Flow visualization studies of a turbulent drag reducing solution

Arunachalam, Vr.; Hummel, R. L.; Smith, James W.

doi:10.1002/cjce.5450500305

Cited by 17 publications

(3 citation statements)

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“…Thus, the elastic sublayer model predicts that, with increasing drag reduction at a given R + , the mean velocity profile should initially tend to be blunter than Newtonian, but eventually become sharper than Newtonian as maximum drag reduction is approached. Qualitative confirmation of this predicted sequence of velocity profile shape changes is available in the resuIts of Rollin and Seyer ( 1972), and, quite strikingly, in the photographs of Arunachalam, Hummel, and Smith (1972). It is also interesting that, at R+ = 100, (Ul/Uau)m is much closer to 2.0 than is ( U I / U , ,~)~, which suggests that the ultimate profile can evolve from a parabolic laminar profile without the large discontinuities that arise in the Newtonian case; this is of possible relevance in the detection of intermittency during transition.…”

Section: Ultimate Profilementioning

confidence: 56%

“…The data of Chung and Graebel ( 1972), an early application of laser-Doppler anemometry, have errors of about & 20% in the velocity measurements alone. Arunachalam, Hummel, and Smith (1972) report an error of about & 5% in their velocity measurements but provide no information about uncertain- 3. In column 10, mdr means the entry is at, or close to, maximum drag reduction.…”

Section: Ultimate Profilementioning

confidence: 93%

“…Concerning the variation of turbulent intensity profi!es with drag reduction, the data of Logan ( S F N 0.4) and Rudd ( S F N 1.0) respectively yield a ratio of maximum axial intensity in polymer solution to that in solvent ( Urnax,; + /Urnax,n'+ ) of 1.3 and 1.8, while in the pipe core the regions where ur+ is the same as in solvent are 1.0 > f > 0.4 and 1.0 > 5 > 0.6, respectively. At (or near) maximum drag reduction, there is only uncertain information from streak photography (Seyer and Metzner, 1969;Arunachalam, Hummel, and Smith, 1972), which suggests that urnax,d+) is 2.0 to 2.5. 1.3.2 Reynolds Stress and Correlation Coeficient.…”

Section: Turbulencementioning

confidence: 99%

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Drag reduction fundamentals

1975

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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. P. S. VlRK Deportment of Chemical Engineering Indian Institute of TechnologyMadras 600036, India SCOPEOur objective is to acquaint the reader with the phenomenon of drag reduction, in which the skin friction caused by turbulent flow of an ordinary liquid is reduced by additives. This phenomenon, discovered ahnut 1947, has received attention because it suggests practical benefits, such as increased pipeline capacities and faster ships, and is also theoretically stimulating, in the areas of wall turbulence and molecular rheology . This review, restricted to drag reduction by polymer solutions in pipe flow, has three sections: (1) the experimental evidence, (2) correlation and analysis, and (3) mechanism. Section 1 presents experimentally established results showing the flow regimes exhibited by polymer solutions, the relationships among flow and macromolecular parameters, and the changes in mean and turbulent flow structures which accompany drag reduction. The conclusions of Section 1 are documented in Section 2. The latter concerns the empirical correlation of experimental results, with analysis (and tabulations) of the data used for this purpose. Section 2 also provides for discussion of evidence not fully enough established to be included in Section 1. Finally, in Section 3 an attempt is made to physically interpret the experimental results, to infer the nature of the polymer-turbulence interaction responsible for drag reduction and its effect on the energy balances of turbulent pipe flow. CONCLUSIONS AND SIGNIFICANCE1. Gross Flow. Drag reduction by dilute polymer solutions in turbulent pipe flow appears bounded between two universal asymptotes, namely, the Prandtl-Karman law [Equation (2)] for Newtonian turbulent flow and a maximum drag reduction asymptote [Equation (4)]. Between these limits is a polymeric regime in which the observed friction factor relations are approximately linear on Prandtl-Karman coordinates and can be characterized by two parameters-the wall shear stress at the onset of drag reduction and the slope increment by which the polymer solution slope exceeds Newtonian. For a given polymer species-solvent pair: The onset wall shear stress is essentially independent of pipe diameter, polymer concentration, and solvent viscosity, and varies inversely as the two to three power of polymer radius of gyration [Equations (19) and ( 5 ) ] . The slope increment is essentially independent of pipe diameter, varies as the square root of polymer concentration, and as the three-halves power of the number of chain links in the polymer backbone [Equation (S)], and seems unaffected by decreases in polymer excluded volume.2. Mean Velocity Profiles. On law of the wall coordinates, these posse...

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Section: Ultimate Profilementioning

confidence: 56%

Section: Ultimate Profilementioning

confidence: 93%

Section: Turbulencementioning

confidence: 99%

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Drag reduction fundamentals

1975

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Momentum and energy transfer in turbulent pipe flow: The penetration model revisited

Katsibas

Gordon

1974

AIChE Journal

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The extreme difficulties involved in trying to describe mathematically heat, mass, and momentum transfer in turbulent pipe flow are well-known, and for practical calculations one is forced to fall back on the empirical correlations. Our qualitative understanding of the turbulent exchange process has increased significantly in recent years, however, due to the careful studies of Corino and Brodkey (1969), Kline et al. (1967), Popovich and Hummel ( 1967), and many others. These researchers have clearly described the unsteady nature of the viscous sublayer and identified the bursting process as a key event in turbulent flow.Corino and Brodkey (1969) offer a lucid picture of the wall region in turbulent pipe flow reminiscent in many ways of the early penetration model of Einstein and Li (1956). In this model, a lump of fluid with axial velocity uo suddenly penetrates into the region immediately adjacent to the pipe wall. The velocity profile then decays according tofor a time period 8, following which the process begins anew. It is important to emphasize that the picture suggested by Equation (1) represents an extreme idealization of the process described by Corino and Brodkey. In spite of this, the model accurately describes a large variety of experimental data. The quantity uo in Equation ( 1 ) was originally chosen by Einstein and Li (1956) as the velocity at a distance equal to three times the displacement thickness from the wall. More recently, Meek and Baer (1970) have evaluated u o by coupling the velocity profile in the sublayer to the velocity profile in the core obtained via a mixing length formulation. Integration over the cross section of the pipe then yields a relation between uo and the average fluid velocity u b . This approach does eliminate the arbitrariness associated with the definition of uo but complicates the mathematical details of the theory and distracts from its conceptual simplicity. The studies of Corino and Brodkey suggest that uo is of order ub, as would be anticipated on purely physical grounds. It is therefore natural, and consistent with the crude nature of the model, to simply equate these two velocities. This simplification greatly reduces the algebraic and numerical difficulties associated with the model and leads to predictions equivalent to and in some instances superior to the Meek and Baer (1970) formulation. Furthermore, the model as thus formulated is useful in interpreting various aspects of turbulent drag reduction. MOMENTUM TRANSFEREquation ( l ) , with the condition uo = ub, yields the following alternative expressions for the friction factor:where is a dimensionless contact time. Equation (2) indicates that at constant bulk velocity, the energy dissipation in turbulent pipe flow is an inverse function of the square root of the contact time, or time between turbulent bursts. Current theories of drag reduction in dilute polymer solutions suggest that the primary function of the macromolecule is to reduce the bursting frequency and hence increase B+. This is a consequence o...

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Bio‐Inspired Passive Drag Reduction Techniques: A Review

2015

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It was believed that fluid flow and the laminar to turbulent transition delay were more easily controlled on smooth surfaces until the discovery of the grooved shark skin surface that changed the whole idea of how smooth the surface should be to have high flow in submerged surfaces. Riblets have gained renewed interest in academic fields of study and in industry due to several advantages in manipulating the turbulence boundary layer. Drag reduction using small, longitudinally grooved surface provides up to 10 % lower energy consumption in several applications. This review provides an overview of the mechanism of drag reduction with riblets, the different geometries and types, and the latest developments in drag reduction riblet technology.

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Flow visualization studies of a turbulent drag reducing solution

Abstract: A nondisturbing photochromic dye trace, technique has been employed t o study the flow profiles of water-alcohol solutions containing the drag reducing polymer Polyox at concentrations , 1967.(AB) Rxndborn.

Cited by 17 publications

References 23 publications

Drag reduction fundamentals

Drag reduction fundamentals

Momentum and energy transfer in turbulent pipe flow: The penetration model revisited

Bio‐Inspired Passive Drag Reduction Techniques: A Review

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