Friction Losses in Turbulent Pipe-flow

1951 ◽  
Vol 165 (1) ◽  
pp. 88-111 ◽  
Author(s):  
L. E. Prosser ◽  
R. C. Worster ◽  
S. T. Bonnington
Keyword(s):  
Reynolds Number ◽  
Friction Coefficient ◽  
Water Flow ◽  
Reynolds Numbers ◽  
Transition Function ◽  
Turbulent Pipe Flow ◽  
Rational Form ◽  
Iron And Steel ◽  
High Reynolds ◽  
Almost All

Significant developments in the theory of turbulent flow in smooth and rough pipes are reviewed to establish a rational basis for the commonly accepted logarithmic laws for pipe friction. The Prandtl (1932)‡ smooth-pipe law, , where f is the friction coefficient in the formula , agrees with measured results on smooth pipes up to Reynolds numbers of at least 3 × 106. With rough pipe walls and sufficiently high Reynolds numbers, viscosity (and hence Reynolds number) ceases to have any direct effect and the friction coefficient depends on wall roughness and pipe size only. Almost all practical cases of water flow in commercial pipes lie between these two extremes of completely smooth and fully rough conditions, where the friction coefficient varies with both Reynolds number and roughness. Exponential flow formulae of the Manning type— V = *** Am1xiy—can be rearranged into a more rational form f = B( Re) p( k/d) q*** relating f to Reynolds number and relative roughness for a given class of pipe carrying a fluid of given viscosity. A detailed study is made of published test data on wrought-iron and steel pipes which generally operate in the transition zone, and an exponential formula is derived which agrees with these results. This is found to be similar to that given by Blair for this class of pipe. The relative merits of these exponential formulae, and of the Colebrook-White transition function, are discussed and it is concluded that, for most practical cases of water flow in pipes, the simple formulae are no less reliable.

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.

scholarly journals Comparison of turbulence profiles in high-Reynolds-number turbulent boundary layers and validation of a predictive model

2017 ◽  
Vol 814 ◽  
Author(s):  
J.-P. Laval ◽  
J. C. Vassilicos ◽  
J.-M. Foucaut ◽  
M. Stanislas
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Salt Lake ◽  
Reynolds Numbers ◽  
Turbulent Pipe Flow ◽  
Test Facility ◽  
Flow Data ◽  
Wide Range ◽  
Layer Flow ◽  
High Reynolds

The modified Townsend–Perry attached-eddy model of Vassilicos et al. (J. Fluid Mech., vol. 774, 2015, pp. 324–341) combines the outer peak/plateau behaviour of root-mean-square streamwise turbulence velocity profiles and the Townsend–Perry log decay of these profiles at higher distances from the wall. This model was validated by these authors for high-Reynolds-number turbulent pipe flow data and is shown here to describe equally well, and with approximately the same parameter values, turbulent boundary layer flow data from four different facilities and a wide range of Reynolds numbers. The model has predictive value as, when extrapolated to the extremely high Reynolds numbers of the SLTEST data obtained at the Great Salt Lake Desert atmospheric test facility, it matches these data quite well.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals Video: DNS of turbulent pipe flow at high Reynolds number

2021 ◽  
Author(s):  
Alessandro Ceci ◽  
Sergio Pirozzoli ◽  
Joshua Romero ◽  
Massimiliano Fatica ◽  
Roberto Verzicco ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Turbulent Pipe Flow ◽  
High Reynolds

Temperature Control of Blow-Down, Supersonic Tunnels

1956 ◽  
Vol 60 (541) ◽  
pp. 67-70
Author(s):  
T. A. Thomson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Stagnation Temperature ◽  
Blow Down ◽  
High Reynolds Numbers ◽  
Experimental Errors ◽  
High Reynolds

The blow-down type of intermittent, supersonic tunnel is attractive because of its simplicity and because relatively high Reynolds numbers can be obtained for a given size of test section. An adverse characteristic, however, is the fall of stagnation temperature during runs, which can affect experiments in several ways. The Reynolds number varies and the absolute velocity is not constant, even if the Mach number and pressure are; heat-transfer cannot be studied under controlled conditions and the experimental errors arising from the effect of heat-transfer on the boundary layer vary in time. These effects can become significant in quantitative experiments if the tunnel is large and the variation of temperature very rapid; the expense required to eliminate them might then be justified.

Reynolds Number Effects on the Freewheeling Behavior of a High Solidity Vertical River Kinetic Turbine

2010 ◽  
Author(s):  
Amir Hossein Birjandi ◽  
Eric Bibeau
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Speed Ratio ◽  
Stream Velocity ◽  
Blade Profile ◽  
Low Reynolds Numbers ◽  
Tip Speed Ratio ◽  
Reynolds Number Effects ◽  
High Reynolds ◽  
The University

A four-bladed, squirrel-cage, and scaled vertical kinetic turbine was designed, instrumented and tested in the water tunnel facilities at the University of Manitoba. With a solidity of 1.3 and NACA0021 blade profile, the turbine is classified as a high solidity model. Results were obtained for conditions during freewheeling at various Reynolds numbers. In this study, the freewheeling tip speed ratio, which relates the ratio of maximum blade speed to the free stream velocity at no load, was divided into three regions based on the Reynolds number. At low Reynolds numbers, the tip speed ratio was lower than unity and blades were in a stall condition. At the end of the first region, there was a sharp increase of the tip speed ratio so the second region has a tip speed ratio significantly higher than unity. In this region, the tip speed ratio increases almost linearly with Reynolds number. At high Reynolds numbers, the tip speed ratio is almost independent of Reynolds number in the third region. It should be noted that the transition between these three regions is a function of the blade profile and solidity. However, the three-region behavior is applicable to turbines with different profiles and solidities.

Stability of non-parabolic flow in a flexible tube

1999 ◽  
Vol 395 ◽  
pp. 211-236 ◽  
Author(s):  
V. SHANKAR ◽  
V. KUMARAN
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Flexible Tube ◽  
Developing Flow ◽  
Parabolic Flow ◽  
High Reynolds ◽  
The Stability

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

Turbulent Annular Pipe Flow in Subcritical Transition Regime: Direct Numerical Simulation of a Large Domain

2015 ◽  
Author(s):  
Takahiro Ishida ◽  
Takahiro Tsukahara
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Reynolds Numbers ◽  
Radius Ratio ◽  
Transition Regime ◽  
Transitional Regime ◽  
Large Domain ◽  
High Reynolds ◽  
Annular Pipe ◽  
Transition Scenario

We performed direct numerical simulations of annular Poiseuille flow (APF) with a radius ratio of η (= rin/rout) = 0.8, in order to investigate the subcritical transition scenario from the developed turbulent state to the laminar state. In previous studies on annular Poiseuille flow, the flows at high Reynolds numbers were well examined and various turbulence statistics were obtained for several η, because of their dependence on η. Since the transitional APF is still unclear, we investigate annular Poiseuille flows in the transitional regime through the large-domain simulations in a range of the friction Reynolds number from Reτ = 150 down to 56. At a transitional Reynolds number, weak-fluctuation regions occur intermittently and regularly in the flow field, and the localized turbulence appears in the form of banded patterns same as in plane Poiseuille flow (PPF). The flow system of APF with a high radius ratio η ≈ 1 can be regarded as PPF and, hence, the transition regime in high radius-ratio of APF and in PPF should be analogous. However, in APF, the banded structure takes on helical shape around the inner cylinder, since APF is a closed system in the spanwise (azimuthal) direction. In this paper, the (dis-)similarity between APF and PPF is discussed.

Asymptotic scaling in turbulent pipe flow

2007 ◽  
Vol 365 (1852) ◽  
pp. 771-787 ◽  
Author(s):  
B.J McKeon ◽  
J.F Morrison
Keyword(s):  
Asymptotic Behaviour ◽  
Pipe Flow ◽  
Physical Space ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Turbulent Pipe Flow ◽  
Inertial Subrange ◽  
Velocity Spectrum ◽  
Mean Velocity ◽  
High Reynolds

The streamwise velocity component in turbulent pipe flow is assessed to determine whether it exhibits asymptotic behaviour that is indicative of high Reynolds numbers. The asymptotic behaviour of both the mean velocity (in the form of the log law) and that of the second moment of the streamwise component of velocity in the outer and overlap regions is consistent with the development of spectral regions which indicate inertial scaling. It is shown that an ‘inertial sublayer’ in physical space may be considered as a spatial analogue of the inertial subrange in the velocity spectrum and such behaviour only appears for Reynolds numbers R + >5×10 3 , approximately, much higher than was generally thought.

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