Experimental correlation for pipe flow drag reduction using relaxation time of linear flexible polymers in a dilute solution

In this study, we investigate the drag reduction property of a linear flexible polymer, PEO (polyethylene oxide) in a fully turbulent pipe flow. The aim of this study is to develop a correlation to predict the drag reduction using the Weissenberg number, a dimensionless number related to the relaxation time of the polymer and the polymer concentration in dilute solutions. The physical meaning of the relaxation time of polymers and overlap concentration between the dilute and semi-dilute polymer solution are clarified. A higher polymer concentration, Reynolds number, and Weissenberg number lead to an increasing drag reduction. A semi-empirical correlation to predict the drag reduction with two dimensionless variables mentioned above is established and can predict the experimental data in this work and other previous works well. Previous correlations that use Reynolds number often require high flow velocity or large pipes in the experimental setup to predict drag reduction in large-scale industrial applications, which involves extra cost and potential safety issues. The current new correlation method uses relatively low velocities to avoid the problems mentioned above.     

Poly(ethylene oxide) × polyacrylamide. Which one is more efficient to promote drag reduction in aqueous solution and less degradable?

The hydrodynamic drag reduction (HDR) in aqueous solutions containing very small amounts of poly(ethylene oxide) (PEO) and polyacrylamide (PAM, 0–100 ppm) was studied under turbulent flow. In this condition, the polymers undergo severe mechanical degradation and loose their capacity to promote drag reduction. The interpretations from a molecular point of view of the mechanical degradation of these flexible polymers under turbulent flow are not consensual. To avoid effects of polymer entanglement and to correlate the mechanical degradation with the intrinsic characteristics of the polymer chain, a polymer concentration lower than 2 ppm was used. For this purpose, a highly accurate rheometer containing a double‐gap cell was used to determine the mechanical degradation kinetics. The kinetics was measured directly from the loss of the polymer's capability to promote drag reduction. The comparisons of degradation kinetics for PEO and PAM in aqueous solution allow us to conclude that the stabilities of the two polymers are similar. This new interpretation can be useful to understand the relative mechanical stability of flexible polymers under drag reduction conditions. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

STUDY ON ADSORPTION ALANINE BY A STRONG-ACID CATION EXCHANGER

The uptake equilibrium and the column dynamics of alanine by “001×7” resin, a strongly acidic cation exchange resin, were investigated. The experimental data indicated that the Langmuir equation could describe the equilibrium isotherm. The implicit difference scheme and the optimization technique were applied to compute the model developed for alanine in fixed-bed column. The results of experiments with different superficial velocities and liquid phase solute concentrations showed that interparticle transport was dominated by the slow diffusion of alanine cations through the liquid phase bulk into the surface of the resin particle. However, the resistance of intraparticle diffusion of alanine cations through the macroreticular polymer structure of the resin was small. The experimental results were in good agreement with the theoretical predictions.     

Electrode kinetics by hydrodynamic voltammetry—study of ferrous-ferric, ferrocyanide-ferricyanide and iodide-iodine systems

Using rotated and circulatory electrolysis cells, rate parameters of electrode processes have been determined at stationary conical and cylindrical platinum microclectrodes in flowing solutions, under judiciously controlled hydrodynamic conditions. Virtually ideal laminar flow was maintained at velocities up to 700 cm/s. Normally reversible d.c. current/voltage waves were made “irreversible in shape”, due to enhancement of convective mass transfer. Thus specific electron-transfer rate constants, ranging up to an estimated limit of 10 cm/s, could be evaluated by a simple and unambiguous “wave analysis” procedure. The electro-oxidation of iodide to iodine, in perchloric acid in the absence of triiodide, is governed by second-order kinetics. A mechanism is proposed to account for this remarkable finding.     

Structural and some physical properties of KCsZnCl4

The structures of the “pure” compounds K₂ZnCl₄ and Cs₂ZnCl₄ are well-known. We have studied the occupation probability in host sites for solid solutions crystals K_xCs_2-xZnCl₄ and specially for KCsZnCl₄. We show that the K substitution in the Cs sites is not random. We also correlate our structural results with the evolution of the physical properties of the crystal KCsZnCl₄.     

Effect of polymer additives on hydrodynamics and oxygen transfer in a bubble column bioreactor

The influence of polymer additives (polyethylene oxide and polyacrylamide) on the hydrodynamics and oxygen transfer in a bubble column bioreactor was examined. The addition of small amounts of these polymers has been known to cause significant drag reduction in turbulent flow circumstances. The gas hold-up was slightly decreased and the liquid-phase mixing was somewhat enhanced due to the addition of the polymers. The addition of polymer additives brought about a reduction of the volumetric oxygen transfer coefficient by about 40%. In dilute polymer solutions, large bubbles formed by bubble coalescence moved with high rise velocities in the presence of many small bubbles and the bubble size distributions were less uniform compared with those in water. The complicated changes in bubble hydrodynamic characteristics were examined to give possible explanations for oxygen transfer reduction.     

Surface Silanization of Polyethylene for Enhanced Adhesion

Low density polyethylene has been treated using a novel surface treatment process “SICOR” (“SIIane-on-CORona” treated polymer) in order to enhance adhesion with a range of adhesives including polyure-thane, methacrylate and cyanoacrylate. The process comprises two steps, i.e corona discharge followed by application of an organo-functional silane. The incorporation of surface hydroxyl groups onto the polymer surface enables organo-silane to create the hydrogen or covalent bonds with the oxidized polymer surface. The possibility of the creation of these bonds has been investigated using FTIR, XPS and wettability studies. The adhesion enhancement due to the new process is significant. Frequently, the strength increase exceeds 200% compared with the corona discharge treatment and more than 300% compared with LDPE priming using the “Loctite 770” polyolefin primer. The process is shown to be as good as, or better than, plasma treatment in terms of the strength increase following substrate treatment prior to adhesive bonding.     

“FORWARD MIXING” MODEL: APPLICATION TO PULSED PLATE EXTRACTION COLUMN OPERATION IN THE EMULSION REGION

The “Forward Mixing” model has been applied to data obtained from a 22 cm diameter pulsed plate extraction column. Measurements of drop size distributions, dispersed phase hold-up and concentration profiles for two systems (toluene-acetone-water and n-butanol-succinic acid-water) of quite different properties were made with the column operating in the emulsion region. Generated drop size distribution function parameters, size-dependent slip velocities and mass transfer coefficients, and continuous phase axial dispersion coefficients were accurate in predicting dispersed phase hold-up and extraction efficiencies (or the related plug flow number of transfer units). These parameters were correlated with phase superficial velocities and pulse velocities. The influence of continuous phase axial dispersion was much greater than the influence of drop size variation, and was not accurately predicted by most previous tracer-based correlations. An inlet dispersed phase distributor was beneficial to the performance with the high interfacial tension system.     

VELOCITY FLUCTUATIONS IN NON-HOMOGENEOUS DRAG REDUCTION

Non-homogeneous drag reduction is obtained by injecting a polymer solution thread into the center of a turbulent pipe flow. Under the proper conditions the magnitude of this non-homogeneous drag reduction is much larger than that for the same polymer molecules uniformly distributed in the flowing solvent. In this work the axial velocities and velocity fluctuations near the wall were examined in such a non-homogeneous drag reduction and also in the flow of a homogeneous (pre-mixed) solution of poly(ethylene oxide). The drag reduction and the Reynolds number were the same for both fluids. Significant differences were found in the velocity profile and in the statistical analysis of the velocity fluctuations. The skewness profile for the non-homogeneous case remained positive to a much greater distance from the wall than the skewness profile for the premix solution. In the injection case the velocity fluctuation spectra had the same sharp peak at 5-10 Hz for y₊ between 11 and 50. This peak corresponded to the bursting frequency measured from the short time autocorrelation. In the pre-mix case a broad increase in velocity fluctuation spectra was seen at y₊ = 11 which was attributed to polymer molecule rotations in the laminar shear flow near the wall. This band was absent in the non-homogeneous drag reduction, suggesting that no polymers were present at y₊ = 11. The observations imply that non-homogeneous drag reduction involves a modification of the large eddy structure.     

INVESTIGATIONS ON TRANSITION TO TURBULENCE IN PIPE FLOW OF NEWTONIAN AND VISCOELASTIC FLUIDS

The linear stability analysis of fully developed pipe flow of a second order and a “contravariant” Maxwell-type fluid predicts stability against twodimensional infinitesimal disturbances of rotational symmetry.

A sinuous perturbation, superposed on the pipe flow of aqueous polymer solutions, produces distinct regions of instability, dependent on disturbance amplitude and frequency.

A broad region of Reynolds numbers is found for natural transition to turbulence with laminarization effect of polymer additions in two extremely different cases of inlet conditions.     

ATOMIZATION IN A VENTURI SCRUBBER

High speed motion pictures were made or the breakup of a single jet of water in the throat of a venturi scrubber for various air and water jet velocities and different nozzle diameters. Atomization seemed to occur as the result of several different mechanisms, depending on the flow conditions, the most common mechanisms being breakup due to either capillary or acceleration waves and also breakup by “steady shear,” all of which have been observed by other investigators. The so-called “cloud-type” atomization proposed by Hesketh (1970) was not observed despite several attempts to achieve it. Measured values of pressure drop across the test section of the scrubber compare well with previously published results.     

An improved correlation for turbulent drag reduction in dilute polymersolutions

The model for turbulent drag reduction in dilute polymer solutions developed by Darby and Chang (1984), and modified by Darby et al. (1989) has been further refined to significantly improve its ability to represent data for a variety of polymer solutions over a wide range of conditions. It is also shown how the rheological parameters in the model can be obtained from two or three data points for turbulent flow, in lieu of laminar viscometric measurements. This technique is applied to a wide variety of turbulent drag reduction data taken from the literature to demonstrate the general applicability of the model. The model is also shown to be consistent with Virk's maximum drag reduction asymptote (Virk, 1975) in the high Reynolds number limit.     

RHEOLOGY OF HIGHLY FLOCCULATED OIL IN WATER EMULSIONS

The viscous flow behavior of highly flocculated oil in water emulsions was studied experimentally using a co-axial cylinder viscometer. The aqueous phase of the emulsions consisted of a non-Newtonian solution of Carbopol-940 in tap water; the oil phase consisted of a Newtonian white mineral oil. The emulsions produced were very viscous and they appeared “gelled”. The shear stress/shear rate behavior of the emulsions was described by the Casson's model. The yield-stress in emulsions was found to depend upon the concentrations of the dispersed phase (oil) and the polymer. The yield-stress increased non-linearly with the dispersed phase concentration and it increased linearly with the polymer concentration     

SYNERGISTIC EFFECTS OF ANIONIC SURFACTANT AND NONIONIC POLYMER ADDITIVES ON DRAG REDUCTION

Turbulent drag reduction (DR) behavior of mixed nonionic polymer and anionic surfactant solutions in water was studied in a pipeline set up to explore the synergic effects of mixed additives on DR. The concentration of polymer polyethylene oxide (PEO) was varied from 0 to 2000 ppm and the concentration of surfactant sodium dodecyl sulfate (SDS) was varied from 0 to 5000 ppm. The critical aggregation concentration (CAC), where the interaction between the polymer and the surfactant begins, and the polymer saturation point (PSP), where the polymer molecules become saturated with the surfactant, were determined using electrical conductivity and surface tension measurements. As the polymer concentration was increased the CAC decreased but the PSP increased. The relative viscosity showed a remarkable increase upon the addition of surfactant to the polymer solution due to extension of polymer chains caused by the formation of micelles on the backbone of the polymer molecules. The data exhibited a considerable increase in DR in the case of mixed polymer/surfactant systems. The percent reduction in friction factor was as high as 79 when 3000 ppm or more surfactant was added to the 500 ppm polymer solution. Furthermore, the drag reduction behavior of the polymer solution changed from so-called Type A to Type B. In Type A drag reduction, a transition from laminar to turbulent regime is observed with a clear-cut onset point. In Type B drag reduction, no transition or onset point is observed; the data fall on a gradual extension of the laminar line.     

Degradation of drag reducing polymers in aqueous solutions

The performance of drag reducing polymers in turbulent flow is restricted by their mechanical degradation. This study examines how the working fluid can affect the degradation behavior of diluted drag reducing polymeric solutions. Solutions having different proportions of tap water and de-ionized water served as the working fluids. Three commercially available water soluble polymeric agents, namely, an anionic copolymer of polyacrylamide, xanthan gum, and polyethylene oxide, were then added to these solutions. All experiments had identical flow rates corresponding to turbulent conditions in a laboratory scale pipe line. Variation of pressure drop in the pipe line was then measured for 2 hours. It was found that polymer degradation is accelerated in tap water solutions compared to that in de-ionized water solutions. However, this is dependent on the specification of the polymer used, namely, the molecular weight of the polymer and the rigidity of its molecular backbone. Furthermore, a new mathematical relation has been developed to investigate degradation of the polymers over time.     

Simulation of Superheated Steam Turbulent Flows and Heat Transfer in an Impingement Dryer

Numerical simulations are presented for two-dimensional flow field and heat transfer characteristics due to a turbulent single slot jet of superheated steam discharging tangentially into a confined cylinder. A finite volumes method was used to solve the equations that describe the problem. Calculations were performed for steady state turbulent flow and unsteady state heat transfer. Constant velocities and superheated steam temperature are imposed at the inflow. Particle properties were assumed to be the same of a cubic particle of carrot. Numerical tests were performed to ensure that the model solutions were “grid independent” and also independent of the turbulence intensity of stated as boundary condition at the inlet slot. The solution procedure developed is fast and that convergence is reached after a few iterations. The results obtained are relevant to flow and heat transfer behaviors of the impingement dryer and it will be useful future studies considering particles interactions.     

Drag coefficients and pressure drops for hydrodynamically suspended spheres in a vertical tube with and without polymer addition

The pressure drops associated with the suspension velocities for single, hydrodynamically suspended spheres were measured for a range of steel spheres in a 5.3 cm diameter vertical glass tube. Nineteen different sphere to tube diameter ratios (d/D) were investigated ranging from 0.191 to 0.967. Three different liquid media were used: pure water, and two polyacrylamide solutions of concentration 25 wppm and 50 wppm of Reten 423. In the range 0 < (d/D) < 0.7 polymer addition increased the drag coefficient. For d/D > 0.7 the drag coefficient was not affected. The available data for air, water and polymer solution were correlated with an equation explicit in pressure drop, and the agreement between theory and experiment was found to be excellent.     

Pretreatments of Fluoropolymers

In the present study the mechanisms and effectiveness of various pretreatments for fluoropolymers were studied. The pretreatments were “Tetra-Etch,” various plasmas, flame and potassium hydroxide. “Tetra-Etch” was found to be much more reactive than potassium hydroxide (KOH) towards fluoropolymers. The plasma treatment of PTFE showed that it was possible to get substantial increases in adhesion with little or no chemical change to the polymer. However, to obtain large increases in adhesion it may be necessary to modify PTFE chemically as with “Tetra-Etch.” Consideration of the bonding of these fluoropolymers shows that sharp interfaces between these substrates and adhesives do not exist.     

COMPREHENSIVE STUDY OF THE GAS HOLD UP AND BUBBLE SIZE DISTRIBUTION IN HIGHLY VISCOUS LIQUIDS I. GLYCEROL SOLUTIONS

The overall gas hold up, E_G, and bubble size distribution were separated into the particular gas hold up, E_GK, and Sauter diameter. d_SG. due to “small bubbles” as well as E_GG and d_SG, due to “intermediate to large bubbles.” Bubbles are defined to be “small” if they remain in the bubbling layer 15 seconds after the gas flow is turned off. The bubbles which leave the layer during this time are considered to be “intermediate to large bubbles.” The time dependences of E_G E_GK and E_GG, as well as of bubble size distribution after initiating the aeration of the liquid, is investigated. The steady state E_G, E_GK and E_GG, Sauter diameter and specific geometrical surface area of “small” and “intermediate to large” bubbles as well as of the entire bubble population were determined in bubble columns employing 50, 70, 90 and 95% glycerol solutions and perforated plates with different hole diameters (d_H = 0.5. 1.0 and 3.0 mm) respectively. In highly viscous media the “small” and “very large” bubble fractions are high. A comparison of the specific geometrical bubble surface areas with the corresponding volumetric mass transfer coefficients, k_La's, measured earlier indicate that the “small” bubbles do not contribute to k_La. The influence of the “small” bubbles on the fluiddynamics of the two phase system is discussed.     

The drag and pressure drops for hydrodynamically suspended cylinders in a vertical tube with and without polymer addition

The pressure drops and the suspension velocities for hydrodynamically suspended aluminum and steel cylindrical bodies were measured for a range of aspect ratios (L/d) in a 5 cm vertical plexiglass tube. Four different body-to-tube diameter ratios (d/D) from 0.432 to 0.864 were investigated. Both water and drag reducing aqueous polymer solutions of Reten 423^* having concentrations in the range 20 to 100 ppm by weight were used. In all cases, the addition of polymer reduced the drag coefficient and the drag coefficient per aspect ratio approached a constant value as (L/d) approaches 14. The available data for cylindrical bodies in vertical pipelines were correlated to obtain semi-empirical equations relating pressure drops, drag coefficients and suspension velocities.