PTV and POD analysis of the instabilities in a quasi two-dimensional convective flow

Abstract

An investigation is made of the motion of fluid in a transparent rectangular vessel, heated beneath by a line source, using Particle-Tracking Velocimetry. The control parameters are the Rayleigh number (computed by the power supplied to the system), the Prandtl number and the aspect ratio (height to width ratio) of the vessel. When convection starts, two counter rotating rolls occur. For certain values of the control parameters, the flow becomes unstable and the rolls start to oscillate on a plane orthogonal to the line source (natural swaying motion). The Lagrangian description of the velocity fields (i.e. particle trajectories), is extracted. Data are converted from Lagrangian to Eulerian framework and the time evolution is analysed. Perturbations and instabilities of the velocity field (due to thermal anomalies), are observed. They are related to the natural swaying motion of the rolls. The Fourier decomposition is applied in several points of the grid to obtain a spatial portrait of the energy distribution in frequency domain. By means of Proper Orthogonal Decomposition a complete set of orthonormal functions (modes) is evaluated and the flow field is reconstructed using a small number of modes: POD theory states that these modes retain a greater amount of energy than that of any other possible decomposition. Reconstructed velocity fields and the original ones are compared. In this experiment the first eight modes are found to retain more than 80% of the flow kinetic energy.