Drag-reducing Polymer Solutions Research Articles

Nested travelling wave structures in elastoinertial turbulence

Elastoinertial turbulence (EIT) is a chaotic flow resulting from the interplay between inertia and viscoelasticity in wall-bounded shear flows. Understanding EIT is important because it is thought to set a limit on the effectiveness of turbulent drag reduction in polymer solutions. Here, we analyse simulations of two-dimensional EIT in channel flow using spectral proper orthogonal decomposition (SPOD), discovering a family of travelling wave structures that capture the sheetlike stress fluctuations that characterise EIT. The frequency-dependence of the leading SPOD mode contains distinct peaks and the mode structures corresponding to these peaks exhibit well-defined travelling structures. The structure of the dominant travelling mode exhibits shift–reflect symmetry similar to the viscoelasticity-modified Tollmien–Schlichting (TS) wave, where the velocity fluctuation in the travelling mode is characterised by large-scale regular structures spanning the channel and the polymer stress field is characterised by thin, inclined sheets of high polymer stress localised at the critical layers near the channel walls. The travelling structures corresponding to the higher-frequency modes have a very similar structure, but are nested in a region roughly bounded by the critical layer positions of the next-lower-frequency mode. A simple theory based on the idea that the critical layers of mode $\kappa$ form the ‘walls’ for the structure of mode $\kappa +1$ yields quantitative agreement with the observed wave speeds and critical layer positions, indicating self-similarity between the structures. The physical idea behind this theory is that the sheetlike localised stress fluctuations in the critical layer prevent velocity fluctuations from penetrating them.

Prediction and New Insight for the Drag Reduction of Turbulent Flow with Polymers and Its Degradation Mechanism.

A physicochemical understanding of the mechanism of turbulent flow drag reduction with polymer and its degradation is of great interest from both science and industry perspectives. Although the correlation based on the Fourier series has been proposed to predict the drag reduction and its degradation, its physical meaning was not clear until now. This letter aims to clarify this issue. We develop a comprehensive model to predict the drag reduction and degradation of polymers in turbulent flow from a chemical thermodynamics and kinetics viewpoint. We demonstrate that the Fourier series employed to predict the drag reduction and its degradation is due to the viscoelastic property of drag-reducing polymer solution, and the phase angle in the model, in physical nature, represents the hysteresis of the polymer in turbulent flow. Besides, our new insight of drag reduction with flexible polymers can also explain why a maximum drag reduction in rotational flow appears before degradation happens.

Impact of Polymer Degradation on Past Studies of the Mean Velocity Profile in Turbulent Boundary Layers

Abstract This study reexamines past studies of how drag-reducing polymer solutions modify the log-region of a developing turbulent boundary layer (TBL). The classical view was that the polymers modify the intercept constant without impacting the von Kármán coefficient, which results in the log-region being unaltered though shifted outward from the wall. However, recent work has shown this to be not accurate, especially at high drag reduction (HDR) (>40%). While the deviations to the von Kármán coefficient were conjectured to be related to polymeric properties, this had not been explored. This work examines the scatter in both log-region parameters and estimates the local polymeric properties. This shows that the scatter of the von Kármán coefficient between studies is related to the inner variable based Weissenberg number. In addition, recent polymer ocean results are included that support the implicit assumption in past studies that the maximum wall concentration should be used to define the local polymeric properties.

Exact Coherent States and the Nonlinear Dynamics of Wall-Bounded Turbulent Flows

Wall-bounded turbulence exhibits patterns that persist in time and space: coherent structures. These are important for transport processes and form a conceptual framework for important theoretical approaches. Key observed structures include quasi-streamwise and hairpin vortices, as well as the localized spots and puffs of turbulence observed during transition. This review describes recent research on so-called exact coherent states (ECS) in wall-bounded parallel flows at Reynolds numbers Re [Formula: see text] 104; these are nonturbulent, nonlinear solutions to the Navier–Stokes equations that in many cases resemble coherent structures in turbulence. That is, idealized versions of many of these structures exist as distinct, self-sustaining entities. ECS are saddle points in state space and form, at least in part, the state space skeleton of the turbulent dynamics. While most work on ECS focuses on Newtonian flow, some advances have been made on the role of ECS in turbulent drag reduction in polymer solutions. Emerging directions include applications to control and connections to large-scale structures and the attached eddy model.

Flow and heat transfer in drag-reducing polymer solution flow through the corrugated tube and circular tube

Flow and heat transfer characteristics of xanthan gum (XG) solutions are experimentally studied to compare the drag reduction (DR) and heat transfer reduction (HTR) behavior in the corrugated tube with that in the circular tube. Effects of XG concentration (C) and bulk velocity (v) on drag enhancement (DE), heat transfer enhancement (HTE) and comprehensive performance index (ξ) in the corrugated tube are also examined. The results show that the DR in the corrugated tube increases and then decreases until becomes negative with increasing bulk velocity under the intense turbulent disturbance of the corrugated wall, which is different from the DR behavior in the circular tube, and the onset of DR is found to occur earlier. In addition, the variation trend of HTR is consistent with that of DR’s absolute value, which is closely related to the interaction between drag reduction property and high viscosity property of XG solutions. Furthermore, the HTE and ξ increase with increasing XG concentration and decreasing bulk velocity, and the maximum HTE and ξ can be up to 25 and 1600, which proves the corrugated tube has a specific applicability in terms of energy saving and heat transfer enhancement for high-concentration XG solutions at low velocity.

Modification of turbulent boundary layer coherent structures with drag reducing polymer solution

The modification of dominant coherent structures that extend through the log-region of a drag reduced turbulent boundary layer is studied via examination of two-point correlations from time-resolved particle-image-velocimetry. Measurements were acquired in polymer oceans (uniform concentration) at drag reduction levels corresponding to the low drag reduction regime (<40%) and the high drag reduction (HDR) regime (>40%) and at an intermediate level (46%). The mean velocity profiles and two-point correlations were compared with those of water (Newtonian, DR = 0%). These results show that, with increasing drag reduction, the inclination of these dominant coherent structures decreases, their streamwise extent increases, and the fluctuations in the correlations are suppressed (especially at HDR). These observations are examined in comparison with the coherent structure literature (Newtonian and polymeric).

Near-wall motion of inertial particles in a drag-reduced non-Newtonian turbulent flow

The kinematics of inertial particles suspended in the near-wall region of Newtonian and non-Newtonian turbulent channel flows was experimentally investigated. The non-Newtonian fluid was a homogeneous solution of 90 part per million of a polyacrylamide polymer in water with 66% drag reduction. All the experiments were performed at the same volumetric flow rate with Reynolds number of 34,300 based on bulk velocity, channel height, and the kinematic viscosity of water. The inertial particles were 250-μm glass beads with St of 35 (in water) at a volumetric concentration of 0.05%. A time-resolved two-dimensional particle tracking velocimetry was used to record particle images at acquisition frequency of 17.6 kHz and detect trajectory of flow tracers and the glass beads. The recorded data were processed using a two-dimensional particle tracking algorithm to obtain the Lagrangian kinematics of the beads. The comparison between laden flows of water and polymer solution showed reduction of number density of the beads and their momentum in the vicinity of the wall in the polymeric flow. The polymer solution remarkably reduced the wall-normal and shear Reynolds stresses of the beads, but had a negligible effect on their streamwise Reynolds stress. The wall-normal fluctuation of the beads reduced in the polymeric flow and their trajectories became parallel with the channel wall. Results also showed that the ejection and sweep motions were not the major mechanism for wall-normal distribution of the beads in the polymeric flow. Outcomes suggest that drag-reducing polymer solutions have the potential of reducing erosive wear in particle-laden pipelines.

Time‐series and extended Karhunen–Loève analysis of turbulent drag reduction in polymer solutions

Direct numerical simulations and statistical analysis techniques are used to study the drag‐reducing effect of polymer additives on turbulent channel flow in minimal domains. Additionally, a new formulation of Karhunen–Loève decomposition for viscoelastic flows is introduced, allowing the dominant features of the polymer stress fields to be characterized. In minimal channels, there are intervals of “active” and “hibernating” turbulence that display very different structural and energetic characteristics; the present work illustrates how the statistics of these intervals evolve over the entire range of drag reduction (DR) levels. The effect of viscoelasticity on minimal channel turbulence is twofold: first, it strongly suppresses the active turbulent dynamics that predominate in Newtonian flow and second, at sufficiently high Weissenberg number it stabilizes the dynamics of hibernating turbulence, allowing it to predominate in the maximum drag reduction regime. In this regime, the stress fluctuations become delocalized from the wall region, encompassing the entire flow domain. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1460–1475, 2014

Modification of the mean near-wall velocity profile of a high-Reynolds number turbulent boundary layer with the injection of drag-reducing polymer solutions

The current study explores the influence of polymer drag reduction on the near-wall velocity distribution in a turbulent boundary layer (TBL) and its dependence on Reynolds number. Recent moderate Reynolds number direct numerical simulation and experimental studies presented in White et al. [Phys. Fluids 24, 021701 (2012)]10.1063/1.3681862 have challenged the classical representation of the logarithmic dependence of the velocity profile for drag-reduced flows, especially at drag reduction levels above 40%. In the present study, high Reynolds number data from a drag reduced TBL is presented and compared to the observations of White et al. [Phys. Fluids 24, 021701 (2012)]10.1063/1.3681862. Data presented here were acquired in the TBL flow on a 12.9-m-long flat plate at speeds to 20.3 m s−1, achieving momentum thickness based Reynolds number to 1.5 × 105, which is an order of magnitude greater than that available in the literature. Polyethylene oxide solutions with an average molecular weight of 3.9 × 106 g mol−1 were injected into the flow at various concentrations and volumetric fluxes to achieve a particular level of drag reduction. The resulting mean near-wall velocity profiles show distinctly different behavior depending on whether they fall in the low drag reduction (LDR) or the high drag reduction (HDR) regimes, which are nominally divided at 40% drag reduction. In the LDR regime, the classical view that the logarithmic slope remains constant at the Newtonian value and the intercept constant increases with increasing drag reduction appears to be valid. However, in the HDR regime the behavior is no longer universal. The intercept constant continues to increase linearly in proportion to the drag reduction level until a Reynolds-number-dependent threshold is achieved, at which point the intercept constant rapidly decreases to that predicted by the ultimate profile. The rapid decrease in the intercept constant is due to the corresponding increase in the profile slope in the HDR regime. There was significant scatter in the observed slope in the HDR regime, but the scatter did not appear to be Reynolds number dependent. Finally, the ultimate profiles for flows at maximum drag reduction were examined and did not exhibit a logarithmic functional relationship, which is the classical empirical relationship suggested by Virk [J. Am. Inst. Chem. Eng. 21, 625–656 (1975)]10.1002/aic.690210402.

Analysis of coherent structures in drag-reducing polymer solution flow based on proper orthogonal decomposition

Direct numerical simulation (DNS) of forcing homogeneous isotropic turbulence with polymers was performed. In order to understand the polymers effect on turbulent coherent structures, proper orthogonal decomposition was performed to identify coherent structures based on DNS data, so as to analyze the remarkable difference due to the addition of polymers. The results showed that the numbers for eigenmodes required for capturing coherent structures were 32 and 24 for the Newtonian fluid and polymer solution flows, respectively, which means the decrease of the complexity in polymer solution flow. Through the POD energy spectrum, it was found that the turbulent kinetic energy is distributed onto a large number of eigenmodes whether in the Newtonian fluid flow or polymer solution flow, suggesting that polymer solution flow is still turbulent in one aspect. Besides, the POD eigenmodes were investigated, which found that the small-scale structures are inhibited in polymer solution flow.

Shear layers in the turbulent pipe flow of drag reducing polymer solutions

A range of high molecular weight polymers (polyethylene oxide) was dissolved at very low concentrations – in the order of few wppm – in a solvent (water). The Newtonian character of the polymer solutions was confirmed by rheological measurements. The polymer solutions were then pumped through a long horizontal pipe section in fully developed turbulent conditions. The flow experienced a reduction in frictional drag when compared to the drag experienced by the equivalent flow of the pure solvent. Specifically, drag reduction was measured at Reynolds numbers ranging from 3.5×104 to 2.1×105 in a pressure driven flow facility with a circular tube section of internal diameter 25.3mm. The turbulent flow was visualized by Particle Image Velocimetry and the resulting data were used to investigate the effect of the drag reducing additives on the turbulent pipe flow. Close attention was paid to the mean and instantaneous velocity fields, as well as the two-dimensional vorticity and streamwise shear strain rate. The results indicate that drag reduction is accompanied by the appearance of “shear layers” (i.e. thin filament-like regions of high spatial velocity gradients) that act as interfaces separating low-momentum flow regions near the pipe wall and high-momentum flow regions closer to the centerline. The shear layers are not stationary. They are continuously formed close to the wall at a random frequency and move towards the pipe centerline until they eventually disappear, thus occupying or existing within a “shear layer region”. It is found that the mean thickness of the shear layer region is correlated with the measured level of drag reduction. The shear layer region thickness is increased by the presence of polymer additives when compared to the pure solvent, in a similar way to the thickening of the buffer layer. The results provide valuable insights into the characteristics of the turbulent pipe flow of a solvent containing drag reducing polymers that can be used to further our understanding of the role of polymers on the mechanism of drag reduction and to develop advanced drag reduction models.

Laminar and Turbulent Friction Factors for Annular Flow of Drag-Reducing Polymer Solutions in Coiled-Tubing Operations

Summary The challenge of theoretical and numerical studies of annular fluid flow with varying eccentricity is mainly a result of the required coordinate systems. Computational-fluid-dynamics (CFD) modeling provides the state-of-the-art approach of investigating fluid flow in such complex geometries. In this study, results from a series of numerical simulations for the fully developed laminar flow of non-Newtonian power-law fluids in concentric and eccentric annular geometries are used to investigate the effect of eccentricity, flow-behavior index, and diameter ratio (ratio of the outer diameter of the inner tubing to the inner diameter of the outer tubing) on axial frictional pressure losses. The frictional pressure-loss gradients predicted by the CFD simulations were verified by comparing with the published studies and flow data from a field-scale experimental setup. At a constant flow rate, it is confirmed that frictional pressure losses decrease with increasing eccentricity. A good agreement was obtained with the Haciislamoglu and Langlinais (1990) correlation, and the results of this study, especially at low values of eccentricity. At very high eccentricities, data from the CFD model yield lower frictional pressure loss compared to Haciislamoglu and Langlinais (1990) correlation. This type of expression is obtained and the improved data of this study is incorporated. Next, this paper presents the results of an experimental study carried out to investigate frictional pressure-loss behavior of drag- reducing polymer solutions, flowing turbulently through an eccentric annulus. The experimental setup includes 30 ft of 3½×2⅜-in., 200 ft of 3½×1¾-in., 69 ft of 5½ × 4-in., and 79 ft of 5 ×3½-in. fully eccentric annuli. Data analysis enabled the development of a new correlation using fluid apparent viscosity at 511 sec–1, generalized Reynolds number, and diameter ratio, all of which can be easily determined in the field as independent variables. These new correlations for laminar and turbulent flow of drag-reducing polymer solutions present an improvement to existing correlations, and also permit undemanding hydraulic-program calculations for varying annular configurations.

Drag Reduction of Biopolymer Flows

Drag reduction of rigid and semi-rigid biopolymers – scleroglucan (0.005% and 0.01% w/w) and xanthan gum (0.0124% and 0.07% w/w) – in a circular pipe and a concentric annular pipe (radius ratio  = 0.5) have been investigated experimentally. The objective here is to assess and study the behaviour of these polymers and compare to the drag reduction by flexible polymers, available in the literature. Pressure-drop, mean axial and complete Reynolds normal stress data measurements on the polymer solutions were conducted using laser Doppler anemometry. Measurements were also performed on the Newtonian solvent (water) for comparison. Rheological characterization of the polymers conducted over a wide range of concentrations (0.005% - 0.75% w/w) showed increased shear-thinning ability of the polymer solutions with increasing solution concentration. The pressure-drop measurements indicate that the effectiveness of these polymers as drag-reducing agents is only mildly dependent on the Reynolds number. Qualitative assessment of the turbulent peak values in the circular pipe flow shows behaviour resembling that of low drag-reducing (DR 40%) flexible polymer solutions data available in the literature such as carboxymethylcellulose with increases in u'+ and decreases both in w'+ and v'+ generally when compared to that of the Newtonian flow at the same Reynolds number. The peak values of the turbulent fluctuation levels (normalized with UB) in the annular pipe, however, shows a decreasing trend of the axial component below 40% drag reduction. Above this drag-reduction “limit”, the peak levels seemed to increase, generally, with drag reduction. Decrease in both w'/UB and v'/UB when compared to that of the Newtonian flow are observed at the same Reynolds number for all drag-reducing flows, similar to what is observed in the pipe-flow study.

Flow-induced degradation of drag-reducing polymer solutions within a high-Reynolds-number turbulent boundary layer

Polymer drag reduction, diffusion and degradation in a high-Reynolds-number turbulent boundary layer (TBL) flow were investigated. The TBL developed on a flat plate at free-stream speeds up to 20ms−1. Measurements were acquired up to 10.7m downstream of the leading edge, yielding downstream-distance-based Reynolds numbers up to 220 million. The test model surface was hydraulically smooth or fully rough. Flow diagnostics included local skin friction, near-wall polymer concentration, boundary layer sampling and rheological analysis of polymer solution samples. Skin-friction data revealed that the presence of surface roughness can produce a local increase in drag reduction near the injection location (compared with the flow over a smooth surface) because of enhanced mixing. However, the roughness ultimately led to a significant decrease in drag reduction with increasing speed and downstream distance. At the highest speed tested (20ms−1) no drag reduction was discernible at the first measurement location (0.56m downstream of injection), even at the highest polymer injection flux (10 times the flux of fluid in the near-wall region). Increased polymer degradation rates and polymer mixing were shown to be the contributing factors to the loss of drag reduction. Rheological analysis of liquid drawn from the TBL revealed that flow-induced polymer degradation by chain scission was often substantial. The inferred polymer molecular weight was successfully scaled with the local wall shear rate and residence time in the TBL. This scaling revealed an exponential decay that asymptotes to a finite (steady-state) molecular weight. The importance of the residence time to the scaling indicates that while individual polymer chains are stretched and ruptured on a relatively short time scale (~10−3s), because of the low percentage of individual chains stretched at any instant in time, a relatively long time period (~0.1s) is required to observe changes in the mean molecular weight. This scaling also indicates that most previous TBL studies would have observed minimal influence from degradation due to insufficient residence times.

Laminar, transitional and turbulent annular flow of drag-reducing polymer solutions

Mean and rms axial velocity-profile data obtained using laser Doppler anemometry are presented together with pressure-drop data for the flow through a concentric annulus (radius ratio κ = 0.506) of a Newtonian (a glycerine–water mixture) and non-Newtonian fluids—a semi-rigid shear-thinning polymer (a xanthan gum) and a polymer known to exhibit a yield stress (carbopol). A wider range of Reynolds numbers for the transitional flow regime is observed for the more shear-thinning fluids. In marked contrast to the Newtonian fluid, the higher shear stress on the inner wall compared to the outer wall does not lead to earlier transition for the non-Newtonian fluids where more turbulent activity is observed in the outer wall region. The mean axial velocity profiles show a slight shift (∼5%) of the location of the maximum velocity towards the outer pipe wall within the transitional regime only for the Newtonian fluid.

Technology Focus: Coiled Tubing Applications (June 2010)

Technology Focus I guess it is no surprise to the people who manufacture coiled tubing (CT) or to those of us in the CT-service industry who actually buy it, but CT is getting bigger. After a decade during which the most common size was 1½ in., the position changed in 2008 when 1¾ in. finally took top spot. Only 1 year later, 2-in. CT took the pole position. What, might you ask, is driving this growth in pipe diameter? The answer is: “Horizontal wells.” In the past few years, we have seen explosive growth in the number of horizontal wells drilled, with much of that growth occurring in the North American shale market. However, the increase in pipe size is driven not only by an increased number of horizontal wells but also because lateral reach is increasing and because completion methods are evolving. Tight-gas-completion methods routinely encompass techniques that use CT for perforating, composite-plug mill-outs, fracture-port ball-seat mill-outs, and fracture-sand cleanouts. The larger-diameter CT is required for greater lateral reach and to enable adequate weight on bit for effective milling operations. Also, because solids removal still requires the same fluid-circulation rates while strings are getting longer, then inevitably, CT diameters must increase to keep surface injection pressures manageable. Bigger, heavier strings inevitably cost more; and because of equipment-size limitations, these strings are subjected to greater bending strain, which in turn results in a shorter working life. One might imagine that we could be reaching an economic limit on string size, but in fact there currently is no sign that this trend is abating. So, is the answer just to build bigger and bigger equipment? One risk of concentrating solely on the CT handling equipment is that the equipment becomes increasingly focused on specific well types and applications, and, in turn, CT loses its versatility for everyday intervention operations. Right now, the jury is still “out,” but it remains a question of whether the various technology initiatives aimed at extending CT horizontal reach will ever meet the operators’ expressed desire for ever-longer horizontal wells and, in turn, how that will influence the CT industry. Coiled Tubing Applications additional reading available at OnePetro: www.onepetro.org SPE 130632 • “Deliquefication of South Texas Gas Wells Using Corrosion-Resistant Coiled Tubing: A 6-Year Case History” by K.L. Poppenhagen, SPE, ConocoPhillips, et al. SPE 130625 • “New Field in East Siberia: Challenges of Performing CT Operations in Vankorskoe Field” by V. Bochkarev, Rosneft, et al. SPE 130579 • “Laminar and Turbulent Friction Factors for Annular Flow of Drag-Reducing Polymer Solutions in Coiled-Tubing Operations” by C.C. Ogugbue, SPE, University of Oklahoma, et al.

Active and Hibernating Turbulence in Minimal Channel Flow of Newtonian and Polymeric Fluids

Turbulent channel flow of drag-reducing polymer solutions is simulated in minimal flow geometries. Even in the Newtonian limit, we find intervals of "hibernating" turbulence that display many features of the universal maximum drag reduction asymptote observed in polymer solutions: weak streamwise vortices, nearly nonexistent streamwise variations, and a mean velocity gradient that quantitatively matches experiments. As viscoelasticity increases, the frequency of these intervals also increases, while the intervals themselves are unchanged, leading to flows that increasingly resemble maximum drag reduction.

Diffusion of drag-reducing polymer solutions within a rough-walled turbulent boundary layer

The influence of surface roughness on diffusion of wall-injected, drag-reducing polymer solutions within a turbulent boundary layer was studied with a 0.94 m long flat-plate test model at speeds of up to 10.6 m s−1 and Reynolds numbers of up to 9×106. The surface was hydraulically smooth, transitionally rough, or fully rough. Mean concentration profiles were acquired with planar laser induced fluorescence, which was the primary flow diagnostic. Polymer concentration profiles with high injection concentrations (≥1000 wppm) had the peak concentration shifted away from the wall, which was partially attributed to a lifting phenomenon. The diffusion process was divided into three zones—initial, intermediate, and final. Studies of polymer injection into a polymer ocean at concentrations sufficient for maximum drag reduction indicated that the maximum initial zone length is of the order of 100 boundary layer thicknesses. The intermediate zone results indicate that friction velocity and roughness height are important scaling parameters in addition to flow and injection conditions. Lastly, the current results were combined with those in Petrie et al. [“Polymer drag reduction with surface roughness in flat-plate turbulent boundary layer flow,” Exp. Fluids 35, 8 (2003)] to demonstrate that the influence of polymer degradation increases with increased surface roughness.

Application of Drag-Reducing Polymer Solutions as Test Fluids for In Vitro Evaluation of Potential Blood Damage in Blood Pumps

In vitro evaluation of the potential of a circulatory-assist device to damage blood cells has generally been performed using blood from various species. Problems with this approach include the variability of blood sensitivity to mechanical stress in different species, preparation of blood including the adjustment of hematocrit to a standard value, changes in the mechanical properties of blood that occur during storage, and necessity to pool blood samples to obtain an adequate amount of blood for in vitro circulating systems. We investigated whether the mechanical degradation of a drag-reducing polymer (DRP) solution resulting in the loss of drag-reducing ability can indicate the degree of shear-induced blood damage within blood pumps. DRP solution (polyethylene oxide, 4,500 kDa, 1,000 ppm) or porcine blood were driven through a turbulent flow system by a centrifugal pump, either the Bio-Pump BPX-80 (Medtronic, Inc.) or CentriMag (Levitronix LLC) at a constant pressure gradient of 300 mm Hg for 120 minutes. DRP mechanical degradation was evaluated by reduction of flow rate and solution viscosity. A proposed index of DRP mechanical degradation (PDI) is similar to the normalized index of hemolysis (NIH) typically used to quantify the results of in vitro testing of blood pumps. Results indicate that the mechanical degradation of DRP solutions may provide a sensitive standard method for the evaluation of potential blood trauma produced by blood pumps without the use of blood.

Asymmetry in transitional pipe flow of drag-reducing polymer solutions

New experimental data are presented and discussed for fully developed pipe flow of shear-thinning, viscoelastic polymer solutions in the transitional regime between laminar and turbulent flow. The data confirm that such transitional flows exhibit significant departures from axisymmetry in contrast to the fully developed pipe flow of Newtonian fluids or both laminar and turbulent flows of such drag-reducing liquids. The azimuthal structure of the asymmetry is investigated together with its axial development and also the velocity fluctuation levels. These data do not lead to an explanation for the asymmetry but do suggest that the influence of the flow geometry both upstream and downstream can be ruled out.