Turbulent Friction Factor Research Articles

Numerical Solution of Convective Heat Transfer for Reverse Transition in the Bend Tube by a Low-Reynolds-Number Turbulent Model

By adopting an appropriate near-wall function in a K-ε model, turbulent convective heat transfer in the 90o-bend tube with a straight tail section has been analyzed numerically for a low-Reynolds-number turbulent-flow regime. The results are presented in the form of velocity profile, temperature distribution, turbulent intensity distribution, friction factor and heat transfer for the condition of a heat flux constant. The proposed model of the near-wall function describes well the low-Reynolds-number turbulence field including a reverse transition mechanism.

Flow of dilute polymer solutions in a two-dimensional channel. 1st report. Turbulent friction factors and velocity distributions.

Turbulent friction factors of dilute aqueous solutions of polyethylene oxide measured in a two-dimensional channel. The influence of viscoelasticity on friction loss is considered by the method of dimensional analysis and the friction factor is correlated with the Reynolds number and the Weissenberg number. Velocity distributions also are measured by using a pitot tube. It is shown that the transition layer in the flow of dilute polymer solutions becomes thicker in comparison with that of Newtonian.

A Review of Explicit Friction Factor Equations

A review of the explicit friction factor equations developed to replace the Colebrook equation is presented. Explicit friction factor equations are developed which yield a very high degree of precision compared to the Colebrook equation. A new explicit equation, which offers a reasonable compromise between complexity and accuracy, is presented and recommended for the calculation of all turbulent pipe flow friction factors for all roughness ratios and Reynold’s numbers.

Predicting turbulent friction factors of non-newtonian fluids in noncircular ducts

On the basis of limited experimental data it appears that the procedure developed by Jones for predicting turbulent friction factors for Newtonian fluids in rectangular and concentric annular ducts may be extended to purely viscous non-Newtonian fluid in noncircular ducts using the Reynolds number introduced by Kozicki.

Empirical correlations of turbulent friction factors and heat transfer coefficients for viscoelastic fluids

Empirical correlations for the friction factor and the dimensionless heat transfer coefficients are proposed as functions of the Reynolds and Weissenberg numbers. If the rheological properties of the polymer solution including the characteristic time are known, the friction factor and dimensionless heat transfer coefficient of a polymer solution in a circular pipe can be estimated. Additionally, these empirical correlations can be used to determine the characteristic time of a dilute or highly degraded polymer solution with a simple pressure drop measurement.

Analytic Prediction of the Friction Factor for Turbulent Flow in Internally Finned Channels

This work develops an analytical model for the friction factor with turbulent flow in internally finned channels. Such channels are an important class of enhanced heat transfer surfaces. Until this work, no analytical models for the turbulent friction factor have been proposed. The present model assumes the validity of the Law of the Wall and applies the logarithmic velocity distribution to the interfin and core regions of the flow. Theoretically based friction factor equations are developed for internally finned circular tubes and rectangular channels. The model predicts Carnavos data for 21 internally finned tubes within ± 10 percent. Friction factor data were taken for five internally finned, rectangular channels. The analytical model predicts these data within ± 10 percent, except for the case of a very high fin.

Analytical studies on local flow blockages in LMFBR subassemblies, using the UZU code

Abstract Extensive experimental and analytical studies on local flow blockages in LMFBR subassemblies have been performed in several countries. However, analytical tools have not yet been established. In the present study, therefore, a three-dimensional analytical code, UZU, has been developed for analysing important factors which affect the flow and temperature fields in locally blocked subassemblies. In the UZU code a subchannel approach was employed and the finite difference equations, consisting of momentum, mass and energy balances, were solved by the SOR method. The special features of this code are: (1) fluid properties are functions of local fluid temperature, consequently buoyancy is included in the momentum equations, (2) fluid flow properties, such as turbulent friction factors and eddy diffusivities, are expressed as functions of local fluid velocities, geometries and physical properties, (3) peripheral subchannels are treated separately from inner ones, (4) thickness and porosity of a blockage plate can be considered and (5) a blockage at the upstream end of a grid spacer can be dealt with. The validity of the code was proven by comparison with the measured velocity, pressure and temperature distributions in simulation experiments conducted in parallel with the code development.

The turbulent flow of non-Newtonian fluids in the absence of anomalous wall effects

For Newtonian fluids, the engineering predictions for pressure drop in turbulent pipe flow are well established. However, in the case of non-Newtonian liquids, only a few design techniques have been proposed and these do not share a common basis with the approach for Newtonian systems. This present work attempts to provide a common basis for both Newtonian and non-Newtonian systems in situations where anomalous wall effects are absent. Previously published experimental data suggest that if the Reynolds number is calculated on the basis of the apparent viscosity at the wall then the standard Newtonian correlations can be used for the prediction of pressure drop. The use of the wall viscosity in defining the Reynolds number also serves as a test for anomalous behaviour. Any departure of the experimental data from the Newtonian turbulent friction factor correlation indicates anomalous behaviour.

Transport of Oils as Oil-in-Water Emulsions

Turbulent flow pressure drop measurements were made for various concentrated oil-in-water emulsions which exhibit non-Newtonian behavior. The effects of oil viscosity, temperature and oil concentration on specific energy loss were evaluated. Measured turbulent friction factors consistently fell below those predicted by the Dodge and Melzner friction factor correlation, probably due to viscoelastic effects of the emulsion. Several polymer and surfactant drag reducers were tested in these emulsions, and high molecular weight polyacrylamides were found to be the most effective in further reducing pumping energy losses. The effectiveness of the polymer additives decreased with time during pump circulation.

Flow and Heat Transfer in Convectively Cooled Underground Electric Cable Systems: Part 1—Velocity Distributions and Pressure Drop Correlations

Velocity distributions and pressure drop correlations have been obtained experimentally for a wide range of physical, flow, and thermal parameters in three models of oil-cooled underground electric cable systems. The flow can be considered as consisting of several, interconnected, parallel channels. If one of these is significantly larger in cross section, it will dominate the behavior of the entire system with velocities up to an order of magnitude greater than in the other channels. Laminar, fully developed flow exists at a dimensionless entrance length as low as x/DH = 100. The turbulent velocity profiles are essentially uniform in the larger, main channel, but not in the small channels with lower velocities. Laminar friction factors can be correlated with an equivalent Reynolds number, based on the main flow channel alone, as fe·Ree = 30. Turbulent friction factors increase with increasing skid wire roughness ratios and approach the asymptotic values of 0.013 and 0.021 for roughness ratios 0.0216 and 0.0293, respectively. Cable heating had no noticeable effect on the friction factor correlations.

Determination of a bed friction factor for Botany Bay, Australia

A method for the determination of the bed friction factor in the rough turbulent regime under field conditions is presented. The method uses prototype wave measurements and hydraulic model data. A relationship between irregular offshore and inshore waves is developed, and this expression is used to transfer measured wave data from a deep water location to locations nearer shore. Waves are also measured at these latter points, and a comparison between measured and calculated spectral data at two near-shore locations is the basis for calculation of the turbulent bed friction factor. Refraction is allowed for through the use of coefficients measured in the hydraulic model of Botany Bay, after correction for the laminar bed friction occurring in the model. The effects of offshore wave direction and tidal stage on refraction are considered. The results show a considerable scatter, as is to be expected because of the wide range of parameters that must be brought into account and the difficulty of measuring some of these. On average the values obtained support the expressions proposed by Jonsson (1966) and by Riedel, Kamphuis and Brebner (1972). They also indicate, in common with other field studies of this question, that the value of the friction factor is substantially more than the 0.01 that has been widely used as an approximation.

Transition from laminar to turbulent flow of purely viscous non-Newtonian fluids in tubes

A criterion for stability of laminar flow of purely viscous non-Newtonian fluids is proposed and compared with the criterion of Ryan and Johnson, and Hank. The proposed criterion is found to be in good agreement with the experimental findings given in the available literature. A generalized relation for the laminar friction is derived in terms of the dimensionless groups. Further, the use of the differential viscosity in Reynolds number is demonstrated to predict the turbulent friction factor to give single valued correlation.

A Method for the Determination of the Local Turbulent Friction Factor and Heat Transfer Coefficient in Generalized Geometries

A method is presented for the determination of the distributions of velocity, local friction, and heat transfer coefficients in a forced axial turbulent flow with an arbitrary cross section. The method uses as basis the characteristics of the laminar flow. A comparison is made with some experimental results concerning different geometries.

Turbulent friction factor and velocity profile in smooth annuli

A new correlation equation, based on available accurate experimental data, is derived for finding the friction factor in a smooth annulus. A single law is proposed giving the velocity profile for an annulus or a circular tube, by improving Spalding's profile with velocity as the independent variable.

Turbulent Flow Properties of Dilute Polymer Solutions

RECENTLY, Gadd1,2 and Hoyt3 reported results of experiments on the turbulent flow characteristics of dilute polymer solutions, and showed that the addition of very low concentrations of polymer molecules (of the order of 50 weight parts per million) to water greatly reduced the turbulent friction acting at surfaces moving relative to the fluid. This phenomenon was attributed to the formation of normal stress differences, because other physical properties such as density and viscosity are sensibly unchanged. Work carried out in this department on the flow of very dilute polymer solutions and other additives in water confirms these findings. Measurements have been made of the turbulent friction factor for flow of these solutions in glass and metal pipes of varying surface roughnesses for Reynolds numbers up to 12,000 and for flow past arrays of spheres. Up to 25 per cent reduction in friction factor was observed in flow in tubes. Although we agree on the formation of normal stress differences on addition of small traces of polymeric substances to water, we would also suggest that in some instances adsorption of the solute at the solid surface can occur which will influence the flow in the boundary layer near the solid surface. Similar work carried out by El'perin and Smolskii confirms this4. The importance of these surface effects can be easily demonstrated in pipes, because it has been shown that when the flow of the solution is stopped and water reintroduced the friction factor measured is initially lower than that expected. This effect can persist for up to 15 min, dependent on the flow conditions, and is several orders of magnitude greater than the residence time of the fluid in the tube.

Measurement and correlation of turbulent friction factors of thoria suspensions at elevated temperatures

Measurement and correlation of turbulent friction factors of thoria suspensions at elevated temperatures

Closure to “Discussion of ‘Plane Turbulent Wall Jet Flow Development and Friction Factor’” (1963, ASME J. Basic Eng., 85, pp. 53–54)

Closure to “Discussion of ‘Plane Turbulent Wall Jet Flow Development and Friction Factor’” (1963, ASME J. Basic Eng., 85, pp. 53–54)

Transport characteristics of suspensions: Part IV. Friction loss of concentrated‐flocculated suspensions in turbulent flow

AbstractTurbulent flow friction factors were determined for flocculated suspensions of thoria, kaolin, and titania in tubes 1/8‐ to 1‐in. diameter. The non‐Newtonian laminar flow data were arbitrarily fitted with the Bingham plastic model. With this model the range of yield stress values was 0.018 to 1.39 lb.f/sq. ft., with a maximum ratio of coefficient of rigidity to viscosity of suspending medium of 11.1. The volume fraction solids were varied from 0.042 to 0.23.Two types of behavior were observed depending on the value of the yield stress. For yield values less than 0.5 lb.f/sq. ft. the turbulent friction factors were always less than those for Newtonian fluids but tended to approach the Newtonian values as the Reynolds number was increased. For yield values greater than 0.5 lb.f/sq. ft. the friction factors were again less than those for New‐tonian fluids but tended to diverge from the Newtonian values as the Reynolds number was increased. Both sets of data were correlated with the Blasius relation with the coefficient and exponent given in terms of the laminar flow properties und the volume fraction solids.

The Effect of a Longitudinal Magnetic Field on Pipe Flow of Mercury

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.