Simplified Interfacial Area Modeling in Polydisperse Two-Phase Flows under Explosion Situations

Abstract

The aim of the present work is to account for polydisperse effects in a two-phase flow with a simple and fast method. Polydisperse two-phase flows arise in numerous applications. Fire sprinkler systems are relevant examples as they release clouds of polydisperse droplets. Another relevant example is the polydisperse two-phase flow created by the detonation of an explosive charge surrounded by a liquid layer. In such a situation, material interfaces are initially present and the created two-phase flow consists of a carrier gas phase and a liquid phase involving many droplets of various sizes. Spherical particles or droplets are usually assumed in two-phase flow computations. When dealing with explosion situations involving both dense and dilute flow regimes, multiple particle diameters can be addressed but at the price of introducing as many additional equations that describe mass, momentum and energy balance of the various particle classes. Consequently, the computation time needed to address numerical resolution increases tremendously. Under explosion situations involving many particle diameters, the method becomes intractable and is usually reduced to a single diameter, which is often insufficient. A simplified approach is developed in the present work to account for a substantial number of particles of different sizes with few extra computational cost. The approach is said to be simplified as a single velocity and a single temperature are considered for all the spherical particles, regardless of their diameters. This type of modeling seems apt for the target explosion situations. The focus is placed on the interfacial area, which is the main parameter involved in the coupling of the two phases. In the present work, Gamma-like continuous probability distributions are considered to address the various sizes of particles. The effects of the size distribution are only summarized in the specific interfacial area, yielding consequently few code modifications while taking into account the polydisperse aspect of the two-phase flow.

Keywords

• two-phase flows
• explosions
• interfacial area
• polydisperse particles
• radius distribution laws