PhD position: POLKA - Pollution Know-how and Abatement

Press: Wolf Dynamics - Formula 1

Master theses

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
Simulazioni instazionarie per la climatizzazione del teatro Carlo Felice di Genova
Paolo Badino (2020) [thesis] [presentation]


Unstationary temperature field in the orchestra pit of the theater Carlo Felice, Genoa, Italy. The whole theater was simulated for extended times in order to capture the relatively slow oscillating motion of air.
Studio e modellazione matematica di protesi vascolari biodegradabili ed ingegnerizzate di piccolo calibro in bioreattore
Veronica De Mattei (2019) [thesis][presentation]


Project outline
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

Optimal oblique transition

Bottaro, Pralits & Cherubini
Journal of Fluid Mechanics, 2017
[abstract] [pdf] [Movie: relaminarization] [Movie: transitional]


A weakly nonlinear approach is described to identify the couple of oblique waves capable to optimally excite transition to turbulence in a plane shear flow. Optimal oblique wave pairs are found to exist in a very narrow wavenumber range – demonstrating the strong selectivity of the identified mechanism – and lead to rapid breakdown past a well defined threshold value of the disturbance amplitude. Direct numerical simulations of the Navier-Stokes equations corroborate the weakly nonlinear results.

recent publications

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.

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

Ðurović, De Vincentiis, Simoni, Lengani, Pralits, Henningson & Hanifi
Journal of Turbomachinery, 2020 accepted


The aerodynamic efficiency of turbomachinery blades is pro- foundly affected by the occurrence of laminar-turbulent transi- tion 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 pri- mary 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 superpo- sition 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 turbu- lence on the suction side, the Kelvin–Helmholz instability dom- inated the transition process and full-span vortices were shed from the separation bubble. Transition on the suction side pro- ceeded 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 longi- tudinal vortical structures, where increasing the turbulence level gives rise to more longitudinal structures. We note that these vortical structures are not produced by G\"ortler instability.

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.

full list of publications