Laminar, Transitional and Turbulent Friction Factors for Gas Flows in Smooth and Rough Microtubes

2008 ◽  
Author(s):  
Marco Lorenzini ◽  
Gian Luca Morini ◽  
Sandro Salvigni
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Turbulent Regime ◽  
Turbulent Friction ◽  
Compressibility Effect ◽  
Flow Acceleration ◽  
Friction Factors ◽  
Macro Scale ◽  
Fully Developed Turbulent Flow ◽  
Microscale Transport

Theoretical and experimental works on microscale transport phenomena have been carried out in the past decade in the attempt to analyse possible new effects and to assess the influence of scaling on the classical correlations which are used in macro-scale heat and fluid flow, following the need to supply engineers with reliable correlations to be used in the design of micro-scale devices. These results were sometimes in mutual contrast, as is the case for the determination of the friction factor, which has been found to be lower, higher or comparable to that for macroscopic channels, depending on the researchers. In this work the compressible flow of nitrogen inside circular microchannels from 26 μm to 508 μm in diameter and with different surface roughness (<1%) is investigated for the whole range of flow conditions: laminar, transitional and turbulence. Over 5000 experimental data have been collected and analysed. The data confirmed that in the laminar regime the agreement with the conventional theory is very good in terms of friction factors both for rough and smooth microtubes. For the smaller microchannels (<100 μm) when Re is greater than 1300 the friction factor tends to deviate from the Poiseuille law because the flow acceleration due to compressibility effect gains in importance. The transitional regime was found to start no earlier than at values of the Reynolds number around 1800–2000. Both smooth and sudden changes in the flow regime have been found, as reported for conventional tubes. Fully developed turbulent flow was attained with both smooth and rough tubes, and the results for smooth tubes seem to confirm Blasius’s relation, while for rough tubes the Colebrook’s correlation is found to be only partially in agreement with the experimental friction factors. In the turbulent regime the dependence of the friction factor on the Reynolds number is less pronounced for microtubes with respect to the prediction of the Colebrook’s correlation and the friction factor tends only to depend on the microtube relative roughness.

Effect of Wetting on Friction Factors for Turbulent Flow of Mercury in Annuli

1976 ◽  
Vol 98 (1) ◽  
pp. 113-116 ◽  
Author(s):  
O. E. Dwyer ◽  
P. J. Hlavac ◽  
B. G. Nimmo
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Maximum Velocity ◽  
Outer Wall ◽  
Limited Range ◽  
Friction Factors ◽  
Fully Developed Turbulent Flow

Friction factors were determined for fully developed turbulent flow of mercury in smooth concentric annuli under conditions where either both walls were unwetted, or both were wetted, or the inner wall was wetted and the outer one unwetted. Three radius ratios (r2/r1) were used, i.e., 2.09, 2.78, and 4.00. Unwetted walls gave the lowest friction factors, which were practically independent of the r2/r1 ratio over the limited range tested. The factors were 10 ± 1 percent higher than the commonly accepted values for smooth pipes (at the same Reynolds number). The highest friction factors were obtained with the inner wall wetted and the outer wall unwetted, and the greater the r2/r1 ratio the greater was the effect. For example, at r2/r1 = 4.00, the friction factors were 9.9% greater than for the situation when both walls were unwetted. The wetting conditions affected the location of the radius of maximum velocity (rm); and it was found that the nearer rm approached r2, the higher was the friction factor.

Numerical and Experimental Analysis of Turbulent Flow in Corrugated Pipes

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Henrique Stel ◽  
Rigoberto E. M. Morales ◽  
Admilson T. Franco ◽  
Silvio L. M. Junqueira ◽  
Raul H. Erthal ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Velocity Magnitude ◽  
Geometric Configurations ◽  
Corrugated Surfaces ◽  
Friction Factors

This article describes a numerical and experimental investigation of turbulent flow in pipes with periodic “d-type” corrugations. Four geometric configurations of d-type corrugated surfaces with different groove heights and lengths are evaluated, and calculations for Reynolds numbers ranging from 5000 to 100,000 are performed. The numerical analysis is carried out using computational fluid dynamics, and two turbulence models are considered: the two-equation, low-Reynolds-number Chen–Kim k-ε turbulence model, for which several flow properties such as friction factor, Reynolds stress, and turbulence kinetic energy are computed, and the algebraic LVEL model, used only to compute the friction factors and a velocity magnitude profile for comparison. An experimental loop is designed to perform pressure-drop measurements of turbulent water flow in corrugated pipes for the different geometric configurations. Pressure-drop values are correlated with the friction factor to validate the numerical results. These show that, in general, the magnitudes of all the flow quantities analyzed increase near the corrugated wall and that this increase tends to be more significant for higher Reynolds numbers as well as for larger grooves. According to previous studies, these results may be related to enhanced momentum transfer between the groove and core flow as the Reynolds number and groove length increase. Numerical friction factors for both the Chen–Kim k-ε and LVEL turbulence models show good agreement with the experimental measurements.

Experimental Investigation of Nitrogen Flow in Long Microtubes

2009 ◽  
Author(s):  
Chengwen Li ◽  
Li Jia ◽  
Tiantian Zhang ◽  
Xing Li
Keyword(s):  
Experimental Data ◽  
Experimental Investigation ◽  
Flow Characteristics ◽  
Nitrogen Flow ◽  
Current Experiment ◽  
Turbulent Region ◽  
Compressibility Effect ◽  
Friction Factors ◽  
Macro Scale ◽  
Predicted Values

Nitrogen flow characteristics in Polyetheretherketone microtubes with inner diameters (D) ranging from 0.255mm to 0.553mm were experimentally investigated. It is indicated that most of the experimental points in laminar region are coincided with the conventional theoretical predicted value, but several plots caused by instrumental errors are lower than predicted values at small Re. In turbulent region, the friction factors for D = 0.255mm microtubes with L = 0.800m and 1.591m are slightly lower than conventional values; the experimental data for D = 0.553mm microtube with L = 0.800m is lower than that in D = 0.255mm pipes. The entrance effect obviously influences friction factor even if the L/D of microtubes is more than 60, where it can always be neglected in macro-scale. Due to the enhancement of compressibility effect as diameter decrease (Kn increase), friction constant is larger in smaller-size microtubes. The transition Reynolds number in current experiment (except for L = 0.200mm and D = 0.553mm) ranges from1600–2000, while a little early transition phenomenon is found in L = 0.200m, D = 0.553mm tube.

Frictional Pressure Drop in Micro-Channel

2004 ◽  
Author(s):  
Yasuo Koizumi ◽  
Hiroyasu Ohtake ◽  
Hiroki Takahashi ◽  
Yoshiaki Ohno
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Friction Factor ◽  
Frictional Pressure Drop ◽  
Turbulent Transition ◽  
Friction Factors ◽  
Turbulent Flow Regime ◽  
Form Pressure ◽  
Laminar And Turbulent Flow ◽  
Flow Through

The friction characteristics of water in a sub-millimeter scale channel were investigated experimentally. The friction factors and the critical Reynolds number were measured using water flow through circular tubes with diameters of 0.5, 0.25 and 0.17 mm. The experimental results show that the measured friction factor for water agreed well with the conventional Poiseuille (λ = 64/Re) and Blasius (λ = 0.316 Re−0.25) equations in laminar and turbulent flow regime; the laminar-turbulent transition Reynolds number was approximately 2300 for diameter 0.5 mm. For diameter 0.25 mm, the friction factor evaluated by the form pressure drop also agreed well with the Poiseuille equation. For diameter 0.17 mm, the measured total friction factor was close to the Poiseuille prediction.

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.

scholarly journals Leakage Characteristic of Helical Groove Seal Designed in Reactor Coolant Pump

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Meng Zhang ◽  
Xiao-fang Wang ◽  
Sheng-li Xu ◽  
Shuo Yin
Keyword(s):  
Reynolds Number ◽  
High Pressure ◽  
Friction Factor ◽  
Helix Angle ◽  
Operation Condition ◽  
Coolant Pump ◽  
Reactor Coolant ◽  
Friction Factors ◽  
Helical Groove ◽  
Groove Seal

Helical groove seal is designed in reactor coolant pump to control the leakage along the front surface of the impeller face due to its higher resistance than the circumferentially grooved seal. The flow and the friction factors in helical groove seals are predicted by employing a commercial CFD code, FLUENT. The friction factors of the helical groove seals with helix angles varying from 20 deg to 50 deg, at a range of rotational speed and axial Reynolds number, were, respectively, calculated. For the helically grooved stator with the helix angle greater than 20 deg, the leakage shows an upward trend with the helix angle. The circumferentially grooved stator has a lower resistance to leakage than the 20 deg and 30 deg stators. It can be predicated that, for a bigger helix angle, the friction factor increases slightly with an increase in high axial Reynolds number, which arises from the high-pressure operation condition, and the friction factor is generally sensitive to changes in the helix angle in this operation condition. The study lays the theoretical foundation for liquid seal design of reactor coolant pump and future experimental study to account for the high-pressure condition affecting the leakage characteristic.

The Effect of Surface Roughness on the Convection Heat-Transfer Coefficient for Fully Developed Turbulent Flow in Ducts With Uniform Heat Flux

1959 ◽  
Vol 81 (2) ◽  
pp. 168-173 ◽  
Author(s):  
R. T. Lancet
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Friction Factor ◽  
Convection Heat Transfer ◽  
Uniform Heat Flux ◽  
Friction Factors ◽  
Fully Developed Turbulent Flow ◽  
The Heat Transfer Coefficient ◽  
Effect Of Surface

Experimental data are presented for the heat-transfer coefficient and friction factor in a smooth and a rough duct with a hydraulic diameter of approximately 0.035 in. The flow was fully developed and turbulent, and the heat addition was uniform over the length of the tube. The rough tube indicated appreciable increases in heat-transfer coefficient and friction factor. The smooth-tube friction factors corresponded to rough-tube values, indicating the difficulty involved in obtaining smooth surfaces for very small ducts.

A Heat-Mass Transfer Analogy Applied to Fully Developed Turbulent Flow in an Annulus

1971 ◽  
Vol 13 (4) ◽  
pp. 286-292 ◽  
Author(s):  
J. S. Lewis
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Friction Factor ◽  
Heat Mass Transfer ◽  
Eddy Diffusivity ◽  
Round Tube ◽  
Fully Developed Turbulent Flow ◽  
The Difference

A heat-mass transfer analogy based on the ‘universal’ velocity profile applied to an annulus is compared with analogy values based on similar but more sophisticated expressions for the eddy diffusivity and hence velocity profile. The difference between these analogy values and those of Chilton and Colburn (I)† are noted to be appreciable and to increase with increasing Reynolds number. Heat transfer predictions from mass transfer measurements using ‘universal’ velocity profile type analogies are compared with established results. Friction factor measurements were made and found to be up to 10 per cent higher than the values for flow in a round tube at the corresponding Reynolds number.

An Experimental and Analytical Investigation of Friction Factors for Fully Developed Flow in Internally Finned Triangular Ducts

1986 ◽  
Vol 108 (3) ◽  
pp. 507-512 ◽  
Author(s):  
H. Chegini ◽  
S. K. Chaturvedi
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Reynolds Numbers ◽  
Analytical Investigation ◽  
Momentum Equation ◽  
Fully Developed Flow ◽  
Finite Difference Technique ◽  
Friction Factors ◽  
Experimental Values ◽  
Good Agreement

Friction factors for fully developed flow in triangular ducts with fins of various height and width are investigated for Reynolds numbers ranging from 150 to 90,000. Two triangular ducts having apex angles of 60 and 38.8 deg are studied. Results are presented in the form of standard plots of friction factor as a function of Reynolds number. Friction factor values for the smooth triangular duct cases are in good agreement with the existing results. For the finned-duct cases, the fully developed axial velocity profiles in laminar flow are determined by solving the x-momentum equation iteratively by the Gauss–Seidel finite-difference technique. The theoretically determined friction factors for these cases are in good agreement with the experimental values of friction factors based on pressure drop measurements.

scholarly journals Turbulent channel flow of an elastoviscoplastic fluid

2018 ◽  
Vol 853 ◽  
pp. 488-514 ◽  
Author(s):  
Marco E. Rosti ◽  
Daulet Izbassarov ◽  
Outi Tammisola ◽  
Sarah Hormozi ◽  
Luca Brandt
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Channel Flow ◽  
Viscosity Ratio ◽  
Turbulent Channel Flow ◽  
Turbulent Regime ◽  
Bingham Number ◽  
Wide Range ◽  
Near Wall

We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier–Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increases monotonically with the Bingham number (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the friction factor is almost independent of the viscosity ratio and decreases with the Bingham number, until the flow eventually returns to a fully laminar condition for large enough yield stresses. Three main regimes are found in the turbulent case, depending on the Bingham number: for low values, the friction Reynolds number and the turbulent flow statistics only slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number, the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flow completely laminarizes. These different behaviours are associated with a progressive increases of the volume where the fluid is not yielded, growing from the centreline towards the walls as the Bingham number increases. The unyielded region interacts with the near-wall structures, forming preferentially above the high-speed streaks. In particular, the near-wall streaks and the associated quasi-streamwise vortices are strongly enhanced in an highly elastoviscoplastic fluid and the flow becomes more correlated in the streamwise direction.

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