Exploring the Origins of Turbulence in Multiphase Flow Using Compressed Sensing MRI

Ultrafast magnetic resonance imaging, employing spiral reciprocal space sampling and compressed sensing image reconstruction, is used to acquire velocity maps of the liquid phase in gas-liquid multiphase flows. Velocity maps were acquired at a rate of 188 frames per second. The method enables quantitative characterization of the wake dynamics of single bubbles and bubble swarms. To illustrate this, we use the new technique to demonstrate the role of bubble wake vorticity in driving bubble secondary motions, and in governing the structure of turbulence in multiphase flows.

Figure 1

(a) Pulse sequence used for ultrafast MRI measurements of multiphase flow, and (b) reciprocal space trajectory. The image acquisition time, AQ, was 2.9 ms. Note that the gradient orientations shown in (a) correspond to a horizontal plane image.

Figure 2

Velocity maps about a single bubble rising freely through stagnant solution. The location of the bubble was identified from the signal intensity maps, and is highlighted by the filled white ellipses. The acquisition rate of these data was 63 fps. The spatial resolution is $390\mu \mathrm{m}\times 586\mu \mathrm{m}$ for a field of view of $20\mathrm{mm}\times 30\mathrm{mm}$.

Figure 3

(a) Example velocity maps recorded immediately under a static bubble of spherically equivalent radius 1.4 mm. These data were acquired at a rate of 63 fps, and at a spatial resolution of $390\mu \mathrm{m}\times 390\mu \mathrm{m}$ for a field of view of $20\mathrm{mm}\times 20\mathrm{mm}$. (b) Schematic of the transverse plane wake structure behind a rising bubble, and definition of coordinate system. (c) The changing direction of bubble motion and secondary wake orientation as a function of time. The antiphase nature of the bubble motion and the wake orientation are consistent with the transverse wake vorticity being directly coupled with bubble secondary motions.

Figure 4

(a) Transverse plane velocity fields during the passage of a swarm of bubbles. Finger-like turbulent structures, resembling those present in single phase turbulence, are evident (as highlighted). (b) Corresponding vorticity maps, which demonstrate the formation of large-scale vortex chains (highlighted) generated by the transverse wake behaviors of passing bubbles. The location of the bubbles was identified from the signal intensity maps, and is highlighted by the filled white ellipses. The vorticity maps were calculated using a 2nd order central difference approximation applied to the in-plane velocity components. These data were acquired at a rate of 63 fps, and at a spatial resolution of $390\mu \mathrm{m}\times 390\mu \mathrm{m}$ for a field of view of $20\mathrm{mm}\times 20\mathrm{mm}$.