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).     

Events of High Polymer Activity in Drag Reducing Flows

The mechanism of drag reduction in turbulent flows due to polymers has been investigated with help of a direct numerical simulation. In particular, we consider the interaction between turbulent velocity fluctuations and polymers in terms of elastic energy that can be stored in the polymer. To this end all the terms of the elastic energy budget have been computed. The most interesting term is the production of elastic energy due to turbulent fluctuations, because it describes the interaction between polymers and turbulence. Although this term appears to be small in the average, it turns out that it can reach very large values instantaneously and intermittently, and the energy transfer from polymer to turbulence is located in very well defined areas inside the channel. This implies that locally there is a strong interaction between the polymer and the turbulent flow structure, and this strong interaction is mostly seen in areas of high velocity fluctuations.     

A study on coherent structures and drag-reduction in the wall turbulence with polymer additives by TRPIV

An experimental measurement was performed using time-resolved particle image velocimetry (TRPIV) to investigate the spatial topological character of coherent structures in wall-bounded turbulence of polymer additive solution. The fully developed near-wall turbulent flow fields with and without polymer additives at the same Reynolds number were measured by TRPIV in a water channel. The comparisons of turbulent statistics confirm that due to viscoelastic structure of long-chain polymers, the wall-normal velocity fluctuation and Reynolds shear stress in the near-wall region are suppressed significantly. Furthermore, it is noted that such a behavior of polymers is closely related to the decease of the motion of the second and forth quadrants, i.e., the ejection and sweep events, in the near-wall region. The spatial topological mode of coherent structures during bursts has been extracted by the new mu-level criteria based on locally averaged velocity structure function. Although the general shapes of coherent structures are unchanged by polymer additives, the fluctuating velocity, velocity gradient, velocity strain rate and vorticity of coherent structures during burst events are suppressed in the polymer additive solution compared with that in water. The results show that due to the polymer additives the occurrence and intensity of coherent structures are suppressed, leading to drag reduction.     

Influence of wavy structured surfaces and large scale polymer structures on drag reduction

Drag reduction was studied for turbulent flow over a structured wall that contained 600 sinusoidal waves with a wavelength of 5 mm and an amplitude of 0.25 mm. A concentrated solution of a co-polymer of polyacrylamide and sodium acrylate was injected into the flow through wall slots. Laser Doppler velocimetry was used to measure turbulence. A fluorescence technique was developed that enabled us to demonstrate the existence, under certain circumstances, of large gelatinous structures in the injected polymer solution and in the flow channel.At maximum drag reduction, the Reynolds shear stress was zero and the velocity field was the same as found for a smooth surface. Larger drag reductions could be realized for a wavy wall because the initial drag was larger. The influences of polymers on the turbulent fields are similar for smooth and wavy boundaries. These results are of interest since the interaction with the wall can be quite different for water flow over smooth and wavy boundaries (which are characterized as being completely rough). An important effect of polymers is a decreasing relative importance of high frequency fluctuations with increasing drag reduction that is characterized by a cut-off frequency. This cut-off is the same for smooth and wavy walls at maximum drag reduction. The sensitivity of drag reduction to the method of preparing and delivering the polymer solution suggests that aggregation of polymers could be playing an important role for the system that was studied. For example, drag reduction was enhanced when large polymer structures are present.     

A study with particle-image velocimetry of the influence of drag-reducing polymers on the structure of turbulence

Particle-image velocimetry has been used to study the effect of drag-reducing polymers on the structure of turbulence in a channel flow, under conditions of 41% and 55% drag reduction. The fluctuating velocity fields in the x-y plane and in one x-z plane were measured. The striking features of these results are the damping of small scales and the repression of fluctuations of the velocity component normal to the wall. The role of the wall in creating turbulence diminishes greatly at large drag reductions; Warholic et al. (1999) have shown that a turbulent flow with zero Reynolds stress exists at maximum drag reduction. Velocity fields presented for conditions approaching this critical behavior are of particular interest. Received: 23 April 1999/Accepted: 12 February 2001     

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.     

Turbulent expansion flow of low molecular weight shear-thinning solutions

A Laser-Doppler anemometer and a pressure transducer were used to carry out detailed measurements of the mean and root mean square of the velocity and wall-pressure in an axisymmetric sudden expansion flow, with 0.4 and 0.5% by weight shear-thinning aqueous solutions of a low molecular weight polymer (6,000), after appropriate rheological characterisation. In spite of their very low molecular weight, these solutions still exhibited elongational elastic effects through drag reduction of up to 35% relative to Newtonian turbulent pipe flow, as shown by Pereira and Pinho (1994). The results showed small variations of the recirculation bubble length with polymer concentration and Reynolds number and reductions of the normal Reynolds stresses of up to 30%, especially in the tangential and radial directions. The reduction in normal Reynolds stresses within the shear layer is an elongational elastic effect, but this elasticity needs to be considerably more intense, such as with high molecular weight polymers, in order to strongly affect the mean flow characteristics. The observed mean flow patterns with these low molecular weight polymer solutions were indeed similar to those exhibited by Newtonian and inelastic fluids.     

Predicting Turbulent Spectra in Drag-reduced Flows

In the present work we describe how turbulent skin-friction drag reduction obtained through near-wall turbulence manipulation modifies the spectral content of turbulent fluctuations and Reynolds shear stress with focus on the largest scales. Direct Numerical Simulations (DNS) of turbulent channels up to Re _τ = 1000 are performed in which drag reduction is achieved either via artificially removing wall-normal turbulent fluctuations in the vicinity of the wall or via streamwise-travelling waves of spanwise wall velocity. This near-wall turbulence manipulation is shown to modify turbulent spectra in a broad range of scales throughout the whole channel. Above the buffer layer, the observed changes can be predicted, exploiting the vertical shift of the logarithmic portion of the mean streamwise velocity profile, which is a classic performance measure for wall roughness or drag-reducing riblets. A simple model is developed for predicting the large-scale contribution to turbulent fluctuation and Reynolds shear stress spectra in drag-reduced turbulent channels in which a flow control acts at the wall. Any drag-reducing control that successfully interacts with large scales should deviate from the predictions of the present model, making it a useful benchmark for assessing the capability of a control to affect large scales directly.     

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.     

Time-dependent drag reduction and ageing in aqueous solutions of a cationic surfactant

The turbulent pipe flow of a highly dilute aqueous cationic surfactant solution is investigated by means of a pulsed ultrasound Doppler method with special emphasis on the wall boundary layer. The velocity profiles are recorded for several Reynolds numbers at varying ages of the solution. The wall shear stress velocities u _τ used for the normalization of the velocity profiles are determined by fitting the measured profiles to the universal linear velocity profile in the viscous sublayer. The theoretical pressure loss is then calculated from the numerical values of u _τ and compared to the experimental values. Two different scaling methods are discussed for the velocity fluctuations concerning the correlation of the root-mean square values with the effect and the amount of drag reduction. It is shown that outer scaling with the mean velocity is appropriate for the detection of drag reduction in surfactant solutions, rather than inner scaling with the wall shear stress velocity, which is common practice in investigations of 'usual' turbulent flows.     

Forcing frequency effects on turbulence dynamics in pulsatile pipe flow

The turbulence dynamics of pulsatile pipe flow are investigated using direct numerical simulation (DNS) at a mean friction Reynolds number of 180. Results are presented for a range of forcing frequencies at a fixed amplitude, which, based on existing classifications, corresponds to the current-dominated regime. This work directs attention towards the phase-variations of single and two-point turbulence statistics, with a particular emphasis on the response of the Reynolds shear stress to systematic changes in the applied forcing frequency. The study has yielded two key outcomes. (i) A new frequency classification procedure for pulsatile turbulent flows (at low-to-moderate friction Reynolds numbers), informed by the Reynolds shear stress frequency co-spectra and the value of the applied forcing frequency. (ii) A detailed account of single- and two-point Reynolds shear stress statistics, in response to high, very-high and ultra-high forcing frequencies in order to study turbulence dynamics in the physical and Fourier domains. Furthermore, the oscillatory velocity field obtained from the DNS data is compared against the laminar Womersley solution in order to assess the interaction (or lack thereof) between the oscillatory velocity field and phase-averaged Reynolds shear stress fluctuations. For the higher frequencies considered in this work, single- and two-point Reynolds shear statistics all enter the so-called “frozen” regime — which occurs as the forcing time-scale becomes smaller than that of the highest-frequency, energy-containing motions in the Reynolds shear stress co-spectra.     

固体颗粒对沟槽湍流边界层影响的实验研究

本文采用粒子图像测速技术(particles image velocimetry, PIV)研究固体颗粒对放置在平板湍流边界层中的平壁和沟槽壁面减阻效果的影响. 实验对清水和加入粒径为155 μm聚苯乙烯颗粒的流法向二维速度场信息进行采集, 对不同工况下的平均速度剖面、雷诺应力和湍流度等统计量进行对比, 分析流体在边界层中的行为. 运用空间局部平均结构函数提取了不同工况湍流边界层喷射?扫掠行为的空间拓扑结构并进行比较. 结果发现, 在不同的壁面条件下, 粒子加入后的对数律区中无量纲速度均略大于清水组, 雷诺切应力有所降低, 湍流度有所减弱. 对于不同流场速度下的沟槽而言, 颗粒的加入均降低了壁面附近的阻力, 而颗粒单独作用于光滑壁面的减阻效果并不明显. 加入粒子后的相干结构数目有所增加, 法向脉动速度下降. 沟槽壁面附近的相干结构数目有所增加, 法向脉动速度在自由来流速度较大时有所上升, 在速度较小时有所下降. 这表明不同减阻状况下的沟槽均能将大涡破碎成更多的涡, 并且粒子的加入强化了这种破碎作用.      

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.     

Direct numerical simulation of turbulence over resolved and modeled rough walls with irregularly distributed roughness

To simulate turbulent flow over a rough wall without resolving complicated rough geometries, a macroscopic rough wall model is developed based on spatial (plane) averaging theory. The plane-averaged drag force term, which arises through averaging the Navier–Stokes equations in a plane parallel to a rough wall, can be modeled using a plane porosity and a plane hydraulic diameter. To evaluate the developed model, direct and macroscopic model simulations for turbulence over irregularly distributed semi-spheres at Reynolds number of 300 are carried out using the D3Q27 multiple-relaxation time lattice Boltzmann method. The results show that the developed model can be used to predict rough wall skin friction. The results agree quantitatively with standard turbulence statistics such as mean velocity and Reynolds stress profiles with the fully resolved DNS data. Since velocity dispersion occurs inside the rough wall and is found to contribute to turbulence energy dissipation, which the developed model cannot account for, the developed model fails to reproduce dispersion-related turbulence energy dissipation. However, it is found that the plane-averaged drag force term can successfully recover the deficiency of dispersion-related turbulence energy dissipation.     

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.     

近壁湍流统计性质研究

采用大涡模拟方法,模拟了槽道湍流,得到了不同雷诺数下槽道湍流的结果. 在此基础上,研究了平均速度、雷诺应力、脉动动能和脉动速度均方根的分布;讨论了平均速度的壁面律问题;给出了雷诺应力、脉动动能和脉动速度均方根随雷诺数的变化规律,其中雷诺应力、脉动动能给出了定量公式.      

Skin-friction drag reduction in a high-Reynolds-number turbulent boundary layer via real-time control of large-scale structures

While large-scale motions are most energetic in the logarithmic region of a high-Reynolds-number turbulent boundary layer, they also have an influence in the inner-region. In this paper we describe an experimental investigation of manipulating the large-scale motions and reveal how this affects the turbulence and skin-friction drag. A boundary layer with a friction Reynolds number of 14 400 is controlled using a spanwise array of nine wall-normal jets operated in an on/off mode and with an exit velocity that causes the jets in cross-flow to penetrate within the log-region. Each jet is triggered in real-time with an active controller, driven by a time-resolved footprint of the large-scale motions acquired upstream. Nominally, the controller injects air into large-scale zones with positive streamwise velocity fluctuations; these zones are associated with positive wall-shear stress fluctuations. This control scheme reduced the streamwise turbulence intensity in the log-region up to a downstream distance of more than five times the boundary layer thickness, δ, from the point of actuation. The highest reduction in spectral energy—more than 30%—was found for wavelengths larger than 5δ in the log-region at 1.7δ downstream of actuation, while scales larger than 2δ still comprised more than 15% energy reduction in the near-wall region. In addition, a 3.2% reduction in mean skin-friction drag was achieved at 1.7δ downstream of actuation. Our reductions of the streamwise turbulence intensity and mean skin-friction drag exceed a base line control-case, for which the jet actuators were operated with the same temporal pattern, but not synchronised with the incoming large-scale zones of positive fluctuating velocity.     

Die Wirkung von Polymerzusätzen auf die Turbulenzstruktur in der ebenen Mischungsschicht zweier Ströme

The plane mixing layer formed between two parallel streams moving with different velocities is one of the simplest types of free turbulent boundary layers and has frequently been studied for Newtonian fluids. As a result of this and because of its good experimental accessibility this type of flow provides a good opportunity for obtaining information about the influence of drag reducing additives on the structure of free turbulence. This is all the more so because of the presence of a characteristic vortex structure which can be clearly distinguished from the overlying statistical fine turbulence. The turbulence field was investigated using an existent laser Doppler anemometer system that had been designed for space-time correlation measurements. This enabled measurements to be made of the mainstream velocity as well as of the longitudinal and transversal turbulent fluctuations and, after a simple modification, also of the Reynolds shear stresses and the cross correlation coefficients. The main result of the addition of 50 ppm of the polymer used (Separan AP30) was found to be an intensification of the Reynolds shear stresses. The resulting substantially more rapid increase (than in water) in the thickness of the shear layer can be explained theoretically; such behaviour has also been observed in free jets. On the other hand, the reduced thickness of the mixing layer in the initial region and the associated enhancement of the longitudinal fluctuations and damping of the transversal fluctuations indicate that the main shear flow induces a flow anisotropy by uncoiling and aligning the polymer molecules. The increase in the spreading angle suggests that the entrainment process at the edges of the mixing layer is intensified. This can be explained by the enhancement of the large energy carrying vortices in the turbulence spectrum. This is probably also the reason for the general increase in the correlation coefficients observed at all positions along the centreline of the flow field. However, a complete discussion of the energy transfer mechanism present here, in particular with inclusion of the fine turbulence responsible for dissipation, is only possible with the help of a detailed analysis of the vortex structure in the mixing layer. This is presented in a following paper. The relation between the degree of drag reduction and the intensity of the Reynolds shear stresses enables the direct influence of the rheological properties of the fluid on the turbulent momentum transfer to be clearly recognized.     

A Reynolds stress model for turbulent flow of homogeneous polymer solutions

Using a priori analyses of direct numerical simulation (DNS) data, a Reynolds stress model (RSM) is developed to account for the influence of polymer additives on turbulent flow over a wide range of flow conditions. The Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) rheological constitutive model is utilized to evaluate the polymer contribution to the stress tensor. Thirteen DNS data sets are used to analyze the budgets of elastic stress–velocity gradient correlations as well as Reynolds stress and dissipation transport. Closures are developed in the framework of the RSM model for all the required unknown and non-linear terms. The polymer stresses, velocity profiles, turbulent flow statistics and the percentage of friction drag reduction predicted by the RSM model are in good agreement with present and those obtained from independent DNS data over a wide range of rheological and flow parameters.