Analytical Solution to the Equation for the Simplest Natural Circulation Loop of Working Fluid in a Steam Boiler

Determining pressure drops upon flowing of a two-phase steam–water mixture in natural circulation loop elements is an integrated engineering problem. The conditions to which each element is exposed exert a significant effect on the operation of the system as a whole, and a large scope of empirical data is required to determine the flow parameters. Modern numerical methods for analyzing two-phase flows have significant limitations and require setting the interphase boundary depending on the flowing mode and initial conditions. As a consequence, it can be set only approximately provided that a reliable methodology for predicting these modes is available. Nowadays, there are only a few examples of solving problems in fluid mechanics by means of numerical methods in such a formulation according to which the interaction between the liquid and gas phases is not set, but can be determined in the course of solving the problem. In this connection, the studies performed by various researchers are based on experiments and are presented in the form of engineering calculation methods within a limited range of initial conditions. The proposed approach to the solution of the circulation equation consists in searching for its analytical solution taking into account empirical data obtained in earlier studies and in assessing their effect on the calculation results as a whole. Further, this approach should be generalized to a wider class of initial conditions, as well as to loops of more complicated configurations to optimize the calculation procedure provided by the standard method and to elaborate more detailed recommendations for designing the evaporation loops of boilers with natural circulation. This novel approach is used as a base for studying the effect of evaporator heat absorption exerted on the loop operation with the same loop design. It is found that a maximum flow rate is observed in the loop. The flow rate limitations depend on the loop design, on the physical properties of the fluid, and on the phase slip.