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Fluids 2017, 2(2), 15; doi:10.3390/fluids2020015

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

1
European Commission, Joint Research Centre, 21027 Ispra VA, Italy
2
Faculty of Mechanical Engineering, University of Niš, 18000 Niš, Serbia
*
Authors to whom correspondence should be addressed.
Academic Editor: William Layton
Received: 1 March 2017 / Revised: 28 March 2017 / Accepted: 1 April 2017 / Published: 6 April 2017
(This article belongs to the Special Issue Turbulence: Numerical Analysis, Modelling and Simulation)

Abstract

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. View Full-Text
Keywords: Colebrook equation; Colebrook–White; Moody diagram; turbulent flow; hydraulic resistance; Darcy friction; pipes; genetic algorithms; optimization techniques; error analysis Colebrook equation; Colebrook–White; Moody diagram; turbulent flow; hydraulic resistance; Darcy friction; pipes; genetic algorithms; optimization techniques; error analysis
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Brkić, D.; Ćojbašić, Ž. Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations. Fluids 2017, 2, 15.

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