![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
In simulating two-phase flows, the volume-of-fluid (VOF) method has the advantage of mass conservation while with the level-set (LS) method, the surface tension force can be calculated more accurately. In this study, we present a coupling method which combines the advantages of both methods. The volume-of-fluid (VOF) method adopted in the calculation is the conservative interpolation scheme for interface tracking method proposed recently by the authors. Based on the location of the interface calculated from the VOF, the LS function is obtained by solving the equation used in the LS method for re-initialization without needing to solve its advection equation. A high-resolution-bounded scheme within the frame of finite-volume methods is used to solve the re-initialization equation. This scheme is verified by considering a variety of interface geometries. A circular bubble at equilibrium is used to assess the coupled LS and VOF method by examining the spurious currents generated in the bubble. Three-dimensional calculations are conducted to study the rising of a bubble in the quiescent water.
Nomenclature
| d | = | diameter of bubble |
| = | distance function | |
| Eo | = | Eotvos number |
| = | surface tension force | |
| = | gravitational acceleration | |
| H(φ) | = | smoothed Heaviside function |
| Mo | = | Morton number |
| = | unit normal vector | |
| P | = | pressure |
| Re | = | Reynolds number |
| S(φ0) | = | sign function |
| = | surface vector for the jth cell face | |
| = | surface vector for the wetted cell face j | |
| = | velocity vector | |
| = | velocity vector on the jth cell face | |
| α | = | volume-of-fluid function |
| δ(φ) | = | Dirac delta function |
| = | distance vector from upstream centroid U to face f | |
| Δh | = | cell size |
| Δt | = | time-step size |
| Δv | = | cell volume |
| ϵ | = | numerical interface width |
| φ | = | level set function |
| φo | = | initial value of the LS |
| γ | = | flux limiter |
| κ | = | interface curvature |
| μ | = | fluid viscosity |
| ρ | = | fluid density |
| σ | = | surface tension |
| = | viscous stress | |
| Subscripts | = | |
| Ci | = | ith neighboring cell |
| f | = | cell face |
| g | = | gas phase |
| j | = | jth cell face |
| l | = | liquid phase |
| ni | = | ith vertex node |
| P | = | primary cell |
| Superscripts | = | |
| n, n + 1 | = | time-step numbers |
| n, o | = | new and old time steps |
| w | = | wetted area of the cell face |
| U | = | upstream cell |
Nomenclature
| d | = | diameter of bubble |
| = | distance function | |
| Eo | = | Eotvos number |
| = | surface tension force | |
| = | gravitational acceleration | |
| H(φ) | = | smoothed Heaviside function |
| Mo | = | Morton number |
| = | unit normal vector | |
| P | = | pressure |
| Re | = | Reynolds number |
| S(φ0) | = | sign function |
| = | surface vector for the jth cell face | |
| = | surface vector for the wetted cell face j | |
| = | velocity vector | |
| = | velocity vector on the jth cell face | |
| α | = | volume-of-fluid function |
| δ(φ) | = | Dirac delta function |
| = | distance vector from upstream centroid U to face f | |
| Δh | = | cell size |
| Δt | = | time-step size |
| Δv | = | cell volume |
| ϵ | = | numerical interface width |
| φ | = | level set function |
| φo | = | initial value of the LS |
| γ | = | flux limiter |
| κ | = | interface curvature |
| μ | = | fluid viscosity |
| ρ | = | fluid density |
| σ | = | surface tension |
| = | viscous stress | |
| Subscripts | = | |
| Ci | = | ith neighboring cell |
| f | = | cell face |
| g | = | gas phase |
| j | = | jth cell face |
| l | = | liquid phase |
| ni | = | ith vertex node |
| P | = | primary cell |
| Superscripts | = | |
| n, n + 1 | = | time-step numbers |
| n, o | = | new and old time steps |
| w | = | wetted area of the cell face |
| U | = | upstream cell |
Acknowledgments
This work was supported by the Ministry of Science and Technology, Republic of China, under the Contract Number MOST 104-2221-E009-152.