Stress field measurement in Jeffery-Hammel flow

Investigation of unsteady shear stress distribution is the key in biomechanical engineering, such as revealing the rupture mechanism of cerebral aneurysms. Therefore, we focused on the photoelastic method to visualize the stress field of flow. The photoelastic method is a non-contact stress visualization technique based on changes in optical anisotropy and has been developed in the field of solids. To apply this method to the flow field, it is necessary to clarify the relationship between the polarization characteristics and the stress tensor. In the previous studies, Calabrese et al. (2021) performed experiments in extensional and shear flow and showed that the effect on the retardation is four times larger in extensional flow than in shear flow. Lane et al. (2022) successfully measured strain rate in shear flow, however, the experimental results in combined extensional-shear flow showed a discrepancy between analytical solutions. The purpose of this study is to investigate the relationship between the polarization state and stress in combined extensional-shear flow. To derive the stress, a Jeffery-Hamel flow in a two-dimensional convergent or divergent channel was used, where the analytical solution for the velocity field exists. The stress field in a steady Jeffery-Hamel flow channel was measured using polarization camera. The measured phase retardation and orientation were compared to the stress analytically calculated to show the relationship.