Large-scale volumetric flow measurement in a pure thermal plume by dense tracking of helium-filled soap bubbles

Abstract

We present a spatially and temporally highly resolved flow measurement covering a large volume (~0.6 m³) in a pure thermal plume in air. The thermal plume develops above an extended heat source and is characterized by moderate velocities (U ~ 0.35 m/s) with a Reynolds number of $\text{Re} \sim 500$ and a Rayleigh number of ${\text{Ra}}\sim 10^{6}$. We demonstrate the requirements and capabilities of the measurement equipment and the particle tracking approach to be able to probe measurement volumes up to and beyond one cubic meter. The use of large tracer particles (300 μm), helium-filled soap bubbles (HFSBs), is crucial and yields high particle image quality over large-volume depths when illuminated with arrays of pulsed high-power LEDs. The experimental limitations of the HFSBs—their limited lifetime and their intensity loss over time—are quantified. The HFSBs’ uniform particle images allows an accurate reconstruction of the flow using Shake-The-Box particle tracking with high particle concentrations up to 0.1 particles per pixel. This enables tracking of up to 275,000 HFSBs simultaneously. After interpolating the scattered data onto a regular grid with a Navier–Stokes regularization, the velocity field of the thermal plume reveals a multitude of vortices with a smooth temporal evolution and a remarkable coherence in time (see animation, supplementary data). Acceleration fields are also derived from interpolated particle tracks and complement the flow measurement. Additionally, the flow map, the basis of a large class of Lagrangian coherent structures, is computed directly from observed particle tracks. We show entrainment regions and coherent vortices of the thermal plume in the flow map and compute fields of the finite-time Lyapunov exponent.