Volume penalization method for simulating flows around a rotating solid with multiple reference frame and sliding mesh

TL;DR

This paper presents a volume penalization method (VPM) integrated with multiple reference frame (MRF) and sliding mesh (SLM) to simulate flows around rotating solids on Cartesian grids using a level-set representation. By formulating unified governing equations for both fluid and solid regions, the authors validate the approach against body-fitted methods, achieving about 5% accuracy in pressure drop and 8–9% in torque for rotating cuboid flows across a range of $Re_{\omega}$. The study demonstrates that VPM-MRF and VPM-SLM can reproduce key flow features while avoiding body-fitted meshing, offering computational efficiency and suitability for forward design and topology optimization in turbomachinery. This framework thus provides a practical, flexible tool for simulating complex rotating flows with potentially significant energy-efficiency implications in turbomachinery applications.

Abstract

Despite the significant role of turbomachinery in fluid-based energy transfer, precise simulation of rotating solid objects with complex geometry is a challenging task. In the present study, the volume penalization method (VPM) is combined with multiple reference frame (MRF) and sliding mesh (SLM), respectively, so as to develop immersed-boundary approaches for simulating flows around a rotating solid. The level-set function is adopted to represent arbitrary geometries embedded in Cartesian grids. The VPM body-forcing terms in the momentum equation are proposed for MRF and SLM, respectively, so as to build unified governing equations for both fluid and solid regions. The flows around a rotating cuboid under various rotating speeds are simulated by the present schemes, namely, VPM with MRF, and VPM with SLM, and compared to corresponding simulations by the body-fitted method (BFM). The results suggest the relative deviations of predicted pressure drop and torque between the present VPM and BFM are around 5%, demonstrating the validity of the present VPM.

Figures (8)

• Figure 1: Schematic for the flow around rotating solids.
• Figure 2: Schematic of the grid systems used in (a) MRF and (b) SLM.
• Figure 3: Profiles of the level-set function $\phi_{0}$ and the phase indicator $\phi$ in the vicinity of the fluid-solid interface.
• Figure 4: Case setting of the flow around a rotating cuboid.
• Figure 5: Distribution of Cartesian grids for (a) VPM with MRF and (b) VPM with SLM and structured grids for (c) BFM with MRF and (d) BFM with SLM. Here, the white and the green line indicate the fluid-solid interface and static-rotating interface, respectively.