Selection Maps of Explicit Colebrook Approximations according to Calculation Time and Precision

Abstract

This paper presents the creation of three-dimensional (3D) maps for selection of best Colebrook friction factor approximation. Twenty Colebrook approximations are observed in range of Reynolds numbers between 4000 and 10⁸ and relative surface roughness less than 0.05. Colebrook approximations with the lowest relative errors at various combinations of Reynolds numbers and relative surface roughness are presented on a 3D map. Elapsed calculation time of each approximation is then taken into account. Two more 3D maps are created by omitting the slowest approximations. Obtained 3D maps enable the selection of the fastest Colebrook approximation with the lowest relative error on a user-defined range of Reynolds numbers and relative surface roughness combinations. Such 3D map was used to determine the optimal Colebrook approximation to calculate the friction factor of the marine steam condenser tubes. Measured friction factor was calculated by physical equation, while other friction factors were determined by implicit Colebrook-White equation and three selected explicit approximations. Difference between calculated and measured Darcy friction factors does not exceed 1.1% at all operating regimes.

Acknowledgments

The authors express their thankful regards to LNG carrier crew and ship-owner for helpful advices during the experimental measurements, numerical model development, and on all necessary additional data which was required for the friction factor calculations inside the tubes of marine steam condenser. This work has been fully supported by the Croatian Science Foundation under the project IP-2018-01-3739, CEEPUS network CIII-HR-0108, European Regional Development Fund under the grant KK.01.1.1.01.0009 (DATACROSS), University of Rijeka scientific grant uniri-tehnic-18-275-1447, University of Rijeka scientific grant uniri-tehnic-18-18-1146 and University of Rijeka scientific grant uniri-tehnic-18-14.

Additional information

Notes on contributors

Lana Škopac

Lana Škopac has obtained the Mechanical Engineering degree at the Faculty of Engineering, University of Rijeka in 2013, after which she enrolled in the Postgraduate Doctoral Study in the field of Thermal Power Engineering. Since 2014 she is employed at the Thermal Power Plant Plomin, in the maintenance department of a 210 MW turbine and its auxiliary systems. She is actively working on analysis of operation of the heat exchangers and heat transfer. She participated in modernization of low pressure turbine part, in modernization of the turbine governor and bypass valves and in other related projects. She regularly takes part and oversees the turbine overhauls.

Vedran Medica-Viola

Vedran Medica-Viola is a junior assistant and PhD student at the Faculty of Engineering, University of Rijeka, Department of Thermodynamics and Energy Engineering, where he leads auditory exercises in the following subjects: internal combustion engines, heat engines and devices, heat turbines, ship systems, ship propulsion engines and devices, and other subjects in the field of thermodynamics and energy engineering. His PhD thesis is based on carbon dioxide heat pumps. As a part of his PhD research, he is researching pressure drop through heat exchanger tubes, which is highly related to the submitted article. In cooperation with other colleagues, he has already published four articles in the renowned journals, in the field of thermodynamics and energy engineering.

Vedran Mrzljak

Vedran Mrzljak obtained the PhD degree at Faculty of Engineering, University of Rijeka, Croatia in the field of Internal Combustion Engines. He develops numerical models for analysis, simulation and management of various systems - energy, intelligent and marine systems. He continued his field of study through his stay at scientific institutions in Slovenia, Hungary, Slovakia and Czech Republic. He has published over 60 scientific papers. As assistant professor, he is teaching in the field of power systems, internal combustion engines, steam turbines and gas turbines. He is currently employed at The Faculty of Engineering, University of Rijeka, Department of Thermodynamics and Energy Engineering. He is an organizing and scientific committee member of several international conferences. In his professional work, he was a team member of a project - Overhaul and retrofit of the Steam Power Plant Plomin 2, Croatia.