Free Surface Flow

There are many problems in fluid dynamics that involve the analysis of two-phase flows.  These flows are characterized by fluids which have large disparities in density and their relative motion is the essence of the multi-phase phenomenon.  Fluid surface tension plays a dominant role in the manner in which the fluids interact and largely determines the nature of the interface between fluids. Examples include droplets dynamics, tank sloshing, capillary motion, hydrodynamic stability and many others.

The Free Surface option provided in STORM predicts the motion of fluid interfaces based on the solution of a conservative transport equation for the fractional volume of fluid (VOF) defined as

Where V represents the volume occupied by the fluid within the control volume under consideration.  The function F obeys the equation

The solution to which provides information on the position and shape of the interface.  The local mixture density is then computed by

The momentum equation is also modified to contain an additional source terms relating to gravity, the curvature of the interface, and the fluid surface tension [1].  When the equation for F is solved within a computational cell, changes in F within the cell are recast as fluxes of  F across the cell faces.  To preserve the sharp definition of the free surface, a high-order TVD scheme [2] with damping is used.

References

[1] Brackbill, J,U., Kothe, D.B., and Zemach, C., “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” Journal of Computational Physics, Vol. 39, P.201,1981.

[2] Chakravarthy, S.R., and Osher, S., “A New Class of High Accuracy TVD Schemes for Hyperbolic Conversation Laws,” AIAA Paper 85-0363, January, 1985.