Normal stress measurements on drag-reducing polymer solutions

Summary The elastic properties of very dilute solutions of a number of drag-reducing polymers differing either in chemical nature or molecular weight were investigated over a range of values of shear stress using the jet thrust method. Parallel drag reduction measurements were also made with the solutions. The results indicate a general relationship between the value of the first normal stress difference at the wall, (p ₁₁-p ₂₂, and the dragreducing ability.The data tends to confirm the generality of the correlation between the value of theWeissenberg number and the drag reduction reported byMetzner for a single polymer sample.     

Evaluation of flush mounted hot-film sensors for skin friction reduction measurements in viscoelastic polymer solutions

The purpose of this investigation was to evaluate the performance of flush mounted hot-film sensors for mean wall shear stress measurement in turbulent flows of dilute drag reducing polymer solution. A series of pipe flow expriments were conducted over a range of Reynolds numbers and polymer solution concentrations to compare the level of skin friction drag reduction measured by hot-film sensors with values calculated from pipe pressure drop. It is shown that water calibrated hot-film sensors consistently underestimate the wall shear stress suggesting that Reynolds analogy is not valid in dilute polymer solutions. The Newtonian form of the relationship between the wall shear stress and the heat transfer remains valid in dilute polymer solutions. However, multiplicative and additive factors in the relationship are shown to increase linearly with the logarithm of the polymer concentration.     

Drag of a sphere in dilute polymer solutions in high Reynolds number range

We have measured by means of four ultrasonic transducers the fall velocity of a sphere at high Reynolds number range in dilute polyacrylamide solutions which have viscoelastic effects. The polymer solutions were 5, 20 and 50ppm in the concentration. Basset-Bousinessq-Oseen equation for the falling sphere was analyzed numerically on Newtonian fluids in order to compare with the fall velocity of a sphere in the polymer solutions, and the experimental data of the fall velocity in tap water is in agreement with the range of no effect of the test tank wall. In polymer solutions, it was shown that the fall velocity is larger than that in Newtonian fluids within the critical Reynolds number range such that the drag reduction occurs and is smaller than that of Newtonian fluids over the range. The experimental data for the drag reduction ratio of polymer solutions is arranged by Weissenberg number calculating the experimental data of the first normal stress differences. It was shown that the maximum drag reduction ratio in the polymer solutions lies in the range of We=3∼10. Received: 15 October 1997 Accepted: 12 May 1998     

Drag reduction effectiveness of dilute and entangled xanthan in turbulent pipe flow

The ability to reduce the frictional drag in turbulent flow in pipes and channels by addition of a small amount of a high molecular weight polymer has application in myriad industries and processes. Here, the drag reduction properties of the polyelectrolyte xanthan are explored in differing solvent environments (salt free versus salt solution) and delivery configurations (homogeneous versus stock solution dilution). Drag reduction effectiveness increases when an entangled xanthan solution is diluted compared to solutions prepared in the dilute regime. Based on dynamic rheological measurements of the elastic modulus, residual entanglements and network structure are hypothesized to account for the observed change in drag reduction effectiveness. Drag reduction effectiveness is unchanged by the presence of salt when the stock solution concentration is sufficiently above the critical concentration c_D. Finally, the drag reduction effectiveness decreases with time when diluted from an entangled stock solution but remains greater than the homogeneous case after more than 24 h.     

Ideal elastic fluids of different viscosity and elasticity levels

Four constant viscosity, highly elastic fluids of different viscosity and elasticity levels are presented. The viscosity ranges from 4 × 10^?3 to 5.0 Pa s and the Maxwell relaxation time varies from 0.09 to 4.5 s. The steady and dynamic shear properties are determined. These fluids comply with the requirements of the simple fluid theory except for theG′ andN ₁/2 data where a slight deviation is observed. The results suggest the possibility of preparing a wide range of constant viscosity elastic fluids with specific values of viscosity and relaxation time by manipulating polymer molecular parameters as well as polymer concentration, solvent viscosity and salt addition. The effects of each of these parameters on the rheological behaviour are examined.     

Drag reduction by coupled systems: microbubble injection with homogeneous polymer and surfactant solutions

 The influence of homogeneous surfactant and homogeneous polymer solutions on the performance of microbubble skin friction reduction was investigated on an axisymmetric body. Carbon dioxide was injected into water, homogeneous surfactant (Aerosol OT) solutions, and homogeneous dilute polymer (Polyethylene oxide) solutions. Integrated skin friction measurements were obtained at two freestream velocities as a function of gas injection rate and polyethylene-oxide concentration. A moderate (50%) decrease in surface tension had little to no effect on the drag reducing characteristics of microbubble injection. At similar gas injection rates, microbubble injection exhibited more drag reduction in the polymer solutions than obtained with microbubble injection into water. However, the increased drag reduction obtained with polymer additives was no more than a multiplicative factor related to the baseline levels of drag reduction achieved by the individual methods, and suggests the mechanism for microbubble skin friction reduction acts independently of the polymer drag reduction. Received: 17 April 1998 / Accepted: 12 October 1998     

Finitely extensible bead spring chains in time-dependent shear flows

The configurational and rheological properties of bead spring chains in time-dependent shear flows are calculated. The finite extensibility is incorporated through the constraint of constant contour length of the chain. Start-up of shear flow yields a stress overshoot, whereas oscillatory shear flow yields the same frequency dependence of the dynamic moduli as the simple bead spring model. The results show that finite extensibility can lead to non-linear rheological behavior of dilute polymer solutions. The influence of preaveraged hydrodynamic interaction on the obtained results is discussed.     

Effects of chemical structures of para-halobenzoates on micelle nanostructure,drag reduction and rheological behaviors of dilute CTAC solutions

Counterion chemical structure and counterion to cationic surfactant molar ratio, ξ, control counterion binding, micelle nanostructures, drag reduction (DR) effectiveness and rheological behavior of quaternary ammonium surfactant systems. The effects of chemical structures of four sodium para-halobenzoate (F, Cl, Br, I) counterions with different ξ values on these properties were compared for dilute solutions of cetyltrimethylammonium chloride (CTAC). Counterion binding was determined by zeta-potential and ¹H NMR measurements. Nanostructures were determined by ¹H NMR and cryo-TEM imaging. Nanostructures, drag reduction effectiveness measured over a range of temperatures and Reynolds numbers, shear viscosities and first normal stress differences N1 were related to the chemical structures of the four counterions and their molar ratios to CTAC.     

Drag reduction in polymer mixtures

Summary Drag reduction was studied in dilute toluene solutions of a mixture of two polymers: polyisobutylene (of three different molecular weights) and 1,4-cis-isoprene rubber in the turbulent region at low (up to 5000) Reynolds numbers. Experiments were carried out with mixed solutions at a concentration equal to optimum concentration of polyisobutylene or higher than it. Drag reduction of the polymer mixtures depending on the ratio of the two polymers showed a positive deviation from the additive straight line at all concentrations investigated. To evaluate the degree of deviation from additivity, the excess drag reduction, was introduced which represents the difference between the actually measured drag reduction and that read from the additive straight line. The excess drag reduction showed almost no dependence on the molecular weight of polyisobutylene in the investigated range of this magnitude. Deviation from additivity depending on the ratio of the two polymers in the mixture growed higher with increasing the flow rate at a given molecular weight of polyisobutylene. The highest excess drag reduction was observed in solutions containing a larger amount of the lower molecular isoprene rubber polymer. The effect of polymer coils on drag reduction in binary polymer solutions was studied. An assumption was made that higher drag reduction in the polymer mixtures as compared to the additive was due to the change of polymer coil dimensions caused by the copresence of the macromolecules of both polymers in the solution. It was further supposed that low shear stresses at which the experiments were carried out caused sufficient orientation and deformation of isoprene rubber enlarged molecules and the contribution of the latter in increasing drag reduction of the mixture was higher.

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Zusammenfassung Die Widerstandsverminderung in verdünnten toluolischen Lösungen einer Mischung von zwei verschiedenen Polymeren wird untersucht. Verwendet werden Polyisobutylene (mit drei verschiedenen Molekulargewichten) und 1,4-cis-Isopren-Kautschuk, und es wird im turbulenten Bereich bei Reynolds-Zahlen bis zu 5000 gemessen. Die Versuche werden bei Konzentrationen, die der Optimalkonzentration von Polyisobutylen entsprechen, oder höheren Konzentrationen durchgeführt. Die Widerstandsverminderung der Polymermischungen zeigt bei allen untersuchten Konzentrationen eine positive Abweichung von der additiven Geraden, deren Größe vom Mischungsverhältnis abhängt. Zur Beschreibung der Abweichung vom additiven Verhalten wird die überschüssige Widerstandsverminderung (excess drag reduction) eingeführt, welche die Differenz zwischen dem wirklich gemessenen Wert und dem zugeordneten Wert auf der additiven Geraden beschreibt. Diese Größe zeigt nur eine geringe Abhängigkeit vom Molekulargewicht der eingesetzten Polyisobutylene. Die Abweichung vom additiven Verhalten als Funktion des Mischungsverhältnisses beider Polymeren wächst mit zunehmendem Volumenstrom. Die größte überschüssige Widerstandsverminderung wird in Lösungen beobachtet, die einen größeren Anteil des weniger hochmolekularen Isopren-Kautschuks enthalten. Der Einfluß der Polymerverknäuelung auf die Widerstandsverminderung wird betrachtet. Es wird angenommen, daß die überschüssige Widerstandsverminderung auf eine Änderung der Knäuelgröße infolge der Anwesenheit des jeweils anderen Polymeren in der Lösung zurückzuführen ist. Weiter wird vermutet, daß die relativ niedrigen Schubspannungen, bei denen die Versuche ausgeführt wurden, doch schon eine hinreichend starke Orientierung und Deformation der aufgeweiteten Isopren-Kautschuk-Moleküle bewirken, so daß deren Beitrag zur Erhöhung der Widerstandsverminderung überwiegt.

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Notations D diameter of capillary - DR drag reduction - DR _add additive drag reduction - DR excess drag reduction,DR = DR – DR _add - DR _mixture theoretical drag reduction of the mixture - DR _mixture ^* actually measured drag reduction of the mixture - DR _1R drag reduction of an IR molecule in a separate IR solution - DR _1R ^* drag reduction of an IR molecule in the presence of molecules of another polymer in the solution - DR _PIB drag reduction of a PIB molecule in a separate PIB solution - DR _PIB ^* drag reduction of a PIB molecule in the presence of molecules of another polymer in the solution - L length of the capillary - flow rate - c concentration - n number of IR molecules - p number of PIB molecules - _w wall shear stress - CMC carboxymethylcellulose - IR isoprene rubber - PAA polyacrylic acid - PAM polyacrylamide - PEI polyethyleneimine - PEO polyethylene oxide - PIB polyisobutylene - PS polystyrene     

An investigation of possible mechanisms of heterogeneous drag reduction in pipe and channel flows

When concentrated polymer solutions are injected into the core-region of a turbulent pipe or channel flow, the injected polymer solution forms a thread which preserves its identity far beyond the injection point. The resulting drag reduction is called heterogeneous drag reduction.This study presents experimental results on the mechanism of this type of drag reduction. The experiments were carried out to find out whether this drag reduction is caused by small amounts of polymer removed from the thread and dissolved in the near-wall region of the flow or by an interaction of the polymer thread with the turbulence. The friction behavior of this type of drag reduction was measured for different concentrations in pipes of different cross-sections, but of identical hydraulic diameter. The parameters of the injection, i.e. injector geometry as well as the ratio of the injection to the bulk velocity, were varied. In one set of experiments the polymer thread was sucked out through an orifice and the friction behavior in the pipe was determined downstream of the orifice. In another experiment, near-wall fluid was led into a bypass in order to measure its drag reducing properties. Furthermore, the influence of a water injection into the near-wall region on the drag reduction was studied.The results provide a strong evidence that heterogeneous drag reduction is in part caused by small amount of dissolved polymer in the near-wall region as well as by an interaction of the polymer thread with the turbulence.Nomenclature a channel height - b channel width - c _p concentration of the injected polymer solution - c _R effective polymer concentration averaged over the cross-section - d pipe or hydraulic diameter - d _i injector diameter - DR drag reduction - f friction factor - l downstream distance from injector - L length of a pipe segment - P polymer type - p differential pressure - Re Reynolds number - U bulk velocity - u ^* ratio of injection to bulk velocity - y ⁺ dimensionless wall distance - v kinematic viscosity - density of the fluid - _w wall shear stress     

Experiments in Turbulent Pipe Flow with Polymer Additives at Maximum Drag Reduction

In this paper we report on (two-component) LDV experiments in a fully developed turbulent pipe flow with a drag-reducing polymer (partially hydrolyzed polyacrylamide) dissolved in water. The Reynolds number based on the mean velocity, the pipe diameter and the local viscosity at the wall is approximately 10000. We have used polymer solutions with three different concentrations which have been chosen such that maximum drag reduction occurs. The amount of drag reduction found is 60–70%. Our experimental results are compared with results obtained with water and with a very dilute solution which exhibits only a small amount of drag reduction. We have focused on the observation of turbulence statistics (mean velocities and turbulence intensities) and on the various contributions to the total shear stress. The latter consists of a turbulent, a solvent (viscous) and a polymeric part. The polymers are found to contribute significantly to the total stress. With respect to the mean velocity profile we find a thickening of the buffer layer and an increase in the slope of the logarithmic profile. With respect to the turbulence statistics we find for the streamwise velocity fluctuations an increase of the root mean square at low polymer concentration but a return to values comparable to those for water at higher concentrations. The root mean square of the normal velocity fluctuations shows a strong decrease. Also the Reynolds (turbulent) shear stress and the correlation coefficient between the stream wise and the normal components are drastically reduced over the entire pipe diameter. In all cases the Reynolds stress stays definitely non-zero at maximum drag reduction. The consequence of the drop of the Reynolds stress is a large polymer stress, which can be 60% of the total stress. The kinetic-energy balance of the mean flow shows a large transfer of energy directly to the polymers instead of the route by turbulence. The kinetic energy of the turbulence suggests a possibly negative polymeric dissipation of turbulent energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

An investigation of non-newtonian flow past a sphere

Any experimental work on the flow of a polymer solution or any theoretical analysis on the basis of a visoelastic constitutive equation does not always bring out viscoelastic effects but may be showing a non-Newtonian viscosity effect. Therefore, in order to obtain a clear understanding about viscoelastic effects, it is desirable to have a sufficient knowledge of the non-Newtonian viscosity effect. To facilitate this, finite-difference numerical solutions of non-Newtonian flow were carried out using a non-Newtonian viscous model for the Reynolds numbers of 0.1, 1.0, 20 and 60.Drag force measurements and flow visualization experiments were also performed over a wide range of experimental conditions using polymer solutions. The present work appears to support the following idea: When compared with the Newtonian case on the basis of DV_∞P/η₀, where η₀ is the zero shear viscosity, it is on account of the non-Newtonian viscosity that the friction and pressure drags decrease, that the separating vortices behind the sphere become larger, and that no shift occurs in the streamlines. On the other hand, it is due to viscoelasticity that the normal force drag increases, that the separating vortices behind the sphere become smaller, and that an upstream shift occurs in the streamlines.     

Extensional flow resistance of dilute polyacrylamide and surfactant solutions

The extensional flow behaviour of dilute aqueous solutions of a partiallyhy-drolyzed polyacrylamide and a surfactant were investigated in an extensional flow cell. The cell was designed such that fluids were subjected to steady shear before undergoing extensional motion in a converging channel. Extensional resistance was monitored by measuring the pressure drop through the channel. Such measurements were made over a range of extensional rates at fixed values of the upstream shear rate. Solutions of different concentrations were tested — up to 40 ppm of polyacrylamide and 450 ppm of surfactant — at various temperatures in the case of surfactant and for different types and amounts of salt in the case of polyacrylamide. Of the results, the more notable are that the extensional resistance of polyacrylamide solutions is affected much more by CaCl₂ than by NaCl and that surfactant solutions do not exhibit extensional resistance unless they are pre-sheared.     

Drag reduction effectiveness and shear stability of polymer-polymer and polymer-fibre mixtures in recirculatory turbulent flow of water

The turbulent drag reduction caused by polymer-polymer and polymerfibre mixtures has been measured in recirculatory flow of water. Shear stability studies have also been made on a number of drag reducing polymers, asbestos fibres and their mixtures in recirculatory turbulent flow of water. Reynolds numbers ranged from 20,000 to 57,000. Both positive and negative deviations from linear additive behaviour have been observed in drag reduction caused by the polymer-polymer mixtures depending upon their compositions, flow rate and polymer species in the mixture. The drag reduction by the mixtures has been predicted by using simple mixture rule equations including an interaction parameter. This interaction parameter is believed to depend upon the polymer interaction in the polymer mixture. The random coil size and rigidity of the polymer molecules appear to be responsible for the synergism observed in the drag reduction caused by the mixture. In general, mixtures having larger solvation number seem to give positive synergism.Synergism in drag reduction by the polymer-fibre mixtures has also been observed. The simple mixture law equation with interaction parameter is also applicable in predicting the drag reduction by the mixtures as above. The random coil size of the polymer molecules and the rigidity of the polymer-fibre system appear to be responsible for the synergism observed in drag reduction. In the shearstability studies it has been observed that the decrement in drag reduction (DR) is higher than the the decrement in absolute viscosity in most cases. Carboxymethyl cellulose is found to be the most shear stable polymer followed by guar gum, xanthan gum and polyacrylamide. The mixtures exhibiting synergism in causing drag reduction are found to be more shear stable.     

Heterogeneous drag reduction in turbulent pipe flows using various injection techniques

The results of an experimental study of the injection of concentrated polymer solutions into the near-wall region of a turbulent pipe flow are reported. The injection experiments described here show drag reduction that was significantly larger than that obtained for homogeneous polymer solutions of the same average concentration. Local drag reduction and friction behavior was obtained by measuring pressure differences over a test section of 13 m in length. Furthermore the flow behaviour of the injected polymer solution was investigated by flow visualization experiments. Velocity profile measurements elucidate in case of near-wall injection that the turbulent structure could be altered in the near-wall and also in the core region of the pipe flow, indicating that the polymer lumps and threads created by the near-wall injection are able to influence a much wider spectrum of turbulent eddies in comparison to centreline injection or, all the more, to homogeneous drag reduction.     

Time-dependent drag reduction and ageing in aqueous solutions of a cationic surfactant

The turbulent pipe flow of a highly dilute aqueous cationic surfactant solution is investigated by means of a pulsed ultrasound Doppler method with special emphasis on the wall boundary layer. The velocity profiles are recorded for several Reynolds numbers at varying ages of the solution. The wall shear stress velocities u _τ used for the normalization of the velocity profiles are determined by fitting the measured profiles to the universal linear velocity profile in the viscous sublayer. The theoretical pressure loss is then calculated from the numerical values of u _τ and compared to the experimental values. Two different scaling methods are discussed for the velocity fluctuations concerning the correlation of the root-mean square values with the effect and the amount of drag reduction. It is shown that outer scaling with the mean velocity is appropriate for the detection of drag reduction in surfactant solutions, rather than inner scaling with the wall shear stress velocity, which is common practice in investigations of 'usual' turbulent flows.     

Influence of molecular weight and molecular conformation of polymers on turbulent drag reduction

Summary An investigation was carried out on drag reduction of diluted solutions of four polyisobutylenes of different molecular weight in diversely good and poor solvents in the turbulent region at small (up to 5000) and average (from 19 000 to 42 000) Reynolds numbers, as well as of mixtures of polyisobutylene and polystyrene and of two polyisobutylenes of different molecular weight. Concentration at maximum drag reduction grows, while drag reduction itself decreases with molecular weight going down. The universal curve established byVirk et al. for aqueous solutions of a polyethylene oxide family is also confirmed for a family of polyisobutylenes in an organic solvent. The effect of polymer coils of various dimensions on drag reduction is assessed. PIB coils of various dimensions are produced in two ways — dissolving polyisobutylenes of different molecular weight in a given solvent and dissolving polyisobutylene of a definite molecular weight in diversely good and poor solvent. Coil dimensions in the solution are increasing with the growth of intrinsic viscosity of a polymer by dissolving it in still better solvents, but probably due to impeded orientation and deformation of the larger polymer coils their drag reduction is smaller at low rather than at high shear stresses. Drag reduction of diluted solutions of two PIB differing in molecular weight shows almost no deviation from the additive straight line both when the overall concentration of solutions is equal and when it exceeds the one at maximum drag reduction of PIB of higher molecular weight. Drag reduction of diluted solutions of PIB and PS mixtures at an overall concentration higher than optimum concentration shows a positive deviation from the additive straight line.

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Zusammenfassung Untersucht wurde die Verringerung des Reibungswiderstandes (VRW) fließender, verdünnter Lösungen von vier Polyisobutylenen mit verschiedenem Molekulargewicht in unterschiedlich guten und schlechten Lösungsmitteln im turbulenten Bereich bei kleinen (bis 5000) und bei mittleren (von 19 000 bis 42 000) Reynoldsschen Zahlen, sowie von Mischungen aus Polyisobutylen und Polystyrol und aus zwei Polyisobutylenen mit verschiedenem Molekulargewicht. Die Konzentration bei maximalem VRW-Effekt nimmt zu, und der maximale VRW-Effekt selbst vermindert sich mit abnehmendem Molekulargewicht. Die vonVirk und Mitarbeitern für wäßrige Lösungen einer Reihe von Polyäthylenen festgestellte universale Kurve wird auch für die Polyisobutylenfamilie in einem organischen Lösungsmittel bestätigt. Der Einfluß der nach ihren Dimensionen unterschiedlichen Polymerknäuel auf die Verringerung des Reibungswiderstandes wurde ausgewertet. Polyisobutylen-Knäuel mit verschiedenen Dimensionen werden auf zwei Weisen realisiert, durch Auflösung von Polyisobutylenen mit verschiedenem Molekulargewicht in einem gegebenen Lösungsmittel und durch Auflösung von Polyisobutylen mit einem gegebenen Molekulargewicht in unterschiedlich guten und schlechten Lösungsmitteln. Mit der durch seine Auflösung in immer besseren Lösungsmitteln steigenden Grenzviskosität eines Polymeren nehmen die Knäueldimensionen in den Lösungen zu. Jedoch ist, wahrscheinlich wegen der damit verbundenen Behinderung der Orientierung und Deformierung der größeren Polymerknäuel, ihr VRW-Effekt bei den niedrigen Scherspannungen kleiner als bei den höheren. Der VRW-Effekt der verdünnten Lösungen aus zwei Polyisobutylenen mit verschiedenem Molekulargewicht weist fast keine Abweichung von der additiven Geraden auf, sowohl wenn die Gesamtkonzentration der Lösungen gleich als auch wenn sie größer als die Konzentration beim maximalen VRW-Effekt des Polyisobutylens mit höherem Molekulargewicht ist. Der VRW-Effekt der verdünnten Lösungen von Mischungen aus Polyisobutylen und Polystyrol mit einer über der optimalen liegenden Gesamtkonzentration zeigt eine positive Abweichung von der additiven Geraden.

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D diameter of capillary - [DR] intrinsic drag reduction - DR _F fractional drag reduction - DR _{F, max} maximum fractional drag reduction - DR_sp specific drag reduction - K constant - L length of capillary - M _v molecular weight of polymer, determined by the viscosimetric method - flow rate - c concentration - [c] intrinsic concentration - _equiv. equivalent sphere density - _{w, p} wall shear stress of polymer solution - _{w, s} wall shear stress of solvent - CMC carboxymethylcellulose - PAA polyacrylamide - PEO polyethylene oxide - PIB polyisobutylene - PS polystyrene - DR drag reduction With 8 figures and 2 tables     

On two distinct types of drag-reducing fluids,diameter scaling,and turbulent profiles

Two distinct scaling procedures were found to predict the diameter effect for different types of drag-reducing fluids. The first one, which correlates the relative drag reduction (DR) with flow bulk velocity (V), appears applicable to fluids that comply with the 3-layers velocity profile model. This model has been applied to many polymer solutions; but the drag reduction versus V scaling procedure was successfully tested here for some surfactant solutions as well. This feature, together with our temperature profile measurements, suggest that these surfactant solutions may also show this type of 3-layers velocity profiles (3L-type fluids).The second scaling procedure is based on a correlation of τ_w versus V, which is found to be applicable to some surfactant solutions but appears to be applicable to some polymer solutions as well. The distinction between the two procedures is therefore not simply one between polymer and surfactants. It was also seen that the τ_w versus V correlation applies to fluids which show a stronger diameter effect than those scaling with the other procedure. Moreover, for fluids that scale according to the τ_w versus V procedure, the drag-reducing effects extend throughout the whole pipe cross section even at conditions close to the onset of drag reduction, in contrast to the behavior of 3L fluids. This was shown by our measurements of temperature profiles which exhibit a fan-type pattern for the τ_w versus V fluids (F-type), unlike the 3-layers profile for the fluids well correlated by drag reduction versus V. Finally, mechanically-degraded polymer solutions appeared to behave in a manner intermediate between the 3L and F fluids.Furthermore, we also showed that a given fluid in a given pipe may transition from a Type A drag reduction at low Reynolds number to a Type B at high Reynolds number, the two types apparently being more representative of different levels of fluid/flow interactions than of fundamentally different phenomena of drag reduction. After transition to the non-asymptotic Type B regime, our results suggest that, without degradation, the friction becomes independent of pipe diameter and that the drag reduction level becomes also approximately independent of the Reynolds number, in a strong analogy to Newtonian flow.     

Influence of wavy structured surfaces and large scale polymer structures on drag reduction

Drag reduction was studied for turbulent flow over a structured wall that contained 600 sinusoidal waves with a wavelength of 5 mm and an amplitude of 0.25 mm. A concentrated solution of a co-polymer of polyacrylamide and sodium acrylate was injected into the flow through wall slots. Laser Doppler velocimetry was used to measure turbulence. A fluorescence technique was developed that enabled us to demonstrate the existence, under certain circumstances, of large gelatinous structures in the injected polymer solution and in the flow channel.At maximum drag reduction, the Reynolds shear stress was zero and the velocity field was the same as found for a smooth surface. Larger drag reductions could be realized for a wavy wall because the initial drag was larger. The influences of polymers on the turbulent fields are similar for smooth and wavy boundaries. These results are of interest since the interaction with the wall can be quite different for water flow over smooth and wavy boundaries (which are characterized as being completely rough). An important effect of polymers is a decreasing relative importance of high frequency fluctuations with increasing drag reduction that is characterized by a cut-off frequency. This cut-off is the same for smooth and wavy walls at maximum drag reduction. The sensitivity of drag reduction to the method of preparing and delivering the polymer solution suggests that aggregation of polymers could be playing an important role for the system that was studied. For example, drag reduction was enhanced when large polymer structures are present.