Comparative Experimental Study of Fixed Temperature and Fixed Heat Flux Boundary Conditions in Turbulent Thermal Convection

We report the first experimental study of the influences of the thermal boundary condition on turbulent thermal convection. Two configurations were examined: one had a constant heat flux at the bottom boundary and a constant temperature at the top (CFCT cell); the other had constant temperatures at both boundaries (CTCT cell). In addition to producing different temperature stability in the boundary layers, the differences in the boundary condition lead to rather unexpected changes in the flow dynamics. It is found that, surprisingly, reversals of the large-scale circulation occur more frequently in the CTCT cell than in the CFCT cell, despite the fact that in the former its flow strength is on average 9% larger than that in the latter. Our results not only show which aspects of the thermal boundary condition are important in thermal turbulence, but also reveal that, counterintuitively, the stability of the flow is not directly coupled to its strength.

Figure 1

Top panel: Time series of normalized temperature fluctuations inside the top and bottom plates at $\mathrm{Ra}=1\times {10}^9$ for the CFCT (a) and CTCT (b) cells, respectively. (c) The corresponding PDFs for the data in (a) and (b). (d) The Ra dependence of the normalized temperature standard deviation inside the conducting plates for all the cells. The solid and open symbols are for the data in the large and small cells, respectively. The square and upward-pointing triangle represent the data from the bottom and top plates of the CFCT cells, while the downward-pointing triangle and circle represent the data from the bottom and top plates of the CTCT cells.

Figure 2

Normalized temperature standard deviation vs normalized vertical distance from the bottom plate measured in the CFCT and CTCT cells ($\mathrm{Ra}=1\times {10}^9$). The inset shows an enlarged portion near the boundary.

Figure 3

The compensated Reynolds number as a function of Ra measured in different cells.

Figure 4

Color-coded contour maps of mean velocity field measured in the CFCT (a) and CTCT (b) cells for $\mathrm{Ra}=1\times {10}^9$. The scale bar represents $(U^2+W^2{)}^{1/2}$ in units of $\mathrm{cm}/\mathrm{s}$.

Figure 5

Ra dependence of the reversal frequency $f$. The solid lines are drawn to guide the eyes. Inset: The ratio of $f_{\mathrm{CTCT}}/f_{\mathrm{CFCT}}$.