Friction Factor For Turbulent Flow Research Articles

Prediction of pressure gradient and hold-up in horizontal liquid-liquid pipe flow

This paper aims to propose correlations to predict pressure gradient, friction factor and fluid phase hold-up in liquid-liquid horizontal pipe flow. To develop the correlations, experiments are conducted using high viscous oils (202 and 630 mPa⋅s) in a steel pipe of length 11.25 m and length-to-diameter ratio of 708. In addition, the experimental data from the literature comprising wide range of flow and fluid properties is analyzed. For the analysis, the liquid-liquid pipe flow data is categorized into two as: stratified and dispersed. The existing friction factor correlations are modified to incorporate the effects of viscosity of the oil phase, interfacial curvature (contact/wetting angle-in lieu of material of the pipe) and fluid phase fraction. In the two-fluid model of stratified flow, the wall stress and interfacial stress correlations are substituted with superficial velocities of fluids and superficial Reynolds numbers of fluid phases replacing fluid phase velocities and fluid Reynolds numbers. Similarly, for dispersed flow, an effective Reynolds number is described as the sum of superficial Reynolds number of oil and water phases. Substituting the generally employed mean or mixture Reynolds number with the effective Reynolds number into the existing single-phase turbulent flow friction factor correlation, an effective friction factor for oil-water flow is proposed. Employing the proposed correlations, the pressure gradient across the oil-water flow and hold-up volume fraction are predicted with significant reduction in error compared with that of conventionally employed correlations. The average error and standard deviation values of −7.06%, 20.72% and 0.31%, 18.79% are found for stratified flow and dispersed flow respectively.

On friction factor of fluid channels fabricated using selective laser melting

ABSTRACT The fabrication quality of horizontal fluid channels without supports using SLM is low, which further affects friction loss in channels. In the paper, circular fluid channels with diameters from 2 to 14 mm were built horizontally using 316L SS. The surface roughness on the top inner channel is 50–80 μm, while the rest part is approximately 10 μm. The cylindricity is around 0.2 and circularity is 0.16. The fabrication quality was significantly improved using reduced energy input with a compensation model. Friction factor measurements indicate that 75/Re is still valid in laminar flow regardless of fabrication quality. The friction factor in turbulent flow is 0.0034–0.0137, which is higher than the classical theory. Improved fabrication quality slightly reduces the friction factor. A corrected Colebrook model is developed to predict the friction factors for SLM horizontal fluid channels. Building orientation and fluid path need to be considered for reducing pressure loss.

A new friction factor formula for single phase liquid flow through geothermal pipelines

Proper selection of pumps has been an important issue for energy efficiency in geothermal energy. In a research conducted among machines that consume electricity, pumps come first with 25 %. Accurate estimation of pressure losses is a key point in order to select pump systems. Hot water from the geothermal area is carried by pipeline systems. In this study, extensive experimental study is conducted at Izmir Katip Celebi University Flow Loop using pure water for fluid temperature from 25 °C to 60 °C, for four various relative roughness values, and for Reynolds Number ranges from 6.2 × 104 to 7.8 × 105. This study has mainly two objectives: First is to identify if the absolute pipe roughness values of commercially available pipes vary according to the pipe diameter. The second objective is to investigate fluid temperature effects on frictional pressure losses in rough pipes and to present a new friction factor correlation for using in geothermal pipelines, considering the fluid temperature effects. Experimental study shows that absolute pipe roughness varies substantially for pipe diameters. The proposed friction factor has a good agreement with explicit formulas of Blasius (1913) and Taler (2016) equations for smooth pipes and Colebrook (1939) equation for rough pipes, as well as experimental data at various temperature values.Additionally, frictional pressure losses are accurately estimated using new friction factor equation. Results show that both relative roughness and temperature have a significant influence on the friction factor for turbulent flow through rough pipes. For this reason, pipe roughness should be determined correctly and the effects of fluid temperature on pressure losses should be considered. This may influence frictional head losses per unit length and, consequently, the predicted pumping requirements in geothermal pipelines.

Explicit solutions for turbulent flow friction factor: A review, assessment and approaches classification

Abstract The Colebrook –white equation is widely used in many fields, like civil engineering for calculation of water distribution systems and in all fields of engineering where fluid flow can be occurred. Numerous formulas have been proposed since 1947 in order to simplify the computation of the friction factor, to avoid the iterative procedures methods and to alter the Colebrook-white equation in practice. most of the existing explicit formulas for computation of the friction factor for turbulent flow in rough pipes proposed are cited, where thirty three “33” equations have been inventoried. The goal of this paper is to assess the accuracy of each model and to propose an arrangement from the best to the lower accuracy according to a proposed method combined of three criteria which are: simplicity of the formula, maximum deviations and the coverage of the entire range of Moody diagram.

Correlations for heat transfer coefficient and friction factor for turbulent flow of air through square and hexagonal ducts with twisted tape insert

The experimental and numerical Nusselt number and friction factor investigation for turbulent flow through a non-circular duct with twisted-tape inserts have been presented. The non-circular ducts include square, hexagonal duct. The results of non-circular ducts are compared with circular duct. All the ducts have same equivalent diameter. The twist ratios used for the experiment are Y = 3.5, 4.5, 5.5 and 6.5. Experiments were carried out on square duct, hexagonal duct and circular duct. The Reynolds number lied between 10,000 and 1, 05,000. The present study is restricted to the flow of air at Pr = 0.7 only and within a narrow temperature range of 40 to 75 ΟC, within which the compressible nature of air can be neglected. The results reveal that, both Nusselt number and friction factor increases as the side of non-circular duct increases. Maximum Nusselt number and friction factor is obtained in case of circular duct with twisted tape. Further the correlations of Nu and f are given for different non circular duct with twisted tape insert for engineering applications for the turbulent regime. Since the thermal performance factor (η) is observed to be within the range of 0.8 to 1.13 for both circular and noncircular ducts, the overall benefit of using twisted tape in the flow field shall nevertheless be marginal.

Determining velocity and friction factor for turbulent flow in smooth tubes

The most popular explicit correlations for the friction factor in smooth tubes are reviewed in this paper. The friction factor for the turbulent flow in smooth tubes is required in some correlations when calculating the Nusselt number. To calculate the friction factor, the velocity profile in a turbulent smooth wall-tube must be estimated at first. The radial velocity distribution was determined using either universal velocity profile found experimentally by Reichardt or by integration the momentum equation using the eddy diffusivity model of Reichardt. The friction factor obtained by using the universal velocity profile gives better results than that obtained from the momentum equation when compared with the Prandtl–von Kármán–Nikuradse equation. Based on the velocity profiles proposed by Reichardt the friction factor was calculated as a function of the Reynolds number and subsequently two formulas for the friction were proposed. They have satisfactory accuracy when comparing with the implicit Prandtl–von Kármán–Nikuradse equation. Thus, it was concluded that the universal velocity profile proposed by Reichardt will provide good results when it is taken into account while integrating the energy conservation equation. There is also a considerable number of experimental correlations for the friction factor in smooth tubes. All these relationships were compared with the experimental data and with the implicit Prandtl–von Kármán–Nikuradse equation that is considered as a standard to test the explicit approximations. The Colebrook and Filonienko explicit correlations are widely used when calculating the Nusselt number for the turbulent flow but they have noticeable errors for small Reynolds number ranged from 3000 to 7000 for the Colebrook relation and from 3000 to 30,000 for the Filonienko relation. For this reason, a new simple and accurate correlation for the friction factor for Reynolds numbers between 3000 and 107 is proposed in the paper.

Theoretical analysis of heat transfer and friction factor for turbulent flow of nanofluids through pipes

AbstractA numerical model for determining the turbulent characteristics of fluid flow and heat transfer is presented, treating certain constants in the van Driest eddy diffusivity equation of momentum and heat as variables. The viscosity and thermal conductivity of nanofluids are estimated using regression equations. It was observed that the turbulent characteristics of nanofluids are different from those of water. The numerical results indicate a higher velocity of SiO2 nanofluid and lower eddy diffusivity compared to Cu under similar operating conditions. The nanofluid temperature gradient increases with concentration and decreases with temperature. However, the temperature gradient is significantly influenced by the particle density. Equations for estimating the coefficient and the Prandtl index in the eddy diffusivity equations of momentum and heat, respectively, are developed as a function of Reynolds number, concentration, and nanofluid properties. The Prandtl index value decreases with increasing concentration, reflecting the reduction in heat transfer coefficients observed at lower operating temperatures.

Improved method of determining friction factor in pipes

Purpose– The purpose of this paper is to present an improved computational method for determining the friction factor for turbulent flow in pipes.Design/methodology/approach– Given that the absolute pipe roughness is generally constant in most systems, and that there are few changes to the pipe diameter, the proposed method uses a simplified equation for systems with a specific relative pipe roughness. The accuracy of the estimation of the friction factor using the proposed method is compared to the values obtained using the implicit Colebrook-White equation while the computational efficiency is determined by comparing the time taken to perform 300 million calculations.Findings– The proposed method offers a significant improvement in computational efficiency for its accuracy and is compared 28 of the explicit equations currently in use.Practical implications– This method enables a simplified equation to offer a significant improvement in computational efficiency for its accuracy and is easier to code, enabling engineers to more efficiently calculate frictional pressure loss for flow in pipes.Originality/value– Due to the complexities in flow regime and pipe roughness, there is a limit to the scope for further computational efficiency through simplification of the explicit equation. This paper presents a new method and simplified equation which combined are able to deliver results with similar accuracy to less computationally efficient explicit equations.

Discussion of “Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation” by Saeed Samadianfard [ J. Pet. Sci. Eng. 92–93 (2012) 48–55

Maximal relative error of the explicit approximation to the Colebrook equation for flow friction presented in the discussed paper by Saeed Samadianfard [J. Pet. Sci. Eng. 92–93 (2012) 48–55; doi. 10.1016/j.petrol.2012.06.005] is investigated. Samadianfard claims that his approximation is very accurate with the maximal relative error of no more than 0.08152%. Here is shown that this error is about 7%. Related comments about the paper are also enclosed.

A review of non iterative friction factor correlations for the calculation of pressure drop in pipes

Pressure drop in pipes can be calculated by using the Darcy-Weisbach formula. In order to use this formula, the Darcy friction factor should be known. The best approximation to the Darcy friction factor for turbulent flow is given by the Colebrook-White equation. This equation can only be solved by numerical root finding methods. There are several other approximate correlations to the Darcy friction factor with some relative error compared to the Colebrook-White equation. It was found that in some of these correlations, the percentage error is so small that they can be used directly in place of the Colebrook equation. In this study, a review of several friction factor correlations is performed. Relative error of these correlations is re-evaluated against the Reynolds number for a different value of relative pipe roughness. Also statistical analyses will be given for each correlation.

Experimental Investigations on Heat Transfer and Friction Factor of Silver Nanofliud in Absorber/Receiver of Parabolic Trough Collector with Twisted Tape Inserts

Heat Transfer and friction factor data at various volume concentrations for flow in absorber/Receiver and with and without twisted tape inserts is determined experimentally (with water and silver Nanofluid). The experiments are conducted in the Reynolds number range 500≤ Re<≤ 6000 with twisted tape inserts of different twist ratios in the range 0.577 ≤H/D/≤1.732. This study shows that twisted tape inserts when used shows great promise for enhancing heat transfer rate in absorber .The heat transfer coefficient and friction factor of 0≤ Ф≤0.1% volume concentration of silver Nanofliud are higher compared to flow of water in absorber/receiver. The experiments show that Nussult Number, friction factor and enhancement efficiency are found to be 1.25 -2.10 times, 1.0 -1.75 times and 135%-205%, respectively, over, plain absorber/receiver of parabolic trough collector. Finally new generalized correlations function for predicting heat transfer and friction factor for turbulent flow of both water and Silver Nanofliud are proposed with tape inserts

Comment on “Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation”

Abstract Recently, it is investigated ( Samadianfard, 2012 ) the potential of genetic programming based technique in estimating flow friction factor in comparison with the most currently available explicit alternatives to the Colebrook's equation. Using iterative solution of the Colebrook's equation which is accurate to six significant digits, this discussion showed that the proposed approximation by the author for friction factor is not very accurate (the errors increase up to 7.374%), thus it is proposed two new accurate approximations (with maximum error less than 0.022% and 0.008%) for estimating flow friction factor.

Very accurate explicit approximations for calculation of the Colebrook friction factor

To date, the Colebrook equation is mostly accepted as an unofficial standard for calculation of the friction factor in turbulent flow through pipes. Unfortunately, the unknown friction factor in the Colebrook equation is given implicitly. Therefore, the implicit Colebrook equation has to be solved in an iterative procedure or using some of the appropriate explicit correlations proposed by many authors. Although the iterative solution is simple and very accurate, it can cause some problems during the calculation of looped network of pipes or similar systems of pipes. Therefore, explicit approximations are favorable in these cases. Up to date, the most accurate approximations have maximal relative error of no more than 0.14% compared to the very accurate iterative solution. Here two explicit approximations are presented, based on already existing models which are improved using genetic algorithms optimization. They are with the maximal relative error of no more than 0.0083% and 0.0026%.

Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes

The implicit Colebrook–White equation is the accepted method for accurately estimating the friction factor for turbulent flow in pipes. This study reviews 28 explicit equations for approximating the friction factor to integrate both the accuracy to the implicit Colebrook–White equation and the relative computational efficiency of the explicit equations. A range of 901 Reynolds numbers were selected for the review between Re ≥ 4 ×103 and ≤ 4 × 108 and 20 relative pipe roughness values were selected between \(\varepsilon \mathord{\left/ {\vphantom {\varepsilon D}} \right.}D\ge 10^{-6}\le 10^{-1}\), thus producing a matrix of 18,020 points for each explicit equation, covering all the values to be encountered in pipeline hydraulic analysis for turbulent flow. The accuracy of the estimation of the friction factor using the explicit equations to the value obtained using the implicit Colebrook–White equation were calculated and reported as absolute, relative percentage and mean square errors. To determine the relative computational efficiency, 300 million friction factor calculations were performed using randomly generated values for the Reynolds number and the relative pipe roughness values between the limits specified for each of the explicit equations and compared to the time taken by the Colebrook–White equation. Finally, 2D and 3D contour models were generated showing both the range and magnitude of the relative percentage accuracy across the complete range of 18,020 points for each explicit equation.

Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation

Estimating head losses due to friction in closed pipes is an important task in the solution of many practical problems in the different branches of the engineering profession. The hydraulic design and analysis of water distribution systems are two prime examples. Many consider the Darcy–Weisbach equation to be the most fundamentally sound method for evaluating head losses due to friction in closed pipe conduits. The implicit Colebrook–White equation has been widely used to estimate the friction factor for turbulent fluid-flow in Darcy–Weisbach equation. A fast, accurate, and robust resolution of the Colebrook–White equation is, in particular, necessary for scientific intensive computations. For instance, numerical simulations of pipe flows require the computation of the friction coefficient at each grid point and for each time step. For long-term simulations of long pipes, the Colebrook–White equation must therefore be solved a huge number of times and hence this is the main reason for attempting to develop an accurate explicit relationship that is a reasonable approximation for the Colebrook–White equation. This paper examines the potential of genetic programming (GP) based technique in estimating flow friction factor in comparison with the most currently available explicit alternatives to the Colebrook–White equation. The performance of the gene expression programming (GEP), a variant of GP, was compared with most available approximations using some statistic parameters for error estimation. The comparison test results reveal that by using GEP, the friction factor can be identified precisely.

HYDRAULIC STUDY OF DRILLING FLUID FLOW IN CIRCULAR AND ANNULAR TUBES

This study investigates the drilling fluid flow behavior of two water-based drilling fluids in circular and annular tubes. The study has four main objectives: 1) to evaluate correlations between the Power Law and the Casson rheological models, 2) to characterize the flow behavior, 3) to evaluate five hydraulic-diameter equations, and 4) to evaluate the correlations of five turbulent flow-friction factors. The experimental fluid flow loop consisted of one positive displacement pump of 25 HP connected to a 500-liter tank agitated by a 3-HP mixer. The fluids passed through six meters long tubes, arranged in three horizontal rows with independent inlets and outlets. The circular tubes had a 1 inch diameter and were configured as two concentric annular tubes. Annular Tube I had an outer diameter of 1 ¼ inch and an inner diameter of ½ inch. Annular Tube II had an outer diameter of 2 inches and an inner diameter of ¾ inch. The results show that, for the fluids in exam, correlations proposed in the literature were inaccurate as far as predicting hydraulic diameter, estimating pressure drop, and defining the flow regime. In general, the performance of those correlations depended on the fluid properties and on the system’s geometry. Finally, literature parameters for some of the correlations were estimated for the two drilling fluids studied. These estimations improved the predictive capacity of calculating the friction factor for real drilling fluids applications for both circular and annular tubes.

Heat transfer enhancement and development of correlation for turbulent flow through a tube with triple helical tape inserts

Influence of triple helical tapes inserted for turbulent flow through a tube on heat transfer enhancement was studied experimentally. The triple helical tapes made of mild steel with different helix angles, α = 9°, 13°, 17°, and 21° were examined for Reynolds number ranging from 22,000 to 51,000. The experiment showed that the Nusselt number, effectiveness and friction factor for the inserts were found to be up to 4.5, 3.45 and 3.0 times, respectively, over the plain tube. The highest enhancement efficiency achieved was 3.7 for the inserts based on constant blower power. Finally, new correlations for predicting heat transfer and friction factor for turbulent flow through a circular tube fitted with the inserts were proposed.

Turbulent heat transfer enhancement in a triangular duct using delta-winglet vortex generators

The augmentation of convective heat transfer of a turbulent flow using delta-winglet vortex generators (VG) in a triangular duct was experimentally investigated. Two side walls of the heated test section are electrically heated with a constant heat flux while the lower wall is indirectly heated. Single, double, and triple pairs of VG are utilized. Each pair of VG was punched on one wall of the test duct. The effects of the number of VG pairs, the VG angle of attack, the VG location from the leading edge of the test duct, the VG geometry, and Reynolds number are examined in this paper. The results indicate that the Nusselt number and friction factor are relatively proportional to the size, number, and the inclination angle of the VG. The Nusselt number increases and the friction factor decreases as the Reynolds number increases. The present results were compared with the available literature and they show good agreement. Correlation equations of Nusselt number and friction factor for turbulent flow are developed, for the cases studied, as a function of Reynolds number and VG angle of attack. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20382

Closure to the Discussion of “Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation” by Dejan Brkić

Closure to the Discussion of “Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation” by Dejan Brkić

New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations

The determination of single-phase friction factor of pipe flow is essential to a variety of industrial applications, such as single-phase flow systems, two-phase flow systems and supercritical flow systems. There are a number of correlations for the single-phase friction factor. It still remains an issue to examine similarities and differences between them to avoid misusing. This paper evaluates the correlations for the single-phase friction factor against the Nikuradse equation and the Colebrook equation, respectively. These two equations are the base for the turbulent portion of the Moody diagram, and are deemed as the standard to test the explicit counterparts. The widely used correlations for smooth pipes, the Blasius correlation and the Filonenko correlation, have big errors in some Re ranges. Simpler forms of the single-phase friction factor covering large ranges are needed. For this reason, two new correlations of single-phase friction factor for turbulent flow are proposed, one for smooth pipes and the other for both smooth and rough pipes. Compared with the Nikuradse equation, the new correlation for smooth pipes has the mean absolute relative error of 0.022%, with the maximum relative error of −0.045% in the Reynolds number (Re) range from 3000 through 108. It is an idea replacement of the correlations of Blasius and Filonenko. The new correlation for both smooth and rough pipes has the mean absolute relative error of 0.16% and the maximum relative error of 0.50% compared with the Colebrook equation in the range of Re=3000–108 and Rr=0.0–0.05, which is the most simplest correlation in that error band.