Experimental study of the global flow-state transformation in a rectangular Rayleigh-Bénard sample. (November 2018) - Horstmann, G.M.; Schiepel, D.; Wagner, C.
Highlights: Large-scale flow structures were captured three-dimensionally to their full extent. A transformation of the mean flow during the laminar-turbulent transition was found including several distinguishable flow modes. An new procedure allowing an unambiguous determination of the scaling law Re Ra γ is proposed. The global velocity distribution of the flow is described analytically in dependence of the Rayleigh number. Abstract: Large-scale flow structures were measured in a rectangular Rayleigh-Bénard sample of equal length and height of 10 cm and a depth of 2.5 cm . The working fluid was water at a Prandtl number of Pr = 6.9 . Aiming to capture flow structures to their full extent and throughout the entire sample, the three-dimensional (3D) Lagrangian measurement technique 3D-Particle Tracking Velocimetry (3D-PTV) was employed. The study provided direct confirmation that the global mean flow field changes significantly in dependence of the Rayleigh number Ra within the investigated range of 2.1 · 10 6 ⩽ Ra ⩽ 4.5 · 10 8 . Several distinguishable flow states were observed in the laminar-turbulent transition regime complementing the well-known mean wind. A two-dimensional (2D)-mode decomposition revealed a breakdown of the mean wind during the transition phase and its new formation in the turbulent regime. Further, the global distribution of magnitudes of the instantaneous velocity fields was used to extract characteristic velocities in the flow field. It was shown, that the Reynolds-number-dependent scaling law Re ∼ Ra γ can be unambiguously determined by means of directly measured Lagrangian velocities, since the same scaling behavior holds true for all chosen reference velocities. In this context, using the product of a polynomial and an exponential function, the global velocity distribution was described analytically in dependence of Ra and four independent fit parameters in the sub-range 2.8 · 10 7 ⩽ Ra ⩽ 4.5 · 10 8 .