scholarly journals Turbulence Intensity Scaling: A Fugue

Fluids ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 180 ◽  
Author(s):  
Nils T. Basse
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Turbulence Intensity ◽  
Pipe Flow ◽  
Rough Wall ◽  
Flow Measurements ◽  
Flow Turbulence ◽  
Intensity Scaling ◽  
Grain Roughness ◽  
Made In

We study streamwise turbulence intensity definitions using smooth- and rough-wall pipe flow measurements made in the Princeton Superpipe. Scaling of turbulence intensity with the bulk (and friction) Reynolds number is provided for the definitions. The turbulence intensity scales with the friction factor for both smooth- and rough-wall pipe flow. Turbulence intensity definitions providing the best description of the measurements are identified. A procedure to calculate the turbulence intensity based on the bulk Reynolds number (and the sand-grain roughness for rough-wall pipe flow) is outlined.

Friction Factor Comparison Between Mixing Length Theory and Empirical Correlation

2022 ◽  
Author(s):  
M Prasad
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Friction Factor ◽  
High Reynolds Number ◽  
Mathematical Representation ◽  
Mixing Length ◽  
Series Form ◽  
High Reynolds ◽  
Mixing Length Theory ◽  
Grain Roughness

Abstract Equivalent sand grain roughness is required for estimating friction factor for engineering applications from empirical relation via Haalands equation. The real surfaces are different from the sand grain profile. The correlations for friction factor were derived from use of discrete roughness elements with regular shapes such as cones, bars etc. The purpose of the paper is to derive analytical expression of friction factor for a 2 dimensional semi-cylindrical roughness (not exactly a 3 dimensional sand grain but for the circular profile of cross- section) using Navier Stoke equation and mixing length theory. This is compared with the modified series mathematical representation of Haalands equation for friction factor in terms of equivalent sand grain roughness. The comparison is valid for high Reynolds number where the velocity profile is almost flat beyond boundary layer and approximately linear all throughout the boundary layer. The high Reynolds number approximation for Haalands equation is derived and the series form of the friction factor compares approximately with the series form derived from first principles, where in the exponents of the series expansion are close.

An Alternative (Preferable) Friction Factor

2006 ◽  
Author(s):  
Richard A. Gaggioli
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Pipe Flow ◽  
Incompressible Flows ◽  
Flow Regimes ◽  
Relative Roughness ◽  
Curve Fit ◽  
Moody Diagram ◽  
Approximate Formulas

An alternative to the traditional friction factor for pipe flow is presented (φ = [R]f). For incompressible flows, the correlation of this new friction factor with Reynolds Number [R] and Relative Roughness [ε] is presented graphically, and appears much simpler and more intuitive than the Moody Diagram (or other equivalents). Moreover, relatively simple curve-fit formulas for representing φ explicitly as a function of R and ε are presented for various flow regimes, along with measures of error associated with these approximate formulas.

Laminarization of turbulent pipe flow by fluid injection

1972 ◽  
Vol 52 (3) ◽  
pp. 451-464 ◽  
Author(s):  
W. T. Pennell ◽  
E. R. G. Eckert ◽  
E. M. Sparrow
Keyword(s):  
Reynolds Number ◽  
Turbulence Intensity ◽  
Pipe Flow ◽  
Streamwise Velocity ◽  
Turbulent Pipe Flow ◽  
Buffer Layers ◽  
Fluid Injection ◽  
Axial Component ◽  
Developed Turbulence ◽  
Porous Pipe

The effects of fluid injection on the structure of an initially fully developed, low Reynolds number, turbulent pipe flow have been studied by means of a hot-film anemometer. Measurements were made of the axial turbulence intensity field and of the time-mean streamwise velocity distribution, both in the porous-walled pipe and in the solid-walled hydrodynamic development section. Oscilloscope traces showing the timewise pattern of the local velocity fluctuations were also monitored. The Reynolds number of the air flow at the inlet of the porous pipe was varied from 3090 to 6350, and the Reynolds number of the injected air ranged from 60 to 160.Near the tube wall, the initial effect of injection is a significant reduction of the axial turbulence level and an increase in the thickness of the viscous and buffer layers. The degree by which turbulence is reduced in this region is more or less proportional to the ratio of the injection to entrance Reynolds numbers. In the core region of the flow, which is centred about the tube axis, there is also an initial reduction in the magnitude of the axial component of turbulence which is thought to be due to injection-induced acceleration of the flow. There is also an annular region, which separates the wall and core regions, in which the turbulence intensity initially increases. In the downstream portion of the porous tube the entire flow undergoes a re-transition to fully developed turbulence.

The Effect of a Longitudinal Magnetic Field on Pipe Flow of Mercury

1961 ◽  
Vol 83 (4) ◽  
pp. 445-453 ◽  
Author(s):  
Samuel Globe
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Friction Factor ◽  
Pipe Flow ◽  
Longitudinal Magnetic Field ◽  
Hartmann Number ◽  
Characteristic Length ◽  
Axial Magnetic Field ◽  
Turbulent Friction ◽  
The Magnetic Field

An experimental investigation has been made of the effect of an axial magnetic field on transition from laminar to turbulent flow and on the turbulent friction factor for pipe flow of mercury. Magnetic-flux densities up to 5700 gauss were obtained with a water-cooled solenoid. Pipes of glass and aluminum were used of approximately 0.1 to 0.2 in. diam. The maximum Hartmann number, with the hydraulic radius (half the actual radius) taken as the characteristic length, was about 20. Measurements were made of the pressure gradient and velocity of flow. The transition Reynolds number was determined from the curve of friction factor against Reynolds number. The results show an increasing value of minimum transition Reynolds number with Hartmann number. The magnetic field also brought about a decrease in the turbulent friction factor and corresponding shear force at the wall.

Rough wall turbulent boundary layers

1969 ◽  
Vol 37 (2) ◽  
pp. 383-413 ◽  
Author(s):  
A. E. Perry ◽  
W. H. Schofield ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Pipe Flow ◽  
Boundary Layer Flow ◽  
Shear Velocity ◽  
Rough Wall ◽  
Pipe Diameter ◽  
Boundary Layer Development ◽  
Layer Flow

This paper describes a detailed experimental study of turbulent boundary-layer development over rough walls in both zero and adverse pressure gradients. In contrast to previous work on this problem the skin friction was determined by pressure tapping the roughness elements and measuring their form drag.Two wall roughness geometries were chosen each giving a different law of behaviour; they were selected on the basis of their reported behaviour in pipe flow experiments. One type gives a Clauser type roughness function which depends on a Reynolds number based on the shear velocity and on a length associated with the size of the roughness. The other type of roughness (typified by a smooth wall containing a pattern of narrow cavities) has been tested in pipes and it is shown here that these pipe results indicate that the corresponding roughness function does not depend on roughness scale but depends instead on the pipe diameter. In boundary-layer flow the first type of roughness gives a roughness function identical to pipe flow as given by Clauser and verified by Hama and Perry & Joubert. The emphasis of this work is on the second type of roughness in boundary-layer flow. No external length scale associated with the boundary layer that is analogous to pipe diameter has been found, except perhaps for the zero pressure gradient case. However, it has been found that results for both types of roughness correlate with a Reynolds number based on the wall shear velocity and on the distance below the crests of the elements from where the logarithmic distribution of velocity is measured. One important implication of this is that a zero pressure gradient boundary layer with a cavity type rough wall conforms to Rotta's condition of precise self preserving flow. Some other implications of this are also discussed.

scholarly journals Effects of Biochar Addition on Rill Flow Resistance

Water ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 3036
Author(s):  
Alessio Nicosia ◽  
Vincenzo Pampalone ◽  
Vito Ferro
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Flow Resistance ◽  
Accurate Estimate ◽  
Power Equation ◽  
Flow Turbulence ◽  
Bed Slope ◽  
The Relationship ◽  
Resistance Equation ◽  
Rill Flow

The development of rills on a hillslope whose soil is amended by biochar remains a topic to be developed. A theoretical rill flow resistance equation, obtained by the integration of a power velocity distribution, was assessed using available measurements at plot scale with a biochar added soil. The biochar was incorporated and mixed with the arable soil using a biochar content BC of 6 and 12 kg m−2. The developed analysis demonstrated that an accurate estimate of the velocity profile parameter Гv can be obtained by the proposed power equation using an exponent e of the Reynolds number which decreases for increasing BC values. This result pointed out that the increase of biochar content dumps flow turbulence. The agreement between the measured friction factor values and those calculated by the proposed flow resistance equation, with Гv values estimated by the power equation calibrated on the available measurements, is characterized by errors which are always less than or equal to ±10% and less than or equal to ±3% for 75.0% of cases. In conclusion, the available measurements and the developed analysis allowed for (i) the calibration of the relationship between Гv, the bed slope, the flow Froude number, and the Reynolds number, (ii) the assessment of the influence of biochar content on flow resistance and, (iii) stating that the theoretical flow resistance equation gives an accurate estimate of the Darcy–Weisbach friction factor for rill flows on biochar added soils.

Pressure Drop and Heat Transfer of Nanofluid in Turbulent Pipe Flow Considering Particle Coagulation and Breakage

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Jian-Zhong Lin ◽  
Yi Xia ◽  
Xiao-Ke Ku
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Friction Factor ◽  
Pipe Flow ◽  
Volume Concentration ◽  
Particle Diameter ◽  
Turbulent Pipe Flow ◽  
Particle Volume ◽  
Friction Factors

Numerical simulations of Al2O3/water nanofluid in turbulent pipe flow are performed with considering the particle convection, diffusion, coagulation, and breakage. The distributions of particle volume concentration, the friction factor, and heat transfer characteristics are obtained. The results show that the initial uniform distributions of particle volume concentration become nonuniform, and increase from the pipe wall to the center. The nonuniformity becomes significant along the flow direction from the entrance and attains a steady state gradually. Friction factors increase with the increase of particle volume concentrations and particle diameter, and with the decrease of Reynolds number. The friction factors increase remarkably at lower volume concentration, while slightly at higher volume concentration. The presence of nanoparticles provides higher heat transfer than pure water. The Nusselt number of nanofluids increases with increasing Reynolds number, particle volume concentration, and particle diameter. The rate increase in Nusselt number at lower particle volume concentration is more than that at higher concentration. For a fixed particle volume concentration, the friction factor is smaller while the Nusselt number is larger for the case with uniform distribution of particle volume concentration than that with nonuniform distribution. In order to effectively enhance the heat transfer using nanofluid and simultaneously save energy, it is necessary to make the particle distribution more uniform. Finally, the expressions of friction factor and Nusselt number as a function of particle volume concentration, particle diameter and Reynolds number are derived based on the numerical data.

Turbulence spectra in smooth- and rough-wall pipe flow at extreme Reynolds numbers

2013 ◽  
Vol 731 ◽  
pp. 46-63 ◽  
Author(s):  
B. J. Rosenberg ◽  
M. Hultmark ◽  
M. Vallikivi ◽  
S. C. C. Bailey ◽  
A. J. Smits
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Turbulent Pipe Flow ◽  
Rough Wall ◽  
Inertial Subrange ◽  
Wall Region ◽  
Turbulence Structure ◽  
High Reynolds

AbstractWell-resolved streamwise velocity spectra are reported for smooth- and rough-wall turbulent pipe flow over a large range of Reynolds numbers. The turbulence structure far from the wall is seen to be unaffected by the roughness, in accordance with Townsend’s Reynolds number similarity hypothesis. Moreover, the energy spectra within the turbulent wall region follow the classical inner and outer scaling behaviour. While an overlap region between the two scalings and the associated${ k}_{x}^{- 1} $law are observed near${R}^{+ } \approx 3000$, the${ k}_{x}^{- 1} $behaviour is obfuscated at higher Reynolds numbers due to the evolving energy content of the large scales (the very-large-scale motions, or VLSMs). We apply a semi-empirical correction (del Álamo & Jiménez,J. Fluid Mech., vol. 640, 2009, pp. 5–26) to the experimental data to estimate how Taylor’s frozen field hypothesis distorts the pseudo-spatial spectra inferred from time-resolved measurements. While the correction tends to suppress the long wavelength peak in the logarithmic layer spectrum, the peak nonetheless appears to be a robust feature of pipe flow at high Reynolds number. The inertial subrange develops around${R}^{+ } \gt 2000$where the characteristic${ k}_{x}^{- 5/ 3} $region is evident, which, for high Reynolds numbers, persists in the wake and logarithmic regions. In the logarithmic region, the streamwise wavelength of the VLSM peak scales with distance from the wall, which is in contrast to boundary layers, where the superstructures have been shown to scale with boundary layer thickness throughout the entire shear layer. Moreover, the similarity in the streamwise wavelength scaling of the large- and very-large-scale motions supports the notion that the two are physically interdependent.

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