
Enrico STALIO
Professore Associato Dipartimento di Ingegneria "Enzo Ferrari"

Home 
Curriculum(pdf) 
Didattica 
Pubblicazioni
2024
 DNS of the Flow About a 5:1 Rectangular Body with Sharp Corners
[Capitolo/Saggio]
Corsini, R.; Cimarelli, A.; Stalio, E.
abstract
2024
 Design of heat pipes on board accelerating vehicles using the 1D/3D cosimulation approach
[Articolo su rivista]
Ermini, M.; Sabato, M.; Brusiani, F.; Baritaud, T.; Corsini, R.; Stalio, E.
abstract
2024
 Energy Cascade Phenomena in Temporal Boundary Layers
[Articolo su rivista]
Cimarelli, A.; Boga, G.; Pavan, A.; Costa, P.; Stalio, E.
abstract
The geometrically complex mechanisms of energy transfer in the compound space of scales and positions of wall turbulent flows are investigated in a temporally evolving boundary layer. The phenomena consist of spatially ascending reverse and forward cascades from the small production scales of the buffer layer to the small dissipative scales distributed among the entire boundary layer height. The observed qualitative behaviour conforms with previous results in turbulent channel flow, thus suggesting that the observed phenomenology is a robust statistical feature of wall turbulence in general. An interesting feature is the behaviour of energy transfer at the turbulent/nonturbulent interface, where forward energy cascade is found to be almost absent. In particular, the turbulent core is found to sustain a variety of largescale wallparallel motions at the turbulent interface through weak but persistent reverse energy cascades. This behaviour conforms with previous results in free shear flows, thus suggesting that the observed phenomenology is a robust statistical feature of turbulent shear flows featuring turbulent/nonturbulent interfaces in general.
2023
 Experimental assessment and predictive model of the performance of Tibased nanofluids
[Articolo su rivista]
D'Adamo, Alessandro; Diana, Martino; Corda, Giuseppe; Cucurachi, Antonio; Cannio, Maria; Pellacani, Andrea; Romagnoli, Marcello; Stalio, Enrico; Santangelo, Paolo Emilio
abstract
The need for innovative propulsion technologies (e.g., fuel cells) in the mobility sector is posing a higherthanever burden on thermal management. When low operative temperature shall be ensured, dissipation of a significant amount of heat is requested, together with limited temperature variation of the coolant; mobile applications also yield limitations in terms of space available for cooling subsystems. Nanofluids have recently become one of the most promising solutions to replace conventional coolants. However, the prediction of their effectiveness in terms of heattransfer enhancement and required pumping power still appears a challenge, being limited by the lack of a general methodology that assesses them simultaneously in various flow regimes. To this end, an experiment was developed to compare a conventional coolant (ethylene glycol/water) and a TiO2based nanofluid (1% particle loading), focusing on heat transfer and pressure loss. The experimental dataset was used as an input for a physical model based on two independent figures of merit, aiming at an a priori evaluation of the potential simultaneous gain in heat transfer and parasitic power. The model showed conditions of combined gain specifically for the laminar flow regime, whereas turbulent flows proved inherently associated to higher pumping power; overall, criteria are presented to evaluate nanofluid performance as compared to that of conventional coolants. The model is generally applicable to the design of cooling systems and emphasizes laminar flow regime as promising in conjunction with the use of nanofluids, proposing indices for a quantitative a priori evaluation and leading to an advancement with respect to an a posteriori assessment of their performance.
2023
 On windwave interaction phenomena at low Reynolds numbers
[Articolo su rivista]
Cimarelli, A.; Romoli, F.; Stalio, E.
abstract
After decades of research efforts, windwave interaction mechanisms have been recognized as extremely elusive. The reason is the complex nature of the problem, which combines complex coupling mechanisms between turbulent wind and water waves with the presence of multiple governing parameters, such as the friction Reynolds number of the wind, the water depth and the wind fetch. As shown unequivocally here, the use of suitable flow settings allows us to reduce the complex problem of windwave interaction to its essential features, mainly as a function of the sole friction Reynolds number of the wind. The resulting numerical solution allows us to study the interactions between water and air layers with their own fluid properties, and to unveil very interesting features, such as an oblique wave pattern travelling upstream and a waveinduced Stokes sublayer. The latter is responsible for a drag reduction mechanism in the turbulent wind. Despite the simulated flow conditions being far from the intense events occurring at the oceanatmosphere interface, the basic flow phenomena unveiled here may explain some experimental evidence in windwave problems. Among other things, the waveinduced Stokes sublayer may shed light on the large scatter of the drag coefficient data in field measurements where swell waves of arbitrary directions are often present. Hence the present results and the developed approach pave the way for the understanding and modelling of the surface fluxes at the oceanatmosphere interface, which are of overwhelming importance for climate science.
2022
 Direct Numerical Simulation of natural, mixed and forced convection in liquid metals: selected results
[Articolo su rivista]
Fregni, A.; Angeli, D.; Cimarelli, A.; Stalio, E.
abstract
Selected results of three Direct Numerical Simulations are presented, on relevant test cases for the thermal hydraulics of liquid–metalcooled nuclear reactors, encompassing a wide spectrum of turbulent convection regimes. The first test case is a RayleighBénard cell at a Grashof number Gr=5×107, representative of the conditions in the unstably stratified layer of coolant in a reactor pool in both standard operating conditions and emergency situations, e.g. shutdown of the cooling system. The second case is the mixed convection in a coldhot–cold triple jet configuration, representative of liquid streams exiting from the core into the pool, and relevant for the modeling of thermal striping and thermal fatigue phenomena on the vessel containment walls. The third case is the fullydeveloped flow in a vertical bare rod bundle with triangular arrangement and a pitchtodiameter ratio P/D=1.4, in both forced and mixed convection conditions. These regimes respectively represent normal operation or decay heat removal conditions in reactor cores. The availability of these numerical databases will allows for an indepth analysis of the turbulent flow and heat transfer in liquid metals under different convection regimes, and is also relevant for the development, calibration and validation of turbulent heat transfer models.
2022
 Flow solutions around rectangular cylinders: The question of spatial discretization
[Articolo su rivista]
Corsini, R.; Angeli, D.; Stalio, E.; Chibbaro, S.; Cimarelli, A.
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 chordtothickness 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.
2021
 An integrated approach for the analysis and modeling of road tunnel ventilation. Part II: Numerical model and its calibration
[Articolo su rivista]
Cingi, P.; Angeli, D.; Cavazzuti, M.; Levoni, P.; Stalio, E.; Cipollone, M.
abstract
The present work represents the second and final part of a twofold study aiming at the definition and validation of an integrated methodology for the analysis and modeling of road tunnel ventilation systems. A numerical approach is presented, based on the Finite Volume integration of the 1D mechanical and thermal energy conservation equations on a network of ducts, representing the ventilation system of the 11.6 km long Mont Blanc Tunnel. The set of distributed and concentrated loss coefficients, representing dissipation of mechanical energy by friction in each part of the ventilation system, is calibrated against a rich experimental dataset, collected throughout a dedicated set of in situ tests and presented in the first part of the work. The calibration of the model is carried out by means of genetic optimization algorithms. Predictions of the flow field using the calibrated parameters are in remarkable agreement with the experimental data, with an overall RMS error of ± 0.27 m/s, i.e. of the same order of the accuracy of the measurement probes. Further validation against a selection of field data recorded by the tunnel monitoring and control system is brought forward, highlighting the robustness and potential general applicability of the proposed approach.
2021
 On the turbulent flow past a realistic opencell metal foam
[Articolo su rivista]
Corsini, R.; Fregni, A.; Spinolo, M.; Stalio, E.
abstract
Turbulence is investigated in the lee of an opencell metal foam layer. In contrast to canonical grids metal foams are locally irregular but statistically isotropic. The solid matrix is characterised by two lengths the ligament thickness and the pore diameter. A direct numerical simulation is conducted on a realistic metal foam geometry for which and the porous layer thickness is five times the pore diameter. The Reynolds number based on the pore size is corresponding to a Taylorscale Reynolds number. Closer to the foam than two pore diameters the pressure and turbulent transports of turbulent kinetic energy are nonnegligible. In the same region undergoes a steep decrease whereas the dissipation coefficient increases like. At larger distances from the porous layer the classical grid turbulence situation is recovered where the mean advection of turbulent kinetic energy equals dissipation. This entails a powerlaw decay of turbulent quantities and characteristic lengths. The decaying exponents of integral Taylor and Kolmogorov scales are close to onehalf indicating that the turbulence simulated here differs from Saffman turbulence. Analysis of the scaling exponents of structure functions and the decorrelation length of dissipation reveals that smallscale fluctuations are weakly intermittent.
2020
 A collaborative effort towards the accurate prediction of turbulent flow and heat transfer in lowPrandtl number fluids
[Articolo su rivista]
Shams, A.; Roelofs, F.; Tiselj, I.; Oder, J.; Bartosiewicz, Y.; Duponcheel, M.; Niceno, B.; Guo, W.; Stalio, E.; Angeli, D.; Fregni, A.; Buckingham, S.; Koloszar, L. K.; Villa Ortiz, A.; Planquart, P.; Narayanan, C.; Lakehal, D.; van Tichelen, K.; Jager, W.; Schaub, T.
abstract
This article reports the experimental and DNS database that has been generated, within the framework of the EU SESAME and MYRTE projects, for various lowPrandtl flow configurations in different flow regimes. This includes three experiments: confined and unconfined backward facing steps with lowPrandtl fluids, and a forced convection planar jet case with two different Prandtl fluids. In terms of numerical data, seven different flow configurations are considered: a wallbounded mixed convection flow at lowPrandtl number with varying Richardson number (Ri) values; a wallbounded mixed and forced convection flow in a bare rod bundle configuration; a forced convection confined backward facing step (BFS) with conjugate heat transfer; a forced convection impinging jet for three different Prandtl fluids corresponding to two different Reynolds numbers of the fully developed planar turbulent jet; a mixedconvection coldhot–cold triple jet configuration corresponding to Ri = 0.25; an unconfined free shear layer for three different Prandtl fluids; and a forced convection infinite wirewrapped fuel assembly. This wide range of reference data is used to evaluate, validate and/or further develop different turbulent heat flux modelling approaches, namely simple gradient diffusion hypothesis (SGDH) based on constant and variable turbulent Prandtl number; explicit and implicit algebraic heat flux models; and a second order turbulent heat flux model. Lastly, this article will highlight the current challenges and perspectives of the available turbulence models, in different codes, for the accurate prediction of flow and heat transfer in lowPrandtl fluids.
2020
 DIRECT NUMERICAL SIMULATION OF NATURAL, MIXED AND FORCED CONVECTION IN LIQUID METALS: SELECTED RESULTS
[Relazione in Atti di Convegno]
Fregni, A.; Angeli, D.; Cimarelli, A.; Stalio, E.
abstract
Selected results of three Direct Numerical Simulations are presented, on relevant test cases for the thermal hydraulics of liquid metalcooled nuclear reactors, encompassing a wide spectrum of turbulent convection regimes. The first test case is a RayleighBenard cell at a moderately high Grashof number, representative of the conditions in the unstably stratified layer of fluid in a reactor pool. The second case is the mixed convection in a coldhotcold triple jet configuration, representative of the mixing liquid streams exiting from the core into the pool, and relevant for the modeling of thermal striping and thermal fatigue phenomena on the vessel containment walls. The third case is the fullydeveloped flow in a vertical bare rod bundle with triangular arrangement and a large pitchtodiameter ratio, in both forced and mixed convection conditions, representative of normal operation or decay heat removal flow conditions in the reactor core, respectively. The availability of these numerical databases will allow for an indepth analysis of the turbulent flow and heat transfer in liquid metals under different convection regimes, and is also relevant for the development, calibration and validation of turbulent heat transfer models.
2020
 Direct numerical simulation of turbulence in the wake of a metal foam
[Articolo su rivista]
Corsini, R.; Stalio, E.
abstract
A Direct Numerical Simulation is carried out to study a turbulent wake. The flow configuration is typical of grid turbulence investigations, but in place of a regular grid or fractal grid, the initially uniform flow passes through a threedimensional, irregular yet statistically isotropic porous matrix. A synthetic, periodic, open cell metal foam of porosity ε = 0.92 is the geometry selected. The flow is at a Reynolds number based on the mean pore diameter dp and the freestream velocity U∞ of Redp = 4000. An approximation to homogeneous and isotropic decaying turbulence is achieved in the lee of the porous layer. Statistics reported include isotropy indicators, skewness, flatness, velocity autocorrelations, the integral scale of turbulence and compensated spectra. Dissipation of turbulent kinetic energy is calculated from its definition and from some known approximations based on different hypotheses, results extracted provide practical advice for experimentalists and give an insight in the isotropic features of the flow.
2020
 Fully developed turbulent convection of Lead Bismuth Eutectic in the elementary cell of the NACIEUP Fuel Pin Bundle
[Articolo su rivista]
Angeli, D.; Di Piazza, I.; Marinari, R.; Stalio, E.
abstract
One of the requirements for achieving high levels of safety in fourth generation nuclear power plants, is that core thermalhydraulics can be simulated numerically at a good level of accuracy. To this aim, detailed validation of turbulent heat transfer models needs to be carried out and discussed, in relevant flow and heat transfer configurations, and for low Prandtlnumber fluids. The focus of this research is the turbulent, fully developed convection in a heated rod bundle with a triangular arrangement, and a pitchtodiameter ratio P/D=1.4. Statistics derived from a set of Direct Numerical Simulations (DNS) at the moderate Reynolds number of Re=8290 are compared to Reynolds Averaged NavierStokes (RANS) solutions where the closure is provided by the twoequation model SST kω and by the ReynoldsStress Model. Comparisons are drawn for forced flow and in mixed convection conditions (Ri≈0.25). Global quantities extracted from experiments performed in very similar conditions are also compared against the numerical results. Profiles of the turbulent Prandtl number about the unit flow cell are also displayed and discussed. This work clarifies through detailed comparison that if, on the one hand, only the ReynoldsStress model is able to reasonably capture important flow features like secondary flow components, on the other hand also the SST kω twoequation model considered is acceptably accurate in predicting the integral quantities of interest.
2019
 A collaborative effort towards the accurate prediction of turbulent flow and heat transfer in lowPrandtl number fluids
[Relazione in Atti di Convegno]
Shams, A.; Roelofs, F.; Tiselj, I.; Oder, J.; Bartosiewicz, Y.; Duponcheel, M.; Niceno, B.; Guo, W.; Stalio, E.; Angeli, D.; Fregni, A.; Buckingham, S.; Koloszar, L. K.; Villa Ortiz, A.; Planquart, P.; Narayanan, C.; Lakehal, D.; van Tichelen, K.; Jager, W.; Schaub, T.
abstract
This article reports the experimental and DNS database that has been generated, within the framework of the EU SESAME and MYRTE projects, for various lowPrandtl flow configurations in different flow regimes. This includes three experiments: confined and unconfined backward facing steps with lowPrandtl fluids, and a forced convection planar jet case with two different Prandtl fluids. In terms of numerical data, seven different flow configurations are considered: a wallbounded mixed convection flow at lowPrandtl number with varying Richardson number (Ri) values; a wallbounded mixed and forced convection flow in a bare rod bundle configuration for two different Reynolds numbers; a forced convection confined backward facing step (BFS) with conjugate heat transfer; a forced convection impinging jet for three different Prandtl fluids corresponding to two different Reynolds numbers of the fully developed planar turbulent jet; a mixedconvection coldhotcold triple jet configuration corresponding to Ri=0.25; an unconfined free shear layer for three different Prandtl fluids; and a forced convection infinite wirewrapped fuel assembly. This wide range of reference data is used to evaluate, validate and/or further develop different turbulent heat flux modelling approaches, namely simple gradient diffusion hypothesis based on constant and variable turbulent Prandtl number; explicit and implicit algebraic heat flux models; and a second order turbulent heat flux model. Lastly, this article will highlight the current challenges and perspectives of the available turbulence models, in different codes, for the accurate prediction of flow and heat transfer in lowPrandtl fluids.
2019
 A fast algorithm for Direct Numerical Simulation of turbulent convection with immersed boundaries
[Articolo su rivista]
Angeli, D.; Stalio, E.
abstract
A parallel algorithm is presented for the Direct Numerical Simulation of convection flows in open or partially confined periodic domains, containing immersed cylindrical bodies of arbitrary crosssection. The governing equations are discretized by means of the Finite Volume method on Cartesian grids. The method presented includes a triperiodic Poisson solver employed irrespective of the actual boundary shape and a second order accuracy for the computational domain, including the near wall regions, when walls are defined as immersed boundaries. The numerical solution of the set of linear equations resulting from discretization is carried out by means of efficient and highly parallel direct solvers. Verification and validation of the numerical procedure is reported in the paper, for laminar and turbulent pipe flow, and for the case of flow around an array of heated cylindrical rods arranged in a triangular lattice. The formal accuracy of the method is demonstrated in laminar flow conditions, and DNS results in turbulent conditions are compared to available literature data, thus confirming the favorable qualities of the method.
2019
 Comparison between cooling strategies for power electronic devices:
fractal minichannels and arrays of impinging submerged jets
[Relazione in Atti di Convegno]
Baraldi, Niccolò; Fregni, Andrea; Sabato, Massimo; Stalio, Enrico; Brusiani, Federico; Tranchero, Maurizio; Baritaud, Thierry
abstract
Power electronic devices like Insulated Gate Bipolar Transistors (IGBTs) and diodes are often characterized by power densities and dimensions that could result in very high heat flux densities. In order to guarantee the expected performance and lifetime for these components, dedicated active cooling devices are usually adopted. In the present paper, the comparison between two different cooling strategies for power electronics is presented: fractal channel design and submerged impinging jets. Each cooling strategy is tested on two different geometrical configurations. Water is used as coolant in all cases. Assessment of the considered cooling methods is done through application of the selected configurations in a simplified system composed by a rectangular chip (heat source) separated from the coolant by a solid block. Threedimensional conjugated heat transfer simulations are performed by using RANS solver implemented in OpenFOAM and twoequations turbulence models, resolving also the viscous sublayer. Numerical results allow to compare the cooling strategies in terms of maximum chip temperature, overall chiptocoolant thermal resistance, and pumping power required. In summary, the fractalchannel design shows limitations in guaranteeing low chip temperatures at an affordable pumping power. The submerged impinging jets approach shows very high local
heat transfer coefficient by which it is possible to tailor the cooling expect on specific hot spots.
2019
 Direct Numerical Simulation of a buoyant triple jet at lowPrandtl number
[Articolo su rivista]
Fregni, A.; Angeli, D.; Cimarelli, A.; Stalio, E.
abstract
Mixing of buoyant streams is a phenomenon of relevance in many practical cases like pollutant emission in the atmosphere, discharges from marine outfalls and cooling of fuel rods in nuclear reactors to name a few. A canonical configuration for this class of flows consists in three buoyant jets at different temperatures vertically entering a pool from the bottom. This work reports a Direct Numerical Simulation study performed on the triple jet configuration. The Reynolds number based on the average jet centerline velocity and jet width is set to Re=5000 and mixed convection regime is established at a Richardson number, Ri=0.25. In order to represent flows occurring inside liquid metal fast reactors, the selected Prandtl number is Pr=0.031. Statistics computed show that in the first stages of development, the three jets undergo a strong interaction. In that same region the shedding of largescale vortices is originated accompanied by lowfrequency undulations. Further from the inlet, the three jets are observed to coalesce in a single, isothermal stream. The analysis of momentum fluxes clarifies the mutual entrainment mechanism behind coalescence, which is commonly known as Coandă effect. At distances larger than ten times the jet width the selfsimilar characteristics of single and isothermal planar jets are recovered. The flow configuration presented includes several peculiar features, namely buoyancy effects at low Prandtl number, interaction between jets and the presence of multiple shear layers. This leads to an irregular behaviour of the turbulent diffusivity of momentum and heat as well as the misalignment between the temperature gradient and turbulent heat flux. Therefore the flow can be considered very complex and might constitute a demanding test bench for the development and validation of turbulence models.
2019
 Direct Numerical Simulation of turbulent mixed convection around a bundle of heated rods at lowPrandtl number
[Relazione in Atti di Convegno]
Angeli, Diego; Fregni, Andrea; Stalio, Enrico
abstract
The present work reports an overview of the results of Direct Numerical Simulations performed on the case of fullydeveloped, mixed convection flow of a liquid metal around a uniformly heated bundle of vertical rods. FiniteVolume computations are performed by an original discretization technique based on the representation of arbitrarilyshaped cylindrical boundaries on a nonuniform Cartesian grid. A domain consisting of four subchannels of a triangular lattice of rods with a pitchtodiameter ratio P/D = 1.4 is considered as the reference geometry. A single friction Reynolds number value is simulated, namely Reτ = 550. Both forced and mixed convection regimes are investigated, buoyancy effects being introduced by imposing a Richardson number value of Ri = 0.25. A Prandtl number Pr = 0.031 is chosen to represent LBE as the working fluid. Instantaneous snapshots and relevant statistics of the velocity and thermal fields are reported here for the considered case, and integral results are compared against available literature data.
2019
 Direct numerical simulation of turbulent forced and mixed convection of LBE in a bundle of heated rods with P/D=1.4
[Articolo su rivista]
Angeli, D.; Fregni, A.; Stalio, E.
abstract
In this work, reference data obtained by means of Direct Numerical Simulations of fullydeveloped flow and heat transfer around a vertical rod bundle are presented. FiniteVolume computations are performed by an original discretization technique based on the representation of arbitrarilyshaped cylindrical boundaries on a nonuniform Cartesian grid. A periodic domain consisting of four subchannels of a triangular lattice of rods with a pitchtodiameter ratio P/D=1.4 is considered as the reference geometry. A Prandtl number Pr = 0.031 is chosen to represent Liquid LeadBismuth Eutectic (LBE) as the working fluid. A single friction Reynolds number value is simulated, namely Reτ=550. Both forced and mixed convection regimes are investigated, buoyancy effects being introduced by imposing a Rayleigh number Ra = 5×105, corresponding to a Richardson number Ri = 0.22. Instantaneous snapshots and relevant statistics of the velocity and thermal fields are reported and discussed for the considered cases, focusing on the effect of aiding buoyancy on turbulent flow and heat transfer. Integral results are also compared against available literature data.
2019
 Numerical study of submerged impinging jets for power electronics cooling
[Articolo su rivista]
Sabato, Massimo; Fregni, Andrea; Stalio, Enrico; Brusiani, Federico; Tranchero, Maurizio; Baritaud, Thierry
abstract
Advancements in power electronic technologies require devices which are small, reliable and capable of handling large power levels. Despite efficiencies of electronic components are usually above 90%, wasted thermal powers can result in heat flux densities in the order of hundreds of W/cm2. To avoid degradation in performance and lifetime of these electronic devices, specific active cooling systems need to be adopted and submerged impinging jets represent one of the most promising solutions. In the present paper a numerical study of different cooling jet configurations is presented, and highefficiency solutions are sought. The configurations investigated are obtained by varying nozzle diameter, aspect ratio, arrangement and number of jets. Simulations are performed on a simplified computational domain which involves a single rectangular chip (representing the heat source) separated from the coolant by a multimaterial solid stack. As compared to more classical solutions like pin fins, submerged impinging jets represent an efficient technique for the cooling of power electronics. Heat is exchanged at low pumping power level. Array of jets are flexible in terms of geometry and can be specifically designed to control temperatures in critical spots.
2019
 Reference numerical database for turbulent flow and heat transfer in liquid metals
[Articolo su rivista]
Shams, A.; Roelofs, F.; Niceno, B.; Guo, W.; Angeli, D.; Stalio, E.; Fregni, A.; Duponcheel, M.; Bartosiewicz, Y.; Tiselj, I.; Oder, J.
abstract
Turbulent heat transfer is a complex phenomenon that has challenged turbulence modellers over various decades. In this regard, in the recent past, several attempts have been made for the assessment and further development/calibration of the available turbulent heat flux modelling approaches. One of the main hampering factors with respect to the further assessment of these modelling approaches is the lack of reference data. In the framework of the EU SESAME and MYRTE projects, an extensive effort has been put forward to generate a wide range of reference data, both experimental and numerical, to fill this gap. In that context, this article reports the numerical database that has been generated within these projects for various liquid metal flow configurations in different flow regimes. These high fidelity numerical data include seven different flow configurations: a wallbounded mixed convection flow at low Prandtl number with varying Richardson number (Ri) values; a wallbounded mixed and forced convection flow in a bare rod bundle configuration; a forced convection confined backward facing step (BFS) with conjugate heat transfer; a forced convection impinging jet for three different Prandtl fluids corresponding to two different Reynolds numbers of the fully developed planar turbulent jets; a mixedconvection coldhotcold triple jet configuration corresponding to Ri=0.25; an unconfined free shear layer for three different Prandtl fluids; and a forced convection infinite wirewrapped fuel assembly. These highfidelity numerical databases will serve the further development of turbulent heat transfer models by providing unique, new and detailed data for the thermalhydraulic behaviour of liquid metals in various flow configurations.
2019
 Thermal management of a Formula E electric motor: Analysis and optimization
[Articolo su rivista]
Cavazzuti, Marco; Gaspari, Gloria; Pasquale, Stefano; Stalio, Enrico
abstract
The thermal analysis of a high performance brushless synchronous electric motor with permanent magnets and water jacket cooling is presented. The analysis is carried out following a lumped parameter thermal network approach which allows to identify the most important thermal paths in the motor and the main parameters influencing them. Thanks to its simplicity, the solution of such a thermal network model is very fast, allowing a large number of whatif scenarios to be computed over a short amount of time. For this reason, the model is coupled with external tools for performing systematic sensitivity analyses and optimizations. Goal of the investigation is the reduction of the windings temperature being this temperature inversely proportional to the efficiency and the power delivered by the motor. The sensitivity analysis, performed over a series of material, geometric, and operational factors, leads to the identification of the most relevant parameters influencing the thermal behaviour of the motor. A series of optimizations, focusing on these parameters and including suitable constraints granting the wellposedness of the problem and the feasibility of the solution, bring to the definition of an optimum layout of the water jacket and of the stator geometries. The optimized geometry allows a significant reduction of the windings temperature to be achieved.
2018
 Direct numerical simulations for liquid metal applications
[Capitolo/Saggio]
Iztok, Tiselj; Stalio, Enrico; Angeli, Diego; Jure, Oder
abstract
Thermal Hydraulics Aspects of Liquid Metal cooled Nuclear Reactors is a comprehensive collection of liquid metal thermal hydraulics research and development for nuclear liquid metal reactor applications. A deliverable of the SESAME H2020 project, this book is written by top European experts who discuss topics of note that are supplemented by an international contribution from U.S. partners within the framework of the NEAMS program under the U.S. DOE. This book is a convenient source for students, professionals and academics interested in liquid metal thermal hydraulics in nuclear applications. In addition, it will also help newcomers become familiar with current techniques and knowledge.
2017
 Numerical simulation of mixing buoyant jets: Preliminary studies
[Relazione in Atti di Convegno]
Angeli, Diego; Cimarelli, Andrea; Fregni, Andrea; Stalio, Enrico; Shams, Afaque; Roelofs, Ferry
abstract
Preliminary numerical analyses are reported for the case of three vertical planar mixing jets at different temperatures, in view of a forthcoming reference DNS to be performed in the frame of the SESAME European project. The reference case stems from the wellknown PLAJEST triple jet experiment, but with a relative increase of the buoyancy effect, achieved by reducing the Reynolds number by a factor 5. Preproduction DNS runs for the reference case and a complementary RANS parametric analysis with varying Prandtl and Richardson numbers are carried out, highlighting that a suitable configuration for a benchmark can be obtained with a hotter central jet and colder lateral jets.
2015
 A fast algorithm for Direct Numerical Simulation of natural convection flows in arbitrarilyshaped periodic domains
[Relazione in Atti di Convegno]
Angeli, Diego; Stalio, Enrico; Corticelli, Mauro Alessandro; Barozzi, Giovanni Sebastiano
abstract
A parallel algorithm is presented for the Direct Numerical Simulation of buoyancyinduced flows in open or partially confined periodic domains, containing immersed cylindrical bodies of arbitrary crosssection. The governing equations are discretized by means of the Finite Volume method on Cartesian grids. A semiimplicit scheme is employed for the diffusive terms, which are treated implicitly on the periodic plane and explicitly along the homogeneous direction, while all convective terms are explicit, via the secondorder AdamsBashfort scheme.
The contemporary solution of velocity and pressure fields is achieved by means of a projection method. The numerical resolution of the set of linear equations resulting from discretization is carried out by means of efficient and highly parallel direct solvers. Verification and validation of the numerical procedure is reported in the paper, for the case of flow around an array of heated cylindrical rods arranged in a square lattice. Grid independence is assessed in laminar flow conditions, and DNS results in turbulent conditions are presented for two different grids and compared to available literature data, thus confirming the favorable qualities of the method.
2015
 Buoyancydriven turbulent convection in a bundle of vertical heated cylinders
[Abstract in Atti di Convegno]
Angeli, D.; Stalio, E.
abstract
Background Buoyant, turbulent convective heat transfer around cylindrical rods arranged in bundles is a technically relevant heat transfer configuration which finds application in steam generators, cooling of reactor core fuel assemblies and heat exchangers in general. Most of the research performed so far considered forced convection conditions on vertical rod bundles, corresponding for example to the configuration of a nuclear reactor primary loop. Fewer works have focused on the effect of buoyancy, with or without an external source of momentum. In their experimental investigation, Hallinan and Viskanta [4] employed a thermosyphon loop to determine the average heat transfer coefficients for water under natural circulation conditions in a tube bundle containing twentyone tubes; their work is mainly focused on the favorable effect of grid spacers on heat transfer enhancement. El Genk et al. performed experiments of upflow and downflowforced turbulent and laminar convection, natural convection and buoyancyassisted combined convection of water in a uniformly heated square lattice of seven [2] and nine [3] rod bundles with variable pitchtodiameter ratio, Reynolds and Rayleigh number. They proposed heat transfer correlations and concluded that the rod arrangement only negligibly affects the overall Nusselt number in both forced and natural convection regimes. Concerning the numerical modeling of this class of flows, only very recent works resort to the Large Eddy Simulation [5], and even less frequently, to the Direct Numerical Simulation [7]. This is largely due to the geometric complexity of the flow domain and the difficulties related to the adoption of numerical techniques allowing for sufficiently accurate results.
2015
 Direct numerical simulation of lowPrandtl number turbulent convection above a wavy wall
[Articolo su rivista]
Errico, Orsola; Stalio, Enrico
abstract
Turbulent forced convection is investigated by Direct Numerical Simulation in a channel with one sinusoidal wavy wall and one flat wall. Fluid flow and heat transfer are periodically fully developed, the simulated Reynolds number of the bulk velocity and the hydraulic diameter is Re = 18, 880 while three Prandtl numbers are considered, i.e. Pr = 0.025, Pr = 0.2, and Pr = 0.71. The fluid flow is characterized by separation, reattachment and a shear layer downstream the wave peak, these are conditions relevant for turbulent heat transfer and passive scalar transport applications. In the range of Péclet numbers investigated, the most important heat transfer mechanism is by mean flow advection. Accordingly, the peak heat transfer region is in the upslope part of the domain. The separation bubble instead acts as a barrier to convection and the heat transfer rate is minimum close to separation. An a priori analysis is performed in order to assess the accuracy of turbulent heat transfer models based on the Generalized Gradient Diffusion Hypothesis.
2015
 Fluiddynamic characterisation of the Mont Blanc tunnel by multipoint airflow measurements
[Articolo su rivista]
Levoni, Paolo; Angeli, Diego; Stalio, Enrico; Agnani, Elia; Barozzi, Giovanni Sebastiano; Cipollone, M.
abstract
Long road and railway tunnels necessitate of a finetuned control of the ventilation system to be activated, for both safety and air quality maintenance reasons. This, in turn, requires that the main fluiddynamic parameters of the tunnel are known with sufficient accuracy, so that the system behaviour can be predicted with reasonable confidence under standard and emergency operative conditions. As a first step in the modelling of the complex system embodying the 11,611. m long Mont Blanc road tunnel, and its ventilation facilities, a movable 5point survey rake was designed and builtup, for detecting the distribution of the axial velocity on the tunnel crosssection. Two extensive experimental campaigns were carried out, where the airflowrates were either measured at different stations along the tunnel length (C1), or at a fixed location, under purely axial mainflow conditions and varying the number of the activated axial fan pairs (C2). A simplified dynamic model of the tunnel was developed, and the airflow data from the experiments were used for the model finetuning, additional CFD analyses having provided extra information on concentrated pressure losses connected with air inlet and discharge through the tunnel ends. The Mont Blanc tunnel was finally characterised in terms of friction factors and jetfans installation efficiency.
2014
 Direct numerical simulation of turbulent forced convection in a wavy channel at low and order one Prandtl number
[Articolo su rivista]
Errico, Orsola; Stalio, Enrico
abstract
Turbulent forced convection in a channel with one planar wall and one wall of sinusoidal shape is investigated by Direct Numerical Simulation. The flow is fully developed and the Reynolds number based on the mean bulk velocity and the average hydraulic diameter is Re ≈ 18,900; in this weakly turbulent flow regime three different Prandtl number values are investigated, Pr = 0.025, 0.20, 0.71. The fluid is in contact with the colder channel walls at an equal, uniform temperature. The main statistical quantities, like the rootmeansquare of temperature fluctuations and the turbulent heat fluxes, the local heat transfer coefficient and turbulent Prandtl number values are reported. Effects of flow separation and reattachment on the local heat transfer rate and turbulent Prandtl number distribution are also presented and discussed. An a priori analysis of the behavior of the simple gradient diffusion model of turbulent heat fluxes is performed in the low Prandtl number, separated flow conditions of the present work. While the low Prandtl number effect can be accounted for by an appropriate selection of the turbulent Prandtl number value to be provided to the model, deviations form the expected behavior of turbulent heat fluxes are seen to occur in the flow separation region and downstream reattachment.
2014
 Multiplicity of solutions for laminar, fullydeveloped natural convection in inclined, parallelplate channels
[Articolo su rivista]
Piller, Marzio; Polidoro, Sergio; Stalio, Enrico
abstract
Natural convection in inclined channels is a rather common flow configuration: it occurs in solar energy systems, ventilated roofs as well as in many industrial applications and chemical processes. Analytical solutions for laminar, fullydeveloped natural convection in inclined parallelplate channels are presented in this paper. The Boussinesq approximation is applied and viscous energy dissipation is neglected. One specific thermal configuration is addressed, where one wall is perfectly insulated and a constant, uniform heat flux is released to the fluid from the other wall. The resulting set of governing equations is nonlinear, as the mean velocity is not assigned a priori but determined as part of the solution. Depending on the channel inclination angle and on the imposed heat flux conditions, either no solution, one solution, multiple or infinite solutions exist. Under restrictive assumptions velocity profiles are selfsimilar with respect to the channel inclination, while the temperature profile is independent of the inclination. The twodimensional, hydraulically and thermallydeveloping natural convection channel flow is simulated numerically for some combinations of channel inclination angle and heating intensity to identify the most physical between the many solutions.
2013
 A PhaseField Approach for LiquidLiquid Flow Simulations
[Articolo su rivista]
Stalio, Enrico; M., Piller
abstract
A phasefield approach is presented for the numerical simulation of twophase forced flow in channels. The difference in physical properties of the two components is handled following a quasiincompressible approach (Lowengrub and Truskinovsky [16]). The axisymmetric form of the Navier − Stokes and Cahn − Hilliard equations system is solved for a narrow pipe of radius R = 1 mm, where buoyancy effects are neglected. Results of three simulations for the evolution of spherical and elongated bubbles are reported.
2013
 Full scale CFD modeling of the Mont Blanc tunnel ventilation system
[Relazione in Atti di Convegno]
Agnani, Elia; Angeli, Diego; I., Spisso; Levoni, Paolo; Stalio, Enrico; Barozzi, Giovanni Sebastiano; M., Cipollone
abstract
A
exible and versatile fullscale CFD modeling strategy of the air
ow in a road
tunnel is described. As applied to the case of the MontBlanc tunnel, the model includes the
entire tunnel length and main characteristic elements of its hybrid ventilation system, including
lateral air intake, longitudinal jet fans and air extraction vents. Each of these elements has
been modeled, tested and calibrated independently with the help of experimental data collected
onsite. In order to simplify the generation of the computational model, seven elementary
modules (each 50 m long) have been singled out and meshed independently; such modules, if
properly combined, can represent the whole tunnel or just one of its segments. Automatic mesh
manipulation scripts were implemented to combine and merge such modules and generate the
whole model, which consist of more than two hundred million cells. The validity of the modeling
strategy, when appropriate, is veried by means of steady state simulations performed using data
from previous in vivo experimental campaigns. Results demonstrate that the deviation between
numerical and experimental data is, in most cases, lower than the measurement error of the
experimental procedure.
2013
 PORESCALE SIMULATION OF LAMINAR FLOW THROUGH A SAMPLE OF ALUMINUM FOAM
[Articolo su rivista]
M., Piller; A., Boschetto; Stalio, Enrico; G., Schena; O., Errico
abstract
Opencell metal foams are used in a growing number of applications like lightweight porous structures, enhanced heat transfer devices and compact heat exchangers, catalytic reactors, and even rotors of centrifugal compressors. In many cases, pressure drops and flow rates through the metal foams are predicted using the macroscopic Darcy–Forchheimer equation. Values obtained can be accurate enough for applications, provided the hydraulic properties of the foam are known. The present work is aimed to describe a numerical approach for calculating the hydraulic permeability and the Ergun coefficient of a real sample of metal foam starting from an xray tomography of the sample. Fluid dynamic simulations are conducted in the digital sample at the scale of the pores and data obtained are postprocessed to obtain the main hydraulic properties of the porous material.
2012
 Numerical analisys of Weakly turbulent mixed convection flows in a horizontal pipe
[Relazione in Atti di Convegno]
Errico, Orsola; Angeli, Diego; Barozzi, Giovanni Sebastiano; Stalio, Enrico; Corticelli, Mauro Alessandro
abstract
Weakly turbulent developing flows in a heated horizontal pipe are investigated numerically, focusing on the effects of mixedconvection, and for two different thermal boundary conditions (BCs), the uniform heat flux condition and the uniform walltemperature condition. The Reynolds number, based on the pipe diameter and bulk velocity, is set equal to Re = 5750 and the molecular Prandtl number Pr = 12. For the sake of comparison, the Grashof number values GrH = 3×108 and GrT = 2.3×1010 are chosen for isoflux and isothermal boundary conditions, respectively. Turbulence is modeled by using alternative RANS approaches. Four RANS models are considered, namely the realizable ke (RKE), the renormalizationgroup ke (ke RNG), the Gibson’s qz model, and the ShearStress Transport kw model (kw SST). Results allow to discriminate the performance ofthe different turbulent models and give hint on the effects of the buoyancy induced flow over the leading forced component.The effect of the thermal boundary condition is finally discussed.
2012
 Numerical investigation of natural convection in inclined parallelplate channels partly filled with metal foams
[Articolo su rivista]
M., Piller; Stalio, Enrico
abstract
Numerical results of laminar fully developed natural convection in an inclined composite channel are presented. The mathematical model relies on the Method of Volume Averaging and thus a single domain approach is applied. The Forchheimer correction and thermal dispersion effects are considered while local thermal equilibrium between the porous matrix and the fluid is assumed.
Velocity and temperature profiles are displayed and their rather weak dependence upon porosity and fluid properties assessed. Forces acting on the fluid are identified and discussed. Thermal performances of the composite channel in laminar conditions are evaluated.
One of the main results of the present investigation is that when nonDarcian effects and thermal dispersion are negligible, the Nusselt number of the composite system in natural convection regime is independent of the channel inclination.
2012
 Numerical simulations of turbulent heat transfer in a channel with one wavy wall
[Relazione in Atti di Convegno]
Errico, Orsola; Cavazzuti, Marco; Angeli, Diego; Stalio, Enrico
abstract
Wavy surfaces are encountered in a large variety of applications, and are wellknown for enhancing heat and mass transfer mechanisms. The present study numerically investigates the flow dynamics and heat transfer for turbulent flow in a channel with one flat and one wavy wall. Investigations have been conducted for a Prandtl number Pr = 0.71 and Reynolds numbers Re = 13840 and Re = 19 000, based on the bulk velocity and the hydraulic diameter. Direct Numerical Simulations (DNSs) have been performed for a deep understanding of the dynamic effects on the heat transfer mechanisms for the case of turbulent flow in the channel with one wavy wall.
The performance of two different ReynoldsAveraged Navier Stokes (RANS) turbulence models, namely the komega SST and the qzeta, selected for their favorable characteristics, is assessed against the DNSs results. The applicability of the two selected RANS model is ascertained from a qualitative point of view.
2012
 T.A.L.P.A.: an innovative facility for cotinous longitudibnal air flow profile acquisition in tunnels
[Relazione in Atti di Convegno]
Levoni, Paolo; A., Scorcioni; Angeli, Diego; Stalio, Enrico; Barozzi, Giovanni Sebastiano; M., Cipollone
abstract
The knowledge of the flow field inside road tunnels under fire conditions and normal operation is only approximate andpartial. The reason is that while the full threedimensional, unsteady problem is out of reach of numerical methods, on theother hand accurate measurement of the airflow in road and railway tunnels constitutes an extremely challenging task.Aiming at performing easy and accurate in situ measurements of the flow field in road tunnel under different conditions, aninnovative experimental facility for the continuous acquisition of the longitudinal velocity profile has been designed and built.The facility is made up with a survey rake with five bidirectional vane anemometers, which is mounted on a small electricvehicle that can travel through the tunnel at constant speed. This paper reports the design procedure of the measurementfacility, with particular focus on the conception and realization of the vehicle carrying the survey rake. Results of the firstexperimental campaign carried out under the 11611 meters long Mont Blanc road tunnel are also presented to corroborate thevalidity of the approach adopted and the accuracy of the measurement chain.
2011
 Concept, design, construction and testing of an experimental facility for multipoint longitudinal air flow measurements in tunnels
[Relazione in Atti di Convegno]
Levoni, Paolo; Angeli, Diego; Stalio, Enrico; Barozzi, Giovanni Sebastiano; M., Cipollone
abstract
Performing accurate measurements during a set of fire tests in a road tunnel is a notoriously difficult task to carry out. As in addition the full threedimensional, unsteady problem is out of reach of numerical methods, the knowledge of the flow field inside road tunnels under fire conditions and also during normal operation is in many cases only approximate and partial. As a consequence, also the influence of road tunnel ventilation on fire development and spread are still not clarified, even for the simple longitudinal ventilation. Aiming at performing easy and accurate in situ measurements of the flow field in road tunnel under different conditions, a portable experimental facility including a survey rake with five bidirectional vane anemometers has been designed and built. This paper reports the design procedure of the measurement facility, all the details of the measurement chain and also results of the first experimental campaign carried out under the 11611 meters long Mont Blanc road tunnel. Unlike data provided by the S.C.A.D.A., a monotonic axial velocity profile resulted, which is theoretically justified in the case of semitransverse ventilation.
2011
 Development of a mixed control volume – Finite element method for the advection–diffusion equation with spectral convergence
[Articolo su rivista]
M., Piller; Stalio, Enrico
abstract
In this paper we attack the problem of devising a finite volume method for computational fluid dynamics and related phenomena which can deal with complex geometries while attaining highorders of accuracy and spectral convergence at a reasonable computational cost. As a first step towards this end, we propose a control volume finite element method for the solution of the advection–diffusion equation. The numerical method and its implementation are carefully tested in the paper where h and pconvergence are checked by comparing numerical results against analytical solutions in several relevant testcases. The numerical efficiency of a selected set of operations implemented is estimated by operation counts, ill conditioning of coefficient matrices is avoided by using an appropriate distribution of interpolation points and controlvolume edges.
2011
 Elementi di fisica tecnica per l'ingegneria
[Traduzione di Libro]
Corticelli, Mauro Alessandro; Barozzi, Giovanni Sebastiano; Muscio, Alberto; Stalio, Enrico; Tartarini, Paolo
abstract
Scopo del testo è introdurre ai principi della termodinamica, della meccanica dei fluidi e della trasmissione del calore attraverso un approccio integrato, assai importante per lo studente ingegnere
2011
 Numerical simulation of forced convection over a periodic series of rectangular cavities at low Prandtl number
[Articolo su rivista]
Stalio, Enrico; Angeli, Diego; Barozzi, Giovanni Sebastiano
abstract
Convective heat transfer in laminar conditions is studied numerically for a Prandtl number Pr = 0.025,representative of liquid lead–bismuth eutectic (LBE). The geometry investigated is a channel with a periodicseries of shallow cavities. Finitevolume simulations are carried out on structured orthogonal curvilineargrids, for ten values of the Reynolds number based on the hydraulic diameter between Rem = 24.9and Rem = 2260. Flow separation and reattachment are observed also at very low Reynolds numbers andwall friction is found to be remarkably unequal at the two walls. In almost all cases investigated, heattransfer rates are smaller than the corresponding flat channel values. LowPrandtl number heat transferrates, investigated by comparison with Pr = 0.71 results, are large only for uniform wall temperature andvery low Re. Influence of flow separation on local heat transfer rates is discussed, together with the effectof different thermal boundary conditions. Dependency of heat transfer performance on the cavity geometryis also considered.
2011
 Numerical simulation of weakly turbulent heat transfer over cavities at low Prandtl numbers
[Relazione in Atti di Convegno]
Errico, Orsola; Stalio, Enrico; Barozzi, Giovanni Sebastiano
abstract
Heat transfer investigations at low Prandtl number values are of interest for different applications, but reliable physicalmodels for turbulent convection in these fluids are still missing. In the present study forced convective heat transfer isinvestigated numerically for weakly turbulent flow in a streamwise periodic channel with cavities. Simulations are performedfor different values of the Prandtl number, with the focus on the case with Prandtl number equal to 0:025, which representsliquid leadbismuth eutectic (LBE). In the paper the main features of the mean and instantaneous flow field are presentedtogether with first order statistics. The influence of flow separation mechanisms and turbulent mixing on local and globalheat transfer rates are discussed, for both isoflux and isothermal boundary conditions (BCs hereafter). The numericalcode used for the simulations is based on a second order, finite volume algorithm, implemented over structured, curvilinearmesh. This work aims to contribute to the development of physical model of turbulent convection for low Prandtl numberfluid flows, by providing information for both velocity and temperature fields.
2010
 Direct Numerical Simulation of Forced Convection over Steps at Low Prandtl Number
[Relazione in Atti di Convegno]
Angeli, Diego; Barozzi, Giovanni Sebastiano; Errico, Orsola; Stalio, Enrico; Tartarini, Paolo
abstract
Convective heat transfer in transitional and weakly turbulent conditions is investigated numerically for a Prandtl number Pr =0.025, representative of liquid leadbismuth eutectic (LBE). The geometry selected is a periodic channel with cavities. Finitevolumesimulations are carried out on structured orthogonal curvilinear grids, for two different values of the Reynolds numberin the weakly turbulent range. The main features of the mean and instantaneous flow fields are described. The influence of flowseparation mechanisms and turbulent mixing on local and global heat transfer rates is also discussed, considering the effect ofdifferent thermal boundary conditions imposed at the channel walls.
2009
 Numerical simulation of forced convection over steps at low Prandtl number
[Relazione in Atti di Convegno]
Angeli, Diego; Cavazzuti, Marco; Stalio, Enrico
abstract
Convective heat transfer in laminar conditions is investigated numerically for a Prandtl number Pr = 0.025, representative of liquid leadbismuth eutectic (LBE). The geometry selected is a periodic channel with a set of backward and forward steps. Finitevolume simulations are carried out on structured orthogonal curvilinear grids, for ten values of the Reynolds number up to the transitional range. It is shown how flow can undergo separation and reattachment also at very lowRe. The influence of flow separation mechanisms on local and global heat transfer rates is discussed, also considering the effect of different thermal boundary conditions imposed at the channel walls.
2008
 Compact finite volume schemes on boundaryfitted grids
[Articolo su rivista]
M., Piller; Stalio, Enrico
abstract
The paper focuses on the development of a framework for highorder compact finite volume discretization of the three dimensional scalar advection–diffusion equation. In order to deal with irregular domains, a coordinate transformation is applied between a curvilinear, nonorthogonal grid in the physical space and the computational space. Advective fluxes are computed by the fifthorder upwind scheme introduced by Pirozzoli [S. Pirozzoli, Conservative hybrid compactWENO schemes for shock turbulence interaction, J. Comp. Phys. 178 (2002) 81] while the Coupled Derivative scheme [M.H. Kobayashi, On a class of Pade´ finite volume methods, J. Comp. Phys. 156 (1999) 137] is used for the discretization of the diffusive fluxes. Numerical tests include unsteady diffusion over a distorted grid, linear freesurface gravity waves in a irregular domain and the advection of a scalar field. The proposed methodology attains highorder formal accuracy and shows very favorable resolution characteristics for the simulation of problems with a wide range of length scales.
2008
 Experimental analysis of flow regimes and pressure drop reduction in oil–water mixtures
[Articolo su rivista]
G., Sotgia; Tartarini, Paolo; Stalio, Enrico
abstract
The physical understanding of twophase flow characteristics in horizontal pipes is of importance in the petroleum industry since significant savings in pumping power can be derived from the waterlubricated transportation of crude oil.An experimental study of water continuous oil–water flow in horizontal pipes is performed using mineral oil and tap water of viscosity ratio about 900 and density ratio 0.9. A set of seven different pipes of Pyrex and Plexiglas where used, with diameters ranging between 21 and 40 mm. Pressure drop measurements, flow pattern maps and clear pictures of the oil–water flow are reported in this article together with comprehensive comments. The results obtained are compared to empirical laws, theoretical findings and experimental results by different authors in the literature.In order to identify the regions with operational conditions that are suitable for applications, a novel criterion for the location of the annular/stratified transition is proposed which is based only on experimental observations.
2008
 Experimental investigation of three phase oil/water/air flow
[Relazione in Atti di Convegno]
G., Sotgia; Stalio, Enrico
abstract
Threephase flow of oil, water and air is investigated in a horizontal pipe of inner diameter 40 mm. The mineral oil used in the experiments is similar to crude oil transported in industrial pipelines with a viscosity of μo = 0.919 Pa s and ro = 889 kg/m3 at 20◦C. Careful measurements of pressure drop are performed at different flow rates of the liquids and with the air superficial velocity being varied in steps between Jg = 0.0 m/s and Jg ≈ 6.5 m/s. The pressure drop behaviour depends upon the initial twophase flow regime of the two liquids, and in most cases it shows a progressive increase caused by the injection of air. A wide variety of flow patterns is observed: pictures of flow configurations obtained by starting with the two liquids in coreannular and wavyannular regimes are provided together with full descriptions.
2007
 Direct numerical simulation of heat transfer in convergingdiverging wavy channels
[Articolo su rivista]
Stalio, Enrico; M., Piller
abstract
Corrugated walls are widely used as passive devices for heat and mass transfer enhancement; they are most effective when operated at transitional and turbulent Reynolds numbers. In the present study, direct numerical simulation is used to investigate the unsteady forced convection in sinusoidal, symmetric wavy channels. A novel numerical method is employed for the simulations; it is meant for fully developed flows in periodic ducts of prescribed wall temperature. The algorithm is free of iterative procedures; it accounts for the effects of streamwise diffusion and can be used for unsteady problems. Results of two simulations in the transitional regime for Reynolds numbers based on average duct height and average velocity of Re=481 and Re=872 are reported. Time averaged and instantaneous velocity and temperature fields together with secondorder statistics are interpreted in order to describe the mechanism associated with heat transfer augmentation. Heat flux distributions locate the most active areas in heat transfer and reveal the effects of convective mixing. Slanted traveling waves of high temperature are identified; peak values of Nusselt number are attained when the hightemperature fluid of the waves reaches the converging walls.
2007
 Investigation of threephase flow in horzontal pipes and its representation in ternary diagrams
[Relazione in Atti di Convegno]
G., Sotgia; Stalio, Enrico; Tartarini, Paolo
abstract
The physical understanding of threephase flow characteristics in horizontal pipes is of importance in the production of hydrocarbons from oil fields since very often oil, water, and natural gas flow together in the transporting pipelines. The work is focused on evaluating the effect of air injection on the pressure drop of a twophase oilwater flow. Experiments reported are performed at the twophase thermofluid dynamics laboratory of the Politecnico di Milano, using mineral oil and tap water of viscosity ratio about 800 and density ratio 0.9, together with ambient air. For the interpretation of the wide set of experimental data we use newly introduced, easily readable threephase flow diagrams. In our experiments, the presence of air always has a negative effect on drag when it is injected into an oilwater flow in annular regime. Conversely, in the stratified regime, air supply at moderate flow rates can increase the drag reduction effect of water, but the stratified regime is not well suited for viscous oil transportation.
2006
 Confronto fra tecniche PIV e UPDV per misure di velocità in convenzione naturale in una cavità chiusa contenente una sorgente termica
[Relazione in Atti di Convegno]
Barozzi, Giovanni Sebastiano; Levoni, Paolo; Stalio, Enrico; Tarozzi, Luca
abstract
tecniche PIV e UPDV, per la determinazione dei campi di velocità nei fluidi in moto, vengono per la prima volta comparate nell’ambito di uno stesso esperimento relativo ai moti di convezione naturale indotti da una sorgente termica all’interno di una cavità chiusa. L’esperimento viene condotto utilizzando una resistenza termica cilindrica orizzontale in una cavità allungata a sezione quadrata, contenente acqua. Il caso analizzato è caratterizzato da numeri di Rayleigh modificato e Prandtl rispettivamente pari a Ra=17400 e Pr=8.03. Il confronto tra tecniche PIV e UPDV è svolto sia in termini quantitativi, determinando l’accuratezza e la precisione di misura, che evidenziando parametri qualitativi, quali la complessità d’uso della strumentazione nel particolare caso di studio. L’accuratezza delle tecniche di misura è anche stimata in riferimento alla risoluzione numerica del problema ottenuta mediante tecnica di simulazione numerica (DNS). Si descrivono l’apparato sperimentale, le procedure di rilevazione della velocità e gli esiti sulla comparazione tra le due tecniche di misura. L’indagine mostra che, nell’ambito dell’esperimento svolto, la tecnica PIV dimostra maggiore precisione, mentre la stima dell’accuratezza porta a risultati analoghi per le due tecniche; entrambe denunciano limiti in prossimità delle pareti solide.
2006
 From two phsae oil water to three phase oil/water/air flows in horizontal pipes: pressure drop and flow regimes.
[Relazione in Atti di Convegno]
G., Sotgia; Stalio, Enrico; Tartarini, Paolo; A., Villa
abstract
The interest in oilwater pipe flow descends from its importance in petrochemical industries; pumping power requirements during oil transportation is considerably reduced in the coreannular flow regime. In petroleum transportation pipelines, an additional phase of natural gas frequently flows with the oil. The prediction of pressure drop and stability characteristics of the threephase flow in these lines is important for proper operation of the transportation plants at reduced power consumption. Results from a set of experiments of threephase flow of high viscosity oil, water and air in horizontal pipes of two different diameters are presented in the paper. Pressure drop measurements are related to three phase flow patterns observations in a defined range of specific flow rates of water, oil and air. When air is supplied in a wavystratified flow of oil and water, the presence of air plugs hinders stratification and ensures a lower resistance as respect the corresponding oilwater case; disturbances induced by the gaseous phase grow rapidly with increasing air specific flow rate and the tendency is reversed by a higer flow rate of air. The presence of air in an annular flow of oil induce large quasiperiodic deformations of the interface between oil and water and has a negative effect on drag.
2005
 A phase field approach for two phase flow simulations
[Relazione in Atti di Convegno]
Stalio, Enrico; Mencinger, J.; Zun, I.
abstract
A phasefield approach is presented for the numerical simulation of two fluid forced flow in channels. The difference in physical properties of the two components is handled following a quasiincompressible approach (J. Lowengrub and L. Truskinovsky, Proc. R. Soc. Lond. A, 1998). The axisymmetric form of the NavierStokes and CahnHilliard equations system is solved, and the numerical results presented here consider a narrow pipe of radius R = 1mm, where buoyancy effects are neglected.Results of three simulations for the evolution of spherical and elongated hexane bubbles in water for Re = 220 and We = 96 are reported
2004
 Finitevolume compact schemes on staggered grids
[Articolo su rivista]
Piller, M.; Stalio, Enrico
abstract
Compact finitedifference schemes have been recently used in several Direct Numerical Simulations of turbulent flows, since they can achieve highorder accuracy and high resolution without exceedingly increasing the size of the computational stencil. The development of compact finitevolume schemes is more involved, due to the appearance of surface and volume integrals. While Pereira et al. [J. Comput. Phys. 167 (2001)] and Smirnov et al. [AIAA Paper, 2546, 2001] focused on collocated grids, in this paper we use the staggered grid arrangement. Compact schemes can be tuned to achieve very high resolution for a given formal order of accuracy. We develop and test highresolution schemes by following a procedure proposed by Lele [J. Comput. Phys. 103 (1992)] which, to the best of our knowledge, has not yet been applied to compact finitevolume methods on staggered grids. Results from several one and twodimensional simulations for the scalar transport and Navier–Stokes equations are presented, showing that the proposed method is capable to accurately reproduce complex steady and unsteady flows.
2004
 Numerical study of turbulent heat transfer above a porous wall
[Relazione in Atti di Convegno]
Stalio, Enrico; Breugem, W. P.; Boersma, B. J.
abstract
This paper presents a numerical study of fully developed turbulent heat transfer in a flat channel half filled with porous material; the simulated fluid is air while an aluminium foam represents the solid matrix. The main focus is on heat transfer performances of a porous wall, the interface between a saturated porous medium and the clear fluid, in forced convection conditions; in the fluid portion a turbulent regime with a Reynolds number based on the mean velocity and the hydraulic diameter Re=9000 is sustained. The Nusselt number and the efficiency computed on the porous wall is sensibly higher than the flat wall value and this is in direct relation with the presence of a higher peak of the wallnormal turbulent heat flux.
2003
 A compact finite volume method for direct numerical simulation of incompressible turbulent flows.
[Relazione in Atti di Convegno]
M., Piller; Stalio, Enrico; E., Nobile
abstract
Direct Numerical Simulation (DNS) of turbulent flow and heat transfer requires that most of the energycontaining length and time scales must be accurately captured. The spatial resolution can be augmented in two complementary ways, i.e. either the grid spacing has to be reduced, by refining the computational mesh, or a more accurate spatial approximation should be used. In this work we present our approach for the development of a fourthorder, compact finite volume scheme for the DNS of incompressible turbulent flow and heat transfer. The numerical method is fourth order accurate, but it is shown that a further increase of accuracy does not represent a difficult task, and can be accomplished in a modular way.A staggered grid arrangement is employed, which presents wellknown advantages concerning properties conservation and absence of unphysical pressure oscillations, of paramount importance in DNS. In this paper, after a concise description of the method, we present several test cases, which illustrate the main characteristics and capabilities of the proposed methodology.
2003
 Direct Numerical Simulation of Heat Transfer Over Riblets
[Articolo su rivista]
Stalio, Enrico; Nobile, E.
abstract
Riblets are wellknown as a passive mean for drag reduction in turbulent flow conditions, but their effectiveness for heat transfer is quite controversial. In this paper we present the numerical results for fully developed laminar and turbulent flow and heat transfer in a channel with triangular riblets. The turbulent study is performed by means of direct numerical simulation at a Reynolds number Re_\tau =180 based on the wallshear velocity, for a fluid with a Prandtl number Pr=0.71. Four different ribbed channels are considered, under a constant heat flux boundary condition, and correspond to ridge angle a \alpha = 45 and 60 degrees, and riblet spacing s^+ = 20 and s^+ = 40. The results obtained, for the flow and turbulent quantities, are in good agreement with past experimental and numerical studies, and correctly reproduce drag reduction over the smaller s^+ = 20 riblets and drag increase over the larger s^+ = 40 riblets. The predicted heat transfer efficiency of riblets do not agree with some experimental results, and is below that of a flat plate for all the configurations. The conditions for heat transfer enhancement are discussed.