Increasing Micro-Rotational Viscosity Results in Large Micro-Rotations: A Study Based on Monolithic Eulerian Cosserat Fluid–Structure Interaction Formulation

Abstract

In classical continuum mechanics, a monolithic Eulerian formulation is used for numerically solving fluid–structure interaction (FSI) problems in the frame of a physically deformed configuration. This numerical approach is well adapted to large-displacement fluid–structure configurations where velocities of solids and fluids are computed all at once in a single variational equation. In the recent past, a monolithic Eulerian formulation for solving FSI problems of finite deformation to study the different physical features of fluid flow has been employed. Almost all the current studies use a classical framework in their approach. Despite producing decent results, such methods still need to be appropriately configured to generate exceptional results. Recently, a number of researchers have used a non-classical framework in their approach to analyze several physical problems. Therefore, in this paper, a monolithic Eulerian formulation is employed for solving FSI problems in a non-classical framework to study the micro-structural characteristics of fluid flow by validating the results with classical benchmark solutions present in the literature. In this respect, the Cosserat theory of continuum is considered where a continuum of oriented rigid particles has, in addition to the three translational degrees of freedom of classical continuum, three micro-rotational degrees of freedom. The mathematical formulation of model equations is derived from the general laws of continuum mechanics. Based on the variational formulation of the FSI system, we propose the finite element method and semi-implicit scheme for discretizing space and time domains. The results are obtained by computing a well-known classical FSI benchmark test problem FLUSTRUK-FSI-3* with FreeFem++. The results of the study indicate that the increase in micro-rotational viscosity μr leads to significantly large micro-rotations in fluid flow at the micro-structural level. Further, it is found that the amplitude of oscillations is related inversely to the material parameters c1 and μr while the increase in c1 stabilizes the amplitude of oscillations relatively more quickly than increasing μr The color snapshots of the numerical results at different times during the computer simulations and general conclusions drawn from the results are presented.

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

“…In this study, the bold characters represent vectors and tensors, with some exceptions, such as x, x 0 ∈ R d , d = 2 or 3. The standard notations used in the entire text are detailed in [10,37,62,[75][76][77][78][79]. The following field variables in the present study are used: X : Ω 0 × (0, T) → Ω t : X x 0 , t is the material location at time t of x 0 (i.e., a material point at x 0 at t = 0 is transported to X at time t by the motion).…”

“…In the above, ρ f and σ f are the density and the stress tensor in the fluid, while ρ s and σ s are the density and the stress tensor in the solid structure, respectively. The set function indicators 1 Ω t f and 1 Ω t s are used in numerical simulation [62]. Unless specified, all spatial derivatives in this mathematical modeling of the CFSI are taken with respect to x ∈ Ω t and not w.r.t…”

“…The present benchmark test was first proposed and studied by [80] and then by [23,30,81], respectively, in a classical framework, and more recently by [62] in a nonclassical framework.…”

“…The configuration, boundary conditions, and initial conditions for the present benchmark test FLUSTRUK-FSI-3* are described in Table 1, as suggested in [23,30,62]:…”

“…Recently, extensive literature has been attributed to the significant analysis of the microstructural characteristics of fluid flow by employing a monolithic Eulerian formulation to FSI problems of finite structural deformation by computing the classical benchmark test in a non-classical classical framework [62]. Nevertheless, the study of the microstructural characteristics of fluid flow using these classical benchmark test solutions still needs to be enhanced and extended further to analyze the combined effect of linearly increasing Reynolds number R e and mean inflow velocity U on flow velocity fields with mesh independence analysis at the micro-structural level in a non-classical framework.…”