M. P. Escudier

Drag reduction in the turbulent pipe flow of polymers

Abstract The paper concerns an experimental study of the fully developed turbulent pipe flow of several different aqueous polymer solutions: 0.25%, 0.3% and 0.4% carboxymethylcellulose (CMC), 0.2% xanthan gum (XG), a 0.09%/0.09% CMC/XG blend, 0.125% and 0.2% polyacrylamide (PAA). The flow data include friction factor vs. Reynolds number, mean velocity and near-wall shear rate distributions, and axial velocity fluctuation intensity u′ at a fixed radial location as a laminar/turbulent transition indicator. For each fluid we also include measurements of shear viscosity, first normal-stress difference and extensional viscosity. At high shear rates we find that the degree of viscoelasticity increases with concentration (0.3% CMC is an exception) for a given polymer, and in the sequence XG, CMC/XG, CMC, PAA, whilst at low shear rates the ranking changes to CMC, CMC/XG, XG, PAA. The extensional viscosity ranking is XG/CMC, XG, CMC, PAA at high strain rates and the same as that for the viscoelasticity at low shear rates. We find that the observed drag-reduction behaviour is consistent for most part with the viscoelastic and extensional-viscosity behaviour at the low shear and strain rates typical of those occurring in the outer zone of the buffer region. Although laminar/turbulent transition is practically indiscernible from the friction factor vs. Reynolds number plots, particularly for PAA and XG, the u′ level provides a very clear indicator and it is found that the transition delay follows much the same trend with elasticity/extensional viscosity as the drag reduction.

Fully developed laminar flow of purely viscous non-Newtonian liquids through annuli, including the effects of eccentricity and inner-cylinder rotation

The results are presented of extensive numerical calculations, carried out using a highly accurate finite-volume method, for the fully developed laminar flow of an inelastic shear-thinning power-law fluid through an eccentric annulus with inner cylinder rotation. Additional calculations are reported for more complex rheological models, including Cross, Carreau and Herschel–Bulkley, which we relate systematically to the power-law model. Comparisons are made with the results of other recent numerical studies. An extensive bibliography is appended of 100 papers additional to those specifically referenced and concerned with theoretical and numerical investigations of laminar flow of non-Newtonian fluids through annular channels. 2002 Elsevier Science Inc. All rights reserved.

On the reproducibility of the rheology of shear-thinning liquids

The independent analysis of flow measurements is frequently hampered by incomplete characterisation of the working fluid. This problem is particularly acute in situations which require working fluids with identical properties, such as the development of scaling laws for the turbulent flow of drag-reducing liquids. In this paper, we demonstrate that the viscometric viscosity, loss and storage moduli for two of the most common polymers used for flow experiments, carboxymethylcellulose (CMC) and xanthan gum (XG), are practically insensitive to the chemistry of the tap water used as a solvent, to the method of mixing, and to the biocide added. However, the properties of CMC from two different manufacturers were found to be significantly different, whereas there was no difference between XG solutions prepared from different batches from the same manufacturer. Our conclusion is that for a given concentration in water, the properties of certain non-Newtonian liquids, such as CMC and XG, are essentially fixed and reproducible. Although the situation is less than ideal, comparisons of fluid-flow data from entirely independent laboratories can thus be made even in the absence of direct rheological measurements.

Pipe flow of a thixotropic liquid

Abstract Detailed measurements of mean velocity and velocity fluctuation levels (axial, tangential and radial) have been carried out using a laser Doppler anemometer for fully developed pipe flow of an aqueous solution of Laponite, a synthetic clay. The equilibrium rheological structure of this thixotropic liquid is well characterised by the Herschel-Bulkley model. Velocity profiles calculated for a Herschel-Bulkley fluid prove to be a very accurate representation of the measurements for laminar flow at reynolds numbers below about 1500. The measured profiles develop an unexplained asymmetry for higher Reynolds numbers until the flow undergoes transition to turbulence. The fluid is drag reducing under turbulent flow conditions with relative levels of tangential and radial turbulence intensity suppressed in comparison with water whilst the axial turbulence intensity is little different. Under all flow conditions it is evident that the fluid rheology is far from structural equilibrium, with values for the apparent yield stress and effective viscosity determined from near-wall velocity measurements considerably below those obtained from a rheometer.

Effects of inner cylinder rotation on laminar flow of a Newtonian fluid through an eccentric annulus

The paper concerns a computational and experimental study of fully developed laminar flow of a Newtonian liquid through an eccentric annulus with combined bulk axial flow and inner cylinder rotation. The results are reported for calculations of the flowfield, wall shear stress distribution and friction factor for a range of values of eccentricity e, radius ratio j and Taylor number Ta. For fully developed flow the radial/tangential motion is decoupled from the axial component of velocity. However, the axial component of velocity is directly aAected by the radial/tangential velocity field and rotation of the inner cylinder is found to have a strong influence on the axial velocity distribution, ultimately leading to two maxima in the case of a highly eccentred inner cylinder at high rotation speeds, a feature not reported hitherto. This influence of rotation on the axial velocity is mirrored in the behaviour of the shear stresses on the inner and outer cylinder walls and hence on the friction factor. An unexpected result is that (at fixed Reynolds number) as the Taylor number is increased the friction factor for high values of eO> 0:9U increases rather than decreases. ” 2000 Elsevier Science Inc. All rights reserved.

Concentric annular flow with centerbody rotation of a Newtonian and a shear-thinning liquid

Measurements of the radial distributions of the axial and tangential components of velocity and rms velocity fluctuations are presented together with friction factor versus Reynolds number data for two liquids, one Newtonian, the other a shear-thinning polymer, in laminar, transitional, and turbulent flow in an annular geometry with a rotating centerbody of radius ratio 0.506. In all flow regimes, the friction factor is increased by centerbody rotation. However, the influence is slight and most apparent for laminar flow of the Newtonian fluid. Laser Doppier anenometry (LDA) measurements of the tangential velocity reveal three distinct regions across the radial gap with a central region of almost constant angular momentum, which diminishes in magnitude as the Reynolds number increases. Axial velocity measurements show only slight deviations from what would be expected for the case without centerbody rotation. In turbulent flow, the axial velocity fluctuations decrease progressively with increasing Reynolds number for all fluids. For the polymeric liquid, the tangential velocity fluctuations are somewhat suppressed, especially at high Reynolds numbers where the influence of centerbody rotation is reduced. Over a limited range of (low) Reynolds numbers and rotation speeds, the generation and advection of Taylor vortices produces complex flow patterns. Limited measurements are reported for the vortex advection speed.

Turbulent flow through a plane sudden expansion of modest aspect ratio

The results are reported of an experimental investigation of turbulent flow through a plane sudden expansion of expansion ratio R=D/d=4 and aspect ratio A=w/h=5.33. It is well known that plane sudden expansions of high aspect ratio (A>10) with R greater than 1.5 produce asymmetric flows and this was again seen in this study. The literature for the asymmetric flow situation is surprisingly limited and only axial velocity and axial turbulence intensity results have been reported previously. A laser Doppler anemometer was used here to measure mean and rms axial velocities, U and u′, as well as the transverse mean and rms velocities, V and v′, and the Reynolds shear stress, uv¯. Not only was the mean flow found to be strongly asymmetric, but integration of the mean axial velocity profiles revealed significant departures from two dimensionality along the centerplane of the expansion duct. Results are reported at three spanwise locations to highlight this three dimensionality and qualitative arguments are made ...

Flow of shear-thinning fluids in a concentric annulus

Distributions of mean axial velocity, axial and tangential turbulence intensities together with friction factor versus Reynolds number (f-Re) data are presented for three non-Newtonian liquids in fully developed laminar, transitional and turbulent flow in an annular geometry in the absence of centrebody rotation. Each of the non-Newtonian fluids was shear thinning and to some extent elastic and one was also thixotropic in character. For comparison purposes, measurements are also reported for a Newtonian fluid.In the case of the Newtonian fluid, a mixture of glucose syrup and water, the f-Re data in both laminar and turbulent flow follow the appropriate relationships for the annular geometry, with a clear demarcation at transition which is confirmed independently by a measured increase in the centre-channel axial turbulence intensities. The measured velocity profiles for laminar flow are in good agreement with those predicted theoretically, whilst the turbulent profiles obey the log-law relationship over much of the mid-channel region and tend to the u+=y+ relationship in the immediate vicinity of both walls.For the first non-Newtonian fluid, an aqueous solution of sodium carboxymethylcellulose (CMC), good agreement with theoretical predictions for a power-law fluid was observed in the f-Re data in the laminar regime with evidence of drag reduction in turbulent flow. Velocity profiles, determined in two planes, indicate minor circumferential asymmetry in laminar flow. Law-of-the-wall plots for fully turbulent flow indicate an upward shift in the data in the log-law region of the annulus consistent with the drag-reduction behaviour, as also observed in pipe-flow experiments for this fluid (Escudier et al. 1992). In the near-surface regions of both the outer and inner tubes the data again tend towards the u+=y+ relationship.Anomalous behaviour was observed in the f-Re curves for the second non-Newtonian fluid, 0.125% and 0.2% aqueous solutions of Xanthan gum, with data for both concentrations falling significantly below the appropriate f-Re relationship for a power-law fluid. The anomalies are attributed to the elastic character of Xanthan gum. In the near-surface region of the outer tube the velocity-profile data again tend towards the u+=y+ relationship but it proved impossible to obtain data in the near vicinity of the inner wall due to slight turbidity of the fluid.The third non-Newtonian fluid, a Laponite/CMC blend, again exhibits anomalous f-Re behaviour, attributed to the thixotropic nature of this fluid. Velocity profiles determined in two planes again indicate some circumferential asymmetry in the laminar regime. Law-of-the-wall plots for the transitional and turbulent profiles tend towards the u+=y+ relationship in both near-wall regions, again with an upward shift in the core of the annulus, consistent with drag reduction.In general terms, the experimental results are consistent with previous work for non-Newtonian fluid flow in circular pipes and with limited data for an annular geometry (Nouri et al. 1993), with regard to drag reduction, modified turbulence structure and scale effects.

Experiments on the effects of aging on compliant coating drag reduction

We report the experimental results from a collaborative effort between USA, Russia, and UK on the development of compliant coatings for undersea application of reduction of drag. The focus is on “shelf-life” of coatings. The coatings are based on a linear interference theory of interaction between turbulence pressure fluctuation and the viscoelastic coating. The phase shift between boundary displacement and pressure fluctuation embodies the interference effect. The natural frequency of the coating is matched to the turbulent boundary layer region of maximum Reynolds stress production. Low-molecular weight rubber-like silicone coatings have been manufactured whose properties include slow and fast damping, slow and fast aging, and varying magnitudes of elasticity, density, and thickness as well as transparency. The dynamic modulus and loss tangent vary weakly over a range of frequencies and temperature allowing compatibility with broad spectrum of turbulence. Drag measurements have been carried out over a y...

Turbulent flow of non-Newtonian liquids over a backward-facing step Part II. Viscoelastic and shear-thinning liquids

Abstract The results are reported of an extensive experimental investigation of turbulent flow of polymeric non-Newtonian liquids (0.01, 0.075, 0.125 and 0.175% polyacrylamide (PAA) solutions) through a plane sudden expansion of expansion ratio R=1.43 and aspect ratio A=13.3. Three water-flows are also reported for comparative purposes. A laser Doppler anemometer was used to measure mean and RMS streamwise velocities, U and u′, as well as the transverse mean and RMS velocities, V and v′, and the Reynolds shear stress uv . For the water-flows we highlight the important influence on the reattachment length of the maximum turbulence intensity at separation. The PAA flows exhibit an increased reattachment length compared with the Newtonian situation. The magnitudes of the recirculating velocities and recirculating flowrates are increased for the lowest concentration (0.01% PAA) but decreased for the more viscoelastic high concentration (0.075–0.175% PAA) flows. In all cases these changes are accompanied by large reductions in the transverse turbulent intensity. The correspondingly high degree of turbulence anisotropy is instrumental in generating increased reattachment lengths for the lower concentration flows. The increased levels of viscoelasticity for the higher concentration PAA solutions lead to a reduction of the turbulence intensity at separation and this effect, coupled with the high turbulence anisotropy, plays an important role in increasing the reattachment length.