Press: Wolf Dynamics - Formula 1

Master theses

Ottimizzazione Aerodinamica dell’ala frontale per una monoposto di Formula1 del 2022, utilizzando il metodo dell’aggiunto.
Eric Segalerba (2021) [thesis] [presentation]


Project description: Computations 4 Competitions
A Numerical Study to Support Clinical Tests of Graft-Gas Coverage after DMEK
Victor Garcia Bennett (2020) [thesis] [presentation]



Example of DMEK analysis clinically and numerically
Numerical Simulations of the Atmospheric Chamber (ChAMBRe) to Study Bioaerosol
Giovanni Curedda (2019) [thesis] [presentation]


Bioaerosol: 200 000 particles in 5 minutes
Microparticle production by spray dryer and validation with CFD simulation
Emanuela Drago (2018) [thesis][presentation]

Calcium Carbonate 5ml/min (temperature, diameter, age)
full list of news

submitted for publication

An adjoint Green's function approach for thermoacoustic instabilities in a duct with mean flow

J. Wei; S. Arabi; J. O. Pralits; A. Bottaro & M. A. Heckl
Journal of Sound and Vibration, 2024


Thermoacoustic instability, a crucial concern in power generation and aeroengine industries, arises due to feedback between the acoustic field and the heat released in a burner, causing self-sustained oscillations. This work introduces a powerful framework for modeling and predicting thermoacoustic instabilities based on an adjoint Green's function (AGF) approach. The versatility of the AGF approach is demonstrated by applying it to a Rijke tube and a quarter-wave resonator with different acoustic boundary conditions. The control parameters include the heat source position, the heater power, and the tube length. The thermoacoustic system examined is one-dimensional and it includes a steady uniform mean flow and a nonlinear heat source characterized by an amplitude-dependent time-delay heat release model. The results reveal that the AGF approach successfully captures the limit cycles, triggering phenomena, hysteresis, and Hopf bifurcations observed in experiments. It is shown that increasing the mean flow velocity is generally stabilizing, with a modification of the bistability characteristics of the system.

Engineered small-diameter vascular prostheses: a study in bioreactor

P.F. Ferrari, G. De Negri Atanasio, J.O. Pralits, D. Di Lisa, L. Pastorino, D. Palombo & P. Perego
Biomaterials Science , 2024


Vascular tissue engineering endeavors to design, fabricate, and validate biodegradable and bioabsorbable small-diameter vascular scaffolds engineered with bioactive molecules, capable of meeting the challenges imposed by commercial vascular prostheses. A comprehensive investigation of these engineered scaffolds in bioreactor is deemed essential as a prerequisite before any in vivo experimentation in order to get information regarding their behavior under physiological conditions and predict the biological activities they will possess. This study focuses on an innovative electrospun scaffold made of poly(caprolactone) and poly(glycerol sebacate), integrating quercetin, able to modulate inflammation, and gelatin, necessary to reduce permeability. A custom-made bioreactor was used to assess the performances of the scaffolds maintained under different pressure regimes, covering the human physiological pressure range. As results, the 3D microfibrous architecture was notably influenced by the release of bioactives, maintaining the adequate properties needed for the in vivo regeneration and scaffolds showed mechanical properties similar to human native artery. Release of gelatin was adequate to avoid blood leakage and useful to make the material porous during the testing period, whereas the amount of released quercetin was useful to counteract the post-surgery inflammation. This study showcases the successful validation of an engineered scaffold in a bioreactor, enabling to consider it as a promising candidate for vascular substitutes in in vivo applications. Our approach represents a significant leap forward in the field of vascular tissue engineering, offering a multifaceted solution to the complex challenges associated with small-diameter vascular prostheses.

recent publications

Stability of turbine-like boundary layers under variable Reynolds number and pressure gradient<

Dotto, Luzzi, Verdoya, Simoni, Hanifi & Pralits
Physics of Fluids, Vol. 36, 034116, doi 10.1063/5.0188024, 2024


The free-stream turbulence induced transition occurring in turbine-like flows is investigated employing linear stability theory and compared with experimental data. Measurements were performed over a flat plate in a test section allowing for the Reynolds number and pressure gradient variation. A test matrix spanning three different Reynolds and four different pressure gradients under high turbulence intensity was investigated to model conditions typically occurring on turbomachinery low-pressure turbine blades. Pressure measurements and Particle Image Velocimetry (PIV) measurements were used to characterize the base flow on a wall-normal plane. Additionally, PIV allowed to detect the spanwise wave number of streaky structures on a wall-parallel plane. A boundary layer solver was first employed to compute base flows from the flat plate leading edge. Successively, a linear stability analysis was performed on the numerical base flows using an adjoint optimization method, and the optimal disturbances were compared with experimental data. Overall, good agreement is found between the linear stability results and the experimentally surveyed perturbations in the transitional region. The sensitivity of the disturbance transient spatial growth is assessed as a function of the spanwise wavenumber, the initial and the final location where the energy of perturbation is maximized. Interestingly, the optimal initial position that maximizes the energy growth of disturbances is close to the geometrical throat of the test section, where minimum pressure occurs for all flow conditions.

On rotor-stator emulsification in the turbulent inertial regime: Experiments towards a robust correlation for the droplet size

Campardelli, De Negri Atanasio, Carotenuto, Griffo, Nabil Ahmed, Corrales González, Tuju, Wei, Mazzino & Pralits
Langmuir, Vol 39 (50), pp. 18518–1852 2023
[abstract] [article]


The Sauter mean diameter, d32, is a representative parameter in emulsions that indicates the averaged size of oil droplets once the emulsion becomes stable. Several mathematical and physical approaches have been employed in the literature to seek expressions for d32 under different conditions. The present work sheds light on this rich literature, and emphasizes that characterization of emulsions is still a fertile field for investigation. In this paper, a new Π-theorem-based model to predict the normalized Sauter mean diameter for the specific case of rotor-stator emulsification is sought by applying a multiple regression analysis on experimental data of oil-in-water (O-W) emulsions produced using three different oils: paraffin, soybean oil, and isopropyl myristate, at different O-W ratios and rotor speeds. The proposed model quantifies the roles of the viscous, the inertial, and the interfacial tension forces, besides the O-W ratio, in the emulsification process within the turbulent inertial subrange. The developed empirical correlation is then contrasted with relevant literature models for reliability assessment; predictions of the present explicit model are proved to be more accurate for the fluid properties and the experimental conditions under study.

On the comparison between pre- and post-surgery nasal anatomies via computational fluid dynamics

E. Segalerba, G. Dini Ciacci, M. Quadrio & J.O. Pralits
Biomechanics and Modeling in Mechanobiology, 2023
[abstract] [article]


Purpose: Nasal breathing difficulties (NBD) are widespread and dif- ficult to diagnose; the failure rate of their surgical corrections is high. Computational Fluid Dynamics (CFD) enables diagnosis of NBD and surgery planning, by comparing a pre-operative (pre-op) situation with the outcome of virtual surgery (post-op). An equivalent comparison is involved when considering distinct anatomies in the search for the functionally normal nose. Currently, this comparison is carried out in more than one way, under the implicit assumption that results are unchanged. The study describes how to set up a meaningful comparison.
Methods: A pre-op anatomy, derived via segmentation from a CT scan, is compared with a post-op anatomy obtained via virtual surgery. State-of-the-art numerical simulations compute the flow for a steady inspiration, under three types of global constraints, derived from the field of turbulent flow control. A constant pressure drop (CPG) between external ambient and throat, a constant flow rate (CFR) through the airways and a constant power input (CPI) from the lungs can be enforced.
Results: A significant difference in the quantities of interest is observed when the type of flow forcing is varied. Global quantities (flow rate, pressure drop, nasal resistance) as well as local ones are affected.
Conclusions: The type of flow forcing affects the outcome of the comparison between pre-op and post-op anatomies. Among the three available forcings, we argue that CPG is the least ade- quate. Arguments favouring either CFR or CPI are presented.

Optimization of patient positioning for improved healing after corneal transplantation

Bennett, Alberti, Quadrio & Pralits
Journal of Biomechanics, 2023
[abstract] [article]


Corneal transplantation is the only solution which avoids loss of vision, when endothelial cells are dramatically lost. The surgery involves injecting gas into the anterior chamber of the eye, to create a bubble that pushes onto the donor cornea (graft), achieving sutureless adherence to the host cornea. During the postoperative period, patient positioning affects the bubble. To improve healing, we study the shape of the gas-bubble interface throughout the postoperative period, by numerically solving the equations of fluid motion. Patient-specific anterior chambers (ACs) of variable anterior chamber depths (ACD) are considered, for either phakic (with natural lens) and pseudophakic (with artificial lens) eyes. For each AC, gas-graft coverage is computed for different gas fill and patient positioning. The results show that the influence of positioning is negligible, regardless of gas filling, as long as the ACD is small. However, when the ACD value increases, patient positioning becomes important, especially for pseudophakic ACs. The difference between best and worst patient positioning over time, for each AC, is negligible for small ACD but significant for larger ACD, especially for pseudophakic eyes, where guidelines for optimal positioning become essential. Finally, mapping of the bubble position highlights the importance of patient positioning for an even gas-graft coverage.

Effects of Upstream Wakes on the Boundary Layer Over a Low-Pressure Turbine Blade

L. De Vincentiis, K. Ðurović, D. Lengani, D. Simoni, J.O. Pralits, D.S. Henningson & A. Hanifi
Journal of Turbomachinery, 2023
[abstract] [pdf]


In the present work, the evolution of the boundary layer over a low-pressure turbine blade is studied using direct numerical simulations, with the aim of investigating the unsteady flow field induced by the rotor-stator interaction. The freestream flow is characterized by the high level of freestream turbulence and periodically impinging wakes. As in the experiments, the wakes are shed by moving bars modeling the rotor blades and placed upstream of the turbine blades. To include the presence of the wake without employing an ad-hoc model, we simulate both the moving bars and the stationary blades in their respective frames of reference and the coupling of the two domains is done through appropriate boundary conditions. The presence of the wake mainly affects the development of the boundary layer on the suction side of the blade. In particular, the flow separation in the rear part of the blade is suppressed. Moreover, the presence of the wake introduces alternating regions in the streamwise direction of high- and low-velocity fluctuations inside the boundary layer. These fluctuations are responsible for significant variations of the shear stress. The analysis of the velocity fields allows the characterization of the streaky structures forced in the boundary layer by turbulence carried by upstream wakes. The breakdown events are observed once positive streamwise velocity fluctuations reach the end of the blade. Both the fluctuations induced by the migration of the wake in the blade passage and the presence of the streaks contribute to high values of the disturbance velocity inside the boundary layer with respect to a steady inflow case. The amplification of the boundary layer disturbances associated with different spanwise wavenumbers has been computed. It was found that the migration of the wake in the blade passage stands for the most part of the perturbations with zero spanwise wavenumber. The non-zero wavenumbers are found to be amplified in the rear part of the blade at the boundary between the low- and high-speed regions associated with the wakes.

A simple mathematical model of retinal reattachment after scleral buckling

Kheirandish, Repetto, Romano, Alishahi, Golneshan, Abouali & Pralits
Journal of Fluids and Structures, 2022
[abstract] [pdf]


Rhegmatogenous retinal detachment (RRD) is a dangerous pathological con- dition that can lead to blindness and requires surgical treatment. Scleral buckling is a surgical technique that has been in use for many years to repair RRD. It consists in the application of a piece of silicone on the outer surface of the sclera, that pushes the eye wall inwards and modifies its curvature in correspondence of the retinal tear. It is observed that this facilitates reti- nal reattachment. Various authors speculated that basic principles of fluid mechanics can be invoked to explain the reattachment process, though a con- vincing explanation of the mechanics underlying the process is still elusive. In this study, we propose an idealized two-dimensional model of a de- tached retina surrounded by liquefied vitreous and study its dynamics sec- ondary to eye movements. This is done using an immersed boundary numer- ical code. The retinal flaps are modeled as slender one-dimensional elastic bodies, one extremity of which is clamped on the retinal wall. For simplicity we model the retina as a rigid, flat wall. We account for the presence of scleral buckling by inserting a wall bump underneath the detached filaments. We show that the dynamics of the detached filaments is very complicated and that the presence of a buckle significantly contributes to reduce the time averaged distance between the detached filaments and the wall, thus facilitating reattachment. The mechanisms involved are inherently associated with the dynamics of the filament.

A procedure for computing the spot production rate in transitional boundary layers

Dellacasagrande, Lengani, Simoni, Pralits, Durovic, Hanifi & Henningson
Experiments in Fluids, Vol. 63, doi 10.10.1007/s00348-022-03485-8, 2022
[abstract] [article]


The present work describes a method for the computation of the nucleation rate of turbulent spots in transitional boundary layers from particle image velocimetry (PIV) measurements. Different detection functions for turbulent events recognition were first tested and validated using data from direct numerical simulation, and this latter describes a flat-plate boundary layer under zero pressure gradient. The comparison with a previously defined function adopted in the literature, which is based on the local spanwise wall-shear stress, clearly highlights the possibility of accurately predicting the statistical evolution of transition even when the near-wall velocity field is not directly available from the measurements. The present procedure was systematically applied to PIV data collected in a wall-parallel measuring plane located inside a flat plate boundary layer evolving under variable Reynolds number, adverse pressure gradient (APG) and free-stream turbulence. The results presented in this work show that the present method allows capturing the statistical response of the transition process to the modification of the inlet flow conditions. The location of the maximum spot nucleation is shown to move upstream when increasing all the main flow parameters. Additionally, the transition region becomes shorter for higher Re and APG, whereas the turbulence level variation gives the opposite trend. The effects of the main flow parameters on the coefficients defining the analytic distribution of the nucleation rate and their link to the momentum thickness Reynolds number at the point of transition are discussed in the paper.

Unsteadiness and resolution effects in experimentally verified simulations of a spray drying process

Pralits, Atzori, Colli, Pettinato, Drago & Perego
Powder Technology, 2022
[abstract] [article]


In this work, time-resolved three-dimensional numerical simulations supported by laboratory experiments aim to provide complementary information in the study of the spray drying process, revealing pivotal details about the flow and particles dynamics, useful for process optimization. A drying model was implemented in the OpenFOAM open-source code and large-eddy simulations (LES) of the flow were performed on a BUCHI Mini-spray dryer using real working conditions and input parameters. The governing equations of the fluid flow were solved in a computational domain based on the complete three-dimensional geometry of the drying chamber in a Eulerian framework, while the two-stage droplet drying kinetics were solved in a Lagrangian framework. Experimental tests were carried out to collect information and to verify the model using calcium carbonate. The total product lost due to wall contamination is in relatively good agreement between the experimental and numerical results. This work involved simulating a realistic number of particles (10000 particles/s), higher than those commonly used. The simulation allowed to describe the average strong recirculation in the drying chamber and how it affected the particle distribution. This flow model explains the wide spread of the residence time of the particles, which was the most significant variable to influence the drying process when the temperature is mostly uniform in the domain. This study demonstrated that the simulation combined to experimental can be used to gain insight into how flow characteristics affect product quality, helping design new devices and products with greater efficiency.

On the receptivity of low-pressure turbine blades to external disturbances

Lengani, Simoni, Pralits, Durovic, De Vincentiis, Hanifi & Henningson
Journal of Fluid Mechanics, 2022
[abstract] [article]


In the present work, the laminar-turbulent transition of the flow evolving around a low-pressure turbine blade has been investigated. Direct numerical simulations have been carried out for two different free-stream turbulence intensity levels (FSTI) to investigatethe role of free-stream oscillations on the evolution of the blade boundary layer. Emphasisis posed on identifying the mechanisms driving the formation and breakup of coherent structures in the high FSTI case and how these processes are affected by the leading-edge receptivity and/or by the continuous forcing in the blade passage. Proper orthogonal decomposition (POD) has been adopted to provide a clear statistical representation of the shape of the structures. Extended POD projections provided temporal and spanwise correlations that allowed us to identify dominant temporal structures and spanwise wavelengths in the transition process.The extended POD analysis shows that the structures on the pressure side are not related to what happens in the leading edge. The results on the suction side shows that leading edge and passage bases correlate with coherent structures responsible for the transition. However, the most energetic mode of the passage basis is strongly related tothe most amplified wavelength in the boundary layer and to breakup events leading to transition. Modes with a smaller spanwise wavelength belong to the band predicted by the optimal disturbance theory, they amplify with a smaller gain in the rear suction side, and they show the highest degree of correlation between the passage region and the rear suction side.

An Effective Mesh Deformation Approach for Hull Shape Design by Optimization

Villa, Furcas, Pralits, Vernengo & Gaggero
Journal of Marine Science and Engineering, 2021
[abstract] [pdf]


A method for the morphing of surface/volume meshes suitable to be used in hydrodynamic shape optimization is proposed. Built in the OpenFOAM environment, it relies on a Laplace equation that propagates the modifications of the surface boundaries, realized by applying a Free-Form Deformation to a Subdivision Surface description of the geometry, into the computational volume mesh initially built through a combination of BlockMesh with cfMesh. The feasibility and robustness of this mesh morphing technique, used as a computationally efficient pre-processing tool, is demonstrated in the case of the resistance minimization of the DTC hull. All the hull variations generated within a relatively large design space were efficiently and successfully realized, i.e. without mesh inconsistencies and quality issues, only by deforming the initial mesh of the reference geometry. Coupled with a surrogate model approach, a significant reduction of the calm water resistance, in the extent of 10%, has been achieved in a reasonable computational time.

On the stability of the boundary layer at the bottom of propagating surface waves

Blondeaux, Pralits & Vittori
Journal of Fluid Mechanics, 2021
[abstract] [article]


This study contributes to an improved understanding of the stability of the boundary layer generated at the bottom of a propagating surface wave characterized by a small but finite amplitude such that the steady streaming, which is superimposed to the main oscillatory flow, assumes significant values. A linear stability analysis of the laminar flow is made to determine the conditions leading to transition and turbulence appearance. The Reynolds number of the phenomenon is assumed to be large and a ’momentary’ criterion of stability is used. The results show that, at a given location, the laminar regime becomes unstable when the flow close to the bottom reverses its direction from the onshore to the offshore direction and the Reynolds number exceeds a first critical value Rδ,c1 which depends on the local water depth and the characteristics (period and amplitude) of the propagating surface wave. However, close to the critical condition, the flow is expected to relaminarize during the other phases of the cycle. Only when the Reynolds number is increased, turbulence tends to pervade a significant part of the wave cycle and to appear also after the passage of the wave trough when the flow close to the bottom reverses from the offshore to the onshore direction. When the Reynolds number is further increased and becomes larger than a second ’threshold’ value, the growth rate of the perturbations becomes positive over the entire wave period and turbulence is always present. The obtained results, along with the results described in Blondeaux & Vittori (2021), provide the existence of the four different flow regimes in the boundary layer under propagating surface waves: the laminar regime, the disturbed laminar regime, the intermittently turbulent regime and the fully developed turbulent regime.

Statistical characterization of free-stream turbulence induced transition under variable Reynolds number, free-stream turbulence and pressure gradient

Dellacasagrande, Lengani, Pralits, Simoni, Durovic, Hanifi & Henningson
Physics of fluids, Vol. 33(9), doi 10.1063/5.0063948, 2021
[abstract] [pdf]


In this work, the free-stream turbulence (FST) induced transition of a flat plate boundary layer is studied using particle image velocimetry (PIV) under variable Reynolds number (𝑅𝑒), FST intensity and adverse pressure gradient (APG). The streak spacing and the probability density function (PDF) of turbulent spot nucleation are computed for all cases. The quadrant analysis of fluctuating velocity is also performed in the transitional and the fully turbulent boundary layer. The streak spacing is shown to be constant in the transition region once 16 scaled with the turbulent displacement and momentum thickness, with resulting values of around 3 and 5, respectively. Nucleation events are shown to occur near the position where the dimensionless streak spacing reaches such a constant value. The FST intensity has the greatest influence on the location where most of nucleation events occur. Additionally, the PDF of spot nucleation becomes narrower at higher APG, while FST has the opposite effect. A common distribution of all the PDFs is provided as a function of a similarity variable accounting for streak spacing, shape factor of the boundary layer and FST intensity. Finally, the quadrant analysis shows that streamwise fluctuations dominate near the wall, whereas turbulence becomes more isotropic towards the edge of the boundary layer. At the highest Re and APG, positive and negative streamwise velocity fluctuations have the same probability at the mid-transition location. In the turbulent boundary layer, 𝑅𝑒 and APG promote the clockwise rotation of the joint PDF of fluctuating velocities, whereas FST has lower effects.

Free-stream turbulence induced boundary-layer transition in low-pressure turbines

Ðurović, De Vincentiis, Simoni, Lengani, Pralits, Henningson & Hanifi
Journal of Turbomachinery, 2021 (online), pp 1-15
[abstract] [pdf]


The aerodynamic efficiency of turbomachinery blades is profoundly affected by the occurrence of laminar-turbulent transition in the boundary layer since skin friction and losses rise for the turbulent state. Depending on the free-stream turbulence level, we can identify different paths towards a turbulent state. The present study uses direct numerical simulation as the primary tool to investigate the flow behaviour of the low-pressure turbine blade. The computational set-up was designed to follow the experiments by Lengani & Simoni [1]. In the simulations, the flow past only one blade is computed, with periodic boundary conditions in the cross-flow directions to account for the cascade. Isotropic homogeneous free-stream turbulence is prescribed at the inlet. The free-stream turbulence is prescribed as a superposition of Fourier modes with a random phase shift. Two levels of the free-stream turbulence intensity were simulated (Tu = 0.19% and 5.2%), with the integral length scale being 0.167c, at the leading edge. We observed that in case of low free-stream turbulence on the suction side, the Kelvin–Helmholz instability dominated the transition process and full-span vortices were shed from the separation bubble. Transition on the suction side proceeded more rapidly in the high-turbulence case, where streaks broke down into turbulent spots and caused bypass transition. On the pressure side, we have identified the appearance of longitudinal vortical structures, where increasing the turbulence level gives rise to more longitudinal structures. We note that these vortical structures are not produced by Goertler instability.

The role of endogenous proteins on the emulsification of Silicone oils used in vitreoretinal surgery

Nepita, Repetto, Pralits, Romano, Ravera, Santini & Liggieri
BioMed Research, 2020
[abstract] [pdf]


Background: Aim of the work is to achieve a chemico-physical characterisation of the interfacial properties between Silicone oils (SOs) and aqueous solutions, in the presence of surfactant biomolecules, possibly responsible for emulsion formation after vitrectomy. Methods: The interfacial tension (IT) and the interfacial dilational viscoelasticity (DV) were measured for the interface between SO (Siluron1000) and serum proteins (albumin and γ-globulins) at various concentrations in a Dulbecco alkaline buffer. Similar measurements were conducted on whole human blood serum (WHBS) solutions. The equilibrium IT value is relevant for the onset of emulsification and the DV influences the stability of an emulsion, once formed. The study is complemented by preliminary emulsification tests. Results: When proteins are dissolved in the aqueous solution, the rheological properties of the interface change. The IT decreases significantly for physiologically protein concentrations and the DV modulus achieves high values, even for small proteins concentrations. The emulsification tests confirm that, in the presence of proteins, emulsions are stable on the time scale of months. Conclusions: The measured values of IT in the presence of serum proteins are compatible with the promotion of droplets formation, which, in addition, are expected to be stable against coalescence, owing to the large values of the DV modulus. This is confirmed by the emulsification tests. Adsorption of biomolecules at the interface with the SO is, therefore, likely to play an important role in the generation of an emulsion. These findings are relevant to identify strategies to avoid or control the formation of emulsions in eyes.

La CFD come strumento predittivo in ambito sportivo per definire i Regolamenti Tecnici del futuro

Giachi, Guerrero & Pralits
In: Analisi e Calcolo, numero 96, Gen./Feb. 2020
ISSN 1128-3874

Gas-graft coverage after DMEK: a clinically validated numerical study

Pralits, Alberti & Cabrerizo
Translational Vision Science & Technology, Vol. 8(6), pp 1-14, 2019
[abstract] [pdf] [link]


Purpose: Optimal surgical use of gas in Descemets membrane endothelial keratoplasty (DMEK) is currently unknown. We investigate how positioning, gas fill and anterior chamber size influence bubble configuration and graft coverage.
Methods: We use a mathematical model to study the bubble shape and graft coverage in eyes of varying anterior chamber depths (ACD). The governing equations are solved numerically using the open source software OpenFOAM. Numerical results are validated clinically so that clinical gas fill measures can be correlated to numerical results providing gas-graft coverage information otherwise clinically inaccessible.
Results: In a phakic eye (ACD = 2.65 mm) with a gas fill of 35%, graft contact ranges 35%-38% depending on positioning and increases to 85%-92% with a 70% fill. In con- trast, positioning of a pseudophakic eye (ACD = 4.35) with a gas fill of 35% results in graft contact ranges 8%-52%, increasing to 63%-94% with a 70% fill. We present cover- age of grafts as a function of parameters that are available to aid clinicians with effective gas use. The differences between air and SF6 results are negligible. Interestingly, a very thin central patch of aqueous humour within the gas bubble is found in some cases.
Conclusions: Graft coverage in phakic eyes (ACD ≤ 3 mm) is dominated by the gas fill and less sensitive to patient positioning. In pseudophakic eyes with larger values of ACD, the graft coverage depends both on gas fill and patient positioning with positioning even more important as ACD increases.

Mathematical Models of Aqueous Production, Flow and Drainage

Dvoriashyna, Pralits, Tweedy & Repetto
In: Ocular Fluid Dynamics. Anatomy, Physiology, Imaging Techniques, and Mathematical Modeling , Springer-Birkhauser, New York, 2019
Editors: G. Guidoboni, A. Harris, R. Sacco.
ISBN 9783030258856

A mathematical model of corneal metabolism in the presence of an iris-fixated phakic intraocular lens

Davvalo Khongar, Pralits, Cheng, Pinsky, Soleri & Repetto
Invest Ophthalmol Vis Sci., Vol. 60, pp 2311-2320, 2019


Purpose: Corneal endothelial cell loss is one of the possible complications associated with the phakic iris-fixated intraocular lenses (PIOL) implantation. We postulate that this might be connected to the alteration of corneal metabolism secondary to the lens implantation.
Methods: A mathematical model of transport and consumption/production of metabolic species in the cornea is proposed, coupled with a model of aqueous flow and transport of metabolic species in the anterior chamber.
Results: Results are presented both for open and closed eyelids. We show that in the presence of a PIOL glucose availability at the corneal endothelium decreases significantly during sleeping.
Conclusions: Implantation of a PIOL significantly affects nutrient transport processes to the corneal endothelium especially during sleeping. It must still be verified whether this finding has a clinical relevance.

Bulbous bow shape optimization using an open-source framework

Guerrero, Cominetti, Pralits & Villa
Mathematical and Computational Applications, Vol. 23(60), pp 1-25, 2018
[abstract] [pdf]


Shape optimization is a very time-consuming and expensive task, especially if experimental tests need to be performed. To overcome the challenges of geometry optimization, the industry is increasingly relying on numerical simulations. This kind of problems typically involves the interaction of three main applications: a solid modeler or shape morpher, a multi-physics solver, and an optimizer. In this manuscript, we present a shape optimization framework entirely based on open-source tools, where we take an initial geometry, and we manipulate it using the MiMMO library, the multi-physics simulations are performed using OpenFOAM, and the optimization loop is controlled with Dakota. To demonstrate the usability and flexibility of the proposed framework, we test it in a practical case related to the naval industry, where we aim at optimizing the shape of a bulbous bow in order to minimize the hydrodynamic resistance. To tackle this problem, we first validate the solver and calibrate the numerical model using a reference geometry for which experimental data are available. After having found the ideal mesh and solver parameters, we setup the optimization loop. As design variables, we consider the protrusion and immersion of the bulbous bow, and we use Surrogate-Based Optimization to minimize the hydrodynamic resistance. Additionally, we highlight the logic behind the choices made, we give a few guidelines on how to deal with some problematic issues encountered during the optimization loop (e.g., sampling, interpolation techniques, infilling, the effect of numerical noise), and we compare the output of the meta-model with the outcome of high-fidelity simulations.

A simple mathematical model of rhegmatogenous retinal detachment

Natali, Repetto, Tweedy, Williamson & Pralits
Journal of Fluids and Structures Vol. 82, pp 245-257, 2018
[abstract] [pdf]


The conditions under which rhegmatogenous retinal detachment occurs are poorly understood, which hampers the success rates of surgery. Fluid dy- namical effects play a major role, and in this paper we analyse the tendency for the retina to detach further in both the case of a free flap giant reti- nal tear (GRT) and in the case of a retinal hole (RH). For this purpose we use a mathematical model to investigate the interaction between the fluid flow and the detached retina during saccadic eye movements. The governing equations are solved numerically using a code developed ad hoc. An idealised two-dimensional geometry is used and realistic values of almost all governing parameters used are taken from the literature. For the cases of both GRT and a RH we investigate the tendency for the detachment to progress, analysing different lengths of the detached retina, different attachment angles and, in the case of a RH, different hole diameters. We find that in both cases in- creasing the length of the detached retina increases the tendency for further detachment, while in the case of a hole, changing its diameter has little or no effect. We also find the existence of an attachment angle that maximises the tendency to detach, and the model indicates that RHs are more prone to de- tach further than GRTs. In spite of the fact that the model is highly idealised the results agree qualitatively well with the available clinical evidence.

A study of the mechanical forces on aphakic iris-fixated intraocular lenses

Davvalo Khongar, Pralits, Soleri, Romano & Repetto
Journal of Biomechanical Engineering, 2018
[abstract] [pdf]


Iris–fixated aphakic intraocular lenses (IFIOL) are used in cataract surgery, when more common intraocular lenses cannot be adopted because of the absence of capsular bag support. These lenses can be implanted either on the posterior or the anterior surface of the iris. In this work we study whether one of these options is preferable over the other from the mechanical point of view. In particular, we focus on the forces that the IFIOL transmits to the iris, which are associated with the risk of lens dislocation. We study the problem numerically and consider aqueous flow induced by saccadic rotations in the cases of an IFIOL in the anterior and posterior side of the iris. The IFIOL considered is the Artisan Aphakia +30.0 D lens (IFIOL) produced by Ophtec BV. We perform the simulations in OpenFOAM. We find that the forces transmitted by the aphakic IFIOL to the iris are significantly higher in the case of posterior implantation. This suggests that lens implantation on the posterior surface of the iris might be associated with a higher risk of lens dislocation, when an inadequate amount of iris tissue is enclavated during implantation.

Effect of an iris-fixated intraocular lens on corneal metabolism: a numerical study

Davvalo Khongar, Pralits, Cheng, Pinsky, Soleri & Repetto
Journal for Modeling in Ophthalmology Vol. 2, pp 97-101, 2018
[abstract] [pdf]


One of the possible risks associated with the implant of iris-fixated phakic intraocular lenses (pIOL) is loss of corneal endothelial cells. We hypothesize that this might be due to alterations in corneal metabolism secondary to the lens implantation. To verify the feasibility of this assumption, we propose a mathematical model of the transport and di usion of metabolic species in the anterior chamber and the cornea, coupled to a model of aqueous flow. Results are obtained both with and without the pIOL in the case of closed eyelids. The results suggest that glucose availability may be significantly reduced at the corneal endothelium. However, it must still be verified whether this finding has clinical relevance.

The effect of serum proteins on dynamic interfacial properties of silicone oils in vitrectomized eyes

Nepita, Liggieri, Santini, Ravera, Romano, Pralits & Repetto
Journal for Modeling in Ophthalmology Vol. 2, pp 52-57, 2018
[abstract] [pdf]


The formation and stability of emulsions in vitrectomized eyes is linked to the properties of the silicone oil-aqueous humor interface, in particular the surface tension. In the presence of natural surfactants, such as serum and plasma, the value of the surface tension is likely to change, but little quantitative information is presently available. To this end, we perform accurate experiments measuring the interfacial properties of the Siluron 1000 (Fluoron GmbH, Ulm, Germany) silicone oil with an aqueous solution in the presence of endogenous-like proteins. It is found that the surface tension is significantly reduced when physiologically realistic concentrations are used. Moreover, the values obtained for the dilational viscoelastic modulus are compatible with the formation of stable emulsions.

Full-order optimal compensators for flow control: the multi-input case

Semeraro & Pralits
Theoretical and Computational Fluid Dynamics, 2018
[abstract] [pdf]


Flow control has been the subject of numerous experimental and theoretical works. In this numerical study, we analyse full-order, optimal controllers for large dynamical systems in presence of multiple actuators and sen- sors. We start from the original technique proposed by Bewley, Luchini & Pralits, Meccanica, 2016, the adjoint of the direct-adjoint (ADA) algorithm. The algorithm is iterative and allows bypassing the solution of the algebraic Riccati equation associated with the optimal control problems, typically unfeasible for large systems. We extend ADA into a more generalized framework that includes the design of multi-input, coupled controllers and robust controllers based on the H∞ framework. The full-order controllers do not require any preliminary step of model reduction or low-order approximation: this feature allows to pre-assess the optimal performances of an actuated flow without relying on any estimation process or further hypothesis. We show that the algorithm outperforms analogous technique, in terms of convergence performances considering two numerical cases: a distributed system and the linearized Kuramoto-Sivashinsky equation, mimicking a full three-dimensional control setup. For the ADA algorithm we find excellent scalability with the number of inputs (actuators) in terms of convergence to the solution, making the method a viable way for full-order controller design in complex settings.

Erratum to: Preliminary design of a small-sized flapping UAV: I. Aerodynamic performance and static longitudinal stability

Guerrero, Pacioselli, Pralits, Negrello, Silvestri, Lucifredi, & Bottaro
Meccanica Vol. 51(6), pp 6-6, 2017


It has come to the attention of the authors that the aforementioned paper contains a typing error in Equation 3. Instead of reading(Formula Presented.)Equation 3 should read:(Formula Presented.).

Flow in the anterior chamber of the eye with an implanted iris-fixated artificial lens

Tweedy, Pralits, Repetto & Soleri
Mathematical Medicine & Biology Vol. 00, pp 1-23, 2017
[abstract] [pdf]


Flow in the anterior chamber of the eye oc- curs in response to the production and drainage of aque- ous humor and also due to buoyancy effects produced y thermal gradients. Phakic intraocular lenses (pIOLs) are inserted in the eyes of patients to correct refractive errors. Their presence has a dramatic effect on the cir- culation of the aqueous humor, resulting a very different flow in the anterior chamber, the effects of which have not been extensively investigated. In this article we use a simplified mathematical model to analyse the flow, in order to assess the effect of the implanted lens on the pressure drop required to drive the flow and also the wall shear stress experienced by the corneal endothelial cells and the cells of the iris. A high pressure drop could result in an increased risk of glaucoma, whilst raised shear stress on the cornea could result in a reduction in the density of endothelial cells there and on the iris it could result in the detachment of pigment cells, which block the outflow of the eye, also leading to glaucoma. Our results show that, although the presence of the lens causes significant differences in the flow topology and direction, the typical magnitudes of the shear stress are not significantly changed from the natural case.

Global stability and control of the confined turbulent flow past a thick flat plate

Carini, Airiau, Debien, Léon & Pralits
Physics of Fluids Vol. 29, pp 024102, 2017
[abstract] [pdf]


This article investigates the structural stability and sensitivity properties of the confined turbulent wake behind an elongated D-shaped cylinder of aspect-ratio 10 at Re = 32000. The stability analysis is performed by linearising the incompressible Navier-Stokes equations around the numerically computed and the experimentally measured mean flows. We found that the vortex-shedding frequency is very well captured by the leading unstable global mode, espe- cially when the additional turbulent diffusion is modelled in the stability equations by means of a frozen eddy-viscosity approach. The sensitivity maps derived from the computed and the measured mean flows are then compared, showing a good qualitative agreement. The careful inspection of their spatial structure highlights that the highest sensitivity is attained not only across the recirculation bubble but also at the body blunt-edge, where tiny pockets of maximum re- ceptivity are found. The impact of the turbulent diffusion on the obtained results is investigated. Finally, we show how the knowledge of the unstable adjoint global mode of the linearised mean-flow dynamics can be exploited to design an active feedback control of the unsteady turbulent wake, which leads, under the adopted numerical framework, to completely suppress its low-frequency oscillation.

Stability of the flow in a plane microchannel with one or two superhydrophobic walls

Pralits, Alinovi & Bottaro
Physical Review Fluids Vol. 2, pp. 013901, 2017
[abstract] [pdf]


The modal and nonmodal linear stability of the flow in a microchannel with either one or both walls coated with a superhydrophobic material is studied. The topography of the bounding wall(s) has the shape of elongated micro-ridges with arbitrary alignment with respect to the direction of the mean pressure gradient. The superhydrophobic walls are modelled using the Navier slip condition through a slip-tensor, and the results depend parametrically on the slip-length and orientation angle of the ridges. The stability analysis is carried out in the temporal framework; the modal analysis is performed by solving a generalized eigenvalue problem, and the nonmodal, optimal perturbation analysis is done with an adjoint optimisation approach. We show theoretically and verify numerically that Squire’s theorem does not apply in the present settings, despite the fact that Squire modes are found to be always damped. The most notable result is the appearance of a streamwise wall-vortex mode at very low Reynolds numbers when the ridges are sufficiently inclined with respect to the mean pressure gradient, in the case of a single superhydrophobic wall. When two walls are rendered water repellent, the exponential growth of the instability results from either a two-dimensional or a three-dimensional Orr-Sommerfeld mode, depending on the ridges orientation and amplitude. Nonmodal results for either one or two superhydrophobic wall(s) display but a mild modification of the no-slip case.

Equilibrium shape of the aqueous humor-vitreous substitute interface in vitrectomized eyes

Isakova, Pralits, Romano, Beenakker, Shamonin & Repetto
Journal for Modeling in Ophthalmology Vol. 3, pp 31-46, 2017
[abstract] [pdf]


Purpose: To predict the shape of the interface between aqueous humor and a tamponade, gas or silicone oil (SO), in vitrectomized eyes. To quantify the tamponated retinal surface for various eye shapes, from emmetropic to highly myopic eyes.
Methods: We use a mathematical model to determine the equilibrium shape of the interface between the two fluids. The model is based on the VOF (volume of fluids) method. The governing equations are solved numerically using the free software OpenFOAM. We apply the model both to the case of idealized, yet realistic, geometries of emmetropic and myopic eyes and to a real geometry reconstructed from MRI images of the vitreous chamber.
Results: The numerical model allows us to compute the equilibrium shape of the inter face between the aqueous humor and the tamponade fluid. From this we can compute the portion of the retinal surface which is effectively tamponated by the fluid. We compare the tamponating ability of gases and SOs. We also compare the tamponating effect in emmetropic and myopic eyes by computing both tamponated area and angular coverage.
Conclusions: The numerical results show that gases have better tamponating properties than SOs. We also show that, for a given filling ratio the percentage of tamponated retinal surface area is smaller in myopic eyes. The method is valuable for clinical purposes, especially in patients with pathological eye shapes, to predict the area of the retina that will be tamponated for a given amount of injected tamponade fluid.

Aqueous flow in the presence of a perforated iris-fixated intraocular lens

Davvalo Khongar, Pralits, Soleri & Repetto
Meccanica, S.I. advances in biomechanics: from foundations to applications Vol. 52, pp 577-586, 2017


The aim of this study is to investigate the characteristics of the aqueous humor flow in the anterior chamber of the eye in the presence of a perforated, phakic, iris-fixated intraocular lens (pIOL). Such pIOLs are implanted in the anterior chamber, in front of the iris and they therefore interfere with aqueous motion. The aim of this work is to investigate whether a perforation in the body of the pIOL can improve its fluid dynamics performance. Numerical simulations are conducted using the free computational fluid dynamics program OpenFOAM. The aqueous humor is modeled as a Newtonian incompressible fluid and, when temperature effects are considered, the Navier-Stokes equations are coupled to the energy equation, using Boussinesq’s approach to account for fluid density changes associated temperature variations. The pressure drop across the anterior chamber is calculated considering perforations in the pIOL of various sizes and also studying the extreme case in which the passage between the iris and the pIOL gets plugged, thus leaving the hole in the pIOL as the only possible pathway for aqueous flow. The study shows that the presence of a hole in the pIOL can only have a significant role on the pressure in the eye if the normal aqueous flow in the region between the pIOL and the iris gets blocked.

Methods for solution of large optimal control problems that bypass open-loop model reduction

Bewley, Luchini & Pralits
Meccanica Vol. 51, pp 2997-3014, 2016
[abstract] [pdf] [springer pdf]


Three algorithms for efficient solution of op- timal control problems for high-dimensional systems are presented. Each bypasses the intermediate (and, unnecessary) step of open-loop model reduction. Each also bypasses the solution of the full Riccati equation corresponding to the LQR problem, which is numeri- cally intractable for large n. Motivation for this effort comes from the field of model-based flow control, where open-loop model reduction often fails to capture the dynamics of interest (governed by the Navier-Stokes equation). Our Minimum Control Energy method is a simplified expression for the well-known minimum- energy stabilizing control feedback that depends only on the left eigenvectors corresponding to the unstable eigenvalues of the system matrix A. Our Adjoint of the Direct-Adjoint method is based on the repeated itera- tive computation of the adjoint of a forward problem, itself defined to be the direct-adjoint vector pair asso- ciated with the LQR problem. Our Oppositely-Shifted Subspace Iteration method is based on our new sub- space iteration method for computing the Schur vectors corresponding, notably, to the m ≪ n central eigenval- ues (near the imaginary axis) of the Hamiltonian ma- trix related to the Riccati equation of interest. These three approaches are compared to the classical Chan- drasekhar’s method for approximate solution of large Riccati equations on a representative control problem.

Stabilizing effect of porosity on a flapping filament

Natali, Pralits, Mazzino & Bagheri
J. Fluid Struct. Vol. 61, pp 362-375, 2016
[abstract] [pdf]


A new way of handling, simultaneously, porosity and bending resistance of a massive filament is proposed. Our strategy extends the previous methods where porosity was taken into account in the absence of bending resistance of the structure and overcomes related numerical issues. The new strategy has been exploited to investigate how porosity affects the stability of slender elastic objects exposed to a uniform stream. To understand under which conditions porosity becomes important, we propose a simple resonance mechanism between a properly defined characteristic porous time-scale and the standard characteristic hydrodynamic time-scale. The resonance condition results in a critical value for the porosity above which porosity is important for the resulting filament flapping regime, otherwise its role can be considered of little importance. Our estimation for the critical value of the porosity is in fairly good agreement with our DNS results. The computations also allow us to quantitatively establish the stabilizing role of porosity in the flapping regimes.

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