A model of the coolant flow in supercritical nuclear reactors based on the highest approximations of the Chapman Enskog method

Among a number of the reactor types, identified by the international GIF-IV program as advanced facilities, the most promising concept is that of a supercritical reactor plant. Close consideration is given to reactors of this type due to the possibility of obtaining a higher efficiency, as compared with the PWR-type reactor facility, thanks to improving the reactor's operating parameters (higher in-core temperature and pressure) and using the supercritical Brayton cycle instead of the Rankine cycle. The supercritical coolant flow in the reactor flow area is characterized by the fact that the change in the flow enthalpy is much greater than the characteristic value of kinetic energy. Besides, the flow in the reactor core flow area is accompanied by a major change in the thermophysical properties of the coolant. The coolant flow is realized in conditions for the parametric Knudsen and Reynolds numbers, Kn → 0, Re >> O(1). With such values of the mode parameters, the Burnett terms in the momentum equation have the same order as the Navier-Stokes terms, and, in the event of turbulent flows, the same order as the «apparent» Reynolds turbulence stresses. Reducing molecular kinetic equations to macroscopic equations is one of the fundamental problems in continuum mechanics. At the present time, this procedure uses the classical Chapman-Enskog approach to resolving the Boltzmann-Maxwell kinetic equation. The final result of using the method is a chain of Euler equations, Navier-Stokes equations, higher approximation equations (Burnett equations, super-Burnett approximation), etc. The proposed model is based on taking into account the contribution of the Burnett terms to the overall balance of forces and their work in transfer equations. The terms, taking into account the thermal convection effects, are introduced to the stress tensor, based on the Chapman-Enskog method. The most general form of initial equations and their parabolized form are presented, which allow taking into account the transverse overflows in fuel assemblies, the effects of gravity and the buoyancy force that acts on the coolant. A method has been proposed for simplifying initial equations based on using the Prandtl-Mises transformation. The transformation makes it possible to simplify considerably the initial equations and reduce these to an equation of the heat conductivity equation type.