Investigations of Tripping Effect on the Friction Factor in Turbulent Pipe Flows

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
A. Al-Salaymeh ◽  
O. A. Bayoumi
Keyword(s):  
Friction Factor ◽  
Reynolds Numbers ◽  
Original Data ◽  
Turbulent Pipe Flow ◽  
Wall Friction ◽  
Mean Flow ◽  
Mean Velocity ◽  
Fully Developed Turbulent Flow ◽  
The Mean ◽  
The Difference

Tripping devices are usually installed at the entrance of laboratory-scale pipe test sections to obtain a fully developed turbulent flow sooner. The tripping of laminar flow to induce turbulence can be carried out in different ways, such as using cylindrical wires, sand papers, well-organized tape elements, fences, etc. Claims of tripping effects have been made since the classical experiments of Nikuradse (1932, Gesetzmässigkeit der turbulenten Strömung in glatten Rohren, Forschungsheft 356, Ausgabe B, Vol. 3, VDI-Verlag, Berlin), which covered a significant range of Reynolds numbers. Nikuradse’s data have become the metric by which theories are established and have also been the subject of intense scrutiny. Several subsequent experiments reported friction factors as much as 5% lower than those measured by Nikuradse, and the authors of those reports attributed the difference to tripping effects, e.g., work of Durst et al. (2003, “Investigation of the Mean-Flow Scaling and Tripping Effect on Fully Developed Turbulent Pipe Flow,” J. Hydrodynam., 15(1), pp. 14–22). In the present study, measurements with and without ring tripping devices of different blocking areas of 10%, 20%, 30%, and 40% have been carried out to determine the effect of entrance condition on the developing flow field in pipes. Along with pressure drop measurements to compute the skin friction, both the Pitot tube and hot-wire anemometry measurements have been used to accurately determine the mean velocity profile over the working test section at different Reynolds numbers based on the mean velocity and pipe diameter in the range of 1.0×105–4.5×105. The results we obtained suggest that the tripping technique has an insignificant effect on the wall friction factor, in agreement with Nikuradse’s original data.

STEADY STATE HEAT TRANSFER TO FULLY DEVELOPED TURBULENT FLOW IN A CURVED CHANNEL

1957 ◽  
Vol 35 (4) ◽  
pp. 410-434
Author(s):  
A. W. Marris
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Mean Flow ◽  
Curved Channel ◽  
Mean Velocity ◽  
Fully Developed Turbulent Flow ◽  
Angular Velocities ◽  
The Mean

A vorticity transfer analogy theory of turbulent heat transfer is developed first for the case of fully developed turbulent flow under zero transverse pressure and temperature gradients such as that in the annulus between concentric cylinders rotating with different angular velocities or in a "free vortex". The mean flow is assumed to be two-dimensional. The theory, which requires that the turbulence be statistically isotropic, yields a temperature distribution in agreement with experiment except in narrow regions immediately adjacent to the boundaries. An argument is given to show that the boundary layer thickness should be of the order of the reciprocal of the square root of the mean velocity, these boundaries are introduced, and Nusselt moduli are defined and their dependence on Reynolds and Prandtl numbers is investigated.The temperature distributions for the case of non-zero transverse temperature and pressure gradients, i.e. for the case of flow in a curved channel in which the fluid does not flow back into itself, are then obtained and the applicability of the simpler equations for zero transverse gradients to this case is investigated.

Nonasymptotic behavior of developing turbulent pipe flow

1976 ◽  
Vol 54 (3) ◽  
pp. 268-278 ◽  
Author(s):  
J. K. Reichert ◽  
R. S. Azad
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Peak Position ◽  
Turbulent Pipe Flow ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Inlet Region ◽  
The Mean ◽  
Hot Film

Detailed measurements of mean velocity U profiles, in the inlet 70 diameters of a pipe, show that the development of turbulent pipe flow is nonasymptotic. Experiments were done at seven Reynolds numbers in the range 56 000–15 3000. Contours of U and V fields are presented for two representative Reynolds numbers. A U component peak exceeding the fully developed values has been found to occur along the pipe centerline. The Reynolds number behavior of the peak position has been determined. Hot film measurements of the mean wall shear stresses in the inlet region also show a nonasymptotic development consistent with the mean velocity results.

Experiments on swirling turbulent flows. Part 1. Similarity in swirling flows

1973 ◽  
Vol 60 (4) ◽  
pp. 665-687 ◽  
Author(s):  
K. S. Yajnik ◽  
M. V. Subbaiah
Keyword(s):  
Turbulent Flows ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Swirling Flows ◽  
Turbulent Pipe Flow ◽  
Extended Form ◽  
Mean Velocity ◽  
Swirl Angle ◽  
The Mean ◽  
Similarity Laws

The effects of swirl on internal turbulent flows are studied by conducting experiments on turbulent pipe flow with variable initial swirl. This first part of the study is primarily concerned with similarity laws. The mean velocity profiles, both away from and close to the wall, are found to admit similarity representations at sufficiently large Reynolds numbers, provided that flow reversal does not take place near the entrance. While the wall law is not sensibly dependent on swirl, the velocity defect law in its extended form is sensitive to swirl. Further, a logarithmic skin-friction law is obtained in which only the additive coefficient depends on swirl. This coefficient is found to vary linearly with the swirl angle in the range of the present experiments.

scholarly journals Ekman Layer Scrubbing and Shroud Heat Transfer in Centrifugal Buoyancy-Driven Convection

2021 ◽  
Vol 143 (7) ◽  
Author(s):  
Feng Gao ◽  
John W. Chew
Keyword(s):  
Heat Transfer ◽  
Reynolds Numbers ◽  
Boussinesq Approximation ◽  
Ekman Layer ◽  
Open Cavity ◽  
Mean Flow ◽  
Large Eddy ◽  
The Mean ◽  
The Difference ◽  
Buoyancy Driven Convection

Abstract This paper presents large-eddy and direct numerical simulations of buoyancy-driven convection in sealed and open rapidly rotating cavities for Rayleigh numbers in the range 107–109, and axial throughflow Reynolds numbers 2000 and 5600. Viscous heating due to the Ekman layer scrubbing effect, which has previously been found responsible for the difference in sealed cavity shroud Nusselt number predictions between a compressible N–S solver and an incompressible counterpart using the Boussinesq approximation, is discussed and scaled up to engine conditions. For the open cavity with an axial throughflow, laminar Ekman layer behavior of the mean flow statistics is confirmed up to the highest condition in this paper. The Buoyancy number Bo is found useful to indicate the influence of an axial throughflow. For the conditions studied the mean velocities are subject to Ra, while the velocity fluctuations are affected by Bo. A correlation, Nu′=0.169(Ra′)0.318, obtained with both the sealed and open cavity shroud heat transfer solutions, agrees with that for free gravitational convection between horizontal plates within 16% for the range of Ra′ considered.

scholarly journals Ekman Layer Scrubbing and Shroud Heat Transfer in Centrifugal Buoyancy-Driven Convection

2020 ◽  
Author(s):  
Feng Gao ◽  
John W. Chew
Keyword(s):  
Heat Transfer ◽  
Reynolds Numbers ◽  
Boussinesq Approximation ◽  
Ekman Layer ◽  
Open Cavity ◽  
Mean Flow ◽  
Large Eddy ◽  
The Mean ◽  
The Difference ◽  
Buoyancy Driven Convection

Abstract This paper presents large-eddy and direct numerical simulations of buoyancy-driven convection in sealed and open rapidly rotating cavities for Rayleigh numbers in the range 107–109, and axial throughflow Reynolds numbers 2000 and 5600. Viscous heating due to the Ekman layer scrubbing effect, which has previously been found responsible for the difference in sealed cavity shroud Nusselt number predictions between a compressible N-S solver and an incompressible counterpart using the Boussinesq approximation, is discussed and scaled up to engine conditions. For the open cavity with an axial throughflow, laminar Ekman layer behaviour of the mean flow statistics is confirmed up to the highest condition in this paper. The Buoyancy number Bo is found useful to indicate the influence of an axial throughflow. For the conditions studied the mean velocities are subject to Ra, while the velocity fluctuations are affected by Bo. A correlation, Nu′ = 0.169(Ra′)0.318, obtained with both the sealed and open cavity shroud heat transfer solutions, agrees with that for free gravitational convection between horizontal plates within 16% for the range of Ra′ considered.

Study on Side-Jet Injection Near a Duct Entry With Various Injection Angles

1999 ◽  
Vol 121 (3) ◽  
pp. 580-587 ◽  
Author(s):  
Tong-Miin Liou ◽  
Chin-Chun Liao ◽  
Shih-Hui Chen ◽  
Hsin-Ming Lin
Keyword(s):  
Recirculation Zone ◽  
Reynolds Numbers ◽  
Reynolds Stress Model ◽  
Main Duct ◽  
Rectangular Duct ◽  
Mean Flow ◽  
Mean Velocity ◽  
Injection Angle ◽  
Mass Entrainment ◽  
The Mean

Turbulent flowfields resulting from an oblique jet injecting from a rectangular side-inlet duct into a rectangular main duct with an aspect ratio 3.75 without a forced crossflow are presented in terms of laser-Doppler velocimetry measurements. The main focuses are the effects of the side-jet angle (θ) and side-jet flow rate (Qs) on the mass entrainment upstream of side-jet port and the flowfield in the rectangular duct. The side-inlet angles investigated were 30, 45, and 60 deg and Reynolds numbers based on the air density, rectangular duct height and bulk mean velocity were in the range of 7.1 × 103 to 3.6 × 104 corresponding to Qs values of 1 × 103 to 5 × 103 L/min. The present study suggests the presence of a critical side-injection angle θc (30 ≤ θc ≤ 45 deg) above which a recirculation zone appears in the rectangular duct, whereas below which the recirculation zone is absent. For the more tangential angle (θ = 30 deg), almost as much fluid is entrained into the main duct as was injected from the side jet. The mean flow field in the rectangular duct is found to be a weak function of the Reynolds-number for the range of Qs investigated. In addition, a simple linear correlation between the mass entrainment upstream of the side-jet port and side-injection angle is obtained. Complementary flow visualizations and numerical computations with an algebraic Reynolds stress model were also performed. The discrepancies between measured and computed results are documented.

scholarly journals Flow in a commercial steel pipe

2008 ◽  
Vol 595 ◽  
pp. 323-339 ◽  
Author(s):  
L. I. LANGELANDSVIK ◽  
G. J. KUNKEL ◽  
A. J. SMITS
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Roughness Height ◽  
Steel Pipe ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Commercial Steel ◽  
The Mean ◽  
The Difference

Mean flow measurements are obtained in a commercial steel pipe with krms/D = 1/26 000, where krms is the roughness height and D the pipe diameter, covering the smooth, transitionally rough, and fully rough regimes. The results indicate a transition from smooth to rough flow that is much more abrupt than the Colebrook transitional roughness function suggests. The equivalent sandgrain roughness was found to be 1.6 times the r.m.s. roughness height, in sharp contrast to the value of 3.0 to 5.0 that is commonly used. The difference amounts to a reduction in pressure drop for a given flow rate of at least 13% in the fully rough regime. The mean velocity profiles support Townsend's similarity hypothesis for flow over rough surfaces.

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.

Mean-flow scaling of turbulent pipe flow

1998 ◽  
Vol 373 ◽  
pp. 33-79 ◽  
Author(s):  
MARK V. ZAGAROLA ◽  
ALEXANDER J. SMITS
Keyword(s):  
Friction Factor ◽  
Friction Velocity ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Mean Velocity ◽  
Velocity Scale ◽  
The Mean ◽  
Log Law ◽  
High Reynolds

Measurements of the mean velocity profile and pressure drop were performed in a fully developed, smooth pipe flow for Reynolds numbers from 31×103 to 35×106. Analysis of the mean velocity profiles indicates two overlap regions: a power law for 60<y+<500 or y+<0.15R+, the outer limit depending on whether the Kármán number R+ is greater or less than 9×103; and a log law for 600<y+<0.07R+. The log law is only evident if the Reynolds number is greater than approximately 400×103 (R+>9×103). Von Kármán's constant was shown to be 0.436 which is consistent with the friction factor data and the mean velocity profiles for 600<y+<0.07R+, and the additive constant was shown to be 6.15 when the log law is expressed in inner scaling variables.A new theory is developed to explain the scaling in both overlap regions. This theory requires a velocity scale for the outer region such that the ratio of the outer velocity scale to the inner velocity scale (the friction velocity) is a function of Reynolds number at low Reynolds numbers, and approaches a constant value at high Reynolds numbers. A reasonable candidate for the outer velocity scale is the velocity deficit in the pipe, UCL−Ū, which is a true outer velocity scale, in contrast to the friction velocity which is a velocity scale associated with the near-wall region which is ‘impressed’ on the outer region. The proposed velocity scale was used to normalize the velocity profiles in the outer region and was found to give significantly better agreement between different Reynolds numbers than the friction velocity.The friction factor data at high Reynolds numbers were found to be significantly larger (>5%) than those predicted by Prandtl's relation. A new friction factor relation is proposed which is within ±1.2% of the data for Reynolds numbers between 10×103 and 35×106, and includes a term to account for the near-wall velocity profile.

scholarly journals The similarity theory of turbulence, and flow between parallel planes and through pipes

1937 ◽  
Vol 159 (899) ◽  
pp. 473-496 ◽  
Keyword(s):  
Kinematic Viscosity ◽  
Friction Velocity ◽  
Similarity Theory ◽  
Turbulent Velocity ◽  
Wall Friction ◽  
Mean Flow ◽  
Viscous Layer ◽  
Mean Velocity ◽  
Turbulence Flow ◽  
The Mean

Before any distribution of mean velocity can be calculated from mixture length theories of turbulent motion, some assumption must be made concerning the mixture length. The only theory so far proposed which yields a formula for the length involved is Kármán’s similarity theory (Kármán 1930 a , b , 1932, 1934 a , pp.7-9 ,1934 b ; see also Noether 1931, 1933; Betz 1931; Dedebant, Schereschewsky and Wehrle 1934; Prandtl 1935). The assumptions of the theory have not, however, been sufficiently tested yet, and further research is needed. Moreover, even in the cases of the fairly simple mean motions to which the theory has so far been applied, there are regions in the field of flow where the assumptions break down, so that care is needed in the applications. It is assumed (1) that the turbulence mechanism is independent of the viscosity (except in the viscous layers near the walls); (2) that in comparing the turbulence mechanisms at two different points, consideration of the fields of turbulent flow may be restricted to the immediate neighbourhoods of these points; and (3) that the turbulence flow patterns at different points are similar (relative to frames of reference moving with the mean velocities at the points), and differ only in the scales of length and time (or velocity). The last assumption implies constant correlation between any two turbulent velocity components: if u, v, w denote the turbulent velocity components, the ratios u 2 ‾ : v 2 ‾ : w 2 ‾ : uv ‾ : vw ‾ : wu ‾ should, in fact, all be constant. Kármán (1934 a , fig. 7; 1934 b , fig. 6) has published curves of uv ‾ / u 2 ‾ for two-dimensional (mean) flow between parallel walls, obtained from measurements by Reichardt and by Wattendorf and Kuethe. The experimental points are rather scattered, but the curves show a fairly constant value for the ratio except near the walls and over the middle 0·6 h of the channel, where 2 h denotes the distance between the walls. Near the walls there is a marked departure from a constant value only when the viscous layer is approached. (The width of the viscous layer is of the order of 30 v / U r , where v is the kinematic viscosity and U r is the so-called “friction velocity”, defined by ρ U 2 r = r 2 0 , r 0 being the intensity of the wall friction.) In the middle of the channel the ratio falls to zero, showing that there is no correlation between u and v , a result to be expected from considerations of symmetry.

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