Analysis of thermal structures in turbulent Rayleigh-Bénard convection at different aspect ratios using temperature sensitive paint

Kurzfassung

Rayleigh-Bénard convection (RBC), where a horizontal fluid layer of height H is heated from below and cooled from above, is an archetypical model system that covers a variety of flow scenarios ranging from pattern formation just above the convection onset to highly turbulent flows at rather strong thermal driving. Herewith, the aspect ratio Γ = L/H between the lateral extension L and the height H plays a crucial role, as it determines the level of interaction between the convective flow and the geometric constraints. Typical for the turbulent RBC system is the occurrence of large-scale, coherent flow structures. If the aspect ratio is close to unity, i.e. the interaction with the side-walls strong, they are termed large scale circulations (LSC) and renowned for their complex and characteristic dynamics. On the other hand, when the aspect ratio is very high, large scale flow structures evolve that resemble the pattern, which occur just above the onset of convection. While these turbulent superstructures (TSS) have gained much attention recently, little is known about the transition from LSC at small Γ to the TSS at large Γ, and even less so about the associated change of their dynamical behaviour. Hence, in order to study the long-term development of temperature fields at the boundaries of RBC at high spatial and temporal resolution, we adopted the temperature sensitive paint (TSP) method to an RB set-up with quadratic vertical cross section and different aspect ratios. A thin layer of TSP, a chemical where a luminescent complex is embedded in a polyurethane matrix, was applied to the transparent cooling plate of our set-up, allowing us to observe the thermal finger prints of the flow structures. Hereto, we used water as working fluid (Prandtl number Pr = 7.0) and illuminated the TSP by four UV-LED (λab ≈ 395 nm) from different angles. The frequency-shifted, luminescent light of the TSP, whose intensity depends upon the temperature, was detected using a CCD camera, installed centrally above the convection cell. By proper calibration of the luminescence signal, spatially and temporally resolved temperature fields of the TSP layer were measured at aspect ratios between Γ = 4 and Γ = 32 as well as at Rayleigh-numbers between 2.6 × 10^4 ≤ Ra ≤ 1.5 × 10^7. The acquired data allows us to study the transition from the LSC to the TSS, to directly observe the interaction between the small and large-scale turbulent structures as well as to evaluate the spatio-temporal statistics of the underlying temperature fields in the boundary layer. We further analyse and compare the spatial distribution of the thermal structures in order to quantify the level of coherence (order) and longevity among the different scenarios. This work was funded by the priority program Turbulent Superstructures (SPP 1881) of the Deutsche Forschungsgemeinschaft (DFG) - 429432497.