Drag reduction in the turbulent pipe flow of polymers

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.     

Drag reduction change of polyethyleneoxide solutions in pipe flow

Change of drag reduction (DR) along a tube (D=2 mm, L=4 m) was experimentally investigated. To attain turbulent flow with Re=8 × 10⁴, a tank operated under high pressure up to 16 MPa. Solutions of different brands of polyethyleneoxide (PEO) with concentrations from 1 ppm to 100 ppm were tested. The results indicate that DR is not a constant value but depends on the time and intensity of interaction between the polymer and the turbulent flow. There are three regions with different behaviors of DR: growth, maximum, and slope down. Maximum DR coincides with the Virk ultimate DR and can be described by the suggested simple formula . A decrease in the DR maximum has not been found even for high shear stresses τ _p < 800 Pa. DR dynamics for four brands of PEO with different molecular weight was studied. Direct experimentally determined DR may be greater than the Virk ultimate value if the change in velocity profile is not taken into account. The corrected DR never exceeds the ultimate DR. Received: 10 April 2000/Accepted: 24 May 2001     

Drag reduction by flow separation control on a car after body

New development constraints prompted by new pollutant emissions and fuel consumption standards (Corporate Average Economy Fuel) require that automobile manufacturers develop new flow control devices capable of reducing the aerodynamic drag of motor vehicles. The solutions envisaged must have a negligible impact on the vehicle geometry. In this context, flow control by continuous suction is seen as a promising alternative. The control configurations identified during a previous 2D numerical analysis are adapted for this purpose and are tested on a 3D geometry. A local suction system located on the upper part of the rear window is capable of eliminating the rear window separation on simplified fastback car geometry. Aerodynamic drag reductions close to 17% have been obtained. Copyright © 2008 John Wiley & Sons, Ltd.     

Drag reduction effectiveness of dilute and entangled xanthan in turbulent pipe flow

The ability to reduce the frictional drag in turbulent flow in pipes and channels by addition of a small amount of a high molecular weight polymer has application in myriad industries and processes. Here, the drag reduction properties of the polyelectrolyte xanthan are explored in differing solvent environments (salt free versus salt solution) and delivery configurations (homogeneous versus stock solution dilution). Drag reduction effectiveness increases when an entangled xanthan solution is diluted compared to solutions prepared in the dilute regime. Based on dynamic rheological measurements of the elastic modulus, residual entanglements and network structure are hypothesized to account for the observed change in drag reduction effectiveness. Drag reduction effectiveness is unchanged by the presence of salt when the stock solution concentration is sufficiently above the critical concentration c_D. Finally, the drag reduction effectiveness decreases with time when diluted from an entangled stock solution but remains greater than the homogeneous case after more than 24 h.     

Drag reduction in polymer mixtures

Summary Drag reduction was studied in dilute toluene solutions of a mixture of two polymers: polyisobutylene (of three different molecular weights) and 1,4-cis-isoprene rubber in the turbulent region at low (up to 5000) Reynolds numbers. Experiments were carried out with mixed solutions at a concentration equal to optimum concentration of polyisobutylene or higher than it. Drag reduction of the polymer mixtures depending on the ratio of the two polymers showed a positive deviation from the additive straight line at all concentrations investigated. To evaluate the degree of deviation from additivity, the excess drag reduction, was introduced which represents the difference between the actually measured drag reduction and that read from the additive straight line. The excess drag reduction showed almost no dependence on the molecular weight of polyisobutylene in the investigated range of this magnitude. Deviation from additivity depending on the ratio of the two polymers in the mixture growed higher with increasing the flow rate at a given molecular weight of polyisobutylene. The highest excess drag reduction was observed in solutions containing a larger amount of the lower molecular isoprene rubber polymer. The effect of polymer coils on drag reduction in binary polymer solutions was studied. An assumption was made that higher drag reduction in the polymer mixtures as compared to the additive was due to the change of polymer coil dimensions caused by the copresence of the macromolecules of both polymers in the solution. It was further supposed that low shear stresses at which the experiments were carried out caused sufficient orientation and deformation of isoprene rubber enlarged molecules and the contribution of the latter in increasing drag reduction of the mixture was higher.

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Zusammenfassung Die Widerstandsverminderung in verdünnten toluolischen Lösungen einer Mischung von zwei verschiedenen Polymeren wird untersucht. Verwendet werden Polyisobutylene (mit drei verschiedenen Molekulargewichten) und 1,4-cis-Isopren-Kautschuk, und es wird im turbulenten Bereich bei Reynolds-Zahlen bis zu 5000 gemessen. Die Versuche werden bei Konzentrationen, die der Optimalkonzentration von Polyisobutylen entsprechen, oder höheren Konzentrationen durchgeführt. Die Widerstandsverminderung der Polymermischungen zeigt bei allen untersuchten Konzentrationen eine positive Abweichung von der additiven Geraden, deren Größe vom Mischungsverhältnis abhängt. Zur Beschreibung der Abweichung vom additiven Verhalten wird die überschüssige Widerstandsverminderung (excess drag reduction) eingeführt, welche die Differenz zwischen dem wirklich gemessenen Wert und dem zugeordneten Wert auf der additiven Geraden beschreibt. Diese Größe zeigt nur eine geringe Abhängigkeit vom Molekulargewicht der eingesetzten Polyisobutylene. Die Abweichung vom additiven Verhalten als Funktion des Mischungsverhältnisses beider Polymeren wächst mit zunehmendem Volumenstrom. Die größte überschüssige Widerstandsverminderung wird in Lösungen beobachtet, die einen größeren Anteil des weniger hochmolekularen Isopren-Kautschuks enthalten. Der Einfluß der Polymerverknäuelung auf die Widerstandsverminderung wird betrachtet. Es wird angenommen, daß die überschüssige Widerstandsverminderung auf eine Änderung der Knäuelgröße infolge der Anwesenheit des jeweils anderen Polymeren in der Lösung zurückzuführen ist. Weiter wird vermutet, daß die relativ niedrigen Schubspannungen, bei denen die Versuche ausgeführt wurden, doch schon eine hinreichend starke Orientierung und Deformation der aufgeweiteten Isopren-Kautschuk-Moleküle bewirken, so daß deren Beitrag zur Erhöhung der Widerstandsverminderung überwiegt.

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Notations D diameter of capillary - DR drag reduction - DR _add additive drag reduction - DR excess drag reduction,DR = DR – DR _add - DR _mixture theoretical drag reduction of the mixture - DR _mixture ^* actually measured drag reduction of the mixture - DR _1R drag reduction of an IR molecule in a separate IR solution - DR _1R ^* drag reduction of an IR molecule in the presence of molecules of another polymer in the solution - DR _PIB drag reduction of a PIB molecule in a separate PIB solution - DR _PIB ^* drag reduction of a PIB molecule in the presence of molecules of another polymer in the solution - L length of the capillary - flow rate - c concentration - n number of IR molecules - p number of PIB molecules - _w wall shear stress - CMC carboxymethylcellulose - IR isoprene rubber - PAA polyacrylic acid - PAM polyacrylamide - PEI polyethyleneimine - PEO polyethylene oxide - PIB polyisobutylene - PS polystyrene     

Drag reduction in riblet-lined pipes

The possibilities of reducing the drag in pipes with a circular cross section by lining them with riblets have been investigated experimentally for developed turbulent air flow. The maximum drag reduction of 6–7% in the riblet-lined as compared with the smooth pipe was obtained for a dimensionless riblet pitch, expressed in law-of-the-wall parameters,s ⁺=14–18.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 57–61, January–February, 1995.     

Drag reduction of motor vehicles by active flow control using the Coanda effect

A test facility has been constructed to realistically simulate the flow around a two dimensional car shaped body in a wind tunnel. A moving belt simulator has been employed to generate the relative motion between model and ground. In a first step, the aerodynamic coefficients c _L and c _D of the model are determined using static pressure and force measurements. LDA-measurements behind the model show the large vortex and turbulence structures of the near and far wake. In a second step, the ambient flow around the model is modified by way of an active flow control which uses the Coanda effect, whereby the base-pressure increases by nearly 50% and the total drag can be reduced by 10%. The recirculating region is completely eliminated. The current work reveals the fundamental physical phenomena of the new method by observing the pressure forces on the model surface as well as the time averaged velocities and turbulence distributions for the near and far wake. A theory resting on this empirical information is developed and provides information about the effectiveness of the blowing method. For this, momentum and energy equations were applied to the flow around the vehicle to enable a validation of the theoretical results using experimental values. Received: 9 June 1998 / Accepted: 20 July 1999     

Drag reduction and thrust generation by tangential surface motion in flow past a cylinder

Sensitivity of drag to tangential surface motion is calculated in flow past a circular cylinder in both two- and three-dimensional conditions at Reynolds number \(\textit{Re} \le 1000\). The magnitude of the sensitivity maximises in the region slightly upstream of the separation points where the contour lines of spanwise vorticity are normal to the cylinder surface. A control to reduce drag can be obtained by (negatively) scaling the sensitivity. The high correlation of sensitivities of controlled and uncontrolled flow indicates that the scaled sensitivity is a good approximation of the nonlinear optimal control. It is validated through direct numerical simulations that the linear range of the steady control is much higher than the unsteady control, which synchronises the vortex shedding and induces lock-in effects. The steady control injects angular momentum into the separating boundary layer, stabilises the flow and increases the base pressure significantly. At \(\textit{Re}=100\), when the maximum tangential motion reaches 50% of the free-stream velocity, the vortex shedding, boundary-layer separation and recirculation bubbles are eliminated and 32% of the drag is reduced. When the maximum tangential motion reaches 2.5 times of the free-stream velocity, thrust is generated and the power savings ratio, defined as the ratio of the reduced drag power to the control input power, reaches 19.6. The mechanism of drag reduction is attributed to the change of the radial gradient of spanwise vorticity (\(\partial _{r} \hat{\zeta }\)) and the subsequent accelerated pressure recovery from the uncontrolled separation points to the rear stagnation point.     

Compressible air flow through a collapsing liquid cavity

We present a multiscale approach to simulate the impact of a solid object on a liquid surface: upon impact a thin liquid sheet is thrown upwards all around the rim of the impactor while in its wake a large surface cavity forms. Under the influence of hydrostatic pressure the cavity immediately starts to collapse and eventually closes in a single point from which a thin, needle‐like jet is ejected. The existing numerical treatments of liquid impact either consider the surrounding air as an incompressible fluid or neglect air effects altogether. In contrast, our approach couples a boundary‐integral method for the liquid with a Roe scheme for the gas domain and is thus able to handle the fully compressible gas stream that is pushed out of the collapsing impact cavity. Taking into account that air compressibility is crucial, since, as we show in this work, the impact crater collapses so violently that the air flow through the cavity neck attains supersonic velocities already at cavity diameters larger than 1 mm. Our computational results are validated through corresponding experimental data. Copyright © 2010 John Wiley & Sons, Ltd.     

Drag reduction in aqueous cationic soap solutions

The pipe flow drag-reducing properties of mixtures of alkyltrimethylammonium halides with 1-naphthol in aqueous solution have been investigated. The effects of solution concentration, soap-naphthol ratio, soap molecular weight and solution temperature upon drag reduction and swirl decay time are reported. The critical wall shear stresses above which the drag-reducing properties cease correlate well with swirl decay time. At low soap concentrations greater than equimolar proportions of 1-naphthol with the soap are required for maximum drag reduction. The drag-reducing properties of these solutions are greatest at and around the Krafft point of the pure soap. A phenomenon similar to onset for polymer solution drag reduction is reported for these soap solutions.     

Turbulent channel flow of dilute polymeric solutions: Drag reduction scaling and an eddy viscosity model

Direct numerical simulation of viscoelastic turbulent channel flows up to the maximum drag reduction (MDR) limit has been performed. The simulation results in turn have been used to develop relationships between the flow and fluid rheological parameters, i.e. maximum chain extensibility, Reynolds number, Re_τ, and Weissenberg number, We_τ and percent drag reduction (%DR) as well as the slope increment of the mean velocity profile. Moreover, based on the trends observed in the mean velocity profile and the overall momentum balance three different regimes of drag reduction (DR), namely, low drag reduction (LDR; 0 ≤ %DR ≤ 20), high drag reduction (HDR; 20 ≤ %DR ≤ 52) and MDR (52 ≤ %DR ≤ 74) have been identified and mathematical expressions for the eddy viscosity in these regimes are presented. It is found that both in LDR and HDR regimes the eddy viscosity varies with the distance from the channel wall. However, in the MDR regime the ratio of the eddy viscosity to the Newtonian one tends to a very small value around 0.1 within the channel. Based on these expressions a procedure that relies on the DNS predictions of the budgets of momentum and viscoelastic shear stress is developed for evaluating the mean velocity profile.     

Drag and lift calculation through a spatial impulsive surface interaction model in free molecule flow

Summary A spatial impulsive interaction model is applied to the calculation of drag and lift coefficients for flat plate, sphere and circular cylinder with side-wind in hyperthermal free-molecule flow. Obtained results for flat plate are also compared with the corresponding coefficients calculated by Hurlbut and Sherman in1968 according to the Nocilla reemission model(1962).

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Sommario Nel presente lavoro viene applicato un modello spaziale impulsivo di interazione superficiale[1] al calcolo dei coefficienti di resistenza e portanza per lamina piana, sfera e cilindro con deriva in regime di molecole libere con velocità ipertermiche. I risultati ottenuti per la lamina piana vengono confrontati con i corrispondenti coefficienti calcolati teoricamente da Hurlbut e Sherman nel1968 [3].

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Presented at the A.I.D.A.A. meeting on «Applicazioni di modelli matematici nello studio di problemi aerospaziali» held in Torino, Italy, 11–12 June 1970. Research carried out under the auspices of the Mathematical Research Groups of the National Research Council.     

基于Busemann双翼构型的超音速导弹减阻技术研究

针对超音速飞行器在飞行过程中要承受的强激波带来的不利波阻,本文与传统单翼进行对比,分析了Busemann超音速双翼构型的减阻原理并充分利用了双翼间激波膨胀波的有利干涉和机翼厚度减小所带来的激波减弱效应。以常规气动布局的超音速导弹为研究对象,数值计算结果表明:设计巡航条件下,来流马赫数为2.5时,采用新型双翼气动布局能够使波阻减小42%。同时,为了消除非设计马赫数下Busemann双翼构型的壅塞问题,本文探索了一种转折变形翼面技术,计算结果表明:通过控制机翼前缘入口处和最大厚度处的面积比,该方案在非设计条件下能够基本消除阻力剧增问题。此外,在Busemann双翼基础上改进的上下翼非对称的超音速双翼构型可进一步改善实际有升力飞行条件下模型的气动性能,将所计算导弹模型巡航状态的升阻比提高了22%。综合以上结果表明,本文介绍的减阻技术可以为超声速导弹的研制和发展提供新的设计思路。     

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.     

Drag reduction by centrally-injected polymer “threads”

In the extensive literature on polymer drag reduction, it has occasionally been reported that a continuous thread of a high-concentration polymer solution injected into the axis of a pipe produces a drag-reduction effect on the water-flow in the pipe. The “thread” seems to persist through the length of the pipe and little if any diffusion of polymer to the walls of the pipe is apparent. All previous experiments have been at a relatively low Reynolds number, and the purpose of the present work was to evaluate the technique at pipe Reynolds numbers above 10⁵. Experiments were carried out in a 53 mm diameter stainless steel pipe 20 m in length, constructed to high tolerances. The polymer, Separan AP-203, was injected as a 0.5% solution from an axially placed nozzle at the bellmouth entrance. The experiments show that the central thread provided drag-reduction almost equivalent to pre-mixed solutions of the same total polymer concentration flowing in the pipe. Overall concentrations of 1, 2, 4, and 20 parts-per-million were used. Moreover, the effects were additive: 2 ppm thread overall concentration plus 2 ppm pre-mixed gave drag reductions equivalent to 4 ppm of either type. Reynolds numbers of up to 300 000 were investigated. Attempts to visualize the polymer thread were inconclusive. The dyed polymer thread was viewed through a window at the downstream end of the pipe. The predominate appearance was that of a dispersion of globules of high-concentration polymer.     

Drag reduction effectiveness and shear stability of polymer-polymer and polymer-fibre mixtures in recirculatory turbulent flow of water

The turbulent drag reduction caused by polymer-polymer and polymerfibre mixtures has been measured in recirculatory flow of water. Shear stability studies have also been made on a number of drag reducing polymers, asbestos fibres and their mixtures in recirculatory turbulent flow of water. Reynolds numbers ranged from 20,000 to 57,000. Both positive and negative deviations from linear additive behaviour have been observed in drag reduction caused by the polymer-polymer mixtures depending upon their compositions, flow rate and polymer species in the mixture. The drag reduction by the mixtures has been predicted by using simple mixture rule equations including an interaction parameter. This interaction parameter is believed to depend upon the polymer interaction in the polymer mixture. The random coil size and rigidity of the polymer molecules appear to be responsible for the synergism observed in the drag reduction caused by the mixture. In general, mixtures having larger solvation number seem to give positive synergism.Synergism in drag reduction by the polymer-fibre mixtures has also been observed. The simple mixture law equation with interaction parameter is also applicable in predicting the drag reduction by the mixtures as above. The random coil size of the polymer molecules and the rigidity of the polymer-fibre system appear to be responsible for the synergism observed in drag reduction. In the shearstability studies it has been observed that the decrement in drag reduction (DR) is higher than the the decrement in absolute viscosity in most cases. Carboxymethyl cellulose is found to be the most shear stable polymer followed by guar gum, xanthan gum and polyacrylamide. The mixtures exhibiting synergism in causing drag reduction are found to be more shear stable.