Turbulent Flow in Smooth and Rough Pipes

1972 ◽  
Vol 94 (2) ◽  
pp. 353-361 ◽  
Author(s):  
H. W. Townes ◽  
J. L. Gow ◽  
R. E. Powe ◽  
N. Weber
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Cross Correlation ◽  
Axisymmetric Flow ◽  
Secondary Flows ◽  
Sand Particle ◽  
Mean Velocity ◽  
Number Range ◽  
Reynolds Equations ◽  
Smooth Pipe

Fully developed turbulent flow in both smooth and rough-walled pipes is investigated for Reynolds numbers from 30,000 to 480,000. The values of mean velocity, root-mean-square values of the fluctuating velocity components, and cross-correlation values of the fluctuating velocities are presented for flow in a smooth pipe and two sand-roughened pipes, R/ε = 208 and R/ε = 26.4. The quantity R/ε is the ratio of the actual pipe radius to the average sand particle size. The experimental measurements for flow in smooth pipes are in good agreement with those of previous investigations throughout the Reynolds number range considered. Several of the rough pipe turbulence quantities show substantial deviations from the corresponding smooth pipe quantities. For rough pipes, the measured uv cross-correlation values approach those predicted empirically from the Reynolds equations for fully developed, axisymmetric flow as the flow approaches the hydraulically smooth case. However, as the Reynolds number is increased and the flow proceeds through the transition region from smooth to fully rough flow and to the fully rough flow region, the values of the uv cross correlation in rough pipes are significantly lower than the predicted values. This difference between predicted and measured data becomes more pronounced as the Reynolds number is further increased and the flow becomes fully rough. The difference between measured and predicted uv values, and other differences between smooth and rough pipe results, suggests that the accepted reduction of the Reynolds equations for flow in smooth pipes is not valid for flow in rough pipes. Thus, the Reynolds equations are re-examined for flow in rough pipes, and it is shown that these equations can be satisfied by the experimental data if secondary flows and angular variations in the mean velocity are postulated.

Turbulent flow in smooth and rough pipes

2007 ◽  
Vol 365 (1852) ◽  
pp. 699-714 ◽  
Author(s):  
J.J Allen ◽  
M.A Shockling ◽  
G.J Kunkel ◽  
A.J Smits
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Outer Layer ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Number Range ◽  
Princeton University ◽  
Smooth Pipe ◽  
Logarithmic Region

Recent experiments at Princeton University have revealed aspects of smooth pipe flow behaviour that suggest a more complex scaling than previously noted. In particular, the pressure gradient results yield a new friction factor relationship for smooth pipes, and the velocity profiles indicate the presence of a power-law region near the wall and, for Reynolds numbers greater than about 400×10 3 ( R + >9×10 3 ), a logarithmic region further out. New experiments on a rough pipe with a honed surface finish with k rms / D =19.4×10 −6 , over a Reynolds number range of 57×10 3 –21×10 6 , show that in the transitionally rough regime this surface follows an inflectional friction factor relationship rather than the monotonic relationship given in the Moody diagram. Outer-layer scaling of the mean velocity data and streamwise turbulence intensities for the rough pipe show excellent collapse and provide strong support for Townsend's outer-layer similarity hypothesis for rough-walled flows. The streamwise rough-wall spectra also agree well with the corresponding smooth-wall data. The pipe exhibited smooth behaviour for , which supports the suggestion that the original smooth pipe was indeed hydraulically smooth for Re D ≤24×10 6 . The relationship between the velocity shift, Δ U / u τ , and the roughness Reynolds number, , has been used to generalize the form of the transition from smooth to fully rough flow for an arbitrary relative roughness k rms / D . These predictions apply for honed pipes when the separation of pipe diameter to roughness height is large, and they differ significantly from the traditional Moody curves.

Influence of Inlet Velocity Condition on Unsteady Flow Characteristics in Piping With a Short-Elbow at High Reynolds Number Condition

2014 ◽  
Author(s):  
Ayako Ono ◽  
Masaaki Tanaka ◽  
Jun Kobayashi ◽  
Hideki Kamide
Keyword(s):  
Reynolds Number ◽  
Flow Separation ◽  
Velocity Fluctuation ◽  
Complex Geometry ◽  
Perforated Plate ◽  
Secondary Flows ◽  
Curvature Radius ◽  
Mean Velocity ◽  
Inlet Velocity ◽  
Velocity Condition

In design of the Japan Sodium-cooled Fast Reactor (JSFR), mean velocity of the coolant is approximately 9 m/s in the primary hot leg (H/L) piping which diameter is 1.27 m. The Reynolds number in the H/L piping reaches 4.2×107. Moreover, a short-elbow which has Rc/D = 1.0 (Rc: Curvature radius, D: Pipe diameter) is used in the hot leg piping in order to achieve compact plant layout and reduce plant construction cost. In the H/L piping, flow-induced vibration (FIV) is concerned due to excitation force which is caused by pressure fluctuation on the wall closely related with the velocity fluctuation in the short-elbow. In the previous study, relation between the flow separation and the pressure fluctuations in the short-elbow was revealed under the specific inlet condition with flat distribution of time-averaged axial velocity and relatively weak velocity fluctuation intensity in the pipe. However, the inlet velocity condition of the H/L in a reactor may have ununiformed profile with highly turbulent due to the complex geometry in reactor vessel (R/V). In this study, the influence of the inlet velocity condition on unsteady characteristics of velocity in the short-elbow was studied. Although the flow around the inlet of the H/L in R/V could not simulate completely, inlet velocity conditions were controlled by installing the perforated plate with plugging the flow-holes appropriately. Then expected flow patterns were made at 2D upstream position from the elbow inlet in the experiments. It was revealed that the inlet velocity profiles affected circumferential secondary flow and the secondary flows affected an area of flow separation at the elbow, by local velocity measurement by the PIV (particle image velocimetry). And it was found that the low frequent turbulence in the upstream piping remained downstream of the elbow though their intensity was attenuated.

On Turbulent Flow Between Parallel Plates

1953 ◽  
Vol 20 (1) ◽  
pp. 109-114
Author(s):  
S. I. Pai
Keyword(s):  
Turbulent Flow ◽  
Velocity Distribution ◽  
Poiseuille Flow ◽  
The Other ◽  
Turbulent Velocity ◽  
Parallel Plates ◽  
Mean Velocity ◽  
Reynolds Equations ◽  
Mean Pressure ◽  
The Mean

Abstract The Reynolds equations of motion of turbulent flow of incompressible fluid have been studied for turbulent flow between parallel plates. The number of these equations is finally reduced to two. One of these consists of mean velocity and correlation between transverse and longitudinal turbulent-velocity fluctuations u 1 ′ u 2 ′ ¯ only. The other consists of the mean pressure and transverse turbulent-velocity intensity. Some conclusions about the mean pressure distribution and turbulent fluctuations are drawn. These equations are applied to two special cases: One is Poiseuille flow in which both plates are at rest and the other is Couette flow in which one plate is at rest and the other is moving with constant velocity. The mean velocity distribution and the correlation u 1 ′ u 2 ′ ¯ can be expressed in a form of polynomial of the co-ordinate in the direction perpendicular to the plates, with the ratio of shearing stress on the plate to that of the corresponding laminar flow of the same maximum velocity as a parameter. These expressions hold true all the way across the plates, i.e., both the turbulent region and viscous layer including the laminar sublayer. These expressions for Poiseuille flow have been checked with experimental data of Laufer fairly well. It also shows that the logarithmic mean velocity distribution is not a rigorous solution of Reynolds equations.

Experiments on transition to turbulence in an oscillatory pipe flow

1976 ◽  
Vol 75 (2) ◽  
pp. 193-207 ◽  
Author(s):  
Mikio Hino ◽  
Masaki Sawamoto ◽  
Shuji Takasu
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Pipe Flow ◽  
Stokes Parameter ◽  
Angular Frequency ◽  
Transition To Turbulence ◽  
Mean Velocity ◽  
Cross Sectional ◽  
Velocity Amplitude ◽  
Turbulent Flow Regime

Experiments on transition to turbulence in a purely oscillatory pipe flow were performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude Û, from 19 to 1530 (or for values of the Reynolds number Re, defined using the pipe diameter d and Û, from 105 to 5830) and for values of the Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·19. Three types of turbulent flow regime have been detected: weakly turbulent flow, conditionally turbulent flow and fully turbulent flow. Demarcation of the flow regimes is possible on Rλ, λ or Re, λ diagrams. The critical Reynolds number of the first transition decreases as the Stokes parameter increases. In the conditionally turbulent flow, turbulence is generated suddenly in the decelerating phase and the profile of the velocity distribution changes drastically. In the accelerating phase, the flow recovers to laminar. This type of partially turbulent flow persists even at Reynolds numbers as high as Re = 5830 if the value of the Stokes parameter is high.

Further Investigation of Discharge Coefficient for PTC 6 Flow Nozzle in High Reynolds Number

2015 ◽  
Author(s):  
Noriyuki Furuichi ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
Kazuo Shibuya
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
High Reynolds Number ◽  
Discharge Coefficient ◽  
Flow Region ◽  
Number Range ◽  
Discharge Coefficients ◽  
Reynolds Number Range ◽  
High Reynolds

The discharge coefficients of the throat tap flow nozzle based on ASME PTC 6 are measured in wide Reynolds number range from Red=5.8×104 to Red=1.4×107. The nominal discharge coefficient (the discharge coefficient without tap) is determined from the discharge coefficients measured for different tap diameters. The tap effects are correctly obtained by subtracting the nominal discharge coefficient from the discharge coefficient measured. Finally, by combing the nominal discharge coefficient and the tap effect determined in three flow regions, that is, laminar, transitional and turbulent flow region, the new equations of the discharge coefficient are proposed in three flow regions.

Direct simulations of low-Reynolds-number turbulent flow in a rotating channel

1993 ◽  
Vol 256 ◽  
pp. 163-197 ◽  
Author(s):  
Reidar Kristoffersen ◽  
Helge I. Andersson
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Complete Suppression ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Computational Mesh ◽  
Developed Pressure ◽  
Rotating Channel

Direct numerical simulations of fully developed pressure-driven turbulent flow in a rotating channel have been performed. The unsteady Navier–Stokes equations were written for flow in a constantly rotating frame of reference and solved numerically by means of a finite-difference technique on a 128 × 128 × 128 computational mesh. The Reynolds number, based on the bulk mean velocity Um and the channel half-width h, was about 2900, while the rotation number Ro = 2|Ω|h/Um varied from 0 to 0.5. Without system rotation, results of the simulation were in good agreement with the accurate reference simulation of Kim, Moin & Moser (1987) and available experimental data. The simulated flow fields subject to rotation revealed fascinating effects exerted by the Coriolis force on channel flow turbulence. With weak rotation (Ro = 0.01) the turbulence statistics across the channel varied only slightly compared with the nonrotating case, and opposite effects were observed near the pressure and suction sides of the channel. With increasing rotation the augmentation and damping of the turbulence along the pressure and suction sides, respectively, became more significant, resulting in highly asymmetric profiles of mean velocity and turbulent Reynolds stresses. In accordance with the experimental observations of Johnston, Halleen & Lezius (1972), the mean velocity profile exhibited an appreciable region with slope 2Ω. At Ro = 0.50 the Reynolds stresses vanished in the vicinity of the stabilized side, and the nearly complete suppression of the turbulent agitation was confirmed by marker particle trackings and two-point velocity correlations. Rotational-induced Taylor-Görtler-like counter-rotating streamwise vortices have been identified, and the simulations suggest that the vortices are shifted slightly towards the pressure side with increasing rotation rates, and the number of vortex pairs therefore tend to increase with Ro.

Heat Transfer to Mercury Flowing In-Line Through a Bundle of Circular Rods

1964 ◽  
Vol 86 (2) ◽  
pp. 180-186 ◽  
Author(s):  
M. W. Maresca ◽  
O. E. Dwyer
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Heat Fluxes ◽  
Transfer Coefficients ◽  
Number Range ◽  
Heat Transfer Coefficients ◽  
Turbulent Flow Regime ◽  
Measuring Surface ◽  
Theoretical Predictions

Experimental results were obtained for the case of in-line flow of mercury through an unbaffled bundle of circular rods, and they were compared with theoretical predictions. The bundle consisted of 13 one-half-in-dia rods arranged in an equilateral triangular pattern, the pitch:diameter ratio being 1.750. Measurements were taken only on the central rod. Six different rods were tested. All rods in the bundle were electrically heated to provide equal and uniform heat fluxes throughout the bundle. The rods were of the Calrod type. The test rods had copper sheaths with fine thermocouples imbedded below the surface for measuring surface temperatures. Some rods were plated with a layer of nickel, followed by a very thin layer of copper, to provide “wetting” conditions, while others were chromeplated to provide “nonwetting” conditions. Heat-transfer coefficients were obtained under the following conditions: (a) Prandtl number, 0.02; (b) Reynolds number range, 7500 to 200,000; (c) Peclet number range, 150 to 4000; (d) “Wetting” versus “nonwetting”; (e) Both transition and fully established flow; (f) Variation of Lf/De ratio from 4 to 46. The precision of the results is estimated to be within 2 to 3 percent. An interesting finding, consistent with earlier predictions, was that the Nusselt number, under fully established turbulent-flow conditions, remained essentially constant, at the lower end of the turbulent flow regime, until a Reynolds number of about 40,000 was reached.

Experimental and Computational Flow Field Studies of an Integrally Cast Cooling Manifold With and Without Rotation

2006 ◽  
Author(s):  
Ioannis Ieronymidis ◽  
David R. H. Gillespie ◽  
Peter T. Ireland ◽  
Robert Kingston
Keyword(s):  
Reynolds Number ◽  
Rotation Number ◽  
Discharge Coefficient ◽  
Thermal Contact ◽  
Leading Edge ◽  
Secondary Flows ◽  
Transfer Coefficients ◽  
Number Range ◽  
High Heat Transfer ◽  
Cooling Passage

This paper presents detailed pressure measurements and discharge coefficient data for a long, low aspect ratio manifold; part of a novel blade cooling scheme. The cooling geometry, in which a series of racetrack passages are connected to a central plenum, provides high heat transfer coefficients in regions of the blade in good thermal contact with the outer blade surface. The Reynolds number changes along its length because of the ejection of fluid through a series of 19 transfer holes in a staggered arrangement, which are used to connect ceramic cores during the casting process. For rotation number RN = 0 the velocity down each hole remains almost constant. A correlation between hole discharge coefficient and Velocity Head Ratio is also presented. Pressure loss coefficients in the passage and through the holes are also discussed. A High Pressure (HP) rig was tested to investigate compressibility effects and expand the inlet Reynolds number range. A CFD model was validated against the experimental data, and then used to investigate the effects of rotation on the hole discharge coefficients. Results are presented for an inlet Reynolds number of 43477. At an engine representative rotation number of 0.08 corresponding buoyancy number of 0.17 there was little effect of rotation. However, at high rotational speeds secondary flows in the cooling passage and the exit plenum greatly reduce the hole discharge coefficient by increasing the local cross flow at the hole entrances and capping the hole exits in a manner similar to that seen in leading edge film-cooling geometries.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

2009 ◽  
Vol 621 ◽  
pp. 69-102 ◽  
Author(s):  
MURALI R. CHOLEMARI ◽  
JAYWANT H. ARAKERI
Keyword(s):  
Reynolds Number ◽  
Rayleigh Number ◽  
Turbulent Flow ◽  
Density Gradient ◽  
Schmidt Number ◽  
Shear Stresses ◽  
Mean Flow ◽  
Vertical Pipe ◽  
Velocity Correlation ◽  
Number Range

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

Effect of Low Reynolds Number Mixed Convection on Channel Flows Structure

2012 ◽  
Author(s):  
Ahmed Elatar ◽  
Kamran Siddiqui
Keyword(s):  
Reynolds Number ◽  
Flow Rate ◽  
Wall Temperature ◽  
Heated Wall ◽  
Mean Velocity ◽  
Number Range ◽  
Flow Rates ◽  
Wall Heating ◽  
The Mean ◽  
Low Reynolds

The effect of wall heating on low Reynolds numbers channel flow has been investigated experimentally. The experiments were conducted at heated bottom wall temperatures from 30 °C to 50 °C for two flow rates 0.0210 and 0.0525 kg/s, corresponding to the Reynolds number range of 150 and 750 (in the absence of heating). The results showed that the initially laminar flow became turbulent due to wall heating, and that wall heating has a significant influence on both the mean and turbulent velocity fields. The mean velocity profiles were altered by the convective currents. The magnitude of mean streamwise velocity near the heated wall increased with an increase in the wall temperature. A back flow near the upper channel wall was also observed primarily at the lower flow rate which diminished for the high flow rate. The magnitude of backflow increased with an increase in the wall temperature. The turbulent intensities were found to increase with an increase in the wall temperature for both flow rates. The result also showed the presence of strong vortices originating from the heated wall and advecting towards the central core of the channel.

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