Scaling analysis for a reactor vessel mixing test

The Westinghouse AP600 advanced pressurized water reactor design uses a gravity-forced safety injection system with two nozzles in the reactor vessel downcomer. In the event of a severe overcooling transient such as a steam-line break, this system delivers boron to the core to offset positive reactivity introduced by the negative moderator defect. To determine if the system design is capable of successfully terminating this type of reactivity transient, a test of the system has been initiated. The test will utilize a 1:9 scale model of the reactor vessel and cold legs. The coolant will be modeled with air, while the safety injection fluid will be simulated with a dense gas. To determine the necessary parameters for this model, a scaling analysis was performed. The continuity, diffusion, and axial Navier-Stokes equations for the injected fluid were converted into dimensionless form. A Boussinesq formulation for turbulent viscosity was applied in these equations. This procedure identified the Richardson, mixing Reynolds, diffusion Fourier, and Euler numbers as dimensionless groups of interest. Order-of-magnitude evaluation was used to determine that the Richardson and mixing Reynolds numbers were the most significant parameters to match for a similar experiment