Utilizing an engineering optimization approach to predict maximum mass flow rates of steam and water mixtures

Two mass flux mathematical models for the study of critical single- and two-phase flows of water are formulated based on optimization theory. Analytical expressions for the mass flux functions are developed for the superheated vapor and saturated liquid-vapor mixtures (Homogeneous Equilibrium Model) by using the generalized equations of state. With the application of the general-purpose sequential gradient-restoration algorithm, the mass flux is maximized for any given upstream stagnation flow condition. Furthermore, the thermodynamic properties at the exit plane are also determined simultaneously. The feasibility of this optimization technique is verified by comparing the results with those reported in the literature.