of Colebrook White formula in an explicit form in open channels is given. A comparative study between this formula and other explicit formulae is also highlighted

ITM Web of Conferences

The key element in design of pipelines is the friction factor estimation. After the brief review of the experimental data and friction factor correlations for isothermal single phase flow, we have checked the validity of well-known correlations through statistical criteria. During this process it was statistically proved that some of the well-known and permanently cited friction factor equations can be improved. Moreover we have prepared, for practical engineering purposes, equations that cover the entire range of laminar, critical and turbulent pipe flow.

Annals of Nuclear Energy, 2004

The present paper is focused on the prediction of stability of single-phase natural circulation in the range of Reynolds numbers characterizing the transition between laminar and turbulent flow. In particular, the predictions obtained by one-dimensional models making use of different assumptions for evaluating wall friction at this transition are discussed, also in front of experimental information from previous investigations.

Journal of Indian Water Works Association, 2006

Present paper proposes a universal resistance equation relating friction factor (λ), the Reynolds number (R) and roughness height (k) for the entire range of turbulent flow in pipes covering all the three regimes: smooth, transition and rough. Experimental data of Nikuradse and others were used. Such an equation is found to be sufficient to predict the friction factor for all ranges of R (≥4000) and different values of k. Present model is found to be equally valid for both cases of commercially available pipes and Nikuradse experiments on sand roughened pipes.

Beni-Suef University Journal of Basic and Applied Sciences, 2014

Enhanced wall treatment keε turbulence model Computational fluid dynamics (CFD) Friction factor a b s t r a c t The aim of this study is to formulate a computational fluid dynamics (CFD) model that can illustrate the fully turbulent flow in a pipe at higher Reynolds number. The flow of fluids in a pipe network is an important and widely studied problem in any engineering industry. It is always significant to see the development of a fluid flow and pressure drop in a pipe at higher Reynolds number. A finite volume method (FVM) solver with keε turbulence model and enhanced wall treatment is used first time to investigate the flow of water at different velocities with higher Reynolds number in a 3D pipe. Numerical results have been presented to illustrate the effects of Reynolds number on turbulence intensity, average shear stress and friction factor. Friction factor is used to investigate the pressure drop along the length of the pipe. The contours of wall function are also presented to investigate the effect of enhanced wall treatment on a fluid flow. A maximum Reynolds number is also found for which the selected pipe length is sufficient to find a full developed turbulent flow at outlet. The results of CFD modeling are validated by comparing them with available data in literature. The model results have been shown good agreement with experimental and corelation data.

Physics of Fluids, 2011

This paper presents an extension of FIK identity [K. Fukagata et al., Phys. Fluids 14, L73 (2002)] to turbulent axial flow along a cylinder. This relation gives the contributions of both the mean flow and the turbulent fluctuating flow to the skin friction coefficient. The later contribution is then further decomposed more precisely as proposed by B. Frohnapfel, Y. Hasegawa, and N. Kasagi, "Reactive Flow Control for Skin Friction Drag Reduction based on Sensing of the Streamwise Wall-Shear Stress," Euromech Fluid Mechanics Conference 8 (EFMC8), Bad Reichenhall, Germany, 13-16 Sept. 2010, S4-30. The Reynolds shear stress can be linked to the eigenvalues of the anisotropy tensor, the angle between the principal axis of the Reynolds stress tensor, and the mean flow direction and the turbulent kinetic energy. These eigenvalues and the alignment are important elements of the Reynolds stress profile. The present analysis is based on high-fidelity Reynolds-Stress-Model-based simulations. The results are first validated using available DNS and experimental data. Then, results are used in order to investigate the variations of the skin friction componential contributions with respect to characteristic dimensionless radius a þ , Reynolds numbers, Re a (cylinder-radius-based Reynolds number) and Re d (boundary-layer-thickness-based Reynolds number), or curvature ratio d=a, and anisotropic decomposition of the Reynolds stress. Explicit empirical formula for surface responses of skin friction and its turbulent component is given. V

Journal of Fluid Mechanics, 2006

International Communications in Heat and Mass Transfer, 1990

A number of correlations for prechcting the turbulent frictmn factor of purely viscous hon-Newtonian fluids flowing in circular and non-circular geometries are presented These correlations are in reasonable agreement vath available data and with each other for values of the power law index close to unity for both circular and rectangular geometries A critical test of these correlations is carried out by comparing the predicted friction factor with experimental pipe flow data at low values of the power law index. It is shown that the Dodge--Metzner correlation gives the best agreement with experiment over the entire range of available power law values, while the simple Yoo correlation and the Irvine correlation are within t 10% of the experimental data for n _) 0.3. The Tam-Tiu correlation is found to underpredict experimental pipe flow data for n values between 0.2 and 0.5