Turbulence measurements in polymer solutions using hot-film anemometry

Hot-film anemometry was used to study the detailed structure of turbulence (intensities, energy spectra, and auto-correlations) in Newtonian solvents, non-drag reducing polymer solutions, and drag reducing polymer solutions. This was done in two smooth wall tubes with diameters of 1.0 inch and 2.0 inches. A probe traversing mechanism was used for measurements at radial positions from the center to as near the wall as possible for both the film probes (r/a=0.85 in the 2-inch tube) and the impact tubes (r/ a=0.98). The impact tubes were used to measure velocities for film probe calibration. The solvents used in this investigation were toluene, cyclohexane, and benzene. Three concentrations of a medium molecular weight polyisobutylene (Vistanex L-80, molecular weight about 720,000) in cyclohexane, two concentrations of the same polymer in benzene, two concentrations of a high molecular weight polymethyl methacrylate (Plexiglas, molecular weight about 1,500,000) in toluene, one concentration of a low molecular weight polymethyl methacrylate (V-100 molding powder, molecular weight about 110,000) in toluene, three concentrations of a high molecular weight polyisobutylene (Vistanex 1-200, molecular weight about 4,700,000) in toluene, and one concentration of the same polymer in cyclohexane were used. In the liquids not showing drag reduction a viscous and/ or elastic effect was found for both turbulence intensities and energy spectra. Turbulence intensities were higher and energy spectrum frequencies were lower for the polymer solutions of high viscosity. Unfortunately the most viscous solutions were also elastic. So purely viscous liquid studies will be necessary to distinguish between elastic and viscous effects. During drag reduction it was found that the energy spectra changed little from purely viscous solvents. The turbulence intensities, however, showed very unusual effects. The intensities relative to friction velocity increased at low drag ratio values (high drag reduction), rather than remain constant as expected from mixing length considerations. This behavior was dependent upon the degree of mechanical polymer degradation, lower intensities occurring for fresh than for degraded solutions during drag reduction. Normal stress differences (P₁₁ - P₂₂) were measured for two of the solutions used in this investigation, one showing drag reduction at attainable flow rates in the l-inch tube, the other showing drag reduction only in 0.5-inch and smaller tubes. Both solutions yielded normal stress differences of about the same level. A quantitative viscoelastic mechanism of drag reduction was tested using the viscosity and normal stress data for the two solutions discussed above. The drag reduction mechanism demonstrated the relative effects of elasticity and viscosity on drag reduction. The adequate prediction of drag ratios for two solutions at two flow rates in each of two tube sizes demonstrated the validity of the mechanism and the reasonableness of the assumptions made --Abstract

Comparison Of Lagrangian Time Correlations Obtained From Dispersion Experiments And From Space‐time Correlation Functions

No Abstracts. Copyright © 1969 American Institute of Chemical Engineer

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

Drag Reduction In Solid‐fluid Systems

Pressure drop measurements were made on a variety of dilute solid‐liquid suspension systems in order to study the effects of particle shape and size, concentration, fluid viscosity, and tube diameter on friction factor. The central objective was to determine under what conditions drag reduction would occur. Copyright © 1975 American Institute of Chemical Engineer

Radial Pressure Gradient In Turbulent Pipe Flow

Measurements made with a Prandtl static pressure probe have demonstrated that a radial pressure gradient does exist in turbulent pipe flow with approximately the magnitude predicted by Sandborn from hot-wire anemometry measurements

Frequency Response Studies for a Wedge Probe in Viscoelastic Fluids

The response of a hot-film wedge probe in viscoelastic fluids has been investigated by imposing on the probe a sinusoidal vibration of known amplitude and frequency. Root-mean-square (rms) velocities calculated from the displacement of the probe were compared to rms velocities obtained with a constant temperature anemometer. The tests were performed under turbulent flow conditions and also at flow rates where viscoelastic effects (i.e., decrease of heat transfer rates from the probe to the fluid and drag reduction) were observed. The frequency range covered was narrow ( \u3c 100 cps). This limitation was imposed by the decision to superimpose the sinusoidal vibrations on the turbulence signal, in order to have dynamic conditions similar to those encountered in actual turbulence measurements. Measurements were performed in mineral oil and four solutions of polyisobutylene (Vistanex L-200) In mineral oil. The experimental technique was established by measuring the response of the probe in mineral oil. These are the first data available in which the frequency response of a hot-film probe in a purely viscous liquid has been observed to be correct in the range studied. The ratios of velocities calculated using the two different methods were approximately 1.0. The results for viscoelastic fluids are similar with ratios ranging from 0.90 to 1.10. These results establish the validity of intensity measurements in viscoelastic fluids performed with hot-film wedge probes. They indicate that objections raised in the literature concerning the use of film probes in this type of fluid are not correct or, at least, not applicable to wedge probes

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