DF_MultiSap©© is an advanced multi-bubble dynamics code suitable to track a distribution of nuclei in a CFD computed or experimental measured flow field. DF_MultiSap©© uses a spherical bubble dynamics model which incorporates knowledge acquired from studying bubble dynamics in complex vortical flow fields using the axisymmetric 2DynaFS© CFD code or the three-dimensional 3DynaFS© code. DF_MultiSap©© is suitable for studying tip vortex and traveling bubble cavitation inception and bubbly flows involving bubble entrainment. DF_MultiSap©© uses a Surface-Averaged Pressure (SAP) scheme to improve the classical spherical bubble dynamics model which is based on the Rayleigh-Plesset equation. In addition, a pressure term acting on bubble surface due to slip velocity between the liquid and the bubble is also taken into account. To include the energy losses due to acoustic emission during the bubble dynamics an option allows solution of Gilmore's equation to replace the Rayleigh-Plesset equation. Several advanced features such as inclusion of gas diffusion and bubble splitting following its elongation are also available in DF_MULTI _SAP©.

DF_MultiSap©© is a Lagrange-based scheme which tracks bubble nuclei along their trajectories and record acoustic signals generated by the bubbles' volume oscillations. DF_MultiSap©© is capable of simulating multiple bubble dynamics for a given nuclei size distribution in the liquid. DF_MultiSap©© can work as standalone software with the flow field provided by the user and can also work as a module coupled with a liquid phase flow solver. An coupled two-phase flow model can be achieved by coupling DF_MultiSap©© with a flow solver.

DF_MultiSap©© is very flexible such that it can be easily coupled with Navier-Stokes solvers based on different numerical schemes including finite difference, finite volume, and finite element methods. It can be incorporated with different flow solvers grid systems including structured grids, unstructured grids, and Chimera overset grids. DF_MULTI _SAP© has been successfully coupled with Navier-Stokes codes UNCLE(1), and coupling with other CFD codes for Navy users such as CFDIOWA-SHIP(2) and Ins3D(3) is underway. It has been coupled to the commercial code Fluent. An add-on package of DF_MultiSap©© in Fluent is available as Discrete Bubble Model (DBM).

(1) Developed by Mississippi State University
(2) Developed by the University of Iowa
(3) Developed by NASA Ames

Cavitation Event Bubble growth and collapse while being captured by a vortex
Multiple Bubbles Dynamics and Acoustic Signals
Cavitating Bubbles on the Blade surfaces and in the tip of a Rotating Propeller
Bubble Entrainment and size change by a Rotating Propeller


  1. “Scaling of Tip Vortex Cavitation Inception Noise with a Bubble Dynamics Model Accounting for Nuclei Size Distribution,” Hsiao, C.-T., Chahine, G.L., ASME Journal of Fluid Engineering, Vol. 127, pp. 55-65, January 2005
  2. “Prediction of Vortex Cavitation Inception Using Coupled Spherical and Non-Spherical Models and Navier-Stokes Computations,” Hsiao, C.-T., Chahine, G.L., Journal of Marine Science and Technology, Vol.8, No 3, pp 99-108, 2004.
  3. “Scaling Effects on Prediction of Cavitation Inception in a Line Vortex Flow,” Hsiao, C.-T., Chahine, G.L., Liu, H., Journal of Fluid Engineering, Vol. 125, pp.53-60, 2003.
  4. “Study of Tip Vortex Cavitation Inception Using Navier-Stokes Computation and Bubble Dynamics Model,” Hsiao, C.-T. and Pauley, L.L., ASME Journal of Fluid Engineering, Vol. 121, pp. 198-204, 1999.

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Multiple Bubble Dynamics Model