Maximum Drag Reduction Asymptote Research Articles

Drag Reduction by Dried Malted Rice Solutions in Pipe Flow

In this study, the friction factor of a turbulent pipe flow for dried rice malt extract solutions was experimentally reduced to that of a Newtonian fluid. The friction factor was measured for four types of solutions at different culture times and concentrations. The results indicate that the experimental data points of the test solutions diverged from the maximum drag reduction asymptote at and above Re√f ≅ 200~250 and aligned parallel to those of Newtonian fluids. This drag reduction phenomenon differed from that observed in artificial high-molecular-weight polymer solutions, called Type A drag reduction, in which the drag reduction level is dependent on the Reynolds number in the intermediate region. This is classified as a Type B drag reduction phenomenon in biopolymer solutions and fine solid particle suspensions. The order of drag reduction corresponded to approximately 5–50 ppm xanthan gum solutions, as reported previously. Furthermore, the velocity profile in a turbulent pipe flow was predicted using a semi-theoretical equation in which the friction factors were determined using the difference between the experimental results of the tested solutions and Newtonian fluids. The results indicate considerable thickening of the viscous sublayer in the turbulent pipe flow of the test solutions compared with that of Newtonian fluids.

The similarity theory of free turbulent shear flows of viscoelastic fluids

A new theory is formulated for the description of the conformation state of the polymer chains in free turbulent shear flows of viscoelastic fluids. Using self-similarity arguments and new scaling relations for the turbulent flux of conformation tensor we show the existence of minimum and maximum solvent dissipation reduction asymptotes, and four different polymer deformation regimes. The similarities with the maximum drag reduction asymptote of turbulent pipe flow is discussed and new scaling laws are obtained for all components of the mean conformation tensor at each deformation regime. Analytical solutions for the self-similar transverse profiles of the conformation tensor components are also obtained, providing the complete solution for the mean flow problem at the far field. The analysis is developed for both planar jets and wakes and covers the two limits of shear flows, with large and small velocity differences, respectively. Comparisons of the new theoretical results with several direct numerical simulations employing the FENE-P rheological model show excellent agreement.

Maximum drag enhancement asymptote in spanwise-rotating viscoelastic plane Couette flow of dilute polymeric solutions

The existence of a maximum drag enhancement (MDE) asymptote at high rotation ( $Ro$ ) and Weissenberg ( $Wi$ ) numbers in turbulent viscoelastic spanwise-rotating plane Couette flow has been demonstrated. Specifically, it is shown that above a critical $Wi$ , drag enhancement plateaus and the MDE asymptote is realized in a broad range of $Ro$ . The mean velocity profiles at MDE appear to closely follow a log-law profile that has a nearly identical slope but different intercepts as a function of $Ro$ . Much like the maximum drag reduction (MDR) asymptote, the logarithmic function in MDE is closely followed if the mean velocity is plotted using the traditional inner variable scaling; however, the logarithmic function is not well defined when examined by the indicator function. Hence, in this study, we have used the logarithmic fit as a visual guide for the mean velocity profile. Last and perhaps the most intriguing finding of this study is that MDE occurs in the elasto-inertial turbulence (EIT) flow state; hence, it is mainly sustained by elastic forces much like the MDR flow state. To that end, a universal picture of elastically induced drag modification asymptotes is emerging, namely these asymptotic states are an inherent property of the elastically sustained EIT flow state.

Polymer drag reduction below and above the overlap concentration

We study the polymer drag reduction (DR) for a range of concentrations below and above the overlap concentration in a Taylor–Couette geometry. We use three kinds of polymers, two flexible (polyacrylamide and polyisobutylene) and one rigid (diutan gum). It is largely known that an increasing concentration accelerates the onset of DR, but it seems that this is true only for diluted solutions. We show that for concentrated solutions, the opposite can occur. Our data also suggest that maximum drag reduction asymptote can be overpassed when one uses solutions with concentrations above the overlap concentration. We attribute this extra DR to polymer aggregation, which is more frequent in more concentrated solutions.

Multistage transitions in viscoelastic turbulent flow: Vortex structures and self-sustaining mechanisms

Viscoelastic dilute polymer solutions are known to display drag reduction in turbulent flows. At constant Re and as the fluid becomes more elastic (increasing Wi), the flow undergoes transitions between several stages of different behaviors. The first is the onset of drag reduction, before which the turbulent friction factor remains indistinguishable from its Newtonian limit. The second is the transition from low-extent (LDR) to high-extent drag reduction (HDR), which increasing evidences have shown to be a qualitative transition between different types of turbulent dynamics. The third is the convergence to the maximum drag reduction (MDR) asymptote, after which the friction factor becomes constant. Although increasing drag reduction with increasing Wi is intuitively expected, transitions between these stages are accompanied by drastic changes in flow statistics and structural patterns, indicating fundamental differences in the underlying turbulent dynamics. Mechanistic understanding into these transitions is far from complete. Our latest work has offered fresh insights into both the LDR-HDR and HDR-MDR transitions. For the former, we developed a new vortex analysis method, called VATIP, and applied it to analyze the differences between the conformation statistics in LDR and HDR regimes. The result links the occurrence of HDR to the dominance of a new turbulence self-sustaining mechanism. For the latter, although a full answer to the MDR problem remains elusive, our analysis of the so-called elastoinertial turbulence (EIT) challenges the long-held presumption of MDR being an ultimate flow state that is no longer affected by polymers. The finding calls for a new direction of thought in constructing a theoretical explanation for MDR.

A Type B Drag Reduction in pipe flows using Complex Mixtures

Experiments were conducted to measure the drag reduction of the complex mixtures in the pipe flow. The friction factor was measured for bio-polymer solutions and aqueous suspensions of fine solid matter. The results indicated that the experimental data points of the test solutions diverged from the maximum drag reduction asymptote at and above Re√f ≅ 200 and aligned parallel to those of Newtonian fluids. Type B drag reduction was observed. The velocity profile in turbulent pipe flow was predicted using a semi-theoretical equation, in which the friction factors were determined using the difference between the experimental results of the tested solutions and Newtonian fluids.

Low- and High-Drag Intermittencies in Turbulent Channel Flows.

Recent direct numerical simulations (DNS) and experiments in turbulent channel flow have found intermittent low- and high-drag events in Newtonian fluid flows, at between 70 and 100, where , h and are the friction velocity, channel half-height and kinematic viscosity, respectively. These intervals of low-drag and high-drag have been termed “hibernating” and “hyperactive”, respectively, and in this paper, a further investigation of these intermittent events is conducted using experimental and numerical techniques. For experiments, simultaneous measurements of wall shear stress and velocity are carried out in a channel flow facility using hot-film anemometry (HFA) and laser Doppler velocimetry (LDV), respectively, for between 70 and 250. For numerical simulations, DNS of a channel flow is performed in an extended domain at = 70 and 85. These intermittent events are selected by carrying out conditional sampling of the wall shear stress data based on a combined threshold magnitude and time-duration criteria. The use of three different scalings (so-called outer, inner and mixed) for the time-duration criterion for the conditional events is explored. It is found that if the time-duration criterion is kept constant in inner units, the frequency of occurrence of these conditional events remain insensitive to Reynolds number. There exists an exponential distribution of frequency of occurrence of the conditional events with respect to their duration, implying a potentially memoryless process. An explanation for the presence of a spike (or dip) in the ensemble-averaged wall shear stress data before and after the low-drag (or high-drag) events is investigated. During the low-drag events, the conditionally-averaged streamwise velocities get closer to Virk’s maximum drag reduction (MDR) asymptote, near the wall, for all Reynolds numbers studied. Reynolds shear stress (RSS) characteristics during these conditional events are investigated for = 70 and 85. Except very close to the wall, the conditionally-averaged RSS is higher than the time-averaged value during the low-drag events.

Early transition, relaminarization and drag reduction in the flow of polymer solutions through microtubes

Experiments are performed to investigate the onset of early transition and drag reduction in the flow of polymer (polyacrylamide and polyethylene oxide) solutions through rigid microtubes of diameters in the range 0.49–2.84 mm. We measure friction factor variation with Reynolds number for varying polymer concentrations and tube diameters, and the Reynolds number, , at which the experimental data deviate from the laminar value represents the onset of transition. Crucially, owing to the high shear rates encountered in our experiments, we show that it is important to account for shear thinning of the fluid in the theoretical estimation of the friction factor in the laminar regime. We accomplish this using a Carreau model, and show that the use of laminar friction factor calculated without shear thinning leads to an erroneous overestimation of . The obtained from friction factor data in the present study is in good agreement with that inferred using micro particle image velocimetry analysis in Chandra et al. (J. Fluid Mech., vol. 844, 2018, pp. 1052–1083). For smaller concentrations of the added polymer, there is a marginal delay in the onset of turbulence, but as the concentration is increased further, the transition Reynolds number decreases much below , the usual value at which transition occurs in Newtonian pipe flows. Thus, the present study further corroborates the phenomenon of early transition leading to an ‘elasto-inertial’ turbulent state in the flow of polymer solutions. For concentrations such that there is a delay in transition, if is maintained above the for Newtonian fluids, the flow is transitional or turbulent in the absence of polymers. At such a fixed , if the concentration of the polymer is increased gradually, the friction factor decreases and the flow relaminarizes. With further increase in polymer concentration, the flow undergoes a transition due to elasto-inertial instability. The effect of addition of small amounts of polymer on turbulent drag reduction in the flow of water through microtubes is also investigated. Increase in polymer concentration, molecular weight and decrease in tube diameter causes an increase in drag reduction. The friction factor data for different polymer concentrations, molecular weights, tube diameters and , when plotted with , show a reasonable collapse, where is the Weissenberg number defined as the product of the longest relaxation time of the polymer solution and the average shear rate in the tube and is the ratio of solvent to total solution viscosity. Interestingly, the onset of the maximum drag reduction asymptote, for experiments using varying tube diameters and polymer concentrations, appears to occur at .

Slickwater hydraulic fracture propagation: near-tip and radial geometry solutions

We quantify the importance of turbulent flow on the propagation of hydraulic fractures (HF) accounting for the addition of friction reducing agents to the fracturing fluid (slickwater fluid). The addition in small quantities of a high molecular weight polymer to water is sufficient to drastically reduce friction of turbulent flow. The maximum drag reduction (MDR) asymptote is always reached during industrial-like injections. The energy required for pumping is thus drastically reduced, allowing for high volume high rate hydraulic fracturing operations at a reasonable cost. We investigate the propagation of a hydraulic fracture propagating in an elastic impermeable homogeneous solid under a constant (and possibly very high) injection rate accounting for laminar and turbulent flow conditions with or without the addition of friction reducers. We solve the near-tip HF problem and estimate the extent of the laminar boundary layer near the fracture tip as a function of a tip Reynolds number for slickwater. We obtain different propagation scalings and transition time scales. This allows us to easily quantify the growth of a radial HF from the early-time turbulent regime(s) to the late-time laminar regimes. Depending on the material and injection parameters, some propagation regimes may actually be bypassed. We derive both accurate and approximate solutions for the growth of radial HF in the different limiting flow regimes (turbulent smooth, rough, MDR) for the zero fracture toughness limit (corresponding to the early stage of propagation of a radial HF). We also investigate numerically the transition(s) between the early-time MDR regime to the late-time laminar regimes (viscosity and toughness) for slickwater fluid. Our results indicate that the effect of turbulent flow on high rate slickwater HF propagation is limited and matters only at early times (at most during the first minutes for industrial hydraulic fracturing operations).

Distinct transition in flow statistics and vortex dynamics between low- and high-extent turbulent drag reduction in polymer fluids

Flexible polymer additives are known to reduce the energy dissipation and friction drag in turbulent flows. As the fluid elasticity increases, the flow undergoes several stages of transitions. Much attention in the area has been focused on the onset of drag reduction (DR) and the eventual convergence to the maximum drag reduction (MDR) asymptote. Between the onset and MDR, recent experimental and numerical observations prompted the need to further distinguish the low- and high-extent drag reduction (LDR and HDR). Fundamental knowledge of this transition will be important for understanding turbulent dynamics in the presence of polymers, as well as for inspiring new flow control strategies for efficient friction reduction. We use direct numerical simulation (DNS) to explore all these transitions in the parameter space and, in particular, demonstrate that the LDR–HDR transition is not merely a quantitative effect of the level of drag reduction, but a qualitative transition into a different stage of turbulence. A number of sharp changes in flow statistics are found to accompany the transition and at HDR, turbulence becomes localized with vortices forming clusters. These observations suggest that polymer-induced drag reduction follows two distinct stages. The first starts at the onset of drag reduction, where the coil-stretch transition of polymers causes an overall suppression of turbulent fluctuations. The second starts at the LDR–HDR transition, where flow statistics become fundamentally changed in the log-law layer and turbulence localization is observed. A mechanism is then proposed for the latter based on the changing vortex regeneration dynamics between LDR and HDR.

Exceeding the Asymptotic Limit of Polymer Drag Reduction.

The drag of turbulent flows can be drastically decreased by adding small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the maximum drag reduction (MDR) asymptote; this asymptote is generally attributed to the dynamics being reduced to a marginal yet persistent state of subdued turbulent motion. Contrary to this accepted view, we show that, for an appropriate choice of parameters, polymers can reduce the drag beyond the suggested asymptotic limit, eliminating turbulence and giving way to laminar flow. At higher polymer concentrations, however, the laminar state becomes unstable, resulting in a fluctuating flow with the characteristic drag of the MDR asymptote. Our findings indicate that the asymptotic state is hence dynamically disconnected from ordinary turbulence.

Study the Characterization of Adding Polymer-Surfactant Agent on the Drag Reduction Phenomena in Pipeline Flow System

Abstract 
 In this study, the effect of carboxylic methyl cellulose (CMC), and sodium dodcyl benzene sulfonate (SDBS) as an aqueous solution on the drag reduction was investigated. Different concentrations of (CMC) and (SDBS) such as (50, 100, 150, 200, 250, 300, 350, 400, 450, and 500 ppm) were used to analyze the aqueous solution properties, including surface tension, conductivity, and shear viscosity. The optimum four concentrations (i.e., 50, 100, 200, and 300 ppm) of fluid properties were utilized to find their effect on the drag reduction. Two different PVC pipe diameters (i.e., 1" and 3/4") were used in this work. The results showed that blending CMC with SDBS gives a good drag reduction percent about (58%) more than using them individually, friction factor decreasing with increasing Reynolds number and gives good agreement with von Karamn equation and maximum drag reduction (MDR) asymptote. Reynolds number, pipe diameter, and polymer-surfactant concentrations were considered as influencing factors. In addition, critical micelle concentration, the onset of drag reduction, and the interactions between the mixed additives were discussed. 
 Keyword: CMC, SDBS, drag reduction, friction factor, blending of additives.

Turbulent drag reduction by polymer additives in parallel-shear flows

In this study, we experimentally investigate the turbulent drag-reduction (DR) mechanism in flow through ducts of circular, rectangular and square cross-sections using two grades of polyacrylamide in aqueous solution having different molecular weights and various semidilute concentrations. Specifically, we explore the relationship between drag reduction and fluid elasticity, purposely exploiting the mechanical degradation of polymer molecules to vary their rheological properties. We also obtain time-resolved velocity data for various DR levels using particle image velocimetry and laser Doppler velocimetry. Elasticity is quantified via relaxation times determined from uniaxial extensional flow using a capillary breakup apparatus. A plot of DR against Weissenberg number ($Wi$) is found to approximately collapse the data, with the onset of DR occurring at $Wi\approx 0.5$ and the maximum drag-reduction asymptote being approached for $Wi\gtrsim 5$. Thus quantitative predictions of DR in a range of shear flows can be made from a single measurable material property of a polymer solution, at least for this particular flexible linear polymer.

Okra as a drag reducer for high Reynolds numbers water flows

The capability of a mixture of okra fiber and mucilage as drag reducer in high Reynolds number flows through a pipeline, in which the flux is maintained by a centrifugal pump with controlled rotation, is analyzed. A DR close to the maximum drag reduction asymptote, which is obtained for polymeric additives, was achieved when concentrations around 1600 ppm were used. The loss of efficiency of the solution over the number of passes through the system was almost the same of that observed for rigid materials like Xanthan Gum and Guar Gum, which suggest that the main cause of a decreasing drag reduction is the de-aggregation instead of mechanical degradation, commonly observed in flexible polymers. As expected, the material degrades biologically, but it seems that it is not a great problem for open systems, since such a degradation is perceptible only after 24 h. We strongly believe that this new bio-drag reducer can be an alternative to synthetic polymers or other biopolymers, since it is extremely cheap and easy to be obtained.

Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions.

Self-consistent direct numerical simulations of turbulent channel flows of dilute polymer solutions exhibiting friction drag reduction (DR) show that an effective Deborah number defined as the ratio of polymer relaxation time to the time scale of fluctuations in the vorticity in the mean flow direction remains O(1) from the onset of DR to the maximum drag reduction (MDR) asymptote. However, the ratio of the convective time scale associated with streamwise vorticity fluctuations to the vortex rotation time decreases with increasing DR, and the maximum drag reduction asymptote is achieved when these two time scales become nearly equal. Based on these observations, a simple framework is proposed that adequately describes the influence of polymer additives on the extent of DR from the onset of DR to MDR as well as the universality of the MDR in wall-bounded turbulent flows with polymer additives.

Exact coherent states and connections to turbulent dynamics in minimal channel flow

Several new families of nonlinear three-dimensional travelling wave solutions to the Navier–Stokes equation, also known as exact coherent states, are computed for Newtonian plane Poiseuille flow. The symmetries and streak/vortex structures are reported and their possible connections to critical layer dynamics are examined. While some of the solutions clearly display fluctuations that are localized around the critical layer (the surface on which the streamwise velocity matches the wave speed of the solution), for others this connection is not as clear. Dynamical trajectories along unstable directions of the solutions are computed. Over certain ranges of Reynolds number, two solution families are shown to lie on the basin boundary between laminar and turbulent flow. Direct comparison of nonlinear travelling wave solutions to turbulent flow in the same channel is presented. The state-space dynamics of the turbulent flow is organized around one of the newly identified travelling wave families, and in particular the lower-branch solutions of this family are closely approached during transient excursions away from the dominant behaviour. These observations provide a firm dynamical-systems foundation for prior observations that minimal channel turbulence displays time intervals of ‘active’ turbulence punctuated by brief periods of ‘hibernation’ (see, e.g., Xi & Graham, Phys. Rev. Lett., vol. 104, 2010, 218301). The hibernating intervals are approaches to lower-branch nonlinear travelling waves. Representing these solutions on a Prandtl–von Kármán plot illustrates how their bulk flow properties are related to those of Newtonian turbulence as well as the universal asymptotic state called maximum drag reduction (MDR) found in viscoelastic turbulent flow. In particular, the lower- and upper-branch solutions of the family around which the minimal channel dynamics is organized appear to approach the MDR asymptote and the classical Newtonian result respectively, in terms of both bulk velocity and mean velocity profile.

Drag reduction and the dynamics of turbulence in simple and complex fluids

Addition of a small amount of very large polymer molecules or micelle-forming surfactants to a liquid can dramatically reduce the energy dissipation it exhibits in the turbulent flow regime. This rheological drag reduction phenomenon is widely used, for example, in the Alaska pipeline, but it is not well-understood, and no comparable technology exists to reduce turbulent energy consumption in flows of gases, in which polymers or surfactants cannot be dissolved. The most striking feature of this phenomenon is the existence of a so-called maximum drag reduction (MDR) asymptote: for a given geometry and driving force, there is a maximum level of drag reduction that can be achieved through addition of polymers. Changing the concentration, molecular weight or even the chemical structure of the additives has little to no effect on this asymptotic value. This universality is the major puzzle of drag reduction. We describe direct numerical simulations of turbulent minimal channel flow of Newtonian fluids and viscoelastic polymer solutions. Even in the absence of polymers, we show that there are intervals of “hibernating” turbulence that display very low drag as well as many other features of the MDR asymptote observed in polymer solutions. As Weissenberg number increases to moderate values the frequency of these intervals also increases, and a simple theory captures key features of the intermittent dynamics observed in the simulations. At higher Weissenberg number, these intervals are altered – for example, their duration becomes substantially longer and the instantaneous Reynolds shear stress during them becomes very small. Additionally, simulations of “edge states,” dynamical trajectories that lie on the boundary between turbulent and laminar flow, display characteristics that are similar to those of hibernating turbulence and thus to the MDR asymptote, again even in the absence of polymer additives. Based on these observations, we propose a tentative unified description of rheological drag reduction. The existence of MDR-like intervals even in the absence of additives sheds light on the observed universality of MDR and may ultimately lead to new flow control approaches for improving energy efficiency in a wide range of processes.

Polymer induced turbulent drag reduction using pressure and gravity-driven methods

Drag reduction using polymer additives has been industrially important for enhancing the flow rates and hence the power consumption. In this study, various polymers like PEG, PAM, HPMC were employed with solvents like water and lubricating oil for drag reduction using gravity and pressure driven methods. The optimum set of parameters for maximum drag reduction—polymer concentration, nature of polymer, polymer combinations, exit pipe diameter, solvent-polymer combinations, experimental methodology—were obtained and then the results validated with well known concepts like the Toms effect and Virk's maximum drag reduction asymptote.

Maximum Drag Reduction Asymptote for Surfactant-Based Fluids in Circular Coiled Tubing

Surfactants are superior to polymers in reducing drag and their advantages are very well established. As drag reducers, several factors, such as concentration, temperature, salinity, shear rate, etc., can affect their behavior. Other unique factors relevant to surfactants may include tubing diameter (scale-up effect), head group structure, counterion, charge, etc. Although, drag reduction envelope is customarily employed to investigate drag reduction phenomena, it is defined only for polymeric fluids in both straight and coiled tubing and for surfactant-based (SB) fluids in straight tubing. No such envelope is available for SB fluids in coiled tubing. The present research aims at experimentally investigating the drag reduction characteristics of the most widely used Aromox APA-T surfactant-based fluids. It is a highly active surfactant used as gelling agent in aqueous and brine base fluids. Flow data are gathered using small and large scale flow loops. Straight and coiled tubing with various sizes (1.27 cm to 7.30 cm o.d.) and curvature ratios (0.01 to 0.031) covering the field application range are utilized. The results show that SB fluids exhibit superior drag reduction characteristics. Their behavior is significantly affected by surfactant concentration, shear, tubing size, and geometry. Higher drag reduction is seen in straight tubing than in coiled tubing and increasing curvature ratio yields higher friction pressure losses. In coiled tubing, SB fluids exhibit better drag reduction characteristics than Shah and Zhou maximum drag reduction (MDR) asymptote for polymeric fluids. Therefore, a new maximum drag reduction asymptote is developed using data gathered in 1.27 cm o.d. tubing. The proposed correlation agrees with Zakin MDR asymptote for SB fluids in straight tubing where the curvature ratio is set to be zero. Employing the proposed correlation, a modified drag reduction envelope can be used to evaluate drag reduction characteristics of SB fluids.

Dynamics on the Laminar-Turbulent Boundary and the Origin of the Maximum Drag Reduction Asymptote

Dynamical trajectories on the boundary in state space between laminar and turbulent plane channel flow-edge states-are computed for Newtonian and viscoelastic fluids. Viscoelasticity has a negligible effect on the properties of these solutions, and, at least at a low Reynolds number, their mean velocity profiles correspond closely to experimental observations for polymer solutions in the maximum drag reduction regime. These results confirm the existence of weak turbulence states that cannot be suppressed by polymer additives, explaining the fact that there is an upper limit for polymer-induced drag reduction.