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Synergistic Effects in Turbulent Drag Reduction by Riblets and Polymer Additives
Abstract
Drag reduction was investigated for the combined system of polymer additives and a riblet pipe. The riblet grooves were V-shaped, the spacing of which was 1.3 mm and the height of which was 1.01 mm. For higher h(+), a triangular riblet system including other geometries increases the drag to levels similar to those of normal transient roughness. This drag increase was generally given as a function of h(+). The polymer additives were Aronfloc N-110 and Separan AP-30. The critical shear stress tau* at which N-110 started the drag reduction, was approximately eight times higher than tau* for AP-30. In the combined system, the synergistic drag reduction for higher h(+) was discussed under the assumption that the additives suppressed the drag increase resulting from riblets. Since the additives thicken a wall layer covering the region from a viscous sublayer to a buffer layer, the relative height of h to this wall layer thickness is lowered. In addition, the flow enhancement due to additives relatively suppresses the riblet-induced drag increase. The analysis based on velocity profiles indicated that these effects can produce synergistic drag reduction for higher h(+).
... Until now, there are only limited studies that considered the combination of these two strategies for flow drag reduction, and the synergy effect is not clear. Mizunuma et al. mentioned that V-shaped riblets could increase the drag, but when drag-reducing polymers were added in the turbulent flow, drag reduction occurred (Mizunuma et al., 1999). Similar observations were reported by Koury & Virk (1995) and Huang & Wei (2017). ...
... This method takes direct use of sharkskin as a replica to realise the complicated sharkskin replication. This method has been regarded as an effective path to achieve the transition from 'appearance imitation' to 'sprit imitation' [26,27]. The replication accuracy was validated to be over 95% as compared with real sharkskin [28]. ...
Nature evolution provides nature surface treasures with special and fascinating surface function to inspire design, such as the drag reduction of sharkskin. In this overview, the morphology and mechanism of the sharkskin explained from different aspects, and various methods of fabricating surfaces with sharkskin morphology are illustrated in details, and then the applications in different fluid engineering are demonstrated in brief. This overview will improve the comprehension of the morphology and mechanisms of sharkskin, and methods of fabricating the surface with morphology, and the recent applications in engineering.
... Sharkskin morphology shows an apparent dragreducing effect in turbulence. Meanwhile, mucus/ polymer additives also possess lubricating and lowering friction functions (Mizunuma et al. 1999). If both of them are combined together, an enhanced drag reduction effect can be achieved. ...
With the rapid development of science and technology, increasing research interests have been focused on environment protection, global warming, and energy shortage. At present, reducing friction force as much as possible has developed into an urgent issue. Sharkskin effect has the potential ability to lower viscous drag on the fluid-solid interface in turbulence, and therefore, how to fabricate bio-inspired sharkskin surfaces is progressively becoming the hot topic. In this review, various methods of fabricating drag reduction surfaces covering biological sharkskin morphology are illustrated and discussed systematically, mainly involving direct bio-replicated, synthetic fabricating, bio/micro-rolling, enlarged solvent-swelling, drag reduction additive low-releasing, trans-scale enlarged three-dimensional fabricating, flexible printing, large-proportional shrunken bio-replicating, ultraviolet (UV) curable painting, and stretching deformed methods. The overview has the potential benefits in better acquainting with the recent research status of fabricating sharkskin surfaces covering the biological morphology.
... Nevertheless, the designed microstructured surface is mostly fabricated with methods, such as PDMS (polydimethylsiloxane) replica [7], vacuum casting [8,9], and polymer coating [10,11], which are generally limited to small size and have hampered the implementation in the industries. Actually, an interfacial elastic-plastic deformation theory may provide us a novel and feasible method for the fabrication of microstructured surface [12]. ...
To reduce friction drag with bionic method in a more feasible way, the surface microstructure of bird feather was analyzed attempting to reveal the biologic features responding to skin friction drag reduction. Then comparative bionic surface mimicking bird feather was fabricated through hot-rolling technology for drag reduction. The microriblet film was formed on a PVC substrate through a self-developed hot-rolling equipment. The bionic surface with micron-scale riblets formed spontaneously due to the elastic-plastic deformation of PVC in high temperature and high pressure environment. Comparative experiments between micro-structured bionic surface and smooth surface were performed in a wind tunnel to evaluate the effect of bionic surface on drag reduction, and significant drag reduction efficiency was obtained. Numerical simulation results show that microvortex induced in the solid-gas interface of bionic surface has the effect of shear stress reduction and the small level of an additional pressure drag resulting from pressure distribution deviation on bird feather like surface, hence reducing the skin friction drag significantly. Therefore, with remarkable drag reduction performance and simple fabrication technology, the proposed drag reduction technique shows the promise for practical applications.
... Choi et al. found that the drag reduction of polymer coated U-groove riblets was superior to only U-groove in a towing tank on a onethird scale model of the America's Cup winning yacht, Australia II [10]. Mizunuma et al. experimentally tested the synergistic effects of turbulent drag reduction by directly pouring large quantities of polymer additive into the fluid 2 Advances in Mechanical Engineering [11][12][13]. Christodoulou et al. carried out experiments on a combination of riblets and polymers to make clear effect of Polyox 301 concentration on drag reduction [14]. Although a positive synthetic effect was demonstrated, almost all drag reduction surfaces were realized via the simple integration of the U/V microgroove with polymer additive, which have several serious problems such as (1) the difficulty in maintaining the groove shape and improvement of drag reduction which is limited by coating; (2) the immense waste of polymer additive by diffusion into whole fluid. ...
Natural shark skin has a well-demonstrated drag reduction function, which is mainly owing to its microscopic structure and mucus on the body surface. In order to improve drag reduction, it is necessary to integrate microscopic drag reduction structure and drag reduction agent. In this study, two hybrid approaches to synthetically combine vivid shark skin and polymer additive, namely, long-chain grafting and controllable polymer diffusion, were proposed and attempted to mimic such hierarchical topography of shark skin without waste of polymer additive. Grafting mechanism and optimization of diffusion port were investigated to improve the efficiency of the polymer additive. Superior drag reduction effects were validated, and the combined effect was also clarified through comparison between drag reduction experiments.
... A more detailed review of drag reduction in multiphase flows is given in Section 2.14.4. [13]). ...
Considerable reductions in drag (pressure drop) are feasible with drag reducing agents. The use of such agents is now widespread and seems certain to grow in the future. The most widely used methodology is the addition of polymers at dilute levels; the large molecules of the polymers and their aggregates suppress the turbulence. Similar effects are produced with surfactants where large structures (micelles) are formed which also suppress the turbulence. Surface modification (e.g. by riblets) produces only modest drag reduction but this can nevertheless be very worthwhile in some circumstances. Drag reduction be using a dispersion of micro-bubbles has the advantage that the drag reducing agent (the bubbles) can be readily separated from the fluid and can be expected to find wider usage in the future.
... The reduction is achieved by the interaction between the polymer molecules and the turbulence components of the flow. Polymers tend to stretch in the flow and absorb the energy in the streak, which in turn stops the burst that produces the turbulence in the core and results in a reduction in turbulence (Lester, 1985;Mizunuma et al., 1996). Thus, the principal effect of DRAs is to reduce the velocity fluctuations in the normal direction and Reynolds stresses thereafter. ...
In this paper, recent work on drag reducing agents in single and multiphase flow pipelines is reviewed. Focus is placed on theories of drag reduction, the influence of drag reduction agent types, and hydrodynamic and heat transfer characteristics of flows in the presence of drag reducing additives. Questions are raised, shortcomings are assessed, and future research needs are outlined.
... Synthetic drag reduction has been explored over the past *Corresponding author (email: zhangdy@buaa.edu.cn) decades, but its bio-drag reduction morphology was simplified and bio-drag reduction interface was formed by injecting drag reduction agent (DRA) or coating polymer, which has serious problems, such as the morphology of micro-grooves being different from the biology and the waste of DRA [5][6][7][8][9][10]. Therefore, a novel synthetic bio-replication forming approach is proposed in this paper for simultaneously grafting nano-long chains to bio-replicated micro-grooves of shark skin, which maintains the simplicity of bio-replicated forming. ...
Nano-long chains were grafted over the replicated micro-grooves of shark skin in a novel attempt to replicate bio-synthetic
drag reduction structure with high precision through synthetic bio-replication. Pre-treated shark skin was used as casting
template to prepare a flexible female die of silicone rubber by soft die formation. A waterborne epoxy resin was then used
to graft long-chains of drag reduction agent and prepare a synthetic drag reduction shark skin with nano-long chain drag reduction
interface and lifelike micro-grooves. Replication precision analysis shows that this technology could replicate the complicated
three-dimensional morphology of a biological drag reduction surface with high precision. Drag reduction experiments show that
the material had an excellent synthetic drag reduction effect, with a maximal drag reduction rate of up to 24.6% over the
velocities tested.
Keywordssynthetic drag reduction–high-precision–shark skin–synthetic bio-replication–micro-groove–nano-long chain
The first part of this section is introduced different preparation methods of artificial shark skin surface, including direct bio-replicated vivid shark skin, large-proportional amplification and shrunken bio-replication of shark skin, embossing forming technology and bionic composite drag reduction surface. Based on the above preparation methods, the drag reduction effects of bionic shark skin surface and composite surface of bionic shark skin are briefly discussed in the second section. It provides technical reference for the preparation of bionic surface. The third part introduced the bioinspired anti-icing surface from superhydrophobic lotus leaf and the mechanism of energy-saving dynamic anti-icing integrated with electric heating; in detail, the melting frost self-jumping phenomenon on Cassie-ice superhydrophobic surfaces and the underlying mechanism was introduced, and the ice delaying, dynamic ice adhesion reduction and energy-saving dynamic anti-icing on fiberglass cloth based superhydrophobic coatings was introduced. The results provided theoretical support for anti-icing applications of superhydrophobic coatings.
The characteristic equations of one-dimensional original Burnett, conventional Burnett, augmented Burnett, BGK-Burnett and Woods equations are derived, linear stability analysis is made. The critical Knudsen number for these unstable equations is calculated. The results show that the critical Knudsen number for the conventional Burnett and Woods equations with material derivatives approximated by the Euler equations are about 2.455 and 0.907, respectively. When no approximation is made for the Burnett equations, the critical Knudsen numbers for original Burnett, augmented Burnett, BGK-Burnett and Woods equations are 0.516, 0.516, 0.775 and 0.365, respectively.
Skin–friction drag accounts for a large portion of resistance encountered by water-based vehicles, such as ships and submarines. Developing drag reduction methods to improve drag reduction performance has drawn worldwide attention recently. UV-induced polymerization has been investigated as a way to graft the drag reduction agent PAM on to a PVC substrate with a biomimetic riblet surface. The effects of AM concentration and irradiation time on the grafting rate were explored to determine optimal grafting parameters. UV grafting polymerization was clarified by comparing the peak absorption variation of the infrared spectrum before and after grafting. The PAM thin film grafted on riblet surface was measured approximately 10 µm in thickness. A rotating disk apparatus was built to measure the synthetic drag reduction performance. The drag reduction rate of the grafted PAM riblet surface was tested at approximately 14%, higher than the 6% of the traditional riblet surface. Moreover, the excellent drag reduction performance of grafted PDMS riblet surface lasted for 12 days. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 42303.
Close-coupled pipes can be applied to a number of HVAC systems. This paper discusses the local drag reduction achieved by components placed in elbow and T-junction close-coupled pipes. The components are necessary to reduce or even eliminate vortices produced by turning flow patterns. It includes a numerical study of drag reduction effects of seven components with different shapes. The shear stress transport (SST) k– ω turbulence model is applied. The local pressure loss coefficients and the drag reduction rate are introduced to compare drag reduction effects. The results show that the drag reduction components studied in this paper all have varying degrees of an effect for most of the cases. Also, the drag reduction effect of components was influenced by the specific flow cases. Therefore, the selection of a suitable shape for the drag reduction component should consider the flow pattern.
Practical application: This paper has studied the local drag reduction achieved by components placed in elbow and T-junction close-coupled pipes, which can be used in the building industry. In order to find the suitable component shapes, we designed seven kinds of drag reduction components. The designs came from drag reduction technologies used in different applications such as commercial, high performance automobiles and aerofoil designs.
In the combined system of polymer additives and riblets, the polymer additives expand the range of non-dimensionalized riblet width s+ where the riblets reduce the frictional drag. Although in the higher region of s+ the riblets increase the frictional drag as the rough surface, the polymer additives thicken the wall layer, which dumps the drag increase due to riblets and then gives the benefical combined effect in this higher region of s+. Based on this scinario, the velocity profile and the pipe frictional coefficient for the combined system were derived from the velocity profile of each system. The turbulent velocity profiles were measured for the combined system using a laser Doppler velocimetry. The measured results agreed well with the derived prediction for the combined system.
Nature has long been an important source of inspiration for mankind to develop artificial ways to mimic the remarkable properties of biological systems. In this work, a new method was explored to fabricate a biomimetic engineering surface comprising both the shark-skin, the shark body denticle, and rib morphology. It can help reduce water resistance and the friction contact area as well as accommodate lubricant. The lubrication theory model was established to predict the effect of geometric parameters of a biomimetic surface on tribological performance. The model has been proved to be feasible to predict tribological performance by the experimental results. The model was then used to investigate the effect of the grid textured surface on frictional performance of different geometries. The investigation was aimed at providing a rule for deriving the design parameters of a biomimetic surface with good lubrication characteristics. Results suggest that: (i) the increase in depression width ratio [Formula: see text] decreases its corresponding coefficient of friction, and (ii) the small coefficient of friction is achievable when [Formula: see text] is beyond 0.45. Superposition of depth ratio Γ and angle's couple under the condition of [Formula: see text] < 0.45 affects the value of friction coefficient. It shows the decrease in angle decreases with the increase in dimension depth [Formula: see text].
A vacuum casting method to replicate shark skin surface accurately in large area was investigated to overcome some difficulties in the replication process. The fresh shark skin was pretreated as a replication sample, and the replication mold of shark skin was manufactured by casting the unsaturated polyester resin under vacuum and laying the multilayer glass fibers. Under vacuum condition, silicone rubber was poured into the resin mold to obtain the replication film of the shark skin with micro-riblets. The contour of the micro-riblet was measured by a Talysurf CLI2000 machine to evaluate the replication accuracy. Based on the contacting angle measurement, the hydrophobic property of the micro-riblet's surface was investigated. It was found that the vacuum casting method was an effective replication technology which was suitable to form large-area and highly accurate micro-riblets on the surface of the shark skin. The experiment of drag reduction was conducted in a water tank. Based on the experimental results, the replicated film of shark skin played a significant role in reducing drag. The maximum and minimum of drag reduction rate were 18.6% and 9.7%, respectively.
Mechanical engineers often are forced to be concerned with cavitation in flows near bodies or within machinery. Viscous effects on cavitation introduce difficulties in design, because these effects often are significantly different for model and full-scale conditions. Therefore, a theoretical analysis would be desirable in numerical prediction of full-scale performances and in interpretation of experimental data. Though cavitation is a very complex nonlinear phenomenon, the numerical analysis of which is difficult even approaching an ideal fluid model, recently certain successes were obtained in the examination of viscous effects on sheet cavitation and vortex cavitation. A part of the theoretical results concerning viscous effects on cavitation was provided by matches of well-known solutions for boundary layers over non-cavitating bodies and solutions for cavities in an ideal fluid. The review of theoretical methods and consideration of the best way to proceed with future research is the objective of this review article, which includes 92 references.
In the present study, we investigate the combined effect of polymer additives and active blowing and suction at the wall on drag reduction using direct numerical simulation. Three different turbulent channel flows having the same bulk Reynolds number but different wall shear velocities are generated to see the role of the strength of near-wall streamwise vortices in polymer drag reduction. From this study, we show that the phenomenon of polymer drag reduction is closely related to the strength of near-wall streamwise vortices as well as the elasticity of polymer solution. On the other hand, the combined drag reduction obtained by both the polymer additives and the blowing and suction is larger than the individual drag reduction either by polymers or by blowing and suction, but is smaller than sum of the two separate drag reductions, indicating that the polymer solution is less efficient in producing drag reduction in the absence of strong near-wall streamwise vortices.
Turbulent drag reduction in fluid flow by additives has been an exotic field of research ever since its reported discovery in 1949. Various technical applications have been envisaged both for polymeric and surfactant drag reduction. Some successful applications include increased flow of oil and other fluids through pipelines, improved fire fighting and irrigation, improved flow in storm sewers, and flow augmentation by drag reducers in pipeline transport of sediments and slurries. Other possible applications include district heating circuits, industrial and agricultural sprays, and slow‐release fertilizers and pesticides. However, the mechanism of drag reduction still eludes exact explanation mainly because of the inability to characterize polymers, surfactants, and their interactions at molecular or micellar levels in turbulent flows.
The main features of polymeric and surfactant homogeneous and heterogeneous drag reduction have been investigated by two‐component laser‐Doppler velocity meter in fully developed, well‐mixed, low concentration (1–2 ppm) drag‐reducing channel flows. Advances in computer technology have led to improved accuracies and reliability of experimental techniques and made possible direct numerical simulation of drag‐reducing turbulent flows. The role of extensional viscosity and elasticity of drag reducers is being keenly debated for the origin of drag reduction in theoretical and experimental investigations. A better understanding is emerging. Some synergistic effects have been observed in combining passive drag‐reducing devices such as riblets with polymers surfactants. Similar observations have been made in combination with microbubbles. This article provides an overview of the latest salient developments in materials, mechanisms, and applications in the field of polymeric drag reduction of various forms and geometries.
When drag-reducing additives are confined entirely to the linear sublayer of a turbulent channel flow of water, both the spanwise spacing and bursting rate of the wall-layer structure are the same as those for a water flow and there is no evidence of drag reduction. Drag reduction is measured downstream of the location where the additives injected into the sublayer begin to mix in significant quantities with the buffer region (10 < y+ < 100) 2 of the channel flow. At streamwise locations where drag reduction does occur and where the injected fluid is not yet uniformly mixed with the channel flow, the dimensionless spanwise streak spacing increases and the average bursting rate decreases. The decrease in bursting rate is larger than the corresponding increase in streak spacing. The wall-layer structure is like the structure in the flow of a homogeneous, uniformly mixed, drag-reducing solution. Thus, the additives have a direct effect on the flow processes in the buffer region and the linear sublayer appears to have a passive role in the interaction of the inner and outer portions of a turbulent wall layer.
Viscous properties and pipe flow resistance of fiber suspensions are experimentally investigated. We employ several synthetic fibers with various aspect ratios and microscopic asbestos fibers. The viscosity of fiber suspensions decreases with an increasing shear rate but it exhibits Newtonian viscous behavior at very high shear rate. The viscous property of synthetic fiber suspensions is correlated experimentally to the aspect ratios. In synthetic fibers, turbulent drag reduction is due to an increase in log profile's gradient. This increase is affected by their stiffness, aspect ratio, concentration and others. Their correlation is experimentally determined. In asbestos fibers, thickening of viscous and buffer layers also contributes to the drag reduction.
Turbulent drag reduction in a mixed fiber-polymer system was observed both in a pipe flow and a flow on a rotating disk. Drag reducing rate in a mixed system was approximately the sum of each rate in separate system, though the effect of fiber additives is weakened a little by mixing with an increase in polymer concentration. In addition, we observed a phenomenon that transition to turbulence was delayed in a mixed system.
Direct numerical simulations of turbulent flows over riblet-mounted surfaces are performed to educe the mechanism of drag reduction by riblets. The computed drag on the riblet surfaces is in good agreement with the existing experimental data. The mean-velocity profiles show upward and downward shifts in the log–law for drag-decreasing and drag-increasing cases, respectively. Turbulence statistics above the riblets are computed and compared with those above a flat plate. Differences in the mean-velocity profile and turbulence quantities are found to be limited to the inner region of the boundary layer. Velocity and vorticity fluctuations as well as the Reynolds shear stresses above the riblets are reduced in drag-reducing configurations. Quadrant analysis indicates that riblets mitigate the positive Reynolds-shear-stress-producing events in drag-reducing configurations. From examination of the instantaneous flow fields, a drag reduction mechanism by riblets is proposed: riblets with small spacings reduce viscous drag by restricting the location of the streamwise vortices above the wetted surface such that only a limited area of the riblets is exposed to the downwash of high-speed fluid that the vortices induce.
In the present Brief Communication, experiments are reported establishing a superposition of drag reduction due to riblets on drag reduction due to polymers, in fully developed turbulent flow of dilute aqueous solutions of polymers (2–50 ppm) through 25.4 mm (1 in.) diameter pipes, lined with a film of grooved isosceles triangles of equal height and base (S=0.11 mm). The range of S+ (which is the base and height of the riblets expressed in wall units), where drag reduction is superimposed, changes with polymer concentration. The higher the concentration, the narrower the range of S+. Also, the amount of superimposed drag reduction changes with the type of polymer used.
The additional skin friction effect produced by a 3M riblet surface, used in conjunction with low concentration polymer solutions, is investigated in fully developed, turbulent pipe flow. Generally at the low concentrations of Polyox 301 and guar gum studied, the absolute drag reduction of the 3M riblets appears to be independent of the polymer presence, with a maximum between 5 and 7 percent occurring around h+ = 12. Comparisons with previous polymer studies with 3M riblets, sand roughened and commercially rough surfaces are made.
Pipes with V shape riblets were tested at Reynolds numbers between 5 x 10(3) and 4 x 10(4). All riblet pipes indicated some drag reduction. The model with h = 0.55 mm and h/S = 0.483 showed the maximum drag reduction of 8 percent and the widest range of Reynolds number over which the riblet reduces drag. The riblet shape desirable for drag reduction in pipe flows was almost the same as that in flat plate boundary layers, but the value of S+ which provided the maximum drag reduction was quite different; S+ = 23 for pipe flows and S+ = 12 for flat plate boundary layers.
Drag reduction by dilute solutions of linear, random-coiling macromolecules in turbulent pipe flow is reviewed. The experimental evidence is emphasized in three sections concerned with the graphical display of established features of the phenomenon, data correlation and analysis, and the physical mechanism of drag reduction.
The flow of 3 to 100 wppm aqueous solutions of a polyethyleneoxide polymer,M
w=6.2;106, was studied in a 10.2 mm i.d. pipe lined with 0.15 mm V-groove riblets, at diametral Reynolds numbers from 300 to 150000. Measurements in the riblet pipe were accompanied by simultaneous measurements in a smooth pipe of the same diameter placed in tandem. The chosen conditions provided turbulent drag reductions from zero to the asymptotic maximum possible. The onset of polymer-induced drag reduction in the riblet pipe occurred at the same wall shear stress, d/Öc = 6\delta /\sqrt c = 6
. The maximum drag reduction observed in the riblet pipe was independent of polymer concentration and well below the asymptotic maximum drag reduction observed in the smooth pipe. Polymer solution flows in the riblet pipe exhibited three regimes: (i) Hydraulically smooth, in which riblets induced no drag reduction, amid varying, and considerable, polymer-induced drag reduction; this regime extended to non-dimensional riblet heightsh
+<5 in solvent andh
+<10 in polymer solutions. (ii) Riblet drag reduction, in which riblet-induced flow enhancementR>0; this regime extended from 5<h
+<22 in solvent and from 10<h
+<30 in the 3 wppm polymer solution, with respective maximaR=0.6 ath
+=14 andR=1.6 ath
+=21. Riblet drag reduction decreased with increasing polymer concentration and increasing polymer-induced flow enhancement S. (iii) Riblet drag enhancement, whereinR<0; this regime extended for 22<h
+<110 in solvent, withR;–2 forh
+>70, and was observed in all polymer solutions at highh
+, the more so as polymer-induced drag reduction increased, withR<0 for allS>8. The greatest drag enhancement in polymer solutions,R=–71 ath
+=55 whereS=20, considerably exceeded that in solvent. Three-dimensional representations of riblet- and polymer-induced drag reductions versus turbulent flow parameters revealed a hitherto unknown dome region, 8<h
+<31, 0<S<10, 0<R<1.5, containing a broad maximum at (h
+,S,R) = (18, 5, 1.5). The existence of a dome was physically interpreted to suggest that riblets and polymers reduce drag by separate mechanisms.
The use of riblets for drag reduction is examined theoretically. For various riblet shapes, the anisotropic properties of the viscous flow over the riblets are determined. The results obtained can be used for riblet optimization and as input data for computer simulations of the complete turbulent flow field. Attention is also given to other concepts, such as hypothetical mechanisms derived from observations of the shark skin. The experimental facilities that would be required to test these new concepts are discussed.
The effect of longitudinal riblet surfaces on viscous drag in fully developed laminar channel flows was investigated. Unlike turbulent flows, drag reduction was not obtained in the laminar flows. Results were independent of Reynolds number. Wall-shear rates on most regions of the cross-sectional perimeter of riblets were smaller than that of corresponding plane channel flow even though the net drag was increased.
Viscous Drag Reduction using Stream-wise Aligned Riblets: Survey and New Results,” Turbulence Management and Relaminarisation
- J M Wallance
- J L Balint
Drag Reduction with a Combined Use of Riblets and Polymer Coating,” Drag Reduction in Fluid Flows
- K-S Choi
- H H Pearcey
- A M Savill
- S Svensson
An Experimental Investigation of the Drag Reducing Effects of Riblets in Pipes,” Drag Reduction in Fluid Flows
- J Rohr
- G W Anderson
- L W Reidy