Closures for the bubble size distribution and interfacial area concentration

Abstract

This chapter is devoted to the presentation of the closure laws for the interfacial area transport equation and other multi-size bubble models. Considering first the single size case, the different forms of the interfacial area transport equation are recalled and their closure laws are reviewed. These closure laws concern essentially the interfacial area variations due to the coalescence, breakup and phase change phenomena. The gas expansion as well as the nucleation and collapse are also considered. In the second part of the chapter, we present some possible closures for the more difficult case of multi-size bubbly flows. Two approaches are followed: the moment’s method with a presumed size NDF and a class method using a discretization of the NDF. In the moment’s method, two different mathematical expressions are used for the NDF: a log-normal law and a quadratic law.