Meccanica (2006) 41:483–499 DOI 10.1007/s11012-006-0005-8 Steady and unsteady motion of one-component two-phase bubbly flow in 1-D Geometry Michele La Rocca · Paolo Mele · Gino Boccardi Received: 3 August 2005/ Accepted 23 January 2006 / Published online: 24 October 2006 © Springer Science+Business Media B.V. 2006 Abstract The aim of this work is to present a mathematical model of the motion of a one-component two-phase bubbly flow in one-dimensional geometry. Bubbles are assumed to be spherical and far enough from each other in order to exclude reciprocal inter- actions. The mathematical model is derived by means of a phase average operation and assuming a suitable description of the velocity field in the liquid phase, in the neighbourhood of the bubbles. Two different sets of experimental conditions are then simulated: a steady motion in a convergent–divergent nozzle and two different unsteady flows: i.e. two water hammer transients. Both the experimental conditions consid- ered are well reproduced, indicating the validity of the proposed model. Keywords Two phase flows · Bubbly flows · Fluid transients · Mechanics of fluids Introduction Multiphase flows are concerned with a huge variety of phenomena, caused both by natural reasons and by M. La Rocca (B ) · P. Mele Department of Civil Engineering Sciences, University RomaTRE, Via Vito Volterra 62, 00146 Rome, Italy E-mail: larocca@uniroma3.it G. Boccardi Institute of Thermal-Fluid Dynamics, ENEA, “Casaccia” Research Center, Via Anguillarese 301, Rome, Italy human activities. Concerning with these latter, multiphase flows occur often in industrial plants with different characteristics. A first gross distinction among multiphase flows in industrial plants can be made with respect to the importance of thermodynamical aspects. In other words, it is possible to distinguish multiphase flows in which such aspects are fundamental, as in solidification [1] and condensation problems [2], typ- ical, respectively, for transfer of steel casting and in heat exchanges in condensers, and multiphase flows in which such aspects are less important with respect to inter phase momentum exchanges, as two phase flows in hydraulic plants. Such flows, which are analysed in the present paper, are often constituted by a liquid phase and gas bubbles and have some particular fea- tures, which render them of particular interest. As a matter of fact, even a dilute concentration of bubbles both dramatically increases the compressibility of the fluid system and endows its motion with a complex internal structure. The most difficult aspect in modeling a multiphase flow is constituted by the inter-phase mass, momen- tum and energy exchanges, which occur in strong non equilibrium conditions. Such exchanges are commonly modeled as interaction terms [3] in a framework, which deals with a set of mass, momentum and energy balance equations for each phase. The unknown variables are the homogenized variables and the interaction terms are defined as functions of these latter by closure rela- tions, while the dispersive terms, which arise due to the decomposition of the velocity field in homogenized