On Reynolds-Averaged Turbulence Modeling with Immersed Boundary Method

Abstract

The immersed boundary (IB) method is an approach in the computational fluid dynamics in which complex geometry conforming meshes are replaced by simple ones and the true simulated geometry is projected onto the simple mesh by a scalar field and adjustment of governing equations. Such an approach is particularly advantageous in topology optimizations (TO) where it allows for substantial speed-up since a single mesh can be used for all the tested topologies. In our previous work, we linked our custom IB variant, the hybrid fictitious domain-immersed boundary method (HFDIB), with a TO framework and successfully carried out an optimization under laminar flow conditions. However, to allow for optimizations of reallife components, the IB approach needs to be coupled with an affordable turbulence modeling. In this contribution, we focus on extending the HFDIB approach by the possibility to perform Reynolds-averaged simulations (RAS). In particular, we implemented the k − ω turbulence model and wall functions for closure variables and velocity.

Reynolds-Averaged Simulation of Turbulent Flows with Immersed Boundaries

“…where p is the turbulence pressure, u the velocity, k the turbulence kinetic energy, ω the specific rate of dissipation of k and ε the rate of dissipation of k. The operator M contains terms of the momentum equation where u is present, operator N sums up the k conservation equation and P the ω or ε (ω|ε) conservation equation (based on the chosen turbulence model). Exact definitions of the operators may be found in Kubíčková and Isoz (2023).…”

Simulating particle-laden flows: From immersed boundaries towards model order reduction

“…In particular, second order polynomial approximation is used to estimate the value of φ at the centroid P (φ P ) of the surface cell Ω h P from the prescribed value in the surface point S (φ S ) and free-stream values in points P 1 (φ P1 ) and P 2 (φ P2 ) located at a line r passing through P and normal to S. The situation is illustrated in Fig. 3, for details see Isoz et al (2022); Kubíčková and Isoz (2023).…”