Enhanced and reduced heat transport in turbulent thermal convection with polymer additives

Abstract

We present an experimental study of turbulent Rayleigh-Bénard convection with polymer additives made in two convection cells, one with a smooth top and bottom plates and the other with a rough top and bottom plates. For the cell with smooth plates, a reduction of the measured Nusselt number (Nu) was observed. Furthermore, the amount of Nu reduction increases with increasing polymer concentration (c), reaching ~12% for c = 120 ppm and an apparent leveling off thereafter. For the cell with rough plates, however, an enhancement (~4%) of Nu was observed when the polymer concentration is greater than 120 ppm. This increase in Nu is corroborated by an increased large-scale circulation (LSC) velocity in the same cell when polymers are added. In contrast, the LSC velocity in the smooth cell is found to be essentially the same with and without polymers. It is further found that in the smooth cell the rms values of the global Nu, σ(Nu), and that of the local temperature, σ(T), both exhibit similar dependence on c as Nu itself. In contrast, σ(Nu) and σ(T) in the rough cell are found to be essentially independent of c.

Heat transport modification by finitely extensible polymers in laminar boundary layer flow

“…In Dubief (2010), a transition from heat reduction to heat enhancement has been observed numerically when b 2 becomes small. We speculate that such a transition is similar in nature to the one observed experimentally by Wei, Ni & Xia (2012), and that it can be explained by our generalized Prandtl-Blasius-Pohlhausen boundary layer theory for the FENE-P polymers presented in this paper.…”

“…This value of Pr s corresponds to that of water at approximately 40 • C. To connect to turbulent RB convection, Re s plays the role of the Reynolds number Re of the large-scale mean flow, which is related to the Rayleigh number Ra by Re = 0.085Ra 0.455 for water at moderate Ra (Grossmann & Lohse 2002); thus, Re s = 4900 corresponds to Ra ∼ 10 10 . These values of Pr s and Re s are chosen to be close to those in the experimental studies (Ahlers & Nikolaenko 2010;Wei, Ni & Xia 2012).…”

“…Thus, ν sol (c) is given by the zero-shear viscosity ν 0 , and ν sol (c)/ν s = 1/(1 − γ ). Using the experimental measurements from Wei, Ni & Xia (2012), we calculate γ as a function of c and show the results in figure 7. It can be seen that γ increases with c. As we are interested in polymer concentrations of the order of a few hundreds of p.p.m.…”

“…More recently, using a convection cell with rough top and bottom plates, Wei, Ni & Xia (2012) showed that when polymers are added to water at 10 8 < Ra 10 10 , heat transport is first reduced and then enhanced when the polymer concentration is increased. An enhancement in heat transport has also been observed numerically (Dubief 2010) in DNS of turbulent RB convection by polymers described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) model (Bird et al 1987) with suitable parameters.…”

Magnetic-field effect on thermal convection of a nematic liquid crystal at large Rayleigh numbers

“…However, recently a significant interest has developed in turbulent convection of complex fluids, including, for instance, dilute polymer solutions (Ahlers & Nikolaenko 2010;Benzi, Ching & De Angelis 2010;Boffetta et al 2010;Benzi, Ching & Chu 2011;Wei, Ni & Xia 2012) and nano-fluids (Ni, Zhou & Xia 2011). Here we contribute to this emerging field by reporting on RBC of a nematic liquid crystal (NLC) (Chandrasekhar 1992;Khoo 2007) at large Rayleigh numbers and on the effect of a vertical magnetic field H upon this system.…”