Friction Factor Data Research Articles

On the use of the stratified momentum balance for the deduction of shear stress in horizontal gas–liquid pipe flow

The use of the stratified flow momentum balance for the deduction of interfacial and liquid wall shear stresses from experimental measurements is examined. A systematic error analysis is applied to the governing equations using the principle of maximum uncertainty. A series of air–water experiments were conducted in 50 and 80 mm diameter pipes, in which gas pressure drop, liquid height and gas wall shear stress were measured. A framework for the correlation of the deduced shear stresses is proposed from the experimental measurements. The uncertainty analysis is used to show that the definition of mean liquid height does not significantly influence the overall results. The development of empirical equations based on such methods may lead to total uncertainties of up to 40%, irrespective of accuracy of the experimental data or the appropriateness of the correlating technique. Comparisons with state-of-the-art correlations for the liquid wall and interfacial friction factor data showed even larger discrepancies between measurement and prediction.

Mean-flow scaling of turbulent pipe flow

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.

Turbulent Flow in Longitudinally Finned Tubes

An experimental investigation of fully developed, steady, turbulent flow in longitudinally finned tubes has been performed. A two-channel, four-beam, laser-Doppler velocimeter was used to measure velocity profiles and turbulent statistics of air flow seeded with titanium dioxide particles. Mean velocities in axial, radial, and circumferential directions were measured over the tube cross sections and pressure drop in the tubes was measured at six stations along the test section length in order to calculate the fully developed friction factor. Four experimental tube geometries were studied: one smooth tube; two 8-finned tubes (fin height-to-radius ratios of 0.333 and 0.167), and one 16-finned tube (fin height-to-radius ratio of 0.167); Detailed measurements were taken at air flow rates corresponding to Reynolds numbers of approximately 5000, 25,000, and 50,000. Friction factor data were compared to literature results and showed good agreement for both smooth and finned tubes. The wall shear stress distribution varied significantly with Reynolds number, particularly for Reynolds numbers of 25,000 and below. Maximum wall shear stress was found at the fin tip and minimum at the fin root. Four secondary flow cells were detected per fin (one in each interfin spacing and one in each core region for each fin); secondary flows were found to be small in comparison to the mean axial flow and relative magnitudes were unaffected by axial flow rate at Reynolds numbers above 25,000. The fluctuating velocities had a structure similar to that of the smooth tube in the core region while the turbulence in the interfin region was greatly reduced. The principal, primary shear stress distribution differed considerably from that of the smooth tube, particularly in the interfin region, and the orientation was found to be approximately in the same direction as the gradient of the mean axial velocity, supporting the use of an eddy viscosity formulation in turbulence modeling.

The vascularized iliac crest and bone graft anatomy, indications and results

This paper introduces new CFD-based correlations for ribbed roughened solar air heater. An absorber plate of SAH (solar air heater) attached with circular ribs is analyzed in this article. ANSYS Fluent v16 is utilized to analyze the turbulent airflow for different arrangements of rib. All results are based on CFD (computational fluid dynamics) simulations. The analysis is carried out within the limits of Re from 3800 to 18,000 and P from 10 to 25. The resulting data is reduced into correlations using a linear stepwise regression algorithm. The developed equations for artificially roughened heater of solar air predict all the data for friction factor and Nusselt number within ±5% relative absolute deviation.

Turbulent Flow in Integrally Enhanced Tubes, Part 2: Analysis and Performance Comparison

Abstract This article analyzes heat transfer and friction factor data for single-phase, turbulent flow inside enhanced tubes for different enhanced tube types and from different data sources. Data are given for several enhanced tube types such as extruded tubes (ribs or disruptions with transverse and intermediate helix angles), spirally indented tubes, and tubes with coil inserts. In general, there is good agreement between the heat transfer data for tubes of the same type—manufactured with the same method—from different investigations with essentially the same disruption height, pitch, and helix angle. The variations increase (20–30%) when comparisons are made with similar core geometries but different types such as indented and extruded, or indented and coil inserts. The performance of tubes with coil inserts is very similar to that of tubes with discrete extruded disruptions. There is substantially more deviation of the friction factor data from different sources, even for the same tube type. Also, the analysis shows that more care is required to obtain repeatable and high-quality friction factor data than heat transfer data.

Turbulent Flow in Integrally Enhanced Tubes, Part 1: Comprehensive Review and Database Development

Abstract Thermal performance improvements through passive and active enhancement methods have been studied intensely for over three decades. Heat exchangers with single-phase lube-side flow are one of the important applications where passive surface-modification methods are popularly employed. Ribs, indentations, spiral flutes, and coil inserts are some common surface modification techniques that are relatively easy to manufacture, are cost effective for many applications, and can be used conveniently for retubing existing heat exchangers. This article describes a comprehensive database that was developed to provide easy access to existing single-phase tube-side heat transfer and pressure drop data for different enhanced tube designs, in a consistent and useful manner. The database contains four files: (1) friction factor data, (2) heat transfer data, (3) tube characteristics, and (4) features of the experiments used by each data source, such as fluid type, boundary conditions, tube material, and tube type. The friction factor database contains nearly 5,000 data points, and the heat transfer database contains more than 4,700 data points. The data encompass more than 360 different tube geometries from over 35 investigations. The information can be used by practicing engineers for validatating and /or developing prediction methods, or to compare or estimate the performance of a specific tube design.

Mixed convection laminar flow and heat transfer of liquids in isothermal horizontal circular ducts

Numerical analysis of thermally developing and simultaneously developing mixed convection flow and heat transfer with variable viscosity in an isothermal horizontal tube has been carried out. Parametric computations were performed to investigate the effect of inlet Prandtl number, inlet Rayleigh number, wall-to-inlet temperature difference, and inlet axial velocity profile on the Nusselt numbers and apparent friction factors for both heating and cooling conditions. The results indicate that the effect of variable viscosity is more pronounced on the friction factor than on Nusselt numbers. In addition, the effect of inlet Rayleigh number and inlet velocity profile on the Nusselt numbers and friction factors exists only in the near-inlet region. A parameter found by scaling analysis was used to empirically correlate the computed Nusselt number and the friction factor data and the available experimental Nusselt number data for both thermally developing and simultaneously developing flow and heat transfer. The developed correlations are more accurate, have wider ranges of applicability than those available in the literature, and should be of much use to designers.

Concentric annular flow with centerbody rotation of a Newtonian and a shear-thinning liquid

Measurements of the radial distributions of the axial and tangential components of velocity and rms velocity fluctuations are presented together with friction factor versus Reynolds number data for two liquids, one Newtonian, the other a shear-thinning polymer, in laminar, transitional, and turbulent flow in an annular geometry with a rotating centerbody of radius ratio 0.506. In all flow regimes, the friction factor is increased by centerbody rotation. However, the influence is slight and most apparent for laminar flow of the Newtonian fluid. Laser Doppier anenometry (LDA) measurements of the tangential velocity reveal three distinct regions across the radial gap with a central region of almost constant angular momentum, which diminishes in magnitude as the Reynolds number increases. Axial velocity measurements show only slight deviations from what would be expected for the case without centerbody rotation. In turbulent flow, the axial velocity fluctuations decrease progressively with increasing Reynolds number for all fluids. For the polymeric liquid, the tangential velocity fluctuations are somewhat suppressed, especially at high Reynolds numbers where the influence of centerbody rotation is reduced. Over a limited range of (low) Reynolds numbers and rotation speeds, the generation and advection of Taylor vortices produces complex flow patterns. Limited measurements are reported for the vortex advection speed.

Prandtl Number Influence on Heat Transfer Enhancement in Turbulent Flow of Water at Low Temperatures

The paper presents the results of an experimental study that was carried out to determine the Prandtl number influence on the thermal-hydraulic performance of enhanced tubes. The enhanced tubes were identical in all aspects, except the roughness height. Emphasis was placed on turbulent flow, with water as the working fluid. Experiments were performed for Prandtl numbers from 10.2 to 5.8. Data for friction factor were obtained under both isothermal and heating conditions. The study confirmed the strong influence of rib roughness on heat transfer and pressure drop increase. In addition, the results of the investigation strongly suggest that the optimum roughness is application specific, because it is dependent on Reynolds and Prandtl numbers. The results show that the presence of entrance effects and the influence of temperature on the friction factor of enhanced tubes may be significant. The experiments show that a rib height-to-diameter ratio of 0.02 provides the best overall performance for water at Pr = 10; while at Pr = 6.0, the optimum e/d depends on the Reynolds number.

Heat Transfer and Pressure Drop Characteristics of Spirally Fluted Annuli: Part II—Heat Transfer

This paper is the second of two papers that present the results of a comprehensive study of heat transfer and pressure drop in annuli with spirally fluted inner tubes for the laminar, transition, and turbulent flow regimes. Fourteen fluted tubes with varying geometries were studied, with up to three outer smooth tubes for each fluted tube. Flow patterns and transitions between flow regimes investigated through visualization tests, friction factor data (from Part I), and tube surface-temperature measurements were used to explain the enhancement phenomena. The fluted inner tubes induced a significant degree of swirl in the flow, and transition occurred in the 310 < Re < 1000 range. A Nusselt number correlation was developed in terms of the fluted annulus friction factor developed in Part I and geometric parameters. Nusselt numbers were between 4 and 20 times the smooth annulus values in the low Re range, while turbulent enhancements were between 1.1 and 4.0. These enhancement values can be used in conjunction with friction factor increase values reported in Part I to determine appropriate ranges of applicability for spirally enhanced annuli.

Flow of shear-thinning fluids in a concentric annulus

Distributions of mean axial velocity, axial and tangential turbulence intensities together with friction factor versus Reynolds number (f-Re) data are presented for three non-Newtonian liquids in fully developed laminar, transitional and turbulent flow in an annular geometry in the absence of centrebody rotation. Each of the non-Newtonian fluids was shear thinning and to some extent elastic and one was also thixotropic in character. For comparison purposes, measurements are also reported for a Newtonian fluid.

Thermal and Friction Factor Data for Three Packed Block Construction Wavy Fin Surfaces

This paper describes an experimental work undertaken to determine performance data for packed block wavy fins. A purpose-built heat exchanger testing wind tunnel was used to investigate three wavy surfaces. The data were then presented in the form of Colburn (j) factors and friction (f) factors versus Reynolds number. Results showed a favourable comparison with published works pertaining to similar surface geometries; in addition, geometries were also tested which varied considerably from those in the literature to date.

Heat transfer performance comparisons of five different rectangular channels with parallel angled ribs

This paper systematically presents the results of heat transfer and friction factor data measured in five short rectangular channels with turbulence promoters. The project investigated the combined effects of the channel aspect ratio, rib angle-of-attack, and flow Reynolds number on heat transfer and pressure drop in rectangular channels with two opposite ribbed walls. The channel aspect ratio (width-to-height, W/ H, ribs on side W) varied from 1 4 to 1 2 , to 1, 2. and 4, while the corresponding rib angles-of-attack a were 90°, 60°, 45°, and 30°, respectively. The Reynolds number range was 10,000–60,000. The results suggest that the narrow aspect ratio channels ( W/ H < 1) give much better heat transfer performance than the wide aspect ratio channels ( W/ H > 1). For the square channel ( W/ H = 1), the 60° 45° angled ribs provide the best heat transfer performance. For the narrow aspect ratio channel ( W/H = 1 4 or 1 2 ), the 45° 60° angled ribs are recommended while the 30° 45° angled ribs are better for wide aspect ratio channels ( W/ H = 4 or 2).

Experimental investigation of heat transfer and pressure drop characteristics of flow through spirally fluted tubes

Spirally fluted tubes are used extensively in the design of tubular heat exchangers. In previous investigations, results for tubes with flute depths e/ D vi < 0.2 were reported, with most correlations applicable for Re ≥ 5000. This paper presents the results of an experimental investigation of the heat transfer and pressure drop characteristics of spirally fluted tubes with the following tube and flow parameter ranges: flute depth e/ D vi = 0.1−0.4, flute pitch p/ D vi = 0.4−7.3, helix angle θ/90° = 0.3−0.65, Re = 500−80,000, and Pr = 2−7. The heat transfer coefficients inside the fluted tube were obtained from measured values of the overall heat transfer coefficient using a nonlinear regression scheme. The friction factor data obtained consisted of 507 data points. The proposed correlation for the friction factor predicts 96% of the database within ±20%. The heat transfer correlation for the range 500 ≤ Re ≤ 5000 predicts 76% of the database (178 data points) within ±20%, and the correlation for the higher Re range predicts 97% of the 342 data points within ±20%. Comparison of heat transfer and friction data show that these tubes are most effective in the laminar and transition flow regimes. The present results show that the increase of flute depth in the range considered does not improve heat transfer.

Friction-Factor Characteristics for Narrow Channels With Honeycomb Surfaces

The experimental determination of friction-factors for the flow of air in a narrow channel lined with various honeycomb geometries has been carried out. Test results show that, generally, the friction-factor is nearly constant or slightly decreases as the Reynolds number increases, a characteristic common to turbulent flow in pipes. However, in some test geometries this trend is remarkably different. The friction factor dramatically drops and then rises as the Reynolds number increases. This phenomenon can be characterized as a “friction-factor jump.” Further investigations of the acoustic spectrum and friction-factor measurements for a broad range of Reynolds numbers indicate that the “friction-factor jump” phenomenon is accompanied by an onset of a normal mode resonance excited coherent flow fluctuation structure, which occurs at Reynolds number of the order of 104. The purpose of this paper is not to present the friction-factor data but to explain the friction-factor-jump phenomenon and friction-factor characteristics.

Closure to “Discussion of ‘Friction-Factor Data for Flat-Plate Tests of Smooth and Honeycomb Surfaces’” (1992, ASME J. Tribol., 114, pp. 729–730)

Closure to “Discussion of ‘Friction-Factor Data for Flat-Plate Tests of Smooth and Honeycomb Surfaces’” (1992, ASME J. Tribol., 114, pp. 729–730)

Friction-Factor Data for Flat-Plate Tests of Smooth and Honeycomb Surfaces

Friction-factors for honeycomb surfaces are measured with a flat plate tester. The flat plate test apparatus is described and a method is discussed for determining the friction-factor experimentally. The friction-factor model is developed for the flat plate test based on the Fanno Line Flow. The comparisons of the friction-factor are plotted for smooth surface and twelve-honeycomb surfaces with three-clearances, 6.9 bar to 17.9 bar range of inlet pressure, and 5,000 to 130,000 range of the Reynolds number. The optimum geometries for the maximum friction-factor are found as a function of cell width to cell depth and clearance to cell width ratios.

Friction factor and wall heat transfer for laminar and turbulent flow in a cylindrical duct with a wall-stabilized arc

Friction factor and wall heat-transfer data for axially symmetric flow in a wall-stabilized arc analysis are given. Heat transfer results revealed three significant modes: laminar flow with an unstable arc, laminar flow with a wall-stabilized arc, and turbulent flow with a wall-stabilized arc. It was shown that the critical Reynolds number increases, in comparison with the case of the flow without Joule heating. A friction factor from Reynolds-number dependence peculiarities was not discovered for laminar to turbulent flow transition. >

Diamond-Bit Hydraulics Model

Summary This paper describes an analytical technique that calculates the fluid velocities and pressures under a surface-set diamond bit. The technique is based on solving the continuity and energy equations for a series of flow cells that covers the bit face. Each cell is described with geometrical dimensions and an integrated property model to account for flow around the cutters. Experimental data from simulated diamond-bit segments provide friction-factor data and model validation. The results of analyzing a commercial diamond bit are also presented. The model is being developed to improve the hydraulic design of diamond bits.

Measurement and Prediction of Rough Wall Effects on Friction Factor—Uniform Roughness Results

The results of an experimental investigation of the effects of surface roughness on turbulent pipe flow friction factors are presented and compared with predictions from a previously published discrete element roughness model. Friction factor data were acquired over a pipe Reynolds number range from 10,000 to 600,000 for nine different uniformly rough surfaces. These surfaces covered a range of roughness element sizes, spacings and shapes. Predictions from the discrete element roughness model were in very good agreement with the data.