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.

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 Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

2017 ◽  
Author(s):  
Dejan Brkić ◽  
Žarko Ćojbašić
Keyword(s):  
Turbulent Flow ◽  
Friction Factor ◽  
Iterative Solution ◽  
Good Prediction ◽  
Pipe Surface ◽  
Flow Friction ◽  
Relative Roughness ◽  
Complex Models ◽  
Transient Zone ◽  
Maximal Relative Error

Today, Colebrook’s equation is mostly accepted as an informal standard for modeling of turbulent flow in hydraulically smooth and rough pipes including transient zone in between. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of inner pipe surface (ε/D). It is implicit in unknown friction factor (λ). Implicit Colebrook’s equation cannot be rearranged to derive friction factor (λ) directly and therefore it can be solved only iteratively [λ=f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)]. Of course, approximations carry in certain error compared with the iterative solution where the highest level of accuracy can be reached after enough number of iterations. The explicit approximations give a relatively good prediction of the friction factor (λ) and can reproduce accurately Colebrook’s equation and its Moody’s plot. Usually, more complex models of approximations are more accurate and vice versa. In this paper, numerical values of parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After this improvement computational burden stays unchanged while accuracy of approximations increases in some of the cases very significantly.

Pressure Drop and Heat Transfer of Nanofluid in Turbulent Pipe Flow Considering Particle Coagulation and Breakage

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Jian-Zhong Lin ◽  
Yi Xia ◽  
Xiao-Ke Ku
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Friction Factor ◽  
Pipe Flow ◽  
Volume Concentration ◽  
Particle Diameter ◽  
Turbulent Pipe Flow ◽  
Particle Volume ◽  
Friction Factors

Numerical simulations of Al2O3/water nanofluid in turbulent pipe flow are performed with considering the particle convection, diffusion, coagulation, and breakage. The distributions of particle volume concentration, the friction factor, and heat transfer characteristics are obtained. The results show that the initial uniform distributions of particle volume concentration become nonuniform, and increase from the pipe wall to the center. The nonuniformity becomes significant along the flow direction from the entrance and attains a steady state gradually. Friction factors increase with the increase of particle volume concentrations and particle diameter, and with the decrease of Reynolds number. The friction factors increase remarkably at lower volume concentration, while slightly at higher volume concentration. The presence of nanoparticles provides higher heat transfer than pure water. The Nusselt number of nanofluids increases with increasing Reynolds number, particle volume concentration, and particle diameter. The rate increase in Nusselt number at lower particle volume concentration is more than that at higher concentration. For a fixed particle volume concentration, the friction factor is smaller while the Nusselt number is larger for the case with uniform distribution of particle volume concentration than that with nonuniform distribution. In order to effectively enhance the heat transfer using nanofluid and simultaneously save energy, it is necessary to make the particle distribution more uniform. Finally, the expressions of friction factor and Nusselt number as a function of particle volume concentration, particle diameter and Reynolds number are derived based on the numerical data.

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 Reconsideration of the friction factor data and equations for smooth, rough and transition pipe flow

2019 ◽  
Vol 29 ◽  
pp. 02001
Author(s):  
Srbislav Genić ◽  
Branislav Jaćimović
Keyword(s):  
Friction Factor ◽  
Pipe Flow ◽  
Entire Range ◽  
Single Phase ◽  
Turbulent Pipe Flow ◽  
Single Phase Flow ◽  
Practical Engineering ◽  
Factor Data ◽  
Statistical Criteria ◽  
Factor Estimation

The key element in design of pipelines is the friction factor estimation. After the brief review of the experimental data and friction factor correlations for isothermal single phase flow, we have checked the validity of well-known correlations through statistical criteria. During this process it was statistically proved that some of the well-known and permanently cited friction factor equations can be improved. Moreover we have prepared, for practical engineering purposes, equations that cover the entire range of laminar, critical and turbulent pipe flow.

scholarly journals Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

2017 ◽  
Author(s):  
Dejan Brkić ◽  
Žarko Ćojbašić
Keyword(s):  
Friction Factor ◽  
Iterative Solution ◽  
Evolutionary Optimization ◽  
Optimization Strategy ◽  
Pipe Surface ◽  
Turbulent Friction ◽  
Flow Friction ◽  
Relative Roughness ◽  
Transient Zone ◽  
Maximal Relative Error

This paper presents evolutionary optimization of explicit approximations of the empirical Colebrook’s equation that is used for the calculation of the turbulent friction factor (λ), i.e., for the calculation of turbulent hydraulic resistance in hydraulically smooth and rough pipes including the transient zone between them. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of the inner pipe surface (ε/D). It is implicit in the unknown friction factor (λ). The implicit Colebrook’s equation cannot be rearranged to derive the friction factor (λ) directly, and therefore, it can be solved only iteratively [λ = f(λ, R, ε/D)] or using its explicit approximations [λ ≈ f(R, ε/D)], which introduce certain error compared with the iterative solution. The optimization of explicit approximations of Colebrook’s equation is performed with the aim to improve their accuracy, and the proposed optimization strategy is demonstrated on a large number of explicit approximations published up to date where numerical values of the parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After that improvement, the computational burden stays unchanged while the accuracy of approximations increases in some of the cases very significantly.

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.

Heat Transfer in Turbulent Pipe Flow for Liquids Having a Temperature-Dependent Viscosity

1978 ◽  
Vol 100 (2) ◽  
pp. 224-229 ◽  
Author(s):  
O. T. Hanna ◽  
O. C. Sandall
Keyword(s):  
Heat Transfer ◽  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Analytical Approximations ◽  
Constant Viscosity ◽  
Dependent Viscosity

Analytical approximations are developed to predict the effect of a temperature-dependent viscosity on convective heat transfer through liquids in fully developed turbulent pipe flow. The analysis expresses the heat transfer coefficient ratio for variable to constant viscosity in terms of the friction factor ratio for variable to constant viscosity, Tw, Tb, and a fluid viscosity-temperature parameter β. The results are independent of any particular eddy diffusivity distribution. The formulas developed here represent an analytical approximation to the model developed by Goldmann. These approximations are in good agreement with numerical solutions of the model nonlinear differential equation. To compare the results of these calculations with experimental data, a knowledge of the effect of variable viscosity on the friction factor is required. When available correlations for the friction factor are used, the results given here are seen to agree well with experimental heat transfer coefficients over a considerable range of μw/μb.

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