Abstract
The numerical modeling of two-phase flows is a challenging task especially when the density and viscosity ratios of the fluid in different phases are high. Moreover, the complexity increases in the surface tension dominant flows. Precise modeling of the surface tension force is essential in order to capture the flow physics accurately. Different methods have been developed to model such complex flows. Here, we describe the Coupled Level Set and Volume-of-Fluid method to model the two-phase flows which is very efficient in handling complex interface topology. The methodology has been tested with the real fluid flow problems and is found to be robust and accurate in capturing the two-phase flows.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Abbreviations
- D :
-
Diameter (m)
- D :
-
Distance of transition region (m)
- F :
-
Volume fraction (dimensionless)
- G :
-
Gravitational acceleration (m/s2)
- H :
-
Heaviside function
- N :
-
Normal vector (unitless)
- P :
-
Pressure (N/m2)
- T :
-
Time (s)
- \( T_{v} \) :
-
Deformation tensor (s−1)
- U :
-
Velocity (m/s)
- X :
-
Horizontal coordinate (m)
- Y :
-
Vertical coordinate (m)
- \( \delta_{s} \) :
-
Interface delta function (dimensionless)
- \( \delta \) :
-
Numerical thickness of the interface (dimensionless)
- \( \phi \) :
-
Level Set function (dimensionless)
- \( \kappa \) :
-
Mean curvature (m−1)
- \( \mu \) :
-
Dynamic viscosity (Ns/m2)
- \( \rho \) :
-
Density (kg/m3)
- \( \sigma \) :
-
Surface tension (N/m)
- \( \Delta t \) :
-
Time step (s)
- \( \Delta x \) :
-
Grid spacing in x-direction (m)
- \( \Delta y \) :
-
Grid spacing in y-direction (m)
- 1:
-
Fluid 1
- 2:
-
Fluid 2
- F :
-
Father drop
- N :
-
Nth time level
- M :
-
Mother drop
- ^:
-
Unit vector
References
Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354 (1992)
Harlow, F.H., Welch, J.E.: Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189 (1965)
Chang, Y.C., Hou, T.Y., Meriman, B., Osher, S.: A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. J. Comput. Phys. 464(124), 449–464 (1996)
Center for Applied Science Computing, Lawrence Livermore National Laboratory, USA: Hypre 2.0.0 user manual, silver Ed (2006)
Puckett, E.G., Almgren, A.S., Bell, J.B., Marcus, D.L., Rider, W.J.: A high-order projection method for tracking fluid interfaces in variable density incompressible flows. J. Comput. Phys. 130(2), 269–282 (1997)
Rider, W.J., Kothe, D.B.: Reconstructing volume tracking. J. Comput. Phys. 141(2), 112–152 (1998)
Gerlach, D., Tomar, G., Biswas, G., Durst, F.: Comparison of volume-of-fluid methods for surface tension-dominant two-phase flows. Int. J. Heat Mass Transf. 49, 740–754 (2006)
Strang, G.: On the construction and comparison of different schemes. SIAM J. Numer. Anal. 5(3), 506–517 (1968)
Sussman, M., Puckett, E.G.: A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J. Comput. Phys. 162(2), 301–337 (2000)
Son, G., Hur, N.: A coupled level set and volume-of-fluid method for the bouyancy driven motion of fluid particles. Numer. Heat Transf. Part B Fundam. 42(6), 523–542 (2002)
Son, G.: Efficient implementation of a coupled level-set and volume-of-fluid method for threedimensional incompressible two-phase flows. Numer. Heat Transf. Part B Fundam. 43(6), 549–565 (2003)
Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S., Zanetti, G.: Modeling merging and fragmentation in multiphase flows with SURFER. J. Comput. Phys. 113(1), 134–147 (1994)
Zhang, F.H., Li, E.Q., Thoroddsen, S.T.: Satellite formation during coalescence of unequal size drops. Phys. Rev. Lett. 102, 104502 (2009)
Bouwhuis, W., Huang, X., Chan, C.U., Frommhold, P.E., Ohl, C.D., Lohse, D., Snoeijer, J.H., van der Meer, D.: Impact of a high-speed train of microdrops on a liquid pool. J. Fluid Mech. 792, 850–868 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Deka, H., Biswas, G., Dalal, A. (2020). A Coupled Level Set and Volume-of-Fluid Method for Modeling Two-Phase Flows. In: Biswal, B., Sarkar, B., Mahanta, P. (eds) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-0124-1_7
Download citation
DOI: https://doi.org/10.1007/978-981-15-0124-1_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-0123-4
Online ISBN: 978-981-15-0124-1
eBook Packages: EngineeringEngineering (R0)