Effect of Polymer Additives on Heat Transport in Turbulent Thermal Convection

In this Letter, we explore the possible effects of polymer additives on heat transport in turbulent thermal convective flows. Using both direct numerical simulations and shell-model calculations, we show that polymer additives can significantly enhance the heat transport in homogeneous turbulent thermal convection, which mimics the bulk of turbulent Rayleigh-Bénard convection. We also discuss the implication of our results for turbulent Rayleigh-Bénard convection, in which there are boundary layers in addition to the central bulk.

Figure 1

$\mathrm{Nu}/{\mathrm{Nu}}_0$ (circles) and $[T_{\mathrm{rms}}/T_{\mathrm{rms}0}{]}^{3/2}$ (triangles) (see text for definitions) as a function of De obtained in the DNS. The largest error bars are shown.

Figure 2

$\mathrm{Nu}/{\mathrm{Nu}}_0$ as a function of $\tau$ in the shell model with $\alpha g\beta =1$, ${\nu }_s=\kappa ={10}^{-6}$. The red dashed curve is the ${\tau }^{3/2}$ fit for small $\tau$ and the blue solid curve is the $1/\tau$ fit for large $\tau$. The error bar shown is almost the size of the symbols. Inset: $\mathrm{Nu}/{\mathrm{Nu}}_0$ as a function of $1/\tau$ to highlight the $1/\tau$ behavior at large $\tau$.

Figure 3

The length scales $l_0$ (squares) and $l_T$ (circles), normalized by their corresponding Newtonian values, obtained in DNS (left panel) and in the shell model (right panel). The errors are about 10% in DNS and 3% in the shell model.

Figure 4

Two-dimensional cross section of the temperature fluctuation obtained in DNS for Newtonian flow without polymers and with polymers calculated at the largest De.

Figure 5

Nu as a function of Ra in the shell model with Ra increased in two different ways: (i) by decreasing ${\nu }_s=\kappa$ while keeping $\beta$ fixed for the case with (circles) and without (squares) polymers, and (ii) by keeping ${\nu }_s=\kappa$ fixed and increasing $\beta$ for the case with polymers (triangles).