scholarly journals Discussion of “Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” by Dejan Brkić and Pavel Praks, Mathematics 2019, 7, 34; doi:10.3390/math7010034

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 793
Author(s):  
Majid Niazkar
Keyword(s):  
Friction Factor ◽  
Evaluation Criteria ◽  
Standard Approach ◽  
Accuracy Evaluation ◽  
Engineering Applications ◽  
Flow Friction ◽  
Friction Factors ◽  
One Step

Estimating the Darcy–Weisbach friction factor is crucial to various engineering applications. Although the literature has accepted the Colebrook–White formula as a standard approach for this prediction, its implicit structure brings about an active field of research seeking for alternatives more suitable in practice. This study mainly attempts to increase the precision of two explicit equations proposed by Brkić and Praks. The results obviously demonstrate that the modified relations outperformed the original ones from nine out of 10 accuracy evaluation criteria. Finally, one of the improved equations estimates closer friction factors to those obtained by the Colebrook–White formula among 18 one-step explicit equations available in the literature based on three of the considered criteria.

A Review of Explicit Friction Factor Equations

1985 ◽  
Vol 107 (2) ◽  
pp. 280-283 ◽  
Author(s):  
D. J. Zigrang ◽  
N. D. Sylvester
Keyword(s):  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Explicit Equation ◽  
Flow Friction ◽  
Friction Factors ◽  
High Degree ◽  
Very High

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.

scholarly journals Review of explicit approximations to the Colebrook relation for flow friction

2017 ◽  
Author(s):  
Dejan Brkić
Keyword(s):  
Friction Factor ◽  
Iterative Solution ◽  
Pipe System ◽  
Flow Friction ◽  
Relative Roughness ◽  
Wide Range ◽  
Accepted Standard ◽  
One Step ◽  
Hydraulic Friction Factor ◽  
Moody Diagram

Because of Moody's chart has demonstrated applicability of the Colebrook equation over a very wide range of Reynolds number and relative roughness values, this equation becomes the accepted standard of accuracy for calculated hydraulic friction factor. Colebrook equation suffers from being implicit in unknown friction factor and thus requires an iterative solution where convergence to 0.01% typically requires less than 7 iterations. Implicit Colebrook equation cannot be rearranged to derive friction factor directly in one step. Iterative calculus can cause a problem in simulation of flow in a pipe system in which it may be necessary to evaluate friction factor hundreds or thousands of times. This is the main reason for attempting to develop a relationship that is a reasonable approximation for the Colebrook equation but which is explicit in friction factor. A review of existing explicit approximation of the implicit Colebrook equation with estimated accuracy is shown in this paper. Estimated accuracy compared with iterative solution of implicit Colebrook equation is shown for the entire range of turbulence where Moody diagram should be used as the reference. Finally, it can be concluded that most of the available approximations of the Colebrook equation, with a few exceptions, are very accurate with deviations of no more than few percentages.

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

1988 ◽  
Vol 110 (4) ◽  
pp. 385-391 ◽  
Author(s):  
W. F. Scaggs ◽  
R. P. Taylor ◽  
H. W. Coleman
Keyword(s):  
Friction Factor ◽  
Roughness Element ◽  
Discrete Element ◽  
Turbulent Pipe Flow ◽  
Number Range ◽  
Flow Friction ◽  
Friction Factors ◽  
Roughness Model ◽  
Factor Data ◽  
Good Agreement

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.

scholarly journals New explicit correlations for turbulent flow friction factor

2017 ◽  
Author(s):  
Dejan Brkić
Keyword(s):  
Turbulent Flow ◽  
Friction Factor ◽  
Pipe Flow ◽  
Single Phase ◽  
Turbulent Pipe Flow ◽  
Pipe Surface ◽  
Flow Friction ◽  
Total Absence ◽  
Friction Factors ◽  
Transient Zone

Two new correlations of single-phase friction factor for turbulent pipe flow are shown in this paper. These two formulas are actually explicit approximations of iterative Colebrook's relation for calculation of flow friction factor. Calculated friction factors are valid for whole turbulent flow including hydraulically smooth and rough pipes with special attention on transient zone of turbulence between them. Hydraulically smooth regime of turbulence does not occur only in total absence of roughness of inner pipe surface, but also, four new relations for this theoretical regime are presented. Some recent formulas for turbulent flow friction calculation are also commented.

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.

Characterization of the Effect of Corrugation Angles on Hydrodynamic and Heat Transfer Performance of Four-Start Spiral Tubes

2001 ◽  
Vol 123 (6) ◽  
pp. 1149-1158 ◽  
Author(s):  
X. D. Chen ◽  
X. Y. Xu ◽  
S. K. Nguang ◽  
Arthur E. Bergles
Keyword(s):  
Heat Transfer ◽  
Evaluation Criteria ◽  
Geometry Optimization ◽  
Longitudinal Direction ◽  
Experimental Results ◽  
Neural Network Modeling ◽  
Transfer Coefficients ◽  
Correlation Models ◽  
Friction Factors ◽  
Double Pipe

A series of four-start spirally corrugated tubes has been subjected to heat transfer and hydrodynamic testing in a double-pipe heat exchanger. The study has been focused on the non-symmetric nature of the corrugation angles along the longitudinal direction. Both friction factors and heat transfer coefficients inside the tubes have been correlated against various process parameters. It can be shown that by altering the internal non-symmetric wavy shapes of the tubes, one is able to manipulate heat transfer and friction characteristics. The experimental results have been compared with some popular correlation models developed previously for both friction and heat transfer for corrugated tubes. Considerable differences between the experimental results and the predictions made using the existing correlations have been found and the probable causes have been discussed. Performance evaluation criteria are presented using the standard constant power criterion. A neural network modeling approach has been taken so that, based on the limited data, one can generate the contour showing the effect of corrugation angle on heat transfer coefficient for geometry optimization purposes.

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 130 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation is implicitly given in respect to the unknown flow friction factor λ; λ = ζ ( R e , ε * , λ ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. A common approach to solve it is through the Newton–Raphson iterative procedure or through the fixed-point iterative procedure. Both require in some cases, up to seven iterations. On the other hand, numerous more powerful iterative methods such as three- or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require, in the worst case, only two iterations to reach the final solution. The recommended representatives are Sharma–Guha–Gupta, Sharma–Sharma, Sharma–Arora, Džunić–Petković–Petković; Bi–Ren–Wu, Chun–Neta based on Kung–Traub, Neta, and the Jain method based on the Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between the iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

Friction factor analysis for a nanofluid circulating in a microchannel filled with a homogeneous porous medium

2022 ◽  
Author(s):  
Francisco Fernando Hernandez ◽  
Federico Mendez ◽  
Jose Joaquin Lizardi ◽  
Ian Guillermo Monsivais
Keyword(s):  
Porous Medium ◽  
Friction Factor ◽  
Porous Matrix ◽  
Velocity Profiles ◽  
Momentum Equation ◽  
Volumetric Concentration ◽  
Forchheimer Equation ◽  
Viscosity Models ◽  
Friction Factors ◽  
Homogeneous Porous Medium

Abstract This work presents the numerical solution for different velocity profiles and friction factors on a rectangular porous microchannel fully saturated by the flow of a nanofluid introducing different viscosity models, including one nanofluid density model. The Darcy-Brinkman-Forchheimer equation was used to solve the momentum equation in the porous medium. The results show that the relative density of the fluid, the nanoparticle diameters and their volumetric concentration have a direct influence on the velocity profiles only when the inertial effects caused by the presence of the porous matrix are important. Finally, it was found that only viscosity models that depend on temperature and nanoparticle diameter reduce the friction factor by seventy percent compared to a base fluid without nanoparticles; furthermore, these models show a velocity reduction of even ten percent along the symmetry axis of the microchannel.

scholarly journals Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function: Reply to the Discussion by Majid Niazkar

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 796
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Monte Carlo ◽  
Friction Factor ◽  
Large Scale ◽  
Optimization Procedure ◽  
Flow Friction ◽  
Quasi Monte Carlo

In this reply, we present updated approximations to the Colebrook equation for flow friction. The equations are equally computational simple, but with increased accuracy thanks to the optimization procedure, which was proposed by the discusser, Dr. Majid Niazkar. Our large-scale quasi-Monte Carlo verifications confirm that the here presented novel optimized numerical parameters further significantly increase accuracy of the estimated flow friction factor.

Sign in / Sign up

Export Citation Format

Share Document