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ANDREA CIMARELLI

Professore Associato
Dipartimento di Ingegneria "Enzo Ferrari"

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Pubblicazioni

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 fourth-order finite difference scheme and third-order Adams-Bashforth 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 - 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/non-turbulent interface, where forward energy cascade is found to be almost absent. In particular, the turbulent core is found to sustain a variety of large-scale wall-parallel 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/non-turbulent interfaces in general.

2023 - On wind-wave interaction phenomena at low Reynolds numbers [Articolo su rivista]
Cimarelli, A.; Romoli, F.; Stalio, E.
abstract

After decades of research efforts, wind-wave 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 wind-wave 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 wave-induced 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 ocean-atmosphere interface, the basic flow phenomena unveiled here may explain some experimental evidence in wind-wave problems. Among other things, the wave-induced 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 ocean-atmosphere 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–metal-cooled nuclear reactors, encompassing a wide spectrum of turbulent convection regimes. The first test case is a Rayleigh-Bénard 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 cold-hot–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 fully-developed flow in a vertical bare rod bundle with triangular arrangement and a pitch-to-diameter 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 in-depth 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, 865-896 (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 second-order 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 chord-to-thickness ratio equal to 5 (BARC). Despite the interest in the topic, a widely accepted set of guidelines for grid generation about these blunt bodies is still missing. In this work a new, well resolved Direct Numerical Simulation (DNS) around the BARC body at Re=3000 is presented and its results compared to previous DNSs of the same case but with different numerical approaches and mesh. Despite the simulations use different numerical approaches, mesh and domain dimensions, the main discrepancies are ascribed to the different grid spacings employed. While a more rigorous analysis is envisaged, where the order of accuracy of the schemes are kept the same while grid spacings are varied alternately along each spatial direction, this represents a first attempt in the study of the influence of spatial resolution in the Direct Numerical Simulation of flows around elongated rectangular cylinders with sharp corners.

2022 - Implicit Large Eddy Simulations of a rectangular 5:1 cylinder with a high-order 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 high-order accurate spatial scheme and an implicit high-order accurate time integration method. The spatial approximation is based on a discontinuous Galerkin (dG) method, while the time integration exploits a linearly-implicit Rosenbrock-type Runge-Kutta scheme. The aim of this work is to show the feasibility of high-fidelity flow simulations with a moderate number of DOFs and large time step sizes. Moreover, the effect of different parameters, i.e., dimension of the computational domain, mesh type, grid resolution, boundary conditions, time step size and polynomial approximation, on the results accuracy is investigated. Our best dG result at Re=3 000 perfectly agrees with a reference DNS obtained using Nek5000 and about 40 times more degrees of freedom. The Re=40 000 computations, which are strongly under-resolved, show a reasonable correspondence with the experimental data of Mannini et al. (2017) and the LES of Zhang and Xu (2020).

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 three-dimensional spatial correlation functions are considered. It is found that the flow is characterized by large-scale spanwise vortices whose motion is felt in the entire flow field. Superimposed to this large-scale motion, a hierarchy of turbulent structures is present. The most coherent ones take the form of quasi-streamwise 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 free-shear 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 free-shear 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 second-order structure function tensor in the space of scales and in the physical space. Scale-space energy fluxes show that forward and reverse energy transfers occur simultaneously in the flow, with interesting modelling implications. Over the longitudinal cylinder side, the Kelvin-Helmholtz instability of the leading edge shear layer generates large spanwise rolls, which get stretched into hairpin-like vortices and eventually break down into smaller streamwise vortices. Independent sources of velocity fluctuations act at different scales. The flow dynamics is dominated by pressure-strain: 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 streamwise-aligned vortices. In the near wake, large von Kármán-like 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 pressure-strain.

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 so-called 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 steady-state, a Hopf bifurcation and, seemingly, a period-doubling 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 large-scale coherent motions and small-scale fluctuations. The turbulent spectrum can be split into active and inactive flow structures. The large-scale 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, small-scale 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 large-eddy 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 high-order implicit discontinuous Galerkin method, numerical simulations of a two-dimensional 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 multi-dimensional statistical formalism for the description and understanding of turbulence in free-shear flows is proposed and applied to the symmetries of planar temporal jets. The theoretical framework is based on the exact equation for the second-order moment of the two-point 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 two-dimensional 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 cross-flow layer of these large-scale structures. Finally, the external non-turbulent region of the jet is also found to be active from an energetic point of view. It is found that pressure-mediated non-local phenomena of displacement of almost quiescent fluid give rise to non-turbulent fluctuations that in time, through transitional mechanisms, would contribute to the growth of the turbulent jet. Overall, the unexpected paths taken by the scale-energy 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 scale-dependent 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 under-resolved 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 metal-cooled nuclear reactors, encompassing a wide spectrum of turbulent convection regimes. The first test case is a Rayleigh-Benard 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 cold-hot-cold 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 fully-developed flow in a vertical bare rod bundle with triangular arrangement and a large pitch-to-diameter 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 in-depth 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 - High-order DG solutions of separating and reattaching flows [Capitolo/Saggio]
Cimarelli, A.; Franciolini, M.; Crivellini, A.
abstract

We report high-order 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 leading-edge corners and the presence or not of a trailing-edge 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 high-order Discontinuous Galerkin (DG) discretization of the three-dimensional incompressible Navier-Stokes equations. The algorithm uses a linearly implicit Runge-Kutta scheme of the Rosenbrock type, and a p-multigrid preconditioned matrix-free linear solver.

2020 - Numerical experiments in separating and reattaching flows [Articolo su rivista]
Cimarelli, A.; Franciolini, M.; Crivellini, A.
abstract

We report high-order 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 leading-edge corner, the presence of a trailing-edge flow separation, and of a flow coupling between the two sides of the plate. The results reveal that flows with right-angled corners develop taller flow recirculations, which promote very-slow instability of the bubble itself. This large-scale 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 self-sustained cycle. The absence of these phenomena in flows with smooth leading-edge corners is also found to explain their high sensitivity to free-stream 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 wall-turbulence [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 wall-turbulent flows at moderately high Reynolds numbers. Two driving mechanisms are identified for the energy fluxes. The first stronger one, here called driving scale-range (DSR), belongs to the near-wall 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 scale-range (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 second-order structure function tensor, where is the difference of the th fluctuating velocity component between two points, are used to study the two-point 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 inter-component and multi-scale 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 half-trace, the AGKE can describe inter-component energy transfers occurring via the pressure-strain term and contain also budget equations for the off-diagonal components of. The non-trivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the near-wall cycle of a turbulent channel flow at a friction Reynolds number of is considered. The off-diagonal component, which cannot be interpreted in terms of scale energy, is discussed in detail. Wall-normal 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 spanwise-vortex 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 self-sustained 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 leading-edge shear layer and the low-frequency 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 high-Re wall-bounded 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 3-4 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 four-dimensional domain. It is shown that the space and scale properties of the scale-energy fluxes change for increasing values of the Reynolds number. Among all scale-energy fluxes, the wall-normal flux is found to show the richest behaviour for increasing streamwise scales.

2019 - Direct Numerical Simulation of a buoyant triple jet at low-Prandtl 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 large-scale vortices is originated accompanied by low-frequency 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 self-similar 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 Navier-Stokes 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 scale-dependent 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 small-scale stresses in turbulence. The analysis in a turbulent channel shows the rich physics of the small-scale 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 third-order 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 filtered-out motions and, hence, this information could be leveraged to improve the prediction of the main unknown features of small-scale 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 leading-edge 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 large-scale 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 wall-bounded 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 second-order 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 single-point 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 two-point 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 small-scale 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 small-scale 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 Rayleigh-Bénard 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 scale-by-scale budget equations for the second-order 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 quasi-homogeneous range, characterized by turbulent kinetic energy and temperature variance cascades towards dissipation, and an inhomogeneity-dominated range, where the production and the transport in physical space are important. This theoretical framework is then extended to the context of large-eddy simulation to quantify the effect of a low-pass filtering operation on both resolved and subgrid dynamics of turbulent Rayleigh-Bénard convection. It consists of single-point and scale-by-scale 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 cross-over 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 near-wall 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 eddy-viscosity/diffusivity models employed in large-eddy 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 subgrid-scale 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 large-scale 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 leading-edge 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 leading-edge 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 chord-to-thickness ratio B/D=5 and Reynolds number Re=3000. Global and single-point 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 self-similarity in the fully developed wake. Finally, by means of two-point 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 well-converged 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 double-glazing 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 high-accuracy pseudospectral codes. While all these studies correctly capture the first bifurcation from the so-called 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 second-order, Finite-Volume 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 steady-state, a Hopf bifurcation and, seemingly, a period-doubling 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 skin-friction 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 wall-normal 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 control-dependent 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 inter-relations and connection to flow control, so that a clear target for flow control can be identified.

2018 - On the structure of the self-sustaining 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 multi-scale features of the flow and to assess the self-sustaining mechanisms that form the basis of the main unsteadinesses of the flows. We first analyse the statistically dominant flow structures by means of three-dimensional spatial correlation functions. The developed flow is found to be statistically dominated by quasi-streamwise vortices and streamwise velocity streaks as a result of flow motions induced by hairpin-like 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 well-separated characteristic scales are identified in the near-wall reverse flow and in the leading-edge shear layer. The first is recognized to represent trains of small-scale structures triggering the leading-edge shear layer, whereas the second is found to be related to a very large-scale phenomenon that embraces the entire flow field. A picture of the self-sustaining mechanisms of the flow is then derived. It is shown that very-large-scale fluctuations of the pressure field alternate between promoting and suppressing the reverse flow within the separation region. Driven by these large-scale dynamics, packages of small-scale motions trigger the leading-edge 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 self-sustaining 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 high-fidelity 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 so-called 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 chord-to-thickness ratio $C/D = 5$, for a Reynolds number value $Re=3000$. The problem at hand has already been tackled by means of a well-resolved 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 shear-wake 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 well-defined recurrent patterns. This encouraging outcome leaves room for further utilization of the technique for the description of transitional and turbulent flows in thermo-fluid 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 disc-shaped 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, disc-shaped 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 high-pressure region at the bottom surface to the low-pressure 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 well-known PLAJEST triple jet experiment, but with a relative increase of the buoyancy effect, achieved by reducing the Reynolds number by a factor 5. Pre-production 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 three-dimensional domain is decomposed with Chebychev polynomials in the wall-normal direction and with Fourier modes in the wall-parallel 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 so-called 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 Ra-values 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 real-world 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 chord-to-thickness ratio of the plate is 5 and the Reynolds number is Re = U∞ · D/ν = 3 × 103 where U∞ and D are the free-stream velocity and the thickness, respectively. The flow separates at the leading edge corner developing in a strong free-shear. The flow reattaches on the solid surface upstream the trailing edge and evolves in typical large-scale shedding beyond it. To the authors knowledge, this is the first time that high-fidelity three-dimensional 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 three-dimensional turbulent structures via λ2 vortex criterion will be examinated.

2017 - Study of energetics in drag-reduced 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 skin-friction 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 space-and scale properties of the scale energy source and fluxes are significantly modified in the near-wall region, while remain unaltered elsewhere.

2017 - Towards an improved subgrid-scale 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 purely-dissipative to a more complex behaviour. This study highlights the possibility that eddy-viscosity and diffusivity models, commonly employed in large-eddy simulation of RBC, does not work well for large filter widths and that alternative closures should be considered.

2016 - A numerical study of the shear-less turbulent/non-turbulent 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 non-turbulent region is presented here. The analysis of the instantaneous fields highlight a complex multi-scale behaviour at the turbulent/non-turbulent 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 wall-turbulence [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 wall-normal 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 scale-energy production, transfer and dissipation in wall-bounded turbulent flows. This approach allows us to understand the cascade mechanisms by which scale energy is transmitted scale-by-scale among different regions of the flow. Two driving mechanisms are identified. A strong scale-energy source in the buffer layer related to the near-wall cycle and an outer scale-energy 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 near-wall 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 wall-bounded 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 scale-energy 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 hot-wire spatial resolution in turbulent round jet [Capitolo/Saggio]
Fiorini, T.; Bellani, G.; Cimarelli, A.; Talamelli, A.
abstract

Hot-wire spatial-resolution effects are investigated in a round jet, using custom-made 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. 10-30% compared to 1-2%. Power spectra show this attenuation to be located at high frequencies, in agreement with the hypothesis of spatial-filtering 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 - Multi-scale analysis of turbulent Rayleigh-Bénard convection [Capitolo/Saggio]
Togni, R.; Cimarelli, A.; De Angelis, E.
abstract

We report the results from a direct numerical simulation of turbulent Rayleigh-Bénard convection for Rayleigh number of 105 and Prandtl number of 0.7. The flow topology is characterized by the presence of coherent structures, the so-called 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 wall-parallel 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 wall-parallel 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 near-wall region.

2016 - Space and time behaviour of the temperature second-order structure function in Rayleigh-Bénard convection [Capitolo/Saggio]
Togni, Riccardo; Cimarelli, Andrea; Lozano Durán, Adrián; Angelis, Elisabetta De
abstract

One of the most peculiar aspects of turbulence in wall bounded-flows is the ability of the turbulent fluctuations to regenerate themselves through self-sustained processes. The dynamics of these self-sustaining 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 so-called coherent structures. From the other side, the multi-scale and inhomogeneous features of the self-sustaining mechanisms of turbulence have been addressed by means of global statistical quantities based on two-point averages such as second-order 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 second-order structure function. To this aim we use Direct Numerical Simulation data of thermally driven turbulence in the Rayleigh-Bénard convection and we analyse for the first time the behaviour of the second-order structure function of temperature in the complete four-dimensional space of spatio-temporal scales and wall-distances. The observed behaviour is then interpreted in terms of the dynamics of coherent thermal structures and of their commonly accepted model of life-cycle.

2016 - Temperature effects in hot-wire measurements on higher-order 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 Rayleigh-Bénard 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 subgrid-scale 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 subgrid-scale flux that will be tested by means of a posteriori analysis of LES simulations performed in the same flow conditions.

2015 - Analysis of turbulent Rayleigh-Bénard 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 Rayleigh-Bénard 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 no-slip and free-slip 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 second-order velocity structure function. It has been found that the dynamics of the coherent structures in RBC, the so-called thermal plumes, are clearly reflected in the multi-scale energy budgets. In particular, the enlargement of thermal plumes following the impingement at the wall entails a transfer of scale-energy 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 small-scale 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 lighter-than-air 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 scale-by-scale analysis of Rayleigh-Bénard convection [Articolo su rivista]
Togni, Riccardo; Cimarelli, Andrea; De Angelis, Elisabetta
abstract

A novel approach for the study of turbulent Rayleigh-Bénard 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 single-point balances. Detailed scale-by-scale budgets for the second-order 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 self-sustained 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 scale-energy source are identified. The first, stronger one, belongs to the near-wall 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 near-wall modulation. The second source peak is found further away from the wall in the putative overlap layer, and it is separated from the near-wall source by a layer of significant scale-energy sink. The dynamics of the second outer source appears to be strongly dependent on the Reynolds number. The detailed scale-by-scale analysis of this source highlights well-defined 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 scale-energy source with the presence of an outer region of turbulence production whose mechanisms are well separated from the near-wall region and whose statistical features agree with the hypothesis of an overlap layer dominated by attached eddies. Inner-outer interactions between the near-wall and outer source region in terms of scale-energy fluxes are also analysed. It is conjectured that the near-wall modulation of the statistics at increasing Reynolds number can be related to a confinement of the near-wall turbulence production due to the presence of increasingly large production scales in the outer scale-energy source region.

2015 - Spectral enstrophy budget in a shear-less flow with turbulent/non-turbulent 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 single-point and two point levels. The single-point 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 multi-dimensional 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 large-scale 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 wall-parallel 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 so-called 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 above-mentioned 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 finite-amplitude disturbances to the initial flow field.

2014 - Study of the outer self-regeneration 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 multi-dimensional description of turbulence given by the Kolmogorov equation generalized to wall-flows 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 well-defined outer energy source region appears. The possibility to analyze its effects on the energy tranfer among scales and wall-distances is shown important to clarify the influences of the external region on the inner layer.

2014 - The attached reverse and detached forward cascades in wall-turbulent flows [Capitolo/Saggio]
Cimarelli, A.; De Angelis, E.; Talamelli, A.; Casciola, C. M.; Jimenez, J.
abstract

The present work describes the multidimensional behaviour of wall-bounded turbulence in the space of cross-scales (spanwise and wall-normal) and distances from the wall. This approach allows us to understand the cascade mechanisms by which scale-energy is transmitted scale-by-scale 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 near-wall region, scale-energy 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 wall-bounded 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 scale-energy that sustains larger attached scales farther from the wall and smaller detached scales that are responsible for connecting the scale-energy 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 hot-wire measurements in wall-bounded 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 hot-wire 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 near-wall turbulence. Another, so far unattended, issue is the effect of temperature fluctuations - as they are, e.g. encountered in non-isothermal flows - on the low and higher-order moments in wall-bounded turbulent flows obtained through hot-wire anemometry. The present investigation is dedicated to document, understand, and ultimately correct these effects. For this purpose, the response of a hot-wire 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 wall-normal direction, introduces - despite a local mean temperature compensation of the velocity reading - significant errors. The results serve as a note of caution for hot-wire measurements in wall-bounded 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 Springer-Verlag Berlin Heidelberg.

2014 - The physics of energy transfer toward improved subgrid-scale 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 large-eddy 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 near-wall 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 post-processing 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 wall-turbulence has been recently proven to give a detailed description of the multi-dimensional features of such flows[1]. As emerging from this approach, the small scales of wall turbulence are found to drive the quasi-coherent 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 wall-turbulence. 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 wall-turbulent flows. The unexpected behaviour of the energy fluxes consists of spiral-like 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 near-wall region and a second one further away from the wall. The former, stronger, one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the eventual log layer and could explain the debated mixed inner/outer scaling of the near-wall 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 shear-dominated 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 well-known spanwise-oscillating-wall technique for drag reduction, non-sinusoidal oscillations of a solid wall are considered as a means to alter the skin-friction 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 skin-friction 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 well-known spanwise-oscillatingwall technique for drag reduction, non-sinusoidal oscillations of a solid wall are considered as a means to alter the skin-friction 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 sub-grid energy transfer in wall-turbulence [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 multi-dimensional description of the anisotropic behavior of turbulent energy production, transportdissipation is shown to be relevant for the understanding and modeling of the wall-turbulent physics with special care to the phenomenon of reverse energy flux. These results are proven instrumental also for the correct computation of wall-turbulence when a large eddy simulation approach is considered. The capability of a filtered velocity field to correctly reproduce the wall-turbulent dynamics at different ranges of scales and wall-distances 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 - Scale-Energy Fluxes in Wall-Turbulent 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 wall-turbulence where a reverse cascade in the near-wall 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 near-wall cycle. The data used for the analysis are obtained with a pseudo-spectral code in a channel at Re-tau = 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 wall-turbulent flows [Articolo su rivista]
Cimarelli, A.; De Angelis, E.
abstract

The analysis of the energy transfer mechanisms in a filtered wall-turbulent 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 cross-over scale between production-dominated 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 wall-turbulent flows [Capitolo/Saggio]
Cimarelli, A.; De Angelis, E.
abstract

2011 - Assessment of the turbulent energy paths from the origin to dissipation in wall-turbulence [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 (3-dimensional space of scales plus wall-distance) of wall-turbulent flows. As already shown in Cimarelli et al. (2010), an interesting behavior of the energy fluxes comes out from this analysis consisting of spiral-like 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 wall-turbulence. 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 near-wall cycle. The second suggests an outer self-sustaining 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 hot-wire probes in a wall-bounded 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 wall-bounded turbulent flows has raised different questions concerning the accuracy of hot-wire 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 hot-wire probes on the main statistical moments in turbulent wall-bounded flows is presented. The model, which is based on the two-point velocity correlation function, shows that the filtering is directly related to the transverse Taylor micro-scale. 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 second-order terms in the model equations are also taken into account and discussed. In order to use the model in a practical situation, the Taylor micro-scale 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 wall-turbulent 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 cross-over scale between production dominated scales and inertial range, lc, and the reverse energy cascade region ΩB.