Approximate analytical analysis on the two-phase flow for a gas/liquid metal magnetohydrodynamic generator

The gas/liquid metal magnetohydrodynamic generator (G/LM-MHD) using the mixture working-medium of gas and liquid metal is a promising energy conversion technique, especially due to the development of liquid metal cooled nuclear reactors technology in recent years. The research before has proven that the G/LM-MHD can achieve a higher electrical power density and efficiency than the traditional thermodynamic cycle. However, the analysis of G/LM-MHD is quite difficult because of the two-phase flow and electromagnetic effect. Most of the earlier studies on G/LM-MHD are focused on the conception design, preliminary experiment and numerical simulation, while lack of intuitive or analytical theory explanations. In this paper, an one-dimensional analytical analysis of the variable-height rectangular ideal Faraday-type G/LM-MHD generation channel is carried out. The coupled two-phase MHD equations are approximatively solved by dimensionless processing and calculus method, under the assumptions of uniform mixing model, quasi-equal temperature and linearization of electrical conductivity. Finally, the one-dimensional approximate explicit analysis solution is obtained, and several particular dimensionless parameters that have a great influence on the G/LM-MHD generator are determined. The approximate distribution functions of the main parameters including the volume fraction, pressure, velocity, electrical conductivity, voltage and current density are given in explicit analytical expressions, and also the output electrical power can be calculated easily due to the analysis results. The obtained one-dimensional approximate analytical solution agrees well with the numerical calculation results under the coupled equation, which means that it can greatly simplify the difficulty and efficiency of the study on the G/LM-MHD channel. Meanwhile, the approximate explicit analysis provides a practical theory to select proper gas and liquid metal as working fluid, and also it provides some guidance for the basic geometric design of the MHD channel, which enlightens a fresh angle for a more efficient design for the Faraday-type MHD generator. (author)