On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows
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Cites background from "On the coherent drag-reducing and t..."
...The existing theories of drag reduction all share the same conceptual feature: They interpret the resulting flow as a modified form of ordinary Newtonian shear flow turbulence, with its properties being determined by the balance between elastic and viscous stresses (11, 15, 16, 30, 31)....
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References
1,097 citations
"On the coherent drag-reducing and t..." refers result in this paper
...Nevertheless, the turbulence was found to be self-sustained in a similar fashion to the minimal channel flow of Jiménez & Moin (1991) which contains only a pair of streaks and vortices....
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867 citations
"On the coherent drag-reducing and t..." refers background or methods in this paper
...Based on these results, we propose to include the effects of polymers in the autonomous regeneration cycle put forward by Jiménez & Pinelli (1999)....
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...These distinct behaviours are used to propose an autonomous regeneration cycle of polymer wall turbulence, in the spirit of Jiménez & Pinelli (1999)....
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...The numerical method is essentially that of Min et al. (2003b) modified to simulate very elastic and long polymer molecules and is described and validated in Dubief et al....
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...Finally, a model of drag-reduced near-wall turbulence is proposed based on the autonomous regeneration cycle of near-wall turbulence of Jiménez & Pinelli (1999)....
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797 citations
"On the coherent drag-reducing and t..." refers background or methods in this paper
...These structures are the quasi-streamwise vortices which occupy less than 10% of the volume of the buffer layer (Dubief & Delcayre 2000), yet they are essential to momentum exchanges between outer and inner regions in the flow and are responsible for turbulent skin friction drag (Kravchenko et al.…...
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...in drag-reduced flows has been established by simple numerical experiments reported in Dubief et al. (2004). Based on these results, we propose to include the effects of polymers in the autonomous regeneration cycle put forward by Jiménez & Pinelli (1999). This cycle, shown in figure 5, explains how wall turbulence is self-sustained through mean shear, nonlinear interactions, near-wall vortices and streaks, in the Newtonian case. Polymers fit at the centre of this cycle by extracting energy from the vortices and releasing energy in the streaks. The stretching of polymers is governed by the mean shear and nonlinear interactions as shown in Terrapon et al. (2004). This simple mechanism appears to apply to LDR and HDR regimes, and it should apply to any regime where streaks and vortices are present....
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...…wall friction (Kravchenko, Choi & Moin 1993), occupy a volume of about 10% of the buffer region in Newtonian flows and the streamwise vorticity fluctuations they generate in their core and immediate surroundings exceed the standard deviation of ωx by a factor of 2 or more (Dubief & Delcayre 2000)....
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...(2003b) modified to simulate very elastic and long polymer molecules and is described and validated in Dubief et al. (2004). In the present paper only a brief outline of the method is given. The momentum equations are solved on a staggered grid with second-order central finite differences. The divergence of the polymer stress (2.1) and the spatial derivatives of c̃ij are computed using a fourthorder compact scheme and a third-order upwind compact scheme, respectively. Time advancement of (2.1) and (2.2) is performed by the classical semi-implicit secondorder Crank–Nicolson/third-order Runge–Kutta scheme. In the momentum equation, the Newtonian viscous stress is treated implicitly in the wall-normal direction. Equation (2.2) is solved with a new semi-implicit time scheme which ensures that the trace of the c̃ij remains upper bounded (c̃kk <L (2)). A local artificial viscosity (LAD), proposed by Min et al. (2003b), is necessary to ensure the stability of the advection term as well as a lower diffusive effect than a global dissipation as adopted in Dimitropoulos et al....
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...in drag-reduced flows has been established by simple numerical experiments reported in Dubief et al. (2004). Based on these results, we propose to include the effects of polymers in the autonomous regeneration cycle put forward by Jiménez & Pinelli (1999). This cycle, shown in figure 5, explains how wall turbulence is self-sustained through mean shear, nonlinear interactions, near-wall vortices and streaks, in the Newtonian case....
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317 citations
"On the coherent drag-reducing and t..." refers background or methods or result in this paper
...In drag-reduced flow, the maximum of u′+ x is higher than or comparable with the DR = 0% case, as found in experiments (Warholic et al. 1999; Ptasinski et al. 2003; White et al. 2004)....
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...At DR =60%, its near-wall contribution to (3.1) has the same magnitude as the Reynolds shear stress, thus showing that polymers have a significant mean effect in the mechanism of HDR flows, as argued by Warholic et al. (1999)....
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...In drag-reduced flows, a stress deficit is observed in the stress balance whose large magnitude at HDR has been interpreted as the necessary input of energy from the polymers to the flow for the sustenance of the asymptotic MDR turbulence (Warholic et al. 1999)....
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...In drag-reduced flow, the maximum of u′+x is higher than or comparable with the DR = 0% case, as found in experiments (Warholic et al. 1999; Ptasinski et al. 2003; White et al. 2004)....
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...As expected from experiments (Warholic et al. 1999), DR = 35% produces a velocity profile whose log region is only shifted upward, while DR = 47% and DR =60% show significant changes in the slope of the log law (figure 1)....
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257 citations
"On the coherent drag-reducing and t..." refers background or result in this paper
...In drag-reduced flow, the maximum of u′+ x is higher than or comparable with the DR = 0% case, as found in experiments (Warholic et al. 1999; Ptasinski et al. 2003; White et al. 2004)....
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...It contains the damping of near-wall vortices discussed by Dimitropoulos et al. (2001), Stone et al. (2001), Min et al. (2003b) and Ptasinski et al. (2003)....
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...Statistical results reproduce the main features observed experimentally and in other numerical studies (Ptasinski et al. 2003; Min et al. 2003a)....
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...In drag-reduced flow, the maximum of u′+x is higher than or comparable with the DR = 0% case, as found in experiments (Warholic et al. 1999; Ptasinski et al. 2003; White et al. 2004)....
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...At higher drag reductions, larger than about 40%, the flow enters the HDR regime for which the slope of the log-law is dramatically augmented and the Reynolds shear stress is small (Warholic et al. 1999; Ptasinski et al. 2003)....
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