Impact of neglecting the variations in the relative surface roughnesses of capillary tubes on the accuracy of a capillary tube model

Capillary tube models frequently rely on friction factor correlations, which are functions of the Reynolds number, and the tube's relative surface roughness. However, this study shows that explicitly correlating the friction factor with the relative surface roughness is unnecessary, at least when the latter is lower than 0.0025. To test this a correlation was fitted directly onto friction factor measurements obtained in an adiabatic flow of R600a, through nine capillary tubes from three manufacturers. The friction factor was correlated exclusively as a function of the Reynolds number, meaning that the impacts of the relative sur-face roughnesses on the friction factor were averaged, and included only implicitly. This correlation, and an existing correlation, which allows the specification of the relative surface roughness, were then imple-mented in a capillary tube model. The accuracy of the capillary tube model, using either the developed or existing correlation was then evaluated by comparing the results to experimental data. No significant decrease in the accuracy of the model was observed when the relative surface roughnesses, ranging from 0.0012 to 0.0025, were not individually specified for each capillary tube. To further verify this, the proce-dure was repeated on a larger database of friction factor and mass flow rate measurements, which also consisted of data from independent studies. Similar conclusions were drawn, as the average accuracy of the model differed only by 1 to 3% among different studies, and not always in favor of the correlation where the relative surface roughnesses could be specified. (c) 2021 Elsevier Ltd and IIR. All rights reserved.

Automated summary

The study found that explicitly correlating the friction factor with relative surface roughness is unnecessary in capillary tube models. The accuracy of the model was not significantly decreased when relative surface roughnesses were not individually specified for each capillary tube. Experimental results supported the conclusion that the impacts of relative surface roughness can be averaged out when correlating friction factor solely with the Reynolds number.