Experimental determination of first bifurcations to unsteady natural convection in a differentially-heated cavity tilted from 0° to 180°

Abstract

This paper focuses on an experimental study of the natural convection unsteadiness occurring in an air-filled cavity having two opposite walls respectively heated and cooled at constant and uniform temperature. The other walls are made of insulating materials. The cavity can be tilted in order to obtain an angle of inclination, θ, from 0° (heating from below) to 180° (heating from above). For these extreme angles, the two active walls are horizontal. For each investigated angle of inclination, instantaneous temperature measurements have been carried out in selected areas where temperature signal should became unsteady first, when the temperature difference between the two plates was increased. The location where fluctuations are close to the maximum was then identified. A critical value of temperature difference, ΔT, was calculated after extrapolation of PSD obtained for several values of ΔT. It was highlighted, that for ΔT lower than this critical value, the power spectral density was close to 0 and grew like (ΔT)0.5 for ΔT greater than this critical value. The same critical value was obtained when increasing or decreasing ΔT, showing that it corresponds to a supercritical bifurcation. Spectral analyses reveal that for all the angles of tilt, the first bifurcation appears at the specific and unique value 8.5×107 of a modified Rayleigh number, defined from H∗ equal to H/[tan(θ/2)]0.5, with H referring to the height of the cavity. In addition, for all the tilt angles, the measured frequencies describe the successive bifurcations occurring until turbulence is encountered with the temperature increase. The exception to this is the angle of 180° where the flow remains always in a steady state. Visualizations have been performed in order to characterise flow patterns obtained between two successive bifurcations. Different class of natural convection flows were then identified, showing Rayleigh–Bénard flow types, boundary layer flows, or typical structures obtained with stably stratified fluids. Time oscillations are also due to completely different modes of unsteadiness: thermal instabilities (gravity or Kelvin – Helmholtz waves) or dynamical instabilities (Tollmien–Schlichting progressive waves).