Drag reduction induced by superhydrophobic surfaces in turbulent pipe flow

Simulating drag reduction phenomenon in turbulent pipe flows

Certain types of macromolecules added to otter and salt solutions flouting in turbulent motion can reduce the pressure gradient. Alternatively, the volumetric capacity of a pipe for these fluids is increased by the presence of these material. Examples presented show that the drag reduction can become significant. Thus, the presence of 0.28 per cent of a gum derivative in a solution of sodium chloride flowing at 200 gal/min in a 1.89- in. pipe yields a pressure drop which is 0.44 of the single-phase drop measured under the same conditions of turbulent flow; the addition of 0.1 per cent of a vinyl derivative to a 1-in. water line yields a through put capacity which is 1.78 of the single-phase capacity at the same pressure drop. It is further shown that these phenomena are distinctly different from previous observations with other classes of non-Newtonian systems. There a simple lowering of friction factors below the levels predicted from the resistance laws for Newtonian fluids is associated with a suppression of turbulent motion. A rational physical explanation for drag reduction is advanced. Briefly, the proposed mechanism is a storage by the molecular elastic elements of the macromolecules in solution of the kinetic energy of the turbulent motion. Introduction This study was inspired by a recent review of some paradoxical drag reduction phenomena in turbulent pipe flow. Under very moderate conditions of turbulent flow, the pressure gradient necessary to pump solutions containing certain specific kinds of polymers, fibers and metallic soaps may become appreciably lower than that required to pump the solvent, i.e., water or a low-viscosity hydrocarbon, under identical flow rates in the same conduit. As shown by our review, this phenomenon of drag reduction in turbulent duct flow was first noted during the second world war, apparently arising in connection with the development of flame warfare weapons. Since that time several papers illustrating this phenomenon have appeared: Toms, Oldroyd, Agoston et al., Bundrant and Matthews, Robertson and Mason, Ousterhout and Hall, Daily and Bugliarello, Lummus, Anderson, and Fox. That there are practical applications for techniques which increase discharge or decrease the pressure necessary to transport a liquid through a pipeline is illustrated in the patents which have issued which take advantage of this peculiar phenomenon, e.g., Mysels, Dever, Harbour, and Seifert. One also finds fragmentary evidence of this effect in the data pertaining to a few of the polymeric solutions studied by Shaver and Dodge. However, these investigators were concerned with the development of friction factor vs Reynolds number correlations for a variety of non-Newtonian solutions and suspensions, rather than in a study of drag reduction. A similar kind of drag reduction effect has been observed in gases. Sproull, for example, reports that adding dust to air flowing in turbulent motion through a pipe results in a lowering of the pressure gradient at identical flow rates. There are also military applications for reducing the drag on hydrodynamic vehicles. For example, the possibility of injecting a rheologically complex fluid into the boundary layers of bodies to reduce the skin friction has been investigated by Fabula and Granville. Along somewhat different lines are the drag reduction studies of Kramer. He has shown that skin friction can be reduced by covering the surface of a vehicle with a flexible skin. The effect is apparently due to the boundary layer being stabilized by the presence of the skin. Drag reduction by means of coexisting gas and liquid boundary layers, e.g., film boiling and continuous gas injection, has been proposed by Bradfield, Barkdoll, and Byrne, Cess and Sparrow, Sparrow, Jonsson, and Eckert. Here the skin friction occurs between a vapor and a surface rather than between a liquid and a surface. There are several references in the literature to friction-factor correlations for non-Newtonian solutions and suspensions: Shaver and Merrill, Dodge and Metzner, Clapp, and Thomas. SPEJ P. 203ˆ

Pulsating turbulent flows in a square pipe are studied numerically. The flow dominance regime in which the fluid flow rate remains positive in all phases of the oscillatory cycle is considered. The flows are studied at several oscillation frequencies. The results are compared with oscillating laminar flows and a steady turbulent flow in a square pipe, as well as with pulsating turbulent flows in a round pipe. The integral and fluctuating characteristics of turbulence and their dependence on the oscillation frequency are determined. In particular, it is found that at the considered Reynolds number Re = 2200 the friction coefficient in pulsating flows turns out to be lower than that in the stationary flows. The drag reduction increases with growth of the oscillation period and reaches 14.7%. A distinctive feature of turbulent flows in pipes of rectangular cross-section is the occurrence of secondary flows of Prandtl’s 2nd kind. The details of secondary flows under the pulsating flow conditions are studied at length.

Slick-water with excellent performance on drag reduction (DR) is the preferred fracturing fluid for shale gas fracturing. In order to select appropriate slick-water for hydraulic fracturing under varying formations and construction conditions, this experiment focused on measuring the DR performance of different kinds of slick-water. Using polymer and viscoelastic surfactant as DRA, the frictions of slick-water were measured by friction tester; DR rate was calculated by using friction of fresh water as blank. The principle is to test the pressure drop between inlet and outlet of pipeline when the fluid flows through a certain tube under a range of flow rates. Specifically, in this work, a kind of modified acrylamide (MPAM) and cetyltrimethylammonium bromide/sodium salicylate (CTAB/NaSal) were adopted as DRA. In comparison, frictions and DR of MPAM solutions are quite different from those of surfactant solutions. The frictions of water and MPAM solutions increase with the increase of flow rate, and the relationship of friction and flow rate is approximately linear. For MPAM solution, DR is related to the concentration of MPAM, high concentration result in high DR rate. But for surfactant based viscoelastic fluid, frictions are very low; with the increasing of flow rate, the friction increases greatly. DR of viscoelastic fluids is related to the modulus of the fluid, the better the viscoelastic fluid conforms to the Maxwell model, the higher DR rate can be obtained, and this is proved by rheological experiments. Under high flow rate, viscoelastic fluid becomes thinner due to shearing and DR decrease substantial as a result. From the experiments, polymer solution shows good shear resistance performance, DR increase with the increase of flow rate, but in the application of slick-water fracturing, a large amount of hard-to-degrade polyacrylamide entering the formation may cause pollution to reservoirs, while degradable surfactant-based viscoelastic fluids were poor shear resistance. As a result, neither MPAM nor surfactant-based viscoelastic fluid are suitable for all reservoirs, it is necessary to select a suitable fluid according to pump speed, environment protecting and other factors in applications.

Experimental studies of drag reduction and polymer degradation in turbulent pipe flow with dilute water solutions of unfractionated polyethylene oxide are described. Drag reduction results indicate that the magnitude of the reduction cannot be correlated on the basis of weight average molecular weight, rather the phenomenon depends strongly on the concentration of the highest molecular weight species present in the molecular weight distribution. Polymer degradation in turbulent flow is found to be severe for high molecular weight polymers causing appreciable changes in drag reduction and molecular weight with the duration of flow. Data indicates that drag reduction exists in the limit of infinite dilution suggesting that the phenomenon is due to the interaction of individual polymer molecules with the surrounding solvent and that the extent of reduction is relatively independent of pipe diameter when a comparison is carried out at equal solvent wall shear stresses. Consideration of the high viscosity obtained with solutions in an irrotational laminar flow field suggests this is due to polymer molecule deformation and that this phenomenon is central to the mechanism of turbulent flow drag reduction.

Effect of megestrol acetate on uroflow rates in patients with benign prostatic hypertrophy: Double-blind study

Energy conservation and environmental protection have become pivotal components of the green economy. In recent years, underwater drag reduction technology has garnered significant interest. This study discusses a novel composite surface that combines divergent riblets with a superhydrophobic coating (D-rib&SHS) to enhance the drag reduction rate. Alongside this new surface, a riblet surface with a superhydrophobic coating (rib&SHS, without yaw angles) and a smooth surface are used as comparison groups. The turbulent boundary layer flow of these three surfaces is measured using a two-dimensional particle image velocimetry system. The results indicated that the maximum drag reduction rate of D-rib&SHS is approximately 27% higher than that of rib&SHS, and the drag reduction range is increased to Reθ≈4100 compared to rib&SHS (Reθ≈2200). Using correlation algorithms, it observed that the spacing between low-speed streaks over D-rib&SHS is larger than that of rib&SHS and the smooth surface. This finding suggested that the spacing between the hairpin vortex legs of D-rib&SHS is wider. The increased spacing between the hairpin vortex legs reduces the likelihood of vortex head formation between the two quasi-streamwise vortices, ultimately suppressing the auto-generation of hairpin vortices. Consequently, the development of hairpin vortex packets over D-rib&SHS is also inhibited. These phenomena observed over D-rib&SHS can be attributed to the combined effects of velocity slip on the superhydrophobic coating and the secondary flow over the divergent riblets near the wall. In addition, unlike divergent riblets that are not covered with a superhydrophobic coating, where the drag reduction effect is more pronounced with a yaw angle of 30° compared to 10°, D-rib&SHS with a 10° yaw angle demonstrated a superior drag reduction effect compared to D-rib&SHS with a 30° yaw angle. This innovative composite surface enhances the drag reduction effect and expands the drag reduction Reynolds number range, offering a new approach to mitigating drag in turbulent boundary layer flows.

In situ monitoring is the most insightful technique to examine superhydrophobic surface degradation as it provides real-time information on the liquid–solid interface in a continuous, noninvasive manner. Using reflecting-pixel intensity, we introduced a simple method to characterize in situ the air-plastron over a superhydrophobic surface in a turbulent channel flow. Prior to the turbulent experiments, a no-flow hydrostatic test was carried out to determine a critical absolute pressure under which the surfaces are able to maintain the air layer for a prolonged period of time. Pressure-drop and velocity measurements were conducted in a series of turbulent flow tests. Resulting from the coupling effects of normal and shear stresses over the plastron, the air layer was progressively lost with flow time which caused the drag ratio (i.e., the friction factor ratio between superhydrophobic and smooth surfaces) to increase. Meanwhile, the average pixel intensity also increased with time and exhibited a consistent trend with the drag ratio evolution. At a fixed near-wall y/h location (within the viscous sublayer), the velocity increased with time since the shear stress increased. However, a velocity measurement at the center of the channel exhibited a decrease, consummate with an overall downward shift of the velocity profile. Both pressure-drop and velocity results were observed to be correlated with the average pixel intensities of the images captured over the surfaces, and therefore, this is a suitable proxy measure of the plastron. This technique is confirmed to be valid for monitoring the air layer and, hence, predicting the consequent loss of drag reduction.

We present a theoretical prediction for the drag reduction rate achieved by superhydrophobic surfaces in a turbulent channel flow. The predicted drag reduction rate is in good agreement with results obtained from direct numerical simulations at Reτ≃180 and 400. The present theory suggests that large drag reduction is possible also at Reynolds numbers of practical interest (Reτ∼105–106) by employing a hydrophobic surface, which induces a slip length on the order of ten wall units or more.

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

The optimal amplifications of small coherent perturbations within turbulent pipe flow are computed for Reynolds numbers up to one million. Three standard frameworks are considered: the optimal growth of an initial condition, the response to harmonic forcing and the Karhunen-Loève (proper orthogonal decomposition) analysis of the response to stochastic forcing. Similar to analyses of the turbulent plane channel flow and boundary layer, it is found that streaks elongated in the streamwise direction can be greatly amplified from quasistreamwise vortices, despite linear stability of the mean flow profile. The most responsive perturbations are streamwise uniform and, for sufficiently large Reynolds number, the most responsive azimuthal mode is of wave number m=1 . The response of this mode increases with the Reynolds number. A secondary peak, where m corresponds to azimuthal wavelengths λ_{θ}^{+}≈70-90 in wall units, also exists in the amplification of initial conditions and in premultiplied response curves for the forced problems. Direct numerical simulations at Re=5300 confirm that the forcing of m=1,2 and m=4 optimal structures results in the large response of coherent large-scale streaks. For moderate amplitudes of the forcing, low-speed streaks become narrower and more energetic, whereas high-speed streaks become more spread. It is further shown that drag reduction can be achieved by forcing steady large-scale structures, as anticipated from earlier investigations. Here the energy balance is calculated. At Re=5300 it is shown that, due to the small power required by the forcing of optimal structures, a net power saving of the order of 10% can be achieved following this approach, which could be relevant for practical applications.

Drag reduction in fully developed turbulent pipe flow with 4 concentrations (200 to 500 wppm or mg/kg) of low molecular weight sodium carboxymethylcellulose (CMC) in aqueous solutions was investigated experimentally. Drag reduction was determined by pressure drop measurements. Maximum drag reduction achieved was 22% using 500 wppm CMC solution. To observe the impact of the presence of CMC on the flow, ultrasound Doppler velocimetry (UDV) was employed to monitor the instantaneous velocity distributions. Experimental measurements were used to calculate Fanning friction factor and radial distributions of the axial time-averaged velocity, velocity fluctuation (turbulent intensity), and eddy viscosity. Two impacts of increasing CMC concentration on the flow field were observed. The first effect was the decrease in the mean velocity gradient, especially near the wall, with increasing polymer amount, which in turn gave rise to a lower friction factor or pressure drop. Furthermore, smaller eddy viscosities were obtained in the flow. The second impact of polymer addition was on the velocity fluctuation or turbulent intensity variation along the radial distribution. Presence of the polymer suppressed the velocity fluctuations near the wall while the intensity in the turbulent core region became stronger than in the case of lower or no polymer addition.

This paper presents an experimental study on drag reduction induced by PEO (Polyethylene oxide) in a fully turbulent pipe flow. The objective of this work is to develop a correlation to predict drag reduction using the relaxation time of the polymer additives under dilute solution conditions, i.e., the polymer concentration is less than the overlap concertation. This paper discusses the meaning of relaxation time of polymers, and why the Weissenberg number, a dimensionless number that is related to the relaxation time and shear rate, is independent on the concentration in the dilute solution. Experimental data of drag reduction in a pipe flow are obtained from measurements using a flow loop. A correlation to predict drag reduction with the Weissenberg number and polymer concentration is established and a good agreement is shown between the predicted values and experimental data. The new correlation using the Weissenberg number and polymer concentration is shown to cost less to develop than one using the Reynolds number, in which larger pipes or higher flow rates are required.

The excellent drag reduction effect of the bubble drag reduction technique has been proved through many experiments since it was proposed. In this paper, the authors investigate the bubble-turbulence interaction and the corresponding drag reduction effect with a two-way coupled Euler–Lagrange code. The liquid phase is simulated by using a large eddy simulation method with the immersed bubbles treated using a nonlinear collision model to accurately simulate the bubble–wall interaction. A Gaussian distributed method is adopted to obtain the void fraction and interphase forces in the two-way coupled algorithm. Two typical wall-bounded turbulent flow problems (turbulent channel flow and boundary layer flow) are simulated to validate the accuracy and stability in bubbly flows and investigate the drag reduction mechanism. First, the effect of bubbles on the turbulent flow is studied in the channel flow cases in which the bubbles are observed attaching to the upper plate and swaying in the spanwise direction. In this case, Reynolds stress near the wall is decreased, which contributes to the drag reduction. Moreover, drag reduction of a turbulent boundary layer flow with bubble injection is studied in which the drag reduction under different air flow rates is in good agreement with experimental results. The contribution of turbulence and different liquid forces to the migration of bubbles away from the wall is investigated. The bubble trajectory in the turbulent boundary layer is divided into three distinct stages and discussed in detail finally.

Salvinia leaf and sharkskin are prime examples of nature's marvel. Salvinia leaf‐inspired superhydrophobic surfaces keep themselves clean and reduce drag in fluid flow. Sharkskin also reduces drag in turbulent flow and inhibits biofouling. Therefore, the prospect of having a drag‐reducing surface with both salvinia leaf and sharkskin properties is attractive. However, fabricating such a surface is difficult, and the current fabrication methods require at least two separate steps. In addition, the mechanisms of drag reduction of salvinia leaf and sharkskin are different, and their combined effect on the flow field is not well understood. In this study, we produced a PTFE surface that mimics sharkskin in its surface pattern and copies the superhydrophobic nature of the salvinia leaf in its microstructure. This surface was fabricated by laser machining and tested in a closed channel under turbulent flow conditions. We measured the pressure drop at different Reynolds numbers on this surface both in pre‐wet and non‐pre‐wet conditions and compared the result with pressure drop data on four other PTFE samples: two types of non‐superhydrophobic sharkskin inspired surface (riblets), a superhydrophobic surface, and a non‐machined surface. Both the non‐superhydrophobic riblets and the superhydrophobic sample reduced drag compared to the non‐machined surface. However, we observed a lack of drag reduction by the superhydrophobic riblets sample. We presented a qualitative explanation for the lack of drag reduction and concluded that the modifications of the flow field by the two drag reduction mechanisms are not beneficial for overall drag reduction in our experiment.