Abstract
The international Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder (BARC)
addresses the high Reynolds number, external, unsteady flow around a stationary, sharp-edged
rectangular cylinder, and the associated aerodynamic actions (Bartoli et al. 2020). In spite of the
simple geometry of the cylinder, BARC is a paradigmatic example of the intricate flows around
elongated bodies having a low degree of bluffness, often encountered in Engineering design
practice.
BARC has been initially conceived as a double-blind benchmark, i.e., without a-priori selected
reference measurements, and open to side-ground parametrical studies around the main setup.
Thanks to such an approach, the benchmark attracted the attention of a number of researchers and
practitioners adopting both numerical and experimental approaches in several academic and
industrial sectors. More than 30 scientific papers on international journals have been devoted to
BARC up to now.
The present special issue follows some major milestones of the BARC past activities: the
BARC launching on July 2008 at BBAA VI Conference; the BARC website online since 2009,
hosted by the Italian Association of Wind Engineering (ANIV), and renewed on June 2020
(www.aniv-iawe.org/barc-home); the overview paper on BARC studies after the first four years of
activity published on January 2014 (Bruno et al. 2014). Since May 2014 BARC enters as Silver
content among the Underlying Flow Regimes (UFR_2-15) in the Knowledge Base Wiki of the
European Research Community in Turbulence and Combustion (ERCOFTAC, Bruno & Salvetti,
2017). On February 2021 the BARC-MYOC (Make Your Own Comparison) web application is
made available at the BARC website to collect, postprocess and compare the large amount of
scientific results obtained so far (Bruno and Mannini 2021).
On the one side, BARC is nowadays a mature test-bench for calibration of WT facilities,
validation of CFD codes, training of the new generation of early stage researchers. On the other
side, open issues still remain in the understanding and modelling of the BARC main flow, and
towards new BARC-related problems.
This special issue aims at gathering researchers from both Fluid Mechanics and Wind
Engineering communities, promoting exchanges and complementary approaches between them,
crossing the borders of contiguous, but sometimes shamefully apart, disciplinary fields.
Both numerical and experimental approaches are deployed: the special issue collects 13 studies,
carried out in equal part by wind tunnel tests and computational simulations. They effectively
complement each other with respect to methods and applications. Computational studies span over
a rich variety of approaches to turbulence, from DNS (Chiarini and Quadrio, Corsini et al.) to LES
(Crivellini et al. Lunghi et al. Sakuma et al.) and RANS (Xu et al. Ma et al. Sakuma et al.), and
over different numerical approaches. Experimental tests move from classical pressure and force
measurements (Cárdenas-Rondón et al. Yang et al. Wang et al. Lei et al. Pasqualetto et al.) to
Particle Image Velocimetry and other anemometric techniques (Guissart et al. Pasqualetto et al.).
Beside the main setup, new problems are proposed and investigated. Among them, let us cite the
'rounded BARC' (Chiarini and Quadrio, Lunghi et al. Sakuma et al.), the 'porous BARC' (Xu et
al.), the 'gust BARC' (Cardenas-Rondon et al. Yang et al.), the 'BARC at incidence' (Guissart et
al. Cardenas-Rondon et al. Sakuma et a.), the 'oscillating BARC' (Wang et al. Lei et al.). All of
them are paradigmatic setups of recurrent problems in wind engineering applications.
BARC is come of age. This special issue is a turning point from past activities to future ones.
Good winds to BARC!
Abstract
In this work the flow through a hollow porous 5:1 rectangular cylinder made of perforated plates is numerically
investigated by means of 2D URANS based simulations. Two approaches are adopted to account for the porous surfaces: in the
first one the pores are explicitly modeled, so providing a detailed representation of the flow. In the second one, the porous
surfaces are modeled by means of pressure jumps, which allow to take into account the presence of pores without reproducing
the flow details. Results obtained by using the two aforementioned techniques are compared aiming at evaluating differences
and similarities, as well as identifying the main flow features which might cause discrepancies. Results show that, even in the
case of pores remarkably smaller than the immersed body, their arrangement can lead to local mechanisms able to affect the
global flow arrangement, so limiting the accuracy of pressure jumps based simulations. Despite that, time-averaged fields often
show a reasonable agreement between the two approaches.
Key Words
porosity; porous bluff-body; porous surface; pressure jump
Address
Mao Xu: DICAM, University of Bologna, Bologna, Italy
Luca Patruno: DICAM, University of Bologna, Bologna, Italy
Yuan-Lung Lo: Department of Civil Engineering, National Taipei University of Technology, Taipei, Taiwan
Stefano de Miranda: DICAM, University of Bologna, Bologna, Italy
Francesco Ubertini: DICAM, University of Bologna, Bologna, Italy
Abstract
This work comes within the framework of the "Benchmark on the Aerodynamics of a Rectangular Cylinder" that
investigates a rectangular cylinder of length-to-depth ratio equal to 5. The present study reports and discusses velocity fields
acquired using planar Particle Image Velocitmetry for several angles of attack and Reynolds numbers. In particular, for a
cylinder depth-based Reynolds number of 2x104
and zero incidence angle, the flow features along the lateral (parallel to the
freestream) upper and lower surfaces of the cylinder are reported. Using first and second order statistics of the velocity field, the
main flow features are discussed, especially the size and location of the time-averaged flow structures and the distribution of the
Reynolds stresses. The variation of the flow features with the incidence is also studied considering angles of attack up to 6°. It is
shown that the time-averaged flow is fully detached for incidence higher than 2°. For an angle of attack of 0°, the effects of the
Reynolds number varying between 5x103
and 2x104
are investigated looking at flow statistics. It is shown that the time averaged location of the reattachment point and the shape and position of the time-averaged main vortex are mostly constant
with the Reynolds number. However, the size of the inner region located below the time-averaged shear layer and just
downstream the leading edge corner appears to be strongly dependent on the Reynolds number.
Abstract
Following the BARC initiative, wind tunnel measurements have been performed on a 5:1 rectangular cylinder.
Pressure distribution has been measured in several sections, checking the two-dimensionality of the flow around the model.
Mean values compare well with previous data. These measurements have been processed using the standard Proper Orthogonal
Decomposition (POD) and the snapshot POD to obtain phase-resolved cycles. This decomposition has been used to analyze the
characteristics of the flow around the cylinder, in particular, the behavior of the recirculation bubble in the upper/lower surfaces.
The effect of the angle of attack, the turbulence intensity and the Reynolds number has been studied. First and second modes
extracted from POD have been found to be related to the reattachment of the flow in the upper surface. Increasing the angle of
attack is related to a delay in the reattachment position, while an increase in turbulence intensity makes the reattachment point to
move towards the windward face.
Key Words
BARC; POD; wind tunnel
Address
Juan A. Cardenas-Rondon: Instituto Universitario "Ignacio Da Riva" (IDR/UPM), Universidad Politecnica de Madrid,
Plaza Cardenal Cisneros, 3, E-28040, Madrid, Spain
Mikel Ogueta-Gutierrez: Instituto Universitario "Ignacio Da Riva" (IDR/UPM), Universidad Politecnica de Madrid,
Plaza Cardenal Cisneros, 3, E-28040, Madrid, Spain
Sebastian Franchini: Instituto Universitario "Ignacio Da Riva" (IDR/UPM), Universidad Politecnica de Madrid,
Plaza Cardenal Cisneros, 3, E-28040, Madrid, Spain
Omar Gomez-Ortega: Instituto Universitario "Ignacio Da Riva" (IDR/UPM), Universidad Politecnica de Madrid,
Plaza Cardenal Cisneros, 3, E-28040, Madrid, Spain
Abstract
The BARC flow is studied via Direct Numerical Simulation at a relatively low turbulent Reynolds number, with
focus on the geometrical representation of the leading-edge (LE) corners. The study contributes to further our understanding of
the discrepancies between existing numerical and experimental BARC data. In a first part, rounded LE corners with small
curvature radii are considered. Results show that a small amount of rounding does not lead to abrupt changes of the mean fields,
but that the effects increase with the curvature radius. The shear layer separates from the rounded LE at a lower angle, which
reduces the size of the main recirculating region over the cylinder side. In contrast, the longitudinal size of the recirculating
region behind the trailing edge (TE) increases, as the TE shear layer is accelerated. The effect of the curvature radii on the
turbulent kinetic energy and on its production, dissipation and transport are addressed. The present results should be contrasted
with the recent work of Rocchio et al. (2020), who found via implicit Large-Eddy Simulations at larger Reynolds numbers that
even a small curvature radius leads to significant changes of the mean flow. In a second part, the LE corners are fully sharp and
the exact analytical solution of the Stokes problem in the neighbourhood of the corners is used to locally restore the solution
accuracy degraded by the singularity. Changes in the mean flow reveal that the analytical correction leads to streamlines that
better follow the corners. The flow separates from the LE with a lower angle, resulting in a slightly smaller recirculating region.
The corner-correction approach is valuable in general, and is expected to help developing high-quality numerical simulations at
the high Reynolds numbers typical of the experiments with reasonable meshing requirements.
Key Words
BARC; DNS
Address
Alessandro Chiarini: Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Maurizio Quadrio: Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Abstract
In this work the numerical results of the flow around a 5:1 rectangular cylinder at Reynolds numbers 3 000 and
40 000, zero angle of attack and smooth incoming flow condition are presented. Implicit Large Eddy Simulations (ILES) have
been performed with a high-order accurate spatial scheme and an implicit high-order accurate time integration method. The
spatial approximation is based on a discontinuous Galerkin (dG) method, while the time integration exploits a linearly-implicit
Rosenbrock-type Runge-Kutta scheme. The aim of this work is to show the feasibility of high-fidelity flow simulations with a
moderate number of DOFs and large time step sizes. Moreover, the effect of different parameters, i.e., dimension of the
computational domain, mesh type, grid resolution, boundary conditions, time step size and polynomial approximation, on the
results accuracy is investigated. Our best dG result at Re=3 000 perfectly agrees with a reference DNS obtained using Nek5000
and about 40 times more degrees of freedom. The Re=40 000 computations, which are strongly under-resolved, show a
reasonable correspondence with the experimental data of Mannini et al. (2017) and the LES of Zhang and Xu (2020).
Key Words
BARC benchmark; discontinuous Galerkin method; Implicit Large Eddy Simulation; (ILES); implicit time
integration
Address
Andrea Crivellini: Department of Industrial Engineering and Mathematical Science, Marche Polytechnic University, Via Brecce Bianche 12, 60131 Ancona, Italy
Alessandra Nigro: Department of Industrial Engineering and Mathematical Science, Marche Polytechnic University, Via Brecce Bianche 12, 60131 Ancona, Italy
Alessandro Colombo: Department of Engineering and Applied Sciences, Universita degli Studi di Bergamo, Viale Marconi 5, 24044 Dalmine, Italy
Antonio Ghidoni: Department of Mechanical and Industrial Engineering, Universita degli Studi di Brescia, Via Branze 38, 25121 Brescia, Italy
Gianmaria Noventa: Department of Mechanical and Industrial Engineering, Universita degli Studi di Brescia, Via Branze 38, 25121 Brescia, Italy
Andrea Cimarelli: Department of Engineering "Enzo Ferrari", Universita degli Studi di Modena e Reggio Emilia, Via Vivarelli 10, 41125 Modena, Italy
Abstract
This paper presents a study on amplitude-dependent self-excited aerodynamic forces of a 5:1 rectangular cylinder
through free vibration wind tunnel test. The sectional model was spring-supported in a single degree of freedom (SDOF) in
torsion, and it is found that the amplitude of the free vibration cylinder model was not divergent in the post-flutter stage and was
instead of various stable amplitudes varying with the wind speed. The amplitude-dependent aerodynamic damping is determined
using Hilbert Transform of response time histories at different wind speeds in a smooth flow. An approach is proposed to extract
aerodynamic derivatives as nonlinear functions of the amplitude of torsional motion at various reduced wind speeds. The results
show that the magnitude of A2*, which is related to the negative aerodynamic damping, increases with increasing wind speed
but decreases with vibration amplitude, and the magnitude of A3* also increases with increasing wind speed but keeps stable
with the changing amplitude. The amplitude-dependent aerodynamic derivatives derived from the tests can also be used to
estimate the post-flutter response of 5:1 rectangular cylinders with different dynamic parameters via traditional flutter analysis.
Key Words
5:1 rectangular cylinder; aerodynamic derivatives; amplitude-dependence; post-flutter response; wind tunnel test
Address
Qi Wang: Department of Bridge Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031, China
Bo Wu: Wind Engineering Key Laboratory of Sichuan Province, Chengdu, Sichuan, 610031, China
Hai-li Liao: Wind Engineering Key Laboratory of Sichuan Province, Chengdu, Sichuan, 610031, China
Hanyu Mei: Wind Engineering Key Laboratory of Sichuan Province, Chengdu, Sichuan, 610031, China
Abstract
To better understand the vortex-induced vibration (VIV) characteristics of a 5:1 rectangular cylinder, the distribution
of aerodynamic force and the non-dimensional power spectral density (PSD) of fluctuating pressure on the side surface were
studied in different VIV development stages, and their differences in the stationary state and vibration stages were analyzed. The
spanwise and streamwise correlations of surface pressures were studied, and the flow field structure partitions on the side surface
were defined based on the streamwise correlation analysis. The results show that the variation tendencies of mean and root mean
square (RMS) pressure coefficients are similar in different VIV development stages. The RMS values during amplitude growth
are larger than those at peak amplitude, and the smallest RMS values are observed in the stationary state. The spanwise
correlation coefficients of aerodynamic lifts increase with increase of the peak amplitude. However, for the lock-in region, the
maximum spanwise correlation coefficient for aerodynamic lifts occurs in the VIV rising stage rather than in the peak amplitude
stage, probably due to the interaction of vortex shedding force (VSF) and self-excited force (SEF). The streamwise correlation
results show that the demarcation point positions between the recirculation region and the main vortex region remain almost
constant in different VIV development stages, and the reattachment points gradually move to the tailing edge with increasing
amplitude. This study provides a reference to estimate the demarcation point and reattachment point positions through
streamwise correlation and phase angle analysis from wind tunnel tests.
Address
Yongfu Lei: Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu 610031, China
Yanguo Sun: 1)Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu 610031, China
2)Key Laboratory for Wind Engineering of Sichuan Province, Chengdu 610031, China
Tianyi Zhang: Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu 610031, China
Xiongwei Yang: Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu 610031, China
Mingshui Li: 1)Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu 610031, China
2)Key Laboratory for Wind Engineering of Sichuan Province, Chengdu 610031, China
Abstract
Numerical simulations are conducted to investigate the uniform flow (UF) and sinusoidal streamwise flow (SSF)
over an oscillating 5:1 rectangular cylinder with harmonic heaving motion at initial angles of attack of
Key Words
sinusoidal streamwise flow; 5:1 rectangular cylinder; unsteady lift; flow field
Address
Ruwei Ma:1)Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu, 610031, China
2) School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200444, China
Qiang Zhou:1)Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu, 610031, China 2)Key Laboratory for Wind Engineering of Sichuan Province, Chengdu, 610031, China
Peiyuan Wang: Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu, 610031, China
Yang Yang:1)Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu, 610031, China 2)Key Laboratory for Wind Engineering of Sichuan Province, Chengdu, 610031, China
Mingshui Li:1)Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu, 610031, China 2)Key Laboratory for Wind Engineering of Sichuan Province, Chengdu, 610031, China
Abstract
We experimentally investigate the high-Reynolds flow around a rectangular cylinder of aspect ratio 5:1. This
configuration is the object of the international BARC benchmark. Wind tunnel tests have been carried out for the flow at zero
angle of attack and a Reynolds number, based on the crossflow cylinder length and on the freestream velocity, equal, to 40 000.
Velocity measurements are obtained by using hot-wire anemometry along 50 different cross-flow traverses on the cylinder side
and in the near wake. Differential pressure measurements are acquired on multiple streamwise sections of the model. The
obtained measurements are in a good agreement with the state-of-the-art experiments. For the first time among the several
contributions to the BARC benchmark, detailed flow measurements are acquired in the region near the cylinder side and in the
near-wake flow. The edges and the thickness of the shear layers detaching from the upstream edges are derived from velocity
measurements. Furthermore, we compute the flow frequencies characterizing the roll-up of the shear layers, the evolution of
vortical structures near the cylinder side and the vortex shedding in the wake.
Key Words
BARC benchmark; hot-wire anemometry; lateral and near-wake flow features; pressure measurements; windtunnel experiments
Address
Elena Pasqualetto: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso, 8, 56122 Pisa, Italy
Gianmarco Lunghi: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso, 8, 56122 Pisa, Italy
Benedetto Rocchio: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso, 8, 56122 Pisa, Italy
Alessandro Mariotti: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso, 8, 56122 Pisa, Italy
Maria Vittoria Salvetti: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso, 8, 56122 Pisa, Italy
Abstract
The high-Reynolds number flow around a rectangular cylinder, having streamwise to crossflow length ratio equal to
5 is analyzed in the present paper. The flow is characterized by shear-layer separation from the upstream edges. Vortical
structures of different size form from the roll-up of these shear layers, move downstream and interact with the classical vortex
shedding further downstream in the wake. The corresponding mean flow is characterized by a recirculation region along the
lateral surface of the cylinder, ending by mean flow reattachment close to the trailing edge. The mean flow features on the
cylinder side have been shown to be highly sensitive to set-up parameters both in numerical simulations and in experiments.
The results of 21 Large Eddy Simulations (LES) are analyzed herein to highlight the impact of the lateral mean recirculation
characteristics on the near-wake flow features and on some bulk quantities. The considered simulations have been carried out at
Reynolds number Re=DU_
Key Words
BARC benchmark; bulk quantities; Large-Eddy Simulations; lateral and near-wake flow features
Address
Gianmarco Lunghi:Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso, 8, 56122 Pisa, Italy
Elena Pasqualetto: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso, 8, 56122 Pisa, Italy
Benedetto Rocchio: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso, 8, 56122 Pisa, Italy
Alessandro Mariotti: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso, 8, 56122 Pisa, Italy
aria Vittoria Salvetti: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, Via G. Caruso, 8, 56122 Pisa, Italy
Abstract
In this work a multi-fidelity non-intrusive polynomial chaos (MF-NIPC) has been applied to a structural wind engineering problem in architectural design for the first time. In architectural design it is important to design structures that are safe
in a range of wind directions and speeds. For this reason, the computational models used to design buildings and bridges must
account for the uncertainties associated with the interaction between the structure and wind. In order to use the numerical
simulations for the design, the numerical models must be validated by experimental data, and uncertainties contained in the
experiments should also be taken into account. Uncertainty Quantification has been increasingly used for CFD simulations to
consider such uncertainties. Typically, CFD simulations are computationally expensive, motivating the increased interest in
multi-fidelity methods due to their ability to leverage limited data sets of high-fidelity data with evaluations of more
computationally inexpensive models. Previously, the multi-fidelity framework has been applied to CFD simulations for the
purposes of optimization, rather than for the statistical assessment of candidate design. In this paper MF-NIPC method is applied
to flow around a rectangular 5:1 cylinder, which has been thoroughly investigated for architectural design. The purpose of UQ
is validation of numerical simulation results with experimental data, therefore the radius of curvature of the rectangular cylinder
corners and the angle of attack are considered to be random variables, which are known to contain uncertainties when wind
tunnel tests are carried out. Computational Fluid Dynamics (CFD) simulations are solved by a solver that employs the Finite
Element Method (FEM) for two turbulence modeling approaches of the incompressible Navier-Stokes equations: Unsteady
Reynolds Averaged Navier Stokes (URANS) and the Large Eddy simulation (LES). The results of the uncertainty analysis with
CFD are compared to experimental data in terms of time-averaged pressure coefficients and bulk parameters. In addition, the
accuracy and efficiency of the multi-fidelity framework is demonstrated through a comparison with the results of the high fidelity model.
Abstract
In this paper, the fluctuating lift and drag forces on 5:1 rectangular cylinders with two different geometric scales in
three turbulent flow-fields are investigated. The study is particularly focused on understanding the influence of the ratio of
turbulence integral length scale to structure characteristic dimension (the length scale ratio). The results show that both
fluctuating lift and drag forces are influenced by the length scale ratio. For the model with the larger length scale ratio, the
corresponding fluctuating force coefficient is larger, while the spanwise correlation is weaker. However, the degree of influence
of the length scale ratio on the two fluctuating forces are different. Compared to the fluctuating drag, the fluctuating lift is more
sensitive to the variation of the length scale ratio. It is also found through spectral analysis that for the fluctuating lift, the change
of length scale ratio mainly leads to the variation in the low frequency part of the loading, while the fluctuating drag generally
follows the quasi-steady theory in the low frequency, and the slope of the drag spectrum at high frequencies changes with the
length scale ratio. Then based on the experimental data, two empirical formulas considering the influence of length scale ratio
are proposed for determining the lift and drag aerodynamic admittances of a 5:1 rectangular cylinder. Furthermore, a simple
relationship is established to correlate the turbulence parameter with the fluctuating force coefficient, which could be used to
predict the fluctuating force on a 5:1 rectangular cylinder under different parameter conditions.
Key Words
5:1 rectangular cylinder; aerodynamic force; turbulent flow; wind tunnel test
Address
Yang Yang: 1)Research Centre for Wind Engineering, Southwest Jiaotong University, Chengdu, 610031, China
2) Key Laboratory for Wind Engineering of Sichuan Province, Chengdu, 610031, China
Mingshui Li:1)Research Centre for Wind Engineering, Southwest Jiaotong University, Chengdu, 610031, China
2) Key Laboratory for Wind Engineering of Sichuan Province, Chengdu, 610031, China
Xiongwei Yang: Research Centre for Wind Engineering, Southwest Jiaotong University, Chengdu, 610031, China
Abstract
The aerodynamics of blunt bodies with separation at the sharp corner of the leading edge and reattachment on the
body side are particularly important in civil engineering applications. In recent years, a number of experimental and numerical
studies have become available on the aerodynamics of a rectangular cylinder with chord-to-thickness ratio equal to 5 (BARC).
Despite the interest in the topic, a widely accepted set of guidelines for grid generation about these blunt bodies is still missing.
In this work a new, well resolved Direct Numerical Simulation (DNS) around the BARC body at Re=3000 is presented and its
results compared to previous DNSs of the same case but with different numerical approaches and mesh. Despite the simulations
use different numerical approaches, mesh and domain dimensions, the main discrepancies are ascribed to the different grid
spacings employed. While a more rigorous analysis is envisaged, where the order of accuracy of the schemes are kept the same
while grid spacings are varied alternately along each spatial direction, this represents a first attempt in the study of the influence
of spatial resolution in the Direct Numerical Simulation of flows around elongated rectangular cylinders with sharp corners.
Key Words
BARC benchmark; Direct Numerical Simulation
Address
Roberto Corsini: DIEF, University of Modena and Reggio Emilia, 41125 Modena, Italy
Diego Angeli: DISMI, University of Modena and Reggio Emilia, 42122 Reggio Emilia, Italy
Enrico Stalio: DIEF, University of Modena and Reggio Emilia, 41125 Modena, Italy
Sergio Chibbaro: 1)Sorbonne Université, Institut Jean le Rond d
