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64<br />
A Shell-Model Study of Turbulent Drag Reduction by Polymer<br />
Additives<br />
Emily S.C. Ching a<br />
The addition of long-chain polymers to turbulent flows can result in a significant<br />
reduction of the friction drag. This intriguing phenomenon was discovered more than<br />
fifty years ago but many fundamental aspects remain poorly understood. Recent direct<br />
numerical simulations of the finitely extensible nonlinear elastic-Peterlin (FENE-P)<br />
model equations of viscoelastic flows demonstrated that drag reduction also appears<br />
in homogeneous and isotropic turbulence. The FENE-P equations were further<br />
simplified to a shell model of viscoelastic flows. Using this shell model, we<br />
understand 1 two main features observed in experiments, namely, the onset of drag<br />
reduction and the maximum drag reduction asymptote. Moreover, we are able to<br />
recapture 2 the essence of the phenomenon of drag reduction by replacing the<br />
polymers with an effective scale-dependent viscosity.<br />
This work is supported by the Hong Kong Research Grants Council (CUHK<br />
400304).<br />
a Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.<br />
1<br />
Benzi et al., Phys. Rev. Lett. 92, 078302 (2004).<br />
2<br />
Benzi et al., Phys. Rev. E 70, 026304 (2004).
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