Turbulent characteristics of shear-thinning fluids in recirculating flows

 A miniaturised fibre optic Laser-Doppler anemometer was used to carry out a detailed hydrodynamic investigation of the flow downstream of a sudden expansion with 0.1–0.2% by weight shear-thinning aqueous solutions of xanthan gum. Upstream of the sudden expansion the pipe flow was fully-developed and the xanthan gum solutions exhibited drag reduction with corresponding lower radial and tangential normal Reynolds stresses, but higher axial Reynolds stress near the wall and a flatter axial mean velocity profile in comparison with Newtonian flow. The recirculation bubble length was reduced by more than 20% relative to the high Reynolds number Newtonian flow, and this was attributed to the occurrence further upstream of high turbulence for the non-Newtonian solutions, because of advection of turbulence and earlier high turbulence production in the shear layer. Comparisons with the measurements of Escudier and Smith (1999) with similar fluids emphasized the dominating role of inlet turbulence. The present downstream turbulence field was less anisotropic, and had lower maximum axial Reynolds stresses (by 16%) but higher radial turbulence (20%) than theirs. They reported considerably longer recirculating bubble lengths than we do for similar non-Newtonian fluids and Reynolds numbers. Received: 23 February 1999/Accepted: 28 April 1999     

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

This is the second part of a study examining the mechanical properties and capillary flow of fiber suspensions in Newtonian fluids and in polymer solutions. In part I results for the viscous and elastic properties of the fiber suspensions were presented and it was shown that the fiber suspensions exhibited normal stresses in Newtonian as well as in viscoelastic suspending media. It was thus expected that circulating secondary flows would occur near the entrance to a capillary. Four types of fillers (glass, carbon, nylon and vinylon fibers) suspended in glycerin, HEC solutions and Separan solutions were investigated. The entrance flow patterns were visualized and the pressure fluctuations measured. The visualization enabled the eddies occurring in the fiber suspensions in Newtonian fluids to be analysed and classified into two tpyes. The results from the flow visualization were correlated with the pressure fluctuations. Empirical equations for the tube length correction factor due to the elasticity were obtained.     

Turbulent pipe flow of a drag-reducing rigid “rod-like” polymer solution

Fully developed turbulent pipe flow of an aqueous solution of a rigid “rod-like” polymer, scleroglucan, at concentrations of 0.005% (w/w) and 0.01% (w/w) has been investigated experimentally. Fanning friction factors were determined from pressure-drop measurements for the Newtonian solvent (water) and the polymer solutions and so levels of drag reduction for the latter. Mean axial velocity u and complete Reynolds normal stress data, i.e. u′, v′ and w′, were measured by means of a laser Doppler anemometer at three different Reynolds numbers for each fluid. The measurements indicate that the effectiveness of scleroglucan as a drag-reducing agent is only mildly dependent on Reynolds number. The turbulence structure essentially resembles that of flexible polymer solutions which also lead to low levels of drag reduction.     

Experimental investigations and numerical simulations for an open channel flow of a weak elastic polymer solution around a T-profile

The present paper is concerned with experimental and numerical investigations of planar complex flows of weak elastic polymer solutions (whose concentration are below the critical overlap concentration), characterised by small relaxation times (<0.1 s) and almost constant shear viscosities for small and medium shear rates. The main aim of the study is to detect to what extent a very small amount of elasticity present in a viscous fluid can influence its behaviour in complex flows, without introducing major modifications of classical rheological tests. The samples are polymer solutions of low PIB molecular weight dissolved in highly viscous Newtonian mineral oil. The analysed motion is steady, and takes place in an open channel around a T profile. Maximum values of the characteristic parameters for the experiments, the Reynolds and Weissenberg numbers, were 45 and 0.1, respectively. The experiments show a decrease of the wake length downstream the profile for weak elastic solutions in comparison to the Newtonian solvent. Actually, the same wake length as in the Newtonian case was obtained for tested polymer solutions, but at higher Re numbers. Numerical simulations using the Giesekus model predict the same behaviour and are consistent with experiments from both qualitative and quantitative point of views. The results of research conclude that, even in small amounts, the presence of elasticity in pure viscous liquids induces quantitative changes from Newtonian flow in complex dominant elongational flows, at elongational rates for which the sudden thickening of extensional viscosity is remarkable. The study is important, since it should enable better understanding and modelling of viscoelastic flows that involve dilute polymer solutions, or fluids with similar rheology; biofluid mechanics being one area of application of this research. Corroboration of experimental flow visualization with numerical simulation is currently a feasible method used to characterise weak elastic polymer solutions, since classical rheological techniques generally fail to obtain realistic values of relaxation time for these particular viscoelastic fluids. Corneliu Balan dedicates this paper to the anniversary of one hundred years from the birth of Academician Dumitru Dumitrescu (1904–1983), charismatic personality of the Romanian school of fluid mechanics.

---

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     

Is there a relation between the relaxation time measured in CaBER experiments and the first normal stress coefficient?

We investigate a variety of different semidilute polymer solutions in shear and elongational flow. The shear flow is created in the cone-plate-geometry of a commercial rheometer. We use capillary thinning of a filament that is formed by a polymer solution in the Capillary Breakup Extensional Rheometer (CaBER) as an elongational flow. We compare the relaxation time measured in the CaBER with relaxation times based on the first normal stress difference and the zero shear polymer viscosity that we measure in our rheometer. All of these three measurable quantities depend on different fluid parameters—the viscosity of the solvent, the polymer concentration within the solution, and the molecular weight of the polymers—and on the shear rate (in the shear flow measurements). Nevertheless, we find that the first normal stress coefficient depends quadratically on the CaBER relaxation time. Several scaling laws are presented that could help to explain this empirical relation.     

The effect of the expansion ratio on a turbulent non-Newtonian recirculating flow

 Measurements of the mean and turbulent flow characteristics of shear-thinning moderately elastic 0.1% and 0.2% xanthan gum aqueous solutions were carried out in a sudden expansion having a diameter ratio of 2. The inlet flow was turbulent and fully developed, and the results were compared with data for water in the same geometry and with previous published Newtonian and non-Newtonian data in a smaller expansion of diameter ratio equal to 1.538. An increase in expansion ratio led to an increase in the recirculation length and in the axial normal Reynolds stress at identical normalised locations, but the difference between Newtonian and non-Newtonian characteristics was less intense than in the smaller expansion. An extensive comparison of mean and turbulent flow characteristics was carried out in order to understand the variation of flow features. Received: 31 July 2000 / Accepted: 27 August 2001     

A solution birefringence study of polymer elongation in spatially periodic stretching flows

The flow birefringence of dilute polymer solutions in periodically converging/diverging channels has been employed to study the dynamics of flexible chain molecules under transient stretching stresses. The onset of periodic birefringence for chains of high molecular weight is only observed after the chains have experienced several cycles of stress, at a point deep into the channel. This slow onset indicates that the solutions possess a memory on time scales much greater than that normally associated with a relaxed flexible coil. This behavior is recorded for both aqueous and nonaqueous solutions, at concentrations both above and below the entanglement concentration. Centerline birefringence, however, which is associated with purely elongational flow, is only observed for aqueous polymer solutions. An explanation for these birefringence results is suggested, based on a configuration-dependent dumbbell model for polymer chains in dilute solution.     

Influence of dispersion procedure on rheological properties of aqueous solutions of high molecular weight PEO

The linear and nonlinear viscoelastic behaviors of poly(ethylene oxide) (PEO) in aqueous media have been investigated as a function of concentration and molecular weight. A particular interest has been paid to study the effect of turbulent flow under stirring, inducing both shear and elongational stresses, on the rheological behavior of the polymer solutions. The comparison of intrinsic viscosity and viscoelastic properties between shaken and stirred PEO solutions is discussed at the molecular scale in terms of chain scission and aggregation. Results point out that the effect of the mechanical history on the rheological response of PEO solutions depends also on the concentration regime and molecular weight. Indeed, the influence of the dispersion procedure vanishes by decreasing both the concentration and the molecular weight.     

The influence of flow-induced non-Newtonian fluid properties on turbulent drag reduction

Friction factors and velocity profiles in turbulent drag reduction can be compared to Newtonian fluid turbulence when the shear viscosity at the wall shear rate is used for the Reynolds number and the local shear viscosity is used for the non-dimensional wall distance. On this basis, an apparent maximum drag reduction asymptote is found which is independent of Reynolds number and type of drag reducing additive. However, no shear viscosity is able to account for the difference between the measured Reynolds stress and the Reynolds stress calculated from the mean velocity profile (the Reynolds stress deficit). If the appropriate local viscosity to use with the velocity fluctuation correlations includes an elongational component, the problem can be resolved. Taking the maximum drag reduction asymptote as a non-Newtonian flow, with this effective viscosity, leads to agreement with the concept of an asymptote only when the solvent viscosity is used in the non-dimensional wall distance.     

Experimental estimation of elongational stresses of dilute polymer solutions and a related examination of some constitutive equations

Elongational stresses of dilute polymer solutions have been estimated by utilizing the flow through small orifices under the condition of no vortex upstream of the orifice plane. The flow was approximated with a linearly converging flow towards an apex of a cone, its validity being partially confirmed by the measured center velocities, and the elongational stresses are determined from the measured thrusts of dilute polymer solutions. On the other hand, elongational stresses were theoretically obtained with the modified Maxwell model and the second order fluid. A comparison was made between the experimental and the theoretical results and the following points were clarified; below an elongational rate of 2 × 10⁴ s⁻¹ the modified Maxwell model gives elongational stresses close to the experimentally determined ones, but above that elongational rate it deviates from the experimental results. The second order fluid is not sufficient to describe the stresses in this kind of elongational flow and an acceleration term such as δ²e^ij/δt² may be necessary in this case.     

A new elongational rheometer for polymer solutions

Design and operation of a new elongational rheometer for low elastic polymer solutions are described. The free jet elongational rheometer is easy to operate and for suitable operating conditions a transient elongational flow with an approximately constant rate of strain can be realized. In any case, convenient comparative parameters can be obtained. The method of rheological curve fitting leads to a deformation dependent ralaxation time parameter of a modified upper convected Jeffreys-law.     

Uniaxial elongational flow effects and morphology development in LDPE/phosphate glass hybrids

Shear and elongational viscosity measurements were performed on low-density polyethylene/phosphate glass (LDPE/Pglass) hybrid materials in the liquid state. Under shear deformation, the hybrids with low concentrations of Pglass showed a Newtonian region at low frequencies, followed by shear-thinning behavior at high frequencies. High Pglass concentrations displayed shear-thinning behavior over the whole range of frequencies studied. Deviations from the log-additivity rule for viscosity were found to be compositionally dependent and generally indicated an immiscible mixture. The elongational viscosity of the hybrids increased at very low Pglass concentrations (1–2 vol.% Pglass) and then was drastically reduced at higher concentrations (i.e., >10 vol.% Pglass). In addition, elongational flow was found to induce the formation of Pglass fibrils in hybrids containing at least 10 vol.% Pglass. This was correlated to the elongational capillary number; the critical elongational capillary number was estimated to be 0.22. The elongational deformation was also found to greatly increase the overall crystallinity of the system due to molecular orientation of the LDPE polymer chains as confirmed by wide angle X-ray diffraction. A critical composition of 5 vol.% Pglass was found to be the point at which LDPE hybrid rheological properties, molecular orientation, and morphology changed drastically.     

弹性湍流及其对微混合效率影响研究的若干进展

介绍和评述弹性湍流的产生及其对于微混合效率的影响等问题上的若干研究进展. 弹性 湍流和惯性湍流具有类似的流场特征,但引发机理有所不同. 惯性湍流产生的原因 是惯性引起的Reynolds应力,而弹性湍流则是由弹性应力所引起的. 鉴于在微流动 中,惯性力可忽略不计,因此牛顿流体的混合变得十分困难. 此时可在流体中加入 微量高分子聚合物以生成黏弹性流体. 由黏弹性流体所引发的弹性湍流在提高流体 微混合的效率上可发挥重要作用.     

Shear rheology of polymer solutions near the critical condition for elastic instability

The use of constant viscosity, highly elastic polymer solutions, so called Boger fluids, has been remarkably successful in elucidating the behavior of polymeric materials under flowing conditions. However, the behavior of these fluids is still complicated by many different physical processes occurring within a narrow window of observation time and applied shear rate. In this study, we investigate the long-time shear behavior of an ideal Boger fluid: a well characterized, athermal, dilute, binary solution of high molecular weight polystyrene in oligomeric polystyrene. Rheological measurements show that under an applied steady shear flow, this family of polymer solutions undergoes a transient decay of normal stresses on a timescale much longer than the polymer molecule's relaxation time. Rheological and flow visualization results demonstrate that the observed phenomenon is not caused by polymer degradation, phase separation, viscous heating, or secondary flows from elastic instabilities. Although the timescale is much shorter than that associated with polymer migration in the same solutions (MacDonald and Muller, 1996), the appearance of this phenomenon only at the rates where migration has been observed suggests that it may be a prerequisite for observing migration. In addition, we note that through sufficient preshearing of the sample, the normal stress decrease suppresses the elastic instability. These results show that there is considerable uncertainty in choosing the appropriate measure of the fluid relaxation time for consistently modeling the critical condition for the elastic instability, the decay of normal stresses, and the migration of polymer species.     

A FENE-P k–ε turbulence model for low and intermediate regimes of polymer-induced drag reduction

A new low-Reynolds-number k–ε turbulence model is developed for flows of viscoelastic fluids described by the finitely extensible nonlinear elastic rheological constitutive equation with Peterlin approximation (FENE-P model). The model is validated against direct numerical simulations in the low and intermediate drag reduction (DR) regimes (DR up to 50%). The results obtained represent an improvement over the low DR model of Pinho et al. (2008) [A low Reynolds number k–ε turbulence model for FENE-P viscoelastic fluids, Journal of Non-Newtonian Fluid Mechanics, 154, 89–108]. In extending the range of application to higher values of drag reduction, three main improvements were incorporated: a modified eddy viscosity closure, the inclusion of direct viscoelastic contributions into the transport equations for turbulent kinetic energy (k) and its dissipation rate, and a new closure for the cross-correlations between the fluctuating components of the polymer conformation and rate of strain tensors (NLT_ij). The NLT_ij appears in the Reynolds-averaged evolution equation for the conformation tensor (RACE), which is required to calculate the average polymer stress, and in the viscoelastic stress work in the transport equation of k. It is shown that the predictions of mean velocity, turbulent kinetic energy, its rate of dissipation by the Newtonian solvent, conformation tensor and polymer and Reynolds shear stresses are improved compared to those obtained from the earlier model.     

Creation of very-low-Reynolds-number chaotic fluid motions in microchannels using viscoelastic surfactant solution

Solutions of flexible high-molecular-weight polymers or some kinds of surfactant are viscoelastic fluids. The elastic stress is induced in such viscoelastic fluid flows and grows nonlinearly with the flow-rate resulting in many particular flow phenomena, including purely elastic instability. The purely elastic instability can even result in a kind of chaotic fluid motion, the so-called elastic turbulence, which is a recently discovered flow phenomenon and arises at arbitrarily small Reynolds number. By using viscoelastic surfactant solution, we attempted to create the peculiar chaotic fluid motions in several specially designed microchannels in which flows with curvilinear streamlines can be generated. The viscoelastic working fluids were aqueous solutions of surfactant, CTAC/NaSal (cetyltrimethyl ammonium chloride/sodium salicylate). CTAC solutions with weight concentration of 200 ppm (part per million) and 1000 ppm, respectively, at room temperature were tested. For comparison, water flows in the same microchannels were also visualized. The Reynolds numbers for all the microchannel flows were quite small (for solution flows, the Reynolds numbers were the order of or smaller than one) and the flow should be definitely laminar for Newtonian fluid. It was found that the regular laminar flow patterns for low-Reynolds-number Newtonian fluid flow in different microchannels were strongly deformed in solution flows: either asymmetrical flow structures or time-dependent vortical fluid motions appeared. These chaotic flow phenomena were considered to be induced by the viscoelasticity of the CTAC solutions. Discussions about the potential applications using such kind of chaotic fluid motions were also made.     

The role of elongational viscosity in the mechanism of drag reduction by polymer additives

The role of elongational viscosity in the mechanism of drag reduction by polymer additives is investigated qualitatively by means of direct numerical simulations of a turbulent pipe flow. For the polymer solution, a generalised Newtonian constitutive model is utilised in which the viscosity depends on the second and third invariant of the rate-of-strain tensor via an elongation parameter. This elongation parameter is capable of identifying elongational type of regions within the flow. The simulations show that complementary to stretching of the polymers, also compression must be incorporated to have drag reduction, contrary to many suggestions done in the literature on the mechanism which assume that stretching of the polymers is most important.     

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.