An application of the method of moments to the modeling of bubbly flow

Bubbly flows are relevant in nuclear reactors thermalhydraulics and safety analysis. Regularly, empirical constitutive laws are required to close the two-fluid equations, particularly in relating the interfacial area and the bubble number densities to the local void fraction. In this article, starting from a generalized Boltzmann transport equation for the bubble size spectrum, a convection equation for the bubble number density is derived using the method of moments. The equation is analyzed for a vertical bubbly flow in stagnated liquid, showing excellent agreement with experimental data. The model is useful as a mean to provide conservation-based correlations to complement the existing two-fluid models.