Wall Friction Factor Research Articles

A new approach for modeling of gas-condensate flow through pipelines under industrial operating conditions

The main objective of this study is to achieve a comprehensive integrated two-phase/single-phase hydrodynamic model for gas-condensate flows through transmission pipelines under industrial operating conditions, i.e. large pipe size and elevated pressure. The model developed in the present work covers single-phase gas, mist flows, and also all flow patterns occurring in transition from stratified to annular having liquid volume fraction from 0.005 to 0.3. Flanigan's correlation was corrected in the way that it was applicable for mist two-phase flow under industrial operating conditions. For liquid film holdup, Grolman and Fortuin model and Taitel and Duckler approaches were employed for uphill and downhill two-phase flows respectively. Grolman and Fortuin and BJA methods were applied to find pressure drop through upward and downward pipelines respectively. Two new relations for predicting liquid–gas and liquid–wall friction factors, which were obtained based on fitting to the field data, were used in Grolman and Fortuin model. 200 field pressure data were collected by conducting a field experiment on an industrial gas-condensate pipeline. 160 of these field data were applied to make the required corrections to the model including the development of two new correlations for both liquid–gas and liquid–wall friction factors. The rest of the data points were utilized to verify the model. The comparison of the present model results with the field data revealed that the proposed model is capable of predicting pressure drop accurately in gas-condensate pipelines.

Investigations on single-phase natural circulation loop dynamics. Part 2: Role of wall constitutive laws

Unlike forced circulation systems, natural circulation systems need to be started from the state of zero flow. Literature study shows that under low flow conditions, the velocity field near the wall is significantly modified by secondary convection currents particularly during diabatic conditions. In view of this, the applicability of conventional forced convection wall constitutive laws to these systems has been investigated both theoretically and experimentally. First the applicability of conventional wall constitutive laws derived from steady state forced convection experiments is examined. Next, the results of experimental investigations carried out in a rectangular natural circulation loop are presented. Finally, a new correlation for wall friction factor is proposed for flow in horizontal pipes under diabatic conditions.

Influence of geometrical parameters of hexagonal, circular, and rhombus microchannel heat sinks on the thermohydraulic characteristics

Microchannel heat sink (MCHS) can be done with several cross-section channel shapes. Water flow and heat transfer characteristics are affected by the geometrical parameters of the microchannel which are numerically investigated in this paper. This study covers Reynolds number values in the range of 100–1000 and heat flux is maintained at 500kW/m2. Finite volume method (FVM) is used to solve the governing equations and 3D steady state conjugate heat transfer problem. The effects of three different channel shapes (hexagonal, circular, and rhombus) on the MCHS performance are investigated in details. The assessment of MCHS performance is based on a number of exclusive attributes which are temperature profile, heat transfer coefficient, pressure drop, friction factor, and thermal resistance. The results show that the smallest hydraulic diameter of the hexagonal cross-section MCHS has the highest pressure drop and heat transfer coefficient among other shapes. The highest value of the top wall temperature, friction factor and thermal resistance are found with the use of rhombus cross-section MCHS.

Effect of bubbles and additives on friction factor in pipeline flow

AbstractThis work investigated drag reduction in turbulent flow of water using air bubbles and other additives. The first phase of the experimental program dealt with the effects of small air bubbles on wall shear stress and friction factor. The friction factor versus Reynolds number data exhibited different trends at low and high Reynolds numbers. At high Reynolds number, the two‐phase mixture behaved as a pseudo‐homogeneous system and the friction factor followed the single‐phase behaviour. At low Reynolds number, the observed friction factor was significantly higher than that of single‐phase fluids. The observed trends were interpreted in terms of the average bubble sizes predicted from a well‐known empirical equation. The second phase of the experimental program investigated the effects of additive/air‐bubble combinations on drag reduction in water flow where the additives used were frother and polymer. The addition of frother made the flow more homogeneous and the mixture followed the single‐phase behaviour more closely. In the absence of polymer, the injection of air bubbles generally increased the wall shear stress and friction factor compared to single‐phase flow, especially at low Reynolds number. However, the addition of polymer to two‐phase water/bubbles mixture induced drag reduction up to as high as 60%. The friction factor data for polymer‐solution/bubbles combination followed the polymer‐solution line, regardless of the presence of frother.

Numerical simulation to evaluate gas diffusion of turbulent flow in mine ventilation system

Tracer gas technique is a method to analyze the airflow path, measure the airflow quantity, and detect any recirculation or leakages in underground mine. In addition, it is also possible to evaluate the axial gas diffusion of gas in turbulent bulk flow by utilizing the tracer gas data. This paper discussed about the measurement using tracer gas technique in Cibaliung Underground Mine, Indonesia and the evaluation of effective axial diffusion coefficient, E, by numerical simulation. In addition, a scheme to treat network flow in mine ventilation system was also proposed. The effective axial diffusion coefficient for each airway was evaluated based on Taylor’s theoretical equation. It is found that the evaluated diffusion coefficient agrees well with Taylor’s equation by considering that the wall friction factor, f, is higher than those for smooth pipe flow. It also shows that the value of effective diffusion coefficient can be inherently determined and the value is constant when matching with other measurements. Furthermore, there are possibilities to utilize the tracer gas measurement data to evaluate the airway friction factors.

Experimental study on heat transfer and pressure drop in mercury flow system for spallation neutron source

In the design of MW-class spallation target system, using mercury to produce practical neutron applications, keeping the highest level of safety is vitally important. To establish the safety of spallation target system, it is essential to understand the thermal hydraulic properties of mercury. Through thermal hydraulic experiments using a mercury experimental loop, which flows at the rate of 1.2 m3/hr maximum, the following facts were experimentally confirmed. The wall friction factor was relatively larger than the Blasius correlation due to the effects of wall roughness. The heat transfer coefficients agreed well with the Subbotin correlation. Furthermore, for validation of the design analysis code, thermal hydraulic analyses were conducted by using the STAR-CD code under the same conditions as the experiments. Analytical results showed good agreement with the experimental results, using optimized turbulent Prandtl number and mesh size.

Roughness effects of commercial steel pipe in turbulent flow: universal scaling

The mean turbulent flow over a transitional rough commercial steel pipe is considered in terms of alternate inner roughness variables. The matching of inner layer and outer layer in the overlap region leads to the universal log laws for velocity profile and friction factor, explicitly independent of surface roughness of all kinds. The roughness function, for commercial steel pipe differs from inflectional (sand grain) roughness. The traditional wall law and friction factor depends on type of surface roughness.

Laminar Mixed Convection in the Entrance Region of Horizontal and Inclined Semicircular Ducts

Laminar mixed convection in the entrance region of horizontal and inclined semicircular ducts has been investigated. The governing momentum and energy equations were solved numerically using a marching technique with finite control volume approach following the SIMPLER algorithm. Results were obtained for thermal boundary condition of uniform heat input axially and uniform wall temperature circumferentially, incorporating Pr = 7, Re = 500, inclination angles (α = 0° and 20°), and a wide range of Grashof numbers. These results include velocity and temperature distributions at different axial locations as well as axial distribution of local Nusselt number and local wall friction factor. It was found that Nusselt number is close to the forced convection values near the entrance region, then decreases to minimum value as the distance from the entrance increases, and then rises due to the effect of free convection before reaching a constant value (fully developed). As Grashof number increases Nusselt number and wall friction factor increase in both developing and fully developed regions for horizontal and inclined ducts. A comparison with the experimental data in the thermal entrance region was also conducted and the comparison was satisfactory.

Prediction of pressure gradient and holdup in wavy stratified liquid–liquid inclined pipe flow

Pressure gradient and holdup data are presented for oil–water flow in a horizontal and inclined 0.026m i.d. pipe (borosilicate glass, 15.5m length and pipe inclinations of −10°, −20° and +10°). A wavy stratified flow in the laminar-turbulent regime with no dispersion whatsoever at the interface was observed. The relatively high-viscosity oil flow (280mPas) dominates the friction and the low Eötvös number indicates the existence of a wavy and curved interface. A new closure relation for the interfacial friction factor is suggested. Recent interfacial wave amplitude data are used for the proposition of a correlation for the interfacial friction factor based on the equivalent-sand-roughness concept. An explicit equation for the interface shape based on the constant-curvature-arc model is proposed, which is a function of the Eötvös number, holdup and contact angle. A discussion on the typical contact angles observed in liquid–liquid flow in pipes of different materials is carried out. It was found that for the slower lighter phase (oil) the effective wall friction factor is significantly lower than the single-phase friction factor, corresponding to an increase of the respective hydraulic diameter. CFD simulations provided an estimate of the cross-sectional wave shape and delivered holdup and pressure gradient results. The phenomenological model is validated against data from the literature and its predictions are compared with present data, models from the literature and CFD results. The favorable comparisons and simplicity of the proposed closure relations are promising, aiming to practical application.

Integration of large-scale experiments and numerical simulations for the calibration of friction laws in volcanic conduit flows

The eruptive columns of explosive volcanism are fed by a gas–particle conduit flow, which characteristics determine the eruptive regime and are important for assessing the hazard of active volcanoes. In this paper, by means of the combined use of large-scale experiments and numerical modeling, a study on some parameters of the gas–particle conduit flow of explosive eruptions is carried out. A 1D two-phase non-homogeneous Eulerian–Eulerian model has been developed for checking the influence of some crucial quantities: interphase drag, particle–wall friction and particle shape factor. Hundreds of different parameters combinations are tested and used for the simulation of controlled experimental runs. The parameter combination that best fits the whole set of experiments, including both column collapses and convective plumes, results into an average error of about 10%. A further analysis has been carried out to determine the sensitivity of solutions to model parameters. The choice of the interphase drag does not influence dramatically the solution, except for highly concentrated flows. The particle shape factor severely affects gas and particle velocities. The influence of various particle–wall friction laws, which were originally obtained in pneumatic engineering, is thoroughly investigated, as the suitability of these laws has never been proved in volcanology. A detailed parametric analysis allowed the re-calibration of two of these laws, which are now specifically tailored for the case of highly concentrated conduit flows that feed collapsing columns, and dilute flows that feed convective plumes.

Non-Newtonian multi-phase flows: On drag reduction, pressure drop and liquid wall friction factor

The present work focuses on the non-Newtonian liquid drag reduction by gas injection. Two regimes are taken in consideration: fully stratified gas shear-thinning liquid flow and gas shear-thinning liquid slug flow regimes. Predictions of drag reduction ratio and holdup are presented for the stratified flow of gas and non-Newtonian Ostwald-de Waele liquid. Fully stratified flow is considered and the approach developed in Taitel and Dukler (1976) is used. For these regimes, CMC (CarboxyMethyl Cellulose) solution is used in order to investigate the behaviour of the gas and non-Newtonian liquids in horizontal pipes. Results have been reformulated and an extension to interfacial Andreussi and Persen (1987) correlation has been carried out for stratified regimes. For slug flow regimes, the mechanistic slug unit model is adopted in order to estimate the pressure gradients along the slug unit. The slug unit model is rearranged and reinterpreted as inviscid Burgers's equation for incompressible phases. For both stratified and slug flow regimes, three dimensional CFD (computational fluid dynamics) simulations were performed in order to compare the drag reduction ratio and pressure gradients. In stratified flows, CFD is also used in an attempt to evaluate the liquid wall friction factor and to compare the obtained values with those given by empirical standard correlations.

Investigations on the role of mixed convection and wall friction factor in single-phase natural circulation loop dynamics

The objective of the present paper is to present a 1-D model for simulating the startup from rest of water cooled single-phase natural circulation loops having horizontal heaters. The starting point of analysis is the inability of the 1-D codes to account for natural convection in the heater. Present 1-D models are unable to account for axial diffusion in the fluid caused by natural convection. Start-up from rest and many other characteristics cannot be simulated using classical 1-D models because of the inherent tendency of the predicted dynamics to be attracted by zero flow condition. The paper presents an elegant approach for taking into account both natural and forced convection. The enhancement of fluid motion and thermal mixing by natural convection is an important consideration in the design of nuclear reactors. Hence, the model developed is of direct relevance to nuclear reactor thermal hydraulics. The model developed for natural convection has been validated against the CFD simulations. The model developed has been incorporated in a classical 1-D model developed by the authors previously. The application of model to a rectangular single-phase natural circulation loop show that the model can predict the loop behavior from start-up with fidelity. The model reproduces most of the characteristics like unidirectional oscillation, bidirectional oscillations and chaotic switching reasonably well. Finally, model has been used to investigate the phenomenon of hysteresis observed in experimental loop. The paper also brings out the role of constitutive laws for wall friction in predicting the loop dynamics.

Effect of void fraction and friction factor models on the prediction of pressure drop of R134a during downward condensation in a vertical tube

The theoretical flow models of homogeneous and separated flow are applied to in-tube condensation to predict the pressure drop characteristics of R134a. The homogeneous flow model is modified by ten different dynamic viscosity correlations and various alternative correlations of total, frictional and momentum pressure drops to take account of the partial condensation inside the tube. Numerical analyses were performed to determine the average and local homogeneous wall shear stresses and friction factors by means of a CFD program. The equivalent Reynolds number model is modified by six different two-phase friction factors to determine the total condensation pressure drop in the separated flow model. The refrigerant side total pressure drops, frictional pressure drops, friction factors and wall shear stresses are determined within a ±30% error band. The importance of using the alternative total, momentum and frictional pressure drop correlations for the homogeneous flow model is also shown.

Mechanism Analysis on Stress Accumulation in Cylindrical Vertical-Placed Metal Hydride Reactor

It’s known that the pulverization-densification mechanism of metal hydride may cause the stress accumulation in metal hydrides reactors. In this paper, this idea is proved based on granulometry and a new idea of cycling compression effect is presented, which is caused by the friction between wall and metal hydrides. Through theoretical analysis, the cycling compression effects is shown to increase the localized packing rate from top to down in vertical-placed reactors and thus lead to the maximum deformation in the bottom of reactors, proving that it is the interaction of pulverization-densification effect and cycling compression effect resulting in the stress problems of vertical-placed reactors. Further study points that the effective methods relieving the cycling compress effect are to decrease hydrogen absorption/desorption cycle number, slenderness ratio of reactor, wall friction factor and initial packing rate, or to lower the thermal conductivity and the volume expansion coefficient of metal hydrides.

1603 流れ加速型腐食におけるCFDの活用(OS16.エネルギー機器システムの設計・保守へのCFD適用,OS・一般セッション講演)

Turbulent mass transfer, which is one of the key factors on the evaluation of flow accelerated corrosion (FAC), was considered using the analogy with the turbulent heat transfer. The mass transfer in the straight pipe is suggested to be proportional to the wall friction factor as well as the turbulence energy. We proposed the effective friction velocity taking the turbulent velocity near wall surface into account, which is used to evaluate the mass transfer at the turbulent region such as elbow and the downstream of orifice. STAR-CCM+ code with realizable k-ε two-layer model is used to evaluate the mass transfer at the turbulent region, in which wall function is not used and lattice points are taken in the viscous sublayer to evaluate mass transfer near wall surface of turbulent region. By introducing a concept of "Threshold Mass Transfer Coefficient", geometry factor correlations were evaluated for elbow, orifice, T-union and separation, quantitatively.

Interfacial friction factor determination using CFD simulations in a horizontal stratified two-phase flow

Stratified two-phase gas–liquid flow in three-dimensional (3D) is challenging because of the difficulty in determining the shear stresses at the walls and at the gas–liquid interface. The study is simplified by considering only the gas and the gas–liquid interface. The gas flows between the fixed wall of the pipe and the interface, which is regarded as wall moving at liquid velocity. It is shown, using a CFD code, that one can determine the correct horizontal and vertical profiles of the longitudinal velocity of the gas. Seven experiments done by Strand (1993) for a horizontal stratified gas–liquid flow are simulated. The simulation results are compared with experimental results, and also to the numerical results of Meknassi et al. (2000). We deduce from these comparisons that the approach suggested in this work is very valuable. Then expressions for calculating the gas–wall friction factor, and the gas–liquid interface friction factor are presented. These factors are crucial for evaluating the shear stresses. It appears, after comparison with the experimental values that the correlation proposed for calculating the friction factor at the interface, in the present work, agree with the experimental values better than that given by Taitel and Duckler (1976a, b).

Wall friction effects and viscosity reduction of gel propellants in conical extrusion

Influence of wall friction on mean apparent viscosity reduction of gel propellants in conical radial flow extrusion is investigated analytically and numerically. A parametric study has been conducted to evaluate the effects of injector geometry, rheological constants, wall friction factor and volumetric flow rate on fluid viscosity profile. Gel propellants were modeled by the non-Newtonian power law constitutive relation. The influence of wall friction on the mean apparent viscosity, on wall slip and on pressure gradient is found to be substantial. Central results are supported by asymptotic analysis for small cone angles and low wall friction. Contact is made with lubrication type flow pattern.

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

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.

Wall surface effects on particle–wall friction factor in upward gas–solid flows

The variation of the particle–wall friction factor along the riser is investigated in an Internal Circulating Fluidized Bed (ICFB) riser 1 m in length and 0.052 m in diameter. The results obtained are based on calculating the normal and the shear forces at the wall under dynamic conditions rather than the static ones usually obtained in shear box experiments. The strength of the method used resides in the measurement technique applied to measure the particle velocity field in the riser. The radioactive particle tracking program was developed for coaxial systems and is used to build dynamic pictures of particle trajectories in the vicinity of the wall of the ICFB riser. The experiments were conducted using sand ( d p = 250 µm) and alumina ( d p = 170 µm) materials in the gas velocity range between 2 and 12 m/s. The most common correlations for calculating the particle–wall friction factor are reviewed and compared to the results obtained in this work. The data obtained demonstrates that the particle–wall friction factor is not a constant value but changes along the riser and with change in the gas superficial velocity. The results also show the effect of the roughness of the wall surface and define the particle–wall friction factor area.

応力比が粉体圧推定結果に及ぼす影響

Janssen's equation is widely used to calculate the powder pressure in a silo. Physical properties necessary for the powder pressure calculation are bulk density, wall friction factor and stress ratio. In the physical properties, bulk density and wall friction factor can be measured directly by the mechanical tests of the powder. But the stress ratios are evaluated indirectly from the Yield Loci of powder beds. Therefore, if the evaluated results of stress ratios differ by the approximation methods of a yield locus, it would be considered that the approximation methods affect the calculated results of powder pressures. But few studies on the effects of approximation method of Yield Locus on stress ratios can be found.In this paper, we describe Yield Locus from shear test results by Coulomb's equation, Warren-Spring's equation and our proposed equation and evaluate stress ratios. We also evaluated the stress ratio using the equation recommended by ISO and compared it with other methods. Furthermore, we calculated the powder pressure in a silo from the stress ratios by Janssen's equation. These calculated results are compared with experimental results and the effectiveness of our proposed equation is confirmed.