Examination of mhd fluid flow in geometric elements of a fusion reactor blanket using the core flow approach

Abstract

The attractiveness of liquid metal blankets depends strongly on the degree of which peak pressures and temperatures can be controlled. These, in turn, are determined by the MHD pressure drop and velocity field. Accurate methods of predicting the pressure drop, velocity and temperature profiles in liquid metal blankets are necessary for blanket design and for planning and analysis of experiments. The governing equations for MHD fluid flow are well known. However, solution of the full set of MHD equations is difficult in some geometries and parameter ranges of interest. In many cases, the most important MHD effects can be accurately modeled using a simplified approach, known as the “core flow approximation”, which neglect inertial and viscous terms. A core flow solution method has been developed utilizing the special properties of the MHD equations to reduce them to, at most, four two-dimensional partial differential equations. The method has been formulated in a very general way, to allow treatment of problems with three-dimensional magnetic field and complex channel shapes. Solutions have been obtained numerically for several cases of interest to fusion. These include conducting pipes with variable radius, variable transverse magnetic field strength, and arbitrary angle of the field with respect to the flow direction. Initial analysis has focused on localized perturbations, including expansions, contractions, and magnetic field entrance/exit regions. Benchmarking has been performed in cases for which data exist. The results indicate that the method is very powerful and could be generalized to treat most geometric elements of liquid metal blankets and high heat flux components.