An Experimental Study of Bulk Turbulence in Dilute Polymer Solutions
Final Report Abstract
The interaction between the elastic freedom of flexible, long-chain polymers and fluid turbulence is an interesting problem in physics and also finds important applications in engineering and industry. Perhaps the most well-known phenomenon is the “polymer drag reduction” – addition of very small amount of polymers into a turbulent pipe flow could lead to dramatic increase in flow rate under the same pressure drop. Here, we address another, but related, question: How does polymers affect bulk-turbulence, away from any walls? The focus is on the energy cascade, the central property of fluid turbulence. Several theories have been proposed, however, there is a lack of detailed experimental tests of these theories. In this project, we carried out detailed measurements of bulk turbulence in dilute polymer solutions, using three-dimensional Lagrangian Particle Tracking technique. We focused on the turbulence dynamics in the so-called inertial range, scales between the forcing scale, at which energy is supplied to the flow, and the dissipative scale, at which kinetic energy is converted to heat by dissipation mechanisms such as viscosity. For fully-developed turbulent flows with pure Newtonian fluids, the turbulence fluctuation energy transfer from large to small scales at a constant rate through the inertial range, called energy cascade, which is a definitive feature of fluid turbulence. The first question we ask is how does the existence of polymers alter this energy cascade. Based on a seminal work by Tabor & de Gennes in 1986, we proposed a theory on the energy flux into the elastic degrees of freedom of the polymer chains. This elastic energy flux, which increases as length scale decreases, gradually reduces the energy transferred to smaller scales through turbulence cascade and hence suppresses small scale fluctuations. The balance of the elastic energy flux and the turbulence energy cascade gives an elastic length scale, which describes the effect of polymer elasticity on turbulence in the inertial range. Predictions of this new “energy flux balance theory” agree excellently with our experimental results. We further studied the effect of polymers on both the large scales, i.e., the velocity fluctuations, and small scales, represented by the acceleration fluctuations. These quantities are also of direct importance to engineering applications as they are related to the force and pressure fluctuations. Our results confirm previous observations that both the acceleration fluctuation a and the velocity fluctuation u of the flow are suppressed when the polymer additives are present and the suppression effect on a is much stronger. In addition, we found that polymer additives enhance the anisotropy of the flow at small-scales, but do not affect the anisotropy at large-scale very much. These results are qualitatively in agreement with our energy flux balance theory, which predicts that only sales smaller than a critical scale are affected by the polymer additives. We are continuing the work in this project by investigating the existence of a critical concentration, a prediction by the energy flux balance theory, and also studying the Lagrangian properties in turbulent flows with and without polymers.
Publications
- 2013. Elastic energy flux by flexible polymers in fluid turbulence. Phys. Rev. Lett. 111:024501
H.-D. Xi, E. Bodenschatz, and H. Xu
- 2013. Generation of Lagrangian intermittency in turbulence by a self-similar mechanism. New J. Phys. 15:055015
M. Wilczek, H. Xu, N. T. Ouellette, R. Friedrich, and E. Bodenschatz
(See online at https://doi.org/10.1088/1367-2630/15/5/055015) - 2013. Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow. Phys. Fluids, 25:035101
A. Pumir, E. Bodenschatz, and H. Xu
(See online at https://doi.org/10.1063/1.4795547) - 2014. Effects of polymer additive on turbulent bulk flow: The polymer concentration dependence. Y. Zhou et al. (eds.), Lecture Notes in Mechanical Engineering: Fluid-Structure-Sound Interactions and Control, pp. 57–62
H.-D. Xi, H. Xu, and E. Bodenschatz
- 2014. Flight-crash events in turbulence. Proc. Natl. Acad. Sci. USA, May 27, 2014. 111 (21) 7558-7563
H. Xu, A. Pumir, G. Falkovich, E. Bodenschatz, M. Shats, H. Xia, N. Francois, and G. Boffetta
(See online at https://doi.org/10.1073/pnas.1321682111)
