Comparison among five hydrodynamic codes with a diverging-converging nozzle experiment

A realistic open-cycle gas-core nuclear rocket simulation model must be capable of a self-consistent nozzle calculation in conjunction with coupled radiation and neutron transport in three spatial dimensions. As part of the development effort for such a model, five hydrodynamic codes were used to compare with a converging-diverging nozzle experiment. The codes used in the comparison are CHAD, FLUENT, KIVA2, RAMPANT, and VNAP2. Solution accuracy as a function of mesh size is important because, in the near term, a practical three-dimensional simulation model will require rather coarse zoning across the nozzle throat. In the study, four different grids were considered. (1) coarse, radially uniform grid, (2) coarse, radially nonuniform grid, (3) fine, radially uniform grid, and (4) fine, radially nonuniform grid. The study involves code verification, not prediction. In other words, the authors know the solution they want to match, so they can change methods and/or modify an algorithm to best match this class of problem. In this context, it was necessary to use the higher-order methods in both FLUENT and RAMPANT. In addition, KIVA2 required a modification that allows significantly more accurate solutions for a converging-diverging nozzle. From a predictive point of view, code accuracy with no tuning is an important result. The most accurate codes on a coarse grid, CHAD and VNAP2, did not require any tuning. Their main comparison among the codes was the radial dependence of the Mach number across the nozzle throat. All five codes yielded a very similar solution with fine, radially uniform and radially nonuniform grids. However, the codes yielded significantly different solutions with coarse, radially uniform and radially nonuniform grids. For all the codes, radially nonuniform zoning across the throat significantly increased solution accuracy with a coarse mesh. None of the codes agrees in detail with the weak shock located downstream of the nozzle throat, but all the codes indicated the presence of a weak downstream shock