Towards Immersed Boundary Modeled-LES: a priori Analysis

We present preliminary work on the development of a consistent approach for Immersed Boundary-Modeled LES method designed to incorporate IBs, turbulence closures, and wall-models consistently. To this end, we perform a priori analysis of volume-filtered DNS data of turbulent channel flow at friction Reynolds number of 5200. Volume-filtering differs from regular LES filtering in the treatment of the solid-fluid interface and represents the basis of the Volume-Filtering Immersed Boundary Method. Volume-filtered quantities are found by convolving with a filter kernel pre-multiplied by a phase-indicator function. Applying this procedure to the Navier-Stokes equations leads to volume-filtered equations that depend on the fluid volume fraction and exhibit additional terms representing a residual viscous stress tensor and a bodyforce concentrated on the solid-fluid interface akin to an Immersed Boundary forcing. Further, the resulting volume-filtered velocity has a slip on the solid-fluid interface which also controls the IB forcing term. To inform future modelling attempts, we characterize these unclosed terms using a priori volume-filtered DNS data with filter sizes from 50 to 300 wall units. In particular, we investigate the function dependence of the slip velocity on filter size, as it is needed to model the IB forcing term.