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.     

DNS of the Turbulent Channel Flow of a Dilute Polymer Solution

A direct numerical simulation of the turbulent channel flow of a dilute polymer solution has been performed in order to compare its turbulence statistics with those obtained in a Newtonian channel flow. The viscoelastic flow has been simulated by solving the whole set of continuity, momentum and constitutive equations for the six independent components of the extra-stress tensor induced by polymer addition. The Finitely Extensible Nonlinear Elastic dumbbell model was adopted in order to simulate a non-linear modulus of elasticity and a finite extendibility of the polymer macromolecules. Simulations were carried out under the narrow channel assumption at a Reynolds number of 169 based on the channel half height and on the friction velocity; they showed a significant reduction in drag, dependent on the influence of the elastic properties of the chains. A qualitative comparison with experiments at a higher Reynolds number has shown that the model here adopted is capable of reproducing all the main features of the polymer solution flow. Analysis of the turbulence statistics suggests that a dilute polymer solution can affect the intensity of the streamwise vortices, leading to an increase in the spacing between low speed streaks and eventually to a turbulent shear stress reduction.     

材料表面润湿性调控及减阻性能研究

设计合成不同结构的自组装分子,使其可以在不改变表面粗糙度的情况下改变表面的润湿性能;利用低表面能涂层修饰粗糙表面得到超疏水表面.采用流变仪和水洞试验分别在层流和湍流流动状态下测试了具有不同润湿行为的亲、疏水材料的减阻性能.结果表明:在层流流动状态,随着不同表面的接触角从13°增加到45°、113°和161°,减阻率随之从1.8%增大到7.2%、7.9%和14.9%;在湍流流动状态下,自组装涂层接触角为13°、45°和113°的三组模型的平均减阻率为0.8%、1.9%和6.8%,最大减阻率分别可达3.6%、9.2%和18.0%.两种流体流动中均存在材料表面水接触角增加减阻效率增大的行为.     

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.     

New Answers on the Interaction Between Polymers and Vortices in Turbulent Flows

Numerical data of polymer drag reduced flows is interpreted in terms of modification of near-wall coherent structures. The originality of the method is based on numerical experiments in which boundary conditions or the governing equations are modified in a controlled manner to isolate certain features of the interaction between polymers and turbulence. As a result, polymers are shown to reduce drag by damping near-wall vortices and sustain turbulence by injecting energy onto the streamwise velocity component in the very near-wall region.     

Polymer Induced Drag Reduction in a Turbulent Pipe Flow Subjected to a Coriolis Force

The skin friction factor f in a turbulent wall-bounded flow can be greatly reduced by using polymer solutions. In this paper we discuss experimental results on the effect of the Coriolis force on turbulent drag reduction. To study this, a horizontal smooth-walled pipe with internal diameter 25?mm is placed on a horizontal table rotating about its vertical axis. The rotation is made non-dimensional with friction velocity and pipe diameter, to form the Rotation number Ro. For a range of bulk Rotation number (Ro _b ) between 0 and 0.6 for two different Reynolds numbers (Re _b = 15 & 30 × 10³), the pressure drop is measured, from which the average friction factor f is obtained. Additionally the effect of four different polymer concentrations has been investigated. The single-phase results show that the friction factor increases monotonic but gradual with Rotation. With polymer additives a drag reduction is found that increases with concentration, but which is not affected by the rotation.     

Analysis of Streamwise Velocity Fluctuations in Turbulent Pipe Flow with the Use of an Ultrasonic Doppler Flowmeter

Data collected from several studies of experimental and numerical nature in wall-bounded turbulent flows and in particular in internal flows (channel and pipe flows, Mochizuki and Nieuwstadt [1]) at different Reynolds numbers R ⁺(Ru _*/ν), indicate that: (i) the peak of the rms-value (normalized by u _*) of the streamwise velocity fluctuations (σ _u ⁺|_peak) is essentially independent of the Reynolds number, (ii) the position of the rms peak value (y ⁺|_peak) is weakly dependent of the Reynolds number, (iii) the skewness of the streamwise velocity fluctuations (S _u ) is close to zero at the position in which the variance has its peak. A series of measurements of streamwise velocity fluctuations has been performed in turbulent pipe flow with the use of an Ultrasonic Doppler Velocimeter and our results support those reported in [1]. This revised version was published online in July 2006 with corrections to the Cover Date.     

二维平板湍流边界层减阻研究

利用一套以位移传感器为主的弹性平衡装置,测量几种不同表面形状设计的平板在充分发展的二维湍流边界层中的减阻效果,并对其减阻机理进行研究。结果表明,大涡破碎器 LEBU(Large Eddy Break-up)和其它减阻装置的形状和布置对表面摩擦阻力有较大影响,在有些设计状态下的平板得到了净减阻。     

Wall Versus Centerline Polymer Injection in Turbulent Channel Flows

This experimental study compares the mean and turbulence characteristics of turbulent channel flows with polymer injection at the wall and at the centerline to assess the impact of the injection location on drag reduction. It also contrasts the drag reduction performance of a hydrolyzed polymer versus a non-ionic polymer under the same conditions. Wall injection of non-ionic and hydrolized polymers resulted in 23% and 9% larger drag reduction than corresponding centerline injection, respectively. In all cases, the polymer was structured and the presence of macromolecular polymer structures, even when concentrated mostly away from the wall, seemed to be able to affect the turbulence structure in the flow.     

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.     

边界层对壁面湍流流动高分子减阻的影响

以“粘性”机制为理论基础,近年来在壁面湍流高分子减阻研究中提出了一种拉伸的高分子会产生自洽的等效粘度模型,这种等效粘度随离开壁面的距离而改变.通过等效粘度模型与Navier-Stokes方程的结合,运用雷诺应力模型计算壁面湍流减阻,并与基于高分子有限拉伸的非线性弹性哑铃模型的直接数值模拟结果进行比较,进一步校验了此等效粘度理论.通过肋条破坏槽道流中的边界层,显示了边界层对高分子减阻的影响,结果表明只有形成稳定的边界层,高分子才能有减阻作用.边界层是高分子减阻的首要条件,边界层中的粘性底层和对数率分布区之间的缓冲层可能是减阻的主要影响区域.     

湍流管径问题算法的改进

本文采服无量纲参数（ｇＪＯ＾３／ｖ＾５）及ＫｓＶ／Ｑ）由最小二乘法以指数函数拟合Ｐｒａｎｄｔｌ及Ｋａｒｍａｎ公式，得出分别适用于光滑区和粗糙区的管径算式。再对以上两式作粘性关联偶合，得出适用于湍流过渡区的管径算式。可直接求出管径，避免繁复试算和迭代。计算结果与Ｐｒａｎｄｔｌ，Ｋａｒｍａｎ及Ｃｏｌｅｌｒｏｏｋ－Ｗｈｉｔｅ等经典公式能精确吻合，较Ｓｗａｍｅｅ－Ｊａｉｎ湍流管径算式误差减少一半以上。     

Invariant Analysis of Turbulent Pipe Flow

The anisotropy analysis of Lumley provides a useful tool to quantify the degree of anisotropy in turbulent flows. Also included in the analysis are relations which may be used to check if the flow is axisymmetric or two-dimensional. However, the method does not provide any scale information about the structures. The analysis has therefore been extended here to Fourier space, which allows scale information to be derived. The method was applied to fully developed pipe flow and it was shown that the large-scale motion is everywhere close to axisymmetric. The intermediate scales are strongly influenced by the restrictions posed by the pipe walls. At the centre line, the flow structure appears axisymmetric at all scales, but the measurement sindicate that true axisymmetry is lost very quickly away from the centre line. The structure of the smallest scales could not be determined reliably due to a singularity in the analysis which develops as the scales go to zero. This revised version was published online in July 2006 with corrections to the Cover Date.     

Reynolds Number Dependence of Velocity Structure Functions in a Turbulent Pipe Flow

Low-order moments of the increments δu andδv where u and v are the axial and radial velocity fluctuations respectively, have been obtained using single and X-hot wires mainly on the axis of a fully developed pipe flow for different values of the Taylor microscale Reynolds numberR _λ. The mean energy dissipation rate〉ε〈 was inferred from the uspectrum after the latter was corrected for the spatial resolution of the hot-wire probes. The corrected Kolmogorov-normalized second-order structure functions show a continuous evolution withR _λ. In particular, the scaling exponentζ _v , corresponding to the v structure function, continues to increase with R _λ in contrast to the nearly unchanged value of ζ _u . The Kolmogorov constant for δu shows a smaller rate of increase with R _λ than that forδv. The level of agreement with local isotropy is examined in the context of the competing influences ofR _λ and the mean shear. There is close but not perfect agreement between the present results on the pipe axis and those on the centreline of a fully developed channel flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the Electric Potential Induced by a Homogeneous Magnetic Field in a Turbulent Pipe Flow

In this paper we study a turbulent pipe flow of a weakly electrical conducting fluid subjected to a homogeneous magnetic field which is applied perpendicular to the flow. This configuration forms the basis of a so-called electromagnetic induction flow meter. When the Hartmann number is small so that modification of flow by the Lorenz force can be neglected, the influence of the magnetic field results only in a spatially and temporally varying electric potential. The magnitude of the potential difference across the pipe is then proportional to the flow rate and this constitutes the principle of the flow meter. In this study the flow and electric potential are computed with help of a numerical flow simulation called Large-Eddy Simulation (LES) to which we have added an equation for the electrical potential. The results of the LES have been compared with experiments in which the electric potential is measured as a function of time at several positions on the circumference of the pipe. Both the experimental and numerical results for the mean potential at the pipe wall agree very well with an exact solution that can be obtained in this particular case of a homogeneous magnetic field. Furthermore, it is found that fluctuations in the electric potential due to the turbulence, are small compared to the velocity fluctuations. Based on the results we conclude that electrical-magnetic effects in pipe flow can be accurately computed with LES.     

Drag Reduction of a Circular Cylinder Using an Upstream Rod

Experimental studies on the drag reduction of the circular cylinder were conducted by pressure measurement at a Reynolds number of 82 000 (based on the cylinder diameter). A rod was placed upstream of and parallel to the cylinder to control the flow around the cylinder. The upstream rod can reduce the resultant force of the cylinder at various spacing between the rod and the cylinder for α < 5^∘(α defined as the staggered angle of the rod and the cylinder). For α > 10^∘, the resultant force coefficient has a large value, so the upstream rod cannot reduce the force on the cylinder any more. For α = 0^∘ and d/D = 0.5 (where d and D are the diameter of the rod and the cylinder, respectively), the maximum drag of the cylinder reduces to 2.34% that of the single cylinder. The mechanism of the drag reduction of the cylinder with an upstream rod in tandem was presented by estimating the local contributions to the drag reduction of the pressure variation. In the staggered arrangement, the flow structures have five flow patterns (they are the cavity mode, the wake splitting mode, the wake merge mode, the weak boundary layer interaction mode and the negligible interaction mode) according to the pressure distribution and the hydrogen bubble flow visualization. The half plane upwind of the cylinder can be divided to four regions, from which one can easily estimates the force acting on the circular cylinder with an upstream rod in staggered arrangement.     

Vibro-Acoustic Response of a Pipe Excited by a Turbulent Internal Flow

This article presents an experimental study of the vibro-acoustic response of a pipe excited by a fully-developed turbulent air flow. First, the wall pressure field acting on the internal pipe wall is investigated. The power spectral density of the wall pressure fluctuations is analyzed after cancellation of contaminating background noise. The convection velocity and correlation lengths are calculated from measured cross-spectra, and the cross-spectra are expressed in Corcos model form. Second, the vibro-acoustic response of the pipe is analyzed by referring to the structural modes of the pipe. This revised version was published online in July 2006 with corrections to the Cover Date.     

Polymer “threads” and drag reduction

A number of different polymer fluids were ejected on the centerline of a water pipe-flow facility. Two distinct flow regions were identified: Reynolds numbers above 25000, where centerline injection acted as a rather efficient mixing device for water-soluble polymer — and no drag-reduction resulted from non water-soluble materials; and Reynolds numbers from 10000 to 25000, where strong evidence exists that under certain conditions, a viscoelastic fluid thread can interact with turbulence eddies and reduce the overall flow friction in the pipe.On Sabbatical leave from San Diego State University.     

Spray Penetration in a Turbulent Flow

Analytical expressions for mass concentration of liquid fuel in a spray are derived taking into account the effects of gas turbulence, and assuming that the influence of droplets on gas is small (intitial stage of spray development). Beyond a certain distance the spray is expected to be fully dispersed. This distance is identified with the maximum spray penetration. Then the influence of turbulence on the spray stopping distance is discussed and the rms spray penetration is computed from a trajectory (Lagrangian) approach. Finally, the problem of spray penetration is investigated in a homogeneous two-phase flow regime taking into account the dispersion of spray away from its axis. It is predicted that for realistic values of spray parameters the spray penetration at large distances from the nozzle is expected to be proportional to t ^2/3 (in the case when this dispersion is not taken into account this distance is proportional to t ^1/2). The t ^2/3 law is supported by experimental observations for a high pressure injector. This revised version was published online in July 2006 with corrections to the Cover Date.     

添加聚合物对混合层流场特性影响的实验研究

叙述了适用于粘弹性流体混合层流场的实验装置的设计和研制．采用二维激光多普勒系统对混合层流场进行了测量，得到了平均速度剖面、动量厚度、湍流脉动强度、雷诺应力等一些流场的基本特征量．结果表明，混合层中加入聚合物后流场将有较大的变化，同时也说明本文所研制的实验装置满足实验的要求．