M.Belan - research

Research Topics

Experiments
Analytic Models for Fluid Dynamics

Experiments

Experiments -- plasma/gas flow interactions

These experiments deal with the interaction between non-thermal plasma and gas flows, where non-thermal plasma is created by DC or AC discharges. The possible plasma-gas flow interactions cover a wide field of research, virtually including flow control problems, free coupling of electrical and inertia forces and even plasma control by means of an airflow.

Powered multi-tip DBD on the leading edge of a NACA0015 airfoil	Separation control by corona discharge at low Reynolds numbers

M. Belan, Plasma-gas flow interaction of a discharge normal to a bluff body wake, IEEE Trans Plasma Science, Vol.42 Issue 9, sept 2014
M. Belan, A gas discharge normal to a wake: experimental investigation of the plasma-flow interaction. Progress in Turbulence V - A. Talamelli et al. (Eds), Springer Proceedings in physics 149 (2014)

Electrohydrodynamic propulsion in atmosphere is a promising technology aimed to create thrust by exploiting the ionic wind generated by suitable devices.
It provides several advantages such as absence of moving parts and low noise production. Recent developments point out the importance of electrodes design to maximize thrust and reduce aerodynamic drag.

Propulsion system at test bench	Photograph of the system sketched in the left panel

M. Belan, J. Baldo, O. Kahol, D. Montenero, Blade Emitters for Atmospheric Ionic Thrusters, J Phys D: Appl Phys 57, N. 19, 2024, 195201
O. Kahol, M. Belan, M. Pacchiani, D. Montenero, Scaling Relations for the Geometry of Wire-To-airfoil Atmospheric Ionic Thrusters, J Electrostat 123 (2023), 103815
M. Belan, R. Terenzi, S. Trovato, D. Usuelli, Effects of the emitters density on the performance of an atmospheric ionic thruster, J. Electrostat 120 (2022), 103767
M. Belan, L. Arosti, R. Polatti, F. Maggi, S. Fiorini, F. Sottovia, A parametric study of electrodes geometries for atmospheric electrohydrodynamic propulsion, J. Electrostat. 113 (2021) 103616
F. Sottovia, S. Fiorini, M. Belan, F. Maggi, L Arosti, A new experimental facility for ionic propulsion studies, abstract, ICTAM 2020+1, 25th International Congress of Theoretical and Applied Mechanics}, 2021

The plasma actuators are widely studied because of their ability to produce a ionic wind, that can be used for several flow control purposes. The shape of the electrodes seems to be a very important parameter: in particular, multiple tips on the edge of the active electrodes can improve the efficiency of the actuators.

Sketch of the gas flow generated by a multi-tip corona actuator	Sketch of the gas flow generated by a multi-tip DBD actuator

F. Messanelli, E. Frigerio, E. Tescaroli, M. Belan. Separation Control by Plasma Actuators: Effects of Direct Momentum Injection and Vortex Generation, Flow Turb. Comb. 104, 895-–926, 2020
F. Messanelli, M. Belan. A Comparison Between Corona and DBD Plasma Actuators for Separation Control on an Airfoil, 55th AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA 2017-0395)
M. Belan, F. Messanelli, Wind tunnel testing of multi-tip corona actuators on a symmetric airfoil, J. Electrostat. 85, 2017
F. Messanelli, M. Belan, Ionic wind measurements on multi-tip plasma actuators, EPJ Web of Conferences 114, 02073 (2016)
M. Belan, F. Messanelli, Compared ionic wind measurements on multi-tip corona and DBD plasma actuators, J Electrostat. 76, 2015
F. Messanelli, M. Belan, A comparison between DBD and corona actuators with non-straight electrodes, Progress in Turbulence VI , Peinke, J., et al. (Eds.) , Springer Proceedings in physics 165 (2016)

Flow control by means of DBD actuators creates local tridimensional flow even when the basic flow is bidimensional. When also the basic flow is inherently tridimensional, the flow topology may remarkably differ from simplified plane representations obtained for instance by a longitudinal section close to the centerline.

Action of a multi-tip DBD actuator installed on the leading edge of a wind tunnel airfoil. The finite span creates a naturally 3D separation which is modified by plasma flow control.

G. Zoppini, M. Belan, A. Zanotti, L. Di Vinci, G. Campanardi, Stall Control by Plasma Actuators: Characterization along the Airfoil Span, Energies 2020, 13, 1374
G. Zoppini, L. Di Vinci, G. Campanardi, A. Zanotti, M. Belan. PIV characterization of a separated flow controlled by a DBD actuator, J. Phys.: Conf. Ser. 1249, 012012 (2019)

The corona discharge is widely known, with numerous applications ranging from engineering to chemistry and medicine. The technology for creating it in a volume of gas is well established, whereas the development of a corona discharge along a surface is difficult. Surface corona discharges can be stabilized by feeding an electrode with multiple tips by a suitable waveform.

Pulsed generator for surface corona devices	Operating principle

M. Belan, E. Tescaroli, Discharge Stability Enhancement in Surface Corona Actuators, IEEE Trans. Plasma Sci. 50 n1, 69-78, jan 2022
F. Messanelli, E. Frigerio, E. Tescaroli, M. Belan. Flow separation control by pulsed corona actuators, Exp. Therm. Fluid Sci. 105, 123-135, 2019

Experiments -- hypersonic jets

Highly underexpanded jets

This research project is devoted to the study of hypersonic underexpanded and nearly matched jets. The flows considered here are important both in fluid dynamics and in astrophysics. The facilities are suitable for investigating the spatial evolution of a jet over long scales, in the order of hundreds of initial diameters. It is possible to set the jet-to-ambient density ratio and the jet Mach number independently of each other, this is obtained using different gases for the jet and the ambient. Observations and measurements are performed by means of an electron gun (designed and built in this laboratory), that makes possible to get fluorescent plane sections of the jets, acquired as digital images. After suitable image processing, thanks to an original method purposely developed, each image becomes a measurement field where density and concentration maps of the different gases can be obtained: this gives information on jet substructures, compressible lateral mixing, and long term jet spreading.

Left panel: an argon jet flowing in an helium ambient, Mach number upstream of the normal shock > 30.
Right panel: a pair of Ar concentration curves along radial sections: jet/ambient mixing is more effective after the normal shock.

Nearly matched jets at high Mach numbers

An experiment run in the same facilities as above is devoted to the study of nearly matched jets issuing from de Laval nozzles. These jets have Mach numbers (5 to 20) and jet/ambient density ratios (0.1 to 100) in the same range of the stellar jets known in astrophysics by direct observations and widely studied by means of numerical simulations.The lab tests show that many properties of the stellar jets can be explained in terms of pure fluid dynamics, since MHD and radiation effects are not included in this experiment. In particular, the jet morphology exhibits many known structures as bow and terminal shocks, backward flow cocoons and compression knots .

The research program involves: + Politecnico di Milano, + Universita' di Torino, + Politecnico di Torino, + Max-Planck-Institute for Dynamics and Self-Organization - Göttingen

	Electron beam visualization of a Xenon jet flowing in Argon ambient, reconstruction obtained by juxtaposing adjacent frames of the same movie ( web quality, speed = realtime/1000 ). Nominal Mach number = 15. Gas velocity ~ 0.6 km/s. Jet/Ambient density ratio >> 1.	A video about this research topic (italian version, english subtitles)

Belan M., Tordella D., de Ponte S., Mignone A., Massaglia S., Hypersonic jets in astrophysical conditions: focus on spreading and asymmetric stability properties, New J Phys 16, 085002, 2014
Belan M., Massaglia S., Tordella D., Mirzaei M., de Ponte S., The hydrodynamics of astrophysical jets: scaled experiments and numerical simulations, Astron Astrohpys 554, A99 (2013)
Mirzaei M. and Belan M., An Application of Image Analysis to Hypersonic Flows. EPJ Web of Conferences 45, 01064 (2013)
Belan M., Massaglia S., Mirzaei M., Tordella D., De Ponte S., Mignone A., Ferrari A., Bodenschatz E.,An investigation of the hydrodynamics of hypersonic jets in astrophysical conditions, EAS Publications Series, 58 (2012)
Belan M., Mirzaei M., De Ponte S., Tordella D., An experimental setup for visualizations and measurements on free hypersonic jets, EPJ Web of Conferences 25, 01056 (2012)
Belan M., De Ponte S., Tordella D., Massaglia S., Ferrari A., Mignone A., Bodenschatz E., Hydrodynamics of Hypersonic Jets: Experiments and Numerical Simulations, Astrophys Space Sci, v336 n1, 2011
Tordella D., Belan M., Massaglia S., De Ponte S., Mignone A., Bodenschatz E., Ferrari A., Astrophysical jets: insight into long term hydrodynamics, New J Phys 13, 043011, 2011
Belan M., De Ponte S., Tordella D., Highly under-expanded jets in the presence of a density jump between the ambient and the jet, Phys Rev E, vol. 82 n2, 2010 , selected by PRE website, http://pre.aps.org/kaleidoscope, aug 2010
Belan M., De Ponte S., Tordella D., Determination of density and concentration from fluorescent images of a gas flow, Exp in Fluids , vol.45 n3, 2008
Belan M., De Ponte S., Tordella D., Simultaneous density and concentration measurements on hypersonic jets. Abstract, EFMC6 KTH, Euromech Fluid Mechanics Conference 6 , Royal Institute of technology, Stockholm, 2006.
Belan M., De Ponte S., Massaglia S., Tordella D., Experiments and numerical simulations on the mid-term evolution of hypersonic jets. Astrophys Space Sci 293 (1-2): 225-232 , 2004
Belan M., Tordella D., De Ponte S., A system of fast acceleration of a mass of gas for the laboratory simulation of stellar jets. Proceedings of the ICIASF meeting , Cleveland 2001, 409-416
Belan M., De Ponte S., D'Ambrosio D., Tordella D., Design of an experiment on the spatial evolution of hypersonic jets. Atti XVI Conferenza AIDAA , Palermo, 2001

Experiments -- turbulence

Drag reduction

The ubiquity of turbulent flows, with their large frictional drag brought about by momentum diffusion, makes the reduction of such drag an objective of pervasive importance in many applications. A new method for forcing a turbulent flow, based on streamwise-traveling waves of spanwise velocity at the wall, is tested by means of an experiment, where a pipe was built with the capability of producing the required wall forcing. The drag reduction can reach 30% and more, with saved energy larger than the control energy by almost two orders of magnitude.

Experiment setup: a turbulent flow in a pipe is forced at the wall by a tangential velocity of the kind 'travelling wave'	Drag reduction DR (%) at Re=5000: a comparison between DNS results (grid surface) and experimental results (large dots fall above the surface, small dots fall below) as functions of frequency and wavenumber of the travelling wave

M. Belan and M. Quadrio, A perturbative model for predicting the high-Reynolds-number behaviour of the streamwise travelling waves technique in turbulent drag reduction, ZAMM - Z Angew Math Mech 93, No. 12, 944--962 (2013)
Auteri F., Baron A., Belan M., Campanardi G., Quadrio M., Experimental Assessment of Drag Reduction by Traveling Waves in a turbulent pipe flow, Phys Fluids, Vol. 22 Issue 11, November 2010
Quadrio M., Auteri F., Baron A., Belan M., Bertolucci A., Experimental Assessment of Turbulent Drag Reduction by Wall Traveling Waves, in: Advances in Turbulence XII, B. Eckhardt (Ed.), Springer, Dordrecht, 2010, p. 657-660
Auteri F., Baron A., Belan M., Bertolucci A., Gibertini G., Quadrio M., Streamwise-Traveling Waves of Spanwise Wall Velocity in a Pipe Flow: Experimentally Assessing the Turbulent Drag Reduction, XX Congresso nazionale AIDAA, Milano, I, 2009
see also http://www.aero.polimi.it/~quadrio

Turbulent flow in helically coiled pipe

The study of turbulent flow in helically coiled pipes is important both for its engineering applications and its scientific interest. Aim of this research project is to describe the turbulent flow in a helical pipe of circular cross-section, and in particular to study the secondary structures in turbulent conditions with an endoscopic Particle Image Velocimetry (PIV) technique.

Ceccon S., Auteri F., Baron A., Belan M., Gibertini G., Quadrio M., Turbulent flow in a helically coiled pipe: an endoscopic PIV study. Scientific Report DIA-SR 06-09, Politecnico di Milano, 2006 .
Auteri F., Belan M., Ceccon S., Gibertini G., Endoscopic piv in a helical coil. Proceedings of XIV AIVELA meeting, 2006, Roma

Experiments -- bluff body wakes

A well known problem in wind engineering is the flow around two bodies in tandem configuration. This experimental investigation studies the important case of two flat plates at 90^o incidence. The experiment is carried out by means of smoke visualizations, hot wire (HWA) and laser doppler (LDA) anemometry. Accurate measurements of the Strouhal number were obtained for plate separations ranging from 0.25 chords to 7.5 chords. Different flow regimes are described, depending on the distance between the plates, by exploiting the Strouhal number behaviour and the flow visualizations. A narrow interval of distances where two regimes alternatively appear is found; this intermittence is reported in detail by means of simultaneous visualizations, HWA and LDA measurements. Mean and instantaneous flows fields between the two plates and past the aft plate are determined by LDA for each configuration.

______________________ Graphical outline of the bistable flow ___________________

__________________ One-body mode measurements : __________________

Vorticity and velocity fields

Visualization and velocity field

Gibertini G., Abba' A., Auteri F., Belan M., Flow around Two in-Tandem Flat Plates: Measurements and Computations Comparison. 5th International Conference on Vortex Flows and Vortex Models (ICVFM2010), Caserta, Italy, 2010, paper 48
Auteri F., Belan M., Cassinelli C., Gibertini G., Interacting wakes of two normal flat plates. An investigation based on phase averaging of LDA signals. J. of Visualization, Vol. 12, No. 4 (2009) 307-321
Auteri F., Belan M., Gibertini G., Grassi D., Normal flat plates in tandem: an experimental investigation. J. of Wind Eng. and Industrial Aerodynamics 96 , 2008.
Auteri F., Belan M., Cassinelli C., Gibertini G., The interacting wakes of two flat plates. Collected papers, BBAA VI - 6th International Colloquium on Bluff Bodies Aerodynamics & Applications, Milano, Italy, July, 20-24 2008
Auteri F., Belan M., Cassinelli C., Gibertini G., Grassi D.,LDA investigation of the interfering wakes of two in tandem flat plates, Proceedings of XV AIVELA meeting, 2007, Milano
Auteri F., Belan M., Gibertini G., Grassi D.,Normal flat plates in tandem: an experimental investigation. Summary papers, BBAA V - 5th International Colloquium on Bluff Body Aerodynamics & Applications, Ottawa, 2004
Auteri F., Belan M., Gibertini G., Grassi D., Corrente vorticosa prodotta da due lamine piane in tandem. Atti XVII Conferenza AIDAA , Roma, 2003

Devices and Systems for experimental fluid dynamics

Many electronic devices and systems for the laboratory are designed by the author of these pages
(low and high voltage power supplies, DC and stepper motor controls, pressure sensor controllers, timers...)

    Example: a DC motor closed-loop velocity controller.
    Input: any velocity waveform, Vpp>1.5V;
    Output: 100W (up to 42Vpp for DC motors from 6 to 24V)
    (click on the figure to enlarge)

A pressure probe designed for boundary layer measurements around models not provided with pressure taps
is presented in

E. Tescaroli and M. Belan, An original Pitot-static probe design for subsonic boundary layer investigation, Meas. Sci. Technol. 32 065301, 2021

Analytic Models for Fluid Dynamics

Perturbation methods for the drag reduction problem

Some applications of the perturbation methods to the drag reduction technique described above can be found in

M. Belan and M. Quadrio, A perturbative model for predicting the high-Reynolds-number behaviour of the streamwise travelling waves technique in turbulent drag reduction, ZAMM - Z Angew Math Mech 93, No. 12, 944--962 (2013)
Auteri F., Baron A., Belan M., Campanardi G., Quadrio M., Experimental Assessment of Drag Reduction by Traveling Waves in a turbulent pipe flow, Phys Fluids, Vol. 22 Issue 11, November 2010

Asymptotic expansions for the bluff-body wakes

These works report asymptotic expansion solutions of the momentum equation for the bluff-body wakes at low Re numbers,
particularly useful as basic flow for instability problems.

Tordella D., Belan M., A new matched asymptotic expansion for the intermediate and far flow behind a finite body. Phys Fluids - July 2003, Vol. 15, Issue 7, pp. 1897-1906
Belan M., Tordella D., Asymptotic expansions for two dimensional symmetrical laminar wakes. ZAMM - Z Angew Math Mech 82 (2002) 4, 219-234
Belan M., Tordella D., Asymptotic expansions for 2D laminar wakes. Abstract, 52th APS-DFD, Annual Meeting of the American Physical Society, Division of Fluid Dynamics , 1999, New Orleans, Louisiana, Notre Dame University

Wake Instability at low Re numbers

The reference flow under study is the cylinder wake at low Re numbers, altough the theory may be easily generalized to other wakes. The early works are based on weakly nonlinear models. The most recent make use of a multiscale approach where 1/Re is the small parameter: by introducing a spatio-temporal multiscaling into a linearized instability model, a hyerarchy of ODEs is obtained. The first one is a parametric Orr-Sommerfeld equation, the second one is an inhomogeneous equation that gives the non-parallel corrections to the eigenvalues found at the first step, and leads to a modulation equation for the instability wavetrains.The streamwise variation of the instability characteristics can then be deduced from the wave modulation, as a function of the perturbing wave numbers. It is found that the non-parallel effects are not negligible, and that the absolute instability region in the first wake is larger than what calculated from a parallel model. The dominant frequencies found here are in good agreement with the global modes of the wake known in literature.

Top to bottom:
- analytic velocity field (blue streamlines) for the cylinder wake at Re=38
- local instability pulsation with and without non parallel effects
- local instability growth rate with and without non parallel effects

Tordella D., Scarsoglio S., Belan M., Hydrodynamics linear stability theory. A comparison between Orr-Sommerfeld modal and initial value problem analyses. Acc Sci Torino - Memorie Sc Fis, v31 (2007)
Belan M., Tordella D., Convective instability in wake intermediate asymptotics. J. Fluid Mech. 552(2006), 127 - 136
Tordella D., Scarsoglio S., Belan M., A synthetic perturbative hypothesis for multiscale analysis of convective wake instability. Phys Fluids - May 2006, Vol. 18, Issue 5
Belan M., Tordella D., On the domain of validity of the near-parallel combined stability analysis for the 2D intermediate and far bluff body wake. ZAMM - Z Angew Math Mech 85 , No.1, 51--65 (2005)
Tordella D., Scarsoglio S., Belan M. Analysis of the convective instability of the two-dimensional wake. Abstract, 22nd IFIP TC conference on system modeling and optimization , Torino, 2005
Belan M., Tordella D., Asymptotic method for the non parallel instability of 2D symmetrical laminar wakes. Atti XV Congresso Nazionale AIDAA , Torino, 1999
Belan M., Evoluzione debolmente non lineare dei treni d'onda dispersivi. Applicazione alla scia del corpo tozzo. Tesi di dottorato - PhD Thesis, Biblioteche Nazionali - Roma, Firenze , 1997
Tordella D., Belan M., Instability of weak nonlinear waves. Comparison between the behaviour of spatial and temporal growth modes. Atti XII Congresso AIMETA , Napoli, 1995, v4, 133-138
Belan M., On the traveling waves solutions of the Ginzburg-Landau equation. Atti XII Congresso AIMETA , Napoli, 1995, v4, 127-132

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