Second Law Analysis of Condensing Steam Flows

Abstract

A numerical second law analysis is performed to determine the entropy production due to irreversibilities in condensing steam flows. In the present work, the classical approach to calculate entropy production rates in turbulent flows based on velocity and temperature gradients is extended to two-phase condensing flows modeled within an Eulerian–Eulerian framework. This requires some modifications of the general approach and the inclusion of additional models to account for thermodynamic and kinematic relaxation processes. With this approach, the entropy production within each mesh element is obtained. In addition to the quantification of thermodynamic and kinematic wetness losses, a breakdown of aerodynamic losses is possible to allow for a detailed loss analysis. The aerodynamic losses are classified into wake mixing, boundary layer, and shock losses. The application of the method is demonstrated by means of the flow through a well-known steam turbine cascade test case. Predicted variations of loss coefficients for different operating conditions can be confirmed by experimental observations. For the investigated test cases, the thermodynamic relaxation contributes the most to the total losses and the losses due to droplet inertia are only of minor importance. The variation of the predicted aerodynamic losses for different operating conditions is as expected and demonstrates the suitability of the approach.