Comparison of Moment-Based Methods for Representing Droplet Size Distributions in Supersonic Nucleating Flows of Steam

Abstract

This paper investigates the performance of moment-based methods and a monodispersed model (Mono) in predicting the droplet size distribution and behavior of wet-steam flows. The studied moment-based methods are a conventional method of moments (MOM) along with its enhanced version using Gaussian quadrature, namely the quadrature method of moments (QMOM). The comparisons of models are based on the results of an Eulerian–Lagrangian (E–L) method, as the benchmark calculations, providing the full spectrum of droplet size. In contrast, for the MOM, QMOM, and Mono an Eulerian reference frame is chosen to cast all the equations governing the phase transition and fluid motion. This choice of reference frame is essential to draw a meaningful comparison regarding complex flows in wet-steam turbines as the most important advantage of the moment-based methods is that the moment-transport equations can be conveniently solved in an Eulerian frame. Thus, the moment-based method can avoid the burdensome challenges in working with a Lagrangian framework for complicated flows. The main focus is on the accuracy of the QMOM and MOM in representing the water droplet size distribution. The comparisons between models are made for two supersonic low-pressure nozzle experiments reported in the literature. Results show that the QMOM, particularly inside the nucleation zone, predicts moments closer to those of the E–L method. Therefore, for the test case in which the nucleation is significant over a large proportion of the domain, the QMOM provides results in clearly better agreements with the E–L method in comparison with the MOM.

Study of the Evaporation Process in the Spray Zone of a Mechanical Draft Wet Cooling Tower

“…To calculate the diameter growth, the critical radius theory [17] is needed to represent the phase transition of all non-equilibrium models. During the phase transition, the process of nucleation and supercritical droplet growth occurs to rebuild the equilibrium.…”

“…The droplet diameter growth is affected by the transfer of heat between the droplet and the surrounding vapor, which has been generalized for a wide range of droplet sizes. The theory [17] is adjusted to the measurement of spray at low pressure.…”

Results of the International Wet Steam Modeling Project

“…More recently Afzalifar et al 22 did further investigations and especially Hughes et al 19 considered the influence of different expansion rates. In line with previous findings the differences between the discrete spectrum method and the monodispersed method are remarkable for high as well as for low expansion velocities.…”

Polydispersed droplet spectrum and exergy analysis in wet steam flows using method of moments

“…Hughes et al [11] studied the spectrum pruning method and QMOM to reduce the droplet groups number. Afzalifar et al [38] found the method of moments only solves several transport equations of droplet sizes which can reduce computational time and QMOM method is a better choose to predict the effect of droplet size distribution.…”