Giuseppe Antonio Zampogna

Related publications (6)

Permeability sets the linear path instability of buoyancy-driven disks

François Gallaire, Pier Giuseppe Ledda, Giuseppe Antonio Zampogna

The prediction of trajectories of buoyancy-driven objects immersed in a viscous fluid is a key problem in fluid dynamics. Simple-shaped objects, such as disks, present a great variety of trajectories, ranging from zig-zag to tumbling and chaotic motions. Yet, similar studies are lacking when the object is permeable. We perform a linear stability analysis of the steady vertical path of a thin permeable disk, whose flow through the microstructure is modelled via a stress-jump model based on homogenization theory. The relative velocity of the flow associated with the vertical steady path presents a recirculation region detached from the body, which shrinks and eventually disappears as the disk becomes more permeable. In analogy with the solid disk, one non-oscillatory and several oscillatory modes are identified and found to destabilize the fluid-solid coupled system away from its straight trajectory. Permeability progressively filters out the wake dynamics in the instability of the steady vertical path. Modes dominated by wake oscillations are first stabilized, followed by those characterized by weaker, or absent, wake oscillations, in which the wake is typically a tilting induced by the disk inclined trajectory. For sufficiently large permeabilities, the disk first undergoes a non-oscillatory divergence instability, which is expected to lead to a steady oblique path with a constant disk inclination, in the nonlinear regime. A further permeability increase reduces the unstable range of all modes until quenching of all linear instabilities.

CAMBRIDGE UNIV PRESS2023

, ,

A model to describe the transport across membranes of chemical species dissolved in an incompressible flow is developed via homogenization. The asymptotic matching between the microscopic and macroscopic solute concentration fields leads to a solute flux jump across the membrane, quantified through the solution of diffusion problems at the microscale. The predictive model, written in a closed form, covers a wide range of membrane behaviors, in the limit of negligible Reynolds and Peclet numbers inside the membrane. The closure problem at the microscale, found via homogenization, allows one to link the membrane microstructure to its effective macroscopic properties, such as solvent permeability and solute diffusivity. After a validation of the model through comparison with the corresponding full-scale solution, an immediate application is provided, where the membrane behavior is a priori predicted through an analysis of its microscopic properties. The introduced tools and considerations may find applications in the design of thin microstructured membranes. Published under an exclusive license by AIP Publishing.

AIP Publishing2022

, , ,

A formal framework to characterize and control/optimize the flow past permeable membranes by means of a homogenization approach is proposed and applied to the wake flow past a permeable cylindrical shell. From a macroscopic viewpoint, a Navier-like effective stress jump condition is employed to model the presence of the membrane, in which the normal and tangential velocities at the membrane are respectively proportional to the so-called filtrability and slip numbers multiplied by the stresses. Regarding the particular geometry considered here, a characterization of the steady flow for several combinations of constant filtrability and slip numbers shows that the flow morphology is dominantly influenced by the filtrability and exhibits a recirculation region that moves downstream of the body and eventually disappears as this number increases. A linear stability analysis further shows the suppression of vortex shedding as long as large values of the filtrability number are employed. In the control/optimization phase, specific objectives for the macroscopic flow are formulated by adjoint methods. A homogenization-based inverse procedure is proposed to obtain the optimal constrained microscopic geometry from macroscopic objectives, which accounts for fast variations of the filtrability and slip profiles along the membrane. As a test case for the proposed design methodology, a cylindrical membrane is designed to maximize the resulting drag coefficient.

CAMBRIDGE UNIV PRESS2021

, , ,

We study the flow past a permeable sphere modeled using homogenization theory. The flow through the porous medium is described by the Darcy law, in which the permeability quantifies the resistance for the fluid to pass through the microstructure. A slip condition on the tangential velocity at the interface between the fluid and porous region is employed to account for the viscous effects in the proximity of the interface. The steady and axisymmetric flow is first characterized under the assumption of a homogenous and isotropic porous medium. In a certain range of permeability, the recirculation region penetrates inside the sphere, resulting in a strong modification of the linear stability properties of the flow and in a decrease in the critical Reynolds numbers for the flow instability. However, for very large permeabilities, a critical permeability value is identified, beyond which the steady and axisymmetric flow remains always linearly stable. The hypothesis of a homogenous porous medium is then relaxed, and the effect of polynomial distributions of permeability inside the body is studied. Interestingly, some macroscopic flow properties do not significantly vary with the permeability distributions, provided that their average is maintained constant. The analysis is concluded by outlining a simplified procedure to retrieve the full-scale structure corresponding to a considered distribution of permeability.

AIP Publishing2021

Effective stress jump across membranes

François Gallaire, Giuseppe Antonio Zampogna

A macroscopic condition to simulate the interaction between an incompressible fluid flow and a permeable micro-structured rigid surface (i.e. a thin membrane) has been developed using multiscale homogenization and matching asymptotic expansions between the near membrane and the far region. The condition allows us to write the fluid velocity across the membrane, seen macroscopically as a smooth equivalent surface, as an effective jump between the stresses computed on the two faces of this surface. The coefficients appearing in the jump condition are the entries of tensors which solve Stokes problems within the pores, enforced by boundary conditions depending on the flow outside the membrane. These problems, found via homogenization, definitely characterize the microscopic geometrical properties of thin permeable micro-structured sheets. The new macroscopic model is validated by comparisons with direct numerical simulations of the fluid flow across membranes in different configurations, proving that the formalism adopted to write the jump conditions is valid. As a result, a rational tool able to join a microscopic and a macroscopic analysis of fluid flows across membranes is delivered, showing some potentialities to provide advancement in membrane design. It suggests that the concept of permeability has to be substituted by a more general tensor, called here the Navier tensor, which plays the role of permeability only in some particular situations.

CAMBRIDGE UNIV PRESS2020

Compliant riblets: Problem formulation and effective macrostructural properties

Alessandro Bottaro, Giuseppe Antonio Zampogna

Small-scale, deformable riblets, embedded within the viscous sublayer of a turbulent boundary layer and capable to adapt to the overlying motion, are studied. The wall micro-grooves are made of a linearly elastic material and can undergo small deformations; their collective behavior is assumed to occur over a large, elastic wavelength. The presence of two length scales allows for the use of a multiscale homogenization approach yielding microscopic problems for convolution kernels and parameters, which must then be employed in macroscopic boundary conditions to be enforced at a virtual wall through the riblets. The results found suggest that, in analogy to the case of rigid riblets, compliant, blade-like wall corrugations are more effective than triangular riblets in reducing skin friction drag, provided the spanwise periodicity of the indentations is sufficiently small for the creeping flow approximation to be tenable. (C) 2019 Elsevier Ltd. All rights reserved.

2019