In the paper the combination of collocation and factorization methods applied to numerical investigation of bubble-inside drop system dynamics is presented. Initially assumed bubble and drop have ellipsoidal forms. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 21, 1999, No 1 (8- 24} COMBINATION OF COLLOCATION AND FACTORIZATION METHODS APPLIED TO NUMERICAL SOLUTIONS OF BUBBLE-INSIDE DROP SYSTEM DYNAMICS DUONG NGOC HAl Institute of Mechanics, NCST of Vietnam ABSTRACT. In the paper the combination of collocation and factorization methods applied to numerical investigation of bubble-inside drop system dynamics is presented. Initially assumed bubble and drop have ellipsoidal forms. The initial relative location of the drop in the bubble is determined by equilibrium condition between drop weight and lift-force due to pressure distribution in gas/vapor. Calculations are implemented for the . case of spherical bubble, drop without and with vaporization (thermal effect) and for the experimental case [6] with alumini drop in water in pressure waves. 1. Introduction The investigation of behavior of the system of drop and vapor cover () is important for analysis of different possible kind of situation may be met in chemical, energetic industries and cryogen techniques. To describe dynamics ·of this system the mathematical model improving existed models taking into account thermal effect and vaporization at bubble wall is proposed in [3]. In this paper using combination of collocation and factorization methods some calculation results are presented. r Fluid - (t) 8 2. Mathematical formulation The model with rotational symmetry consists of following equations: * for outside liquid flow: V 2 9 = o, ilt = V9, 89 = _!V9 · V9- g cosO- Pv- Poo(t) at 2 Pt 1 CT + 1 a2 R () 1 lias -liiii2 [1+ (~ ~!ft' - PtR { r --+ oo : aR) 2 2( 1 () + 1 aR cos e } -liao~ [1+ (~ :fr/2 , () () - ilt --+' 0, iit = 0, t = 0: ( v 1a( a) 1 a(. a) ar ': ar + r sine ae sm 'ae , 2 2 = r2 2 . d91 = dt e t = 9 (r, 8, t), a~ ot + a~ or) or at . where i1 is velocity vector; p and p are pressure and density, respectively; g is gravitational .
