Modeling of turbulent precipitation: A transported population balance-PDF method

Abstract

Turbulent precipitation is a complex problem, whose mathematical description of precipitation requires a coupling of fluid dynamics with the population balance equation (PBE). In the case of turbulent flow, this coupling results in unclosed equations due to the nonlinear nature of precipitation kinetics. In this article, we present a methodology for modeling turbulent precipitation using the concept of the transported probability density function (PDF) in conjunction with a discretized PBE, simulated via a Lagrangian stochastic method. The transported PBE-PDF approach resolves the closure problem of turbulent precipitation for arbitrarily complex precipitation kinetics, while retrieving the full particle size distribution (PSD). The method is applied to the precipitation of BaSO₄ in a turbulent pipe flow and comparisons are made with the experimental results of Baldyga and Orciuch (Chem Eng Sci. 2001;56:2435-2444) showing excellent agreement, while insight is drawn into the mechanisms that determine the evolution of the product PSD. © 2009 American Institute of Chemical Engineers AIChE J, 2010