A Comparison of Modeling Techniques for Polydispersed Droplet Spectra in Steam Turbines

Abstract

Within steam turbine flows, condensation phenomena give rise to complex droplet spectra that can span more than two orders of magnitude in size. To predict the behavior of the two-phase flow and the resulting losses, the interactions between the vapor phase and droplets of all sizes must be accurately calculated. The estimation of thermodynamic losses and droplet deposition rates, in particular, depends on the size range and shape of the droplet spectrum. These calculations become computationally burdensome when a large number of droplet groups are present, and it is therefore advantageous to capture the complete droplet spectrum in a compressed form. This paper compares several methods for reducing the complexity of the droplet spectrum: a single representative droplet size (equivalent monodispersion), the moment method (including various growth rate approximations), the quadrature method of moments (QMOM), and spectrum pruning. In spectrum pruning, droplet groups are individually nucleated, but their number is subsequently reduced by combining groups together in a manner that preserves droplet number, wetness fraction, and the shape of the initial spectrum. The various techniques are compared within a Lagrangian framework by tracking the two-phase behavior along predefined pressure–time trajectories. Primary and secondary nucleation, droplet evaporation, and a representative turbomachinery case are modeled. The calculations are compared in terms of speed, accuracy, and robustness. It is shown that both the moment methods and spectrum pruning provide an appreciable improvement in accuracy over the use of an “equivalent” monodispersion without compromising calculation speed. Although all the examined methods are adequate for primary nucleation and droplet growth calculations, spectrum pruning and the QMOM are most accurate over the range of conditions considered.

Overview: Homogeneous nucleation from the vapor phase—The experimental science

“…Particles (droplets) form by condensation from the vapor phase in both ambient and industrial settings and are crucial elements in many current health, 1-5 environmental, [6][7][8][9][10] and industrial [11][12][13][14] challenges. Fine refractory fumes, for example, form in metallurgical and combustion processes, H 2 SO 4 -H 2 O nanodroplets form in exhaust stacks and volcanic eruptions, and water can condense in low pressure turbomachinery, perturbing the flow and reducing efficiency.…”

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.…”

“…The same area based droplet radius is applied to evaluate the droplet growth rates in the moment method. (Note that in White 21 and Hughes et al 19 detailed studies about the moment closure problem are provided.) The various mean radii are defined by…”

Nucleation and wake-chopping in low pressure steam turbines

“…Hughes et al. 25 compared the moment methods with Lagrangian full spectrum methods and demonstrated that it achieves satisfactory accuracy (errors in Sauter mean radius and entropy gain due to phase change ≤ 10%) for primary nucleation at the expansion rates present in LP steam turbines. Further details regarding the modelling methods can be found in Hughes.…”