Generalization of SGIP Surface Tension Force Model in Three-Dimensional Flows and Compare to Other Models in Interfacial Flows
In this paper, the two-dimensional stagger grid
interface pressure (SGIP) model has been generalized and presented
into three-dimensional form. For this purpose, various models of
surface tension force for interfacial flows have been investigated and
compared with each other. The VOF method has been used for
tracking the interface. To show the ability of the SGIP model for
three-dimensional flows in comparison with other models, pressure
contours, maximum spurious velocities, norm spurious flow
velocities and pressure jump error for motionless drop of liquid and
bubble of gas are calculated using different models. It has been
pointed out that SGIP model in comparison with the CSF, CSS and
PCIL models produces the least maximum and norm spurious
velocities. Additionally, the new model produces more accurate
results in calculating the pressure jumps across the interface for
motionless drop of liquid and bubble of gas which is generated in
surface tension force.
[1] Noh, W.F. and Woodward, P.R., "Slic(simple line interface method) ",
in Lecture Notes in Physics, 59, 1976.
[2] Hirt, C.W. and Nichols, B.D., "Volume of fluid (Vof) method for the
dynamics of free boundaries", J. comput. phys., 39, 201-225, 1981.
[3] Youngs, D.L. "Time-dependent multi-material flow with large fluid
distribution", in Numerical methods for fluid dynamics, Morton and
Norman,Editor,187-221,1996
[4] Ashgriz, N and Poo, J.Y., "FLAIR: Flux Line-segment model for
advection and interface reconstruction". J. Comput. Phys., 93,449-468,
1991.
[5] Rider, W.J. and Kothe D.B., "Reconstruction volume tracking", J.
comput. phys., 14, 112, 1998.
[6] Pilliod J.E. and E.G. Puckett, "Second-order accurate volume-of-fluid
algorithms for tracking material interfaces", Lawrence Berkley Lab.
tech. report, No.LBNL-40744, 1997.
[7] Rudman M.,"A volume-tracking method for incompressible multi fluid
flows with large density variations", Int. J. num. methods, 28(2), pp 357-
378, 1998
[8] Landau, L. D. and Lifshitz, E. M., "Fluid Mechanics", Pergoman Press,
New York, 1959
[9] Brackbill, J.U, Kote, D.B. and Zemach, C.,"A continuum Method for
modeling surface tension", J. comput. phys., 100:335-354, 1992.
[10] Kothe, D.B., W.J. Rider, S.J. Mosso, and J.S. Brock, "Volume tracking
of interfaces having surface tension in two and three dimensions" AIAA
96-0859, 1996.
[11] Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S. and Zanetti, G.,
"Modeling merging and fragmentation in multiphase flows with
SURFER", J. comput. phys., 113:134-147, 1994.
[12] Meier, M., Yadigaroglu, H. and Smith, B.L., "A novel technique for
including surface tension in PLIC-VOF methods", Eur. J. B/fluids, 21,
61-73, 2002.
[13] Shirani, E., Ashgriz, N. and Mostaghimi, J.," Interface pressure
calculation based on conservative of momentum for front tracking
methods", J. comp. phys., 203, 153-175, 2005.
[14] Seifollahi, M., Shirani, E. and Ashgriz, N., "An Improved Method for
Calculation of Interface Pressure Force in PLIC-VOF Methods",
Accepted for publication in European Journal of Mechanics- B/Fluids
2007.
[1] Noh, W.F. and Woodward, P.R., "Slic(simple line interface method) ",
in Lecture Notes in Physics, 59, 1976.
[2] Hirt, C.W. and Nichols, B.D., "Volume of fluid (Vof) method for the
dynamics of free boundaries", J. comput. phys., 39, 201-225, 1981.
[3] Youngs, D.L. "Time-dependent multi-material flow with large fluid
distribution", in Numerical methods for fluid dynamics, Morton and
Norman,Editor,187-221,1996
[4] Ashgriz, N and Poo, J.Y., "FLAIR: Flux Line-segment model for
advection and interface reconstruction". J. Comput. Phys., 93,449-468,
1991.
[5] Rider, W.J. and Kothe D.B., "Reconstruction volume tracking", J.
comput. phys., 14, 112, 1998.
[6] Pilliod J.E. and E.G. Puckett, "Second-order accurate volume-of-fluid
algorithms for tracking material interfaces", Lawrence Berkley Lab.
tech. report, No.LBNL-40744, 1997.
[7] Rudman M.,"A volume-tracking method for incompressible multi fluid
flows with large density variations", Int. J. num. methods, 28(2), pp 357-
378, 1998
[8] Landau, L. D. and Lifshitz, E. M., "Fluid Mechanics", Pergoman Press,
New York, 1959
[9] Brackbill, J.U, Kote, D.B. and Zemach, C.,"A continuum Method for
modeling surface tension", J. comput. phys., 100:335-354, 1992.
[10] Kothe, D.B., W.J. Rider, S.J. Mosso, and J.S. Brock, "Volume tracking
of interfaces having surface tension in two and three dimensions" AIAA
96-0859, 1996.
[11] Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S. and Zanetti, G.,
"Modeling merging and fragmentation in multiphase flows with
SURFER", J. comput. phys., 113:134-147, 1994.
[12] Meier, M., Yadigaroglu, H. and Smith, B.L., "A novel technique for
including surface tension in PLIC-VOF methods", Eur. J. B/fluids, 21,
61-73, 2002.
[13] Shirani, E., Ashgriz, N. and Mostaghimi, J.," Interface pressure
calculation based on conservative of momentum for front tracking
methods", J. comp. phys., 203, 153-175, 2005.
[14] Seifollahi, M., Shirani, E. and Ashgriz, N., "An Improved Method for
Calculation of Interface Pressure Force in PLIC-VOF Methods",
Accepted for publication in European Journal of Mechanics- B/Fluids
2007.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:53172", author = "Afshin Ahmadi Nadooshan and Ebrahim Shirani", title = "Generalization of SGIP Surface Tension Force Model in Three-Dimensional Flows and Compare to Other Models in Interfacial Flows", abstract = "In this paper, the two-dimensional stagger grid
interface pressure (SGIP) model has been generalized and presented
into three-dimensional form. For this purpose, various models of
surface tension force for interfacial flows have been investigated and
compared with each other. The VOF method has been used for
tracking the interface. To show the ability of the SGIP model for
three-dimensional flows in comparison with other models, pressure
contours, maximum spurious velocities, norm spurious flow
velocities and pressure jump error for motionless drop of liquid and
bubble of gas are calculated using different models. It has been
pointed out that SGIP model in comparison with the CSF, CSS and
PCIL models produces the least maximum and norm spurious
velocities. Additionally, the new model produces more accurate
results in calculating the pressure jumps across the interface for
motionless drop of liquid and bubble of gas which is generated in
surface tension force.", keywords = "Volume-of-Fluid; SGIP model; CSS model; CSF
model; PCIL model; surface tension force; spurious currents.", volume = "2", number = "3", pages = "277-6", }