The effect of flow unsteadiness on the homogeneous nucleation of water droplets in steam turbines

Abstract

The paper describes a new theory of the formation and growth of water droplets in multistage steam turbines. The essence of the theory is that large-scale static temperature fluctuations caused by the segmentation of blade wakes by successive blade rows have a dominating influence on nucleation and droplet growth in turbines. ‘True’ turbulent fluctuations (due to shear-layer unsteadiness, etc.) are probably less important and are ignored. A Lagrangian frame of reference is adopted and attention is focused on a large number of individual fluid particles during their passage through the turbine. Homogeneous nucleation and growth of droplets in each fluid particle is assumed to be governed by classical theories. All fluid particles are assumed to experience the same pressure variation, but those particles passing close to the blade surfaces suffer greater entropy production and, therefore, have higher static temperatures than those that pursue nearly isentropic paths through the central portions of the blade passages. Particles which suffer high loss therefore nucleate later in the turbine than those that experience little dissipation. Condensation is thus viewed as an essentially random and unsteady phenomenon because the dissipation experienced by a fluid particle in one blade row is assumed to be uncorrelated with its previous history. On a time-averaged basis, the condensation zone is spread over a much greater distance in the flow direction than a simple steady-flow analysis would indicate and may encompass several blade rows, depending on the number of stages in the machine. Predicted droplet size spectra show broad, highly skewed distributions with large mean diameters and sometimes slight bimodality. These are all characteristics of experimentally measured spectra in real turbines. Conventional, steady-flow calculation methods, which predict a fixed Wilson point in a specific blade row and a nearly monodispersed droplet population, cannot reproduce any of these characteristics.