The quadrature method of moments (QMOM) is applied to the particle size distribution (PSD) present in nucleating steam flow, with a particular emphasis on conditions relevant to low-pressure steam turbines. These machines exhibit heterogeneous and homogeneous phase transition in the presence of strong flow discontinuities due to shocks and complex geometry. They offer a particularly difficult two-phase modeling situation. The present work shows that QMOM is a robust and efficient method and, in comparison to current practice of using a monodispersed PSD in computational fluid dynamics (CFD) models, offers promise for dealing with the complex two-phase conditions present in real machines.

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 1-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first-and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.