PhantomCloud® is an advanced multi-bubble dynamics code used to track the dynamics and motion of bubbles interacting with each other and with a background flow field. PhantomCloud® is a part of the Discrete Singularities Model (DSM) module of Dynaflow’s 3DynaFS code. PhantomCloud® uses the Keller-Herring-Rayleigh-Plesset spherical bubble dynamics model along with the Johson-Hsieh equation for bubble motion and incorporates the interaction effects of other bubbles and surrounding medium in the flow domain through pressure and velocity coupling. The pressure/velocity field encountered by an individual bubble is thus a combination of the background pressure/velocity and the pressure/velocity exerted by all the bubbles surrounding the bubble in consideration. Some of the key features of PhantomCloud®© include:

  • Accounting for non-uniformities of the bubble encountered pressure/velocity using a bubble Surface-Averaged Pressure (SAP) scheme.
  • An energy loss model to account for the loss in bubble energy during bubble oscillations.
  • Fluid structure interaction capabilities enabled through coupling with structure solvers.

Since PhantomCloud®© uses a singularity method approach, it is a much faster solver compared to 3DynaFS-BEM; which is Boundary Element Method based and enables description of fine bubble shape details. Even though the PhantomCloud®©  model cannot predict the bubble shapes like 3DynaFS-BEM, validation studies have revealed that the PhantomCloud®© solver is very good in capturing the accurate equivalent bubble radii (volume), the motion of bubbles (position and velocity), resulting changes in the field quantities (pressure, velocity) and the overall flow physics. The figure below shows validation of PhantomCloud®© for a bubble near a free surface. In this case, the boundary is replaced by a second image bubble which is not in phase with the main bubble. PhantomCloud®© is capable of describing the dynamics of the bubbles (i.e. period of oscillation and position) even when they are very close to each other. The predictions are as good as using a full description of the bubble shape with 2DynaFS and compare very well with the experimental observations obtained with Dynaflow’s spark generated bubbles near a free surface. The only region where PhantomCloud®© fails is when the bubble is located at a distance less than 0.5 Rmax below the free surface, which actually corresponds to the bubble venting from the free surface.


PhantomCloud®© is ideally suited for studying bubble cloud behavior and for modeling multi-airgun interactions and signatures and their effects on nearby structures. The animation below demonstrates how the behavior of a bubble cloud subjected to an acoustic field can be captured using PhantomCloud®©. The figure next to the animation shows plots of radius versus time for all the bubbles present in the cloud. 

The Figure below shows a comparison of the monitored field pressure between PhantomCloud®© and Experiments for a multi-airgun interaction case.