An Immersed Boundary Method Based on Penalized Direct Forcing with Immersed Wall Functions using RANS k-ω SST Modeling: Assessment on a Staggered Grid and application to Nuclear Safety Devices
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The accurate and efficient simulation of turbulent thermohydraulic flows in complex geometries is a key requirement for the design and topological optimization of nuclear safety devices. Conventional body-fitted meshing approaches often lead to high computational costs and limited flexibility when moving boundaries or iterative mesh changes are involved. To address these challenges, we propose an Immersed Boundary Method (IBM) based on the Penalized Direct Forcing approach [1], tailored for turbulent nuclear safety applications. A major contribution of this work is the development of immersed wall functions on a staggered Marker-and-Cell (MAC) grid, each velocity component being forced at its own location. These wall functions are coupled with closures for the turbulence quantities (k and ω), enabling the consistent integration of the RANS k-ω SST model within the IBM framework. A forcing curtain seals zero-thickness walls, the wall-model probe is anchored on the immersed surface, and a stress-based target carries the flux balance of wall functions over to the forced degrees of freedom. The methodology has been implemented in the open-source platform TRUST/TrioCFD [2] of the CEA. On a turbulent channel flow at three Reynolds numbers, the stress-based target restores the smooth-wall behavior, brings the friction within a few percent of the measurement and makes it far less sensitive to the grid and to the position of the wall within the cell. The method is also assessed on inclined walls and applied, on a single Cartesian grid, to the flow damper of an advanced accumulator, a passive safety component of pressurized water reactors, in comparison with a body-fitted simulation using wall laws. Beyond static configurations, the method is suited to moving or deformable boundaries, opening perspectives for the optimization of innovative passive safety devices and for fluid-structure interaction.
