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

摘要

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 10~8 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.