Combined Micro-Structural Effects of Linearly Increasing Reynolds Number and Mean Inflow Velocity on Flow Fields with Mesh Independence Analysis in Non-Classical Framework

Nazim Hussain Hajano (), Muhammad Sabeel Khan, Lisheng Liu, Mumtaz Ali Kaloi and Hai Mei
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Nazim Hussain Hajano: Department of Engineering Structure and Mechanics, Wuhan University of Technology, Wuhan 430070, China
Muhammad Sabeel Khan: Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan
Lisheng Liu: Department of Engineering Structure and Mechanics, Wuhan University of Technology, Wuhan 430070, China
Mumtaz Ali Kaloi: Department of Computer Systems Engineering, Sukkur Institute of Business Administration University, Sukkur 65200, Pakistan
Hai Mei: Hubei Key Laboratory of Theory and Application of Advanced Material Mechanics, Wuhan University of Technology, Wuhan 430070, China

Mathematics, 2023, vol. 11, issue 9, 1-21

Abstract: The monolithic Eulerian formulation has widely been employed for solving numerically fluid–structure interaction (FSI) problems of finite structural displacement using the same mathematical variational formulation for fluid and structural dynamics. Recently, different physical features of fluid flow have been analyzed using this approach to such coupling problems by computing the classical benchmark solutions in a non-classical framework. Despite producing decent results, the analysis of micro-structural characteristics of fluid flow by applying the classical benchmark solutions still needs to be enhanced and extended further for such coupling problems. In this paper, the classical benchmark solutions have been enhanced and extended further for analyzing the combined micro-structural effects of linearly increasing Reynolds number R e and mean inflow velocity U ¯ on flow fields with mesh independence analysis by employing a monolithic Eulerian formulation in a non-classical framework. To this aim, the Cosserat fluids theory is taken into account for the present coupling problem by considering three micro-rotational degrees of freedom (dof) of fluid particles. The model equations of the proposed Cosserat fluid–structure interaction (CFSI) problem are derived using underlying laws of continuum mechanics. A numerical section presents the implementation of the benchmark problem with test examples followed by a detailed evaluation of the obtained results. The results obtained indicate that a uniform linear increase in Reynolds number R e and mean inflow velocity U ¯ produce the significant combined micro-structural effects on the micro-rotation velocity field ω , and this effect is found increasing on the increase of both parameters. This combined effect of increasing R e and U ¯ on the velocity field u is also observed to be very significant in a sense that horizontal and vertical flow velocity profiles experience great variation by maintaining the same pattern on each increasing value of R e and U ¯ at any particular location in the computational domain. Further, the mesh independence analysis is employed to verify the convergence of obtained results. The study concludes that the linear increase in Reynolds number and mean inflow velocity affect micro-rotational velocity field significantly at the micro-structural level with mesh independence analysis. Finally, some future recommendations to enhance and extend the study with some of its limitations are presented.

Keywords: Cosserat fluid–structure interaction; monolithic Eulerian variational formulation; finite element; finite structural displacement; FreeFEM++ (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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