Recent Advances in Mechanics and Fluid-Structure Interaction with Applications

In this paper, we study nonlinear problems with an operator depending only on the symmetric gradient. We consider the class of operators, derived from a potential, having (p, δ)-structure for some 1 < p ≤ 2 and some δ ≥ 0. We apply the so -called A-approximation method to approximate the operator by another one with linear growth. This allows us to prove “natural” second-order regularity (up to the boundary) in the case of homogeneous Dirichlet boundary conditions. We focus on the steady (elliptic) case. However, corresponding results are stated also in the time-dependent (parabolic) case.

The study of the three-dimensional fluid model for which the Cauchy stress tensor depends on the cross viscosity function is a challenging and complex model in terms of computational effort. To simplify this computational difficulty presented by the three-dimensional problem, we use an approach based on the Cosserat theory related to fluid dynamics which reduces the three-dimensional problem to a one-dimensional system of ordinary differential equations depending only on time and a single spatial variable. From this new system, we obtain the unsteady equation for the mean pressure gradient depending on the volume flow rate, Womersley number, and viscosity parameters over a finite section of straight, rigid, and impermeable tube with constant circular cross section. In particular, given specific data, we can obtain information about the volume flow rate, and consequently we can illustrate the three-dimensional velocity field.

Consider a rigid body, \(\mathscr S\), moving in a viscous liquid, \(\mathscr L\), subject to a linear elastic restoring force. The motion of the coupled system body liquid is driven by a uniform flow of \(\mathscr L\) at large distance from \(\mathscr S\), characterized by a given time-periodic velocity U = U(t) of period T > 0. Under the assumption of creeping flow for the liquid (Stokes approximation), we show that both \(\mathscr S\) and \(\mathscr L\) will perform a uniquely determined time-periodic motion of period T in a suitable regularity class. Since T is arbitrary, this implies, in particular, that resonance does not occur. The same result holds if, in addition, time-periodic forces of period T are acting on \(\mathscr S\) and/or \(\mathscr L\).

We study the motion of a rigid sphere falling in a two-layer stratified fluid under the action of gravity in the potential flow regime. Experiments at a moderate Reynolds number of approximately 20–450 indicate that a sphere with the precise critical density, higher than the bottom layer density, can display behaviors such as bounce or arrestment after crossing the interface. We experimentally demonstrate that such a critical sphere density increases linearly as the bottom fluid density increases with a fixed top fluid density. Additionally, the critical density approaches the bottom-layer fluid density as the thickness of density transition layer increases. We propose an estimation of the critical density based on the potential energy. Assuming the zero-layer thickness, the estimation constitutes an upper bound of the critical density with less than 0.043 relative difference within the experimental density regime 0.997 g/cm³ ∼1.11 g/cm³ under the zero-layer thickness assumption. By matching the experimental layer thickness, we obtain a critical density estimation with less than 0.01 relative difference within the same parameter regime.

The problem of numerical solution of the viscous incompressible fluid flows in branching (bifurcating) channels is addressed using different discretization techniques. The methods are briefly described, pointing out the main differences in their behavior and numerical implementation on different types of grids. The newly developed finite difference immersed boundary code is compared with two in-house and open-source finite volume methods. The mutual comparison of the predictions from all methods is presented for the case of channel with an oblique branch inclined at different angle. The aim of the paper is to show that the very simple finite difference method implemented on Cartesian grid can provide results that are comparable with those obtained by the presented finite volume methods on structured, wall-aligned grids.

We introduce both distinct quadrature and distinct polynomial degrees for the deviatoric and volumetric terms of the right Cauchy-Green tensor in the context of a Lagrangian-based element-free Galerkin (EFG) discretization. First and second derivatives of the mixed deformation gradient are made available. A finite element mesh is employed for quadrature purposes with the corresponding distribution of Gauss points. In terms of discretization, linear, quadratic, and cubic polynomials are combined, and support is determined from the number of pre-assigned nodes. Due to the adoption of a Lagrangian kernel, finite strain elastoplastic constitutive developments are based on the Mandel stress. These developments are found to be especially convenient from the implementation perspective, as EFG formulations for finite strain plasticity have been limited in terms of generality and amplitude of deformations in both compressible and quasi-incompressibility cases. Three benchmark tests are successfully solved, and it was found that a combination of cubic and quadratic bases provides superior results in the quasi-incompressible case. Besides absence of locking with selective interpolation, outstanding Newton convergence was observed regardless of strain levels.

In this paper, we present a brief tutorial on reduced order model (ROM) closures. First, we carefully motivate the need for ROM closure modeling in under-resolved simulations. Then, we construct step by step the ROM closure model by extending the classical Galerkin framework to the spaces of resolved and unresolved scales. Finally, we develop the data-driven variational multiscale ROM closure, and then we test it in fluid flow simulations.

Our tutorial on ROM closures is structured as a sequence of questions and answers, and is aimed at first year graduate students and advanced undergraduate students. Our goal is not to explain the “how,” but the “why.” That is, we carefully explain the principles used to develop ROM closures, without focusing on particular approaches. Furthermore, we try to keep the technical details to a minimum and describe the general ideas in broad terms while citing appropriate references for details.

This contribution presents an overview and summary of the artificial diffusion concept applied to numerical simulations of viscoelastic fluid flows. The classical Oldroyd-B model is considered as an example and prototype of viscoelastic rate type fluid models. The broader concept of numerical diffusion is presented, with special focus on tensorial artificial stress diffusion that proved to be a valuable tool in stabilizing the viscoelastic fluid flow simulations at higher Weissenberg numbers. Several variants of tensorial artificial diffusion are presented and discussed, focusing on practical aspects of their implementation and use.

A family of cellular automata arising from perturbations of a basic cellular automata rule, represented by 3E6IGS58S, in base 32, is studied. These rules can be seen as modeling idealized fluids in non-equilibrium, subject to interaction on distinct phases. Using adaptive techniques such as assembly and singular perturbation of cellular automata, we present several simulations showing the increase of complexity in the perturbed systems behavior, in particular, showing the increasing number of distinct spatial-temporal patterns exhibited.

Self-organization can be characterized as the emergence of mutual constraint among elements of a system with many flexible degrees of freedom. This mutual constraint emerges from the nonlinear interactivity between the constituents and the driving nonequilibrium boundary conditions. We review here interesting self-organized dynamics in systems where this interactivity among solid elements is mediated by an embedding fluid. In separate electrical and chemical nonequilibrium systems, we observe self-organization of solid elements exhibiting mutual constraint due to reciprocal interactions between the solids and the embedding fluid. This mutual constraint supports a variety of interesting dynamics for the emergent structures, including several behaviors with biological analogues. The reciprocal solid-fluid interactions mirror aspects of biological behavior construed as organism-environment reciprocities. We lay foundations for a mapping between these physical and psychological phenomena to enrich the application of dissipative self-organization theory to biology.

The current study focuses on hydrokinetic energy harvesting by means of vortex-induced autorotation. The vortex-induced turbines rely on the vibrations generated by vortex-shedding trails downstream. Three distinct bladeless rotor designs are evaluated for their performance in terms of energy generation. Here, the power generation of two triangular prisms featured with straight sides and curved sides and a Cross Cylinder turbine model are compared. The triangular designs are selected in this study due to its known autorotation characteristics. The turbine models are printed using PLA, and each turbine is tested in an open water flume for flow speeds ranging from 30 cm/s to 60 cm/s. For each speed, the turbine model is tested under four different conditions: free flow, tandem, and flow with close and far upstream partial obstacles. Results indicate that power generation and maximum possible power, generally, are increasing with the flow speed. The power production of turbines exposed to free flow can be increased by 200% when the partial blockages are applied. The triangular turbine design with curved sides shows better performance compared to one with straight sides and the Cross Cylinder model.

In this paper we study a multiphysics/multidomain system of partial differential equations defined by hyperbolic and parabolic equations. We consider two wave equations and two diffusion equations defined in two different domains. The diffusion equations are considered of different types: a Fickian equation and a non-Fickian equation. In the interface continuity conditions are assumed for the wave equations, while for the diffusion equation only continuity of the mass fluxes is considered. The mathematical problem considered here can be used to model the drug transport in the cancer scenario when ultrasound is used as enhancer. In this case the two spatial domains model the healthy and cancer tissues. The drug transport through the healthy tissue is described by the Fickian diffusion equation, while the non-Fickian diffusion equation is used to model the drug transport in the cancer tissue. To break the physiological barriers increasing the drug transport, ultrasound has been proposed in different contexts. As ultrasound propagates through the target tissues as pressure waves, wave equations are used to describe the pressure wave intensity that induces an increase in the Brownian transport and in the convective transport. The stability of the partial differential system is studied and its behavior is numerically illustrated.

Strokes are the fifth leading cause of death in the United States and can cause long-term disabilities in patients who survive a stroke. The vast majority of these strokes are ischemic, primarily caused by intracranial atherosclerosis. Most therapies to combat intracranial atherosclerosis simply manage it and do not remove the buildup of plaque. Targeted shear-activated nano-therapeutics are currently being developed to remove these plaques. We discuss the roles that aggregate particle density, aggregate particle diameter, vessel geometry, stenosis shape, and breakup threshold play in the efficiency of this new technology. Computational studies were performed to test these parameters in three idealized vessels with varying curvatures (straight, quarter-circle, semi-circle) and two different stenosis shapes (concentric, eccentric). We find that curvature plays a large role in the breakup threshold. The optimal breakup threshold for a semi-circular shaped vessel is 4.5 times that of a straight vessel, yet the less curved quarter-circle shaped vessel has an optimal breakup threshold that is 6.3 times that of the straight vessel. Therefore, no quantifiable pattern was discovered between geometry curvature and optimal threshold value. Curvature also plays a large role in how particle diameter affects the efficiency of these nano-therapeutics. Although the effects of particle size between 1 and 5 μm is minimal, the optimal particle diameter for a straight vessel was located at the smallest end of the tested range while the optimal diameter for the curved case was located at the largest end of the tested range. Particle-specific density was explored and found to have a negligible effect. Finally, curvature and stenosis location (superior, inferior, and ventral/dorsal) play a large role in optimizing breakup position. It is optimal for the stenosis to be in the path of the aggregate particle.

In this paper, we present a simple analysis to explore the possibility of using compressed CO₂ for air-cooling applications based on its Joule-Thomson cooling capability. In the analysis, gaseous CO₂ stored in a high-pressure compressed tank is allowed to expand into a low-pressure heat exchanger having multiple flow paths. Two flow configurations (parallel and counter flows) are used. Five different values (1–5 MPa) for the pressure of the compressed tank are used, while the pressure of the heat exchanger is kept constant at 0.1 MPa. While keeping the dimensions of the flow path (thickness = 2 cm, width = 10 cm, length = 1 m) unchanged, the total heat transfer, exit air, and CO₂ temperatures are calculated. The results show that these depend significantly on the compressed tank pressure, the number of the flow paths, and air mass flow rates. When the pressure of the compressed tank is 5 MPa, our results indicate that the Joule-Thomson cooling capability of CO₂ expansion can effectively generate a cooling power from 3 to 4 kW in the heat exchanger, and a stream of 124 g/s of hot air flowing through it can have a temperature drop from 25 to 30 °C.

This study aims to computationally identify the detailed mechanisms of the adhesion process of mucin and foreign bodies in the human tear film subject to the blinking motion of eyelid. The results give us a clue about the role of mucus as a protective agent for the ocular surface and its role in diseases such as dry eye syndrome (DES). We propose a multi-phase model which models the tear film as an inhomogeneous fluid comprising of a mixture of an aqueous layer in which mucin particles are exponentially distributed in the direction normal to corneal surface. We model the mucin adherence to any immersed foreign object, and its overall clearance through the blinking motion of the eyelid. The motions of mucin in the flow are solved by a force balance equation which accounts for the macroscopic interactions between the fluid and the body. The clearance rates of the foreign particle are explored under various conditions with different varying mechanical properties of mucin such as its adhesion force, distribution profile, as well as its viscosity. Our parametric study shows that a condition for higher clearance rate requires (i) greater mucin population in the entire region of tear film, i.e., larger viscosity, (ii) an optimal mucin distribution profile, and (iii) normal physiologic adhesion force between mucin and immersed particles.