A Lattice Boltzmann Framework for the simulation of boiling hydrodynamics in BWRs

Multi phase and multi component flows are ubiquitous in nature as well as in many man-made processes. A specific example is the Boiling Water Reactor (BWR) core, in which the coolant enters the core as liquid, undergoes a phase change as it traverses the core and exits as a high quality two-phase mixture. Two-phase flows in BWRs typically manifest a wide variety of geometrical patterns of the co-existing phases depending on the local system conditions. Modeling of such flows currently relies on empirical correlations (for example, in the simulation of bubble nucleation, bubble growth and coalescence, and inter-phase surface topology transitions) that hinder the accurate simulation of two-phase phenomena using Computational Fluid Dynamics (CFD) approaches. The Lattice Boltzmann Method (LBM) is in rapid development as a modeling tool to understand these macro-phenomena by coupling them with their underlying micro-dynamics. This paper presents a consistent LBM formulation for the simulation of a two-phase water-steam system. Results of initial model validation in a range of thermodynamic conditions typical for BWRs are also shown. The interface between the two coexisting phases is captured from the dynamics of the model itself, i.e., no interface tracking is needed. The model is based on the Peng-Robinson (P-R) non-ideal equation of state and can quantitatively approximate the phase-coexistence curve for water at different temperatures ranging from 125 to 325 oC. Consequently, coexisting phases with large density ratios (up to ∼1000) may be simulated. Two-phase models in the 200-300 C temperature range are of significant importance to nuclear engineers since most BWRs operate under similar thermodynamic conditions. Simulation of bubbles and droplets in a gravity-free environment of the corresponding coexisting phase until steady state is reached satisfies Laplace law at different temperatures and thus, yield the surface tension of the fluid. Comparing the LBM surface tension thus calculated using the LBM to the corresponding experimental values for water, the LBM lattice unit (lu) can be scaled to the physical units. Using this approach, spatial scaling of the LBM emerges from the model itself and is not imposed externally.