A Communication on the Drag Reduction Correlation Proposed by Astarita, Greco, and Nicodemo

Abstract

-No one of the several methods for correlating drag reduction data (1, 2, 4, 7, 8) has been demonstrated to be the best, and the limitations on some are quite severe.Rodriguez, Zakin and Patterson (RZP) have shown (7) that their correlation will not satisfactorily correlate data for systems of polymers dissolved in polar solvents. A later correlation (1) proposed by Astarita, Greco and Nicodemo (AGN) however used data for the drag reducing system of ET 597 dissolved in water, a polar solvent. But will the AGN correlation work for other systems of polymers dissolved in either polar or nonpolar solvents? It is the purpose of this communication to present the results of a study of the AGN correlation for the polymer polyethylene oxide dissolved in both polar and nonpolar solvents. Also, other important characteristics of the AGN correlation will be discussed.The AGN correlation was tested by means of regression analysis to fit the f / f p u versus log v/v0.5 data to a polynomial of the form log( v 1 V 0 . 5 )The goodness of the fit was characterized by the standard error of the estimate and the average absolute deviation.For PEO WSR-301 and PEO-coagulant dissolved in water, only a second-degree polynomial was used because the value for the sum of the squares of residuals, the criterion used to make the fit, did not change significantly when higher degree fits were made. Data for f / f P u ranged from values of 0.4 to 0.9. The standard error of the estimate for f / f p u for the combined data of both polyethylene oxides was 0.0557 and the average absolute deviation was 0.0436. These data are shown as Curve 1 in Figure 1 When the nonpolar solvent data were tested, no simple relation like those obtained for polar solvents was found. In fact, the log-log plot of V v 0 . 5 versus concentration for nonpolar solvents produced a curve rather than a straight line as theory predicts and as polar solvent data produced. Thus polar and nonpolar solvent systems appear to behave in a similar manner as seen in Figure 1, but differ fundamentally with respect to the relation between W g . 5 and concentration. The maximum deviation of the AGN curve shown in Figure 1 for polar solvents compared with nonpolar solvents is about 20%. It is concluded that neither the AGN nor the RZP correlation adequately correlate both polar and nonpolar solvent systems.One obvious shortcoming of the AGN correlation is that at least 50% drag reduction must be obtained to November,

Drag reduction in external rotational flows

“…Patterson et al (1970) compared the shape of the AGN correlation with that of a correlation based on a model with some phenomenological considerations. Peterson and Beckwith ( 1971) have examined the validity of AGN correlation for systems of polymers dissolved in polar and nonpolar solvents. In this work some interesting features of this type of correlation are examined with respect to drag reduction in certain external flow problems.…”