Non-Classical Modeling of Cosserat Fluid-Structure Interaction System for Analyzing Micro-Rotational Effects of Micro-Viscosities on Flow Velocity Fields - Nazim Hussain Hajano; Muhammad Sabeel Khan; Mumtaz Ali Kaloi; M. Asif Memon; Lisheng Liu (Partial Differential Equations in Applied Mathematics)
Conservation laws of classical continuum mechanics are naturally written in the Eulerian frame where only the expression of the stress tensor distinguish fluids and solid structures, usually with Newtonian’s hypothesis for fluids and Helmholtz potential of energy for hyper-elastic solid structures. In the recent literature, the benchmark solutions of fluid-structure interaction (FSI) phenomenon present in a classical continuum mechanics have been used to study different flow characteristics by taking into account a non-classical Cosserat fluid-structure interaction (CFSI) problems. In these studies, different micro-structural characteristics of flow velocity fields have been analyzed by validating results in a non-classical framework. However, the micro-rotational effects of micro-viscosity parameters λ which combines shear spin viscosity β and rotational spin viscosityγare very significant in analyzing the behavior of flow fields in such coupling problems still needs to be improved and extended at the micro- structural level. Therefore, this paper extends the scope of the study for analyzing micro-rotational effects of micro-viscosity parameters of the Cosserat fluid on flow velocity fields by employing the monolithic Eulerian approach to such non-classical coupling problem. The conservation laws of continuum mechanics are used to derive the governing dynamics and variational formulation of the present Cosserat fluid-structures system. The problem domains are discretized using the proposed schemes and algorithm for computer simulations is implemented with publicly available software freefem++. Results of the present study indicates that, the micro-viscosity parameter λ effects the micro-rotation velocity field ω significantly as compare to the velocity field u such that fluid particles undergo large micro-rotation near the control point A in the computational domain. Further, the micro-rotational effects of fluid particles are found minimum on the axis of symmetry of the control point A and vanishes on the computational boundaries. Finally, the color visualizations of the micro-rotational velocity profile with contour plots are also presented and the study is concluded with some future recommendations and limitations.