Quantitative shadowgraphy for heat transport measurement in turbulent thermal convection

Abstract

We report a quantitative shadowgraphy for measuring both the vertical and horizontal Nusselt numbers ($N{u}_V$ and $N{u}_H$) in turbulent thermal convection. An exact relationship between $N{u}_V$ and the shadowgraph intensity (and a similar one for $N{u}_H$) is derived for the first time. We use a quasi-two-dimensional Rayleigh–Bénard convection cell where an effective horizontal buoyancy is introduced by tilting as a test platform to validate the method. In addition, we conduct complementary direct numerical simulations to confirm the validity of this new method. With increasing horizontal to vertical buoyancy ratio, the measured vertical Nusselt number shows a non-monotonic behavior, whereas the horizontal Nusselt number first increases from approximately zero and then saturates to a value being an order of magnitude smaller than $N{u}_V$. A detailed analysis of the transport properties and flow fields identifies a plume-controlled regime, a transitional regime, and a shear-dominated regime for the present system.