A multi-point, implicit-type, finite-difference method for solving the bubble growth (or collapse) problem in an ultraheated liquid is proposed. The method is applicable to both inertia-controlled growth and heat-diffusion-controlled growth. The results are compared with several asymptotic solutions, involving Plesset-Zwick and Mikic-Rohsenow-Griffith solutions. Present results strongly support the Mikic-Rohsenow-Griffith solution for the wide range of bubble growth conditions, e.g. given fluids, pressure, liquid ultraheat, etc.
Get full access to this article
View all access options for this article.
References
1.
RayleighL. ‘On the pressure developed in a liquid during the collapse of a spherical cavity’, Phil. Mag.191734, 94–98.
2.
PlessetM. S.ZwickS. A. ‘The growth of vapour bubbles in superheated liquids’, J. appl. Phys.195425, 493–500.
3.
ForsterH. K.ZuberN. ‘Growth of a vapour bubble in a superheated liquid’, J. appl. Phys.195425, 474–478.
4.
BirkhoffG.MarguliesR. S.HorningW. A. ‘Spherical bubble growth’, Phys. Fluids19581, 201–204.
5.
ScrivenL. E. ‘On the dynamics of phase growth’, Chem. Engng Sci.195010, 1–13.
6.
ZwickS. A. ‘Growth of vapour bubbles in a rapidly heated liquid’, Phys. Fluids19603, 685–692.
7.
MikicB. B.RohsenowW. M.GriffithP. ‘On bubble growth rates’, Int. J. Heat Mass Transfer197013, 657–666.
8.
LeanY.GriffithP. ‘The bubble growth at reduced pressure’, Int. J. Heat Mass Transfer (to be published).
9.
ChoS. M.SebanR. A. ‘On some aspects of stream bubble collapse’, Trans. A. S. M. E.196991, 537–542.
10.
ChoS. M.On the dynamics of a vapor bubble Ph. D. Dissertation, University of California, Berkeley, 1967.
11.
GuyT. B.LedwidgeT. J. ‘Numerical approach to non-spherical vapour bubble dynamics’, Int. J. Heat Mass Transfer197316, 2393–2406.
12.
KolodnerI. I. ‘Free boundary problem for the heat equation with applications to problems of change of phase’, Communs Pure appl. Math.19569, 1–31.
13.
SaitohT. ‘Numerical method for one-dimensional moving boundary problem’, 11th Japanese Symposium on Heat Transfer1974, 333–336.
14.
LandauH. G. ‘Heat conduction in a melting solid’, Quart. appl. Math.19508, 81–94.
15.
SaitohT. ‘Numerical method by 7-point implicit difference formula for transient heat conduction problems’, Trans. Japan Soc. mech. Engrs197440, 2617–2631.
16.
DergarabedianR. ‘The rate of growth of vapour bubbles in superheated water’, J. appl. Mech.195320, 537–545.
17.
ShimaA.TsujinoT. ‘The growth of spherical bubbles in superheated liquids’, Rep. Inst. High Speed Mech. 197532, 87–101 (Tohoku University).
18.
HooperF. C.AbdelmessihA. H. ‘The flashing of liquids at higher superheats’, Proc. 3rd Int. Heat Transfer Conference1966, 44–50 (Chicago).
19.
KoskyP. G. ‘Bubble growth measurements in uniformly superheated liquids’, Chem. Engng Sci.196823, 695–706.
20.
FlorschuetzL. W.HenryC. L.KahnA. R. ‘Growth rates of free vapour bubbles in liquids at uniform superheats under normal and zero gravity conditions’, Int. J. Heat Mass Transfer196912, 1465–1489.
21.
StewartJ. K.ColeR. ‘Bubble growth rates during nucleate boiling at high Jakob numbers’. Int. J. Heat Mass Transfer197215, 655–664.
