Non-intrusive Measurement of the Pressure Field over a Free Rising Bubble in Quiescent Water

The instantaneous pressure field surrounding an air bubble free rising in quiescent water has been successfully measured by using time-resolved planar Particle Image Velocimetry at Reynolds number of 1840, Weber number of 6.48 and Eotvos number of 8.5. The pressure reconstruction was performed using the parallel ray omni-directional integration method. Time-resolved consecutive images with image size of 1K x 1K pixels were acquired at 1000 frames per second using a Photron FastCam SA-Z camera. Analysis shows that the viscous term contributes no more than 1% to the reconstructed hydrodynamic pressure, while the hydrostatic pressure presents a dominant share of the final entire hydro pressure at a magnitude of about 60 times of that of the hydrodynamic part for this bubble rising flow. The ascending motion of the bubble generated vorticity, and vortex rings were shed off the bubble surface. The pressure measurement result was verified by comparing the buoyancy force calculated using the Archimedes' Principle with that obtained through the numerical integration of the reconstructed hydro pressure on the bubble outer surface. Excellent agreement was also achieved by comparing the drag coefficient calculated from the force balance with that calculated using an empirical formula.