Precise prediction of the drag reduction efficiency of polymer in turbulent flow considering diameter effect

Abstract

One important issue for drag reduction of turbulent flow with polymers is the pipe diameter effect. Although this scale-up effect has been extensively investigated, there are still debates. For instance, when using the traditional scaling law to predict the friction factor in pipe flow of wide pipe diameters, the relative errors between experimental data and predicted values can be up to 1000%. This paper develops a new method to predict the friction factor in pipe flow applicable to a wide range of pipe diameters. The new method developed in this study transforms the Reynolds number (Re) vs friction factor (f) to log10(Ref) vs 1/f in the Prandtl–von Karman coordinate, where the latter two parameters are correlated on straight lines. We find that the slope and intercept of these straight lines can be predicted by empirical correlations involving diameters and polymer concentrations. Thus, if Re and f from a pipe flow of small diameter are known, these two correlations for slope and intercept can predict the cases for large pipe diameters. With our method, most relative errors between the predicted values and experimental data are within 20%, much better than the traditional scaling law. Finally, we point out the physical meaning of the slope and intercept, and make it clear why the previous scaling law becomes not reliable when it is employed to predict the friction factor for pipe flow with a too wide range of pipe diameters.

Critical Role of Ionic Properties on the Turbulence Drag Reduction Performance of Various Polyacrylamide Polymers in Liquid

“…Hoyt et al , proposed one model for the prediction of friction factor: R e f / d was a constant when polymer type, molecular weight, and polymer concentration were the same. In our previous work, , we extract data from previous research and rearrange them in a Prandtl–von Karman coordinate with log 10 ( Re f ) vs 1 / f . The results showed that all data can be fitted in a straight line, which follows the format in eq .…”