Shear layers in the turbulent pipe flow of drag reducing polymer solutions
Highlights
► Drag reduction of polymer solutions was measured in a turbulent pipe flow. ► PIV was used to assess the effect of the additives on the instantaneous flow. ► Flows with additives underwent a separation into low- and high-momentum regions. ► The two regions were separated by a thin layer of intense vorticity and strain rate. ► The thickness of these regions correlates with the measured level of drag reduction.
Introduction
It is well known that the frictional resistance caused by turbulent flow of a Newtonian fluid (solvent) in a pipe can be considerably reduced by the addition of a polymer to the solvent (Toms, 1948). An important consequence of this phenomenon, known as drag reduction, is that a fluid (liquid) solution containing the polymer additive will exhibit a lower pressure drop in a pipe flow compared to the pure solvent at the same flow-rate. The phenomenon of drag reduction occurs exclusively in turbulent flow and is of great industrial importance. Specifically, it is relevant in a broad array of applications that involve liquid transport through pipelines (Burger et al., 1980), ranging from fire fighting to field irrigation (Singh et al., 1995) and flows in urban sewage networks (Sellin and Ollis, 1980), hydraulic fracturing (Lucas et al., 2009, Morgan and McCormick, 1990), oil pipeline systems and secondary oil well operations.
Polymers have been identified as the most efficient drag reducers with respect to other drag reduction additives such as surfactants or bubbles (Bismarck et al., 2005). The amount of polymer additive required to alter the turbulent flow structure is in the order of few parts per million by weight (wppm). Drag reduction was for example observed for polymer concentrations as low as 0.02 wppm (20 wppb) by Oliver and Bakhtiyarov (1983).
Virk et al. (1967) were the first to propose an important universal asymptote of maximum drag reduction, sometimes called Virk's asymptote, which is independent of experimental set-up or polymer additive. In a follow-up paper Virk (1975) established common characteristics of velocity profiles associated with the turbulent flow of polymeric solutions. An increasing presence of polymer additives was found to be associated with a thickening of the buffer layer and a shift of the log-law region away from the Newtonian law of the wall, or viscous sublayer. At maximum drag reduction the buffer layer was found to extend to the centerline and the log-law region disappeared.
Drag reduction has been studied extensively since its discovery (Brostow, 2008, Lumley and Blossey, 1998, Virk, 1975, White and Mungal, 2008), but direct phenomenological insight into the effect of polymer additives on the turbulent flow intensity and structure was lacking until recently when non-intrusive flow visualization techniques were used (den Toonder et al., 1997, Ptasinski et al., 2001). The advancement and employment of planar flow measurement techniques, such as Particle Image Velocimetry (PIV), have been a key development that has provided valuable insight into the instantaneous turbulent flow structure (Willert and Gharib, 1991). Warholic et al. (2001) used the PIV technique to identify turbulent structures close to the wall that the authors designated as being typical of flows involving Newtonian solvents. These structures were characterized by the ejection of low-momentum fluid to the outer velocity region, or defect region, and by quasi-streamwise vortices. Such structures were recognized as locations of large Reynolds stresses. For high measured drag reduction the authors observed reduction or elimination of the ejections from the wall (Warholic et al., 2001). Liberatore et al. (2004) observed that the presence of polymers lead to a decrease in the frequency and the intensity of large-scale ejections when compared to a Newtonian solvent. The polymer induced drag reduction effect was also found to reduce the small-scale fluctuations, as determined from spectral functions (Warholic et al., 2001), and to reduce the magnitude and frequency of the small-scale eddies (Liberatore et al., 2004). Additionally, large regions of almost unidirectional fluctuating velocity vectors were observed for solutions exhibiting high levels of drag reduction (Liberatore et al., 2004, Warholic et al., 2001).
The aim of this work is to study the effect of drag reducing polymers on the instantaneous structure of turbulent pipe flow and to extend our knowledge to practically relevant conditions with measurements at Reynolds numbers up to . Three different molecular lengths, and thus three different corresponding weights, of the same linear drag reducing polymer (polyethylene oxide, or PEO) have been studied. The Newtonian character of the polymer solutions was first verified by rheological measurements. A pressure-driven horizontal pipe flow apparatus was then used to generate the turbulent flow, and to measure pressure drops over a range of flow-rates. The turbulent flow was characterized with the use of a PIV system.
In the sections below, firstly, the rheological and drag reduction measurements are reported for the various polymers, at different concentrations, over the investigated range of Reynolds numbers. We then present corresponding profiles of the mean flow velocity and of the root mean square (rms) of its fluctuations and, based on the former, measures of the thickness of the buffer layers. This is followed by a presentation of instantaneous images of the turbulent flow with and without the polymer additives. The main contribution of the current study is the uncovering of the presence of two distinct momentum regions of turbulent pipe flow for solutions containing polymer additives, separated by a thin interface layer that is associated with high strain (and shear). It will be shown that these flow structures (i.e. thin layers) propagate far from the wall towards the center of the pipe flow, within an overall region that is larger than that which is investigated typically in turbulent drag reduction studies (e.g. by numerical simulations due to the computational cost). Finally, the spanwise extent of the regions within which these layers are found is correlated to the level of independently measured drag reduction, and also compared to the extent of the velocity buffer layer.
Section snippets
Drag reducing polymers
Three different molecular lengths and thus also weights of polyethylene oxide (PEO) were chosen for this investigation. PEO is a linear non-ionic water soluble polymer. All three PEOs were purchased from Sigma-Aldrich, Inc. (Steinhelm, Germany). The molecular weights as given by the manufacturer are , and and the corresponding abbreviations used in the following text are PEO2, PEO4 and PEO8, respectively. Tap water was used throughout as the solvent.
During the
Rheology
A rheological characterization was performed in order to assess the Newtonian character of the polymer solutions. All solutions show a linear, flat (zero-gradient) dependency of apparent shear viscosity on strain rate, which is an indicator of Newtonian behavior. As an indicative result, the apparent shear viscosity as a function of strain rate for solutions with different concentrations c of PEO8 from 10 to 250 wppm are shown in Fig. 4(a). Fig. 4(b) shows the dependence of the mean
Conclusions
The drag reduction efficiency of polyethylene oxide was measured in a turbulent pipe flow over 122 conditions with varying polymer molecular weight, concentration and Reynolds numbers up to 210 000. Different levels of drag reduction were observed with a maximum of 72%. Particle Image Velocimetry was used to assess the effect of the polymer additives on the instantaneous turbulent pipe flow. The presence of the drag reducing polymers was associated with a thickening of the buffer layer and a
Acknowledgments
The authors gratefully acknowledge the financial support of Halliburton Energy Services.
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