Degradation effects of dilute polymer solutions on turbulent drag reduction in pipe flows

An important practical problem in the application and study of drag reduction by polymer additives is the degradation of the polymer, for instance due to intense shearing, especially in recirculatory flow systems. Such degradation leads to a marked loss of the drag-reducing capability of the polymer.Three different polymer types were tested on degradation effects in a closed pipe flow system. The polymers used were Polyox WSR-301, Separan AP-273 and Superfloc A-110, dissolved in water in concentrations of 20 wppm each. The flow system consisted of a 16.3 mm pipe of 4.25 m length. Two different pumps were used: a centrifugal pump and a disc pump. Different solution-preparation procedures were tried and the experiments were performed at different flow rates.Superfloc A-110 proved to be both the most effective drag reducer and most resistant to degradation. Because of very fast degradation, Polyox WSR-301 was found to be unsuitable for being used as a drag reducer in re-circulatory systems. The disc pump proved to be much better suited for pumping the polymer solutions than the centrifugal pump. The degradation curve of the combination Superfloc/disc pump showed a plateau-like region with reasonable drag reduction, which makes it possible to perform (laser Doppler) measurements under nearly constant circumstances during a sufficient time.     

Mechanism of drag reduction by spanwise oscillating Lorentz force in turbulent channel flow

Numerical simulations and experimental research are both carried out to investigate the controlled effect of spanwise oscillating Lorentz force on a turbulent channel flow. The variations of the streaks and the skin friction drag are obtained through the PIV system and the drag measurement system, respectively. The flow field in the near-wall region is shown through direct numerical simulations utilizing spectral method. The experimental results are consistent with the numerical simulation results qualitatively, and both the results indicate that the streaks are tilted into the spanwise direction and the drag reduction utilizing spanwise oscillating Lorentz forces can be realized. The numerical simulation results reveal more detail of the drag reduction mechanism which can be explained, since the spanwise vorticity generated from the interaction between the induced Stokes layer and intrinsic turbulent flow in the near-wall region can make the longitudinal vortices tilt and oscillate, and leads to turbulence suppression and drag reduction.     

Drag reduction by polymer solutions in a riblet-lined pipe

The flow of 3 to 100 wppm aqueous solutions of a polyethyleneoxide polymer,M _w=6.2×;10⁶, was studied in a 10.2 mm i.d. pipe lined with 0.15 mm V-groove riblets, at diametral Reynolds numbers from 300 to 150000. Measurements in the riblet pipe were accompanied by simultaneous measurements in a smooth pipe of the same diameter placed in tandem. The chosen conditions provided turbulent drag reductions from zero to the asymptotic maximum possible. The onset of polymer-induced drag reduction in the riblet pipe occurred at the same wall shear stress, * _w =0.65 N/m², as that in the smooth pipe. After onset, the polymer solutions in the riblet pipe initially exhibited linear segments on Prandtl-Karman coordinates, akin to those seen in the smooth pipe, with specific slope increment . The maximum drag reduction observed in the riblet pipe was independent of polymer concentration and well below the asymptotic maximum drag reduction observed in the smooth pipe. Polymer solution flows in the riblet pipe exhibited three regimes: (i) Hydraulically smooth, in which riblets induced no drag reduction, amid varying, and considerable, polymer-induced drag reduction; this regime extended to non-dimensional riblet heightsh ⁺<5 in solvent andh ⁺<10 in polymer solutions. (ii) Riblet drag reduction, in which riblet-induced flow enhancementR>0; this regime extended from 5<h ⁺<22 in solvent and from 10<h ⁺<30 in the 3 wppm polymer solution, with respective maximaR=0.6 ath ⁺=14 andR=1.6 ath ⁺=21. Riblet drag reduction decreased with increasing polymer concentration and increasing polymer-induced flow enhancement S. (iii) Riblet drag enhancement, whereinR<0; this regime extended for 22<h ⁺<110 in solvent, withR;–2 forh ⁺>70, and was observed in all polymer solutions at highh ⁺, the more so as polymer-induced drag reduction increased, withR<0 for allS>8. The greatest drag enhancement in polymer solutions,R=–7±1 ath ⁺=55 whereS=20, considerably exceeded that in solvent. Three-dimensional representations of riblet- and polymer-induced drag reductions versus turbulent flow parameters revealed a hitherto unknown dome region, 8<h ⁺<31, 0<S<10, 0<R<1.5, containing a broad maximum at (h ⁺,S,R) = (18, 5, 1.5). The existence of a dome was physically interpreted to suggest that riblets and polymers reduce drag by separate mechanisms.     

On the mechanism of drag reduction in dilute polymer solutions

Experimental evidence is given that drag reducing polymer molecules are preferentially collected by strained vortices. This can explain why extremely small amounts of additives can be so effective. They become concentrated in areas of a turbulent flow where they are most efficient.     

Rheotens-mastercurves and elongational viscosity of polymer melts

In a Rheotens experiment, the tensile force needed for elongation of an extruded filament is measured as a function of the draw ratio. For thermo-rheologically simple polymer melts, the existence of Rheotens-mastercurves was proved by Wagner, Schulze, and Göttfert (1995). Rheotens-mastercurves are invariant with respect to changes in melt temperature and changes in the average molar mass. By use of purely viscous models, we convert Rheotens-mastercurves of a branched and a linear polyethylene melt to elongational viscosity as a function of strain rate. The resulting elongational viscosity from constant force extension experiments is found to be in general agreement with what is expected as steady-state viscosity of polyethylene melts measured in either constant strain-rate or constant stress mode.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

The influence of the injection system on drag reduction

The influence of the injection system for centerline injected polymer solutions (threads) on drag reduction in a turbulent pipe flow was studied using injectors of different length and grids. Compared with a short injector, the long injector showed a different behavior: the drag reduction was lower and its onset point was shifted to higher Reynolds numbers.The velocity profiles for the polymer-phase and the water-phase were measured simultaneously with a combination of laser-Doppler-velocimetry LDV and laser-induced fluorescence LIE It was found that the analysis of the LDV measurements with respect to the difference in velocity between the polymer-phase and the water-phase can give information about the mixing between both phases. For a Reynolds number of 30000 the difference between the phases is comparatively large for low drag reduction and very small for high drag reduction. The results indicate that the drag reduction achieved by injecting a concentrated polymer solution is mainly caused by a mixing process between polymer and water.     

Turbulent drag reduction by spanwise wall oscillations

In the present work a technique is numerically investigated, which is aimed at reducing the friction drag in turbulent boundary layers and channel flows. A cyclic spanwise oscillation of the wall with a proper frequency and amplitude is imposed, allowing a reduction of the turbulent drag of up to 40%. The present work is based on the numerical simulation of the Navier-Stokes equations in the simple geometry of a plane channel flow. The frequency of the oscillations is kept fixed at the most efficient value determined in previous studies, while the choice of the best value for the amplitude of the oscillations is evaluated not only in terms of friction reduction, but also by taking into consideration the overall energy balance and the power spent for the motion of the wall. The analysis of turbulence statistics allows to shed some light on the way oscillations interact with wall turbulence, as illustrated by visual inspection of some instantaneous flow fields. Finally, a simple explanation is proposed for this interaction, which leads to a rough estimate of the most efficient value for the frequency of the oscillations.     

The role of small scale coherent structures in turbulent drag reduction

With a new visualization technique, a strong suppression of small scale coherent structures (filaments) in turbulence is observed when a drag reducing polymer is added. Simultaneously, the rate of formation of large scale structures (eddies) out of these filaments decreases, which may be an important observation in the explanation of turbulent drag reduction.     

The mechanism of polymer thread drag reduction

One very effective method of reducing the drag of a turbulent fluid flow is through the use of soluble, viscoelastic, long-chain, high-molecular-weight polymer additives. These additives have produced drag reduction of up to 80% in pipe flows. Polymers are typically added by injecting high concentration solutions into an established Newtonian flow.This study investigated the mechanism of drag reduction that occurs when a long-chain, high-molecular-weight polymer is injected along the centerline of a pipe with a concentration high enough to form a single, coherent, unbroken thread. In the present experiments, the unbroken threads existed for more than 200 pipe diameters downstream of the injector and produced drag reductions on the order of 40%. Previous authors have contended that this type of drag reduction is caused by the interaction of the thread with the outer flow. However, it has been proven in cases where the polymer is mixed throughout the flow that drag reduction requires the existence of polymer in the near-wall region. The objective of this study was to test the hypothesis that drag reduction from a polymer thread is caused by transport of polymer molecules from the thread into the near-wall region of the pipe. The objective was realized through the measurement of the drag reduction, the radial location of the thread, and the polymer concentration in the near-wall region. The concentration was measured by laser-induced fluorescence utilizing fluorescein dye as the tracer. This study provides strong evidence that the drag reduction from a polymer thread is caused by the transport of very low concentrations of polymer from the thread into the near-wall region.     

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     

Numerical investigation of turbulent channel flow controlled by spatially oscillating spanwise Lorentz force

A formulation of the skin-friction drag related to the Reynolds shear stress in a turbulent channel flow is derived. A direct numerical simulation (DNS) of the turbulent control is performed by imposing the spatially oscillating spanwise Lorentz force. Under the action of the Lorentz force with several proper control parameters, only the periodically well-organized streamwise vortices are finally observed in the near-wall region. The Reynolds shear stress decreases dramatically, especially in the near-wall area, resulting in a drag reduction.     

On the boundary layer/riblets interaction mechanisms and the prediction of turbulent drag reduction

Turbulent drag reduction experienced by ribletted surfaces is the result of both (1) the interaction between riblet peaks and the coherent structures that characterize turbulent near-wall flows, and (2) the laminar sublayer flow modifications caused by the riblet shape, which can balance, under appropriate conditions, the drag penalty due to the increased wetted surface. The latter “viscous” mechanism is investigated by means of an analytical model of the laminar sublayer, which removes geometrical restrictions and allows us to take into account “real” shapes of riblet contours, affected by manufacturing inaccuracies, and to compute even for such cases a parameter, called protrusion height, related to the longitudinal mean flow. By considering real geometries, riblet effectiveness is clearly shown to be related to the difference between the longitudinal and the transversal protrusion heights. A simple method for the prediction of the performances of ribletted surfaces is then devised. The predicted and measured drag reduction data, for different riblet geometries and flow characteristics, are in close agreement with each other. The soundness of the physical interpretation underlying this prediction method is consequently confirmed.     

Numerical viscosity reduction in the resolution of the shallow water equations with turbulent term

A first‐order finite volume model for the resolution of the 2D shallow water equations with turbulent term is presented. An upwind discretization of the equations that include the turbulent term is carried out. A method to reduce the excess of numerical viscosity (or diffusion) produced by the upwinding of the flux term is proposed. Two different discretizations of the turbulent term are compared, and results for uniform distributions of the viscosity are presented. Finally, two discretizations of the time derivative which are more efficient than Euler's are proposed and compared. Copyright © 2008 John Wiley & Sons, Ltd.     

Drag reduction by an elastic rubber band?

The influence on the friction behaviour caused by a rubber band held fixed at one end of a circular tube containing a fully developed turbulent flow was investigated. The drag was slightly higher under these conditions with the drag approaching the Prandtl-Karman law at high Reynolds numbers. The results are in contrast to the behaviour of a polymer thread in heterogeneous drag reduction.     

基于壁面主动变形的湍流减阻控制研究

采用谱方法, 对反向控制下壁面主动变形的槽道湍流进行了直接数值模 拟研究. 结果表明, 在壁面最大变形量小于5倍黏性尺度条件下, 压差阻力可略, 摩擦阻力 降低7.6%. 施加控制后, 湍流强度和雷诺应力受到明显抑制, 平均速度剖面对数区上移. 受壁面法向运动的影响, 条带结构强度减弱、尺度变大; 流向涡外移且强度减弱, 其倾斜和 抬起的角度均有不同程度的减小. 壁面变形呈现流向拉长的凹槽结构, 其平均间距 为90倍黏性尺度.     

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.     

Sensitivity computations of eddy viscosity models with an application in drag computation

This paper presents a numerical study of the sensitivity of an eddy viscosity model with respect to the variation of the eddy viscosity parameter for the two‐dimensional driven cavity problem and flow around a cylinder. The main objective is to provide a comparison between computing the sensitivity using sensitivity equation and computing the sensitivity using finite difference methods and also numerically illustrate the application of the sensitivity computations in improving drag flow functional. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust design and numerical simulation on drag reduction by a mixture film for liquid turbulence in a channel

An important way of increasing the speed and lowering the fuel consumption of ships is by decreasing the frictional drag. One of the most promising techniques for reducing drag is the use of air bubbles. The goal of this investigation is to establish a set of optimum robust parametric levels for drag reduction by a mixture (air–water) film in turbulent channel flow. Based on the conditions laid out by the Taguchi orthogonal array method, turbulent flows, with air bubbles injected into a channel, are simulated using commercial computational fluid dynamics software. The local shear stress on the upper wall is computed to evaluate the efficiency of drag reduction. Many factors can affect drag reduction. The factors investigated in this study are the rate of air injection, bubble size, area of air injection, flow speed, and measured position of the shear stress. These factors have been investigated through the analysis of variance, which has revealed that the rate of air injection and water flow speed dominate the efficiency of drag reduction by a mixture film. According to the results, the drag can be reduced by an average of 83.4%; and when the configuration of the parametric levels is optimum the maximum drag reduction of 88.5% is achieved. Copyright © 2008 John Wiley & Sons, Ltd.     

Determination of the elongational viscosity of polymer melts by melt spinning experiments. A comparison with different experimental techniques

In this work, melt spinning experiments were tentatively used for the determination of the elongational viscosity of polymer melts at different levels of tensile strain and strain rate. The materials examined were two high-density polyethylene grades for blow moulding with similar number-average molecular mass but different polydispersity index. The data from melt spinning tests were compared with transient extensional viscosity data obtained by uniform isothermal tensile tests, performed by means of an extensional rheometer, as well as with those produced by converging flow tests (Cogswell model). The results showed that for high strain and strain rate levels, the melt spinning experiments provide elongational viscosity data quite close to the transient extensional viscosity values obtained from the tensile tests.     

Analysis of polymer drag reduction mechanisms from energy budgets

The transfer of energy in drag reducing viscoelastic flows is analyzed through a sequence of energetic budgets that include the mean and turbulent kinetic energy, and the mean polymeric energy and mean elastic potential energy. Within the context of single-point statistics, this provides a complete picture of the energy exchange between the mean, turbulent and polymeric fields. The analysis utilizes direct simulation data of a fully developed channel flow at a moderately high friction Reynolds number of 1000 and at medium (30%) and high (58%) drag reduction levels using a FENE-P polymeric model.Results show that the primary effect of the interaction between the turbulent and polymeric fields is to transfer energy from the turbulence to the polymer, and that the magnitude of this transfer does not change between the low and high drag reduction flows. This one-way transfer, with an amplitude independent of the drag reduction regime, comes in contradiction with the purely elastic coupling which is implicit within the elastic theory of the polymer drag reduction phenomenon by Tabor and De Gennes (Europhys. Lett. 2, pp. 519–522, 1986).