Numerical Simulation of the Transient Shape Variation of a Rotating Liquid Droplet
Transient shape variation of a rotating liquid dropletis
simulated numerically. The three dimensional Navier-Stokes
equations were solved by using the level set method. The shape
variation from the sphere to the rotating ellipsoid, and to the two-robed
shapeare simulated, and the elongation of the two-robed droplet is
discussed. The two-robed shape after the initial transient is found to be
stable and the elongation is almost the same for the cases with different
initial rotation rate. The relationship between the elongation and the
rotation rate is obtained by averaging the transient shape variation. It is
shown that the elongation of two-robed shape is in good agreement
with the existing experimental data. It is found that the transient
numerical simulation is necessary for analyzing the largely elongated
two-robed shape of rotating droplet.
<p>[1] I. Egry, G. Lohoefer, G. Jacobs,“Surface tension of liquid metals: results
from measurements on ground and in space,”Phys. Rev. Lett.75, 1995,pp.
4043-4046.
[2] V. Shatrov, V., Priede, J. and Gerbeth, G., “Three-Dimensional Linear
Stability Analysis of the Flow in a Liquid Spherical Droplet driven by an
Alternating Magnetic Field,”Physics of Fluid,15,2003, pp. 668-678.
[3] W.K. Rhim, andS. K. Chung, “Isolation of CystallizingDroplets by
EectrostaticLvitation,”Methods:A Companion to Methods in Enzymology,
1, 1990, pp. 118-127.
[4] A.L. Yarin, D.A. Weiss, B. Brenn and D. Rensink,“Acoustically
Levitated Drops: Drop Oscillation and Break-Up Driven by Ultrasound
Modulation,”Journal of Multiphase Flow, 28, 2002, pp. 887-910
[5] Y. Abe, S. Matsumoto, T. Watanabe, K. Nishinari, H. Kitahata, A.
Kaneko, K. Hasegawa, R. Tanaka, K. Shitanishi and S. Sasaki,
“Nonlinear dynamics of levitated droplet,” in Pint. J. Microgravity Sci.
Appl. 30, 2013, pp. 42–49.
[6] T. Watanabe, “Numerical simulation of oscillations and rotations of a free
liquid droplet using the level set method,”Computers and Fluids, 37, 2008,
pp. 91-98 .
[7] T. Watanabe, “Zero frequency shift of an oscillating-rotating liquid
droplet,”Phys. Lett. A, 372, 2008, pp. 482-485 .
[8] T. Watanabe, “Frequency shift and aspect ratio of a rotating-oscillating
liquid droplet,”Phys. Lett. A, 373, 2009, pp. 867-870.
[9] R.A. Brown and L.E. Scriven, “The shape and stability of rotating liquid
drops,”Proc. Royal Soc.London A 371, 1980, pp. 331-357.
[10] M. Sussman, P.Smereka, “Axisymmetric free boundary problems,”J.
Fluid Mech.341, 1997, 269-294.
[11] M. Sussman, P.Smereka, S. Osher, “A level set approach for computing
solutions to incompressible two-phase flow,”J. Comp. Phys.114, 1994,pp.
146-159.
[12] Y.C. Chang, T.Y.Hou, B. Merriman, S. Osher,“A level set formulation of
Eulerian interface capturing methods for incompressible fluid flows.”J.
Comp. Phys. 124, 1996, 449-464.
[13] T. Watanabe, “Nonlinear oscillations and rotations of a liquid droplet,”Int.
J. Geology, vol. 4, 2010, pp. 5-13 .
[14] A.A. Amsden, F.H. Harlow, “Simplified MAC technique for
incompressible fluid flow calculations,”J. Comp. Phys. 6, 1970, pp.
322-325.
[15] T. Watanabe, “Parallel computations of droplet oscillations,”LNCSE, 67,
2009, 163-170.
[16] T. Watanabe, “Flow field and oscillation frequency of a rotating liquid
droplet,”WSEAS Trans. Fluid Mech., vol. 3, 2008, pp. 164-174 .</p>
<p>[1] I. Egry, G. Lohoefer, G. Jacobs,“Surface tension of liquid metals: results
from measurements on ground and in space,”Phys. Rev. Lett.75, 1995,pp.
4043-4046.
[2] V. Shatrov, V., Priede, J. and Gerbeth, G., “Three-Dimensional Linear
Stability Analysis of the Flow in a Liquid Spherical Droplet driven by an
Alternating Magnetic Field,”Physics of Fluid,15,2003, pp. 668-678.
[3] W.K. Rhim, andS. K. Chung, “Isolation of CystallizingDroplets by
EectrostaticLvitation,”Methods:A Companion to Methods in Enzymology,
1, 1990, pp. 118-127.
[4] A.L. Yarin, D.A. Weiss, B. Brenn and D. Rensink,“Acoustically
Levitated Drops: Drop Oscillation and Break-Up Driven by Ultrasound
Modulation,”Journal of Multiphase Flow, 28, 2002, pp. 887-910
[5] Y. Abe, S. Matsumoto, T. Watanabe, K. Nishinari, H. Kitahata, A.
Kaneko, K. Hasegawa, R. Tanaka, K. Shitanishi and S. Sasaki,
“Nonlinear dynamics of levitated droplet,” in Pint. J. Microgravity Sci.
Appl. 30, 2013, pp. 42–49.
[6] T. Watanabe, “Numerical simulation of oscillations and rotations of a free
liquid droplet using the level set method,”Computers and Fluids, 37, 2008,
pp. 91-98 .
[7] T. Watanabe, “Zero frequency shift of an oscillating-rotating liquid
droplet,”Phys. Lett. A, 372, 2008, pp. 482-485 .
[8] T. Watanabe, “Frequency shift and aspect ratio of a rotating-oscillating
liquid droplet,”Phys. Lett. A, 373, 2009, pp. 867-870.
[9] R.A. Brown and L.E. Scriven, “The shape and stability of rotating liquid
drops,”Proc. Royal Soc.London A 371, 1980, pp. 331-357.
[10] M. Sussman, P.Smereka, “Axisymmetric free boundary problems,”J.
Fluid Mech.341, 1997, 269-294.
[11] M. Sussman, P.Smereka, S. Osher, “A level set approach for computing
solutions to incompressible two-phase flow,”J. Comp. Phys.114, 1994,pp.
146-159.
[12] Y.C. Chang, T.Y.Hou, B. Merriman, S. Osher,“A level set formulation of
Eulerian interface capturing methods for incompressible fluid flows.”J.
Comp. Phys. 124, 1996, 449-464.
[13] T. Watanabe, “Nonlinear oscillations and rotations of a liquid droplet,”Int.
J. Geology, vol. 4, 2010, pp. 5-13 .
[14] A.A. Amsden, F.H. Harlow, “Simplified MAC technique for
incompressible fluid flow calculations,”J. Comp. Phys. 6, 1970, pp.
322-325.
[15] T. Watanabe, “Parallel computations of droplet oscillations,”LNCSE, 67,
2009, 163-170.
[16] T. Watanabe, “Flow field and oscillation frequency of a rotating liquid
droplet,”WSEAS Trans. Fluid Mech., vol. 3, 2008, pp. 164-174 .</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56082", author = "Tadashi Watanabe", title = "Numerical Simulation of the Transient Shape Variation of a Rotating Liquid Droplet", abstract = "Transient shape variation of a rotating liquid dropletis
simulated numerically. The three dimensional Navier-Stokes
equations were solved by using the level set method. The shape
variation from the sphere to the rotating ellipsoid, and to the two-robed
shapeare simulated, and the elongation of the two-robed droplet is
discussed. The two-robed shape after the initial transient is found to be
stable and the elongation is almost the same for the cases with different
initial rotation rate. The relationship between the elongation and the
rotation rate is obtained by averaging the transient shape variation. It is
shown that the elongation of two-robed shape is in good agreement
with the existing experimental data. It is found that the transient
numerical simulation is necessary for analyzing the largely elongated
two-robed shape of rotating droplet.
", keywords = "Droplet, rotation, two-robed shape, transient
simulation.", volume = "7", number = "7", pages = "1147-5", }
