Existence Of Two Types Of Drag Reduction In Pipe Flow Of Dilute Polymer Solutions

Drag reduction in the pipe flow of polymer solutions is shown to be of two types which apparently occur by two separate mechanisms. In turbulent flow, drag reduction is probably caused by viscoelastic effects. The critical solvent Reynolds number at the onset of drag reduction is proportional to about the first power of the diameter. Thus, the critical velocity is independent of tube diameter. Polymers dissolved in good solvents show more drag reduction than in poor solvents. The other type of drag reduction occurs when the laminar region is extended to high Reynolds numbers. It is followed by a transition region and a turbulent region in which the drag is not affected. © 1967, American Chemical Society. All rights reserved

Hot‐film Anemometry Measurements Of Turbulence In Pipe Flow: Organic Solvents

Longitudinal turbulence intensities, autocorrelations, and energy spectra have been measured in the flow of toluene, benzene, and cyclohexane in smooth, round 1‐ and 2‐in. I.D. tubes. These measurements were made with a constant‐temperature hot‐film anemometer and covered radial positions from the center to r/a = 0.85 in the 2‐in. tube and to r/a = 0.75 in the 1‐in. tube. The turbulence intensity data were found to be similar to those obtained for air in a 10‐in. pipe by Laufer. A slight diameter effect was observed, the intensities in the 1‐in. tube being slightly lower than those in the 2‐in. tube at equal Reynolds numbers. The energy spectra were similar to the spectrum reported by Lee and Brodkey for water. The spectra reached higher frequencies at the lowest measurable energy levels for higher velocities. There was little effect of tube diameter or radial position on the spectra from the center to r/a = 0.85. A short inertial subrange with a log‐log slope of −5/3 seemed evident in high velocity spectra, and the log‐log slope of −7 was approached at high frequencies by the lowest velocity spectrum. The peak energy dissipation frequencies for all the energy spectra measured were approximately proportional to bulk mean velocity to the 1.4 power with little effect of tube diameter or radial position from the center to r/a = 0.85. Integral scales of the turbulence were proportional to bulk mean velocity to a power less than one for a given tube. These measurements indicated that the ratio of integral scale to pipe diameter is not a function of Reynolds number only. Microscale values were relatively independent of velocity and pipe diameter. Copyright © 1967 American Institute of Chemical Engineer

Numerical Differentiation Of Equally Spaced And Not Equally Spaced Experimental Data

Procedures are given for smoothing and differentiating experimental data with both equal and nonequal spacing in the independent variable. Selection of the number of points to be included in the movable strip technique and of the degree of the polynomial is discussed. Equations are given to estimate the error by calculating a confidence interval on each slope. A technique for handling certain types of nonrandom errors is presented. © 1967, American Chemical Society. All rights reserved

Mechanical Degradation Of Dilute Solutions Of High Polymers In Capillary Tube Flow

Experimental results on mechanical degradation in capillary tubes of polyisobutylene polymers in dilute solution are described. In laminar flow, degradation is independent of tube length, indicating that entrance effects are dominant. This shows that capillary experiments do not yield explicit information on the effect of shear stress on mechanical degradation. In turbulent flow, large entrance effects are also observed, but some degradation does take place in the fully developed flow region. Copyright © 1975 John Wiley & Sons, Inc

A molecular approach to predicting the onset of drag reduction in the turbulent flow of dilute polymer solutions

The significant variables in drag reduction have been separated into two classifications, flow variables and solution variables. A theory has been offered which permits prediction of the critical Reynolds number in the turbulent flow of polymer solutions. The theory states that the relaxation time of the polymer molecule in solution equals a characteristic flow time for the tube in question at the point of incipient turbulent suppression. This is equivalent to a Deborah number near unity. Reasonable agreement has been shown between the experimental results of this investigation and predictions of flow rates based on this theory for the presence or absence of drag reduction and for the onset of turbulence suppression. No adjustable parameters were used in the analysis. The theory seems to be applicable at values of C[η] greater than 0·10. The theory leads to the prediction that the wall shear rate at the point of incipient turbulence suppression decreases as the product of reduced viscosity, molecular weight and solvent viscosity increases. Thus for large effects this product should be made as large as possible. Friction factor measurements in both good and poor (Theta) solvents showed that the maximum drag reduction in the poor solvent was only about 40% of that in the good solvent at similar flow rates in the same tube. Thus the effect of an expanded configuration of the polymer molecule in solution is to increase drag reduction. © 1967

Effects Of Molecular Characteristics Of Polymers On Drag Reduction

Turbulent measurements in capillary tubes and in pipes were made on nonpolar solutions of seven polymer species, three at more than one molecular weight, over wide concentration ranges. A critical concentration, Cc, was taken as the minimum concentration for disappearance of the turbulence transition region. Above this concentration, friction factor‐generalized Reynolds number data show only a gradual deviation from extension of the laminar line. Cc increases with tube diameter and decreases with molecular weight. The critical dimensionless volume friction Cc [η] is less dependent on molecular weight. The levels of Cc [η] for different polymer species in a given tube show marked differences which are related to β, the molecular rigidity parameter. Low β values, or high flexibility, are associated with low Cc [η] values. Available data for Cc [η] in good and in poor solvents show little solvency effect. Polymer samples of low m′, the ratio of the polymer molecular weight to the critical tanglement molecular weight of the polymer, give solutions with little or no drag‐reducing capacity, even those with low β values. Samples must have m′ values of 50 or more to show significant drag reduction. This allows prediction of the minimum useful molecular weights for drag reduction for any polymer species. For solutions above Cc, all of these data and literature data (for aqueous and nonaqueous systems with a wide range of n′ values) fit a single f/fpv versus generalized Reynolds number relationship. Copyright © 1971 American Institute of Chemical Engineer