1,721,063 research outputs found
Drag reduction in homogeneous turbulence by scale-dependent effective viscosity
No full textThe drag reduction phenomena under homogeneous turbulence conditions was analyzed in terms of a self-dependent effective viscosity. The differences between drag reduction in wall bounded and homogeneous flows were also discussed. It was observed that the effective velocity will be different from the Newtonian one in terms of scale. The drag reduction in homogeneous flow appeared as an increase of the rms fluctuations of the large scale while in case of wall bounded flows the drag reduction corresponds to the increase in the mean flow velocity
Shell model of two-dimensional turbulence in polymer solutions
No full textWe address the effect of polymer additives on two-dimensional turbulence, an issue that was studied recently in experiments and direct numerical simulations. We show that the same simple shell model that reproduced drag reduction in three-dimensional turbulence reproduces all the reported effects in the two-dimensional case. The simplicity of the model offers a straightforward simulation of all the major effects under consideration
Identification and calculation of the universal asymptote for drag reduction by polymers in wall bounded turbulence
No full textDrag reduction by polymers in wall turbulence is bounded from above by a universal maximal drag reduction (MDR) velocity profile that is a log law, estimated experimentally by Virk as V+(y(+))approximate to 11.7logy(+)-17. Here V+(y) and y(+) are the mean streamwise velocity and the distance from the wall in "wall" units. In this Letter we propose that this MDR profile is an edge solution of the Navier-Stokes equations (with an effective viscosity profile) beyond which no turbulent solutions exist. This insight rationalizes the universality of the MDR and provides a maximum principle which allows an ab initio calculation of the parameters in this law without any viscoelastic experimental input
Comparison of theory and direct numerical simulations of drag reduction by rodlike polymers in turbulent channel flows
No full textNumerical simulations of turbulent channel flows, with or without additives, are limited in the extent of the Reynolds number (Re) and Deborah number (De). The comparison of such simulations to theories of drag reduction, which are usually derived for asymptotically high Re and De, calls for some care. In this paper we present a study of drag reduction by rodlike polymers in a turbulent channel flow using direct numerical simulation and illustrate how these numerical results should be related to the recently developed theory
Theory of concentration dependence in drag reduction by polymers and of the maximum drag reduction asymptote
No full textA simple model of the effect of polymer concentration on the amount of drag reduction in turbulence is presented, simulated, and analyzed. The qualitative phase diagram of drag coefficient versus Reynolds number (Re) is recaptured in this model, including the theoretically elusive onset of drag reduction and the maximum drag reduction (MDR) asymptote. The Re-dependent drag and the MDR are analytically explained, and the dependence of the amount of drag on material parameters is rationalized
Statistical properties of nonlinear shell models of turbulence from linear advection models: rigorous results
No full textIn a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and nonlinear fields coincide. The argument depended on an assumption of continuity of the solutions as a function of a parameter. The aim of this paper is to provide a rigorous proof for the validity of the assumption. In addition we clarify here when the swap of a nonlinear model by a linear one will not work
Additive equivalence in turbulent drag reduction by flexible and rodlike polymers
No full textWe address the "additive equivalence" discovered by Virk and co-workers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar maximum drag reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations
Colloquium: Theory of drag reduction by polymers in wall-bounded turbulence
No full textThe flow of fluids in channels, pipes, or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases manyfold when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a "skin" or a "bulk" effect. In this Colloquium the phenomenology of drag reduction by polymers is summarized, stressing both its universal and nonuniversal aspects, and a recent theory is reviewed that provides a quantitative explanation of all the known phenomenology. Both flexible and rodlike polymers are treated, explaining the existence of universal properties like the maximum drag reduction asymptote, as well as nonuniversal crossover phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally other agents for drag reduction are discussed with a stress on the important example of bubbles
Maximum drag reduction asymptotes and the cross-over to the Newtonian plug
No full textWe employ the full FEN E-P model of the hydrodynamics of a dilute polymer solution to derive a theoretical approach to drag reduction in wall-bounded turbulence. We recapture the results of a recent simplified theory which derived the universal maximum drag reduction (MDR) asymptote, and complement that theory with a discussion of the cross-over from the MDR to the Newtonian plug when the drag reduction saturates. The FENE-P model gives rise to a rather complex theory due to the interaction of the velocity field with the polymeric conformation tensor, making analytic estimates quite taxing. To overcome this we develop the theory in a computer-assisted manner, checking at each point the analytic estimates by direct numerical simulations (DNS) of viscoelastic turbulence in a channel
- …
