ANALYTICAL SOLUTION OF THE NATURAL CIRCULATION EQUATION FOR A SIMPLE LOOP

Abstract

Determining the hydraulic resistance of evaporator elements during the flow of a two-phase steam-water mixture is a complex engineering problem. The conditions experienced by each element significantly affect the operating mode of the entire system, and empirical data are used to determine the flow parameters. Modern numerical methods for calculating two-phase flows are considerably limited and require defining the phase interface, which depends on the flow regime and can only be approximately specified given a reliable methodology for regime prediction. Currently, there are only isolated examples of solving gas-liquid flow mechanics problems using numerical methods in a formulation where the shape of the interphase surface is not prescribed but is determined in the course of solving the problem. In this regard, the present study is based on a general analysis of the dependencies proposed for engineering calculations within a limited range of initial conditions, and on identifying critical points for which an analytical approach to solving the circulation equation is possible. Subsequently, this approach can be generalized to a broader class of initial conditions as well as to loops of complex configuration, with the aim of optimizing the standard methodology and providing more detailed recommendations for design. The paper presents the conditions under which the maximum flow rate in the loop is achieved.