(679e) An Open-Source Adaptive and Distributed Nitsche Immersed Boundary Method for the Simulation of Laminar, Transitional and Turbulent Mixing

Computational Fluid Dynamics (CFD) has demonstrated that it can be a powerful tool to simulate the dynamics of a mixing system for both single and multiphase scenarios. In single phase mixing, it can be used to predict the residence time distribution, the mixing time, the occurrence of dead zones or the power consumption. This has led to a more widespread use of CFD in the mixing community.

The simulation of mixing system by CFD remains challenging because of the presence of a rotating impeller. The simplest approach is to formulate the CFD problem in a rotating frame of reference, but this breaks down for cases where the system does not present rotational symmetry: when baffles are present or when the impeller is off-centered. Two alternative solution exist to this problem: sliding-mesh strategies or the use of immersed boundaries.

Sliding-mesh strategies are available in multiple commercial or open source software (e.g. OpenFOAM). Although they are reliable, it is difficult and time-consuming to generate good quality (e.g. high orthogonality) meshes for these types of geometries. Furthermore, they are very cumbersome to use for configurations in which there are multiple impellers, each rotating with their own velocities. This hinders a more widespread usage of CFD, especially when it must be combined with other tools such as topology optimization or neural networks.

Immersed boundaries (IB) are an alternative approach in which the impeller is not meshed with a conformal mesh but is instead represented by discrete or continuous forcing terms [1]. Multiple IB approaches exist and have demonstrated they capabilities. However, most of them are either only available in closed-source CFD code or in commercial software. Additionally, they often suffer from a degradation of the accuracy of the underlying CFD scheme.

In this work, we present a novel parallel IB strategy that uses Nitsche’s method to weakly impose the boundary conditions associated with the impeller. This Nitsche’s method is implemented in a high-performance open-source FEM software: Lethe [2]. Lethe uses a Galerkin Least-Squares (GLS) approach to solve implicitly and at arbitrary order the incompressible Navier-Stokes equation. By leveraging the p4est and the deal.II library, it has the capacity to carry out parallel simulations with dynamic mesh adaptation and load balancing. Hence, using a Kelly error estimator, the mesh can be dynamically adapted to changing flow patterns in the mixing system, without degrading the computational performance of the underlying scheme.

In this talk, we first present Lethe and the GLS formulation used therein. We introduce our novel parallel distributed Nitsche’s method and how it can be used to impose the motion of the impeller starting from a simple surface or volumetric mesh of the impeller itself. This approach is then first verified on test cases that related to mixing, but for which analytical/reference solution for the torque or the forces are available. Then, it is used to study the mixing in baffled and unbaffled systems over a large range of Reynolds number that cover the laminar to the early turbulent regime. This demonstrates that the model is capable of robustly simulate mixing system with minimal user input, since mesh generation and adaptation can be made fully automatic.

Finally, we conclude by discussing future application of the Lethe software and of this Nitsche’s approach, notably in the field of multiphase mixing and granular mixing.

[1] Blais, B., Lassaigne, M., Goniva, C., Fradette, L., & Bertrand, F. (2016). A semi-implicit immersed boundary method and its application to viscous mixing. Computers & Chemical Engineering, 85, 136-146.

[2] Blais, Bruno, et al. "Lethe: An open-source parallel high-order adaptative CFD solver for incompressible flows." SoftwareX 12 (2020): 100579.