
ANDREA CIMARELLI
Professore Associato Dipartimento di Ingegneria "Enzo Ferrari"

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2024
 A Turbulent Plume in Crossflow
[Capitolo/Saggio]
Fenton, D.; Cimarelli, A.; Mollicone, J. P.; van Reeuwijk, M.; De Angelis, E.
abstract
The behaviour of a turbulent forced buoyant plume subjected to uniform crossflow is investigated utilising Direct Numerical Simulation (DNS) employing a fourthorder finite difference scheme and thirdorder AdamsBashforth temporal integration. The flow features are assessed phenomenologically in the statistically steady state obtained by averaging 1,200 instantaneous 3D fields. Preliminary results on the structure of turbulent production and dissipation are shown in view of future discussions on LES modeling assumptions.
2024
 Countergradient turbulent transport in a plume with a crossflow
[Articolo su rivista]
Fenton, D.; Cimarelli, A.; Mollicone, J. P.; van Reeuwijk, M.; De Angelis, E.
abstract
Direct numerical simulation of a turbulent forced buoyant plume in a crossflow is performed at a source Reynolds number Re0=1000\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$${\text{ Re }}_0=1000$$\end{document}, Richardson number Ri0=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$$\mathrm{{Ri}}_0=1$$\end{document}, Prandtl number Pr=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$$\mathrm{{Pr}}=1$$\end{document} and sourcetocrossflow velocity ratio R0=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$$R_0=1$$\end{document}. The instantaneous and temporally averaged flow fields are assessed in detail, providing an overview of the flow dynamics. The velocity, temperature and pressure fields are used together with enstrophy fields to describe qualitatively the evolution of the plume as it is swept downstream by the crossflow, and the mechanisms involved in its evolution are outlined. The plume trajectory is determined quantitatively in a number of ways, and it is shown that the central streamline and the centre of buoyancy of the plume differ significantlyas with jets in crossflow, the central streamline is seen to follow the top of the plume, whereas the centre of buoyancy, by definition, describes the plume as a whole. We then investigate the turbulence properties inside the plume; in particular the eddy viscosity and diffusivity are presented, which are significant parameters in turbulence modelling. Assessment of turbulence production demonstrates the presence of regions where turbulence kinetic energy is redistributed to the kinetic energy of the mean flow, implying a negative eddy viscosity within certain regions of the domain. Similarly, the observation that the buoyancy flux and buoyancy gradient are antiparallel in specific regions of the flow implies a negative eddy diffusivity in said regions, which must be realised in models of such flows in order to capture the countergradient transport of thermal properties. A characteristic eddy viscosity and diffusivity are presented, and shown to be approximately constant in the fully developed regime, resulting in a constant characteristic turbulent Prandtl number, in turn signifying selfsimilarity.
2024
 DNS of the Flow About a 5:1 Rectangular Body with Sharp Corners
[Capitolo/Saggio]
Corsini, R.; Cimarelli, A.; Stalio, E.
abstract
2024
 Effect of Variable Density on Subgrid Scales
[Capitolo/Saggio]
Abba, A.; Aliyoldashi, M. H.; Cimarelli, A.; Germano, M.
abstract
Variable density flows are very common in nature, in technology and in industry. The numerical simulation of complex flows of applicative interest and with relevant variable density flows requires the truncation of turbulent scales of the resolved velocity field, in order to reduce the required computational resources.
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.
2024
 Numerical experiments on scalar transport and mixing in turbulent boundary layers
[Relazione in Atti di Convegno]
Boga, G.; Giancola, A.; Cimarelli, A.
abstract
In this work, we present numerical experiments aimed at dynamically establishing the separate role of the inner and outer cycles on the scalar transport in the configuration of a temporally evolving boundary layer. The experiments are based on the study of the evolution of passive scalars driven by velocity fields where inner and outer cycles are alternately suppressed. Two different approaches are implemented. In the first, the discrimination between inner and outer cycle activities is based on the scale dimension of the involved motions. The second instead, discriminates on the basis of the distance from the wall of the turbulent motions. The two approaches depict the same scenario. Both the inner and outer cycles appear to be autonomous and, in a sense, independent, since their dynamics remain qualitatively unaltered despite facing two different conditions. The outer cycle faces a free boundary at the top and simply rescales according to what is supplied by the inner cycle. The inner cycle, on the other hand, resides between the wall and the outer region. As a result, the reduction of the scalar fluxes in the outer region due to the suppression of the outer cycle causes a damping in the nearwall region activities.
2024
 On the WaveInduced Stokes Sublayer and Drag Reduction in the Turbulent Wind
[Relazione in Atti di Convegno]
Cimarelli, A.; Romoli, F.; Stalio, E.
abstract
The interactions of a turbulent wind with a water surface represents a very fundamental problem for many atmospheric processes. The momentum and heat exchanges across the interface with oceans abruptly affects the atmosphere and the understanding of the driving mechanisms would certainly improve weather predictions capabilities. We performed a Direct Numerical Simulation of the windwave interaction problem using realistic values of the fluid properties of air and water [3]. The simulation reveals that at low Reynolds numbers, an interesting windwave pattern propagating at an angle in the upstream direction is generated. This pattern is recognized to be at the basis of the generation of a spanwise oscillating Stokes sublayer that is responsible for a drag reduction mechanism in the turbulent wind. Despite the simulated flow conditions are far from the intense events occurring at the oceanatmosphere interface, this basic flow phenomenon may actually explain the large scatter of the drag coefficient data in field measurements where swell waves of arbitrary directions are often present.
2024
 Reynolds number effects in separating and reattaching flows with passive scalar transport
[Articolo su rivista]
Cimarelli, A.; Corsini, R.; Stalio, E.
abstract
2024
 Spatially evolving cascades in wall turbulence with and without interface
[Articolo su rivista]
Cimarelli, A.; Boga, G.; Pavan, A.; Costa, P.; Stalio, E.
abstract
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
 Dynamic tensorial eddy viscosity model: Effects of compressibility and of complex geometry
[Articolo su rivista]
Abba, A.; Cimarelli, A.; Germano, M.
abstract
A previous paper by Cimarelli et al. ["General formalism for a reduced description and modelling of momentum and energy transfer in turbulence,"J. Fluid Mech. 866, 865896 (2019)] has shown that every decomposition of turbulent stresses is naturally approximated by a general form of tensorial eddy viscosity based on velocity increments. The generality of the formalism is such that it can also be used to give a reduced description of subgrid scalar fluxes. In the same work, this peculiar property of turbulent stresses and fluxes has been dynamically exploited to produce tensorial eddy viscosity models based on the secondorder inertial properties of the grid element. The basic idea is that the anisotropic structure of the computational element directly impacts, although implicitly, the large resolved and small unresolved scale decomposition. In the present work, this new class of turbulence models is extended to compressible turbulence. A posteriori analysis of flow solutions in a compressible turbulent channel shows very promising results. The quality of the modeling approach is further assessed by addressing complex flow geometries, where the use of unstructured grids is demanded as in real world problems. Also in this case, a posteriori analysis of flow solutions in a periodic hill turbulent flow shows very good behavior. Overall, the generality of the formalism is found to allow for an accurate description of subgrid quantities in compressible conditions and in complex flows, independent of the discretization technique. Hence, we believe that the present class of turbulence closures is very promising for the applications typical of industry and geophysics.
2022
 Erratum: Numerical experiments on turbulent entrainment and mixing of scalars(Journal of Fluid Mechanics 27 (A34) DOI: 10.1017/jfm.2021.779)
[Articolo su rivista]
Cimarelli, A.; Boga, G.
abstract
The publisher apologises that upon publication of this article a typographical error was introduced with [4pt] being added to equation 2.1.The equation should read.
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.
2022
 Implicit Large Eddy Simulations of a rectangular 5:1 cylinder with a highorder discontinuous Galerkin method
[Articolo su rivista]
Crivellini, A.; Nigro, A.; Colombo, A.; Ghidoni, A.; Noventa, G.; Cimarelli, A.; Corsini, R.
abstract
In this work the numerical results of the flow around a 5:1 rectangular cylinder at Reynolds numbers 3 000 and 40 000, zero angle of attack and smooth incoming flow condition are presented. Implicit Large Eddy Simulations (ILES) have been performed with a highorder accurate spatial scheme and an implicit highorder accurate time integration method. The spatial approximation is based on a discontinuous Galerkin (dG) method, while the time integration exploits a linearlyimplicit Rosenbrocktype RungeKutta scheme. The aim of this work is to show the feasibility of highfidelity flow simulations with a moderate number of DOFs and large time step sizes. Moreover, the effect of different parameters, i.e., dimension of the computational domain, mesh type, grid resolution, boundary conditions, time step size and polynomial approximation, on the results accuracy is investigated. Our best dG result at Re=3 000 perfectly agrees with a reference DNS obtained using Nek5000 and about 40 times more degrees of freedom. The Re=40 000 computations, which are strongly underresolved, show a reasonable correspondence with the experimental data of Mannini et al. (2017) and the LES of Zhang and Xu (2020).
2022
 Structure of turbulence in temporal planar jets
[Articolo su rivista]
Cimarelli, A.; Fregni, A.; Mollicone, J. P.; Van Reeuwijk, M.; De Angelis, E.
abstract
A detailed analysis of the structure of turbulence in a temporal planar turbulent jet is reported. Instantaneous snapshots of the flow and threedimensional spatial correlation functions are considered. It is found that the flow is characterized by largescale spanwise vortices whose motion is felt in the entire flow field. Superimposed to this largescale motion, a hierarchy of turbulent structures is present. The most coherent ones take the form of quasistreamwise vortices and high and low streamwise velocity streaks. The topology of these interacting structures is analyzed by quantitatively addressing their shape and size in the different flow regions. Such information is recognized to be relevant for a structural description of the otherwise disorganized motion in turbulent freeshear flows and can be used for the assessment of models based on coherent structure assumptions. Finally, the resulting scenario provides a phenomenological description of the elementary processes at the basis of turbulence in freeshear flows.
2022
 Structure of turbulence in the flow around a rectangular cylinder
[Articolo su rivista]
Chiarini, A.; Gatti, D.; Cimarelli, A.; Quadrio, M.
abstract
The separating and reattaching turbulent flow past a rectangular cylinder is studied to describe how small and large scales contribute to the sustaining mechanism of the velocity fluctuations. The work is based on the anisotropic generalised Kolmogorov equations, exact budget equations for the secondorder structure function tensor in the space of scales and in the physical space. Scalespace energy fluxes show that forward and reverse energy transfers occur simultaneously in the flow, with interesting modelling implications. Over the longitudinal cylinder side, the KelvinHelmholtz instability of the leading edge shear layer generates large spanwise rolls, which get stretched into hairpinlike vortices and eventually break down into smaller streamwise vortices. Independent sources of velocity fluctuations act at different scales. The flow dynamics is dominated by pressurestrain: the flow impingement on the cylinder surface in the reattachment zone produces spanwise velocity fluctuations very close to the wall, and at larger wall distances reorients them to feed streamwisealigned vortices. In the near wake, large von Kármánlike vortices are shed from the trailing edge and coexist with smaller turbulent structures, each with its own independent production mechanism. At the trailing edge, the sudden disappearance of the wall changes the structure of turbulence: streamwise vortices vanish progressively, while spanwise structures close to the wall are suddenly turned into vertical fluctuations by the pressurestrain.
2021
 Direct numerical simulation of transition in a differentially heated vertical channel
[Articolo su rivista]
Cingi, P.; Cimarelli, A.; Angeli, D.
abstract
The transition mechanisms of natural convection flows ensuing in a fluid layer between two differentially heated vertical plates at Prandtl number Pr = 0.71 are investigated by means of Direct Numerical Simulations. In accordance with several previous studies, results show a first bifurcation from the socalled laminar conduction regime to steady convection at Rayleigh number Ra = 5708. On the other hand, the subsequent transition to turbulence appears to be accompanied by a great sensitivity to some fundamental numerical choices such as domain size, accuracy, resolution and amplitude of the imposed perturbations. Results reveal the occurrence of a bifurcation branch which leads the system to chaos via a second bifurcation to a steadystate, a Hopf bifurcation and, seemingly, a perioddoubling cascade. Although the described scenario compares well with previous findings, some doubts persist upon the possible pitfalls in the use of numerical simulation for the study of transition in this kind of systems. Indeed, several numerical aspects are found to become of crucial importance for the prediction of the dynamical behaviour and heat transfer rate of the system.
2021
 Dynamic Tensorial Eddy Viscosity and Turbulent Stresses
[Relazione in Atti di Convegno]
Abba, A.; Cimarelli, A.; Germano, M.
abstract
In the theoretical framework provided by an alternative decomposition of the turbulent stresses, a new formalism for their approximation and understanding has been proposed in [1] that spontaneously directs to a tensorial turbulent eddy viscosity. Based on this, new modelling approaches for LES, representing subgrid fluxes for momentum, energy and heat fluxes, based on the second order inertial properties of the grid element are developed. The new model has firstly tested in the case of typical LES benchmark for compressible flow, such as the turbulent channel flow. A numerical simulation of turbulent flows in a more complex geometry using unstructured meshes has been performed, exploiting the properties of the eddy viscosity model based on the inertial tensor of the numerical grid element. The analysis highlights the capability of the model to well reproduce the anisotropic character of the turbulent flows.
2021
 Numerical experiments on turbulent entrainment and mixing of scalars
[Articolo su rivista]
Cimarelli, A.; Boga, G.
abstract
Numerical experiments on the turbulent entrainment and mixing of scalars in a incompressible flow have been performed. These simulations are based on a scale decomposition of the velocity field, thus allowing the establishment from a dynamic point of view of the evolution of scalar fields under the separate action of largescale coherent motions and smallscale fluctuations. The turbulent spectrum can be split into active and inactive flow structures. The largescale engulfment phenomena actively prescribe the mixing velocity by amplifying inertial fluxes and by setting the area and the fluctuating geometry of the scalar interface. On the contrary, smallscale isotropic nibbling phenomena are essentially inactive in the mixing process. It is found that the inertial mechanisms initiate the process of entrainment at large scales to be finally processed by scalar diffusion at the molecular level. This last stage does not prescribe the amount of mixing but adapts itself to the conditions imposed by the coherent anisotropic motion at large scales. The present results may have strong repercussions for the theoretical approach to scalar mixing, as anticipated here by simple heuristic arguments which are shown able to reveal the rich dynamics of the process. Interesting repercussions are also envisaged for turbulence closures, in particular for largeeddy simulation approaches where only the large scales of the velocity field are resolved.
2021
 On the kinematics and dynamics parameters governing the flow in oscillating foils
[Articolo su rivista]
Cimarelli, A.; Franciolini, M.; Crivellini, A.
abstract
Based on a highorder implicit discontinuous Galerkin method, numerical simulations of a twodimensional oscillating foil are performed to explore the origin of basic aspects of the flow such as the generation of interesting flow structures in the wake and the associated aerodynamic forces. Dimensional arguments suggest that the flow is characterized by non dimensional aerodynamic coefficients depending on the kinematics of the oscillation, such its frequency and amplitude, and on the dynamics of the flow, such as the Reynolds number. Most of the studies have concentrated their attention on the role played by the kinematic of the oscillation with less or no attention to the effect of the Reynolds number. Here, we show that this effect cannot be neglected in the study of the phenomena at the basis of the generation of lift and thrust. We found that the Reynolds number plays a fundamental role for the development of thrust by defining critical values Rec for the switch from drag to thrust conditions. It is also shown that for Re>Rec, the Reynolds number defines additional subcritical values which are at the basis of flow instabilities leading to smooth and sharp transitions of the structure of the wake and of the related aerodynamic forces. For the analysis of the behaviour of the flow, the space of phases composed by the instantaneous lift and thrust (cL,cT) is introduced. It is shown how the orbits in the (cL,cT)space allow us for a clear understanding of the physical evolution of the flow system and of the cyclical phenomena composing it.
2021
 Spatially evolving cascades in temporal planar jets
[Articolo su rivista]
Cimarelli, A.; Mollicone, J. P.; Van Reeuwijk, M.; De Angelis, E.
abstract
Starting from an alternative decomposition of the turbulent field, a multidimensional statistical formalism for the description and understanding of turbulence in freeshear flows is proposed and applied to the symmetries of planar temporal jets. The theoretical framework is based on the exact equation for the secondorder moment of the twopoint velocity increment and allows us to trace, for the first time, the spatially evolving cascade processes at the basis of turbulence mixing and entrainment. Fascinating reverse energy cascade mechanisms are found to be responsible for the generation of long and wide structures in the interface region. Analogously to twodimensional turbulence, the energy provided by these spatially ascending reverse cascades is found to be eventually dissipated by viscosity at large scales through friction shearing processes involving a thin crossflow layer of these largescale structures. Finally, the external nonturbulent region of the jet is also found to be active from an energetic point of view. It is found that pressuremediated nonlocal phenomena of displacement of almost quiescent fluid give rise to nonturbulent fluctuations that in time, through transitional mechanisms, would contribute to the growth of the turbulent jet. Overall, the unexpected paths taken by the scaleenergy flux in the combined physical/scale space, which are a substantial novelty with respect to known descriptions of turbulent mixing and entrainment, may have major repercussions on our theoretical understanding and modelling, as anticipated here by reduced equations capable of giving a simple scaledependent description of the rich dynamics of the flow.
2021
 The Filtering Approach as a Tool for Modeling and Analyzing Turbulence
[Relazione in Atti di Convegno]
Germano, M.; Abba, A.; Cimarelli, A.; Ferrero, A.; Grinstein, F. F.; Klein, M.; Larocca, F.; Saenz, J. A.; Scovazzi, G.
abstract
The Filtering Approach (FA) is a simple multiscale method of analysis, it extends the statistical formalism to a generic filtering operator and main ingredients are the Generalized Central Moments (GCM) homomorphic to the Statistical Central Moments (SCM). In the past this technique was intensively used to model turbulent flows in the context of the Large Eddy Simulation (LES) and at present is more and more applied to analyze turbulence and extract statistical data from underresolved databases. In this paper we will briefly summarize the main multiscale characters of the FA, the well known identity relating GCM of the second order at different levels is discussed in detail, and a new identity relating GCM of the third order at different levels is presented. Finally some recent developments are illustrated. The structure of the subfilter stresses and the decomposition of the Reynolds stresses is examined, hybrid LES modeling procedures are applied and metrics that measure the statistical homogeneity of a turbulent flow are proposed.
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
 Highorder DG solutions of separating and reattaching flows
[Capitolo/Saggio]
Cimarelli, A.; Franciolini, M.; Crivellini, A.
abstract
We report highorder implicit Large Eddy Simulations of flows around elongated bluff bodies with massive flow separation and reattachment. The aim is to provide evidence of the influence of relevant flow parameters such as the geometry of the leadingedge corners and the presence or not of a trailingedge flow separation, on the behaviour of the initially laminar recirculating flow. Attention will be devoted also on the possible repercussions of such a results on the understanding of the nature of the main unsteadinesses of separating and reattaching flows. We finally prove the computational efficiency and the reliability of the proposed solution strategy for the time implicit highorder Discontinuous Galerkin (DG) discretization of the threedimensional incompressible NavierStokes equations. The algorithm uses a linearly implicit RungeKutta scheme of the Rosenbrock type, and a pmultigrid preconditioned matrixfree linear solver.
2020
 Numerical experiments in separating and reattaching flows
[Articolo su rivista]
Cimarelli, A.; Franciolini, M.; Crivellini, A.
abstract
We report highorder implicit large Eddy simulations of flows around flat plates with massive flow separation and reattachment. The aim is to provide evidence of the influence of relevant flow parameters such as the geometry of the leadingedge corner, the presence of a trailingedge flow separation, and of a flow coupling between the two sides of the plate. The results reveal that flows with rightangled corners develop taller flow recirculations, which promote veryslow instability of the bubble itself. This largescale unsteadiness is then found to be the basis of negative turbulence production mechanisms that in turn enhance the height of the bubble itself, thus closing a selfsustained cycle. The absence of these phenomena in flows with smooth leadingedge corners is also found to explain their high sensitivity to freestream turbulence. The observed behaviors may have strong repercussions for theories and closures of separating and reattaching flows and should be carefully taken into account in control strategies used in the applications.
2020
 Scalings of the outer energy source of wallturbulence
[Relazione in Atti di Convegno]
Cimarelli, A.; de Angelis, E.; Schlatter, P.; Brethouwer, G.; Talamelli, A.; Casciola, C. M.
abstract
By means of the multidimensional description given by the Kolmogorov equation we study the energy transfer physics and the production mechanisms of wallturbulent flows at moderately high Reynolds numbers. Two driving mechanisms are identified for the energy fluxes. The first stronger one, here called driving scalerange (DSR), belongs to the nearwall cycle. As expected, its topology remains unaltered with Reynolds number while its intensity is found to slightly increase with Re. The second mechanism, here called outer scalerange (OSR), takes place in the overlap layer and highlights different features in agreement with the attached eddies hypothesis usually considered to describe the overlap dynamics.
2020
 Structure function tensor equations in inhomogeneous turbulence
[Articolo su rivista]
Gatti, D.; Chiarini, A.; Cimarelli, A.; Quadrio, M.
abstract
Exact budget equations for the secondorder structure function tensor, where is the difference of the th fluctuating velocity component between two points, are used to study the twopoint statistics of velocity fluctuations in inhomogeneous turbulence. The anisotropic generalised Kolmogorov equations (AGKE) describe the production, transport, redistribution and dissipation of every Reynolds stress component occurring simultaneously among different scales and in space, i.e. along directions of statistical inhomogeneity. The AGKE are effective to study the intercomponent and multiscale processes of turbulence. In contrast to more classic approaches, such as those based on the spectral decomposition of the velocity field, the AGKE provide a natural definition of scales in the inhomogeneous directions, and describe fluxes across such scales too. Compared to the generalised Kolmogorov equation, which is recovered as their halftrace, the AGKE can describe intercomponent energy transfers occurring via the pressurestrain term and contain also budget equations for the offdiagonal components of. The nontrivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the nearwall cycle of a turbulent channel flow at a friction Reynolds number of is considered. The offdiagonal component, which cannot be interpreted in terms of scale energy, is discussed in detail. Wallnormal scales in the outer turbulence cycle are then discussed by applying the AGKE to channel flows at and. In a third example, the AGKE are computed for a separating and reattaching flow. The process of spanwisevortex formation in the reverse boundary layer within the separation bubble is discussed for the first time.
2019
 A priori analysis and benchmarking of the flow around a rectangular cylinder
[Capitolo/Saggio]
Cimarelli, A.; Leonforte, A.; Angeli, D.
abstract
The flow around bluff bodies is recognized to be a rich topic due to its huge number of applications in natural and engineering sciences. Of particular interest is the case of blunt bodies where a reattachment of the separated boundary layer before the definitive separation in the wake occurs. One of the main feature of this type of flows is the combined presence of small scales due to the occurrence of selfsustained turbulent motions and large scales due to classical vortex shedding. The complete understanding of these multiple interacting phenomena would help for a correct prediction and control of relevant features for engineering applications such as wind loads on buildings and vehicles, vibrations and acoustic insulation, heat transfer efficiency and entrainment. Archetypal of these kind of flows is the flow around a rectangular cylinder. Many studies have been carried out in the past. The general aim is the understanding of the main mechanisms behind the two unstediness of the flow, the shedding of vortices at the leadingedge shear layer and the lowfrequency flapping mode of the separation bubble, see e.g Cherry et al (J Fluid Mech, 144:13–46, 1984, [1]), Kiya and Sasaki (J Fluid Mech, 154:463–491, 1985[2]), Nakamura et al (J Fluid Mech, 222:437–447, 1991, citeNakamura).
2019
 An efficient numerical method for the generalised Kolmogorov equation
[Articolo su rivista]
Gatti, D.; Remigi, A.; Chiarini, A.; Cimarelli, A.; Quadrio, M.
abstract
An efficient algorithm for computing the terms appearing in the Generalised Kolmogorov Equation (GKE) written for the indefinite plane channel flow is presented. The algorithm, which features three distinct strategies for parallel computing, is designed such that CPU and memory requirements are kept to a minimum, so that highRe wallbounded flows can be afforded. Computational efficiency is mainly achieved by leveraging the Parseval's theorem for the two homogeneous directions available in the plane channel geometry. A speedup of 34 orders of magnitude, depending on the problem size, is reported in comparison to a key implementation used in the literature. Validation of the code is demonstrated by computing the residual of the GKE, and example results are presented for channel flows at Reτ=200 and Reτ=1000, where for the first time they are observed in the whole fourdimensional domain. It is shown that the space and scale properties of the scaleenergy fluxes change for increasing values of the Reynolds number. Among all scaleenergy fluxes, the wallnormal flux is found to show the richest behaviour for increasing streamwise scales.
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
 Experimental and Numerical Analysis of the Hydrodynamics around a Vertical Cylinder in Waves
[Articolo su rivista]
Corvaro, Sara; Crivellini, Andrea; Marini, Francesco; Cimarelli, Andrea; Capitanelli, Loris; Mancinelli, Alessandro
abstract
The present study provides an extensive analysis on the hydrodynamics induced by a vertical slender pile under wave action. The authors carried out the study both experimentally and numerically, thus enabling a deep understanding of the flow physics. The experiments took place at a wave flume of the Universita Politecnica delle Marche. Two different experimental campaigns were performed: In the former one, a mobile bed model was realized with the aims to study both the scour process and the hydrodynamics around the cylinder; in the latter one, the seabed was rigid in order to make undisturbed optical measurements, providing a deeper analysis of the hydrodynamics. The numerical investigation was made by performing a direct numerical simulation. A second order numerical discretization, both in time and in space, was used to solve the NavierStokes equations while a volume of fluid (VOF) approach was adopted for tracking the free surface. The comparison between experimental and numerical results is provided in terms of velocity, pressure distributions around the cylinder, and total force on it. The analysis of the pressure gradient was used to evaluate the generation and evolution of vortices around the cylinder. Finally, the relation between scour and bed shear stresses due to the structure of the vortex pattern around the pile was assessed. It is worth noting that the physical understanding of this last analysis was enabled by the combined use of experimental data on scour and numerical data on the flow pattern.
2019
 General formalism for a reduced description and modelling of momentum and energy transfer in turbulence
[Articolo su rivista]
Cimarelli, A.; Abba, A.; Germano, M.
abstract
Based on hierarchies of filter lengths, the large eddy decomposition and the related subgrid stresses are recognized to represent generalized central moments for the study and modelling of the different modes composing turbulence. In particular, the subgrid stresses and the subgrid dissipation are shown to be alternative observables for quantitatively assessing the scaledependent properties of momentum flux (subgrid stresses) and the energy exchange between the large and small scales (subgrid dissipation). In this work we present a theoretical framework for the study of the subgrid stress and dissipation. Starting from an alternative decomposition of the turbulent stresses, a new formalism for their approximation and understanding is proposed which is based on a tensorial turbulent viscosity. The derived formalism highlights that every decomposition of the turbulent stresses is naturally approximated by a general form of turbulent viscosity tensor based on velocity increments which is then recognized to be a peculiar property of smallscale stresses in turbulence. The analysis in a turbulent channel shows the rich physics of the smallscale stresses which is unveiled by the tensorial formalism and usually missed in scalar approaches. To further exploit the formalism, we also show how it can be used to derive new modelling approaches. The proposed models are based on the second A nd thirdorder inertial properties of the grid element. The basic idea is that the structure of the integration volume for filtering (either implicit or explicit) impacts the anisotropy and inhomogeneity of the filteredout motions and, hence, this information could be leveraged to improve the prediction of the main unknown features of smallscale turbulence. The formalism provides also a rigorous definition of characteristic lengths for the turbulent stresses, which can be computed in every type of computational elements, thus overcoming the rather elusive definition of filter length commonly employed in more classical models. A preliminary analysis in a turbulent channel shows reasonable results. In order to solve numerical stability issues, a tensorial dynamic procedure for the evolution of the model constants is also developed. The generality of the procedure is such that it can be employed also in more conventional closures.
2019
 On negative turbulence production phenomena in the shear layer of separating and reattaching flows
[Articolo su rivista]
Cimarelli, A.; Leonforte, A.; De Angelis, E.; Crivellini, A.; Angeli, D.
abstract
The analysis of Direct Numerical Simulation data of the separating and reattaching flow over a blunt bluff body with sharp edges, reveals the presence of negative turbulence production mechanisms in the leadingedge shear layer. Contrary to what is commonly observed in fully developed turbulent flows, this phenomenon represents flow reversal of energy from the fluctuating field to the mean flow. The detailed study of the data reveals that at the origin of such mechanisms is a statistically positive relation between Reynolds shear stresses and vertical shear. We argue that such a positive relation is a result of largescale interactions of the fluctuating field with the streamwise inhomogeneity. The analysis of time cospectra confirms this picture by highlighting the presence of a net separation of scales consisting in a range of small scales positively contributing to turbulence production in opposition to a range of large scales giving to a reversal of flow energy from the fluctuating to the mean field. By means of a reduced description of the interactions of the fluctuating field with the mean field given by a generalized mixing length hypothesis, we finally also provide conceptual arguments for the modelling of turbulence production in the transitional shear layer. A model for the mixing length is also proposed which is found to work nicely in shear flows. The simplicity of the formulation supports its use especially in experiments of wallbounded turbulence.
2019
 On the eddy viscosity associated with the subgrid stresses
[Capitolo/Saggio]
Cimarelli, A.; Abba, A.; Germano, M.
abstract
Thanks to its simplicity and robustness, the models based on the eddy viscosity concept represent the most common procedure to introduce the effect of the unresolved scales in the equations of motion for the Large Eddy Simulation (LES) approach. Indeed, the subgrid scale (sgs) viscosity approach allows from an energetic point of view to respect the dissipative nature of turbulence.
2019
 Production, transport and dissipation of turbulent stresses across scales and space
[Capitolo/Saggio]
Gatti, D.; Chiarini, A.; Cimarelli, A.; Frohnapfel, B.; Quadrio, M.
abstract
We present a theoretical framework for describing production, transport, redistribution and dissipation of every Reynolds stress component occurring among different scales and along directions of statistical inhomogeneity. It is based on the exact budget equations for the secondorder structure function tensor ‹δuiδuj›. This set of equations, that we name Anisotropic Generalized Kolmogorov Equations or AGKEs adds the scale information to the classic analysis of the singlepoint budget of the Reynolds stresses, while it allows the consistent definition of scales in directions of statistical inhomogeneity compared to a spectral analysis of the twopoint Reynolds stress budgets. Fluxes of Reynolds stresses in space and across scales can be defined and their properties analysed.
2019
 Reduced description and modelling of smallscale turbulence by means of a tensorial turbulent viscosity
[Capitolo/Saggio]
Cimarelli, A.; Crivellini, A.; Abba, A.; Germano, M.
abstract
Starting from an alternative decomposition of the subfilter stresses, we present a tensorial turbulent viscosity for a reduced description of smallscale turbulence. The formalism is based on velocity increments and, through the analysis of Direct Numerical Simulation data, is recognized to capture relevant flow features that are actually missed in scalar approaches.
2019
 Resolved and subgrid dynamics of RayleighBénard convection
[Articolo su rivista]
Togni, R.; Cimarelli, A.; De Angelis, E.
abstract
In this work we present and demonstrate the reliability of a theoretical framework for the study of thermally driven turbulence. It consists of scalebyscale budget equations for the secondorder velocity and temperature structure functions and their limiting cases, represented by the turbulent kinetic energy and temperature variance budgets. This framework represents an extension of the classical Kolmogorov and Yaglom equations to inhomogeneous and anisotropic flows, and allows for a novel assessment of the turbulent processes occurring at different scales and locations in the fluid domain. Two relevant characteristic scales, for the velocity field and for the temperature field, are identified. These variables separate the space of scales into a quasihomogeneous range, characterized by turbulent kinetic energy and temperature variance cascades towards dissipation, and an inhomogeneitydominated range, where the production and the transport in physical space are important. This theoretical framework is then extended to the context of largeeddy simulation to quantify the effect of a lowpass filtering operation on both resolved and subgrid dynamics of turbulent RayleighBénard convection. It consists of singlepoint and scalebyscale budget equations for the filtered velocity and temperature fields. To evaluate the effect of the filter length on the resolved and subgrid dynamics, the velocity and temperature fields obtained from a direct numerical simulation are split into filtered and residual components using a spectral cutoff filter. It is found that when is smaller than the minimum values of the crossover scales given by , the resolved processes correspond to the exact ones, except for a depletion of viscous and thermal dissipations, and the only role of the subgrid scales is to drain turbulent kinetic energy and temperature variance to dissipate them. On the other hand, the resolved dynamics is much poorer in the nearwall region and the effects of the subgrid scales are more complex for filter lengths of the order of or larger. This study suggests that classic eddyviscosity/diffusivity models employed in largeeddy simulation may suffer from some limitations for large filter lengths, and that alternative closures should be considered to account for the inhomogeneous processes at subgrid level. Moreover, the theoretical framework based on the filtered Kolmogorov and Yaglom equations may represent a valuable tool for future assessments of the subgridscale models.
2019
 Resolved dynamics and subgrid stresses in separating and reattaching flows
[Articolo su rivista]
Cimarelli, A.; Leonforte, A.; De Angelis, E.; Crivellini, A.; Angeli, D.
abstract
Direct numerical simulation data of the separating and reattaching flow around a blunt bluff body are used for the assessment of the combined role played by the numerical resolution and subgrid turbulence closure in large eddy simulation. The ability of the largescale resolved field to capture the main flow features is first analyzed. The behavior of the intensity of the resolved fluctuations as a function of the filter lengths reveals a higher sensitivity of the resolved flow on a reduction of resolution in the streamwise direction rather than in the spanwise one. On the other hand, the analysis of the subgrid stresses shows the presence of two challenging phenomena, a reversal of flow of energy from the fluctuating to the mean field in the leadingedge shear layer and a backward energy transfer from small to large scale within the main recirculating bubble. These two phenomena challenge for subgrid closures that should be able to reproduce a flow of energy from the space of small unknown subgrid scales to drive the resolved mean and fluctuating motion. In particular, it is found that the formalism of subgrid viscosity models allows us to capture neither the negative turbulence production of the leadingedge shear layer nor the backward energy transfer within the main flow recirculation. On the other hand, the subgrid similarity models are able to capture both these two phenomena but, from a quantitative point of view, the intensity of the reproduced stresses is very weak. In conclusion, the need of subgrid closures based on a mixed modeling approach for the solution of the flow is envisaged.
2018
 Direct numerical simulation of the flow around a rectangular cylinder at a moderately high Reynolds number
[Articolo su rivista]
Cimarelli, Andrea; Leonforte, Adriano; Angeli, Diego
abstract
We report a Direct Numerical Simulation (DNS) of the flow around a rectangular cylinder with a chordtothickness ratio B/D=5 and Reynolds number Re=3000. Global and singlepoint statistics are analysed with particular attention to those relevant for industrial applications such as the behaviour of the mean pressure coefficient and of its variance. The mean and turbulent flow is also assessed. Three main recirculating regions are found and their dimensions and turbulence levels are characterized. The analysis extends also to the asymptotic recovery of the equilibrium conditions for selfsimilarity in the fully developed wake. Finally, by means of twopoint statistics, the main unsteadinesses and the strong anisotropy of the flow are highlighted. The overall aim is to shed light on the main physical mechanisms driving the complex behaviour of separating and reattaching flows. Furthermore, we provide wellconverged statistics not affected by turbulence modelling and mesh resolution issues. Hence, the present results can also be used to quantify the influence of numerical and modelling inaccuracies on relevant statistics for the applications.
2018
 Direct simulation of transition in a differentially heated vertical channel
[Relazione in Atti di Convegno]
Cingi, Pietro; Cimarelli, Andrea; Angeli, Diego
abstract
Transition to turbulence of natural convection flows ensuing in a fluid layer between two differentially heated vertical plates is a topic of substantial interest for many applications. Among these, notable examples are the air gaps in doubleglazing panes or in ventilated façades, and passive heat exchangers. The correct prediction and control of flow regimes, air flow rates and heat transfer coefficients has a significant impact in the correct design of such elements and, in turn, on their efficiency.
In recent studies the early stages of transition have been explored by means of Direct Numerical Simulation (DNS) with highaccuracy pseudospectral codes. While all these studies correctly capture the first bifurcation from the socalled laminar conduction regime to steady convection, the detection of the subsequent transition to turbulence appears to be accompanied by a great sensitivity to some fundamental numerical choices, such as domain size, spectral resolution and amplitude of the imposed perturbations. In turn, these aspects become of crucial importance for the prediction of the heat transfer performance of the system.
In this work, the problem is tackled by means of a secondorder, FiniteVolume based Direct Numerical Simulation technique, specifically devised for convection problems, and which already proved successful in the simulation of transitional scenarios. Results reveal the occurrence of a bifurcation branch which leads the system to chaos via a second bifurcation to a steadystate, a Hopf bifurcation and, seemingly, a perioddoubling cascade. Such a scenario compares well with previous findings, except for minor discrepancies. All in all, though, some doubts persist upon the possible pitfalls in the use of DNS for the study of transition in this kind of systems.
2018
 Global energy fluxes in turbulent channels with flow control
[Articolo su rivista]
Gatti, D.; Cimarelli, A.; Hasegawa, Y.; Frohnapfel, B.; Quadrio, M.
abstract
This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skinfriction drag reduction techniques allow a more efficient use of the available power. We study whether the increased efficiency shows any general trend in how energy is dissipated by the mean velocity field (mean dissipation) and by the fluctuating velocity field (turbulent dissipation). Direct numerical simulations (DNS) of different control strategies are performed at constant power input (CPI), so that at statistical equilibrium, each flow (either uncontrolled or controlled by different means) has the same power input, hence the same global energy flux and, by definition, the same total energy dissipation rate. The simulations reveal that changes in mean and turbulent energy dissipation rates can be of either sign in a successfully controlled flow. A quantitative description of these changes is made possible by a new decomposition of the total dissipation, stemming from an extended Reynolds decomposition, where the mean velocity is split into a laminar component and a deviation from it. Thanks to the analytical expressions of the laminar quantities, exact relationships are derived that link the achieved flow rate increase and all energy fluxes in the flow system with two wallnormal integrals of the Reynolds shear stress and the Reynolds number. The dependence of the energy fluxes on the Reynolds number is elucidated with a simple model in which the controldependent changes of the Reynolds shear stress are accounted for via a modification of the mean velocity profile. The physical meaning of the energy fluxes stemming from the new decomposition unveils their interrelations and connection to flow control, so that a clear target for flow control can be identified.
2018
 On the structure of the selfsustaining cycle in separating and reattaching flows
[Articolo su rivista]
Cimarelli, A.; Leonforte, A.; Angeli, D.
abstract
The separating and reattaching flows and the wake of a finite rectangular plate are studied by means of direct numerical simulation data. The large amount of information provided by the numerical approach is exploited here to address the multiscale features of the flow and to assess the selfsustaining mechanisms that form the basis of the main unsteadinesses of the flows. We first analyse the statistically dominant flow structures by means of threedimensional spatial correlation functions. The developed flow is found to be statistically dominated by quasistreamwise vortices and streamwise velocity streaks as a result of flow motions induced by hairpinlike structures. On the other hand, the reverse flow within the separated region is found to be characterized by spanwise vortices. We then study the spectral properties of the flow. Given the strongly inhomogeneous nature of the flow, the spectral analysis has been conducted along two selected streamtraces of the mean velocity field. This approach allows us to study the spectral evolution of the flow along its paths. Two wellseparated characteristic scales are identified in the nearwall reverse flow and in the leadingedge shear layer. The first is recognized to represent trains of smallscale structures triggering the leadingedge shear layer, whereas the second is found to be related to a very largescale phenomenon that embraces the entire flow field. A picture of the selfsustaining mechanisms of the flow is then derived. It is shown that verylargescale fluctuations of the pressure field alternate between promoting and suppressing the reverse flow within the separation region. Driven by these largescale dynamics, packages of smallscale motions trigger the leadingedge shear layers, which in turn created them, alternating in the top and bottom sides of the rectangular plate with a relatively long period of inversion, thus closing the selfsustaining cycle.
2018
 Pattern recognition by Recurrence Analysis in the flow around a bluff body
[Relazione in Atti di Convegno]
Angeli, Diego; Cimarelli, Andrea; Leonforte, ADRIANO DAVIDE SERAFINO; Pagano, Arturo
abstract
The identification of scales, patterns and structures in a turbulent flow, starting from a highfidelity experimental or numerical database, is an aspect of primary importance for the understanding of the dynamics of transition to turbulence and the energy cascade. In this frame, the present study represents a preliminary effort to evaluate a time series analysis tool, the socalled Recurrence Analysis (RA), for the identification of the dominant features of a relatively complex flow. The test case is represented by the turbulent flow around a rectangular cylinder with a chordtothickness ratio $C/D = 5$, for a Reynolds number value $Re=3000$. The problem at hand has already been tackled by means of a wellresolved Direct Numerical Simulation, whose results highlighted the presence of a multiplicity of scales and structures. Due to this interesting combination of features, the case appears as a promising benchmark for the development of a novel tool for pattern recognition. To this aim, the system dynamics are condensed to pointwise observations at various abscissas along the flow. The analysis is aimed at verifying whether or not it is possible to isolate regular structures that: i) represent characteristic features of the flow and ii) can be used to distinguish the various phase of the shearwake development along the flow. Results, cast in the form of Recurrence Plots (RP), reveal that the main scales of the flow, reflected in the sampled time series, are associated with welldefined recurrent patterns. This encouraging outcome leaves room for further utilization of the technique for the description of transitional and turbulent flows in thermofluid dynamics.
2017
 A priori and a posteriori analysis of the flow around a rectangular cylinder
[Capitolo/Saggio]
Cimarelli, A.; Leonforte, A.; Franciolini, M.; Angelis, E. De; Angeli, D.; Crivellini, A.
abstract
The definition of a correct mesh resolution and modelling approach for the Large Eddy Simulation (LES) of the flow around a rectangular cylinder is recognized to be a rather elusive problem as shown by the large scatter of LES results present in the literature. In the present work, we aim at assessing this issue by performing an a priori analysis of Direct Numerical Simulation (DNS) data of the flow. This approach allows us to measure the ability of the LES field on reproducing the main flow features as a function of the resolution employed. Based on these results, we define a mesh resolution which maximize the opposite needs of reducing the computational costs and of adequately resolving the flow dynamics. The effectiveness of the resolution method proposed is then verified by means of an a posteriori analysis of actual LES data obtained by means of the implicit LES approach given by the numerical properties of the Discontinuous Galerkin spatial discretization technique. The present work represents a first step towards a best practice for LES of separating and reattaching flows.
2017
 Aerodynamic Study of Advanced Airship Shapes
[Articolo su rivista]
Cimarelli, Andrea; Madonia, Mauro; Angeli, Diego; Dumas, Antonio
abstract
The present paper reports a numerical study of the aerodynamic properties for a novel discshaped airship. Different configurations are considered, some of which present a circular opening connecting the bottom and top surface of the airship. The aim of the study is to understand the flow dynamics, in order to define the aerodynamic efficiency and the stability properties of the flying vehicle. Such information is crucial for the design of the propulsion system and of the mission profile of these innovative airships. Results show that, in general, discshaped airships are characterized by large values of drag and small levels of lift. Interestingly, it appears that lift keeps increasing up to very high angles of attack. This feature is found to be related with strong tip effects, which induce a significant flow of air from the highpressure region at the bottom surface to the lowpressure region at the top surface. This air flow energizes the upper boundary layer, thus contrasting the flow separation on the top surface. This phenomenon is found to be useful for the stability properties of the airship: in fact, it shifts the center of pressure closer to the geometrical center of the airship, hence implying a reduction of the aerodynamic moment. The role of openings is also addressed and found to positively contribute to the stability properties of the airship, by further reducing the levels of aerodynamic moment.
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.
2017
 Routes to chaos of natural convection flows in vertical channels
[Articolo su rivista]
Cimarelli, Andrea; Angeli, Diego
abstract
The aim of the present study is the analysis of the transition to turbulence of natural convection flows between two infinite vertical plates. For the study of the problem, a number of Direct Numerical Simulations (DNSs) have been performed. The continuity, momentum and energy equations, cast under the Boussinesq assumption, are tackled numerically by means of a pseudospectral method, through which the threedimensional domain is decomposed with Chebychev polynomials in the wallnormal direction and with Fourier modes in the wallparallel directions. For low Rayleigh number values, the predictions of the flow regimes are consistent with the classical analytical results and linear stability analyses. In particular, the first bifurcation (Ra ≈ 5800) from the socalled laminar conduction regime to steady convection is correctly captured. By increasing the Rayleigh number beyond a second critical value (Ra ≈ 10200), the flow regime becomes chaotic. This transition to chaos is found to be related with the amplification of spanwise instabilities occurring at scales larger than the channel gap, H. The study of the return of the system from the chaotic regime to the laminar base flow reveals a phenomenon of hysteresis, i.e. the chaotic regime persists even at Ravalues lower than the second critical value. From a numerical point of view, the predicted flow regimes appear to be extremely sensitive to the domain size, grid resolution and perturbation amplitude. These aspects are shown to be of crucial importance for the prediction of the heat transfer performance, and, hence, should be taken into consideration when numerical methods are used for the simulation of realworld problems.
2017
 Structure of turbulence in a flow around a rectangular cylinder
[Capitolo/Saggio]
Leonforte, Adriano; Cimarelli, Andrea; Angeli, Diego
abstract
The behaviour of the flow over a finite blunt plate with square leading and trailing edge corners at moderate Reynolds number is studied by means of a Direct Numerical Simulation. The chordtothickness ratio of the plate is 5 and the Reynolds number is Re = Uâ Â· D/Î½ = 3 Ã 103 where Uâ and D are the freestream velocity and the thickness, respectively. The flow separates at the leading edge corner developing in a strong freeshear. The flow reattaches on the solid surface upstream the trailing edge and evolves in typical largescale shedding beyond it. To the authors knowledge, this is the first time that highfidelity threedimensional data are produced to analyze in detail the flow features of such a system. Preliminary results on the flow topology will be presented in this work. In particular, the streamlines of the mean flow and the instantaneous threedimensional turbulent structures via Î»2 vortex criterion will be examinated.
2017
 Study of energetics in dragreduced turbulent channel flows
[Capitolo/Saggio]
Gatti, D.; Quadrio, M.; Cimarelli, A.; Hasegawa, Y.; Frohnapfel, B.
abstract
Changes in integral power budgets and scale energy fluxes as induced by certain active flow control strategies for turbulent skinfriction drag reduction are studied by performing Direct Numerical Simulation of turbulent channels. The innovative feature of the present study is that the flow is driven at Constant total Power Input (CtPI), which is a necessary enabling choice in order to meaningfully compare a reference unmanipulated flow with a modified one from the energetic standpoint. Spanwise wall oscillation and opposition control are adopted as model strategies, because of their very different control input power requirements. The global power budget show that the increase of dissipation of mean kinetic energy is not always related to drag reduction, while the preliminary analysis of the scale energy fluxes through the generalized Kolmogorov equation shows that the spaceand scale properties of the scale energy source and fluxes are significantly modified in the nearwall region, while remain unaltered elsewhere.
2017
 Towards an improved subgridscale model for thermally driven flows
[Capitolo/Saggio]
Togni, R.; Cimarelli, A.; De Angelis, E.
abstract
The effect of the filtering on the resolved and subgrid dynamics of turbulent Rayleigh–Bénard convection (RBC) is studied a priori using a Direct Numerical Simulation dataset. To this end, the velocity and temperature fields, split into resolved and subgrid components by a spectral cutoff filter, are analyzed with the filtered turbulent kinetic energy and temperature variance budgets. At small filter lengths, the resolved processes correspond to the exact ones except for the decreases of the dissipations which, in turn, are balanced by the sink actions of the subgrid scales. At large filters lengths, the resolved dynamics depletes close to the walls and the effect of the subgrid scales drifts from purelydissipative to a more complex behaviour. This study highlights the possibility that eddyviscosity and diffusivity models, commonly employed in largeeddy simulation of RBC, does not work well for large filter widths and that alternative closures should be considered.
2016
 A numerical study of the shearless turbulent/nonturbulent interface
[Capitolo/Saggio]
Cocconi, G.; Cimarelli, A.; Frohnapfel, B.; De Angelis, E.
abstract
A DNS simulation of an interface between a decaying turbulent flow without mean shear and a quiescent nonturbulent region is presented here. The analysis of the instantaneous fields highlight a complex multiscale behaviour at the turbulent/nonturbulent interface. According to previous results in the literature, by analysing the enstrophy budgets it is possible to observe that enstrophy propagate from the turbulent region mainly by inviscid process while viscous diffusion is relevant only at the interface.
2016
 Backward energy transfer and subgrid modeling approaches in wallturbulence
[Capitolo/Saggio]
Cimarelli, A.; de Angelis, E.
abstract
We report here results from a Large Eddy Simulation (LES) of a turbulent channel flow at a friction Reynolds number Reτ = 550 performed with a new subgrid modeling approach proposed by the same authors in Cimarelli et al., Phys. Fluids, 26, 055103 (2014), [1]. This subgrid scale model aims at reproducing the double feature of energy sink and source of the small scales of wall flows which become relevant when large filter lengths are adopted. Here we report a further analysis of the model by considering the instantaneous behavior of events of backward and forward energy transfer.
2016
 Cascades and wallnormal fluxes in turbulent channel flows
[Articolo su rivista]
Cimarelli, Andrea; De Angelis, E.; Jiménez, J.; Casciola, C. M.
abstract
The present work describes the multidimensional behaviour of scaleenergy production, transfer and dissipation in wallbounded turbulent flows. This approach allows us to understand the cascade mechanisms by which scale energy is transmitted scalebyscale among different regions of the flow. Two driving mechanisms are identified. A strong scaleenergy source in the buffer layer related to the nearwall cycle and an outer scaleenergy source associated with an outer turbulent cycle in the overlap layer. These two sourcing mechanisms lead to a complex redistribution of scale energy where spatially evolving reverse and forward cascades coexist. From a hierarchy of spanwise scales in the nearwall region generated through a reverse cascade and local turbulent generation processes, scale energy is transferred towards the bulk, flowing through the attached scales of motion, while among the detached scales it converges towards small scales, still ascending towards the channel centre. The attached scales of wallbounded turbulence are then recognized to sustain a spatial reverse cascade process towards the bulk flow. On the other hand, the detached scales are involved in a direct forward cascade process that links the scaleenergy excess at large attached scales with dissipation at the smaller scales of motion located further away from the wall. The unexpected behaviour of the fluxes and of the turbulent generation mechanisms may have strong repercussions on both theoretical and modelling approaches to wall turbulence. Indeed, actual turbulent flows are shown here to have a much richer physics with respect to the classical notion of turbulent cascade, where anisotropic production and inhomogeneous fluxes lead to a complex redistribution of energy where a spatial reverse cascade plays a central role.
2016
 Experimental study on hotwire spatial resolution in turbulent round jet
[Capitolo/Saggio]
Fiorini, T.; Bellani, G.; Cimarelli, A.; Talamelli, A.
abstract
Hotwire spatialresolution effects are investigated in a round jet, using custommade probes with Platinum wires of 5 and 2.5 μmof diameter. Characteristic turbulent scales are varied by both moving the probes along the jet centerline (10 < x/D < 30), and using two different nozzle diameters at a constant Reynolds number of ReD = 7 × 104. The variance of spatial derivatives shows an attenuation of one order of magnitude greater than the velocity variance, i.e. 1030% compared to 12%. Power spectra show this attenuation to be located at high frequencies, in agreement with the hypothesis of spatialfiltering effect.
2016
 Large eddy simulation of turbulent flows: Benchmarking on a rectangular prism
[Capitolo/Saggio]
Patruno, L.; Ricci, M.; Cimarelli, A.; de Miranda, S.; Talamelli, A.; Ubertini, F.
abstract
Preliminary results of a Large Eddy Simulation (LES) of rectangular cylinder performed with Open Foam are presented. This is the preliminary part of a longer research project aimed at systematically study the ability of Computational Fluid Dynamics (CFD) techniques in reproducing the flow around slender bodies with sharp edges at high Reynolds numbers. In spite of the simple geometry, the problem is influenced by a number of parameters which makes its correct solution difficult to be achieved. The LES approach presented here appears to be a good candidate for this purpose but further analysis must be performed. Indeed, we highlight the need to adopt a finer resolution in the spanwise direction in order to capture the very anisotropic turbulent dynamics. Furthermore, it emerges the need of Direct Numerical Simulation (DNS) data in order to shed light on the compound role played by the turbulence model, the grid resolution and the inlet conditions.
2016
 Multiscale analysis of turbulent RayleighBénard convection
[Capitolo/Saggio]
Togni, R.; Cimarelli, A.; De Angelis, E.
abstract
We report the results from a direct numerical simulation of turbulent RayleighBénard convection for Rayleigh number of 105 and Prandtl number of 0.7. The flow topology is characterized by the presence of coherent structures, the socalled thermal plumes, consisting of localized portions of fluid having a temperature contrast with the background. Two distinct events are identified close to the walls by using the wallparallel divergence divπ of the velocity field: the impingement (divπ > 0) and the ejection of thermal plumes (divπ < 0). The impingement leads to the formation of larger velocity and temperature structures in the wallparallel planes. Contrary to the classical picture of turbulence consisting of a direct transfer of energy from large toward smaller turbulent fluctuations, the impingement is conjectured to be probably responsible for a reverse transfer from small towards large scales in the nearwall region.
2016
 Space and time behaviour of the temperature secondorder structure function in RayleighBénard convection
[Capitolo/Saggio]
Togni, Riccardo; Cimarelli, Andrea; Lozano Durán, Adrián; Angelis, Elisabetta De
abstract
One of the most peculiar aspects of turbulence in wall boundedflows is the ability of the turbulent fluctuations to regenerate themselves through selfsustained processes. The dynamics of these selfsustaining mechanisms has been extensively investigated in the past via two complementary approaches. From one side, the possibility to identify very robust kinematic features within the flow feeds the hope of the scientific community to obtain a complete and consistent dynamical description of the physics of the turbulent regeneration cycles in terms of the socalled coherent structures. From the other side, the multiscale and inhomogeneous features of the selfsustaining mechanisms of turbulence have been addressed by means of global statistical quantities based on twopoint averages such as secondorder structure functions. The present work attempts to link these two approaches, by identifying how turbulent cycle mechanisms and turbulent structures reflect on the global statistical properties of secondorder structure function. To this aim we use Direct Numerical Simulation data of thermally driven turbulence in the RayleighBénard convection and we analyse for the first time the behaviour of the secondorder structure function of temperature in the complete fourdimensional space of spatiotemporal scales and walldistances. The observed behaviour is then interpreted in terms of the dynamics of coherent thermal structures and of their commonly accepted model of lifecycle.
2016
 Temperature effects in hotwire measurements on higherorder moments in wall turbulence
[Capitolo/Saggio]
Talamelli, A.; Malizia, F.; Orlu, R.; Cimarelli, A.; Schlatter, P.
abstract
2015
 Analysis of the Yaglom equation and subgrid modelling approaches for thermally driven turbulence
[Relazione in Atti di Convegno]
Cimarelli, A.; Togni, R.; de Angelis, E.
abstract
We report a Direct Numerical Simulation (DNS) of turbulent RayleighBénard convection in a laterally unbounded domain confined between two horizontal parallel walls, for Rayleigh number 105 and Prandtl number 0.7. The DNS data are used to study the properties of the subgridscale flux of the active temperature field in the framework of Large Eddy Simulation (LES). In particular, starting from the generalized Yaglom equation, we analyze how the thermal energy is produced, transferred and dissipated in the augmeneted space of scales and positions of the flow. The understanding of these processes is then used to propose appropriate formulations for the subgridscale flux that will be tested by means of a posteriori analysis of LES simulations performed in the same flow conditions.
2015
 Analysis of turbulent RayleighBénard convection in the compound physical/scale space domain
[Relazione in Atti di Convegno]
Togni, R.; Cimarelli, A.; de Angelis, E.
abstract
We report the results from two distinct direct numerical simulations (DNS) of turbulent RayleighBénard convection (RBC) for Rayleigh number of 105 and Prandtl number of 0.7 in a laterally unbounded domain confined between two horizontal isothermal plates with noslip and freeslip boundary conditions respectively. The central aim of the present work consists in a simultaneous description of both flows in a compound physical/scale space domain by using a generalized form of the classical Kolmogorov equation for the secondorder velocity structure function. It has been found that the dynamics of the coherent structures in RBC, the socalled thermal plumes, are clearly reflected in the multiscale energy budgets. In particular, the enlargement of thermal plumes following the impingement at the wall entails a transfer of scaleenergy from small turbulent scales toward larger ones. This aspect shed light on the role of thermal plumes in turbulent RBC and could have a direct impact on future attempts to model the effects of smallscale motions in thermal convection.
2015
 Maat cruiser/feeder airship design: Intrinsic stability and energetic flight model
[Relazione in Atti di Convegno]
Trancossi, Michele; Dumas, Antonio; Cimarelli, Andrea; Pascoa, Jose
abstract
Airships are expected to have in future an increasing diffusion in the aeronautic scenario. The use of airships is not necessary expected to be the same proposed in the past. Several new uses will assume a relevant importance in the next 20 years. The resurgence of airships has created a need for dynamics models and simulation capabilities of these lighterthanair vehicles. A theoretical framework for designing flexible airships has developed deriving the equations for determining the flight behavior of an airship directly form the data of wind tests and CFD simulations. This model has been a fundamental part of the final design activities of the MAAT (Multibody Advanced Airship for Transport) EU FP7 project, which has studied an innovative cruiser feeder airship based transport system. Main results relates to the definition of a specific mathematical model, which allow approximating the behavior of a flexible or low structured semi rigid airship in presence of external oscillations, in pitch or yawing. Different shapes of airships with different shapes, also not conventional, are assumed and aerodynamic behavior has been evaluated when slightly disturbed from steady forward motion or from hovering conditions in presence of an impacting wind. New uses and the exigency of adopting photovoltaic energy for long endurance missions, is producing airship shapes, which are slightly different from traditional Parsifal. The model presents defines effective criteria based on constructal law, which allow designing an airship with an intrinsic stability in pitch and yaw. An approximate condition for a dynamically stable motion, such as unamplifying pitch, has been expressed in familiar aerodynamic quantities. These results allow stating the following theorem, which has been demonstrated: "Stable pitch flight conditions can be ensured if damping moment is in rotational equilibrium with the disturbing moment and if the disturbing force, the damping force, and the inertia force, are in translational balance". If pitch angle and angular speed are small it can be obtained a relation that must be necessarily satisfied for ensuring a stability condition. An effective flight model based on energetic model of flight is also produced and results have been compared with traditional models giving a good accordance in terms of results.
2015
 Physical and scalebyscale analysis of RayleighBénard convection
[Articolo su rivista]
Togni, Riccardo; Cimarelli, Andrea; De Angelis, Elisabetta
abstract
A novel approach for the study of turbulent RayleighBénard convection (RBC) in the compound physical/scale space domain is presented. All data come from direct numerical simulations of turbulent RBC in a laterally unbounded domain confined between two horizontal walls, for Prandtl number 0:7 and Rayleigh numbers 1:7 ± 105, 1:0 ± 106 and 1:0 ± 107. A preliminary analysis of the flow topology focuses on the events of impingement and emission of thermal plumes, which are identified here in terms of the horizontal divergence of the instantaneous velocity field. The flow dynamics is then described in more detail in terms of turbulent kinetic energy and temperature variance budgets. Three distinct regions where turbulent fluctuations are produced, transferred and finally dissipated are identified: a bulk region, a transitional layer and a boundary layer. A description of turbulent RBC dynamics in both physical and scale space is finally presented, completing the classic singlepoint balances. Detailed scalebyscale budgets for the secondorder velocity and temperature structure functions are shown for different geometrical locations. An unexpected behaviour is observed in both the viscous and thermal transitional layers consisting of a diffusive reverse transfer from small to large scales of velocity and temperature fluctuations. Through the analysis of the instantaneous field in terms of the horizontal divergence, it is found that the enlargement of thermal plumes following the impingement represents the triggering mechanism which entails the reverse transfer. The coupling of this reverse transfer with the spatial transport towards the wall is an interesting mechanism found at the basis of some peculiar aspects of the flow. As an example, it is found that, during the impingement, the presence of the wall is felt by the plumes through the pressure field mainly at large scales. These and other peculiar aspects shed light on the role of thermal plumes in the selfsustained cycle of turbulence in RBC, and may have strong repercussions on both theoretical and modelling approaches to convective turbulence.
2015
 Sources and fluxes of scale energy in the overlap layer of wall turbulence
[Articolo su rivista]
Cimarelli, A.; De Angelis, E.; Schlatter, P.; Brethouwer, G.; Talamelli, A.; Casciola, C. M.
abstract
Direct numerical simulations of turbulent channel flows at friction Reynolds numbers (Re) of 550, 1000 and 1500 are used to analyse the turbulent production, transfer and dissipation mechanisms in the compound space of scales and wall distances by means of the Kolmogorov equation generalized to inhomogeneous anisotropic flows. Two distinct peaks of scaleenergy source are identified. The first, stronger one, belongs to the nearwall cycle. Its location in the space of scales and physical space is found to scale in viscous units, while its intensity grows slowly with Re, indicating a nearwall modulation. The second source peak is found further away from the wall in the putative overlap layer, and it is separated from the nearwall source by a layer of significant scaleenergy sink. The dynamics of the second outer source appears to be strongly dependent on the Reynolds number. The detailed scalebyscale analysis of this source highlights welldefined features that are used to make the properties of the outer turbulent source independent of Reynolds number and wall distance by rescaling the problem. Overall, the present results suggest a strong connection of the observed outer scaleenergy source with the presence of an outer region of turbulence production whose mechanisms are well separated from the nearwall region and whose statistical features agree with the hypothesis of an overlap layer dominated by attached eddies. Innerouter interactions between the nearwall and outer source region in terms of scaleenergy fluxes are also analysed. It is conjectured that the nearwall modulation of the statistics at increasing Reynolds number can be related to a confinement of the nearwall turbulence production due to the presence of increasingly large production scales in the outer scaleenergy source region.
2015
 Spectral enstrophy budget in a shearless flow with turbulent/nonturbulent interface
[Articolo su rivista]
Cimarelli, A.; Cocconi, G.; Frohnapfel, B.; De Angelis, E.
abstract
A numerical analysis of the interaction between decaying shear free turbulence and quiescent fluid is performed by means of global statistical budgets of enstrophy, both, at the singlepoint and two point levels. The singlepoint enstrophy budget allows us to recognize three physically relevant layers: a bulk turbulent region, an inhomogeneous turbulent layer, and an interfacial layer. Within these layers, enstrophy is produced, transferred, and finally destroyed while leading to a propagation of the turbulent front. These processes do not only depend on the position in the flow field but are also strongly scale dependent. In order to tackle this multidimensional behaviour of enstrophy in the space of scales and in physical space, we analyse the spectral enstrophy budget equation. The picture consists of an inviscid spatial cascade of enstrophy from large to small scales parallel to the interface moving towards the interface. At the interface, this phenomenon breaks, leaving place to an anisotropic cascade where large scale structures exhibit only a cascade process normal to the interface thus reducing their thickness while retaining their lengths parallel to the interface. The observed behaviour could be relevant for both the theoretical and the modelling approaches to flow with interacting turbulent/nonturbulent regions. The scale properties of the turbulent propagation mechanisms highlight that the inviscid turbulent transport is a largescale phenomenon. On the contrary, the viscous diffusion, commonly associated with small scale mechanisms, highlights a much richer physics involving small lengths, normal to the interface, but at the same time large scales, parallel to the interface.
2015
 Transition to Chaos of Natural Convection Flows in Differentially Heated Vertical Slots
[Relazione in Atti di Convegno]
Angeli, Diego; Cimarelli, Andrea; Leonforte, ADRIANO DAVIDE SERAFINO; De Angelis, Elisabetta; Dumas, Antonio
abstract
Aim of the present study is the preliminary numerical analysis of the transition to turbulence of natural convection of air between two infinite vertical plates, with a focus on the effect of modeling and discretization choices on the predicted transitional patterns. In particular, the effect of the domain size, grid resolution and perturbation amplitude are explored. For the study of the problem, different Direct Numerical Simulations (DNS) have been performed. The
governing equations of the problem are the continuity, momentum and temperature equations under the Boussinesq assumption. Such equations are tackled numerically by means of a pseudospectral method which discretizes space with Chebychev polynomials in the direction normal to the walls and with Fourier modes in the wallparallel directions.
For low Rayleigh number values, the predictions of the flow regimes are consistent with the results classical analytical results and linear stability analyses. In particular, the first bifurcation from the socalled conduction regime to steady convection is correctly captured. By increasing the Rayleigh number beyond a second critical value (Ra ≈ 10200), the predicted flow regime is observed to be extremely sensitive to all the abovementioned numerical parameters, which lead to physically sound results only in some cases. In particular, the appearance of 3D structures is seen to be linked either to the adoption of a large enough domain or to the superimposition of finiteamplitude disturbances to the initial flow field.
2014
 Study of the outer selfregeneration of turbulence in wall flows
[Capitolo/Saggio]
Cimarelli, A.; De Angelis, E.; Talamelli, A.; Casciola, C. M.
abstract
A new approach for the study of the overlap layer of wallturbulence is proposed. The multidimensional description of turbulence given by the Kolmogorov equation generalized to wallflows is used and shown relevant for the identification of very robust features of the overlap layer. Numerical data of a turbulent channel are used. Despite the low Reynolds, a welldefined outer energy source region appears. The possibility to analyze its effects on the energy tranfer among scales and walldistances is shown important to clarify the influences of the external region on the inner layer.
2014
 The attached reverse and detached forward cascades in wallturbulent flows
[Capitolo/Saggio]
Cimarelli, A.; De Angelis, E.; Talamelli, A.; Casciola, C. M.; Jimenez, J.
abstract
The present work describes the multidimensional behaviour of wallbounded turbulence in the space of crossscales (spanwise and wallnormal) and distances from the wall. This approach allows us to understand the cascade mechanisms by which scaleenergy is transmitted scalebyscale away from the wall, through the overlap layer, and into the bulk flow. Two distinct cascades are identified involving the attached and detached scales of motion, respectively. From the nearwall region, scaleenergy is transferred towards the bulk, flowing through the attached scales of motion, while among the detached scales it converges towards small scales, ascending again to the channel centre. It is then argued that the attached scales of wallbounded turbulence are involved in a reverse cascade process that starts from the wall and ends in the bulk flow. On the other hand, the detached scales belong to a direct forward cascade process towards dissipation. Hence, at a given distance from the wall the attached motion is fed by smaller attached scales located closer to the wall. In turn this attached motion is responsible for creating the scaleenergy that sustains larger attached scales farther from the wall and smaller detached scales that are responsible for connecting the scaleenergy at large scales to the dissipation at small scales through a forward cascade. © Published under licence by IOP Publishing Ltd.
2014
 The influence of temperature fluctuations on hotwire measurements in wallbounded turbulence
[Articolo su rivista]
Orlu, R.; Malizia, F.; Cimarelli, A.; Schlatter, P.; Talamelli, A.
abstract
There are no measurement techniques for turbulent flows capable of reaching the versatility of hotwire probes and their frequency response. Nevertheless, the issue of their spatial resolution is still a matter of debate when it comes to high Reynolds number nearwall turbulence. Another, so far unattended, issue is the effect of temperature fluctuations  as they are, e.g. encountered in nonisothermal flows  on the low and higherorder moments in wallbounded turbulent flows obtained through hotwire anemometry. The present investigation is dedicated to document, understand, and ultimately correct these effects. For this purpose, the response of a hotwire is simulated through the use of velocity and temperature data from a turbulent channel flow generated by means of direct numerical simulations. Results show that ignoring the effect of temperature fluctuations, caused by temperature gradients along the wallnormal direction, introduces  despite a local mean temperature compensation of the velocity reading  significant errors. The results serve as a note of caution for hotwire measurements in wallbounded turbulence, and also where temperature gradients are more prevalent, such as heat transfer measurements or high Mach number flows. A simple correction scheme involving only mean temperature quantities (besides the streamwise velocity information) is finally proposed that leads to a substantial bias error reduction. © 2014 SpringerVerlag Berlin Heidelberg.
2014
 The physics of energy transfer toward improved subgridscale models
[Articolo su rivista]
Cimarelli, A.; De Angelis, E.
abstract
Starting from physical insight on the energy transfer phenomena in wall turbulent flows, it is shown how modeling of subgrid stresses in largeeddy simulations can be improved. Each model should aim at reproducing the double feature of energy sink and source of the small scales of wall flows which become relevant when large filter lengths are considered. Here we propose one possible choice where the main ingredient is the coupling of the classical linear formulation of eddy viscosity with the nonlinear anisotropic features of the velocity increments tensor. This approach, which actually presents most of the features of the mixed models, captures the nearwall dynamics for very large filter lengths reproducing the small scales source physics responsible for backward energy transfer. A posteriori tests show excellent agreement with direct numerical simulation of turbulent channel flows even when very coarse grids are considered. The capability of the balance of the filtered second order structure function as a postprocessing tool to evaluate the physics of any model is also shown. © 2014 AIP Publishing LLC.
2014
 Turbulent production and subgrid dynamics in wall flows
[Capitolo/Saggio]
Cimarelli, A.; De Angelis, E.
abstract
The Kolmogorov equation generalized to wallturbulence has been recently proven to give a detailed description of the multidimensional features of such flows[1]. As emerging from this approach, the small scales of wall turbulence are found to drive the quasicoherent motion at large scales through a reverse energy transfer. At the base of this phenomenology is the focusing of production of turbulent fluctuations at small scales. These observations may have strong repercussion on both theoretical and modeling approaches to wallturbulence. Here, we aim at using the Kolmogorov equation not only for the study of the mechanisms altering the energy transfer but also for modeling purpose.
2013
 Paths of energy in turbulent channel flows
[Articolo su rivista]
Cimarelli, A.; De Angelis, E.; Casciola, C. M.
abstract
Abstract The paper describes the energy fluxes simultaneously occurring in the space of scales and in the physical space of wallturbulent flows. The unexpected behaviour of the energy fluxes consists of spirallike paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the nearwall region and a second one further away from the wall. The former, stronger, one is related to the dynamics involved in the nearwall turbulence regeneration cycle. The second suggests an outer selfsustaining mechanism which is asymptotically expected to take place in the eventual log layer and could explain the debated mixed inner/outer scaling of the nearwall statistics. The observed behaviour may have strong repercussions on both theoretical and modelling approaches to wall turbulence, as anticipated by a simple equation which is shown able to capture most of the rich dynamics of the sheardominated region of the flow. © Cambridge University Press 2013.
2013
 Prediction of turbulence control for arbitrary periodic spanwise wall movement
[Articolo su rivista]
Cimarelli, A.; Frohnapfel, B.; Hasegawa, Y.; De Angelis, E.; Quadrio, M.
abstract
In order to generalize the wellknown spanwiseoscillatingwall technique for drag reduction, nonsinusoidal oscillations of a solid wall are considered as a means to alter the skinfriction drag in a turbulent channel flow. A series of direct numerical simulations is conducted to evaluate the control performance of nine different temporal waveforms, in addition to the usual sinusoid, systematically changing the wave amplitude and the period for each waveform. The turbulent average spanwise motion is found to coincide with the laminar Stokes solution that is constructed, for the generic waveform, through harmonic superposition. This allows us to define and compute, for each waveform, a new penetration depth of the Stokes layer which correlates with the amount of turbulent drag reduction, and eventually to predict both turbulent drag reduction and net energy saving rate for arbitrary waveforms. Among the waveforms considered, the maximum net energy saving rate is obtained by the sinusoidal wave at its optimal amplitude and period. However, the sinusoid is not the best waveform at every point in the parameter space. Our predictive tool offers simple guidelines to design waveforms that outperform the sinusoid for given (suboptimal) amplitude and period of oscillation. This is potentially interesting in view of applications, where physical limitations often preclude the actuator to reach its optimal operating conditions. © 2013 AIP Publishing LLC.
2013
 Turbulent skinfriction drag reduction by spanwise wall oscillation with generic temporal waveform
[Relazione in Atti di Convegno]
Cimarelli, A.; Frohnapfel, B.; Hasegawa, Y.; De Angelis, E.; Quadrio, M.
abstract
To generalize the wellknown spanwiseoscillatingwall technique for drag reduction, nonsinusoidal oscillations of a solid wall are considered as a means to alter the skinfriction drag in a turbulent channel flow. A series of Direct Numerical Simulations is conducted to evaluate the control performance of nine different waveforms, in addition to the usual sinusoid, systematically changing the maximum wave amplitude and the period for each waveform. The turbulent average spanwise motion is found to coincide with the laminar Stokes solution that can be constructed, for the generic waveform, through harmonic superposition. A newly defined penetration depth of the Stokes layer is then used to build a simple tool that allows predicting turbulent drag reduction and net energy saving rate for any waveform. Among all the cases considered, the sinusoid at optimal amplitude and period is found to yield the maximum net energy saving rate. However, when the wave amplitude and period deviate from the optimal values, other waves are found to perform better than the sinusoid. This is potentially interesting in view of applications, where a particular actuator limitations might preclude reaching the optimal operating conditions for the sinusoidal wall oscillation. It is demonstrated that the present model can predict the locally optimal waveform for given wave amplitude and period, as well as the globally optimal sinusoidal wave.
2012
 Anisotropic dynamics and subgrid energy transfer in wallturbulence
[Articolo su rivista]
Cimarelli, A.; De Angelis, E.
abstract
Purpose of the present work is the analysis of the generalized Kolmogorov equation applied to the direct numerical simulation data of a turbulent channel flow. The multidimensional description of the anisotropic behavior of turbulent energy production, transportdissipation is shown to be relevant for the understanding and modeling of the wallturbulent physics with special care to the phenomenon of reverse energy flux. These results are proven instrumental also for the correct computation of wallturbulence when a large eddy simulation approach is considered. The capability of a filtered velocity field to correctly reproduce the wallturbulent dynamics at different ranges of scales and walldistances as a function of the filter length will be assessed via filtered direct numerical simulation (DNS) and large eddy simulation data. The possibility of new modeling approaches is also highlighted. © 2012 American Institute of Physics.
2012
 ScaleEnergy Fluxes in WallTurbulent Flows
[Capitolo/Saggio]
Cimarelli, A; De Angelis, E; Casciola, Cm
abstract
According to the Kolmogorov theory, the most important feature of high Reynolds number turbulent flows is the energy transfer from large to small scales. This energy cascade is believed to universally occur in a certain interval of scales, known as inertial range. This phenomenology has been shown to occur in a wide range of flows but not in wallturbulence where a reverse cascade in the nearwall region is observed [1]. In order to analyse this new scenario, in the present work a study of a generalized Komogorov equation is performed. The results reveal an energy fluxes loop in the space of scales where the reverse cascade plays a central role. At the base of this phenomena it is found the anisotropic energy injection due to the action of the turbulent structures involved in the nearwall cycle. The data used for the analysis are obtained with a pseudospectral code in a channel at Retau = 550. The computational domain is 8 pi h x 2h x 4 pi h with a resolution in the homogeneous directions of Delta x(+)  13.5 and Delta z(+)  6.7.
2011
 Analysis of the Kolmogorov equation for filtered wallturbulent flows
[Articolo su rivista]
Cimarelli, A.; De Angelis, E.
abstract
The analysis of the energy transfer mechanisms in a filtered wallturbulent flow is traditionally accomplished via the turbulent kinetic energy balance, as in HÃrtel et al. (Phys. Fluids, vol. 6, 1994, p. 3130) or via the analysis of the energy spectra, as in Domaradzki et al. (Phys. Fluids, vol. 6, 1994, p. 1583). However, a generalized Kolmogorov equation for channel flow has recently been proven successful in accounting for both spatial fluxes and energy transfer across the scales in a single framework by Marati, Casciola & Piva (J. Fluid Mech., vol. 521, 2004, p. 191). In this context, the same machinery is applied for the first time to a filtered velocity field. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter scale compared to the crossover scale between productiondominated scales and inertial range, lc, and the reverse energy cascade region ΩB. Finally, we will briefly discuss how the filtered Kolmogorov equation can be used as a new tool for the assessment of large eddy simulation (LES) models. Classical purely dissipative eddy viscosity models will be analysed via an a priori procedure. © 2011 Cambridge University Press.
2011
 Anisotropic dynamics in filtered wallturbulent flows
[Capitolo/Saggio]
Cimarelli, A.; De Angelis, E.
abstract
2011
 Assessment of the turbulent energy paths from the origin to dissipation in wallturbulence
[Capitolo/Saggio]
Cimarelli, A.; De Angelis, E.; Casciola, C. M.
abstract
The present study is devoted to the description of the energy fluxes from production to dissipation in the augmented space (3dimensional space of scales plus walldistance) of wallturbulent flows. As already shown in Cimarelli et al. (2010), an interesting behavior of the energy fluxes comes out from this analysis consisting of spirallike paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. The observed behaviour conflicts with the classical notion of the Richardson/Kolmogorov energy cascade and may have strong repercussions on both theoretical and modeling approaches to wallturbulence. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one further away from the wall. The former, stronger one is related to the dynamics involved in the nearwall cycle. The second suggests an outer selfsustaining mechanism. Here we extend these results to larger Reynolds number using LES data of a turbulent channel flow at Reτ = 970 confirming the presence of an outer regeneration cycle which seems to be composed by systems of attached eddies.
2011
 Effect of the spatial filtering and alignment error of hotwire probes in a wallbounded turbulent flow
[Articolo su rivista]
Segalini, A.; Cimarelli, A.; Ruedi, J. D.; De Angelis, E.; Talamelli, A.
abstract
The effort to describe velocity fluctuation distributions in wallbounded turbulent flows has raised different questions concerning the accuracy of hotwire measurement techniques close to the wall and more specifically the effect of spatial averaging resulting from the finite size of the wire. Here, an analytical model which describes the effect of the spatial filtering and misalignment of hotwire probes on the main statistical moments in turbulent wallbounded flows is presented. The model, which is based on the twopoint velocity correlation function, shows that the filtering is directly related to the transverse Taylor microscale. By means of turbulent channel flow DNS data, the capacity of the model to accurately describe the probe response is established. At the same time, the filtering effect is appraised for different wire lengths and for a range of misalignment angles which can be expected from good experimental practice. Effects of the secondorder terms in the model equations are also taken into account and discussed. In order to use the model in a practical situation, the Taylor microscale distribution at least should be provided. A simple scaling law based on classic turbulence theory is therefore introduced and finally employed to estimate the filtering effect for different wire lengths. © 2011 IOP Publishing Ltd.
2011
 Energy cascade and spatial fluxes of filtered wallturbulent flows
[Capitolo/Saggio]
Cimarelli, A.; De Angelis, E.
abstract
The analysis of the subgrid energy transfer which is traditionally accomplished with the turbulent kinetic energy [1], and with the energy spectrum [2], is performed by a scale energy balance. A generalized Kolmogorov equation for filtered velocity field will be applied and discussed. The results will show which are the effects of subgrid scales on the resolved motion in both physical and scale space, singling out the prominent role of the filter scale compared to the crossover scale between production dominated scales and inertial range, lc, and the reverse energy cascade region ΩB.