Bullet Time Taylor-Couette: Unwrapping the 360 Degree Field of View for Rheoscopic Flow Visualization

Abstract

The circular Taylor-Couette flow is one of the archetypical model systems for the study of flow transitions and dynamic pattern formation in experimental fluid dynamics. The emergence of the internal vortical flow structures are commonly visualized through a rheoscopic flow visualization, while their spatio-temporal dynamics can be extracted by the construction of a space-time diagram using a single camera. Although the latter is an effective method to map the various flow regimes for different inner and outer cylinder rotations, it suffers from limitations in the frame rate while the full extent of the azimuthal vortex structure along the circumference, together with its dynamic evolution through space and time, remains unclear. In this work, we perform the full 360-degree field of view panorama imaging for the rheoscopic flow visualization of the azimuthal vortex structure that wraps around the circumference. We use a set of 12 GoPro cameras that are commercially available and can be triggered remotely. We calibrate and position our cameras using methods from computer vision while we synchronize their audio channels at an inter-frame precision much greater than the frame rate. We unwrap the physical coordinates along the circumference of the outer cylinder through texture mapping its surface using a spatially weighted image interpolation and present a single representation of the azimuthal vortex structure from the rheoscopic flow visualization. We validate our methods within a submillimeter precision and showcase the application to study the steady-state and transient dynamics of a single- phase wavy vortex flow. Furthermore, we discuss the current limitations as we add neutrally buoyant PMMA particles at increasing volume fractions up to 30 %. Our methods allow us to fully decouple space and time, and study the dynamic pattern formation at bullet time accuracy.