Abstract
This chapter is devoted to the dynamics of isotropic turbulence in dilute polymer solutions. Governing equations associated to the very popular FENE-P rheological model are exhaustively discussed. The three main physical regimes are discussed in both physical and spectral space, along with associate kinetic and elastic energy cascades.
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Notes
- 1.
This model is formally equivalent to a linearized model for MagnetoHydroDynamics, Aflven waves being replaced by elastic waves. It also predicts equipartition of kinetic and elastic energy, which is not reported in non linear DNS results. This equilibrium shares many features of the equilibrium between kinetic and acoustic energy found in linearized theory for weakly compressible isentropic turbulence, see Sect. 13.2.2.
References
Balkovsky, E., Fouxon, A., Lebedev, V.: Turbulence of polymer solutions. Phys. Rev. E 64, 056301 (2001)
Berti, S., Bistagnino, A., Boffetta, G., Celani, A., Musacchio, S.: Small-scale statistics of viscoelastic turbulence. Europhys. Lett. 76, 63–69 (2006)
Cai, W.H., Li, F.C., Zhang, H.N.: DNS study of decaying homogeneous isotropic turbulence with polymer additives. J. Fluid Mech. 665, 334–356 (2010)
Cai, W.H., Li, F.C., Zhang, H.N.: DNS study of the interaction between the polymer effect and velocity gradient tensor in decaying homogeneous isotropic turbulence. Chin. Phys. B 20, 124702 (2011)
Casciola, C.M., De Angelis, E.: Energy transfer in turbulent polymer solutions. J. Fluid Mech. 581, 419–436 (2007)
De Angelis, E., Casciola, C.M., Benzi, R., Piva, R.: Homogeneous isotropic turbulence in dilute polymer solutions. J. Fluid Mech. 531, 1–10 (2005)
Dubief, Y., Terrapon, V.E., Soria, J.: On the mechanism of elasto-inertial turbulence. Phys. Fluids 25, 110817 (2013)
Fouxon, A., Lebedev, V.: Spectra of turbulence in dilute polymer solutions. Phys. Fluids 15, 2060–2072 (2003)
Groisman, A., Steinberg, V.: Elastic turbulence in a polymer solution flow. Nature 405(6872), 53–55 (2000)
Horiuti, K., Matsumoto, K., Fujiwara, K.: Remarkable drag reduction in non-affine viscoelastic turbulent flows. Phys. Fluids 25, 015106 (2013)
Jin, S., Collins, L.R.: Dynamics of dissolved polymer chains in isotropic turbulence. New J. Physics 9, 360 (2007)
Li, F.C., Cai, W.H., Zhang, H.N., Wang, Y.: Influence of polymer additives on turbulent energy cascading in forced homogeneous isotropic turbulence studied by direct numerical simulations. Chin. Phys. B 21, 114701 (2012)
Liberzon, A., Guala, M., Kinzelbach, W., Tsinober, A.: On turbulent kinetic energy production and dissipation in dilute polymer solutions Phys. Fluids 18, 125101 (2006)
Lumley, J.L.: Turbulence in NonNewtonian fluids. Phys. Fluids 7, 335–337 (1964)
Ouellette, N.T., Xu, H., Bodenschatz, E.: Bulk turbulence in dilute polymer solutions. J. Fluid Mech. 629, 375–385 (2014)
Perlekar, P., Mitra, D., Pandit, R.: Manifestations of drag reduction by polymer additives in decaying, homogeneous, isotropic turbulence. Phys. Rev. Lett. 97, 264501 (2006)
Perlekar, P., Mitra, D., Pandit, R.: Direct Numerical Simulations of statistically steady, homogeneous, isotropic fluid turbulence with polymer additives. Phys. Rev. E 82, 066313 (2010)
Sreenivasan, K., White, C.M.: The onset of drag reduction by dilute polymer additives, and the maximum drag reduction asymptote. J. Fluid Mech. 409, 149–164 (2000)
Valente, P.C., da Silva, C.B., Pinho, F.T.: The effect of viscoelasticity on the turbulent kinetic energy cascade. J. Fluid Mech. 760, 39–62 (2014)
Valente, P.C., da Silva, C.B., Pinho, F.T.: Energy spectra in elasto-inertial turbulence. Phys. Fluids 28, 075108 (2016)
Vincenzi, D., Perlekar, P., Biferale, L., Toschi, F.: Impact of the Peterlin approximation on polymer dynamics in turbulent flows. Phys. Rev. E 92, 053004 (2015)
Vonlanthen, R., Monkewitz, P.A.: Grid turbulence in dilute polymer solutions: PEO in water. J. Fluid Mech. 730, 76–98 (2013)
Xi, H.D., Bodenschatz, E., Xu, H.: Elastic energy flux by flexible polymers in fluid turbulence. Phys. Rev. Lett. 111, 024501 (2013)
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Sagaut, P., Cambon, C. (2018). Isotropic Turbulence with Coupled Microstructures. I: Visco-Elastic Turbulence. In: Homogeneous Turbulence Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-73162-9_5
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