New explicit correlations for turbulent flow friction factor

Brkić, Dejan

doi:10.1016/j.nucengdes.2011.07.042

Cited by 50 publications

(36 citation statements)

References 24 publications

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“…In this paper, 25 approximations are optimized: Brkić [19,20] [34], Shacham (available from [35]), Chen [36], Swamee and Jain [37], Eck [38], Wood [39] and Moody [40].Ćojbašić and Brkić [42] already optimized the numerical values of the parameters by Romeo et al [27] and by Serghides [30].…”

Section: Explicit Approximations Of Colebrook's Equationmentioning

confidence: 99%

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Brkić

Ćojbašić

2017

Fluids

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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.

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Section: Explicit Approximations Of Colebrook's Equationmentioning

confidence: 99%

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Brkić

Ćojbašić

2017

Fluids

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“…Finally, the maximal relative error was calculate as ɷ max = (ʄ 0 Ͳʄ)/ʄ 0 ͼ100%. It is also useful to note that the Moody diagram (Moody 1944) is only graphical interpretation of the Colebrook equation (Colebrook 1939 (YŦldŦrŦm 2009, Brkiđ 2011b, Fang et al 2011, which is maybe possible cause of the value of the error estimated in Samadianfard (2012). In this case, source of the error is not then calculative, but rather systematic, where the main source of the error is in inaccuracy of ʄ 0 (which should be accurate by default).…”

Section: Source Of the Errormentioning

confidence: 99%

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]

Brkić¹

2017

Preprint

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“…It should be taken into account that the Moody diagram cannot be used as a reliable and accurate replacement for the Colebrook equation as its reading error can be even more than few percent [10,34,35]. Using iterative methods, namely, the Newton-Raphson, the friction factor ( ) can be calculated from the Colebrook equation with high accuracy where the convergence of 0.01% requires less than 7 iterations.…”

Section: Definition Of the Problemmentioning

confidence: 99%

Intelligent Flow Friction Estimation

Brkić¹,

Ćojbašić²

2017

Preprint

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Nowadays, the Colebrook equation is used as a mostly accepted relation for the calculation of fluid flow friction factor. However, the Colebrook equation is implicit with respect to the friction factor ( ). In the present study, a noniterative approach using Artificial Neural Network (ANN) was developed to calculate the friction factor. To configure the ANN model, the input parameters of the Reynolds Number (Re) and the relative roughness of pipe ( / ) were transformed to logarithmic scales. The 90,000 sets of data were fed to the ANN model involving three layers: input, hidden, and output layers with, 2, 50, and 1 neurons, respectively. This configuration was capable of predicting the values of friction factor in the Colebrook equation for any given values of the Reynolds number (Re) and the relative roughness ( / ) ranging between 5000 and 10 8 and between 10 −7 and 0.1, respectively. The proposed ANN demonstrates the relative error up to 0.07% which had the high accuracy compared with the vast majority of the precise explicit approximations of the Colebrook equation.

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New explicit correlations for turbulent flow friction factor

Cited by 50 publications

References 24 publications

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

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]

Intelligent Flow Friction Estimation

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